Determination of Compatibility in Polymer-Polymer and Polymer-Resin Systems through Molecular Dynamics Simulations

Determination of Compatibility in Polymer-Polymer and Polymer-Resin Systems through Molecular Dynamics Simulations | 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 Research Article Determination of Compatibility in Polymer-Polymer and Polymer-Resin Systems through Molecular Dynamics Simulations Arpita Srivastava, Debabrata Ganguly, Anubhav Kumar, Sharad Goyal, and 3 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6957788/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Tyre is a complex composite comprising of various rubber compounds, metal cords and fabrics having dynamic utility. The rubber compounds are further composed of various components such as polymers, fillers, resin and antioxidants. For homogeneous mixing of ingredients, compatibility between two polymers and/or polymer-resin is very essential which in turn improves the thermodynamic mechanical properties of the rubber vulcanizate and reduces tyre failure. This study focusses on understanding compatibility between polymer-polymer and polymer-resin systems through molecular dynamics (MD) simulations. For this study, we have selected commonly used rubbers in tyre compounds such as Natural Rubber (NR), Butadiene Rubber (BR), Styrene-Butadiene Rubber (SBR), Isobutylene-Isoprene Rubber (IIR) as well as compatibility of these polymers with commonly used resins in tyres, such as dicyclopentadiene (DCPD), phenolic resin (PF), and C9 and C5 which are branched hydrocarbons resins. In simulations, we quantified compatibility using Hildebrand’s solubility parameter ( δ ) and experimentally characterized it via Atomic Force Microscopy (AFM) experiments, which confirmed our simulation results. Our findings indicate that competing non-bonded interactions such as π-π stacking, polar and non-polar interactions, and steric effects play a critical role for compatibility in both polymer-polymer and polymer-resin mixtures. The alignment between our computational and experimental findings underscores the robustness of our modeling approach. These simulations offer valuable insights into the interactions within two-component systems, aiming to further understand multi-component systems by reducing physical trials and costs along with enlightening towards innovative tyre formulations. Computational Chemistry Polymer Science Molecular Dynamics Simulations Compatibility Polymer Resins Solubility Parameter Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Introduction Homogenous mixing in tyre matrix improves thermodynamic mechanical properties like flex, heat build-up, crack abrasion and durability. If two polymers and/or polymer-resin system is compatible, it will lead to homogenous composite matrix, giving improved properties and less failure due to separation among components [ 1 ], [ 2 ], [ 3 ]. By improving rubber compatibility, manufacturers can develop tyre blends that not only improve performance but also extend longevity and reduce fuel consumption due to less heat build-up, ultimately leading to safer and more efficient tyres. Rubber blend technology is a key area of focus for tyre technologists, particularly the combinations of Styrene-Butadiene Rubber (SBR) with Butadiene Rubber (BR) or Natural Rubber (NR) [ 4 ],[ 5 ], [ 6 ]. Research has shown that incorporating BR into the tyre tread compound can significantly enhance wear resistance, thereby improving overall performance and longevity. This advancement highlights the importance of selecting and optimizing rubber blends to meet the demanding requirements of modern tyres. SBR-BR blends play a crucial role in high-performance tyres, primarily used in tread [ 6 ],[ 7 ]. This combination leverages the strengths of both materials, offering enhanced abrasion resistance and improved wet traction. By optimizing this blend, manufacturers can create tyres that perform effectively in both dry and wet conditions, thereby enhancing safety [ 8 ]. SBR-NR blends are commonly used in the tread area of tyres due to their excellent balance of elasticity, wear resistance, and grip [ 9 ][ 10 ][ 5 ]. Natural Rubber (NR) provides superior traction and flexibility, while Styrene-Butadiene Rubber (SBR) enhances durability and resistance to aging. This combination is particularly effective in achieving optimal performance across various driving conditions, ensuring that tyres maintain grip and resilience. BR-NR blends are utilized in both the tread and sidewall areas, where superior resilience and dynamic properties are necessary. Butadiene Rubber (BR) enhances the tyre's ability to absorb shocks and maintain structural integrity under stress, while NR contributes to overall grip. This compatibility is vital for tyres that need to perform reliably in demanding conditions [ 11 ]. Apart from tread and sidewalls which are majorly