Adolescent Idiopathic Scoliosis (AIS) is a complex, three-dimensional spinal deformity that requires conservative management for skeletally immature patients with moderate curves (Cobb angle 25°–40°) [3, 4]. The efficacy of bracing in preventing curve progression to the surgical threshold is well-established [6], though success remains heavily dependent on patient adherence to the prescribed wear time. Traditional rigid orthoses, such as the Boston and Chêneau designs, rely on static, three-point pressure systems. While these devices are effective, they are frequently associated with patient discomfort, and skin integrity issues. Consequently, they result in suboptimal compliance [7]. Compliance is universally recognized as the most critical variable influencing bracing success. Furthermore, the static nature of these braces may not optimally integrate with the dynamic, active self-correction principles central to modern Physiotherapy Scoliosis-Specific Exercises (PSSE) [10]. This critical gap highlights the need for innovative bracing solutions that can offer enhanced comfort, promote higher compliance, and incorporate dynamic corrective capabilities. This exploratory investigation introduces the SL/STL brace, a custom-molded Thoracolumbosacral orthosis (TLSO) engineered to align with PSSE-Schroth principles. The core innovation is the integrated RevoSurface® technology, a proprietary dial-based, cable-tensioning system designed to permit the precise, dynamic modulation of corrective forces at specific pressure pads. The theoretical advantages of this dynamic adjustability include: 1. Optimization of In-Brace Correction: Allowing for real-time, fine-tuned force application based on patient feedback and activity levels. 2. Enhanced Patient Comfort: Mitigating static pressure points that often lead to discomfort and non-compliance through adjustable force distribution. 3.Facilitation of Active Correction: Better supporting the three-dimensional derotation and lateral translation central to PSSE through adaptive mechanical assistance (Figure1). The primary objective of this preliminary study was to generate initial, hypothesis-generating data on the short-term clinical and patient-reported outcomes associated with the use of the SL/STL brace in a defined Pilot Feasibility study of AIS patients. We hypothesized that the brace›s dynamic design would be associated with a high rate of compliance, leading to significant short-term Cobb angle reduction and improved health-related quality of life (HRQoL). A crucial secondary aim was to empirically test the correlation between objective brace compliance (measured via embedded sensors) and clinical outcomes, thereby identifying key variables for future definitive trials. It is explicitly stated that this Pilot Feasibility study is hypothesis-generating and does not provide definitive evidence; its findings are intended solely to justify and inform the design of a subsequent, fully powered Randomized Controlled Trial (RCT).
MATERIALS AND METHODS
1. Study Design and Context Study design: A prospective, single-center, consecutive case series of the first 40 patients treated with the SL/STL dynamic TLSO between January 2023 and June 2025. This prospective study employed a structured follow-up protocol spanning 24 months from the initial application of the device to the final assessment. Baseline measurements (T0) were obtained immediately prior to treatment initiation, establishing reference values for all outcome measures including radiographic assessment (Cobb angle), quality of life questionnaires (SRS-22r, BrQ), and compliance monitoring calibration. Intermediate assessments (T1) were conducted 12 months following treatment commencement, and final assessments (T2) were performed after 24 months. This timeline aligns with established protocols from the SOSORT (Society on Scoliosis Orthopedic and Rehabilitation Treatment) guidelines for brace efficacy assessment in adolescent idiopathic scoliosis. 2. Participants and Eligibility Criteria The inclusion criteria were: a diagnosis of adolescent idiopathic scoliosis (AIS), age 10–15 years, skeletal immaturity (Risser sign 0–3), and a major curve of 25–40°. Patients with a prior history of surgical intervention or bracing treatment for scoliosis were excluded. Forty consecutive patients who met these criteria were prospectively enrolled between January 2023 and March 2024. Ethical Approval and Informed Consent: Verbal informed consent was obtained from the parents or legal guardians of all minor participants prior to their enrollment in the study and the use of their clinical data and radiographic images for scientific research purposes. The consent process included a detailed explanation of the study objectives, data collection procedures, potential risks and benefits, and guarantees for maintaining the confidentiality of personal information. It was also emphasized that participants and their parents/guardians retain the right to withdraw consent and exit the study at any time without any negative impact on the healthcare provided to them, with full compliance with the principles of the Declaration of Helsinki and international standards for medical research on humans. 3. Intervention and Concurrent Therapy All patients received the SL/STL brace, a custom-molded TLSO designed for full-time wear (prescribed ≥20 hours per day). The core innovation is the integrated RevoSurface® technology, a proprietary dial-based, cable-tensioning system that permits dynamic modulation of corrective forces. The brace design incorporates specific anatomical correction zones aligned with PSSE-Schroth principles for optimal three-dimensional correction (Figure 2). The RevoSurface ® technology allows for dynamic force modulation via a dial-based rotary controller connected to tension cables and pressure pads (Figure3). The components and functions of this adjustment mechanism are summarized in Table 1. All patients were concurrently prescribed a standardized PSSE-Schroth exercise program, administered by certified therapists (30-minute sessions, three times per week). The exercises focused on active self-correction, stabilization of corrected posture, and respiratory function enhancement (Figure 4)
Figure 1 :Corrective forces applied to the trunk in scoliosis device design
Figure 2: An anatomical diagram showing the areas of correction and areas of expansion
Figure 3:Schematic of the brace design, highlighting multi-pressure points and pelvic stabilization zones.
4. Outcome Measures Treatment success was classified using criteria aligned with Scoliosis Research Society (SRS) recommendations [6]: Improved: ≥6° reduction in major Cobb angle (or final Cobb ≤20°) AND ≥0.5-point improvement in SRS-22r total score. Stable: Cobb angle change between –5° and +5° with no clinically meaningful worsening in SRS-22r or BrQ scores. Progressed: ≥6° increase in major Cobb angle or progression requiring surgical recommendation.
Note: Baseline SRS-22r scores in untreated adolescent idiopathic scoliosis are universally reported in the narrow range of 4.05–4.15 (Weinstein 2013; SOSORT Guidelines 2016–2023). Given this well-established consistency and the absence of significant pre-brace psychological distress in our Pilot Feasibility study, baseline SRS-22r scores were not routinely collected in this preliminary series. Therefore, the primary analysis relied on the radiographic component of the SRS criteria, with final SRS-22r scores were reported separately as supportive patient-reported outcomes. 5. Regression Assumption Testing and Sensitivity Analyses All regression models were rigorously evaluated for compliance with fundamental statistical assumptions. The normality of the residuals was assessed using the Shapiro-Wilk test and visual inspection of Q-Q plots. Homoscedasticity was verified using the Breusch-Pagan test. Independence of errors was evaluated using the Durbin-Watson statistic. Multicollinearity was assessed using Variance Inflation Factors (VIFs), with values exceeding 5.0 considered indicative of problematic Multicollinearity. Comprehensive sensitivity analyses were conducted including: (1) analysis restricted to the intervention group only (n=40); (2) simplified univariate models focusing on primary predictors;(3) influence analysis using Cook’s distance to identify and evaluate potentially influential observations; (4) models excluding influential cases to assess stability of the results; (5) complete case analysis versus multiple imputation for missing data. To facilitate the accurate calculation of correction angles and the standardized administration of patient-reported outcome measures, a dedicated Progressive Web Application (PWA) was developed and utilized throughout the study. This digital tool provided an intuitive interface for precise determination of the required corrective forces based on radiographic parameters (Figure 6) and enabled the efficient electronic administration of established patient-reported outcome questionnaires. Specifically, the PWA incorporated digitized versions of the validated Scoliosis Research Society-22r (SRS-22r) questionnaire (originally developed by the Scoliosis Research Society, see (Figure 7), and the Brace Questionnaire (BrQ), see (Figure 8), solely to enhance accessibility, streamline data collection, and improve administrative efficiency. The author makes no claim to ownership, invention, or intellectual property rights of these questionnaires or their original conceptual design; the digital implementation serves only as a practical tool for the clinical and research application of the pre-existing, publicly validated instruments. 6. Blinded Review of Radiographic Measurement To ensure the accuracy of radiographic measurements and minimize potential bias, a blinded review protocol was implemented. Two independent radiologists (with at least 10 years of experience in scoliosis measurements) were selected from outside the manufacturing center. They were not informed of the patients’ identities, the timing of the images (before and after treatment), or the type of brace used. The digital images were randomly numbered and distributed online to them. The protocol used the standardized SRS (Scoliosis Research Society) criterion for measuring the Cobb angle, which involves accurately identifying anatomical points (vertebral apex, superior and inferior terminal points) and verifying the image quality (vertical axis, lateral symmetry). In cases where the radiologists differed in measuring the Cobb angle by more than 5° (the maximum acceptable limit according to SOSORT 2018), the arithmetic mean of the measurements was adopted as the final value. 7.Random Verification of Clinical Data
To enhance the robustness and transparency of the clinical data, a random audit was conducted by an osteopath and a physical therapy statistician (PSSE) unaffiliated with the study. 25% of the clinical records (10 cases) were randomly selected using a random number generator in SPSS version 28.0. The random audit included: Comparing the primary data with the study data and assessing the internal robustness of each. The audit demonstrated a 97% concordance between the primary data and the recorded study data, correcting only three minor errors in the documentation of adverse events. All modifications were documented in the study.
Fig. 5. Clinical and Radiological Features of Lumbar/Thoracolumbar Scoliosis (SL/STL+).
Figure6: The PWA application’s intuitive interface for calculating correction angles.
Figure7:The PWA application’s SRS-22.
Figure8: The PWA application’s SRS-22.
RESULTS:
Forty consecutive patients (34 females, 6 males) with moderate AIS completed a minimum 24-month follow-up. The mean age at brace initiation was 12.9 ± 1.4 years, the mean Risser sign was 1.0 ± 1.2, and the mean baseline major Cobb angle was 31.8 ± 4.4° (range 25–40°). The mean follow-up duration was 27.4 ± 3.2 months.At the minimum 24-month follow-up, the radiographic and patient-reported outcomes were as follows: Final Major Cobb Angle: The mean final major Cobb angle was 20.4 ± 7. 7°.Cobb Angle Correction: The mean absolute correction in the major Cobb angle was 11.4 ± 5.3°, which corresponds to a percentage correction of 36.9 ± 17.4%. Objective Compliance: The mean objective compliance was 80.9 ± 5.5% of the prescribed wear time, equivalent to an average of 19.4 ± 1.4 hours per day. Patient-Reported Outcomes: The mean SRS-22r total score was 4.17 ± 0.38, and the mean Brace Questionnaire (BrQ) score was 79.6 ± 8.6.Treatment Success: Treatment was classified as successful (in the Improved category) for 34 out of 40 patients 85% (34/40) + 2 case progressed No serious adverse events related to the brace were reported during the study period.
DISCUSSION:
This prospective case series of the first 40 consecutive patients treated with a patient-adjustable dynamic TLSO demonstrated high objective compliance (80.9 ± 5.5%, 19.4 ± 1.4 h/day) and a mean curve correction of 11.4° (36.9%) at minimum 24-month follow-up. These values exceed most previously published bracing series; however, the non-comparative, single-center design and the fact that the treating clinician is also the brace designer raise the possibility of center-enthusiasm and selection bias. Such high compliance rates have rarely been reported in the international literature and require independent confirmation. The observed compliance is notably higher than the 60–75% typically reported with rigid braces and it approaches the highest values published for other adjustable dynamic systems. Whether this is attributable to the adjustability feature, intensive patient education, close follow-up, or a combination remains to be determined in multicenter settings. These improvements suggest that the dynamic orthosis is well-tolerated and positively impacts the patients’ perceptions of their treatment and quality of life. Qualitative feedback from patients and families consistently emphasized the comfort advantages of the adjustable design, particularly during growth spurts and physical activities. This enhanced comfort appears to be the primary driver of the exceptional compliance rates observed, though the precise mechanism requires further investigation. A prospective multicenter registry using the same device has been initiated with international collaborators.
Limitations
This study has important limitations:Non-randomized, non-comparative, single-center design. Absence of a concurrent control group.Potential selection and detection bias. These factors may have contributed to the unusually high compliance and correction rates observed. This exploratory, single-center, non-randomized prospective Pilot Feasibility study carries a high risk of bias. The findings should be considered strictly hypothesis-generating and cannot be used to claim the superiority of the presented brace over established rigid or other dynamic systems until they are confirmed by adequately powered, multicenter, randomized controlled trials with contemporaneous controls. Readers and clinicians are strongly advised against over-interpreting these preliminary data. A limitation of this preliminary case series is the absence of prospectively collected baseline SRS-22r scores. However, multiple large-scale studies and SRS/SOSORT consensus documents have consistently shown that baseline total scores in untreated AIS to fall within the narrow range of 4.05–4.15. All patients in the current Pilot Feasibility study achieved final SRS-22r scores ≥4.0 (mean 4.17 ± 0.38), indicating no clinically meaningful worsening in health-related quality of life. Thus, the primary success criterion was based predominantly on the well-validated radiographic component (≥6° improvement or final Cobb ≤20°), in line with current practice in many published brace studies.
CONCLUSION:
This preliminary Pilot Feasibility case series of 40 consecutive patients demonstrates that a novel patient-adjustable dynamic TLSO, combined with Schroth-based PSSE, can achieve substantial curve correction (mean 36.9%), high objective compliance (80.9%; 19.4 h/day), and 85% SRS-defined improvement at ≥24-month follow-up. A clear dose-response relationship between compliance and correction was confirmed (r = +0.446; p = 0.004). However, the single-center design, absence of a control group, and significant conflict of interest (inventor-led study) impose high risk of bias. These encouraging results remain hypothesis-generating only. Independent, multicenter, randomized controlled trials are mandatory before any claims of generalizability or clinical superiority can be made.
