Molecular Dynamics Investigation of Interfacial Energy and Mechanical Behavior in Braid-Reinforced Hollow Fiber Membranes

Molecular Dynamics Investigation of Interfacial Energy and Mechanical Behavior in Braid-Reinforced Hollow Fiber Membranes | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Molecular Dynamics Investigation of Interfacial Energy and Mechanical Behavior in Braid-Reinforced Hollow Fiber Membranes Mostafa Jafari, Ali Vatani, Ahmadreza Andarz This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7961374/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 11 You are reading this latest preprint version Abstract This study presents a comprehensive molecular dynamics (MD) investigation of braid-reinforced hollow fiber membranes (BRHFMs) to elucidate the interfacial and mechanical behaviors of polymeric composites composed of cellulose acetate (CA) and polyacrylonitrile (PAN). The analysis focuses on three representative configurations—homogeneous (CA/CA-II), semi-heterogeneous (PAN|CA/CA-I), and heterogeneous hybrid (CA/PAN-III)—to evaluate their interfacial energies, adhesion mechanisms, and tensile responses. The calculated interfacial energies of − 1.20 eV, − 1.45 eV, and − 1.61 eV for CA/CA-II, PAN|CA/CA-I, and CA/PAN-III, respectively, reveal that chemical homogeneity promotes stronger interfacial bonding, whereas polarity mismatches between functional groups (–OH, –OCOCH₃, and –CN) weaken adhesion and increase diffusivity at the interface. Mechanical testing through MD tensile simulations further demonstrates that the CA/PAN-III composite exhibits pronounced stress fluctuations and higher local interfacial activity. At the same time, the CA/CA-II system maintains the highest cohesive stability and elastic modulus due to structural uniformity. The CA/PAN-III hybrid achieves an optimal balance between flexibility and strength, indicating its suitability for water treatment membranes requiring both mechanical resilience and interfacial durability. These findings provide molecular-level insight into how polymer compatibility governs the performance of BRHFMs and offer valuable guidelines for designing next-generation high-strength composite membranes. Physical sciences/Chemistry Physical sciences/Engineering Physical sciences/Materials science Braid-reinforced Interfacial Energy Mechanical Properties Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 1. Introduction The global water crisis, intensified by rapid population growth, industrial expansion, and climate change, has created an urgent demand for efficient and sustainable water purification technologies [ 1 – 4 ]. Among the available approaches, membrane-based separation processes have emerged as one of the most energy-efficient and environmentally friendly solutions for wastewater treatment and desalination, owing to their high selectivity, compact design, and operational flexibility [ 5 – 9 ]. Within this field, membrane bioreactors (MBRs) have attracted significant attention because they combine biological degradation with membrane filtration, providing superior effluent quality and a smaller footprint compared to conventional treatment systems [ 10 – 13 ]. Hollow fiber membranes are the most common configuration used in MBRs, primarily because of their large surface-area-to-volume ratio and ease of module integration [ 14 ]. However, maintaining both sufficient mechanical strength and high permeability remains a significant challenge, especially under harsh industrial conditions involving pressure fluctuations, fouling, and long-term chemical exposure [ 15 , 16 ]. To overcome these limitations, braid-reinforced hollow fiber membranes (BRHFMs) have been developed, in which a braided fabric serves as a mechanical skeleton that enhances structural durability and prevents fiber collapse [ 17 ]. The overall performance of BRHFMs depends strongly on the interfacial adhesion between the polymer coating and the braid reinforcement, as well as on the degree of compatibility between the two materials [ 18 , 19 ]. Extensive experimental research has focused on improving the mechanical integrity and permeability of composite membranes through strategies such as porous matrix incorporation, polymer blending, and braid structure optimization [ 20 , 21 ]. Despite these advances, several challenges remain unresolved. Experimental methods alone often fail to capture the detailed interfacial mechanisms that govern adhesion, molecular diffusion, and stress transfer at the polymer–braid interface. Furthermore, achieving an optimal balance between interfacial bonding strength and water permeability remains difficult. Strong interfacial bonding can reduce porosity and limit water flux, whereas weak bonding may cause delamination or mechanical failure during operation [ 21 , 22 ]. In recent years, molecular dynamics (MD) simulation has become a powerful computational method for studying molecular-scale interactions and predicting the mechanical behavior of polymer composites. Many researchers have used MD to investigate polymer–nanofiller interactions [ 23 , 24 ], interfacial adhesion in fiber-reinforced composites [ 25 ], and the deformation behavior of polymeric membranes [ 26 ]. However, to the best of the authors’ knowledge, systematic MD studies focusing specifically on BRHFMs, particularly those examining the effects of homogeneous and heterogeneous polymer combinations on interfacial energy and mechanical properties, are still lacking in the literature. This study aims to fill this research gap by performing a comprehensive molecular dynamics analysis of BRHFMs designed for water treatment applications. The main objectives are to examine the interfacial energy and bonding mechanisms between the polymer coating and the braid reinforcement, to evaluate the influence of polymer homogeneity (CA/CA, PAN/PAN) and heterogeneity (CA/PAN) on mechanical performance, and to provide molecular-level insights into how interfacial characteristics affect membrane strength. The findings of this work are expected to contribute to the rational design of next-generation BRHFMs with improved mechanical stability, interfacial compatibility, and filtration efficiency. 2. Simulation method All simulations in this study were performed using MD, a robust and precise computational technique for exploring the physical, mechanical, and interfacial behavior of materials at the atomic scale. MD enables detailed analysis of structural evolution, stress distribution, and transport phenomena such as particle diffusion, thereby providing a microscopic understanding of system behavior under various conditions [ 27 , 28 ]. In this work, the MD framework was employed to investigate three key aspects: mechanical performance, interfacial interactions, and water purification mechanisms. Each of these required dedicated modeling strategies, simulation parameters, and analytical procedures, which are outlined in the subsequent subsections. The initial molecular configurations were constructed through a combination of custom-developed scripts, Packmol for spatial arrangement of molecules, and Visual Molecular Dynamics (VMD) for preliminary visualization and geometry optimization. All dynamic simulations were executed using the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS), while structural analyses and visualizations were carried out with the Open Visualization Tool (OVITO). Post-processing and quantitative analyses were performed using in-house scripts in conjunction with OVITO to extract the desired structural and mechanical parameters from the simulation trajectories [ 27 , 29 ]. 2.1. Young’s Modulus of the Braid Layer In the MD simulation, because of the large dimensions of the braid structure, a polymer layer with the same density is generated to measure the mechanical properties of the braid layers. In BR-HFM systems, the mechanical strength of the membranes depends on the braid structure; therefore, the mechanical analysis focuses solely on the braid layers. To examine the mechanical behavior of CA, PAN, and their composite (CA/PAN), each system was individually constructed and simulated under identical conditions. The molecular structures of the initial polymer chains are presented schematically in Fig. 1 . For the pure systems, three-dimensional simulation boxes were generated with dimensions of 4.5 × 8.0 × 4.0 nm 3 for CA and 4.75 × 8.20 × 4.32 nm 3 for PAN. A total of 436 CA chains and 245 PAN chains were randomly distributed within their respective boxes to reproduce bulk densities of 1.32 g/cm 3 and 1.18 g/cm 3 [ 2 , 30 , 31 ]. In the case of the CA/PAN composite, an initial weight ratio of 75:25 (CA:PAN) was adopted. The composite system was constructed in a simulation domain measuring 4.8 × 8.2 × 4.2 nm 3 , where 184 PAN chains were arranged at the lower region of the box and 110 CA chains were placed above them, forming a vertically stacked bilayer configuration as depicted in Fig. 1 . Interatomic interactions for all systems—pure polymers and composites—were described using the second-generation Reactive Force Field (ReaxFF). This potential function provides an accurate representation of chemical bonding and bond-breaking phenomena, effectively bridging quantum-mechanical insights with classical molecular mechanics to capture both structural and reactive behaviors within polymeric materials [ 32 , 33 ]. The simulation workflow, corresponding to the configurations illustrated in Fig. 1 , comprised three sequential stages: energy minimization, curing–equilibration, and tensile deformation. Periodic boundary conditions were imposed in all Cartesian directions throughout the entire simulation to reproduce bulk polymer behavior and eliminate surface effects. In the energy minimization stage, a time step of 0.1 fs was employed. The total potential energy of each system was minimized under the microcanonical (NVE) ensemble combined with a Langevin thermostat at 1 K for 1 ps, ensuring a relaxed and energetically stable configuration. Subsequently, the curing–equilibration phase was carried out using a time step of 0.25 fs under the isothermal–isobaric (NPT) ensemble with the Nosé–Hoover thermostat and barostat at zero external pressure. The temperature was gradually increased from 1 K to 500 K over a span of 2.5 ps to activate molecular rearrangements and relieve internal stresses. The system was then maintained at 400 K and 0 bar for 1 ns to allow complete curing. Thereafter, the temperature was decreased to ambient conditions (~ 298 K) over 2.5 ps and held for an additional 1 ns to achieve complete thermodynamic equilibration. At the end of this stage, the simulated densities of pure CA and PAN were consistent with reported experimental values, confirming the structural stability of the equilibrated configurations and their readiness for mechanical testing. During the tensile deformation stage, uniaxial tension was applied along the longitudinal axis of the simulation box at a constant strain rate of 10 − 2 ps − 1 . The simulation box itself was elongated in the same direction at the same rate to preserve homogeneous deformation and prevent artificial void formation. To avoid ensemble-induced artifacts, the tensile direction was decoupled from the NPT ensemble during loading. The virial stress was computed along the tensile axis, incorporating both kinetic and potential (virial) components. The resulting stress–strain data were used to construct the corresponding stress–strain curves, from which Young’s modulus (Y) and fracture characteristics were derived. The same computational algorithm was applied to all three systems—pure CA, pure PAN, and the CA/PAN composite—ensuring comparable initial equilibration and consistent mechanical loading conditions. This unified approach enabled a direct and reliable evaluation of the elastic and failure behavior of each system. 