composed of NR, BR and SBR, the inner liners of tubeless tyres play a crucial role in maintaining air pressure, which is vital for performance, fuel efficiency, and longevity. Various rubber blends are employed in these liners to enhance their effectiveness, particularly Isobutylene-Isoprene Rubber (IIR) in combination with other rubber types [ 12 ][ 13 ], [ 14 ]. Understanding compatibility between SBR/BR/NR with butyl is also essential to obtain better adhesion between tyre inner liner and transition liner. Ensuring compatibility helps mitigate safety risks associated with issues like layer separation. As the tyre industry faces increasing pressures for innovation and sustainability, compatibility studies pave the way for exploring new material combinations that can enhance performance while adhering to regulatory standards. Apart from these rubbers, resins are essential in tyre formulations as they enhance adhesion between rubber and reinforcing materials, improve grip on various surfaces, and reduce hysteresis loss, leading to better fuel efficiency[ 15 ]. Rubber in tyres exhibits viscoelastic properties, combining elasticity and viscosity, which affects energy recovery during rotation. Incompatible materials may cause more hysteresis loss or heat build-up, increasing tyre failure, rolling resistance and decreasing overall fuel efficiency, while also playing a key role in grip performance. The integration of hydrocarbon resins into rubber compounds can significantly alter their performance attributes, including traction in wet conditions and rolling resistance [ 16 ]. The degree to which these properties are optimized depends largely on the compatibility between the resin and the rubber matrix. When resins do not blend well, they may cause an undesirable increase in the damping response, leading to higher rolling resistance. On the other hand, when compatibility is achieved, it allows for enhanced wet grip without compromising rolling efficiency. Lower molecular weight and similar structural features to rubber polymers often facilitate this compatibility, ensuring a more effective blend [ 17 ] [ 18 ]. The use of dicyclopentadiene (DCPD) and phenolic (PF) resins has become increasingly important in enhancing these properties. It is reported that DCPD-modified phenolic resins optimize the viscoelastic behavior of rubber compounds, improving traction on both wet and dry surfaces while increasing resistance to chips and cuts[ 19 ]. Achieving this balance is essential for developing high-performance tyres that ensure safety and efficiency across diverse driving conditions. Other synthetic resins, C9 and C5 are well reported for their significant contribution in enhancing the mechanical properties and damping performance of rubber vulcanizates [ 20 ], [ 21 ]. Addition of C5/C9 petroleum resins has shown to enhance the wet traction in tread compositions of passenger cars [ 22 ]. This increasing demand in upgrading the tyre performance calls for a detailed study in a comprehensive manner to understand the driving forces regulating the compatibility between tyre components, which, in turn may guide for a better formulation for an improved performance. Molecular simulation is one such rising technique for investigating both the compatibility and the properties of materials at the microstructural level without using expensive equipment and complicated experiments. In particular, atomistic molecular dynamics (MD) simulations are invaluable, as they offer detailed quantitative insights into the intrinsic characteristics of materials, including their mechanical, thermal, and chemical properties, as well as their dynamic behavior over time. Researchers increasingly rely on MD simulations to complement experimental work, especially in the study of polymers and their composites [ 23 ]. These simulations allow for a deeper exploration of how different components interact at the molecular level, providing a clearer picture of compatibility between materials [ 24 ] [ 25 ]. By assessing factors such as phase separation, diffusion, and mechanical stress responses, MD simulations can reveal potential challenges and synergies in material combinations [ 26 ], [ 27 ] [ 28 ]. The results from these simulations indicate that, when conducted with appropriate methodologies, the findings closely align with those observed in experimental samples [ 29 ]. This correspondence enhances our understanding of how molecular interactions influence both compatibility and overall properties, guiding the development of more effective materials for various applications . The aim of this research is to build molecular dynamics simulation model to determine the compatibility between two polymers chosen from the commonly used polymers in tyres such as NR, BR, SBR and IIR as well as compatibility of these polymers with various petroleum resins, including dicyclopentadiene (DCPD), phenolic