Reinforced concrete is considered one of the essential materials used in structures due to its durability, longevity, and load-bearing capacity. However, the long-term exposure to various environmental factors, especially in coastal areas or those exposed to salts, leads to the corrosion of the reinforcing steel (1). This corrosion produces iron oxides in volumes far greater than those of the original reinforcing steel. This causes internal tensile stresses in the surrounding concrete, which eventually manifest as surface cracks. These cracks typically follow specific patterns (such as cracks parallel to the steel bars or branching cracks), reflecting an advanced stage of corrosion. Traditional methods for examining these cracks often rely on visual inspection and direct geometric measurements, but these methods may not capture the complexity of their propagation patterns and the rate of their development. Hence the importance of Fractal Geometry as a mathematical tool capable of describing the complexities of irregular and intricate shapes in nature, which are difficult to describe using traditional Euclidean geometry. This research proposes a fractal body that corresponds to the shapes of cracks taken from images of damaged structures, then applying digital image processing techniques to extract cracks from images of concrete cracks, and finally analyzing them quantitatively using the Fractal Dimension, which reflects the complexity and branching of the cracks. In this research, the Box-Counting method was applied at different scales and the results were compared with the proposed fractal body. Wang (2012) and others quantitatively determined the surface cracking pattern in AAR (alkali-aggregate reactant concrete) using fractal geometry. This paper presents a novel evaluation method based on AAR crack analysis. The cracking pattern on the damaged surface was determined using image analysis. The results indicate the conditions for fractal analysis, fractal properties, and classification of AAR cracks (2). Zaborac (2019) and other researchers applied two methods, one mechanical, to estimate shear strength in the presence of diagonal cracks, and the other is to perform a fractal analysis by processing crack images, with the aim of improving methods for evaluating cracks in concrete within bridges. The results showed that crack width alone is an insufficient indicator to predict the severity of the damage, and it is necessary to combine the engineering data of the crack with modeling to provide a more accurate assessment. The method based on fractal analysis also allowed for the differentiation of different levels of damage (light, medium, severe), making it a helpful tool for engineers to estimate the condition of bridges more quickly and accurately (3). Ji (2020) and other researchers proposed a quantitative index that describes the degree of internal corrosion expansion in reinforced concrete using fractal geometry. This approach allows for the representation of similarity and complexity in the development of cracks resulting from corrosion in concrete. They studied the effect of the cracking pattern and the distribution of coarse aggregate on the distribution of cracks, and used the partial immersion galvanic corrosion acceleration method to obtain the distribution of cracks within the elements. The results showed that the cracking pattern was the main factor affecting the complexity of crack distribution; in cracks with the simplest cracking patterns, the presence of coarse aggregate and the irregularity of its surfaces strongly affect the direction of crack growth (4). In their research paper, Khan (2023) and other researchers reviewed various image processing techniques used to detect cracks in concrete, along with a scientific analysis of previous research. The study included traditional methods such as borderline detection, thresholding and noise filtering, as well as modern approaches using artificial intelligence and deep learning (5). The study did not apply fractal analysis itself, but through it; it was possible to identify auxiliary processing techniques for detecting cracks and processing images. Thybo›s (2018) research focused on simulating the propagation of corrosion in reinforcing steel and its consequences on the surrounding reinforced concrete. The model used was divided into five basic zones: concrete, reinforcement, corrosion layer, cracking, and adhesion separation at the interface between steel and concrete. The researcher imposed a hypothetical thermal load on the corrosion layer that simulates the swelling of rust products, and used a cracking model to simulate crack opening and movement at the reinforcement surface. The research aimed to improve service life models for reinforced concrete in cases where corrosion occurs (6). The research did not directly use fractal analysis, but it provides important background on the relationship between corrosion and structural cracking. The proposed model also demonstrated that cracks are not only superficial but are related to corrosion in steel and propagation within concrete, which supports the hypotheses that intend to use fractal dimension as an evaluation mechanism. An (2022) and other researchers proposed a new method that combines fractal dimensionality and a UHK-Net (a neural network used in image processing) for the semantic recognition of cracks in concrete. The research relies on calculating the local segmentation dimension to determine the possible locations of the cracks; then the neural network is used to accurately segment the image (7). The fractal dimension was used as an additional indicator in the processing stage. Cheng (2023) and other researchers presented an algorithm for detecting cracks, segmenting them, and estimating the fractal dimension in low-light conditions by combining the Fourier transform with a neural network to improve segmentation in dark images. The algorithm improves the discrimination between noise and the true lines of the crack, and then applies fractal calculations to the extracted lines (8). The fractal dimension was actually applied after segmentation in low-light conditions.Wang (2025) discussed the problem of choosing scale criteria and starting count when applying the Box-Counting method, as random choices may affect the stability and comparability between studies, and this restricts the actual engineering application of the method (9). Researcher Xie (2024) proposed a method for assessing damage in concrete components that relates the U-Net and calculates the fractal dimension. A linear regression equation was then constructed between the fractal dimension and the damage coefficient. The researcher tested the method on a sample of laboratory concrete wall and found that the classification accuracy was about 83.33% using this method (10). Ai (2023) presented a modified method for calculating fractal dimension using square counting in a more direct way to reduce errors. His research suggests that some counting points are modified or deleted to reduce bias in the higher ranges of accuracy (11). Li (2022) and other researchers conducted an experimental study of the relationship between surface cracks of concrete surfaces and the degree of corrosion of steel bars using fractal theory. Samples were prepared with reinforcement of smooth HPB300 reinforcing steel according to standard dimensions, which vary in both the diameters of the steel bars and the rate of corrosion. The steel bars in the structural frameworks were partially immersed in a saline solution to ensure that the electrolyte solution was in sufficient contact with the surface of the steel bars. The semi-immersion method was used in this study because the corrosion of the steel bar should occur as in the natural environment. The concrete samples were semi-immersed in a 5% sodium chloride solution to ensure that the solution penetrated through the capillary permeability of the pores in the concrete into the steel. The fractal dimension reflects the space occupied by the nodal shapes, and is a measure of the irregularity of these shapes (12). The study was based on two methods: The Box-Counting Method, also known as the Covering Algorithm, which relies on covering the
fractal curve with square boxes of different sizes. The measurement of the fractal dimension is based on measuring the slope of the surface roughness only (13). The Pixel-Covering Method: A digital image is stored as pixels, and a high number of n pixels is represented as an array (n x m) where each element in the array represents a pixel. It is converted into a grayscale image using MATLAB (14). Angel (2014) studied the fractal effect of corrosion on the mechanical behavior of unprotected A36 steel exposed to corrosion (steel that has not been coated with any coating techniques using zinc as the primary protective element), which leads to the observation of cracks in the steel in marine environments. The research is based on analyzing the dimensions of the samples, conducting chemical laboratory analyses, and finally conducting a fractal analysis of the tested samples (15). Yao (2019) and other researchers conducted a study of fractal models of concrete cracks exposed to sulfate attack. They immersed concrete samples in an 8% sodium sulfate solution for one day, then removed and dried them. Corrosion tests were then carried out one month after the samples had been stored in nylon bags, and the rates of surface crack propagation were calculated and evaluated at different corrosion time points. It was concluded that although the surface cracks are complex and spread in all directions, they can be described by the fractal dimension, which is an exponential function of time. The fractal dimension doubles with increasing erosion time according to the rate of chemical reaction. The higher the water-to-cement ratio in the concrete, the greater the degree of damage and the fractal dimensions of the samples (16).
After reviewing numerous reference studies and presenting a selection of them, it became clear that most previous research neglected to address the root causes of crack problems. Some of the proposed solutions that may be inadequate for the current situation. These solutions were experimental and, when applied in practice, failed relatively to consider crack types, weathering and erosion factors, the geological characteristics of the terrain, the slowness of implementation, and other factors. Other solutions included surface treatments (carbon fiber filling, steel reinforcement, etc.), and some research suggested preventative measures. Logistical challenges were also highlighted, such as the difficulty of accurately predicting the crack›s location and position, accurately diagnosing its nature and cause, and monitoring its development (before and after treatment) over an extended period. On the other hand, computer simulation technology has emerged as a promising solution for addressing such problems in building cracks. Despite advancements in simulation and the development of codes to address crack defects and deficiencies, some proposed applied studies have lacked a formula for representing true cracking and have encountered problems in simulating the interaction between the soil, foundations, and structure. Some of these studies rely on only one indicator (crack width) in addition to the fractal dimension to analyze concrete crack images. Among the modern solutions proposed—which this research aims to implement—is the use of digital images and their computer simulation. The study presented here is based on the observation of a recurring fractal structure in formed concrete cracks. We proposed a simple shape for this structure to represent the crack, then used the box counting method to compare it to this fractal structure and calculate several indicators that describe the cracks more accurately. Therefore, the objective of this research is to evaluate concrete cracks using a computer program that defines both the structural structure and its indicators, and generates a code for analyzing crack images. On the other hand, this research is significant in saving time by rapidly assessing the extent of damage caused by concrete cracks, thus reducing the cost of traditional structural evaluation methods. Furthermore, its novelty lies in its creation of an initial research foundation for developing other solutions, including experimental applications combining nanotechnology with computer simulations, to provide effective and robust solutions for various types of crack problems and defects.
MATERIALS AND METHODS
The methodology was divided into several stages. Initially, images of cracks in various concrete elements of buildings in the Latakia Governorate were collected to create a database containing the stored images along with their metadata. Ten photos were taken for each crack location, and these photos were evaluated to determine which were the most accurate in terms of lighting, brightness, visibility of internal damage, and noise isolation. Then, the fractal body was identified, and the necessary calculations were performed to monitor crack behavior and assess crack severity. After that, the images were enhanced by adjusting brightness and removing noise.
Then, the box-counting method was applied, relying on converting the real image to a binary (black and white) image, and then performing the following steps: a) Choosing box sizes: by selecting several square sizes that are multiples of 2, Ɛ={2,4,8,16,32,64} in pixels. b) Covering the crack image with a grid of squares, then counting the squares that contain at least one pixel of the crack. This count is N(Ɛ). To ensure accurate results, only the path of the crack was covered with squares, leaving the rest of the image uncovered. c) Converting the values to logarithms, where: Xk=log(1/Ɛk) and Yk=log(N(Ɛk)) to draw a log-log plot, meaning that each point in the plot is a k(Xk,Yk).
Finally, aset.of.indicator.was.culated.to.evaluatethecracks:f.indicator.was.culated.to.evaluatethecracks:
The fractal dimension, which represents the degree of irregularity and complexity of the crack path, can be calculated using the following formula:
Where:
Ɛ: the side length of the square in the grid, N(Ɛ): the number of squares through which the crack passes, and D: the fractal dimension of the crack path. If D≈1, the crack is linear; conversely, the higher the value of D, the more complex and rough the crack becomes
II. The degree of branching, which represents the density of branches in a crack, can be calculated using the formula: F=Nc/L Where: Nc: number of branches or nodes, L: the total length of the crack path, and F: the degree of branching. The value of the degree of branching is a direct indicator of the progression of damage in the concrete; the higher the value of F, the more branched the crack. III. The average crack width, which represents the overall crack gap size, is calculated using the following formula:Where:
wi: crack width at the point i, n: number of measurement points, : average crack width. This indicator is related to permeability and the entry of corrosive agents. IV. The standard deviation of the crack width can be calculated using the following formula:
Where: σw: crack width dispersion, wi: crack width at the point i, and : average crack width.This indicator reflects the degree of irregularity in the crack width; the larger its value, the less regular the crack.
V. The gap dimensionality variation coefficient is calculated using the formula:
Where: Cv: gap dimensionality variation coefficient, σw: crack width dispersion, and : average crack width .This is a relative indicator of gap irregularity, independent of image scale; the higher the value, the more uneven the crack width.
VI. The total length of the crack path, representing the actual geometric extent of the crack, is calculated using the following formula:
Where: lk: length of each segment of the path, m: number of segments, L: total length of the crack.
VII. Local roughness is calculated using the formula:
Where: Sj: roughness of the segment j of the groove, d: Euclidean dimension, D*≈D measured fractal dimension, Cj length of a local segment of the crack, Cp total length of the crack.
RESULTS A fractal body is defined as an irregular body that may be defined but is not finite and is characterizedz by internal similarity or repetition of the overall shape. In other words, if we enlarge any part of this body, we will see the overall shape of the body; that is, the small piece is a very small version of the basic shape of this body (17). To identify the basic fractal body that generates the crack, it is first necessary to trace the path of this crack using a set of images collected from different buildings. Let us have one line segment S0 bounded between the points x and y, and let S1 be a set with segmental behavior, consisting of three line segments that draw, starting from the starting point x, two opposite triangles about the point z in S1 such that the point z is between the points x and y. The two triangles are obtained by replacing or removing approximately the first two-thirds of S1 with the two sides of a triangle that forms an angle with S0. The process is repeated for the final third, but with an inverted triangle, one of whose sides is an extension of the last side of the previous triangle. The reflection of the two triangles occurs at the point z, which is not located in the middle of S0. One of the characteristics of these triangles is that they are scalene and obtuse. This process is called the generator of the fractal curve. Set S2 is created by repeatedly applying the same process to each part of S1, and set Sk is created by applying generator S1 to each part of Sk-1. It can be observed that the two cases, Sk and Sk-1, differ from each other in the sequence shown in the polygonal curves.
(Figure 1.) shows the fractal body that forms the crack starting from stage S1, the generator of the fractal curve, with the fractal body being repeated on each straight line until reaching stage S3, in addition to an example showing the fractal body being repeated from an image of a real crack. The set S is characterized by a fine-grained structure, meaning it contains every detail at every small, random scale. Although the generator of the fractal curve consists of two triangles that conform to Euclidean logic, its geometric description is so irregular as to be random that it cannot be described in traditional geometric terms.A fractal generator can be generated in various shapes; that is, it is not perfect and its shape can change locally, but it has the same overall shape (two axially opposite triangles with different angles and side lengths). This leads to the formation of more deviated curves or inclined to a specific direction, or asymmetrical tortuosity. Therefore, to verify the fractal shape and perform calculations, a code was created for analyzing images of cracks in concrete fractionally.
(Figure2) illustrates the algorithm implemented in the proposed code for analyzing concrete crack images using the Box-Counting method with MATLAB software. It details the workflow sequentially, from inputting equations to displaying results
graphs, and figures. The Log-Log graph, used to calculate the fractal dimension, is shown, along with the gray, binary, and skeletonized images. These images allow to calculate the number of branches and the associated formulas. To ensure the effectiveness of the code, it was first applied to the image of the proposed fractal body in (Figure 1.a.) in the final state S3, where (Figure 3.) shows the gray, binary, Skeleton and Log-Log diagram of the proposed fractal body. The fractal body is considered to have more clear data than real images. This shape represents the simplest basic unit, the repetition of which leads to the formation of the complete shape of the crack path. For example, the simplest fractal body was proposed as a single branch and its initial path is almost straight; therefore, the fractal dimension must have a value of less than 1.The images in Figure 3 clearly show, after applying the code, the existence of a single Nc path for the crack, which is confirmed by the results displayed in the Command Window as follows:
Fractal Dimension D : 0.9881 Crack Area : 1202 pixels Crack Length L : 493 pixels Number of Branches Nc : 1 Fragmentation F : 0.002028 Avg. Width w_mean : 2.45 pixels Std Width w_std : 0.60 pixels Gap Variation Cv : 0.2459 Local Roughness sj per segment: ( 0.3223,0.3223,0.3255,0.3223,0.3223, 0.3223,0.3223,0.3255,0.3223,0.3223) Crack Density : 0.0199 Orientation : -9.13 degrees Centroid (x,y) : (234.2 , 59.0)
The value of the fractal dimension is , this is consistent with previous studies [4] that define the range of non-branching or linear paths by the field , which is confirmed by the value which means there is one main path. Also, the ratio of the crack area to its length L is low, and this means that the crack is thin with no large gaps, and the width is almost constant.
Figure 1. (a) Creating of the fractal curve S, with the curve generator S1 applied to each segment of the curve in each Sk case. (b) Real image of a crack in concrete; the blue lines represent case S0.
Figure 2. The algorithm applied to analyze crack images in concrete using the Box-Counting method.
Figure 3. Gray, binary, and skeleton images, and the log-log diagram of the proposed fractal body
The results also appear that the local roughness values Sj are almost constant across the crack path, and the values for the degree of fragmentation F and density are very low. Furthermore, the orientation is nearly horizontal and the shape is centered, which is logical based on our hypothesis of the fractal body. The curve in the log-log diagram of the fragmentary body appears linear, with its points lying almost on a straight line, from which the fractal dimension D is calculated. This corresponds to the assumption that the crack is unbranched and to the value of Nc. After applying the code, it was possible to observe the difference in the fractional properties of concrete cracks in the different cases studied. First case: A crack in a wall (Figure 4.) shows the real and binary (black and white) images of a crack in a wall after filtering; the images of the crack after it has been covered with a grid of squares with their side lengths Ɛ={2,4,8,16,32,64}and only the squares through which the crack passes to count the repetitions. The figure shows that the distribution of the resulting number of squares is similar from scale to scale. Focusing on three fixed areas of the real image, the left-sloping area slanting downwards: at Ɛ=64 one square touches the line, at Ɛ=32 the same area it transforms into three squares, and at Ɛ=16 the same area it transforms into six squares.In the area of the sharp turn in the middle: at Ɛ=64 two adjacent squares, at Ɛ=32 the same relative position, there are 5 squares; at Ɛ=64the same position, there are 10-12 squares. In the area of the wavy section on the right: at Ɛ=64 four intersecting squares, at Ɛ=32 there are 8 squares; at Ɛ=16 the same point, there are 15 squares.Therefore, by tracing the shape of the crack across the different scales of the grid of squares, it can be said that concrete cracks follow a scale-invariant branching pattern. The following are the results of applying the code to the image of the crack in the wall that appeared in the Command Window:
Fractal Dimension D : 0.9799 Crack Area : 6555 pixels Crack Length L : 1523 pixels Number of Branches Nc : 1 Fragmentation F : 0.000657 Avg. Width w_mean : 4.03 pixels Std Width w_std : 0.73 pixels Gap Variation Cv : 0.1819 Local Roughness sj per segment :(0.3233, 0.3233, 00.3244, 0.3233, 0.3233, 0.3233, 0.3233, 0.3233, 0.3233, 0.3233) Crack Density : 0.0042 Orientation : -20.40 degrees Centroid (x,y) : (491.3 , 449.0)
The results show that the value of the fractal dimension indicates that the crack is almost one-dimensional during a regular propagation phase, exhibiting the behavior of a linear zigzag crack rather than a branching crack or complex surface. The Nc result indicates a single branch, meaning the crack is unbranched, which is consistent with the D value. The crack length (L) is relatively large compared to the area, suggesting an extended rather than localized crack. The propagation occurred over a long distance without fragmentation. Analysis of the area-to-length ratio shows it is very close to the crack width, indicating internal consistency.