2.2. Simulation setups for interfacial characteristics The interfacial energy plays a vital role in determining the strength and stability of surface bonding in BR-HFMs. It represents the amount of work required to separate the interfacial region between two polymers and directly influences the mechanical integrity and structural cohesion of the membrane. A higher interfacial energy indicates stronger molecular-scale interactions, leading to improved adhesion and compatibility between the braid layer and the polymeric separation layer—an essential feature for high-strength membrane applications. In systems composed of PAN and CA, the interfacial energy is primarily governed by intermolecular forces such as hydrogen bonding, van der Waals interactions, and dipole–dipole forces. Functional groups such as hydroxyl and acetate in CA and nitrile groups in PAN play a key role in forming strong interfacial interactions and enhancing phase miscibility. However, quantitative information on the exact interfacial energy between PAN and CA remains limited. To address this, MD simulations were conducted to evaluate two primary aspects: (i) the cohesive or interfacial energy between the polymeric phases, and (ii) the mechanical stability of the resulting interface. The preliminary steps of energy minimization and curing–equilibration followed the methodology described in Section 2.1 to ensure structural relaxation and thermal equilibrium prior to interfacial analysis. A CA/PAN composite with an equal weight ratio (50:50) was constructed as the interfacial model. Based on experimentally determined densities, the system consisted of 152 CA chains and 85 PAN chains within a nanometric simulation box. The configuration was arranged such that the PAN phase occupied the lower half of the box and the CA phase the upper half, forming a distinct interfacial boundary between the two polymers. To control compression and facilitate interface formation, the entire system was confined between two graphene pistons, as shown in Fig. 2 . All atomic interactions—including those between the polymers and the graphene layers—were modeled using the Reactive Force Field (ReaxFF) potential, which accurately captures bond formation, bond dissociation, and charge redistribution during interfacial evolution. The pistons were driven toward each other under an applied pressure of 1 bar at 500 K, maintained via a Nosé–Hoover thermostat in the canonical (NVT) ensemble. This compression brought the CA and PAN chains into close contact, enabling molecular interdiffusion and interfacial bonding, thereby promoting the natural development of an adhesive interface. After the formation of chemical bonds and intimate contact between the polymer phases, the system underwent a curing–equilibration stage identical in duration and temperature profile to that of the mechanical simulations, allowing complete relaxation of interfacial stresses. Once equilibrium was reached, the graphene pistons were carefully removed, yielding a self-standing CA/PAN composite with a well-defined and relaxed interfacial region, suitable for subsequent evaluation of interfacial strength and energy. The final equilibrated configuration of the composite system is illustrated in Fig. 3 . This integrated approach enabled a controlled, reproducible, and physically consistent assessment of interfacial properties—providing valuable molecular-level insight into the adhesion behavior, bonding mechanisms, and structural stability of the CA/PAN interface in BR-HFM systems. This approach enabled a controlled and reproducible evaluation of interfacial properties, ensuring consistency with the mechanical simulation framework while providing additional insight into the adhesion behavior and structural integrity of the CA/PAN interface. After obtaining the equilibrated CA/PAN composite, the interfacial energy was calculated following the procedure proposed by Jiang et al [ 34 ]. In this method, the total potential energy of the composite system ( \(\:{\text{E}}_{\text{S}\text{y}\text{s}\text{t}\text{e}\text{m}}\) ) was first evaluated, as illustrated in Fig. 3 . Subsequently, two separate simulations were performed for pure CA and pure PAN systems, each having the same weight and volume as the corresponding phases in the composite. The potential energies of these individual systems were denoted as \(\:{\text{E}}_{\text{C}\text{A}}\) and \(\:{\text{E}}_{\text{P}\text{A}\text{N}}\) , respectively. The interfacial energy ( \(\:{\text{E}}_{\text{i}\text{n}\text{t}\text{e}\text{r}}\) ) between CA and PAN was then determined using the following equation (Eq. 1 ): $$\:{\text{E}}_{\text{I}\text{n}\text{t}\text{e}\text{r}}={\text{E}}_{\text{S}\text{y}\text{s}\text{t}\text{e}\text{m}}-({\text{E}}_{\text{P}\text{A}\text{N}}+{\text{E}}_{\text{C}\text{A}})$$ 1 A negative value of \(\:{\text{E}}_{\text{i}\text{n}\text{t}\text{e}\text{r}}\) ​ indicates a thermodynamically favorable interface, implying good adhesion between the two polymer phases. For comparison, a homogeneous CA–CA system and a hybrid configuration consisting of a CA layer combined with a CA–PAN braid were analyzed. Their interfacial energies were computed as: Their interfacial energies were computed as: $$\:{\text{E}}_{\text{I}\text{n}\text{t}\text{e}\text{r}}={\text{E}}_{\text{S}\text{y}\text{s}\text{t}\text{e}\text{m}}-\left(2{\text{E}}_{\text{C}\text{A}}\right)$$ 2 $$\:{\text{E}}_{\text{I}\text{n}\text{t}\text{e}\text{r}}={\text{E}}_{\text{S}\text{y}\text{s}\text{t}\text{e}\text{m}}-({\text{E}}_{\text{P}\text{A}\text{N}|\text{C}\text{A}}+{\text{E}}_{\text{C}\text{A}})$$ 3 In this study, three interfacial configurations were examined: one heterogeneous (CA/PAN), two homogeneous (CA–CA and PAN–PAN), and one hybrid structure (CA layer combined with a CA–PAN braid). This comparison enabled a clear assessment of how interfacial composition affects the cohesion, adhesion strength, and mechanical integrity of the composite membranes. To further assess the mechanical stability of the interphase, a uniaxial tensile load was applied perpendicular to the interface of the equilibrated CA/PAN composite. As shown in Fig. 4 , two boundary regions were designated as clamps—one in the upper CA domain and the other in the lower PAN domain. Both clamps were rigidly constrained, and a constant velocity of 10 − 2 ps − 1 was imposed in opposite directions, causing them to move apart and generate tensile stress normal to the interfacial plane. Throughout the loading process, the remainder of the system (excluding the fixed clamps) was equilibrated under the canonical (NVT) ensemble at ambient temperature to ensure thermal stability and prevent artificial fluctuations. The evolution of stress during deformation was computed using the same virial formulation described earlier, which allowed for the derivation of the corresponding stress–strain response. This setup enabled a detailed examination of interfacial deformation and separation mechanisms, thereby revealing the intrinsic adhesive strength and failure behavior of the CA/PAN interface under tensile stress. 3. Results and Discussion To evaluate the mechanical integrity of the membrane materials, the tensile and burst strengths of three representative structures—pure CA, pure PAN, and the hybrid CA/PAN composite—were analyzed through MD simulations. The corresponding results are summarized in Table 1 . The Young’s modulus values obtained for these systems were 0.231 GPa for CA, 3.0 GPa for PAN, and 2.73 GPa for the CA/PAN composite. These results are in good agreement with both the experimental data reported in the literature and the theoretical predictions derived from the Karkkainen et al. composite modulus model (Eqs. (4)–(7)) [ 35 ]. In these equations, \(\:{\text{Y}}_{\text{C}\text{o}\text{m}\text{p}\text{o}\text{s}\text{i}\text{t}\text{e}}\) ​ represents the overall Young’s modulus of the composite, \(\:{\text{Y}}_{\text{P}\text{A}\text{N}}\) ​ and \(\:{\text{Y}}_{\text{C}\text{A}}\) ​ are the Young’s moduli of the PAN and CA components, respectively, and \(\:{\text{f}}_{\text{P}\text{A}\text{N}}\) ​ and \(\:{\text{f}}_{\text{C}\text{A}}\) ​ denote their corresponding volume fractions within the composite. The sum of the volume fractions equals one, indicating that the composite is entirely composed of these two constituents. \(\:{\text{Y}}_{\text{C}\text{o}\text{m}\text{p}\text{o}\text{s}\text{i}\text{t}\text{e}}={\text{f}}_{\text{P}\text{A}\text{N}}{\text{Y}}_{\text{P}\text{A}\text{N}}+{\text{f}}_{\text{C}\text{A}}{\text{Y}}_{\text{C}\text{A}}\) (4) \(\:{\text{f}}_{\text{P}\text{A}\text{N}}=\frac{{\text{V}}_{\text{P}\text{A}\text{N}}}{{\text{V}}_{\text{C}\text{o}\text{m}\text{p}\text{o}\text{s}\text{i}\text{t}\text{e}}}\) (5) \(\:{\text{f}}_{\text{C}\text{A}}=\frac{{\text{V}}_{\text{C}\text{A}}}{{\text{V}}_{\text{C}\text{o}\text{m}\text{p}\text{o}\text{s}\text{i}\text{t}\text{e}}}\) (6) \(\:{\text{f}}_{\text{P}\text{A}\text{N}}+{\text{f}}_{\text{C}\text{A}}=1\) (7) Using \(\:{\text{f}}_{\text{P}\text{A}\text{N}}\) ​=0.75, \(\:{\text{f}}_{\text{C}\text{A}}\) ​=0.25, \(\:{\text{Y}}_{\text{P}\text{A}\text{N}}\) ​=3.0 GPa, and \(\:{\text{Y}}_{\text{C}\text{A}}\) ​=0.231 GPa, the theoretical modulus of the CA/PAN composite is calculated as \(\:{\text{Y}}_{\text{C}\text{o}\text{m}\text{p}\text{o}\text{s}\text{i}\text{t}\text{e}}\) ​=2.30 GPa, which is in close agreement with the MD-predicted value of 2.73 GPa. This excellent consistency confirms the validity and accuracy of the MD simulation methodology and the reliability of the employed force field (ReaxFF) in reproducing realistic mechanical responses. The analysis of burst (tensile rupture) strength, as summarized in Table 2 , also corroborates the reinforcement effect of the PAN braid. The pure CA layer exhibited a burst strength of 0.83 MPa, reflecting its high flexibility but low stiffness. In contrast, the pure PAN layer showed a higher stiffness (3 GPa modulus) but a lower burst strength of 0.24 MPa, indicating its brittle nature under multiaxial stress. The hybrid structure containing 75% PAN / 25% CA achieved an intermediate burst strength of 0.40 MPa, representing an optimal balance between tensile rigidity and flexibility. These findings demonstrate that increasing the PAN content within the braid structure significantly enhances the overall tensile strength of the BR-HFM, while maintaining adequate ductility. The hybrid configuration thus offers a promising design for mechanically robust and durable membranes, capable of withstanding high mechanical loads in industrial filtration and water treatment applications. Table 1 Comparison of the Young’s modulus obtained from MD simulation with theoretical and experimental data for CA, PAN, and CA/PAN composite structures. No. System Young’s Modulus Method / Source Description Reference 1 CA layer 231 MPa MD simulation (this study) — 2 250 MPa MD simulation [ 36 ] 3 248 MPa MD simulation [ 37 ] 4 375 MPa MD simulation [ 38 ] 5 205 MPa Braided CA layer (Fan et al.) [ 30 ] 1 PAN layer 3 GPa MD simulation (this study) — 2 2–3 GPa MD simulation [ 39 , 40 ] 3 2.65 GPa Braided PAN layer (Fan et al.) [ 31 ] 1 CA/PAN composite 2.73 GPa MD simulation (this study) — 2 2.30 GPa Karakin et al. model [ 35 ] 3 2.20 GPa Braided CA/PAN (1:2 ratio, Fan et al.) [ 31 ] Table 2 Comparison of the burst (tensile failure) strength of CA, PAN, and CA/PAN braid layers obtained from MD simulation and experimental results. No. Braided Layer Burst Strength (MPa) Reference 1 CA (simulation) 0.83 — 2 0.76 [ 30 ] 3 0.241 — 4 0.22 [ 30 ] 5 0.399 — 6 75% PAN / 25% CA (Fan et al.) 0.34 [ 30 ] Figure 5 presents the calculated interfacial energies for three composite configurations—CA/PAN–III, PAN|CA/CA–I, and CA/CA–II—obtained from MD simulations. The corresponding interfacial energies were − 1.61 eV, − 1.45 eV, and − 1.20 eV, respectively. As shown in the figure, the CA/CA–II configuration demonstrates the strongest interfacial cohesion, followed by PAN|CA/CA–I, while CA/PAN–III exhibits the weakest interfacial adhesion and structural stability. A lower (i.e., more negative) interfacial energy indicates stronger bonding and greater stability between the polymer layers. The high stability of the CA/CA–II structure can be attributed to the chemical homogeneity of the two CA layers, both consisting of identical polymer chains with hydroxyl (–OH) and acetate (–OCOCH₃) groups. This molecular similarity promotes strong hydrogen bonding and van der Waals interactions at the interface, thereby enhancing adhesion and reducing interdiffusion between the layers. In contrast, the PAN|CA/CA–I system exhibits about 15% lower interfacial stability compared with CA/CA–II, which mainly arises from the chemical dissimilarity between the two polymer phases. The nitrile (–CN) groups in PAN create dipolar interactions that are inherently weaker than the hydrogen bonds within CA, resulting in reduced compatibility and weaker interfacial cohesion. The CA/PAN–III hybrid structure shows the lowest interfacial energy, roughly 27% lower than CA/CA–II and about 13% below PAN|CA/CA–I. This decrease stems from the poor compatibility between the polar –CN groups in PAN and the acetate (–OCOCH₃) groups in CA, leading to weaker molecular attractions and