resin (PF), and branched C9 and C5 hydrocarbon resins. Our initial step involved validating chemical parameters to ensure that the polymer densities we calculated were consistent with existing literature. In our investigation, we discovered that an interplay of various non-bonded interactions plays a pivotal role in determining the compatibility of polymer-polymer and polymer-resin mixtures. By analyzing these interactions, we assessed compatibility through Hildebrand’s solubility parameter (δ), derived from our molecular dynamics simulations. To further validate our findings, we conducted Atomic Force Microscopy (AFM) experiments, which corroborated our simulation results, providing a comprehensive understanding of how these materials behave together at the molecular level. The strong alignment between our computational and experimental data emphasizes the reliability of our approach. Methodology Computational Modeling In this study, we conducted all-atom molecular dynamics (MD) simulations on rubber polymer and resin systems pertinent to tyre applications. Our primary objective was to understand the compatibility between two-component systems and how temperature influences polymer interactions. The polymers under investigation include Natural Rubber (NR), Butadiene Rubber (BR), Styrene-Butadiene Rubber (SBR), and Butyl Rubber (IIR). Their respective molecular weights are detailed in Table 1 . To explore compatibility, we simulated these polymers both as pure systems and in mixtures at a 50/50 wt./wt. ratio. This approach allows us to assess the interactions between different polymer components and their ability to blend effectively. Furthermore, this work delves into the compatibility of polymers (NR, BR, and SBR) with various resins, namely Dicyclopentadiene (DCPD), Phenol Formaldehyde (PF) and two branched resins, C9 and C5. The chemical structures of all the molecules studied are presented in Fig. 1 , offering a visual reference for their structural properties. The simulations of pure polymers, as well as the two-component systems comprised of polymer-polymer and polymer-resin combinations, are conducted at a temperature of 300 K. To further investigate the effects of temperature on polymer interactions, we conducted additional simulations at elevated temperatures of 373 K and 433 K for the polymer mixtures. This temperature variation is crucial for understanding how thermal conditions impact the compatibility and performance of rubber formulations in practical applications. Furthermore, the compatibility between all the binary mixtures is validated by Atomic Force Microscopy (AFM) experiments which measure the phase behavior of the mixtures. Overall, our research aims to provide a comprehensive understanding of the interactions within polymer-polymer and polymer-resin systems, contributing valuable insights for the development of more effective materials in tyre manufacturing and related industries. Simulation details The initial configuration of the above polymers units is drawn in J − OCTA [ 30 ] followed by molecular mechanics (MM) calculations using OPLS-AA [ 31 ] force-field. Next, the final configuration of each polymer is used to simulate both pure and mixed component systems. First, we simulated pure polymeric systems having 100 chains of each polymer, randomly inserted in a cubical box. The box dimensions are presented in Table 1 . The simulations of all the systems are carried out using GROMACS [ 32 ], [ 33 ], [ 34 ]. In molecular dynamics, total potential energy in the system is a sum of bonded and non-bonded potential energy, $$\:{U}_{total}={U}_{bonded}+{U}_{non-bonded}$$ 1 The bonded potential energy ( U bonded ) is caused by the vibrations in bond length, bond angle and dihedrals whereas the non-bonded terms ( U non−bonded ) arise from Coulombic interactions and van der Waals interactions, modeled by 12 − 6 type Lennard Jones interactions. Their functional forms are given as, $$\:{U}_{bonded}=\:\frac{1}{2}\sum\:{k}_{b}{\left(r-{r}_{0}\right)}^{2}\:+\:\frac{1}{2}\sum\:{k}_{\theta\:}{\left(\theta\:-{\theta\:}_{0}\right)}^{2}+\:\sum\:\frac{{V}_{n}}{2}\left[1+\text{cos}\left(n\varphi\:-\gamma\:\right)\right]$$ 2 $$\:{U}_{non-bonded}=\:\sum\:_{i<j}\left[\frac{{q}_{i}{q}_{j}}{4\pi\:{ϵ}_{0}{r}_{ij}}\right]+\:\sum\:_{i<j}\left[4{ϵ}_{ij}\left\{{\left(\frac{{\sigma\:}_{ij}}{{r}_{ij}}\right)}^{12}-{\left(\frac{{\sigma\:}_{ij}}{{r}_{ij}}\right)}^{6}\right\}\right]\:$$ 3 In the above equations, the force constant for bond stretching is represented by k b whereas r denotes the bond length and r 0 ​ signifies the equilibrium bond length. For angle bending, k θ is the force constant, θ refers to the bond angle, and θ 0 ​ indicates the equilibrium bond angle. In the dihedral angle term, V n represents the amplitude of the n th Fourier component, n specifies the periodicity of the dihedral angle, ϕ denotes the dihedral angle, and γ stands for the phase angle. Regarding non-bonded interactions, r ij ​ represents the distance between atoms i and j , q i ​ and q j are charges on atoms i and j and ϵ 0 ​ signifies the permittivity of free space. ϵ ij ​ is the depth of the potential well in the Lennard-Jones potential for atoms i and j , while σ ij ​ is the finite distance at which the inter-particle potential reaches zero. All systems are energy-minimized and simulated in an NVT [ 35 ] ensemble for 1 ns at 300 K using a velocity-rescale thermostat to reach thermal equilibrium. Once the desired temperature is reached, NPT [ 36 ], [ 37 ] simulations are conducted for 10 ns at 1 bar pressure. The temperature and pressure of the systems are held constant velocity-rescale thermostat and Berendsen barostat with a coupling constant of 1.0 ps respectively. An integration timestep of 2 fs is followed in all the cases. The electrostatic interactions are treated with the PME [ 37 ] method while the van der Waals interactions are computed using cut-off method. The non-bonded interactions are cutoff at 1 nm. The convergence of the systems is confirmed by monitoring their total potential energy and density. Following this, a series of simulations are performed for mixed component systems considering a combination of two polymers in each system and along with polymer-resin combinations using the same simulation parameters as in the pure systems. The effect of heating on the mixed polymeric systems from 300 K to 373 K to 433 K is done by using simulated-annealing method with a scan rate of 20 K ns − 1 in an NVT ensemble. Once the desired temperature is reached, 1 ns NVT simulation and 10 ns NPT simulations are conducted at both 373 K and 433 K to measure the compatibility. All other simulation protocols followed for each of the systems using the above three approaches are same as that for the pure systems. Once the systems are equilibrated, the final configurations are visualized in VMD [ 38 ] and Hildebrand’s solubility parameter (δ) [ 39 ],[ 40 ] is computed to identify the compatibility between various polymeric mixtures. The Hildebrand solubility parameter (δ) is a critical concept in polymer science and materials chemistry that provides insight into the compatibility of different materials, particularly polymers and solvents. It is defined as the square root of the cohesive energy density (CED) [ 41 ], which reflects the energy required to create a cavity in a solvent for a solute molecule. The solubility parameter can be expressed mathematically as: $$\:{\delta\:}_{AB}=\sqrt{\frac{{E}_{coh}}{{V}_{m}}}$$ 4 where δ is the Hildebrand solubility parameter (in (J/cm³) 1/2 ), E coh is the cohesive energy (in J/cm³) and V m is the molar volume (in cm³/mol). In the context of solubility, the cohesive energy density (CED) is defined as, $$\:CED=\frac{{E}_{coh}}{{V}_{m}}$$ 5 In this work, we use the Hildebrand solubility parameter to quantify the compatibility of various polymer-polymer and polymer-resin systems. By comparing the solubility parameters of the components, we can predict their miscibility and enhance our understanding of their interactions in the context of tyre applications. To validate the compatibility obtained from the simulation models, we also compared the results with AFM experiments. The experimental results are in good agreement with the simulations, validating the suitability of our models. Experimental methodology The respective rubbers and resins were mixed in the ratio of 50:50 wt/wt in a HAAKE internal mixer employing a mixing temperature of 130 o C. The mixed compound is dumped from the internal mixer after mixing for 10 mins at 60 rpm are sheeted out using a two-roll mill. The compounds are then pressed in between two plates to form thin sheets to conduct different experiments. The AFM studies were conducted using Bruker Multimode 8 AFM employing contact mode and the surface morphologies were captured and compared along with the simulation results. Results and Discussion In the initial phase of our modeling approach, we focused on simulating pure polymer systems to establish a foundational understanding of their behavior. During these simulations, we allowed the simulated box to reach a state of equilibrium, which is crucial for obtaining reliable data. The time evolution of the density for each of the pure polymer systems is depicted in Figure 2, which illustrates a clear convergence towards a stable density value over the simulation period. To quantify this convergence, we computed the average density for the last 5 ns of the simulation for each polymer. These averaged density values are presented in Table 1. The results obtained from our simulations demonstrate reasonable agreement with values reported in the literature, indicating that our modeling approach and force-field parameters are appropriate and effective. Table 1: Details of molecular weights of