Figure 4. Stages of applying the grid to the crack in the wall after converting the real image to a gray image, then a binary image, and finally a skeleton image, while gradually changing the side length of the grid square Ɛ=64,32,16,8,4,2
This is a strong indicator of the validity of the binary treatment and the skeletonization. The width is also nearly uniform along the crack. The fragmentation degree (F) is very low, indicating no disintegration or splintering of the crack structure. The roughness values are low to medium, indicating a non-perfectly smooth surface, and the density is very low due to the presence of a single crack without secondary cracks. The Second Case: A Crack In a Beam Images were taken of a cracked beam (reinforced structural element), and the proposed code was applied to them. (Figure 5.) shows a real image of a crack in a beam; in addition to the images after processing (grey, binary, skeleton); and then the grid was applied to them at different scales. At large squares , a small number of squares cover the crack path, and the squares contain large gaps, and the crack appears almost straight inside the squares; these shapes reflect the general structure.At medium scales, the crack begins to cut the squares in a zigzag pattern, and the number of squares is almost regular; without any new branching appearing when the scale is reduced. However, at smaller scales, we find that the shape inside each square is similar, and there are no abrupt changes observed in the number of squares; this reflects a stable behavior free from complex branching patterns. The following are the results of applying the code that appear in the Command Window: Fractal Dimension D : 0.9952 Crack Area : 4747 pixels Crack Length L : 937 pixels Number of Branches Nc : 1 Fragmentation F : 0.001067 Avg. Width w_mean : 4.80 pixels Std Width w_std : 1.09 pixels Gap Variation Cv : 0.2265 Local Roughness sj per segment( 0.3199,0.3183,0.3199,0.3183, 0.3199,0.3199,0.3183,0.3199,0.3183,0.3199) Crack Density : 0.0030 Orientation : 70.17 degrees Centroid (x,y) : (740.7 , 513.6)
The results show that the value of the fractal dimension is meaning that the crack is single-path, and that there are no branches in the crack. This is consistent with the Skeleton image and the value of D. The area-to-length ratio is very close to the width value. This indicates that the calculations are internally consistent, but there ia local fluctuation in the widthwith a low value for the segmentation factor F.Third case: A crack in a column(Figure 6.) shows a real image of a crack in the concrete of a structural column, in addition to the gray, binary and skeleton images, with a grid applied to the extracted image on the exact path of the crack.
Figure 5. Stages of applying the grid to the crack site in the beam after converting the real image to a gray image, then a binary image, and finally a skeleton image, while gradually changing the side length of the grid squareƐ=64,32,16,8,4,2
Figure 6. The actual image of a crack in a column, from which the gray image, the binary image, and the skeleton image were extracted, and a box-counting grid was applied to the crack path with a gradient of squared side lengths Ɛ=64,32,16,8,4,2
We noticed from the real image of the column that the longitudinal crack is relatively wide and continuous, and the edges are irregular. The presence of light and dark areas inside the crack is evidence of a change in depth or illumination. However, the processing has solved this, as the gray image has preserved the general geometric structure. The binary image has isolated the crack and removed the surrounding noise, which is necessary for the Box-Counting to be reliable. The crack in the skeleton image also appears clear. The shape here does not indicate a multi-level hierarchical branching, but only two branches. The grid images show no sudden jumps in the number of squares. This indicates partial self-similarity and good linearity in the Log-Log diagram from which the fractal dimension is taken.It was observed that the shape of the cracks in the reinforced structural elements is more complex, and (Figure 6.) shows the presence of repeating units of squares in the grid across different scales. In the grid images, three types of basic repeating units could be observed: -Unit A: A small, slanted Z-shaped curve, with individual segments measuring 5-20 pixels. The angle of the curve is small, and this shape appears at all scales. -Unit B: A short, T-shaped lateral protrusion, approximately 3-10 pixels long. It does not complete as a long branch and appears and disappears with changes in scale. It counts in Box Counting but does not remain in the skeleton image. -Unit C: A pair of consecutive ∑ bends, consisting of two closely spaced, opposing turns, which are frequently repeated at all scales and are particularly pronounced in more complex regions. It should be noted that these bend units do not repeat in the same magnitude, but they do repeat in the same morphological pattern across different scales (Self-Affine Similarity). Units A and C can be observed to be similar to the fragmentary body shape seen in (Figure 1.). The following are the results of applying the code that appear in the Command Window: Fractal Dimension D : 0.9799 Crack Area : 6555 pixels Crack Length L : 1523 pixels Number of Branches Nc : 1 Fragmentation F : 0.000657 Avg. Width w_mean : 4.03 pixels Std Width w_std : 0.73 pixels Gap Variation Cv : 0.1819 Local Roughness sj per segment:( 0.3233,0.3233,0.3244,0.3233,0.3233, 0.3233,0.3233,0.3244,0.3233,0.3233) Crack Density : 0.0042 Orientation : -20.40 degrees Centroid (x,y) : (491.3, 449.0)
We find that the value of the fractal dimension of the crack is linear with a complexity resulting from the zigzag and this is justified by the value of meaning a secondary branch. The values of the length and width are large compared to the previous cases; this is due to the fact that the studied element is a column (a crack resulting from the corrosion of the reinforcing steel), and the width is irregular, but the value of F is very low, implying that the crack is continuous, meaning there is no dissociation into independent sections, with an average oscillation and a uniformly distributed roughness, as the roughness values are close across the sections.Fourth Case: A Crack In a Slab(Figure 7.) shows a real image of a crack in a slab concrete (reinforced structural element) as well as a gray, binary and skeleton images with a grid applied to the extracted image along the crack path at different scales At scale , the crack takes on a simple geometric form as a one-dimensional object without obvious roughness. At , the actual geometry of the crack path begins to emerge, with large curves appearing, but the behavior is still regular. At , this scale seems to fall within the range of true fractal behavior, where squares line up along the perimeter of the crack, and the tortuosity becomes more pronounced. At , the squares follow almost every curve and cover irregular edges, but their number increases regularly. At , the squares begin to reveal small bumps and local variations at the edges. At the highest scale , the squares follow every vibration or local variation and every small change in direction, but there is no large increase in the number of squares . This indicates that the fractal dimension remains close to the value , and therefore the behavior of the squares across scales takes the form of a regular growth in the number of squares without sharp jumps or loss of linearity. This indicates scale consistency across scales. Also, the squares always line up on the path; they do not fill the inner region, so the value of the fractal dimension is very close to 1. We also note the self-similarity of the shape of the square distribution when reducing .
The following are the results of applying the code that appear in the Command Window: Fractal Dimension D : 1.0358 Crack Area : 10483 pixels Crack Length L : 1477 pixels Number of Branches Nc : 2 Fragmentation F : 0.001354 Avg. Width w_mean : 6.43 pixels Std Width w_std : 1.01 pixels Gap Variation Cv : 0.1570 Local Roughness sj per segment:( 0.3063,0.3052,0.3063,0.3052,0.3063, 0.3063,0.3052,0.3063,0.3052 0.3063) Crack Density : 0.0258 Orientation : 4.55 degrees Centroid (x,y) : (430.7, 285.9
The results show that the value of the fractal dimension is D = 1.0358, meaning that the crack is semi-linear, and this is the largest among the fractal dimension values studied in the previous images. This is also consistent with the fact that the crack consists of two branches without dense branching. The length of the crack is relatively long compared to the area. This is due to the accumulation of the products of the corrosion of the reinforcing steel.
DISCUSSION
Analysis of concrete crack images, after applying a code to process images of damaged structures for different cases (wall, beam, column, slab) using fractal geometry, revealed that these cracks follow a recurring fractal shape. This shape consists of two similar triangles that are axially opposite. With the repetition of this shape several times, the true crack shape that can be observed in the damaged structures is created. The simple fractal body shape was proposed in (Figure 1.), illustrating the fractal crack formation process across three stages. It was shown that the proposed shape can indeed be observed as recurring units in different cracks. After its presence was confirmed in these cracks, the fractal analysis code was applied, which involves calculating several indicators that can describe the crack state from a fractal perspective. The most important of these indicators is the fractal dimension, which allows us to measure the complexity of the shape (the crack) (17). Therefore, the code was initially applied to the fractal body proposed in (Figure 1.) and its indicators were calculated. The result showed that the fractal dimension is approximately equal to 1, which corresponds to the formation of a simple, quasi-linear crack and often indicates that there are no branchings in the crack (4). It should be noted that the higher the value of D (above 1), the more complex the crack is and the more urgent it needs maintenance. This is consistent with studies conducted on the fractal dimension (7). The fractal analysis code was applied to the remaining images, and box-counting grids were applied and displayed only along the crack path to calculate the number of squares that the crack passes through, decreasing the square scale each time. The indices were calculated to ensure that the results were consistent with the proposed fractal body and to characterize the cracks.By tracking the number of squares and their distribution pattern across different scales, starting with the first case of the wall, it became clear that there were repetitions of the distribution pattern with proportionally multiple numbers across the scales, and therefore it can be considered a constant branching pattern across the scales. The calculated indicators also proved to be consistent with the fractal body indicators, showing that the resulting cleft is unbranched, one-dimensional, and proportional to a simple, uncomplicated crack shape.In the second case, that of the beam, an uncomplicated pattern of the crack shape was observed, where the number of squares remained regular across scales, without any sudden jumps in this number, reflecting stability or consistency across scales.However, in the third (column) and fourth (slab) cases, the effect of corrosion on the crack shapeis clearly evident. In the column case, corrosion products accumulate under the concrete cover, forming a more complex crack pattern. The calculated indicators show a higher fractal dimension value compared to the previous cases. This value is consistent with the presence of two crack branches, confirming that the structure is more complex, yet it still maintains regularity. The study of the shape and number of squares reveals three repeating unit shapes across the scales,most of which resemble the proposed fractal shape. It was also observed that the crack width, density, and length are larger.The slab case study shows the largest value for the fractal dimension, which is indeed consistent with the large area of the gap formed in the slab and the volume of the corrosion products. This is the reason for the formation of two crack branches. However, through studies of the number and shape of the squares that define the crack path, their distribution can be considered regular across the scales without any sudden jumps. The consistency of the shape across scales in all studied images is considered evidence that the crack shape is a fractal shape, as the study showed that the proposed fractal body is consistent with the results obtained from multi-scale Box-Counting tests in terms of the shape of the formed crack and its calculated indices.It turns out that the more complex the crack path is and the larger the area it spreads over, the more the proposed structure of the fractal body has a different dimension and an advanced stage of fragmentation (the images of the column and slab showed that the crack consisted of two branches and was more complex, and the fractal dimension increased compared to the images of the wall and beam and the basic simple fractal body image).
CONCLUSIONS AND RECOMMENDATIONS In conclusion, using fractal geometry provides a quantitative and objective tool for diagnosing the condition of damaged concrete structures, thus aiding in the assessment of maintenance and reinforcement requirements. Furthermore, combining image processing and fractional analysis constitutes an effective method for evaluating damaged buildings without the need for destructive testing. The consistency of shape across scales in all studied images indicates that the crack shape is fractional. The study demonstrated the agreement of the proposed fractal body with the results obtained from multi-scale box counting tests in terms of the shape of the formed crack and its indices. Therefore, a single cracking indicator is insufficient; the more indicators studied, the more accurate the early prediction of structural element failure or maintenance needs. This study demonstrated the effectiveness of analyzing multiple indicators based on a fractal model. The structural element itself plays a crucial role in the risk of cracking. Load-bearing elements (columns, slabs) are more impactful because any loss of their strength directly affects the building’s overall load-bearing capacity and corrosion. It is recommended to expand the database by applying the methodology to a larger number of images and a variety of structures (bridges, columns, slabs) to generalize the results. Multiscale analysis can also be applied instead of singular fractal dimension to obtain a more accurate characterization of the crack network, in addition to select different fractal structures that closely resemble cracks for use in an early warning system for building and bridge maintenance, and to increase the number of indicators studied for crack characterization.
Large Language Models (LLMs) [1] have demonstrated significant capabilities in handling complex reasoning tasks, enabling the development of intelligent agents that can operate in dynamic and unpredictable environments. However, creating effective agents requires more than just leveraging the raw power of LLMs. It necessitates a modular and extensible framework that seamlessly integrates memory management, external tool usage, and advanced reasoning mechanisms. In response to these needs, we introduce LLM-Agent+, an open-source, modular framework for constructing intelligent agents powered by LLMs. The architecture is designed to be highly extensible, supporting experimentation across different agent components and reasoning strategies. Key features of LLM-Agent+ include:
A dual-layer memory architecture [2,3] that combines short-term conversational memory with long-term vector-based retrieval, allowing agents to maintain context over extended interactions.
A sequential reasoning engine utilizing Chain-of-Thought (CoT) prompting [4,9] to enhance the agent’s ability to decompose and solve complex tasks.
External tool integration [5], via a standardized interface, enabling access to APIs, calculators, search engines, and other systems.
A novel Reasoning Trace Compression (RTC) mechanism [6], which compresses the agent’s step-by-step reasoning trace to improve memory efficiency, reduce context window usage, and preserve the interpretability of extended reasoning chains. Inspired by recent methods such as LightThinker [11], RTC dynamically optimizes token usage while maintaining logical coherence.
The evolution of agent frameworks such as LangChain [7] and Auto-GPT [8] has emphasized prompt engineering and tool usage, but these systems often lack robust memory management and transparent reasoning flows. Similarly, approaches like ReAct [10] and Toolformer [5] integrate reasoning with tool use, yet operate within rigid context constraints and do not offer adaptive compression or flexible memory strategies. Memory-augmented architectures, including Memory-Augmented Transformers [3], have attempted to address long-context [13] reasoning via hybrid memory models. However, scalability remains a challenge. By contrast, LLM-Agent+ combines short-term buffers with semantic retrieval through tools like FAISS or Pinecone, enabling effective long-term context retention. Our core innovation, RTC, extends prompt optimization techniques by enabling salience-aware summarization of reasoning chains under token constraints, dynamically triggered at runtime. This allows agents to operate efficiently in long-context settings while preserving interpretability. In summary, while prior systems have explored components such as tool integration, structured reasoning, or memory augmentation in isolation, LLM-Agent+ brings these elements together into a unified and extensible framework. Its architecture is empirically validated in reasoning-intensive scenarios such as multi-step planning and software debugging, demonstrating strong performance with a reduced memory footprint and increased reasoning transparency—positioning it as a practical platform for future research in intelligent agents and human-AI collaboration. Recent progress in LLM-based agent frameworks has focused on integrating reasoning capabilities, memory optimization, and tool usage. Notably, LangChain [7] enables modular prompt and tool orchestration but lacks memory trace management. ReAct [10] combines reasoning and acting in a loop, yet suffers from fixed context limitations and lacks memory layering. Auto-GPT [8] introduced autonomous goal decomposition, but prompt expansion and memory scaling remain significant issues. Toolformer [5], on the other hand, offers token-level tool use but provides limited control over memory or interpretability. Several recent works address these challenges with targeted innovations. G-Memory [15] proposes a hierarchical memory tracing approach for multi-agent coordination. Task Memory Engine (TME) [16] introduces a spatial memory graph that enhances multi-step robustness and eliminates hallucinations in agent responses. ACBench [17] evaluates the behavior of compressed LLMs, demonstrating trade-offs between model efficiency and action quality. Further, KG-Agent [18] leverages knowledge graphs for multi-hop reasoning with autonomous agents, while OmniThink [19] enriches CoT reasoning via multimodal expansion and visual-textual trace fusion. Compared to these systems, LLM-Agent+ introduces a unified architecture that integrates dual-layer memory, structured reasoning via Chain-of-Thought prompting, and a novel runtime. Reasoning Trace Compression (RTC) mechanism. This positions it as a scalable, token-efficient, and interpretable alternative for long-context and reasoning-intensive applications.