diminished hydrogen-bonding capacity. Consequently, the interface becomes more diffusive and less cohesive, with greater molecular mobility across the boundary region. Overall, Fig. 5 clearly illustrates that interfacial adhesion strength decreases in the following order: CA/CA–II > PAN|CA/CA–I > CA/PAN–III. This trend confirms that homogeneous polymer interfaces exhibit superior adhesion and structural stability due to their molecular compatibility, whereas heterogeneous or hybrid systems suffer from interfacial discontinuities and weaker bonding. In the context of BR-HFMs, this finding implies that although hybrid layers can improve flexibility, their interfacial bonding remains inherently weaker. Therefore, optimizing the chemical compatibility between the braid and the selective polymer layer is essential for developing mechanically robust and durable membrane structures. The tensile strength calculations at the interfacial junction for the three structures — CA/PAN-III, PAN|CA–CA-I, and CA/CA-II — are presented in the following section. As an example, Fig. 6 illustrates the behavior of the heterogeneous PAN/CA-III composite from the beginning of the simulation (zero strain) up to the point of complete yielding, corresponding to the full separation of the two polymers at the interface, at a temperature of 298 K. Figure 7 shows comparison of the stress–strain curves of three composite structures — PAN|CA/CA-I, CA/CA-II, and CA/PAN-III — under ambient conditions. The CA/PAN-III composite exhibits sharp stress fluctuations, indicating strong but localized interfacial bonding that fails abruptly under strain due to chemical and structural heterogeneity. In contrast, the PAN|CA/CA-I and CA/CA-II systems display smoother stress–strain behavior, suggesting more gradual chain separation and weaker interfacial interactions. Overall, the heterogeneous hybrid structure (CA/PAN-III) demonstrates enhanced mechanical responsiveness and higher interfacial activity compared with the more homogeneous composites. 4. Conclusion This work systematically explored the interfacial energetics and mechanical performance of CA- and PAN-based composites using molecular dynamics simulations. The results revealed that interfacial adhesion strength follows the order CA/CA–II > PAN|CA/CA–I > CA/PAN–III, indicating that homogeneous polymer systems possess stronger cohesive forces and superior structural stability. The CA/CA–II configuration exhibited the most negative interfacial energy (− 1.20 eV) and the smoothest stress–strain profile, reflecting robust hydrogen bonding and van der Waals interactions. Conversely, the heterogeneous CA/PAN–III interface showed more negative energy (− 1.61 eV) accompanied by pronounced stress oscillations, signifying localized strong bonding but weaker overall stability due to interfacial chemical mismatch. The mechanical simulations further demonstrated that increasing PAN content enhances the tensile modulus and burst resistance of BRHFMs, while CA incorporation improves flexibility. The hybrid CA/PAN structure thus achieves an effective balance between stiffness and ductility, making it an excellent candidate for membrane applications under mechanical load. Overall, this study confirms the reliability of the ReaxFF-based MD framework for predicting interfacial and mechanical properties of polymer composites and provides practical molecular-level guidance for tailoring the composition and architecture of high-performance braid-reinforced membranes. Numenclature MD Molecular Dynamics BRHFMs Braid-Reinforced Hollow Fiber Membranes CA Cellulose Acetate PAN Polyacrylonitrile MBRs Membrane Bioreactors VMD Visual Molecular Dynamics LAMMPS Large-scale Atomic/Molecular Massively Parallel Simulator OVITO Open Visualization Tool ReaxFF Reactive Force Field E System Total Potential Energy of the Composite System E inter Interfacial Energy Declarations Conflicts of interest / Competing interest s : The authors declare that they have no conflicts of interest. Funding: This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors. Author Contribution Author Contributions StatementM.J. performed all molecular dynamics simulations, data analysis, and manuscript preparation.A.V. supervised the research, reviewed the results, and provided critical revisions and analytical guidance.A.A. contributed to manuscript refinement, including grammatical and structural editing.All authors read and approved the final version of the manuscript. Acknowledgments: The authors gratefully acknowledge the use of the LAMMPS molecular dynamics package developed by Sandia National Laboratories. Data Availability The molecular dynamics simulation data that support the findings of this study are available from the corresponding author upon reasonable request. References Barmaki, M., Jalilnejad, E., Ghasemzadeh, K. & Iulianelli, A. Performance Analysis of Silica Fluidized Bed Membrane Reactor for Hydrogen Production as a Green Process Using CFD Modelling. Membr. (Basel) . 15 , 248 (2025). Jafari, M., Vatani, A. & Mohammadi, T. CFD modeling of braid-reinforced hollow fiber membranes for efficient water and bovine serum albumin (BSA) separation. J. Water Process. Eng. 65 , 105746 (2024). Torabi, T., Ghasemzadeh, K., Cassano, A. & Basile, A. Membrane based processes for municipal wastewater reuse. in Municipal Wastewater Treatment 207–239Elsevier, (2025). Jafari, M., Nezhadfard, M. & Khalili-Garakani, A. Simulation and Economic Analysis of Combined Desalinated Water and Power Generation from Associated Gases of Cheshmeh Khosh. Iran. J. Oil Gas Sci. Technol. 10 , 1–14 (2021). Basile, A., Ghasemzadeh, K. & Jalilnejad, E. Current Trends and Future Developments on (Bio-) Membranes: Ceramic Membrane Bioreactors (Elsevier, 2019). Ghasemzadeh, K. & Basile, A. & Aghaeinejad-Meybodi, A. Solar membrane reactor. Integrated membrane Syst. processes 307–341 (2016). Rafiee, R., Seiiedhoseiny, M. & Ghasemzadeh, K. Transport Mechanism and Modeling of Microporous Polymeric Membranes. in Current Trends and Future Developments on (Bio-) Membranes 259–280 (Elsevier, (2019). Ghasemzadeh, K., Aghaeinejad-Meybodi, A. & Basile, A. Polymeric Membrane Reactors. Membrane Reactor Engineering: Appl. Greener Process. Industry 104–137 (2016). Jalilnejad, E., Jabbari, B. & Ghasemzadeh, K. Application of computational fluid dynamics technique in membrane bioreactor systems. in Current trends and future developments on (Bio-) membranes 345–375 (Elsevier, (2022). Torabi, T., Ferrari, M. C., Liguori, S. & Ghasemzadeh, K. Green hydrogen production in methylcyclohexane dehydrogenation by ceramic membrane reactor as net-zero approach: Optimisation via digital twin methodology. Chem. Eng. J. 520 , 165783 (2025). Torabi, T., Ghasemzadeh, K. & Basile, A. Dehydration processes in membrane reactors. in Current Trends and Future Developments on (Bio-) Membranes 159–180 (Elsevier, (2025). Basile, A. & Ghasemzadeh, K. Current Trends and Future Developments on (Bio-) Membranes: Recent Achievements for Ion-Exchange Membranes (Elsevier, 2023). Jalilnejad, E., Jabbari, B. & Ghasemzadeh, K. Application of computational fluid dynamics technique in membrane bioreactor systems. in Current trends and future developments on (Bio-) membranes 345–375 (Elsevier, (2022). Jalilnejad, E., Sadeghpour, P. & Ghasemzadeh, K. Advances in membrane bioreactor technology. in current trends and future developments on (bio-) membranes 1–29 (Elsevier, (2020). Lin, Z. et al. Optimization of mechanical properties and finite element simulation analysis of hollow fiber membranes in gas-liquid membrane separation technology. Desalination 599 , 118456 (2025). Sukitpaneenit, P. & Chung, T. S. Molecular elucidation of morphology and mechanical properties of PVDF hollow fiber membranes from aspects of phase inversion, crystallization, and rheology. in Hollow Fiber Membranes 333–360Elsevier, (2021). Li, J. et al. Synergistic mechanism of dual-surfactant systems in the heterogeneous braid-reinforced hollow fiber membrane for enhanced comprehensive performance. J Memb. Sci 124532 (2025). Nazif, A., Karkhanechi, H., Saljoughi, E., Mousavi, S. M. & Matsuyama, H. Effective parameters on fabrication and modification of braid hollow fiber membranes: a review. Membr. (Basel) . 11 , 884 (2021). Kim, S. H., Lee, J. H., Kim, J. W., Lee, S. Y. & Park, S. J. Interfacial behaviors of basalt fiber-reinforced polymeric composites: a short review. Adv. Fiber Mater. 4 , 1414–1433 (2022). Turken, T., Sengur-Tasdemir, R., Ates-Genceli, E., Tarabara, V. V. & Koyuncu, I. Progress on reinforced braided hollow fiber membranes in separation technologies: A review. J. Water Process. Eng. 32 , 100938 (2019). El-badawy, T. et al. Braid-reinforced PVDF hollow fiber membranes for high-efficiency separation of oily wastewater. J. Environ. Chem. Eng. 10 , 107258 (2022). Kollannoor, A. J., John, V. L., Jose, J. & PX, R. T. V. Cellulose nanostructure-based membranes: Structure, synthesis, and applications (& TP, 2022). Wang, Y. et al. Understanding the graphene-polymer interfacial mechanical behavior via coarse-grained modeling. Comput. Mater. Sci. 222 , 112109 (2023). Reil, M., Hoffman, J., Predecki, P. & Kumosa, M. Graphene and graphene oxide energetic interactions with polymers through molecular dynamics simulations. Comput. Mater. Sci. 211 , 111548 (2022). Chen, J., Li, B., Gu, B. & Sun, B. Molecular dynamics insights into temperature-dependent interfacial properties and failure behaviors of carbon fiber/epoxy composites. Compos Struct 119758 (2025). Wang, W. & Qu, Z. Molecular dynamics simulation of the mechanical properties and thermal conductivity of aromatic electrolytes in proton exchange membrane fuel cells. J. Power Sources . 585 , 233622 (2023). Badar, M. S., Shamsi, S., Ahmed, J. & Alam, M. A. Springer,. Molecular dynamics simulations: concept, methods, and applications. in Transdisciplinarity 131–151 (2022). Oda, K. & Yasuda, S. Synchronized molecular dynamics simulation using LAMMPS: application to pressure-driven flows of polymer melts. Model. Simul. Mat. Sci. Eng. 33 , 055007 (2025). Bone, M. A., Howlin, B. J., Hamerton, I., Macquart, T. & AutoMapper A python tool for accelerating the polymer bonding workflow in LAMMPS. Comput. Mater. Sci. 205 , 111204 (2022). Fan, Z., Xiao, C., Liu, H., Huang, Q. & Zhao, J. Structure design and performance study on braid-reinforced cellulose acetate hollow fiber membranes. J. Memb. Sci. 486 , 248–256 (2015). Fan, Z., Xiao, C., Liu, H. & Huang, Q. Preparation and performance of homogeneous braid reinforced cellulose acetate hollow fiber membranes. Cellulose 22 , 695–707 (2015). Vashisth, A., Ashraf, C., Zhang, W., Bakis, C. E. & Van Duin A. C. T. Accelerated ReaxFF simulations for describing the reactive cross-linking of polymers. J. Phys. Chem. A . 122 , 6633–6642 (2018). Kowalik, M. et al. Atomistic scale analysis of the carbonization process for C/H/O/N-based polymers with the ReaxFF reactive force field. J. Phys. Chem. B . 123 , 5357–5367 (2019). Jiang, B., Zhang, M., Fu, L., Zhou, M. & Zhai, Z. Molecular dynamics simulation on the interfacial behavior of over-molded hybrid fiber reinforced thermoplastic composites. Polym. (Basel) . 12 , 1270 (2020). Kohestanian, M., Sohbatzadeh, Z. & Rezaee, S. Mechanical properties of continuous fiber composites of cubic silicon carbide (3C-SiC)/different types of carbon nanotubes (SWCNTs, RSWCNTs, and MWCNTs): a molecular dynamics simulation. Mater. Today Commun. 23 , 100922 (2020). Gopiraman, M., Fujimori, K., Zeeshan, K., Kim, B. S. & Kim, I. S. Structural and mechanical properties of cellulose acetate/graphene hybrid nanofibers: spectroscopic investigations. Express Polym. Lett 7 , (2013). Salama, A., Mohamed, A., Aboamera, N. M., Osman, T. & Khattab, A. Characterization and mechanical properties of cellulose acetate/carbon nanotube composite nanofibers. Adv. Polym. Technol. 37 , 2446–2451 (2018). Aboamera, N. M., Mohamed, A., Salama, A., Osman, T. A. & Khattab, A. Characterization and mechanical properties of electrospun cellulose acetate/graphene oxide composite nanofibers. Mech. Adv. Mater. Struct. 26 , 765–769 (2019). Yusof, N. & Ismail, A. F. Polyacrylonitrile/acrylamide-based carbon fibers prepared using a solvent‐free coagulation process: Fiber properties and its structure evolution during stabilization and carbonization. Polym. Eng. Sci. 52 , 360–366 (2012). Sanchaniya, J. V. & Kanukuntla, S. Morphology and mechanical properties of PAN nanofiber mat. in Journal of Physics: Conference Series vol. 2423 012018IOP Publishing, (2023). Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 04 Dec, 2025 Reviews received at journal 03 Dec, 2025 Reviewers agreed at journal 27 Nov, 2025 Reviews received at journal 04 Nov, 2025 Reviewers agreed at journal 02 Nov, 2025 Reviewers agreed at journal 01 Nov, 2025 Reviewers invited by journal 30 Oct, 2025 Editor invited by journal 30 Oct, 2025 Editor assigned by journal 28 Oct, 2025 Submission checks completed at journal 28 Oct, 2025 First submitted to journal 27 Oct, 2025 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-7961374","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":542204548,"identity":"ba135831-bdea-47c3-b645-10c621831b70","order_by":0,"name":"Mostafa 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11:43:49","extension":"html","order_by":18,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":114486,"visible":true,"origin":"","legend":"","description":"","filename":"earlyproof.html","url":"https://assets-eu.researchsquare.com/files/rs-7961374/v1/6d84f2d99107cd70405c947b.html"},{"id":95632296,"identity":"233815f7-d3b4-4486-a7e4-1c36bf11ff72","added_by":"auto","created_at":"2025-11-11 11:43:47","extension":"jpg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":169485,"visible":true,"origin":"","legend":"\u003cp\u003eThe initial configuration of (a) pure CA, (b) pure PAN, and (c) CA/PAN composites\u003c/p\u003e","description":"","filename":"1.jpg","url":"https://assets-eu.researchsquare.com/files/rs-7961374/v1/370a51ff8f7683fe76e068f2.jpg"},{"id":95632297,"identity":"0e32886f-d50f-4b54-ac7c-b90e5a5bb4a4","added_by":"auto","created_at":"2025-11-11 11:43:48","extension":"jpg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":186867,"visible":true,"origin":"","legend":"\u003cp\u003eProcess of constructing the CA/PAN composite and its initial structure.\u003c/p\u003e","description":"","filename":"2.jpg","url":"https://assets-eu.researchsquare.com/files/rs-7961374/v1/5bf7abdd7c7f7e033f4e022a.jpg"},{"id":95657590,"identity":"3e902f4d-9fad-4cf0-8ae1-9ebe85c1c3be","added_by":"auto","created_at":"2025-11-11 16:21:17","extension":"jpg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":261952,"visible":true,"origin":"","legend":"\u003cp\u003eThe snapshot of the CA/PAN configuration at the initial and final steps of simulation, as well as after deleting graphene pistons. The final configuration without a piston was used to calculate interfacial energy and mechanical stability.\u003c/p\u003e","description":"","filename":"3.jpg","url":"https://assets-eu.researchsquare.com/files/rs-7961374/v1/c6cb378b24c9d7cc6949bb87.jpg"},{"id":95632298,"identity":"6e6739a4-5222-4ec1-9082-bb5c73df4ab6","added_by":"auto","created_at":"2025-11-11 11:43:48","extension":"jpg","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":163674,"visible":true,"origin":"","legend":"\u003cp\u003eThe CA/PAN configuration with clamped-clamped geometry to apply tensile perpendicular to the interface of the CA/PAN composite.\u003c/p\u003e","description":"","filename":"4.jpg","url":"https://assets-eu.researchsquare.com/files/rs-7961374/v1/0e2f882cbc0198fcc2bbb01c.jpg"},{"id":95657976,"identity":"fccd0270-51ea-406c-becb-96aa75183ed4","added_by":"auto","created_at":"2025-11-11 16:22:36","extension":"jpg","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":56860,"visible":true,"origin":"","legend":"\u003cp\u003eInterfacial energy of different composite structures (CA/PAN–III, PAN|CA/CA–I, and CA/CA–II) obtained from molecular dynamics simulations.\u003c/p\u003e","description":"","filename":"5.jpg","url":"https://assets-eu.researchsquare.com/files/rs-7961374/v1/04a179a38e630093ebd6610d.jpg"},{"id":95632310,"identity":"064be82a-5a5e-4ecb-835e-48dd2a214595","added_by":"auto","created_at":"2025-11-11 11:43:48","extension":"jpg","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":295489,"visible":true,"origin":"","legend":"\u003cp\u003eSnapshot images of the PAN/CA composite under strain loading at different strain percentages at 298 K.\u003c/p\u003e","description":"","filename":"6.jpg","url":"https://assets-eu.researchsquare.com/files/rs-7961374/v1/6d633499a001d2c08269e8bd.jpg"},{"id":95657138,"identity":"07c22818-bcc0-4cc4-9803-4dcb74f9dc79","added_by":"auto","created_at":"2025-11-11 16:20:10","extension":"jpg","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":70854,"visible":true,"origin":"","legend":"\u003cp\u003eComparison of the stress–strain curves of three composites — PAN|CA/CA-I, CA/CA-II, and CA/PAN-III — under ambient temperature and pressure conditions.\u003c/p\u003e","description":"","filename":"7.jpg","url":"https://assets-eu.researchsquare.com/files/rs-7961374/v1/d77a6bd3d076a45276207012.jpg"},{"id":95660369,"identity":"c6580495-886d-40d5-a9a0-170a3ebea8a6","added_by":"auto","created_at":"2025-11-11 16:32:00","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1852929,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7961374/v1/cbbc2af0-696b-4882-92c0-daf4c9cedf5f.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Molecular Dynamics Investigation of Interfacial Energy and Mechanical Behavior in Braid-Reinforced Hollow Fiber Membranes","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eThe global water crisis, intensified by rapid population growth, industrial expansion, and climate change, has created an urgent demand for efficient and sustainable water purification technologies [\u003cspan additionalcitationids=\"CR2 CR3\" citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e]. Among the available approaches, membrane-based separation processes have emerged as one of the most energy-efficient and environmentally friendly solutions for wastewater treatment and desalination, owing to their high selectivity, compact design, and operational flexibility [\u003cspan additionalcitationids=\"CR6 CR7 CR8\" citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e]. Within this field, membrane bioreactors (MBRs) have attracted significant attention because they combine biological degradation with membrane filtration, providing superior effluent quality and a smaller footprint compared to conventional treatment systems [\u003cspan additionalcitationids=\"CR11 CR12\" citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e].\u003c/p\u003e\u003cp\u003eHollow fiber membranes are the most common configuration used in MBRs, primarily because of their large surface-area-to-volume ratio and ease of module integration [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e]. However, maintaining both sufficient mechanical strength and high permeability remains a significant challenge, especially under harsh industrial conditions involving pressure fluctuations, fouling, and long-term chemical exposure [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e, \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e]. To overcome these limitations, braid-reinforced hollow fiber membranes (BRHFMs) have been developed, in which a braided fabric serves as a mechanical skeleton that enhances structural durability and prevents fiber collapse [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e]. The overall performance of BRHFMs depends strongly on the interfacial adhesion between the polymer coating and the braid reinforcement, as well as on the degree of compatibility between the two materials [\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e, \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e].\u003c/p\u003e\u003cp\u003eExtensive experimental research has focused on improving the mechanical integrity and permeability of composite membranes through strategies such as porous matrix incorporation, polymer blending, and braid structure optimization [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e, \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e]. Despite these advances, several challenges remain unresolved. Experimental methods alone often fail to capture the detailed interfacial mechanisms that govern adhesion, molecular diffusion, and stress transfer at the polymer\u0026ndash;braid interface. Furthermore, achieving an optimal balance between interfacial bonding strength and water permeability remains difficult. Strong interfacial bonding can reduce porosity and limit water flux, whereas weak bonding may cause delamination or mechanical failure during operation [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e, \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e].\u003c/p\u003e\u003cp\u003eIn recent years, molecular dynamics (MD) simulation has become a powerful computational method for studying molecular-scale interactions and predicting the mechanical behavior of polymer composites. Many researchers have used MD to investigate polymer\u0026ndash;nanofiller interactions [\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e, \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e], interfacial adhesion in fiber-reinforced composites [\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e], and the deformation behavior of polymeric membranes [\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e]. However, to the best of the authors\u0026rsquo; knowledge, systematic MD studies focusing specifically on BRHFMs, particularly those examining the effects of homogeneous and heterogeneous polymer combinations on interfacial energy and mechanical properties, are still lacking in the literature.\u003c/p\u003e\u003cp\u003eThis study aims to fill this research gap by performing a comprehensive molecular dynamics analysis of BRHFMs designed for water treatment applications. The main objectives are to examine the interfacial energy and bonding mechanisms between the polymer coating and the braid reinforcement, to evaluate the influence of polymer homogeneity (CA/CA, PAN/PAN) and heterogeneity (CA/PAN) on mechanical performance, and to provide molecular-level insights into how interfacial characteristics affect membrane strength. The findings of this work are expected to contribute to the rational design of next-generation BRHFMs with improved mechanical stability, interfacial compatibility, and filtration efficiency.\u003c/p\u003e"},{"header":"2. Simulation method","content":"\u003cp\u003eAll simulations in this study were performed using MD, a robust and precise computational technique for exploring the physical, mechanical, and interfacial behavior of materials at the atomic scale. MD enables detailed analysis of structural evolution, stress distribution, and transport phenomena such as particle diffusion, thereby providing a microscopic understanding of system behavior under various conditions [\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e, \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e].\u003c/p\u003e\u003cp\u003eIn this work, the MD framework was employed to investigate three key aspects: mechanical performance, interfacial interactions, and water purification mechanisms. Each of these required dedicated modeling strategies, simulation parameters, and analytical procedures, which are outlined in the subsequent subsections.\u003c/p\u003e\u003cp\u003eThe initial molecular configurations were constructed through a combination of custom-developed scripts, Packmol for spatial arrangement of molecules, and Visual Molecular Dynamics (VMD) for preliminary visualization and geometry optimization. All dynamic simulations were executed using the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS), while structural analyses and visualizations were carried out with the Open Visualization Tool (OVITO). Post-processing and quantitative analyses were performed using in-house scripts in conjunction with OVITO to extract the desired structural and mechanical parameters from the simulation trajectories [\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e, \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e].\u003c/p\u003e\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e\u003ch2\u003e2.1. Young\u0026rsquo;s Modulus of the Braid Layer\u003c/h2\u003e\u003cp\u003eIn the MD simulation, because of the large dimensions of the braid structure, a polymer layer with the same density is generated to measure the mechanical properties of the braid layers. In BR-HFM systems, the mechanical strength of the membranes depends on the braid structure; therefore, the mechanical analysis focuses solely on the braid layers.