polymer compositions, size of cubical box, density obtained from simulations and comparison from the density provided in literature . Polymer Molecular Weight Box Size (nm) Density (kg/m 3 ) Simulation Literature NR 682.06 9.0 0.87 0.92 BR 570.99 9.0 0.87 0.91-0.92 SBR 829.35 11.5 0.96 0.94 IIR 603.16 8.0 0.87 0.90 This validation step is essential as it confirms the feasibility of our model. By ensuring that the simulated densities align well with established data, we can confidently proceed to model more complex two-component systems using these configurations. The successful validation of the pure systems establishes a solid groundwork, allowing us to explore interactions between different polymers and resins in subsequent simulations. By employing a reliable force-field and ensuring equilibrium, we enhance the accuracy of our predictions regarding the compatibility and behavior of polymer compositions. Once the force-field parameters are validated, the same molecular model is used to prepare two component systems for polymer-polymer and polymer-resin studies. The compatibility between these systems assists in determining the likability of both components as a blend. This is determined by computing the Hildebrand’s solubility parameter ( δ ), given in equation (4). For the mentioned polymers, we considered six compositions and computed the compatibility, shown in figure 3. A higher value δ indicates a stronger compatibility which dictates a higher cohesive energy density between the two components. From the figure, it is seen that SBR-NR and SBR- BR systems have the highest solubility parameters which makes them the most compatible systems. This can be attributed to the strong π-π interactions held due to the aromatic rings in SBR and the double bonds present in NR and BR polymers. These interactions cause a strong packing between the chains and increase the likeability between the two chemical units. Next, the BR-NR systems show a moderate value for the solubility parameter. The non-polar tendency of both these hydrophobic polymers facilitates effective van der Waals interactions between them and allows for an effective blending. Thus, the hydrophobic interactions drive the miscibility in this systems. The trend of compatibility becomes moderate in the case of BR-IIR and SBR-IIR polymers. The IIR polymers are predominantly composed of butyl groups which cause a steric hinderance with the other polymers. In BR-IIR system, the two polymers are held together by π-π interactions present in BR and isoprene units of IIR but are the δ lowers due to steric hinderance originating from butyl groups of IIR. In the further case of SBR-IIR systems, the π-π interactions still operate between aromatic styrene units and isoprene of IIR. But at the same time, the compatibility lowers due to the rising steric hinderance caused from butyl of IIR and bulky rings in styrene- which, is elsewise not so dominant in BR-IIR system. Thus, the competing forces in BR-IIR and SBR-IIR make these two systems moderately compatible. In the last case of NR-IIR systems, NR is primarily made of isoprene, which is less polar than SBR or BR and has limited functional groups for interaction with IIR. Moreover, the butyl groups in IIR and methyl group in NR may cause a strong steric hinderance, making these two polymers as least compatible amongst all other systems studied here. We further investigate the findings of compatibility from MD simulations with the AFM experiments. A blend of all the systems studied is prepared and their AFM images are presented in figure 4 [42]. A uniform surface morphology signifies systems with no phase separation and are highly compatible, whereas a non-uniform morphology and agglomeration if any components denote a phase separated system which is less compatible. As seen, the systems SBR-NR, SBR-BR and BR-NR have a clean uniform surface morphology. This indicates a strong likeability of the two components towards each other as their surface stays even with no phase separation. This is also in-line with the high δ -value obtained from simulations. Next, the BR-IIR and SBR-IIR systems show medium uniformity in surface with a slight distinction in surface morphology. These indicate some extent of phase separation which is also reflected by their intermediate δ -value from simulations. In the last case of NR-IIR polymers, there lies a distinct difference in the surface morphology with agglomerate formation which is attributed to the localization of NR and IIR polymers on the surface indicating towards their poor compatibility. Similar findings from simulations and the weak underlying molecular interactions make this system the least compatible system amongst all. Overall, the AFM experiments are in good correlation with the δ -value obtained from simulations. This suggests the suitability of molecular simulations to study compatibility between two