MATERIALS AND METHODS
This section outlines the architecture, implementation, and experimental setup used to develop and evaluate LLM-Agent+. We detail the system’s modular components, memory and reasoning mechanisms, and tool integration layer. The agent was implemented in Python using state-of-the-art libraries for NLP, semantic retrieval, and LLM interaction. Experiments were conducted on reasoning-intensive tasks using a controlled evaluation environment.
System Overview
The system is composed of the following major modules:
Natural Language Understanding (NLU) Responsible for parsing user inputs and extracting intents and entities. This module transforms free-form language into structured semantic representations suitable for reasoning and action planning.
Memory System Implements a hybrid memory model consisting of:
Short-term memory (STM): Stores recent conversational history and task context.
Long-term memory (LTM): Vector-embedded, persistent storage used for retrieving semantically similar past information. Libraries such as FAISS and Pinecone are supported for fast semantic search [12].
Reasoning Engine Core module that drives problem-solving using LLM prompting strategies such as Chain-of-Thought (CoT) and Self-Refinement. It supports structured reasoning and multi-turn planning, enhanced by access to memory and tools.
Reasoning Trace Compression (RTC) A novel module introduced in LLM-Agent+, RTC analyzes and compresses the reasoning trace dynamically to:
Minimize token usage in long reasoning chains.
Improve coherence by summarizing intermediate thoughts.
Maintain logical flow while reducing context overload. This approach is inspired by recent work on efficient LLM chaining such as LightThinker [13].
Tool Integration Layer Interfaces with external APIs, search engines, computational tools, and file systems. A standardized tool schema enables seamless addition of new capabilities without modifying core agent logic.
Action Generation Module Takes the output from the reasoning engine and formulates final responses or commands. It ensures alignment with user intent and applies safety filters to validate tool calls or external actions.
Interfaces The agent can be deployed via: – Command-Line Interface (CLI) for lightweight testing. – Web Interface (FastAPI-based) with rich visualization, logging, and memory exploration.
Interaction Flow
The typical execution loop in LLM-Agent+ proceeds as follows:
The user submits input via CLI or web UI.
NLU module extracts structured meaning.
Memory modules retrieve relevant short- and long-term context.
Reasoning engine constructs a CoT reasoning chain.
RTC module compresses the reasoning trace to maintain context within token limits.
If needed, tools are invoked through the Tool Integration Layer.
The reasoning engine integrates tool results, finalizes the plan, and passes it to the Action Generator.
The final response is presented to the user, and memory is updated with the new experience.
This modular structure empowers developers and researchers to experiment with alternative strategies for memory retrieval, reasoning techniques, and tool orchestration. Additionally, the RTC component makes LLM-Agent+ particularly suitable for complex, multi-step tasks under token constraints as illustrated in Fig. 1. Architecture of the LLM-Agent+ framework, showing core components including Natural Language Understanding (NLU), dual-layer memory (Short-Term and Long-Term), Reasoning Engine with RTC compression, and Tool Integration Layer. Arrows indicate the data flow from user input to the final output.
Fig. 1. Architecture of the LLM-Agent+ framework.
Implementation Details
The LLM-Agent+ framework is implemented in Python and is structured for modularity and extensibility. It leverages state-of-the-art libraries for natural language processing, memory management, semantic search, and external tool invocation. This section provides a detailed description of each system component and the key implementation choices.
Core System Components
Natural language understanding
The NLU module is responsible for parsing user inputs and extracting actionable semantics. It is built using:
spaCy: for syntactic parsing and named entity recognition.
Hugging Face Transformers: for intent detection and contextual embedding.
The parsed inputs are converted into structured representations, such as JSON objects containing intents and slots.
Domain adaptation is supported through fine-tuning on custom task-specific data.
Dual-layer memory system
Short-Term Memory (STM):
Implemented as a fixed-size FIFO buffer (default: last 10 turns).
Stores raw dialogue history and metadata (timestamps, speaker roles).
Long-Term Memory (LTM):
Uses FAISS for efficient vector similarity search over embedded memories.
Memories are encoded via Sentence-BERT (all-MiniLM-L6-v2) for semantic retrieval.
Supports optional integration with Pinecone for cloud-based persistent storage.
Reasoning Engine
Supports Chain-of-Thought (CoT) prompting with dynamic context selection.
Implements Self-Refinement: up to 3 iterative loops to improve reasoning.
Salience Scoring: Uses a lightweight BERT-based classifier to rank blocks by importance (trained on human-annotated traces).
Summarization: Retains high-salience blocks verbatim; summarizes low-salience blocks via LLM (GPT-3.5-turbo), constrained to preserve logical dependencies.
Token Budgeting:
Dynamic compression is triggered when trace exceeds 75% of context window (e.g., 6K tokens for 8K models).
Summary fidelity is validated via automated logical consistency checks (e.g., entailment verification with NLI models).
Tool Integration Layer
Tools are defined via a JSON schema (name, description, I/O specs, safety constraints).
Supports OpenAPI/Swagger for automatic API wrapping (e.g., calculators, web search).
Tools are invoked via a semantic router that matches queries to tool descriptions using cosine similarity.
Interfaces
CLI: Built with Click, supports interactive chat and scripted task execution.
Web UI: FastAPI backend with React frontend, featuring:
Real-time reasoning trace visualization.
Memory exploration via nearest-neighbor search over LTM embeddings.
Reasoning Trace Compression (RTC) Pseudocode
Optimization and Resource Management
This section outlines the framework’s runtime performance optimization strategies and how resource usage is dynamically managed. Key evaluation benchmarks—such as latency, memory efficiency, and embedding performance—are presented to assess LLM-Agent+’s operational viability under real-world workloads. We explain each metric in detail and support the data with empirical evidence gathered during experimentation unless otherwise indicated.
Latency Benchmarks
To assess the responsiveness of LLM-Agent+, we measured end-to-end latency for key system components across 10,000 task samples using an 8K token context window.
Table 1 shows latency values in milliseconds for:
P50 (median latency): Time under which 50% of requests were completed.
P95 (tail latency): Indicates the worst-case performance scenario for 95% of tasks.
Hardware used: Indicates the hardware on which each module was evaluated.
NLU (spaCy): Achieved median latency of 12 ms and P95 of 18 ms using CPU.
Long-Term Memory (LTM) Retrieval: FAISS-based retrieval showed a P50 of 45 ms, P95 of 110 ms on RTX 3090 GPU.
RTC Compression: GPT-3.5-turbo based summarization introduced higher latency (P50: 320 ms, P95: 650 ms), due to API calls and LLM processing.
These values were derived from direct measurements during our benchmark experiments.
Embedding Trade-offs
This subsection compares different embedding models in terms of vector dimensions, retrieval accuracy, query throughput (QPS), and memory usage per million vectors.
Models evaluated: all-MiniLM-L6-v2, OpenAI text-embed-3, and BAAI/bge-small.
Dimensions (Dims): Reflect the size of each embedding vector. For example, OpenAI’s model uses 1536 dimensions vs. 384 in others.
Accuracy@1: Denotes the proportion of top-1 correct matches during semantic search.
QPS (queries per second): Indicates how many similarity queries can be handled per second.
Memory usage: Measured in GB for storing 1M vectors.
The OpenAI text-embed-3 model shows highest accuracy (82.1%) but at a high memory cost (5.8 GB/1M vectors), and lower QPS due to API latency.
Values for all-MiniLM-L6-v2 and BAAI/bge-small are from HuggingFace benchmarks [source: Johnson et al., 2017; OpenAI API docs].
All measurements, except OpenAI QPS, were obtained from local benchmarks in this study.
Resource Management
Dynamic Load Balancing
The ResourceMonitor class is used to dynamically adjust system resources during runtime. The logic includes:
GPU Offloading: If GPU utilization exceeds 90%, embedding tasks are transferred to CPU.
RAM Management: If RAM usage goes above 80%, memory caches are reduced.
These strategies ensure system stability during high-load scenarios.
Failure Recovery
Checkpointing: LTM updates are atomic writes with WAL logging
Retry Policies: Exponential backoff for tool calls (max 3 retries)
Validation Pipeline
Compression Ratio: Target 3:1 for traces >1K tokens
Logical Consistency: >95% entailment score on ANLI test set
Token Savings: 58-72% in empirical evaluations (Sec 5.3)
Experimental Evaluation
We evaluate LLM-Agent+ across a set of reasoning-intensive tasks to assess its effectiveness in memory efficiency, reasoning trace compression, and tool-augmented problem solving. The evaluation focuses on runtime behavior, token usage, trace coherence, and task success rates.
Evaluation Setup
We conducted experiments on a workstation with:
CPU: Intel Xeon 12-core
GPU: NVIDIA RTX 3090
Memory: 64 GB RAM
LLM backend: OpenAI GPT-3.5-turbo (via API)
Tasks were selected from three categories:
Multi-step reasoning tasks (math word problems, logical puzzles)
Code debugging scenarios (error trace identification and patch suggestion)
Research synthesis (retrieving and summarizing prior work)
Each task was executed with and without RTC enabled to measure compression effectiveness and reasoning quality.
Evaluation Scope and Comparative Analysis
While our experiments demonstrate LLM-Agent+’s efficacy in reasoning-intensive tasks, we further contextualize its performance through:
Comparative Benchmarks:
Baselines: We compare against two frameworks:
LangChain[7]: Represents modular tool integration but lacks explicit memory optimization.
ReAct[6]: Embeds reasoning+action loops but uses fixed-context windows.
Results: LLM-Agent+ reduces token usage by 35% ReAct and improves success rates by 18%vs. LangChain in multi-step planning.
Ablation Studies:
RTC Impact: Disabling RTC increases prompt length by 1×and degrades logical consistency (entailment scores drop to 82%).
Memory Layers: STM-only setups fail in long dialogues (success rate drops by 40%after 20 turns).
Domain Generalization: Tests on clinical diagnosis (MedQA dataset) and financial planning (FinSim benchmarks) show consistent RTC efficacy (token savings: 62–68%), though tool integration requires domain-specific adaptations.
Figure 2. Represent Performance of LLM-Agent+ Against Baseline Frameworks
Notes:
Task Success Rate: Human-rated correctness of final outputs. LLM-Agent+ outperforms baselines by 17.8% (LangChain) and 8.6% (ReAct).
Tokens/Step: RTC reduces token consumption by 35% vs. ReAct (210 → 120).
Latency: Includes NLU, reasoning, and tool calls. LLM-Agent+ balances speed and compression overhead.
Memory: Hybrid memory (STM+LTM) reduces footprint vs. LangChain’s raw buffer.
Uncertainty: Standard deviation in parentheses (±).
Limitations: Current comparisons focus on open-source frameworks; proprietary systems (e.g., OpenAI’s Assistant) are excluded due to reproducibility constraints.
Metrics
We tracked the following metrics:
Compression Ratio: Number of tokens before vs. after RTC
Token Savings (%): Percentage of reduced tokens
Logical Consistency: Validity of final answers (measured with entailment score using an NLI model)
Latency (ms): Time taken per reasoning loop
Task Success Rate: Human-rated success on final outputs (pass/fail)
Case Study: Tool-Augmented Debugging with RTC:
To illustrate the practical benefits of LLM-Agent+, we present a case study in which the agent was tasked with diagnosing and resolving a real-world software issue: a Python script failing with a ValueError during runtime.
Task Setup
Input: A user provided an error message and a portion of the failing script.
Goal: Identify the root cause and suggest a valid code correction.
Context: The error stemmed from improper list indexing in a nested loop function.
LLM-Agent+ Behavior
NLU parsed the exception trace and extracted intent (debug) and relevant entities (ValueError, function_name).
Short-Term Memory (STM) retained the ongoing session dialogue.
Long-Term Memory (LTM) retrieved a past interaction with a similar indexing bug using FAISS-based semantic search.
Reasoning Engine initiated a multi-turn CoT reasoning chain:
Step-by-step hypothesis testing
Code structure analysis
External lookup via a documentation API
RTC was triggered when the CoT trace exceeded 3,000 tokens. The reasoning was segmented, salience-scored, and compressed to fit within the model’s token window.
Tool Integration Layer executed a dry-run of the suggested patch using a sandboxed Python runner.
Action Generator returned a corrected function version and explained the fix in natural language.
Consistency: High logical agreement with original reasoning (validated via NLI score of 96.4%)
This case highlights the benefits of RTC in managing long reasoning chains without losing coherence, and the value of tool integration for grounded, verifiable actions.
RESULTS
We evaluated LLM-Agent+ across three domains—multi-step reasoning, code debugging, and research synthesis—to assess its effectiveness in memory efficiency, reasoning trace compression, and tool-augmented decision-making. The framework achieved a task success rate of 92.3% (±3.1), significantly outperforming baseline frameworks such as LangChain (74.5%) and ReAct (83.7%). When Reasoning Trace Compression (RTC) was enabled, the average token usage per step decreased from 210 to 120 tokens, representing a reduction of approximately 40% compared to ReAct. Latency measurements demonstrated that RTC introduces minimal overhead: the average reasoning cycle time with compression was 320 ms per step, which is within practical bounds for interactive agents. Memory usage remained efficient, with the hybrid memory architecture consuming 1.8 GB on average, compared to 2.4 GB in LangChain’s buffer-based setup. In the debugging case study, LLM-Agent+ successfully diagnosed a runtime error and proposed a corrected function. The reasoning trace was reduced from 3,640 tokens to 1,280 tokens (65% reduction) via RTC, while maintaining a logical entailment score of 96.4%, confirming coherence preservation. These results confirm the framework’s ability to manage long-context tasks while improving interpretability and efficiency—without sacrificing accuracy or response quality.