\u003c/p\u003e\u003cp\u003eTo examine the mechanical behavior of CA, PAN, and their composite (CA/PAN), each system was individually constructed and simulated under identical conditions. The molecular structures of the initial polymer chains are presented schematically in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. For the pure systems, three-dimensional simulation boxes were generated with dimensions of 4.5 \u0026times; 8.0 \u0026times; 4.0 nm\u003csup\u003e3\u003c/sup\u003e for CA and 4.75 \u0026times; 8.20 \u0026times; 4.32 nm\u003csup\u003e3\u003c/sup\u003e for PAN. A total of 436 CA chains and 245 PAN chains were randomly distributed within their respective boxes to reproduce bulk densities of 1.32 g/cm\u003csup\u003e3\u003c/sup\u003e and 1.18 g/cm\u003csup\u003e3\u003c/sup\u003e [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e, \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e, \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e]. In the case of the CA/PAN composite, an initial weight ratio of 75:25 (CA:PAN) was adopted. The composite system was constructed in a simulation domain measuring 4.8 \u0026times; 8.2 \u0026times; 4.2 nm\u003csup\u003e3\u003c/sup\u003e, where 184 PAN chains were arranged at the lower region of the box and 110 CA chains were placed above them, forming a vertically stacked bilayer configuration as depicted in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e.\u003c/p\u003e\u003cp\u003eInteratomic interactions for all systems\u0026mdash;pure polymers and composites\u0026mdash;were described using the second-generation Reactive Force Field (ReaxFF). This potential function provides an accurate representation of chemical bonding and bond-breaking phenomena, effectively bridging quantum-mechanical insights with classical molecular mechanics to capture both structural and reactive behaviors within polymeric materials [\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e, \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e].\u003c/p\u003e\u003cp\u003eThe simulation workflow, corresponding to the configurations illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, comprised three sequential stages: energy minimization, curing\u0026ndash;equilibration, and tensile deformation. Periodic boundary conditions were imposed in all Cartesian directions throughout the entire simulation to reproduce bulk polymer behavior and eliminate surface effects. In the energy minimization stage, a time step of 0.1 fs was employed. The total potential energy of each system was minimized under the microcanonical (NVE) ensemble combined with a Langevin thermostat at 1 K for 1 ps, ensuring a relaxed and energetically stable configuration.\u003c/p\u003e\u003cp\u003eSubsequently, the curing\u0026ndash;equilibration phase was carried out using a time step of 0.25 fs under the isothermal\u0026ndash;isobaric (NPT) ensemble with the Nos\u0026eacute;\u0026ndash;Hoover thermostat and barostat at zero external pressure. The temperature was gradually increased from 1 K to 500 K over a span of 2.5 ps to activate molecular rearrangements and relieve internal stresses. The system was then maintained at 400 K and 0 bar for 1 ns to allow complete curing.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eThereafter, the temperature was decreased to ambient conditions (~\u0026thinsp;298 K) over 2.5 ps and held for an additional 1 ns to achieve complete thermodynamic equilibration. At the end of this stage, the simulated densities of pure CA and PAN were consistent with reported experimental values, confirming the structural stability of the equilibrated configurations and their readiness for mechanical testing.\u003c/p\u003e\u003cp\u003eDuring the tensile deformation stage, uniaxial tension was applied along the longitudinal axis of the simulation box at a constant strain rate of 10\u003csup\u003e\u0026minus;\u0026thinsp;2\u003c/sup\u003e ps\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e. The simulation box itself was elongated in the same direction at the same rate to preserve homogeneous deformation and prevent artificial void formation. To avoid ensemble-induced artifacts, the tensile direction was decoupled from the NPT ensemble during loading. The virial stress was computed along the tensile axis, incorporating both kinetic and potential (virial) components. The resulting stress\u0026ndash;strain data were used to construct the corresponding stress\u0026ndash;strain curves, from which Young\u0026rsquo;s modulus (Y) and fracture characteristics were derived. The same computational algorithm was applied to all three systems\u0026mdash;pure CA, pure PAN, and the CA/PAN composite\u0026mdash;ensuring comparable initial equilibration and consistent mechanical loading conditions. This unified approach enabled a direct and reliable evaluation of the elastic and failure behavior of each system.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec4\" class=\"Section2\"\u003e\u003ch2\u003e2.2. Simulation setups for interfacial characteristics\u003c/h2\u003e\u003cp\u003eThe interfacial energy plays a vital role in determining the strength and stability of surface bonding in BR-HFMs. It represents the amount of work required to separate the interfacial region between two polymers and directly influences the mechanical integrity and structural cohesion of the membrane. A higher interfacial energy indicates stronger molecular-scale interactions, leading to improved adhesion and compatibility between the braid layer and the polymeric separation layer\u0026mdash;an essential feature for high-strength membrane applications. In systems composed of PAN and CA, the interfacial energy is primarily governed by intermolecular forces such as hydrogen bonding, van der Waals interactions, and dipole\u0026ndash;dipole forces. Functional groups such as hydroxyl and acetate in CA and nitrile groups in PAN play a key role in forming strong interfacial interactions and enhancing phase miscibility. However, quantitative information on the exact interfacial energy between PAN and CA remains limited.\u003c/p\u003e\u003cp\u003eTo address this, MD simulations were conducted to evaluate two primary aspects: (i) the cohesive or interfacial energy between the polymeric phases, and (ii) the mechanical stability of the resulting interface. The preliminary steps of energy minimization and curing\u0026ndash;equilibration followed the methodology described in Section \u003cspan refid=\"Sec3\" class=\"InternalRef\"\u003e2.1\u003c/span\u003e to ensure structural relaxation and thermal equilibrium prior to interfacial analysis.\u003c/p\u003e\u003cp\u003eA CA/PAN composite with an equal weight ratio (50:50) was constructed as the interfacial model. Based on experimentally determined densities, the system consisted of 152 CA chains and 85 PAN chains within a nanometric simulation box. The configuration was arranged such that the PAN phase occupied the lower half of the box and the CA phase the upper half, forming a distinct interfacial boundary between the two polymers. To control compression and facilitate interface formation, the entire system was confined between two graphene pistons, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e.\u003c/p\u003e\u003cp\u003eAll atomic interactions\u0026mdash;including those between the polymers and the graphene layers\u0026mdash;were modeled using the Reactive Force Field (ReaxFF) potential, which accurately captures bond formation, bond dissociation, and charge redistribution during interfacial evolution. The pistons were driven toward each other under an applied pressure of 1 bar at 500 K, maintained via a Nos\u0026eacute;\u0026ndash;Hoover thermostat in the canonical (NVT) ensemble. This compression brought the CA and PAN chains into close contact, enabling molecular interdiffusion and interfacial bonding, thereby promoting the natural development of an adhesive interface.\u003c/p\u003e\u003cp\u003eAfter the formation of chemical bonds and intimate contact between the polymer phases, the system underwent a curing\u0026ndash;equilibration stage identical in duration and temperature profile to that of the mechanical simulations, allowing complete relaxation of interfacial stresses. Once equilibrium was reached, the graphene pistons were carefully removed, yielding a self-standing CA/PAN composite with a well-defined and relaxed interfacial region, suitable for subsequent evaluation of interfacial strength and energy. The final equilibrated configuration of the composite system is illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e.\u003c/p\u003e\u003cp\u003eThis integrated approach enabled a controlled, reproducible, and physically consistent assessment of interfacial properties\u0026mdash;providing valuable molecular-level insight into the adhesion behavior, bonding mechanisms, and structural stability of the CA/PAN interface in BR-HFM systems. This approach enabled a controlled and reproducible evaluation of interfacial properties, ensuring consistency with the mechanical simulation framework while providing additional insight into the adhesion behavior and structural integrity of the CA/PAN interface.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eAfter obtaining the equilibrated CA/PAN composite, the interfacial energy was calculated following the procedure proposed by Jiang et al [\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e]. In this method, the total potential energy of the composite system (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{E}}_{\\text{S}\\text{y}\\text{s}\\text{t}\\text{e}\\text{m}}\\)\u003c/span\u003e\u003c/span\u003e) was first evaluated, as illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e. Subsequently, two separate simulations were performed for pure CA and pure PAN systems, each having the same weight and volume as the corresponding phases in the composite. The potential energies of these individual systems were denoted as \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{E}}_{\\text{C}\\text{A}}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{E}}_{\\text{P}\\text{A}\\text{N}}\\)\u003c/span\u003e\u003c/span\u003e, respectively. The interfacial energy (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{E}}_{\\text{i}\\text{n}\\text{t}\\text{e}\\text{r}}\\)\u003c/span\u003e\u003c/span\u003e) between CA and PAN was then determined using the following equation (Eq.\u0026nbsp;\u003cspan refid=\"Equ1\" class=\"InternalRef\"\u003e1\u003c/span\u003e):\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$\\:{\\text{E}}_{\\text{I}\\text{n}\\text{t}\\text{e}\\text{r}}={\\text{E}}_{\\text{S}\\text{y}\\text{s}\\text{t}\\text{e}\\text{m}}-({\\text{E}}_{\\text{P}\\text{A}\\text{N}}+{\\text{E}}_{\\text{C}\\text{A}})$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eA negative value of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{E}}_{\\text{i}\\text{n}\\text{t}\\text{e}\\text{r}}\\)\u003c/span\u003e\u003c/span\u003e​ indicates a thermodynamically favorable interface, implying good adhesion between the two polymer phases. For comparison, a homogeneous CA\u0026ndash;CA system and a hybrid configuration consisting of a CA layer combined with a CA\u0026ndash;PAN braid were analyzed. Their interfacial energies were computed as: Their interfacial energies were computed as:\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$$\\:{\\text{E}}_{\\text{I}\\text{n}\\text{t}\\text{e}\\text{r}}={\\text{E}}_{\\text{S}\\text{y}\\text{s}\\text{t}\\text{e}\\text{m}}-\\left(2{\\text{E}}_{\\text{C}\\text{A}}\\right)$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equ3\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ3\" name=\"EquationSource\"\u003e\n$$\\:{\\text{E}}_{\\text{I}\\text{n}\\text{t}\\text{e}\\text{r}}={\\text{E}}_{\\text{S}\\text{y}\\text{s}\\text{t}\\text{e}\\text{m}}-({\\text{E}}_{\\text{P}\\text{A}\\text{N}|\\text{C}\\text{A}}+{\\text{E}}_{\\text{C}\\text{A}})$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e3\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eIn this study, three interfacial configurations were examined: one heterogeneous (CA/PAN), two homogeneous (CA\u0026ndash;CA and PAN\u0026ndash;PAN), and one hybrid structure (CA layer combined with a CA\u0026ndash;PAN braid). This comparison enabled a clear assessment of how interfacial composition affects the cohesion, adhesion strength, and mechanical integrity of the composite membranes.\u003c/p\u003e\u003cp\u003eTo further assess the mechanical stability of the interphase, a uniaxial tensile load was applied perpendicular to the interface of the equilibrated CA/PAN composite. As shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e, two boundary regions were designated as clamps\u0026mdash;one in the upper CA domain and the other in the lower PAN domain. Both clamps were rigidly constrained, and a constant velocity of 10\u003csup\u003e\u0026minus;\u0026thinsp;2\u003c/sup\u003e ps\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e was imposed in opposite directions, causing them to move apart and generate tensile stress normal to the interfacial plane.