components which can fairly reduce the number of physical trials and experimental time. We have expanded our MD simulations to examine the effects of temperatures relevant to the mixing of composites and curing processes of tyres and during its service period. Specifically, we subjected the mixed polymer systems to elevated temperatures of 373 K (100°C) and 433 K (160°C) to evaluate their compatibility, as illustrated in Figure 5. We plotted the solubility parameter values as a function of temperature, revealing a systematic trend. As the temperature increases from 300 K to 373 K and further to 433 K, we observed a consistent decrease in the δ-value (solubility parameter). This phenomenon can be attributed to several factors related to thermal energy's impact on polymer interactions. The lowering of the δ-value indicates a reduction in cohesive energy within the polymer systems. This reduction can be linked to the weakening of non-bonded interactions, such as hydrophobic forces and π-π stacking interactions, as thermal energy increases. As temperature rises, the kinetic energy of the polymer chains also increases, leading to greater molecular motion. This heightened activity disrupts the stability of non-bonded interactions, which are crucial for maintaining compatibility between different polymer systems. As cohesive energy diminishes, the networking between polymer chains weakens. This disruption can adversely affect the overall compatibility of the mixed systems. When the polymer chains are less tightly interconnected, the material properties can change, potentially leading to phase separation. The most significant observation is that the trend of compatibility between two polymers us similar- both at room temperature and at higher temperature. In a nutshell, our models provide detailed insights to deeply investigate compatibility at molecular resolution operating at nanoscales which are important for material performance. Further, resins are important components in tyres as they provide bonding strength, flexibility, elasticity and strength. Thus, it becomes an important aspect to investigate the compatibility of polymers with resin. Hence, we have simulated 12 two-component systems formed from the combination of polymers and resins shown in figure 1 and calculated their solubility parameters. As our simulation models have held good for polymer-polymer system, the polymer-resin simulations are followed in a similar manner. Figure 6 shows the δ -value of the four resins- DCPD, PF, C9 and C5 with SBR, BR and BR polymers. The compatibility and performance of SBR-DCPD, BR-DCPD, and NR-DCPD resins are significantly influenced by their distinct chemical structures and features. SBR has both non-polar butadiene segment with a polar styrene segment, introducing functional groups that facilitate favorable van der Waals interactions. On the other side, DCPD possesses double bonds due to its bicyclic structure. This results in homogeneity with enhanced interactions, making SBR-DCPD highly compatible. In contrast, BR, primarily composed of non-polar polybutadiene, lacks polar characteristics necessary for effective interactions with DCPD. Consequently, BR-DCPD may exhibit limited mixing and increased phase separation due to weaker dispersive interactions and lower cohesive energy density compared to SBR-DCPD. NR, primarily consisting of polyisoprene, also presents compatibility challenges due to its non-polar nature. The absence of polar functional groups in NR results in significant phase separation and reduced interfacial adhesion when blended with DCPD. With PF resins, the compatibility lowers from BR to NR to SBR. This can be connected with the structure of PF resin, shown in figure 1. As this resin is larger in size, the steric repulsions between SBR and PF due to their aromatic counterparts dominate. This leads to an ineffective interactions sights and hence causes SBR to be least compatible with PF-resin. NR polymer, on the other hand, does not have bigger side groups as in the case of SBR. This permits a better van der Waals interaction between PF and NR and causes an improvement in the δ -value for compatibility. The δ-value is highest for BR-PF combination which is again an outcome of the chemical framework. The polybutadiene in BR supports stronger π-π interactions with aromatic sings of PF-resin. Alongside, an absence of any hinderance from the side chain effectively improves the compatibility between these two molecules, reflected from their high δ -value. The C9 resin is a branched molecule having benzene rings substituted in the parent chain. Thus, the polymers exhibit an obvious trend in compatibility, moving from SBR to BR and then to NR. The high compatibility with SBR is credited to the favorable π-π interactions in SBR and C9 aromatic rings, favored by the smaller and more flexible size of C9. The lower polarity in BR than SBR