DISCUSSION
The results presented in this paper demonstrate the feasibility and versatility of LLM-Agent+ as a modular framework for constructing intelligent agents capable of reasoning, memory integration, and external tool use. The Reasoning Trace Compression (RTC) mechanism proved particularly effective in reducing token usage while preserving logical coherence, which is critical for managing the limitations of transformer-based LLMs in long-context scenarios. Compared to LangChain [7], which offers flexible tool integration but lacks robust memory handling and reasoning trace management, LLM-Agent+ provides structured memory via a dual-layer architecture and compresses reasoning steps for more efficient context usage. Similarly, while Auto-GPT [8] facilitates task decomposition through autonomous loops, it suffers from prompt length inflation and lacks semantic trace optimization, which LLM-Agent+ addresses through RTC. The dual-layer memory system allowed the agent to maintain contextual awareness over extended interactions—an advantage over ReAct [10], which embeds actions and reasoning in fixed prompt buffers without adaptive memory retrieval. Furthermore, unlike Toolformer [5], which integrates tools at the token level but lacks control over memory or trace structure, LLM-Agent+ offers a standardized tool schema and explicit reasoning trace management, improving both extensibility and interpretability. In our case study, the agent leveraged semantic retrieval and multi-turn reasoning to debug a complex code snippet—an example of real-world utility that highlights the agent’s autonomy and robustness. These empirical outcomes reinforce the benefits of combining modular reasoning, context-aware memory, and token-efficient trace compression. Despite these strengths, there are several limitations to address. First, the RTC mechanism, while effective, currently relies on pretrained models (e.g., BERT, GPT-3.5) for salience scoring and summarization, which may introduce domain or language biases. Second, the framework assumes reliable access to external APIs and LLM services, which could limit its applicability in offline or constrained environments. Third, although we demonstrated task success qualitatively and via metrics such as token savings and entailment scores, conducting broader user studies or benchmarking against standardized agent evaluation datasets would strengthen the empirical foundation. Looking ahead, there are multiple avenues for extending this work. Adaptive compression policies driven by reinforcement learning could further improve trace optimization. The framework can also be extended to support richer tool ecosystems, including domain-specific knowledge bases and symbolic planners. Finally, integrating feedback loops with human users could enhance transparency, trust, and collaborative intelligence — aligning with the growing interest in human-AI [14] co-agents.
CONCLUSION
In this work, we introduced LLM-Agent+, a modular and extensible framework for building intelligent agents powered by Large Language Models (LLMs). The system brings together key components—such as dual-layer memory, structured reasoning via Chain-of-Thought prompting, external tool integration, and the novel Reasoning Trace Compression (RTC) mechanism—to address limitations in existing frameworks related to memory handling, trace interpretability, and long-context reasoning. Our evaluation demonstrated that LLM-Agent+ achieves notable improvements in token efficiency, task success rates, and reasoning transparency, outperforming established systems like LangChain, ReAct, and Auto-GPT. Through both quantitative benchmarks and qualitative case studies, we showed that RTC enables up to 40% reduction in token usage while preserving logical consistency, making the framework particularly well-suited for long and complex reasoning scenarios. Unlike prior systems that often treat memory, reasoning, and tool usage in isolation, LLM-Agent+ unifies these capabilities within a modular architecture that supports experimentation and scalability. This design makes it suitable for both research and production contexts. Future directions include reinforcement learning-driven compression strategies, support for more domain-specific toolchains, and human-in-the-loop feedback mechanisms to promote transparency and collaborative decision-making. We release LLM-Agent+ as open-source to facilitate further development and encourage community contributions to the growing field of intelligent agent systems.
In recent years, the digital transformation of government services has emerged as a critical global priority. Nevertheless, e-government remains an active and evolving research field, as many countries have only implemented partial solutions and continue to face unresolved technical and organizational challenges. As stated in [1], “the development of a shared e-government knowledge base is one of the key challenges of many e-government strategies”. This challenge arises from the heterogeneity of government entities, which hinders seamless interoperability and secure data exchange. To overcome such challenges, Semantic Web technologies – such as RDF, OWL, and SPARQL -have been increasingly adopted to construct unified, standards-based knowledge frameworks. These technologies support semantic interoperability across distributed systems and offer promising tools for integrating government services. However, as noted in [2], “much research in the Semantic Web and Linked Data domain has focused on enabling the sharing of open datasets” often overlooking essential security and access control requirements that are critical in sensitive domains such as public administration. This research focuses on a critical aspect of secure e-government: access control. Although ensuring robust security in public administration is imperative, the integration of semantic web methods into these systems frequently exposes vulnerabilities—particularly within access control mechanisms. In response, we propose an innovative solution that reinforces the conventional Role-Based Access Control (RBAC) model. Our approach integrates ontology-driven methodologies to dynamically implement access policies, ensuring that only authorized users gain access to sensitive information. The central hypothesis of this study is that embedding semantic web technologies into access control frameworks not only improves data interoperability but also significantly enhances security by preventing unauthorized access and ensuring proper user authentication. To validate this hypothesis, we designed and implemented a prototype using Apache Jena Fuseki alongside semantic web technologies such as RDF, OWL, and SPARQL. The prototype was evaluated in an e-government context, demonstrating that dynamic semantic reasoning and flexible policy updates can effectively meet the complex security requirements of distributed public services. The results indicate that our approach supports scalable, interoperable, and secure e-government systems, paving the way for broader adoption of semantic web technologies in public administration. This paper contributes to bridging the gap between theoretical research and practical application in the fields of information security, semantic web, and public administration. By integrating semantic reasoning with enhanced access control, our work presents a practical framework that addresses the key challenges of data interoperability and security within e-government systems. A review of the literature reveals extensive research on both Semantic Web applications and e-government systems. Previous studies have tackled issues such as data heterogeneity, interoperability challenges, and security vulnerabilities. Multiple methodologies have been proposed for integrating semantic technologies into public administration, with particular attention to the dynamic enforcement of access control policies and the use of ontologies for modeling complex governmental data. Building on these findings, our work presents a comprehensive solution that unifies semantic data sharing with enhanced access control, thereby addressing both integration and security requirements in e-government environments.
Semantic Web-Based E-Government
Semantic Web technologies have become a cornerstone for achieving interoperability and data integration in e-government systems. Study [3] mapped a range of case studies; for example, [4] developed a domain ontology for Nepal’s citizenship certificates, improving issuance accuracy and efficiency, and [5] introduced semantically reusable Web Components that measurably enhance response time and interoperability—while also noting that practical deployment details remain underexplored. Concrete prototypes further illustrate these insights: [6] harmonized civil, health, and education schemas into a unified OWL ontology, enhancing consistency and query precision; and [7] implemented an OWL-based integration platform in Kuwait, enabling real-time semantic queries across ministries. At the national level, [8] showcases Finland’s Semantic Web infrastructure: a cross-domain ontology “layer cake” and a series of Linked Open Data portals built on SPARQL endpoints. For over two decades, this infrastructure has supported hundreds of applications, proving that scalable, government-wide semantic integration is both feasible and impactful. Study [9] surveyed RDF, OWL, and SPARQL applications across public-sector services, categorizing technical and socio-economic challenges—particularly around security and real-world deployment— and concluded that the semantic web lacks the maturity of a production-grade artifact, calling for increased focus from both academia and industry. Together, these studies trace the evolution from targeted domain ontologies to large-scale national frameworks, paving the way for our ontology-based RBAC solution that combines semantic data sharing with dynamic access control.
Semantic Web-Based Access Control
Since the inception of semantic web technologies, many studies have investigated their application in access control to address security vulnerabilities in distributed systems. Researchers have explored various models, including DAC (Discretionary Access Control), MAC (Mandatory Access Control), RBAC, and ABAC (Attribute-based Access Control). These studies have often yielded the following findings:
For MAC and DAC, studies such as [10] have focused on defining vocabularies that support multiple access control models using DAML+OIL (Darpa Agent Markup Language + Ontology Inference Layer) ontologies. Similarly, [11] proposed an attribute-based model to overcome heterogeneity in distributed environments, supporting MAC, DAC, and RBAC.
In the domain of RBAC, recent works have advanced semantic role modeling and multi-domain integration. [12] proposes an intelligent RBAC framework that defines “semantic business roles” via OWL ontologies and enables policy evaluation across organizational boundaries. Additionally, [13] introduced a semantic security platform that implements an enhanced RBAC model (merging RBAC and ABAC) using ontology modeling techniques. [14] presents a feature-oriented survey of ontology- and rule-based access control systems with a focus on conflict resolution and dynamic decision making. [15] demonstrates an ontology-based data access case study in which semantic queries enforce role assignments and permissions within a distributed environment, validating practical applicability.
Regarding ABAC, studies have focused on attribute-driven policy enforcement and fine-grained control. [16] introduces a semantic ABAC model based on ontology-defined attributes and context rules for adaptive access decisions. [17] extends semantic ABAC to e-Health, designing an ontology that maps user, resource, and contextual attributes to enable secure, fine-grained medical data access, and [18] presents a general ontology for access control that performs effectively in large-scale, heterogeneous environments.
Collectively, these studies demonstrate that semantic web technologies can effectively support various access control models. However, challenges remain when applying these technologies in environments with sensitive data, such as e-government systems.
MATERIALS AND METHODS
In this section, we propose a solution for information sharing in an e-government environment, as well as an access control mechanism within that environment. Our approach builds on foundational ontology‐design methodologies from recent research studies [19, 20, 21], adheres to widely accepted semantic web standards, including RDF, RDFS (Resource Description Framework Schema), OWL, and SPARQL, and employs Protégé platform and GraphDB’s visual graph feature for ontology development and visualization. Semantic data is stored, queried, and managed in an Apache Jena Fuseki triple store, while the Semiodesk Trinity framework provides seamless .NET integration with Fuseki. The web application layer is implemented using ASP.NET MVC 5 and ASP.NET Core within Visual Studio 2022. This foundation enables the implementation of a scalable, interoperable, and secure e-government system that integrates semantic reasoning and dynamic access control policies.
Proposed Solution for E-Government Information Sharing
In this study, we assume the existence of four government entities, each developing its own application while enabling information and knowledge sharing among themselves. These entities are:
*Ministry of Health
*Ministry of Labor
*Ministry of Higher Education
*Civil Registry
To facilitate interoperability, a simplified yet expandable ontology was designed for each entity.
Ministry of Health Ontology: This ontology consists of the following classes: mc-Patient, mc-Hospital, mc-Injury, and mc-InjuryDetails. See Figure 1.
Figure 1 – Ministry of Health Proposed Ontology
Ministry of Labor Ontology: This ontology includes the classes: mc-Beneficiary, mc-EmploymentRequest, and mc-FamilySupport.
Ministry of Higher Education Ontology: This ontology is composed of the classes: mc-StudentProfile, mc-Course, and mc-Exam.
Civil Registry Ontology: It contains a single core class: mc-PersonProfile, which stores the personal information of citizens. And an auxiliary class mc-Citizen is introduced as a container to link the other ontologies. See Figure 2.
Figure 2 – Civil Registry Proposed Ontology
The ontology model ensures that each government entity maintains its own structured data while remaining interoperable through shared concepts.
Information Sharing Among E-Government Ontologies
The proposed solution establishes semantic relationships between different government entities by defining mc-Patient (Ministry of Health), mc-Beneficiary (Ministry of Labor), and mc-StudentProfile (Ministry of Higher Education) as subclasses of mc-PersonProfile class (Civil Registry). See Figure 3. By applying inheritance principles, any instance created in the sub-classes automatically inherits its personal data from the corresponding mc-PersonProfile instance in the Civil Registry. This ensures that all citizens—whether they are students, beneficiaries, or patients—are first recognized as individuals within the national Civil Registry system before being associated with specific government sectors. This ontology-driven approach enhances data consistency, reduces redundancy, and enables seamless information retrieval across multiple government institutions, forming the foundation for a unified and interoperable e-government system.
Figure 3 – E-Gov Proposed Ontologies
To demonstrate information sharing among e-government ontologies, several SPARQL query examples are provided in the supplementary materials.
Proposed Solution for Access Control
The RBAC (Role-Based Access Control) model was selected as the foundation of the proposed solution due to the structured role-based nature of e-government institutions. Since government environments typically have well-defined actor roles, RBAC provides a policy-neutral, manageable, and scalable approach to access control. As stated in study [22]: “Role-Based Access Control models appear to be the most attractive solution for providing security features in multidomain e-government infrastructure. RBAC features such as policy neutrality, principle of least privilege, and ease of management make them especially suitable candidates for ensuring safety in e-government environment”. RBAC is commonly classified into four levels, ranging from the simplest to the most advanced: Flat RBAC, Hierarchical RBAC, Constrained RBAC, Symmetric RBAC. Each level builds upon the previous one. Since the goal of this research is to develop a simple yet expandable solution, the proposed approach implements Flat RBAC, while ensuring that future extensions to Hierarchical and Constrained RBAC are feasible. Following ontology design principles, we begin by modeling a core RBAC ontology, depicted in Figure 4, that conforms to the Flat RBAC standard.
Figure 4 – Conceptual RBAC Ontology Based on the Flat RBAC Model
This conceptual design captures the essential components of role-based access control (User, Role, Permission) and serves as a foundation for a more practical implementation. By decoupling permissions into explicit (Action-Resource) pairs, this ontology enforces clear semantics for each access right. However, while theoretically sound, the core model is not optimally structured for direct use in real-world applications due to its abstract handling of permission granularity and lack of support for multi-application contexts. To address these limitations and enable the application of RBAC in real deployment environments, we extend and restructure the initial model into a more implementation-oriented ontology, as shown in Figure 5.
Figure 5 – Application-Oriented RBAC Ontology for E-Government Access Control
This model replaces the triplet of Permission, Action, and Resource with a single Method class, which represents functions or procedures within the system that users interact with. It also adds two more classes: Credential (for user authentication), and Application (for managing access within multiple systems). This ontology enables administrators to assign methods (i.e., grouped action-resource operations) to roles per application, and to authenticate users via credentials before role activation. The proposed model successfully meets the fundamental requirements of the Flat RBAC standard:
Users acquire permissions (Methods in our case) through roles.
Both user-role assignments and permission-role assignments (Method-Role assignments in our case) follow a many-to-many relationship.
The system supports user-role review.
Users can exercise permissions associated with multiple roles simultaneously.
These compliance criteria were verified through SPARQL queries, which are provided in the supplementary materials for reference.
RESULTS
The research resulted in the development of the following applications:
Access Control Application:
This application enables administrators to define users, roles, and permissions, effectively implementing the Role-Based Access Control (RBAC) model.
Additionally, it provides an API service that allows e-government applications to request user access verification and make allow/deny decisions accordingly.
E-Government Applications:
These applications utilize the access control system for managing secure access while supporting interoperable data exchange among government entities.
Implementation of the Access Control Management Web Application
A web-based application was developed to serve as the administrative interface for the Access Control System. This application was built using ASP.NET MVC5, leveraging the Semiodesk Trinity platform for data layer integration. It provides system administrators with full control over Applications, Users, Roles and Permissions (Methods). Additionally, the system is designed to manage itself, incorporating authentication and authorization mechanisms.
Authentication and Authorization Process
User Login (Authentication):
The system verifies user credentials by searching for a matching username and password in the stored user data.
Upon successful authentication, the system retrieves the roles assigned to the user and the permissions linked to those roles.
Authorization Mechanism:
Once authenticated, the system determines whether the user is authorized to access a specific method.
For example, when a user requests the home page (Index) within the HomeController of the Access Control Application, the system evaluates whether the method’s signature (AppRbac_Home_Index) exists within the user’s assigned permissions.
If a match is found, the user is granted access, and the requested page is displayed.
This authorization mechanism is enforced throughout the application. Each time a user navigates between interfaces or performs an action, the system validates their authorization to invoke the corresponding method, ensuring role-based access control. The following Figure 6 illustrates one of the user interfaces of the application.
Figure 6 – Roles Management in Access Control Application
Integration with E-Government Applications via AppMgr.Api
A dedicated API service (AppMgr.Api) was developed to facilitate communication between the Access Control System and e-government applications. This service is invoked by e-government applications whenever a user attempts to log in.
When an e-government application sends a login request, it includes the username and password of the user.
The authentication process follows the same mechanism described earlier:
The system verifies the credentials.
If authentication is successful, the user’s roles and permissions are retrieved.
The API response includes:
The user’s assigned roles and permissions.
The URL to which the user should be redirected upon successful login.
Unlike the Access Control Management Web Application, authorization is not handled by the API itself. Instead, each e-government application processes authorization internally, relying on the permissions received from the API.
This modular approach ensures flexibility, allowing each e-government system to enforce role-based access control (RBAC) policies based on its specific operational requirements.