\u003c/p\u003e\u003cp\u003eThroughout the loading process, the remainder of the system (excluding the fixed clamps) was equilibrated under the canonical (NVT) ensemble at ambient temperature to ensure thermal stability and prevent artificial fluctuations. The evolution of stress during deformation was computed using the same virial formulation described earlier, which allowed for the derivation of the corresponding stress\u0026ndash;strain response. This setup enabled a detailed examination of interfacial deformation and separation mechanisms, thereby revealing the intrinsic adhesive strength and failure behavior of the CA/PAN interface under tensile stress.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003c/div\u003e"},{"header":"3. Results and Discussion","content":"\u003cp\u003eTo evaluate the mechanical integrity of the membrane materials, the tensile and burst strengths of three representative structures\u0026mdash;pure CA, pure PAN, and the hybrid CA/PAN composite\u0026mdash;were analyzed through MD simulations. The corresponding results are summarized in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. The Young\u0026rsquo;s modulus values obtained for these systems were 0.231 GPa for CA, 3.0 GPa for PAN, and 2.73 GPa for the CA/PAN composite. These results are in good agreement with both the experimental data reported in the literature and the theoretical predictions derived from the Karkkainen et al. composite modulus model (Eqs.\u0026nbsp;(4)\u0026ndash;(7)) [\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e].\u003c/p\u003e\u003cp\u003eIn these equations, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{Y}}_{\\text{C}\\text{o}\\text{m}\\text{p}\\text{o}\\text{s}\\text{i}\\text{t}\\text{e}}\\)\u003c/span\u003e\u003c/span\u003e​ represents the overall Young\u0026rsquo;s modulus of the composite, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{Y}}_{\\text{P}\\text{A}\\text{N}}\\)\u003c/span\u003e\u003c/span\u003e​ and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{Y}}_{\\text{C}\\text{A}}\\)\u003c/span\u003e\u003c/span\u003e​ are the Young\u0026rsquo;s moduli of the PAN and CA components, respectively, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{f}}_{\\text{P}\\text{A}\\text{N}}\\)\u003c/span\u003e\u003c/span\u003e​ and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{f}}_{\\text{C}\\text{A}}\\)\u003c/span\u003e\u003c/span\u003e​ denote their corresponding volume fractions within the composite. The sum of the volume fractions equals one, indicating that the composite is entirely composed of these two constituents.\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"No\" id=\"Taba\" border=\"1\"\u003e\u003ccolgroup cols=\"2\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{Y}}_{\\text{C}\\text{o}\\text{m}\\text{p}\\text{o}\\text{s}\\text{i}\\text{t}\\text{e}}={\\text{f}}_{\\text{P}\\text{A}\\text{N}}{\\text{Y}}_{\\text{P}\\text{A}\\text{N}}+{\\text{f}}_{\\text{C}\\text{A}}{\\text{Y}}_{\\text{C}\\text{A}}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003e(4)\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{f}}_{\\text{P}\\text{A}\\text{N}}=\\frac{{\\text{V}}_{\\text{P}\\text{A}\\text{N}}}{{\\text{V}}_{\\text{C}\\text{o}\\text{m}\\text{p}\\text{o}\\text{s}\\text{i}\\text{t}\\text{e}}}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e(5)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{f}}_{\\text{C}\\text{A}}=\\frac{{\\text{V}}_{\\text{C}\\text{A}}}{{\\text{V}}_{\\text{C}\\text{o}\\text{m}\\text{p}\\text{o}\\text{s}\\text{i}\\text{t}\\text{e}}}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e(6)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{f}}_{\\text{P}\\text{A}\\text{N}}+{\\text{f}}_{\\text{C}\\text{A}}=1\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e(7)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eUsing \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{f}}_{\\text{P}\\text{A}\\text{N}}\\)\u003c/span\u003e\u003c/span\u003e​=0.75, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{f}}_{\\text{C}\\text{A}}\\)\u003c/span\u003e\u003c/span\u003e​=0.25, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{Y}}_{\\text{P}\\text{A}\\text{N}}\\)\u003c/span\u003e\u003c/span\u003e​=3.0 GPa, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{Y}}_{\\text{C}\\text{A}}\\)\u003c/span\u003e\u003c/span\u003e​=0.231 GPa, the theoretical modulus of the CA/PAN composite is calculated as \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\text{Y}}_{\\text{C}\\text{o}\\text{m}\\text{p}\\text{o}\\text{s}\\text{i}\\text{t}\\text{e}}\\)\u003c/span\u003e\u003c/span\u003e​=2.30 GPa, which is in close agreement with the MD-predicted value of 2.73 GPa. This excellent consistency confirms the validity and accuracy of the MD simulation methodology and the reliability of the employed force field (ReaxFF) in reproducing realistic mechanical responses.\u003c/p\u003e\u003cp\u003eThe analysis of burst (tensile rupture) strength, as summarized in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e, also corroborates the reinforcement effect of the PAN braid. The pure CA layer exhibited a burst strength of 0.83 MPa, reflecting its high flexibility but low stiffness. In contrast, the pure PAN layer showed a higher stiffness (3 GPa modulus) but a lower burst strength of 0.24 MPa, indicating its brittle nature under multiaxial stress. The hybrid structure containing 75% PAN / 25% CA achieved an intermediate burst strength of 0.40 MPa, representing an optimal balance between tensile rigidity and flexibility.\u003c/p\u003e\u003cp\u003eThese findings demonstrate that increasing the PAN content within the braid structure significantly enhances the overall tensile strength of the BR-HFM, while maintaining adequate ductility. The hybrid configuration thus offers a promising design for mechanically robust and durable membranes, capable of withstanding high mechanical loads in industrial filtration and water treatment applications.\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eComparison of the Young\u0026rsquo;s modulus obtained from MD simulation with theoretical and experimental data for CA, PAN, and CA/PAN composite structures.\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"5\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eNo.\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eSystem\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eYoung\u0026rsquo;s Modulus\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eMethod / Source Description\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c5\"\u003e\u003cp\u003eReference\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\" morerows=\"4\" rowspan=\"5\"\u003e\u003cp\u003eCA layer\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e231 MPa\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eMD simulation (this study)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e\u0026mdash;\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e250 MPa\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eMD simulation\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e[\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e]\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e248 MPa\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eMD simulation\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e[\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e]\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e4\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e375 MPa\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eMD simulation\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e[\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e]\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e205 MPa\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eBraided CA layer (Fan et al.)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e[\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e]\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\" morerows=\"2\" rowspan=\"3\"\u003e\u003cp\u003ePAN layer\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e3 GPa\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eMD simulation (this study)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e\u0026mdash;\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e2\u0026ndash;3 GPa\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eMD simulation\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e[\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e, \u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e40\u003c/span\u003e]\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e2.65 GPa\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eBraided PAN layer (Fan et al.)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e[\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e]\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\" morerows=\"2\" rowspan=\"3\"\u003e\u003cp\u003eCA/PAN composite\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e2.73 GPa\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eMD simulation (this study)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e\u0026mdash;\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e2.30 GPa\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eKarakin et al. model\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e[\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e]\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e2.20 GPa\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eBraided CA/PAN (1:2 ratio, Fan et al.)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e[\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e]\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eComparison of the burst (tensile failure) strength of CA, PAN, and CA/PAN braid layers obtained from MD simulation and experimental results.\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"4\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eNo.\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eBraided Layer\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eBurst Strength (MPa)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eReference\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\" morerows=\"4\" rowspan=\"5\"\u003e\u003cp\u003eCA (simulation)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.83\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e\u0026mdash;\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.76\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e[\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e]\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.241\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e\u0026mdash;\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e4\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.22\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e[\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e]\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.399\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e\u0026mdash;\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e6\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e75% PAN / 25% CA (Fan et al.)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.34\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e[\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e]\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eFigure \u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e presents the calculated interfacial energies for three composite configurations\u0026mdash;CA/PAN\u0026ndash;III, PAN|CA/CA\u0026ndash;I, and CA/CA\u0026ndash;II\u0026mdash;obtained from MD simulations. The corresponding interfacial energies were \u0026minus;\u0026thinsp;1.61 eV, \u0026minus;\u0026thinsp;1.45 eV, and \u0026minus;\u0026thinsp;1.20 eV, respectively. As shown in the figure, the CA/CA\u0026ndash;II configuration demonstrates the strongest interfacial cohesion, followed by PAN|CA/CA\u0026ndash;I, while CA/PAN\u0026ndash;III exhibits the weakest interfacial adhesion and structural stability.