causes a lowering in BR-C9 compatibility. The lowest δ -value in NR-C9 is caused due to the least favorable interactions due to non-polar isoprene units of NR which are held poorly with C9 resins. The overall lowering in δ -value of polymers with C9 as compared to DCPD and PF is caused due to the steric factors. The C5 resin branch makes it sterically unfavorable along with its aliphatic feature makes it highly non-polar as well. Thus, all the polymers are least compatible with C5 resin as compared to other resins. We confirmed our findings for SBR-resin system using AFM experiments in a similar manner as done for polymer-polymer systems, shown in figure 7. As high degree of uniformity in the surface for SBR-DCPD and SBR-PF shows that they in well mixed and compatible with each other. The SBR-C9 system shows an uneven distribution of components, indicating a lower compatibility. In SBR-C5 system, a clear distinction between the two components can be seen. This shows a localization of the two entities within the system, where they prefer a phase-separated behavior. This entire experimental observation of SBR-resin systems is in good correlation with the solubility parameter values obtained from molecular dynamics simulations. Overall, the varying degrees of compatibility among these resin systems arise from their structural and chemical differences and SBR-DCPD system is the most compatible system among all the polymer-resin systems investigated. Conclusion In this work, we have performed MD simulation for different pairs if polymers from the commonly used polymers in tyres such as, Natural Rubber (NR), Butadiene Rubber (BR), Styrene-Butadiene Rubber (SBR), and Isobutylene-Isoprene Rubber (IIR) as well as compatibility of these polymers with commonly used resins such as dicyclopentadiene (DCPD), phenolic resin (PF), and C9 and C5 resins. Our approach involved analyzing these materials both as pure systems and in binary combinations, focusing on polymer-polymer and polymer-resin compatibility through molecular dynamics simulations. To establish a standardized baseline for our chemical parameters, we first simulated the pure systems, which yielded polymer densities that closely match those reported in the literature. This validation ensured the accuracy of the force-field parameters and directed towards our subsequent modeling of binary systems, allowing us to effectively explore and understand their compatibility behaviors. In examining the binary mixtures, we identified that the interplay of molecular-level non-bonded interactions-such as π-π stacking, polar and non-polar interactions, and steric effects have an underlying role in determining the compatibility of the two components. This compatibility is quantified through the solubility parameter ( δ ), with higher values indicating greater likelihood of miscibility. Among all the polymer pairs studied, the compatibility trend is SBR-NR > SBR-BR > BR-NR > BR-IIR > SBR-IIR > NR-IIR and for polymer-resin systems compatibility trend with SBR/BR/NR rubbers is DCPD > PF > C9 > C5. Additionally, we characterized the compatibility through Atomic Force Microscopy (AFM) experiments, which well supported our simulation findings. The alignment of our simulation results with experimental data reinforces the reliability of our modeling approach, suggesting that our computational framework is robust and accurate. Looking ahead, these molecular simulations will facilitate a deeper understanding of the intricate interactions within multi-component systems, particularly the forces that govern compatibility in tyre materials which in turn will help to select most suitable polymers or resins through MD simulations. By minimizing the need for extensive physical trials, these models enable us to save time and costs associated with experimental work while also predicting innovative recipe designs in material formulation. This research has the potential to significantly enhance the development of advanced tyre compounds, optimizing their performance and durability through informed design choices based on molecular insights. Declarations We confirmed our findings for SBR-resin system using AFM experiments in a similar manner as done for polymer-polymer systems, shown in Fig. 7 . As high degree of uniformity in the surface for SBR-DCPD and SBR-PF shows that they in well mixed and compatible with each other. The SBR-C9 system shows an uneven distribution of components, indicating a lower compatibility. In SBR-C5 system, a clear distinction between the two components can be seen. This shows a localization of the two entities within the system, where they prefer a phase-separated behavior. This entire experimental observation of SBR-resin systems is in good correlation with the solubility parameter values obtained from molecular dynamics simulations. Overall, the varying degrees of compatibility among these resin