E-Government Applications and Information Sharing Between Them
The e-government applications were developed using ASP.NET Core, in combination with Semiodesk Trinity and the Apache Jena Fuseki triple store. These applications were integrated with the Access Control Service, which manages both authentication and authorization processes.
Example: Patient Registration in the Ministry of Health Application
As shown in Figure 7, when registering a new patient in the Ministry of Health application, the system first performs a query using the citizen’s national ID in the Civil Registry application.
The registry retrieves and returns personal information, and the Ministry of Health user adds the patient’s medical details.
Figure 7 – (Add Patient) Interface in the Ministry of Health Application
Similarly, new beneficiary registrations in the Ministry of Labor application and student registrations in the Ministry of Higher Education application rely on retrieving personal details from the Civil Registry. This demonstrates the seamless interoperability and efficient data sharing enabled by the semantic integration model.
Example: Sharing Medical Records Between Applications
Figure 8 illustrates the family support interface in the Ministry of Labor application, where the amount of support is calculated based on the injury percentage of each beneficiary.
The injury percentages data originates from the Ministry of Health ontology, further validating the effectiveness of semantic information sharing across government applications.
Figure 8 – (Family Support) Interface in the Ministry of Labor Application
Reasoning Activation in E-Government Applications
To enhance data inference capabilities, a reasoning engine was activated within the Fuseki triple store using the OWLMicroFBRuleReasoner. Example of Automated Inference:
The reasoning engine allows the system to derive new knowledge that was not explicitly stored in the triple store.
Consider the following inverse relationships between the Exam and Course classes:
Exam → has_exam → Course
Course → exam_has_course → Exam
If the triple (course1 has_exam exam1) is added, the reasoning engine automatically infers the inverse relationship:
(exam1 exam_has_course course1)
This inference is dynamically added to the e-government dataset, ensuring data consistency and completeness.
The effectiveness of this semantic reasoning mechanism was successfully tested in the student exam details interface, along with several other logical inferences within the applications.
DISCUSSION
Our work advances both semantic information sharing and access control in ways that address the limitations noted in prior studies. Unlike study [7], which proposed ontologies without implementation, we developed a working prototype that demonstrates real-time data exchange across government domains. In contrast to study [1], which lacked a mechanism to identify the appropriate authority for a given service, our model integrates an ontology-driven RBAC system to securely handle such decisions. From an access control perspective, the study validates that Semantic Web technologies can effectively implement a Role-Based Access Control (RBAC) model through ontology-driven mechanisms. While most access control research remains theoretical or limited to less-sensitive domains such as Online Social Networks or cloud platforms [18], our solution is applied in an e-government context, managing sensitive data through a fully implemented, policy-aware system. While this work focused on the Flat RBAC model, its semantic foundation facilitates natural extensions to Hierarchical and Constrained RBAC.
Evaluation Criteria and System Assessment
To further assess the quality and applicability of the proposed system, we evaluated it against commonly accepted criteria in semantic e-government research, as outlined below:
This qualitative evaluation demonstrates that the proposed solution is not only conceptually sound but also practical, modular, and aligned with real-world public-sector requirements.
CONCLUSIONS AND RECOMMENDATIONS
This research introduced a semantic web-based framework for secure information sharing and access control in e-government environments. The study confirmed that by leveraging ontologies and reasoning engines, government systems can achieve improved interoperability, reduced redundancy, and scalable architecture—while also supporting dynamic, fine-grained access control mechanisms. The integration of ontology modeling with access control policies strengthens both security and flexibility in distributed digital services.
Based on these findings, the following recommendations are proposed:
Expand e-government ontologies by integrating additional domain-specific concepts and linking to existing public ontologies on the web to enhance service coverage.
Extend the access control ontology to support Hierarchical RBAC and Constrained RBAC, leveraging OWL constructs to model complex permission structures.
Deploy the developed applications on the public web, hosted by trusted national IT infrastructures, to enable citizen-facing services while maintaining data protection and system integrity.
INTRODUCTION Recently, a growing number of warnings have been issued about the fate of life on planet Earth. Its ecosystem, with all its components, has been constantly polluted -both organic and inorganic- due to the combination of the spread of industrial revolutions and the increase in various human activities. Revolutions in the textile and oil industries have had a great potential to cause terrible and catastrophic deterioration of the aquatic environment, and they did what they did in the past and what these deteriorations have led to today (1). In several Asian and African countries, as a result of population growth and to secure greater economic returns for the country, governments have turned the wheel of production to expand textile, medical, pesticide, and other industries as a central tributary to strengthening and growing their economies. But the development rewards have not been good with regarding the production of organic dyes and petroleum-based pesticides. Production has reached immeasurable levels – tens of thousands of tons of dyes, pesticides, and even raw materials for medicines – causing negative impacts on rivers, drinking water sources, and brackish water sources (1,2). Not all scientific studies have concealed the fact that the gradual accumulation of byproducts from that production process (heavy metals, fillers, lubricants for production equipment, etc.) is being introduced as non-biodegradable waste into water, exposing water bodies to potentially unavoidable hazards in the future. The strong interconnectedness of the living and non-living components of water and the ease of movement of organic contaminants between them increases the complexity of water pollution and the interconnection of this pollution with other media. These contaminants affect light penetration in water, impair the formation of chlorophyll in aquatic plants, increase the rate of anaerobic fermentation, cause the death of marine organisms, decrease the levels of important ions (potassium, sodium, chloride, etc.), and other effects caused by water pollution with organic matter. Organic contaminants fall into different families, classified according to their toxicity or chemical composition: colored azo contaminants (homogeneous and heterocyclic aromatic compounds), petroleum contaminants (monocyclic aromatic compounds), and dozens of dirty groups of hydrocarbon compounds (POPs and PAHs), etc. (3). This group, out of one hundred and twenty-nine known priority contaminants, as described in the U.S. Clean Water Act, silently depletes and kills aquatic resources with dire consequences. This consequence falls within the scope of the characteristics of persistent organic contaminants, including: accumulating capacity, complexity of chemical composition, heterogeneous and unstable distribution between solid and liquid phases, high solubility in lipids, and bioaccumulation in human and animal tissues (4-6). According to the reports of researchers Al-Tohamy (1), Bishnoi (2), and Abu-Nada (7), phenolic hydrocarbons and halogenated monoaromatic hydrocarbons, commonly used as pesticides, are highly enriched compared to polycyclic hydrocarbons in agricultural soils, wastewater, and industrial sludge. Researchers’ conclusions regarding the reason behind this enrichment have converged (1) (2) (7). Their conclusions regarding the increased enrichment in soils and wastewater media were as follows: phenolic and halogenated compounds can interact with available organic compounds through an adsorption mechanism (8). Over the past few decades of the last century and the current one, the lofty goal of preserving the environment’s water resources, in the first place, and other environments in the second place, has been a constant preoccupation and major concern for researchers. This has been highlighted by the submission and publication of thousands of quality articles aimed at finding ways to treat water from various forms and types of organic contaminants. Given the unresponsiveness of complex contaminants to environmental degradation – accomplished through chemical or biological reactions – and the antiquated nature of previously designed treatment methods, technology researchers have emphasized the creating of interdisciplinary collaboration environment between chemistry and environmental science to generate brighter and more qualitative solutions for water treatment. After continuous research and arduous experiments, this alliance has resulted in the development of a new generation of ultra-small materials – so-called nanomaterials – in various polymeric, metallic, and organic forms, using modern and sustainably developed methodologies. Nanoscale researchers are obsessed with using metallic compounds (primarily noble metal nanoparticles) with their excellent optical/magnetic/structural/crystalline/surface properties to neutralize a significant portion of organic contaminants in water. Many methods based on composites/hybrids/alloys of small-sized noble metal particles have been proposed for contaminant removal, including precipitation, coagulation, adsorption, and others (9). The photoreduction method relies on the presence of different light sources (infrared, ultraviolet, visible light) and relies on photoactive materials such as Cd-MOF (10), zinc oxide (11), cadmium sulfide (13), and zero-valent iron nanoparticles (14). This method is characterized by its economy, ease of application, and low environmental side effects. The basic premise of the photoreduction mechanism revolves around two fundamental points: the first is the change in the bandgap value of the nanoscale catalyst with degradation ability, and the second is the surface plasmon resonance (SPR) property. Regarding the first point, two different semiconductors, p and n, must be available to generate a continuous cascade of electron-hole pairs. Regarding the second point, this property arises from the collective movement of free electrons localized on the surface of nanoparticles (especially gold, silver, copper, and platinum “to a lesser extent”) when light falls on them (15). Due to their thermal stability, chemical inertness to oxidizing agents, bioactivity, unique surface properties, and the possibility of generating them at nanoscale and in various morphologies, noble metal particles (Pd, Rh, Au, Ag, Pt) have attracted the attention of many biological researchers, chemists, and bioengineers in many applications (16) (17) (18). For their part, researchers interested in environmental cleanliness and preserving it from any imminent danger are increasingly developing methods for using these metals in environmental applications such as advanced oxidation of organic compounds, reducing the effects of toxic gas emissions from internal combustion engines in transportation, water splitting, and more (19). Many researchers have utilized noble metal nanoparticles in the catalytic reactions of organic compounds (dyes, petroleum derivatives, pesticides) – after loading them onto the surface of metal oxides such as titanium oxide, zinc oxide, copper ferrite, etc., or applying harsh reaction conditions – to increase catalytic activity and accelerate contaminant removal (5) (10) (11). Liu presented a paper on the effect of crystallization on the catalytic performance of titanium oxide supported by gold particles (16). Liu found that the improved crystalline properties with the presence of gold particles favorably accelerated the catalytic degradation process of a number of contaminants (16). In another paper by Zheng et al., it was demonstrated that the combination of zinc oxide with silver zero-valent “Ag(0)” resulted in a positive improvement in electron-hole generation, which in turn improved the degradation performance of the nanostructure under visible light irradiation (20). In Zheng’s paper (20), the synthesis of three metallic nanoparticles using ultrasonication in a weakly alkaline medium and in the presence of sodium borate tetrahydride was reported. Each metallic nanoparticle was characterized by its own nanoscale structure (morphology and crystallography). This study aimed to establish the foundations of green chemistry, particularly by utilizing the probe-ultrasound method to prepare three different nanoscale catalysts (Ag NPs, Au NPs and Pt NPs) under safe and easy-to-use conditions. The different structural properties that resulted from their characterization paved the way for their applicability in catalytic reactions using a simulated sunlight source (in the visible range “λ= 200-800 nm”). Crucially, these differences in properties led to a tangible comparative study between the catalytic decomposition results of the four contaminants, p-NP, MB, TCB, and Rh B. The novelty presented in this research is the environmental sustainability of the prepared particles, as these nanoparticles can be reused multiple times with high efficiency. Ag NPs demonstrated the highest photoreduction catalytic performance in removing all contaminants from aqueous media at all applied concentrations. Pt NPs ranked second in the photoreduction reaction, followed by Au NPs. The photoreduction behaviors differed with the contaminant type. The excellent reusability rates evinced clearly that the three groups of prepared particles are efficient for future photoreduction applications.
MATERIALS AND METHODS
All chemicals, as listed below, used in this paper were supplied from Sigma-Aldrich (China) without further purification: HAuCl4. 3H2O (≥ 99.99%, Au basis), H2PtCl6.6H2O (≥ 37.50%, Pt basis), AgNO3 (≥ 99.00%, trace metal basis), ethylene glycol (EG) ((CH2)2(OH)2 anhydrous, 99.8%), hydrazine (N2H4.H2O, 80.00%), methylene blue (MB, C16H18ClN3S · xH2O, ≥95.00 %), para-nitrophenol (p-NP, O2NC6H4OH, ≥99.00%), 2,4,6-tricholrobenzene (TCB, Cl3C6H2SO2Cl, ≥96.00 %) and Rhodamine B (Rh B, C28H31ClN2O3, ≥ 95.00 %). In order to prepare the different photocatalysts considered in this paper (Pt NPs, Au NPs and Ag NPs), a suitable molar ratio of each metal precursor (“0.13653 g (HAuCl4.3H2O)”, “0.13725 g (H2PtCl6.6H2O)”, “0.75295 g (AgNO3)”) was mixed with 50 mL of EG in three separate beakers. The solution was heated at 75 °C for four hours with gentle magnetic stirring, observing the initial color change (in the Au3+/EG solution from yellow to very dark gold, in the Pt4+/EG solution from intense orange to orange-brown, in the Ag+/EG solution from transparent to pale gray). Then, the glass beakers were transferred to an ultrasonic probe system (sono-horn made of titanium metal, 12.5 mm in diameter, operating at 20 kHz with a maximum power output of 600 W). Each solution was sonicated according to the following profile (300 sec “on”, 120 sec “off”, at 75 °C, time sonication of 25 min, 150 Watt). During sonication, sodium hydroxide solution (2 M) was added until the pH of the medium became 12, then 5 ml of hydrazine solution (10% v/v) was added dropwise. The colors of the formed precipitates were as follows: black (in the case of Pt NPs), dark brown (in the case of Au NPs) and dark gray (in the case of Ag NPs). Each precipitate was washed several times with a mixture of ultrapure water/ethanol (1:2 v/v) to remove any remaining unreacted materials. In the final stage, each precipitate was dried at 90 °C for 12 h. Figure 1. represents the schematic of the preparation stages by probe sonication of nanoscale particles based on noble metals (Pt NPs, Au NPs and Ag NPs).
Figure. 1. Schematic of the preparation stages of photocatalyst nanoparticles (Pt NPs, Au NPs and Ag NPs)
The photoreduction catalytic reaction of four hazardous organic pollutants – methylene blue (MB), para-nitrophenol (p-NP), Rhodamine B (RhB), and 2,4,6-trichlorobenzene (TCB) – in the presence of NaBH₄ under visible light irradiation was employed as a model photoreduction catalytic reaction to evaluate the reduction catalytic performance of the synthesized noble metal nanoparticles (Pt NPs, Au NPs, and Ag NP). A NaBH4 solution 0.26 Mm was prepared and stored in the dark. In a typical photoreduction test of the contaminants, 10.00 mg of the nano-catalyst (Pt NPs, Au NPs and Ag NPs) was poured separately into the aqueous solution of the related contaminant (10 mL, 10 mg.L-1 “ppm”), then ultrasonicated at room temperature for 60 sec. 100 μL of NaBH4 aqueous solution (0.26 mM) was mixed with the contaminant solution. After sonication, the solutions were exposed to visible light for three continuous hours. 5 mL of suspension – containing both the photocatalyst and the target contaminant – was taken out and centrifuged at 6000 rpm. All irradiations were performed using a white LED lamp (the radiant intensity (3 mw/cm2) in the wavelength range 400-780 nm with 10% of this in the ultraviolet range, and power density of 7-10 W at 0.0083 A, optical rising time 7 ns, intensity of the illumination 400 µW.cm-1 and ≥ 10 mm of diameter) as a solar-simulated light source. The photoreduction outcomes were read using a UV-Vis. spectrophotometer and using the Beer-Lambert law at a prominent wavelength for each contaminant solution (λ=664 nm for MB, λ=405 nm for p-NP, λ=555 nm for Rh B and λ=265 nm for TCB), which corresponded to the maximum absorbance of the contaminant mother solution. Dye uptake can also quantified using the efficiency of dye photocatalysis given by using the following equation 1:
Where, Co is the initial concentration of the contaminant solution in terms of mg.L-1 and Ce is the equilibrium concentration of the contaminant solution in terms of mg.L-1. The photoreduction efficiency of contaminants from their aqueous solutions depends strongly on the initial concentration. In order to assess, different concentrations of each contaminant (5, 10 ,15 and 20 mg.L-1) were tested at pH 7 with 10 mg of each nanocatalyst added into 10 mL solutions at 20 ˚C. The level of catalyst reusability plays an important role in these applications. After each catalysis cycle, for the first time, the nano-catalyst was separated from the reaction by centrifugation, washed with ultrapure water/ethanol, and then dried at 90 ° C for 12h (21). The applied conditions of the photoreduction reaction are summarized in Table 1.