\u003c/p\u003e\u003cp\u003eA lower (i.e., more negative) interfacial energy indicates stronger bonding and greater stability between the polymer layers. The high stability of the CA/CA\u0026ndash;II structure can be attributed to the chemical homogeneity of the two CA layers, both consisting of identical polymer chains with hydroxyl (\u0026ndash;OH) and acetate (\u0026ndash;OCOCH₃) groups. This molecular similarity promotes strong hydrogen bonding and van der Waals interactions at the interface, thereby enhancing adhesion and reducing interdiffusion between the layers.\u003c/p\u003e\u003cp\u003eIn contrast, the PAN|CA/CA\u0026ndash;I system exhibits about 15% lower interfacial stability compared with CA/CA\u0026ndash;II, which mainly arises from the chemical dissimilarity between the two polymer phases. The nitrile (\u0026ndash;CN) groups in PAN create dipolar interactions that are inherently weaker than the hydrogen bonds within CA, resulting in reduced compatibility and weaker interfacial cohesion.\u003c/p\u003e\u003cp\u003eThe CA/PAN\u0026ndash;III hybrid structure shows the lowest interfacial energy, roughly 27% lower than CA/CA\u0026ndash;II and about 13% below PAN|CA/CA\u0026ndash;I. This decrease stems from the poor compatibility between the polar \u0026ndash;CN groups in PAN and the acetate (\u0026ndash;OCOCH₃) groups in CA, leading to weaker molecular attractions and diminished hydrogen-bonding capacity. Consequently, the interface becomes more diffusive and less cohesive, with greater molecular mobility across the boundary region.\u003c/p\u003e\u003cp\u003eOverall, Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e clearly illustrates that interfacial adhesion strength decreases in the following order: CA/CA\u0026ndash;II\u0026thinsp;\u0026gt;\u0026thinsp;PAN|CA/CA\u0026ndash;I\u0026thinsp;\u0026gt;\u0026thinsp;CA/PAN\u0026ndash;III.\u003c/p\u003e\u003cp\u003eThis trend confirms that homogeneous polymer interfaces exhibit superior adhesion and structural stability due to their molecular compatibility, whereas heterogeneous or hybrid systems suffer from interfacial discontinuities and weaker bonding. In the context of BR-HFMs, this finding implies that although hybrid layers can improve flexibility, their interfacial bonding remains inherently weaker. Therefore, optimizing the chemical compatibility between the braid and the selective polymer layer is essential for developing mechanically robust and durable membrane structures.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eThe tensile strength calculations at the interfacial junction for the three structures \u0026mdash; CA/PAN-III, PAN|CA\u0026ndash;CA-I, and CA/CA-II \u0026mdash; are presented in the following section. As an example, Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e illustrates the behavior of the heterogeneous PAN/CA-III composite from the beginning of the simulation (zero strain) up to the point of complete yielding, corresponding to the full separation of the two polymers at the interface, at a temperature of 298 K. Figure\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e shows comparison of the stress\u0026ndash;strain curves of three composite structures \u0026mdash; PAN|CA/CA-I, CA/CA-II, and CA/PAN-III \u0026mdash; under ambient conditions.\u003c/p\u003e\u003cp\u003eThe CA/PAN-III composite exhibits sharp stress fluctuations, indicating strong but localized interfacial bonding that fails abruptly under strain due to chemical and structural heterogeneity. In contrast, the PAN|CA/CA-I and CA/CA-II systems display smoother stress\u0026ndash;strain behavior, suggesting more gradual chain separation and weaker interfacial interactions. Overall, the heterogeneous hybrid structure (CA/PAN-III) demonstrates enhanced mechanical responsiveness and higher interfacial activity compared with the more homogeneous composites.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003e\u003c/p\u003e"},{"header":"4. Conclusion","content":"\u003cp\u003eThis work systematically explored the interfacial energetics and mechanical performance of CA- and PAN-based composites using molecular dynamics simulations. The results revealed that interfacial adhesion strength follows the order CA/CA\u0026ndash;II\u0026thinsp;\u0026gt;\u0026thinsp;PAN|CA/CA\u0026ndash;I\u0026thinsp;\u0026gt;\u0026thinsp;CA/PAN\u0026ndash;III, indicating that homogeneous polymer systems possess stronger cohesive forces and superior structural stability. The CA/CA\u0026ndash;II configuration exhibited the most negative interfacial energy (\u0026minus;\u0026thinsp;1.20 eV) and the smoothest stress\u0026ndash;strain profile, reflecting robust hydrogen bonding and van der Waals interactions. Conversely, the heterogeneous CA/PAN\u0026ndash;III interface showed more negative energy (\u0026minus;\u0026thinsp;1.61 eV) accompanied by pronounced stress oscillations, signifying localized strong bonding but weaker overall stability due to interfacial chemical mismatch. The mechanical simulations further demonstrated that increasing PAN content enhances the tensile modulus and burst resistance of BRHFMs, while CA incorporation improves flexibility. The hybrid CA/PAN structure thus achieves an effective balance between stiffness and ductility, making it an excellent candidate for membrane applications under mechanical load. Overall, this study confirms the reliability of the ReaxFF-based MD framework for predicting interfacial and mechanical properties of polymer composites and provides practical molecular-level guidance for tailoring the composition and architecture of high-performance braid-reinforced membranes.\u003c/p\u003e"},{"header":"Numenclature","content":"\u003ctable border=\"0\" cellspacing=\"0\" cellpadding=\"0\" width=\"612\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 32.3529%;\"\u003e\n \u003cp\u003eMD\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 67.6471%;\"\u003e\n \u003cp\u003eMolecular Dynamics\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 32.3529%;\"\u003e\n \u003cp\u003eBRHFMs\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 67.6471%;\"\u003e\n \u003cp\u003eBraid-Reinforced Hollow Fiber Membranes\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 32.3529%;\"\u003e\n \u003cp\u003eCA\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 67.6471%;\"\u003e\n \u003cp\u003eCellulose Acetate\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 32.3529%;\"\u003e\n \u003cp\u003ePAN\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 67.6471%;\"\u003e\n \u003cp\u003ePolyacrylonitrile\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 32.3529%;\"\u003e\n \u003cp\u003eMBRs\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 67.6471%;\"\u003e\n \u003cp\u003eMembrane Bioreactors\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 32.3529%;\"\u003e\n \u003cp\u003eVMD\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 67.6471%;\"\u003e\n \u003cp\u003eVisual Molecular Dynamics\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 32.3529%;\"\u003e\n \u003cp\u003eLAMMPS\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 67.6471%;\"\u003e\n \u003cp\u003eLarge-scale Atomic/Molecular Massively Parallel Simulator\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 32.3529%;\"\u003e\n \u003cp\u003eOVITO\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 67.6471%;\"\u003e\n \u003cp\u003eOpen Visualization Tool\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 32.3529%;\"\u003e\n \u003cp\u003eReaxFF\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 67.6471%;\"\u003e\n \u003cp\u003eReactive Force Field\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 32.3529%;\"\u003e\n \u003cp\u003e\u0026nbsp; E\u003csub\u003eSystem\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 67.6471%;\"\u003e\n \u003cp\u003eTotal Potential Energy of the Composite System\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 32.3529%;\"\u003e\n \u003cp\u003e\u0026nbsp;E\u003csub\u003einter\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 67.6471%;\"\u003e\n \u003cp\u003eInterfacial Energy\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003ch2\u003eConflicts of interest / Competing interest\u003c/h2\u003e\u003cp\u003e\u003cb\u003es\u003c/b\u003e: The authors declare that they have no conflicts of interest.\u003c/p\u003e\u003c/p\u003e\u003ch2\u003eFunding:\u003c/h2\u003e\u003cp\u003eThis research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors.\u003c/p\u003e\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eAuthor Contributions StatementM.J. performed all molecular dynamics simulations, data analysis, and manuscript preparation.A.V. supervised the research, reviewed the results, and provided critical revisions and analytical guidance.A.A. contributed to manuscript refinement, including grammatical and structural editing.All authors read and approved the final version of the manuscript.\u003c/p\u003e\u003ch2\u003eAcknowledgments:\u003c/h2\u003e\u003cp\u003eThe authors gratefully acknowledge the use of the LAMMPS molecular dynamics package developed by Sandia National Laboratories.\u003c/p\u003e\u003ch2\u003eData Availability\u003c/h2\u003e\u003cp\u003eThe molecular dynamics simulation data that support the findings of this study are available from the corresponding author upon reasonable request.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eBarmaki, M., Jalilnejad, E., Ghasemzadeh, K. \u0026amp; Iulianelli, A. Performance Analysis of Silica Fluidized Bed Membrane Reactor for Hydrogen Production as a Green Process Using CFD Modelling. \u003cem\u003eMembr. (Basel)\u003c/em\u003e. \u003cb\u003e15\u003c/b\u003e, 248 (2025).\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eJafari, M., Vatani, A. \u0026amp; Mohammadi, T. CFD modeling of braid-reinforced hollow fiber membranes for efficient water and bovine serum albumin (BSA) separation. \u003cem\u003eJ. Water Process. Eng.\u003c/em\u003e \u003cb\u003e65\u003c/b\u003e, 105746 (2024).\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eTorabi, T., Ghasemzadeh, K., Cassano, A. \u0026amp; Basile, A. Membrane based processes for municipal wastewater reuse. in \u003cem\u003eMunicipal Wastewater Treatment\u003c/em\u003e 207\u0026ndash;239Elsevier, (2025).\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eJafari, M., Nezhadfard, M. \u0026amp; Khalili-Garakani, A. Simulation and Economic Analysis of Combined Desalinated Water and Power Generation from Associated Gases of Cheshmeh Khosh. \u003cem\u003eIran. J. Oil Gas Sci. Technol.\u003c/em\u003e \u003cb\u003e10\u003c/b\u003e, 1\u0026ndash;14 (2021).\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eBasile, A., Ghasemzadeh, K. \u0026amp; Jalilnejad, E. \u003cem\u003eCurrent Trends and Future Developments on (Bio-) Membranes: Ceramic Membrane Bioreactors\u003c/em\u003e (Elsevier, 2019).\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eGhasemzadeh, K. \u0026amp; Basile, A. \u0026amp; Aghaeinejad-Meybodi, A. Solar membrane reactor. \u003cem\u003eIntegrated membrane Syst. processes\u003c/em\u003e 307\u0026ndash;341 (2016).\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eRafiee, R., Seiiedhoseiny, M. \u0026amp; Ghasemzadeh, K. Transport Mechanism and Modeling of Microporous Polymeric Membranes. in Current Trends and Future Developments on (Bio-) Membranes 259\u0026ndash;280 (Elsevier, (2019).\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eGhasemzadeh, K., Aghaeinejad-Meybodi, A. \u0026amp; Basile, A. Polymeric Membrane Reactors. \u003cem\u003eMembrane Reactor Engineering: Appl. Greener Process. Industry\u003c/em\u003e 104\u0026ndash;137 (2016).\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eJalilnejad, E., Jabbari, B. \u0026amp; Ghasemzadeh, K. Application of computational fluid dynamics technique in membrane bioreactor systems. in Current trends and future developments on (Bio-) membranes 345\u0026ndash;375 (Elsevier, (2022).\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eTorabi, T., Ferrari, M. C., Liguori, S. \u0026amp; Ghasemzadeh, K. Green hydrogen production in methylcyclohexane dehydrogenation by ceramic membrane reactor as net-zero approach: Optimisation via digital twin methodology. \u003cem\u003eChem. Eng. J.\u003c/em\u003e \u003cb\u003e520\u003c/b\u003e, 165783 (2025).\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eTorabi, T., Ghasemzadeh, K. \u0026amp; Basile, A. Dehydration processes in membrane reactors. in Current Trends and Future Developments on (Bio-) Membranes 159\u0026ndash;180 (Elsevier, (2025).\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eBasile, A. \u0026amp; Ghasemzadeh, K. \u003cem\u003eCurrent Trends and Future Developments on (Bio-) Membranes: Recent Achievements for Ion-Exchange Membranes\u003c/em\u003e (Elsevier, 2023).