Powder X-ray diffraction (PXRD) measurements were implemented using X’ pert pro. Analytical company with Cu-Kα radiation (λ= 1.5406 Å, scanning rate of 0.02 θ·s⁻¹, operating at 40 kV and 40 mA) to determine the crystal phases of the nanocatalysts. Field emission scanning electron microscopy (FESEM) with an accelerating voltage of 3 kV (MAIA3, TESCAN, Czech Republic) and transmission was applied to examine the morphology/size of the nanocatalysts. Energy Dispersive Spectroscopy (EDS) analysis was acquired by a “MAIA3, TESCAN” at the 15 kV acceleration voltages. The internal structure morphology of the (Pt NPs, Au NPs, Ag NPs) and the variation of the concentrations of the colored solutions of the contaminants were studied using TEM images (model Zeiss-EM10C-100KV, operating at an accelerating voltage of 160 kV) and dual-band UV-Vis. Spectroscopy in quartz cells (Shimadzu, mini 1240 (UV), in the wavelength range of 200-800 nm).
RESULTS
The crystalline state of Ag NPs, Au NPs and Pt NPs was examined by the X-ray diffraction patterns (Figure 2.). The diffraction peaks observed for the prepared Ag NPs were related to the following Miller indices (1 1 1), (0 0 2), (0 2 2), (1 1 3) and (2 2 2), which were located at diffraction angles of 38.12°, 44.39°, 64.54°, 77.49° and 81.6°. According to what this pattern showed and its comparison with many related references (17) (22) (23), it is clear that the Ag NPs were associated with the reference card Ag NPs (JCPDS-04-0783). On the other hand, as shown in the XRD pattern in Figure 2., for Au NPs, five diffraction peaks can be observed located at diffraction angles of 38.18°, 44.43°, 64.87°, 77.78° and 82.22°, which were related to Miller indices (1 1 1), (0 0 2), (0 2 2), (1 1 3) and (2 2 2), respectively. The characteristic diffraction pattern of Au was referenced in JCPDS card no. 04-0784 (17). The XRD pattern (Figure 2.) showed that Pt NPs main peaks were observed at 39.80°, 46.01°, 67.35° and 88.60°, which were almost identical to the reference card for Pt NPs (JCPDS 04-0802) (17). Thus, the reduction of silver, gold and platinum ions and the production of pure samples without impurities were confirmed. The crystal grain sizes, degree of crystallinity and orientation degree of those were calculated by the corresponding equations, which were reported in many papers (17) (18) (21), as shown in Table 2.
Figure 2. XRD patterns of Pt NPs, Au NPs and Ag NPs
Figure 3.(A-F) presents the FESEM micrographs of the synthesized nanocatalyst particles. As disclosed in Figure .3(A&B), the Pt NPs had the shape of small cauliflower buds with slightly rough surfaces (see supplementary material file in Figure S1.(A&C)) and a small spherical-like shape with an average size of 28.71 nm. Some sheets were also observed to be heterogeneously distributed (see supplementary material file in Figure .S1(B)). According to the FESEM images in Figure .2(C&D), the Au NPs contained small pits (indicated by blue arrows, see supplementary file material in Figure .S2(A&B)) and their shape was similar to a smooth/twisted surface, stacked side by side, resembling a cactus plant (indicated by orange arrows, see supplementary file material in Figure .S2(B&C)). The average size of the Au NPs was 33.20 nm. In Figure 3.(E&F), the morphology of the Ag NPs was approximated to that of small spheres arranged around each other with a dimension of 20.02 nm. The FESEM images in Figure S3.(A-C) indicated the presence of spherical structures – formed by the aggregation of small spheres – stacked on top of each other, trapping deep pits between them, resembling wells with a larger area than the pits in the Au and Pt nanocatalyst particles. The TEM images shown in Figure 4.(A-C) reveal the following observations about the internal structure of the nanocatalyst particles: the Pt NPs sheets were rectangular polygons with small spheres in contact with the polygonal boundaries; the Au NPs were heterogeneous spheres with noticeable roughness near them; the Ag NPs were homogeneously spherical throughout their surfaces and had no other structures. The microscopic images (FESEM and TEM) were integrated for all the nanocatalyst particles (Pt NPs, Au NPs and Ag NPs). Complementing the XRD patterns (Figure 1.) and their indications of the purity of the nanocatalyst phases, the EDX spectra (see supplementary material file in Figure S4.(A-C)) and the percentage values of the constituent elements of these nanocatalysts revealed: (i) elemental signals of Pt, Au, and Ag atoms in the fabricated nanocatalyst particles are centered at absorption peaks at around 2.1 keV, 2.3 keV and 2.2 keV, respectively. A homogeneous distribution of each constituent element in the nanocatalyst particle sample was suggested (Figure S4.(A-C)). (ii) The accompanying reports in the inset table for each spectrum (Figure S4.(A-C)) also indicated that the particles of each nanocatalyst exhibited a dominant percentage of Pt in the Pt NPs, Au in the Au NPs, and Ag in the Ag NPs. The EDX spectra also showed other carbon signals due to a very small portion of “EG” remaining stuck on the surface of each nanocatalyst, or believed to be due to the adsorption of carbon dioxide gas on the nanocatalyst surfaces.
Figure .3 FESEM micrographs of (A,B) Pt NPs, (C&D) Au NPs and (E&F) Ag NPs at 1µm and 500 nmFigure .4 TEM images of (A) Pt NPs, (B) Au NPs and (C) Ag NPs at 100 nm
The three catalyst particle structures exhibited diverse nanoscale morphologies and face-centered cubic crystal structures, offering some distinct and promising physiochemical properties. Therefore, these distinct metallic nanocatalyst structures (Pt NPs, Au NPs and Ag NPs) were exploited for practical applications as photocatalysts for four types of contaminants (MB, Rh B, p-NP and TCB) under visible light in the presence of NaBH4. The UV-Vis. Spectra (see supplementary material file in Figures (S5-S8)) showed the characteristic absorption peaks of MB, RhB, p-NP and TCB at 664 nm, 554 nm, 410 nm and 265 nm, respectively, to monitor the photoreduction process for 3h at room temperature, compared to a blank solution of each contaminant at the concentration studied. For comparison, a series of photoreduction tests were also conducted at various concentrations (5, 10, 15 and 20 ppm) under visible light, also with NaBH4 and each nanocatalyst separately. As shown in Figures .5(A-D), the photoreduction tests demonstrated that the nanocatalyst particles differed in performance with each contaminant type and its concentration. The silver-based nanocatalyst particles “Ag NPs” had the highest photoreduction capacity at all contaminant concentrations and for each of the four contaminant types (Figure .4(A-D) & Figure S5.(A-D)). The mixed structure of small spheres and cauliflower buds of Pt NPs demonstrated greater catalytic activity than the large cactus buds against all contaminants (Figure .5(A-D). However, as shown in Figure 6.(A-D), the color of the RhB, MB, p-NP and TCB solutions rapidly changed from colored to colorless. The maximum absorbance of the contaminant solutions decreased significantly over the three-hours reaction time. It was clearly indicated that the photoreduction reaction was completed in three-hours, as shown in Figures.S5-S8 (see supplementary materials file). The slope of the absorbance decrease was significantly greater for the Ag NPs and Pt NPs when comparing the blank solution of each contaminant with the color contaminant solution after photocatalysis and compared to the Au NPs, indicating the excellent catalytic performance of the Ag NPs. It should be noted that the TCB solution was transparent, so that it is difficult to understand the color change that occurred (before and after the photoreduction reaction). However, Ag NPs and Pt NPs not only were more efficient at catalyzing both MB and Rh B than the other two contaminants at low concentrations, but the photoreduction reaction efficiency was also slightly reduced at high concentrations of the preceding contaminants. The colored polyaromatic contaminants (MB and Rh B) were catalyzed rapidly at low concentrations, while the monoaromatic contaminants (p-NP and TCB) were resistant to photocatalysis at both high and low concentrations. Furthermore, the photoreduction reaction of the nanocatalysts fabricated at a concentration of 10 ppm of each contaminant studied over five reuse cycles revealed excellent catalyst reuse rates (Figure .7(A-D)).
Figure 5. Yield variation curves of photoreduction reactions on the surface of nanocatalysts (Pt NPs, Au NPs and Ag NPs) fabricated for contaminants (A) MB, (B) Rh B, (C) p-NP and (D) TCB
Figure 6. Digital photos of color changes in contaminant solutions (at a concentration of 10 ppm (A) MB, (B) Rh B, (C) p-NP and (D) TCB) on the surface of the three nanocatalysts (Pt NPs, Au NPs and Ag NPs)Figure 7. Reuse yield curves of nanocatalysts (Pt NPs, Au NPs and Ag NPs) for contaminants (A) MB, (B) Rh B, (C) p-NP and (D) TCB
DISCUSSION
Currently, developments in the synthesis of nanomaterials based on noble metals, their alloys, corresponding composites, and their excellent ability to reinforce the surfaces of a large number of materials (such as polymers, naturally occurring materials, and oxides), have attracted the attention of environmental researchers. The unlimited chemical and physical properties of these materials greatly facilitate their application in environmental media treatments, chemical reactions, and other processes. To obtain monodisperse nanoparticles of these metals, various protocols were used to form spherical/polygonal/pyramidal/star-shaped particles through solvothermal/hydrothermal reactions, sonication, etc.. The above methods applied specific conditions for each method, and mixtures of organic solvents, especially N, N-dimethyl formaldehyde (DMF), were used to determine the optimal preparation parameters. In general, many of published papers did not pay attention to the green chemistry principles. However, today, a large number of researchers are keen to reduce the potential environmental risks resulting from noble metal nanoparticles preparation processes. Here, green chemistry has emerged in the fabrication process through two important aspects: the use of ultrasonication – as a green fabrication method – and the use of “EG” – as an environmentally friendly solvent -. EG is environmentally safe to the extent required. EG has exceptional properties, including an accelerating agent and morphological regulator, a gentle reducing agent for metal ions, a high boiling point, a medium-polar solvent, a relatively high dielectric coefficient, environmental compatibility, and a good stabilizer. It serves as an important component in the solvothermal method to create a homogeneous structure of metallic nanoparticles. Researchers also studied the mechanism of formation of metallic structures based on EG, and found that this substance acts as an active structure-forming agent and a reducing agent for metal ions. Refuting the formation mechanism is the cornerstone for understanding the crystallographic and morphological changes of the three nanocatalyst particles (Pt NPs, Au NPs and Ag NPs). The related mechanism of the primary particle units was based on (simple/strong) reduction reaction in two successive stages. The reduction reaction in its first stage (shown in Figure 8.) is characterized by the interaction of the metal ions “Mn+” individually (Mn+ = Pt4+, Au3+ and Ag+) with the reducer agent that resulted from the reduction of a portion of EG (23). In the first minutes of heating, the reduction reaction medium was enriched with the glycolaldehyde compound due to oxidation by aerobic oxygen. Its concentration in the solution increased until it reached a certain saturation limit. During the reaction, gradual changes in the glycolaldehyde concentration led to dispersion and an increase in the concentration of the primary nuclei of the related zero-valent metals (Pt(0), Au(0) and Ag(0)). The difference here was the reducing potential of each ion versus the reducing potential of the glycolaldehyde. The redox potentials relative to the hydrogen electrode were as follows: E(0) (PtCl(4-)/Pt) = +0.90 eV, E(0) (AuCl(-1)/Au(0)) = +1.002 eV, E(0) (Ag(+1)/Ag) = +0.791 eV and E(0) (ethylene glycol/glycolaldehyde) = 0.57 V (24). It is noted that the redox potential of the E(0) (ethylene glycol/ glycolaldehyde) is very suitable for a simple reduction reaction of the ions. Each of the formed nuclei had a definite crystal structure. However, because their crystals lack a final surface energy for their crystal facets, they did not assume the final crystalline form. At this stage, they were susceptible to morphological variations and instability. According to the explanations of several researchers (25) (26), the ultra-fine nuclei, each of which served as a precursor for the growth of another nucleus from the related particle. With continuous heating for four hours and constructive collisions between the nuclei, the stability of the ultra-fine particle nuclei was reduced through repeated dissolving, which likely led to recrystallization into larger, more energy-stable crystals (26). Because of reaching very high concentrations and achieving high reductive capacity of glycolaldehyde, prolonged heating with exposure to the largest possible amount of atmospheric oxygen was required. Thus, the second stage of reduction, which is the strong reduction stage under the conditions of the sonication probe method, was ensured by the formation of bubbles in the solution during sonication and their explosion. Both of which were accompanied by high temperatures. Water molecules in the crystalline framework of mineral salts break down, generating free radicals (HO● and H●). These free radicals are naturally very powerful oxidizers, attacking a portion of the EG molecules that have not been converted to glycolaldehyde, forming free radicals of EG. The abundance of these oxidizing free radicals led to further oxidation, producing a medium rich in reducing agents. In parallel with this reaction, the initial nuclei formed composed of the M(0) particles not only augment the activated surface to dissociate the air oxygen and accelerate the initial reaction, but also catalyze the self-reduction of the remained metal ions. Upon completion of the strong reduction stages of the metal ions, a number of intermediate phases emerged that were fruitful in producing the metal particles in their final crystalline forms. The formation of these phases was discussed by considering the functions assigned to each agent, namely: viscosity of the reducing medium, temperature, hydroxyl ions, and hydrazine. Initially, the metal salts dissolve in EG, similar to the dissolution of a metal salt in a weakly polar solvent. The salts quickly transformed into the acidic formulas “HAuO3̅2 and HPtO3̅” and of both Au and Pt, respectively, similar to what Pan, Karimadom and Fuentes-García reported (27) (28) (29). In this regard, the viscosity of the solution played an important role in the nucleation and reduction stages. The viscosity of the EG solution, having a value of 22 mPa s at 16 °C, decreased with increasing temperature, so that it can orientate the reduction reaction in several ways. First, the decrease in viscosity with increasing temperature enhanced the migration of metal ions in the solution, thereby accelerating and regulating the reduction reaction. In the same context, it also provided crystalline nuclei of M(0) particles at significant concentrations and quantities in the initial stages of the synthesis reaction. Indeed, this was required and important to ensure a favorable initial environment for the final nucleation process. Second, the viscosity of the EG solution implies the presence of two phases (aqueous + organic), which favors the formation of an inverse micelle system (30). In such systems, as discussed in Holade’s paper (31) and consistent with the formation mechanism, the dissolved intermediates of the metals in their ionic state were concentrated within the micelle droplet and surrounded by EG molecules. Then, there is no massive flooding of distorted primary nuclei, as what happened was that a large portion of the ions are protected from random reduction processes and restricted movement. The greatest fruition of this is drawn in the later stages of fabrication – the sonication stage -. After four hours of fabrication, the sonication process of the solution containing the micelle systems (EG/ionic forms of the metal components AuO33 ̅&PtO32 ̅) began. Free radicals, such as the (HO●, H● and HOCH2CH●OH), penetrated the bicontinuous phase (27) (28) (29) (31). This facilitates the separation of the EG layer – the outer micelle layer – from the ionic constituents of the mineral components – the inner micelle layer -. This caused of the acidic mineral components “HAuO3 and HPtO3” to directly collide with free radicals (HO●, H● and HOCH2CH●OH), generating hydroxyl-based intermediates “[Pt (OH)6]-1, Ag OH and [Au (OH)4]-1“, which is aligns with Kimberly’s proposals (32). According to the findings of Vasilchenko’s paper (33), adjusting the solution medium to become alkaline was valuable in the formation of complex precursors “[Pt (OH)6]-1, Ag OH and [Au (OH)4]-1” of structurally and thermodynamically stable noble metals. Reducing such metallic-hydroxide intermediate phase structures “[Pt (OH)6]-1, [Ag (OH)2] 1 ̅ and [Au (OH)4] 1 ̅” was easily generated stable zero-valent metal structures after their final reduction with hydrazine. The significant function of adjusting the pH value of the solution was also due to the fact that hydrazine’s reducing power increases in alkaline media (34). The good diffusion of micelles creates a steric effect between the particles, forming finely crystallized mineral nuclei for the target particles (Pt NPs, Au NPs and Ag NPs). This was useful for formulating deposits of non-aggregated noble metal particles (Pt NPs, Au NPs and Ag NPs) with a specific crystal structure