\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eJalilnejad, E., Jabbari, B. \u0026amp; Ghasemzadeh, K. Application of computational fluid dynamics technique in membrane bioreactor systems. in Current trends and future developments on (Bio-) membranes 345\u0026ndash;375 (Elsevier, (2022).\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eJalilnejad, E., Sadeghpour, P. \u0026amp; Ghasemzadeh, K. Advances in membrane bioreactor technology. in current trends and future developments on (bio-) membranes 1\u0026ndash;29 (Elsevier, (2020).\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eLin, Z. et al. Optimization of mechanical properties and finite element simulation analysis of hollow fiber membranes in gas-liquid membrane separation technology. \u003cem\u003eDesalination\u003c/em\u003e \u003cb\u003e599\u003c/b\u003e, 118456 (2025).\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eSukitpaneenit, P. \u0026amp; Chung, T. S. Molecular elucidation of morphology and mechanical properties of PVDF hollow fiber membranes from aspects of phase inversion, crystallization, and rheology. in \u003cem\u003eHollow Fiber Membranes\u003c/em\u003e 333\u0026ndash;360Elsevier, (2021).\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eLi, J. et al. Synergistic mechanism of dual-surfactant systems in the heterogeneous braid-reinforced hollow fiber membrane for enhanced comprehensive performance. \u003cem\u003eJ Memb. Sci\u003c/em\u003e \u003cb\u003e124532\u003c/b\u003e (2025).\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eNazif, A., Karkhanechi, H., Saljoughi, E., Mousavi, S. M. \u0026amp; Matsuyama, H. Effective parameters on fabrication and modification of braid hollow fiber membranes: a review. \u003cem\u003eMembr. (Basel)\u003c/em\u003e. \u003cb\u003e11\u003c/b\u003e, 884 (2021).\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eKim, S. H., Lee, J. H., Kim, J. W., Lee, S. Y. \u0026amp; Park, S. J. Interfacial behaviors of basalt fiber-reinforced polymeric composites: a short review. \u003cem\u003eAdv. Fiber Mater.\u003c/em\u003e \u003cb\u003e4\u003c/b\u003e, 1414\u0026ndash;1433 (2022).\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eTurken, T., Sengur-Tasdemir, R., Ates-Genceli, E., Tarabara, V. V. \u0026amp; Koyuncu, I. Progress on reinforced braided hollow fiber membranes in separation technologies: A review. \u003cem\u003eJ. Water Process. Eng.\u003c/em\u003e \u003cb\u003e32\u003c/b\u003e, 100938 (2019).\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eEl-badawy, T. et al. Braid-reinforced PVDF hollow fiber membranes for high-efficiency separation of oily wastewater. \u003cem\u003eJ. Environ. Chem. Eng.\u003c/em\u003e \u003cb\u003e10\u003c/b\u003e, 107258 (2022).\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eKollannoor, A. J., John, V. L., Jose, J. \u0026amp; PX, R. T. \u003cem\u003eV. Cellulose nanostructure-based membranes: Structure, synthesis, and applications\u003c/em\u003e (\u0026amp; TP, 2022).\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eWang, Y. et al. Understanding the graphene-polymer interfacial mechanical behavior via coarse-grained modeling. \u003cem\u003eComput. Mater. Sci.\u003c/em\u003e \u003cb\u003e222\u003c/b\u003e, 112109 (2023).\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eReil, M., Hoffman, J., Predecki, P. \u0026amp; Kumosa, M. Graphene and graphene oxide energetic interactions with polymers through molecular dynamics simulations. \u003cem\u003eComput. Mater. Sci.\u003c/em\u003e \u003cb\u003e211\u003c/b\u003e, 111548 (2022).\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eChen, J., Li, B., Gu, B. \u0026amp; Sun, B. Molecular dynamics insights into temperature-dependent interfacial properties and failure behaviors of carbon fiber/epoxy composites. \u003cem\u003eCompos Struct\u003c/em\u003e \u003cb\u003e119758\u003c/b\u003e (2025).\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eWang, W. \u0026amp; Qu, Z. Molecular dynamics simulation of the mechanical properties and thermal conductivity of aromatic electrolytes in proton exchange membrane fuel cells. \u003cem\u003eJ. Power Sources\u003c/em\u003e. \u003cb\u003e585\u003c/b\u003e, 233622 (2023).\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eBadar, M. S., Shamsi, S., Ahmed, J. \u0026amp; Alam, M. A. Springer,. Molecular dynamics simulations: concept, methods, and applications. in \u003cem\u003eTransdisciplinarity\u003c/em\u003e 131\u0026ndash;151 (2022).\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eOda, K. \u0026amp; Yasuda, S. Synchronized molecular dynamics simulation using LAMMPS: application to pressure-driven flows of polymer melts. \u003cem\u003eModel. Simul. Mat. Sci. Eng.\u003c/em\u003e \u003cb\u003e33\u003c/b\u003e, 055007 (2025).\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eBone, M. A., Howlin, B. J., Hamerton, I., Macquart, T. \u0026amp; AutoMapper A python tool for accelerating the polymer bonding workflow in LAMMPS. \u003cem\u003eComput. Mater. Sci.\u003c/em\u003e \u003cb\u003e205\u003c/b\u003e, 111204 (2022).\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eFan, Z., Xiao, C., Liu, H., Huang, Q. \u0026amp; Zhao, J. Structure design and performance study on braid-reinforced cellulose acetate hollow fiber membranes. \u003cem\u003eJ. Memb. Sci.\u003c/em\u003e \u003cb\u003e486\u003c/b\u003e, 248\u0026ndash;256 (2015).\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eFan, Z., Xiao, C., Liu, H. \u0026amp; Huang, Q. Preparation and performance of homogeneous braid reinforced cellulose acetate hollow fiber membranes. \u003cem\u003eCellulose\u003c/em\u003e \u003cb\u003e22\u003c/b\u003e, 695\u0026ndash;707 (2015).\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eVashisth, A., Ashraf, C., Zhang, W., Bakis, C. E. \u0026amp; Van Duin A. C. T. Accelerated ReaxFF simulations for describing the reactive cross-linking of polymers. \u003cem\u003eJ. Phys. Chem. A\u003c/em\u003e. \u003cb\u003e122\u003c/b\u003e, 6633\u0026ndash;6642 (2018).\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eKowalik, M. et al. Atomistic scale analysis of the carbonization process for C/H/O/N-based polymers with the ReaxFF reactive force field. \u003cem\u003eJ. Phys. Chem. B\u003c/em\u003e. \u003cb\u003e123\u003c/b\u003e, 5357\u0026ndash;5367 (2019).\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eJiang, B., Zhang, M., Fu, L., Zhou, M. \u0026amp; Zhai, Z. Molecular dynamics simulation on the interfacial behavior of over-molded hybrid fiber reinforced thermoplastic composites. \u003cem\u003ePolym. (Basel)\u003c/em\u003e. \u003cb\u003e12\u003c/b\u003e, 1270 (2020).\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eKohestanian, M., Sohbatzadeh, Z. \u0026amp; Rezaee, S. Mechanical properties of continuous fiber composites of cubic silicon carbide (3C-SiC)/different types of carbon nanotubes (SWCNTs, RSWCNTs, and MWCNTs): a molecular dynamics simulation. \u003cem\u003eMater. Today Commun.\u003c/em\u003e \u003cb\u003e23\u003c/b\u003e, 100922 (2020).\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eGopiraman, M., Fujimori, K., Zeeshan, K., Kim, B. S. \u0026amp; Kim, I. S. Structural and mechanical properties of cellulose acetate/graphene hybrid nanofibers: spectroscopic investigations. \u003cem\u003eExpress Polym. Lett\u003c/em\u003e \u003cb\u003e7\u003c/b\u003e, (2013).\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eSalama, A., Mohamed, A., Aboamera, N. M., Osman, T. \u0026amp; Khattab, A. Characterization and mechanical properties of cellulose acetate/carbon nanotube composite nanofibers. \u003cem\u003eAdv. Polym. Technol.\u003c/em\u003e \u003cb\u003e37\u003c/b\u003e, 2446\u0026ndash;2451 (2018).\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eAboamera, N. M., Mohamed, A., Salama, A., Osman, T. A. \u0026amp; Khattab, A. Characterization and mechanical properties of electrospun cellulose acetate/graphene oxide composite nanofibers. \u003cem\u003eMech. Adv. Mater. Struct.\u003c/em\u003e \u003cb\u003e26\u003c/b\u003e, 765\u0026ndash;769 (2019).\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eYusof, N. \u0026amp; Ismail, A. F. Polyacrylonitrile/acrylamide-based carbon fibers prepared using a solvent‐free coagulation process: Fiber properties and its structure evolution during stabilization and carbonization. \u003cem\u003ePolym. Eng. Sci.\u003c/em\u003e \u003cb\u003e52\u003c/b\u003e, 360\u0026ndash;366 (2012).\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eSanchaniya, J. V. \u0026amp; Kanukuntla, S. Morphology and mechanical properties of PAN nanofiber mat. in \u003cem\u003eJournal of Physics: Conference Series\u003c/em\u003e vol. 2423 012018IOP Publishing, (2023).\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"Braid-reinforced, Interfacial Energy, Mechanical Properties","lastPublishedDoi":"10.21203/rs.3.rs-7961374/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7961374/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis study presents a comprehensive molecular dynamics (MD) investigation of braid-reinforced hollow fiber membranes (BRHFMs) to elucidate the interfacial and mechanical behaviors of polymeric composites composed of cellulose acetate (CA) and polyacrylonitrile (PAN). The analysis focuses on three representative configurations\u0026mdash;homogeneous (CA/CA-II), semi-heterogeneous (PAN|CA/CA-I), and heterogeneous hybrid (CA/PAN-III)\u0026mdash;to evaluate their interfacial energies, adhesion mechanisms, and tensile responses. The calculated interfacial energies of \u0026minus;\u0026thinsp;1.20 eV, \u0026minus;\u0026thinsp;1.45 eV, and \u0026minus;\u0026thinsp;1.61 eV for CA/CA-II, PAN|CA/CA-I, and CA/PAN-III, respectively, reveal that chemical homogeneity promotes stronger interfacial bonding, whereas polarity mismatches between functional groups (\u0026ndash;OH, \u0026ndash;OCOCH₃, and \u0026ndash;CN) weaken adhesion and increase diffusivity at the interface.\u003c/p\u003e\u003cp\u003eMechanical testing through MD tensile simulations further demonstrates that the CA/PAN-III composite exhibits pronounced stress fluctuations and higher local interfacial activity. At the same time, the CA/CA-II system maintains the highest cohesive stability and elastic modulus due to structural uniformity. The CA/PAN-III hybrid achieves an optimal balance between flexibility and strength, indicating its suitability for water treatment membranes requiring both mechanical resilience and interfacial durability. These findings provide molecular-level insight into how polymer compatibility governs the performance of BRHFMs and offer valuable guidelines for designing next-generation high-strength composite membranes.\u003c/p\u003e","manuscriptTitle":"Molecular Dynamics Investigation of Interfacial Energy and Mechanical Behavior in Braid-Reinforced Hollow Fiber Membranes","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-11-11 11:43:43","doi":"10.21203/rs.3.rs-7961374/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2025-12-05T03:33:16+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-12-03T09:45:49+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"48725758116222819871741508978623542204","date":"2025-11-27T22:30:11+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-11-04T22:15:42+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"124721313107830510649565096608145669610","date":"2025-11-02T21:46:02+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"24901187947465030960745944709542797895","date":"2025-11-01T22:46:13+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-10-30T14:47:22+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"","date":"2025-10-30T12:57:05+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-10-28T06:41:10+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-10-28T06:40:35+00:00","index":"","fulltext":""},{"type":"submitted","content":"Scientific Reports","date":"2025-10-27T14:02:13+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"a20b55ce-7888-449a-a383-49b6fef07ac3","owner":[],"postedDate":"November 11th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[{"id":57679654,"name":"Physical sciences/Chemistry"},{"id":57679655,"name":"Physical sciences/Engineering"},{"id":57679656,"name":"Physical sciences/Materials science"}],"tags":[],"updatedAt":"2026-02-18T05:39:03+00:00","versionOfRecord":[],"versionCreatedAt":"2025-11-11 11:43:43","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-7961374","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7961374","identity":"rs-7961374","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}