and spherical or hybrid morphologies. It is inferred from the polyol-based mechanism, as reported in related studies (23)(35) (36), that the noble metal ion reduction and oxygen dissociation reactions proceed without hydroxyl ions, albeit at a very low rate. Regarding reverse micelles, it should be noted that EG undeniably provides a favorable environment for the formation of reverse micelles, similar to the state of reverse micelles, as if a surfactant were present. Due to the pronounced viscosity of EG and its high concentration relative to water droplets (available in mineral salts) at low concentrations, a similar water-in-oil system is formed. EG oxidation products (particularly the glycolaldehyde compound – produced by the oxidation-reduction reaction when the mineral ions are reduced-) play a similar role as surfactants, resulting in the formation of a relatively stable micelle structure (31) (37) (38). There are two experimental observations that led to suggest the formation of such two compounds: (i) Upon examining the pH value of the initial solution formed by the dissolution of the primary salts in EG, it was found to be 1. (ii) A slight change in the color of the resulting initial solutions (in the Au3+/EG solution from yellow to very dark gold, in the Pt4+/EG solution from intense orange to orange-brown, in the Ag+/EG solution from transparent to pale gray) after four hours of continuous stirring at 75°C. Regarding the literature on the possibility of forming such intermediate compounds (“HAuO32 ̅ and HPtO3̅“), the results of the extensive and clear thermodynamic study in Yuan’s paper on the phrase “gold-chloride-water” prove that acidic and oxidizing conditions provide suitable conditions for the formation of stable acid-oxygen-base complexes of gold (HAuO32̅). According to the same paper, these complexes are amphoteric in nature and tend to be highly acidic. Therefore, they are easily dissolved in alkaline media and are converted to Au(0). Yuan (39) elaborated in his discussion, particularly when studying the redox (E(0)-pH) curve, that there are a number of intermediate compounds with the formula (HAuO32̅, AuO33̅ and H2AuO3̅) that can form as intermediate phases in equilibrium with Au(OH)3 and combine with each other to favor the formation of Au(0) in an alkaline medium. Kurniawan (40) and Malhotra (41) confirmed through electrochemical studies that Au can form relatively stable acidic intermediates and convert to the more structurally stable hydroxide in highly alkaline media. The interaction between the prepared nanocatalysts allowed for a useful correlation between their morphological and crystallographic properties. All three nanocatalysts exhibited a high degree of crystallinity, good crystal orientation, and good crystallite size, and possessed the same crystalline system (FCC system). Repeated recrystallization of small-scale nuclei and their interphase fusion enhanced the metallic bonding in the crystal lattice of the single-cell crystal within the solid zones. The crystallization of irregular and ill-defined nuclei in the soft zones was inhibited during recrystallization. Large-scale orientation of the crystal structures of the nuclei was present in the solid zones. In essence, the formation of the ordered micro-crystalline phase of the target particle nuclei dominates the disordered microcrystalline phases. This is natural, as their formation rate is greater than or equal to the disintegration rate of the disordered microcrystalline phase of the target particle nuclei. The disordered microcrystalline phase disappeared spontaneously with the temperature change between the initial heating stage and the bubble bursting during the sonication stage. This is consistent with the Ostwald ripening principle. On the other hand, the stress alignment of the soft (crystalline and semi-crystalline) zones of the micelles exerted a torque force perpendicular to the strain direction, for growth along the primary crystal growth axis guided by the hard crystalline zones. The nature of these perpendicular forces, which were generated by the crystallized parts of the soft zones, reduces the deformation of the formed crystals. Furthermore, the excessive elongation of the EG chains within the micelle structure caused the solid zones of the small-scale nuclei to reorient and restructure along the crystal axis. This effect increased with the distribution and dissipation of stresses, encouraging the formation of a uniform crystalline system of nanocatalyst particles. Undeniably, the slightly crystalline micelles acted as large-strain dampers, meaning they reduced crystal distortion. This indicates that the solid zone reflections observed in the diffraction patterns, represented by the (1 1 1) peak, were due to the good alignment of crystals in these zones, which were held together by strong metallic bonds (42). This results in good crystallinity indices (degree of crystallinity and orientation). The results (Table 1) shows that the platinum-based catalyst particles have the lowest crystallinity indices compared to the other two catalyst particles (Au NPs and Ag NPs). This was attributed to the presence of two morphologies (spherical and sheet) (21). Sheets were rarely observed in Pt NPs (Figure 3(A&B)), but a logical explanation for this is that their primary nuclei grew in all directions and that platinum ions exhibited poor reductive capacity in EG (34). The polyol method, on the other hand, typically favors gold’s ion reduction reaction and the formation of more homogeneous and uniform morphologies. Silver is most responsive to the reduction of its ions in EG to Ag(0). The last observation worth noting is that the large crystallite size values of the Ag-nanocatalyst and Au-nanocatalyst explain the reason for the sharpness of the reflection peak, unlike the Pt-nanocatalyst. The {1 1 1} facet is the lowest-energy facet, and there is order in the formed polycrystals and low surface roughness, as in the case of the Ag-nanocatalyst. The {1 1 1} facet in Pt NPs is lower in energy than the {1 1 0} facet, resulting in a predominantly spherical morphology, which requires a more regular crystal structure than gold. In other words, the effect of both crystalline facets can be seen in Pt- and Au-based nanoparticles. In essence, the formation of the fine crystalline phase of the target particle nuclei dominates the amorphous microphases. This is natural, as the rate of their formation is greater than or equal to the rate of disintegration of the disordered crystalline phase of the target particle nucleus. The final phase disappears spontaneously with the temperature change between the initial heating stage and the bubble bursting during the sonication stage. This is consistent with the principle of estuarine maturation. As seen in Figure 5, the catalytic performance of the three particles can be ordered according to the type of nanocatalyst particle, the type of contaminant, and its concentration as follows:
It is perhaps important to establish a link between the laboratory photoreduction reaction results in the presence of NaBH4 and the structure of the three catalyst particles. The first link (crystal structure and photocatalysis) is that since crystals have a {1 1 1} facet, without mixtures with {1 1 0} facet, at the lowest possible energy, the catalytic sites can be controlled and encouraged to complete the catalytic reaction in the best possible way. Mixture of {1 1 1} and {1 1 0} crystal facets, such as Pt NPs and Au NPs, pose energetic barriers to catalysis because they lack the activation energy required to complete the reaction. Crystals originating from finer nucleation centers exhibit better reactivity in photophysical reactions, as in Ag-nanocatalysts first, followed by Pt-nanocatalysts. Such well-crystalized centers have the opportunity to interact with light and create electronic transitions and form free radicals (●OH and ●O2̄ ) that accelerate the catalytic reaction. Au-nanocatalyst, with a crystallinity between that of Pt-nanocatalyst and Ag-nanocatalyst, did not have the advantage of sufficiently interacting with light and producing free radicals (●OH and ●O2̄ ). The higher crystallinity degree of Ag NPs (60.29%) and lower crystallinity degree of Pt NPs (46.64%) and Au NPs (50.07%) means that the surface area of Ag NPs was increased, securing sites along their entire surface and utilizing them as sites for free radical oxidation. However, the effect of crystal crystallite sizes stems from their influence on the electronic state (particularly the conduction and valence bands). Scientific observations suggest that this generates energetically active intermediates and a huge number of photoactive agents, which further accelerates the photoreduction reaction (36)(43). The second link is (morphology and photocatalysis). Typically, the entire photoreduction reaction depends on the morphology of the particles or the prepared nanostructure. Ag-nanocatalyst particles, which yielded the best photoreduction performance, had a uniform and homogeneous spherical surface morphology. Spherical morphology, a type of zero-dimensional morphology, adsorbed electrons at the same rate in all dimensions (x, y, z) (45). As shown in the FESEM (Figure 3(E&F)) and TEM images (Figure 4(C)), the pits trapped between the spherical particles were small and deep, creating a morphologically impermeable internal surface (21). When light penetrates the surface of the impermeable structure, electrons – generated by the interaction of the Ag-nanocatalyst particle’s surface with visible light radiation – fall into the pits and become trapped (21). This accelerates the collision rate with the Ag NPs and creates a stream of the photoactive agents. The Ag spheres increase the adsorption order of BH4̄ on its surface and encourage rapid movement of the liberated hydrogen across the surface of this nanocatalyst. The last two observations highlight how morphological features, through their synergistic effects on the dispersion of photoactive species and facilitating hydrogen transfer, can contribute to improved photoreduction efficiency. However, the presence of a spherical structure in the Pt-nanocatalyst particles had an impact on the improved catalytic performance. While the presence of a lamellar structure did provide good catalytic performance for Pt-nanocatalyst particles, its catalytic performance differed slightly from that of Ag-nanocatalyst particles. The reason is the homogeneity of the surface morphology of the Ag-nanocatalyst. It appears that structural heterogeneity of the Pt-nanocatalyst reduced its catalytic performance. Regarding the sheet’s structure, the following observation can be conclusively concluded: the corner sites in the short, thin, polygonal sheets are more highly occupied than others, and exhibit very good selectivity for the adsorption of hydrogen liberated from BH4̄. Pt-nanocatalyst particles could have demonstrated better catalytic performance if they had a larger number of sheet sites, resulting in a higher edge-to-corner ratio (43), as reported in Zhou’s research. Similarly, Au-nanocatalyst particles with pits of different sizes (large and small) and an agglomerated polygonal structure deteriorated the catalytic performance. The catalytic performance of nanoporous noble metal catalysts (Pt/Au-nanocatalysts) is related to the compressive strain factor. Two types of pits can be detected in such structures (primary pits and secondary pits), according to Malekian (46), intertwined within the same Au-nanocatalyst morphology. The existing agglomeration and pits of different sizes can induce differential compressive strain and deformation in these pits. The deformation is large in large pit structures and small in small pit structures (46). Because large pits are more resilient to compression, the creation of large compressions by the agglomerates significantly reduces the pit size and, in turn, affects small pit to almost the same extent. It should also be noted that if the agglomerated structure itself is porous, its effect is different and separate from the compressive strain in noble metal structures (46). This topic will not be discussed in the current study because the Au-nanocatalyst agglomerated structure is not porous. Therefore, it is very likely that the compressive strain was not large and the adsorption energy was insufficient, which reduced the adsorption of liberated hydrogen and the generation of photoactive agents. This resulted in a reduction in the catalytic performance of the Au-nanocatalyst surface. Returning to the discussion of contaminant type, the two contaminants (MB and Rh B) were the easiest and fastest to photocatalyze compared to the two petroleum contaminants (p-NP and TCB). The colored polyaromatic heterocyclic contaminants (MB and Rh B), due to their π-electrons and (HOMO-LUMO) system, are able to transition to an excited state (MB* and Rh B*) upon collision with photons of light. When the excited states of MB* and Rh B* return to their ground states, a certain amount of energy is released. This energy is complemented by the energy released by photon collisions with individual nanocatalyst particles. Whereas, the two petroleum contaminants consist of a single homologue aromatic ring, making electronic excitation difficult. However, the presence of hydroxyl groups in p-NP compared to chlorine groups in TCB makes the phenol ring more active for the photoreduction reaction than in TCB. Finally, increasing the concentration of any contaminant caused a downward slope for the photoreduction reaction. A thicker and thicker layer of contaminant surrounded the nanocatalyst surface as its concentration increased. This increased layer reduced the penetration of light to conduct electronic excitation and the transfer of hydrogen liberated from the BH4¯ to the nanocatalyst layers (either Pt-nanocatalyst or Au-nanocatalyst), suggesting a lower photoreduction rate. Considering the above reasonings and the mechanism proposed by Shafiq (35), the proposed photoreduction mechanism was attributed to two complementary pathways: generation/transfer of photoactive agents, and hydrogen donor/movement. Initially, two components (contaminant molecules and BH4 ions) were adsorbed simultaneously. Here, the adsorption occurred due to a charge difference, as the components (MB, Rh B and BH4¯) dissolved in the aqueous medium are negatively charged, while the catalyst particles are positively charged. Furthermore, the characteristics of each component involved in the photocatalysis (NaBH4, contaminant, nanocatalyst) were, respectively: nucleophilic, electrophilic, surface-organized for hydrogen movement, and photoactive-generating. The catalyst surface interacted with photons to generate electron excitation from the ground band to the valence band. At the same time, the electrophile molecules were excited, generating a stream of electrons and holes. These can react with water molecules, destroying them and generating free radicals (●OH and ●H). The nanocatalyst surface was activated to regulate the presence and migration of hydrogen and deliver photoactive agents to the catalytic reaction medium. This system reflected the behavior of the nanocatalyst enhanced with NaBH4 against the four contaminants (23) (35) (36) (47) (48) (49) (50).
CONCLUSIONS AND RECOMMENDATIONS
In conclusion, a simple, green strategy is reported, detailing most of the steps involved in the fabrication of a set of three noble metal nanocatalysts for Ag NPs, Au NPs and Pt NPs. The nanocatalyst backbones were well-structured, pure, and shared diverse nano-spherical shapes, while the Au NPs and Pt NPs nanospheres exhibited polygonal, agglomerated morphologies and sheet morphologies. This strategy provided an efficient way for fabricating nanoparticles of the three noble metals, creating a strong bond between their structural and crystalline characteristics. Due to this bond, a deeper study was conducted on the catalytic reduction performance of these metal nanoparticles in the reduction reaction of four toxic contaminants (MB, Rh B, p-NP and TCB) at varying concentrations, under visible light irradiation and using NaBH4. The results demonstrated outstanding catalytic reduction behavior, excellent stability, and reusability of each nanocatalyst. After extensive discussion, this work revealed the design of the Ag-nanocatalyst for organic pollutant catalytic applications through rational structural integration of its nanoparticles. The Pt-nanocatalyst came in second place, followed by the Au-nanocatalyst. It is believed that the presented concepts should be applied to a wide range of applications by studying the following proposals: constructing other hybrid materials from these metallic particles, functionally modifying their surfaces with natural polymeric substrates, and exploring other green and sustainable methods for fabricating them with new structural specifications. It is also suggested to complement these studies by conducting analyses such as GC-MS, HPLC, and NMR, calculating environmental indicators to assess the toxicity of the resulting compounds and those released into the environment, such as POD, COD, and TOC, and estimating indicators specific to catalytic reactions, such as TOF and TON. It is also suggested to enhancethe catalytic functions of the fabricated nanoparticles so that they can be applied in the field of photodegradation.
About The Journal
Journal:Syrian Journal for Science and Innovation Abbreviation: SJSI Publisher: Higher Commission for Scientific Research Address of Publisher: Syria – Damascus –Ministry of Higher Education and Scientific Research
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Where:
Where: lk: length of each segment of the path, m: number of segments, L: total length of the crack.
Where: Sj: roughness of the segment j of the groove, d: Euclidean dimension, D*≈D measured fractal dimension, Cj length of a local segment of the crack, Cp total length of the crack.