systems arise from their structural and chemical differences and SBR-DCPD system is the most compatible system among all the polymer-resin systems investigated. In this work, we have performed MD simulation for different pairs if polymers from the commonly used polymers in tyres such as, Natural Rubber (NR), Butadiene Rubber (BR), Styrene-Butadiene Rubber (SBR), and Isobutylene-Isoprene Rubber (IIR) as well as compatibility of these polymers with commonly used resins such as dicyclopentadiene (DCPD), phenolic resin (PF), and C9 and C5 resins. Our approach involved analyzing these materials both as pure systems and in binary combinations, focusing on polymer-polymer and polymer-resin compatibility through molecular dynamics simulations. To establish a standardized baseline for our chemical parameters, we first simulated the pure systems, which yielded polymer densities that closely match those reported in the literature. This validation ensured the accuracy of the force-field parameters and directed towards our subsequent modeling of binary systems, allowing us to effectively explore and understand their compatibility behaviors. In examining the binary mixtures, we identified that the interplay of molecular-level non-bonded interactions-such as π-π stacking, polar and non-polar interactions, and steric effects have an underlying role in determining the compatibility of the two components. This compatibility is quantified through the solubility parameter ( δ ), with higher values indicating greater likelihood of miscibility. Among all the polymer pairs studied, the compatibility trend is SBR-NR > SBR-BR > BR-NR > BR-IIR > SBR-IIR > NR-IIR and for polymer-resin systems compatibility trend with SBR/BR/NR rubbers is DCPD > PF > C9 > C5. Additionally, we characterized the compatibility through Atomic Force Microscopy (AFM) experiments, which well supported our simulation findings. The alignment of our simulation results with experimental data reinforces the reliability of our modeling approach, suggesting that our computational framework is robust and accurate. Looking ahead, these molecular simulations will facilitate a deeper understanding of the intricate interactions within multi-component systems, particularly the forces that govern compatibility in tyre materials which in turn will help to select most suitable polymers or resins through MD simulations. By minimizing the need for extensive physical trials, these models enable us to save time and costs associated with experimental work while also predicting innovative recipe designs in material formulation. This research has the potential to significantly enhance the development of advanced tyre compounds, optimizing their performance and durability through informed design choices based on molecular insights. References L. Wang and S. Zhao, “Study on the structure-mechanical properties relationship and antistatic characteristics of SSBR composites filled with SiO2/CB,” Journal of Applied Polymer Science , Vol. 118, 2010, pp. 338–345. S. K. Peddini, C. P. Bosnyak, N. M. Henderson, C. J. Ellison, and D. R. Paul, “Nanocomposites from styrene-butadiene rubber (SBR) and multiwall carbon nanotubes (MWCNT) part 1: Morphology and rheology,” Polymer (Guildford) , Vol. 55, 2014, pp. 258–270. C. H. Shin and D. S. Kim, “Effects of rubber type on the curing and physical properties of silica-filled rubber compounds,” Polymer Advances in Technology , Vol. 19, 2008, pp. 1062–1068. Y.-X. Wang, Y.-P. Wu, W.-J. Li, and L.-Q. Zhang, “Influence of filler type on wet skid resistance of SSBR/BR composites: Effects from roughness and micro-hardness of rubber surface,” Applied Surface Science , Vol. 257, 2011, pp. 2058–2065. P. Sae-oui, K. Suchiva, U. Thepsuwan, W. Intiya, P. Yodjun, and C. Sirisinha, “Effects of blend ratio and SBR type on properties of silica-filled SBR/NR tire tread compounds,” Rubber Chemistry and Technology , Vol. 89, 2016, pp. 240–250. J. Jin, J. W. M. Noordermeer, A. Blume, and W. K. Dierkes, “Effect of SBR/BR elastomer blend ratio on filler and vulcanization characteristics of silica-filled tire tread compounds,” Polymer Testing , Vol. 99, 2021, p. 107212. C. H. Kang and I. Y. Park, “Rubber composition for tire tread and tire manufactured by using the same,” U.S. Patent No. US9624361B2, 2017. A. J. Marzocca, S. Cerveny, and J. M. Méndez, “Some considerations concerning the dynamic mechanical properties of cured styrene–butadiene rubber/polybutadiene blends,” Polymer International , Vol. 49, 2000, pp. 216–222. S. Abbas and T. Alaa, “Effect of the Tires Crumb Rubber Loading Levels on NR/SBR Compounding Properties for Antibacterial Applications,” unpublished. S. Tang et al., “Natural Rubber/Styrene–Butadiene Rubber Blend Composites Potentially Applied in Damping Bearings,” Polymers (Basel) , Vol. 16, 2024, p. 1945. H.-T. Chiu and P.-A. Tsai, “Aging and mechanical properties of NR/BR blends,” Journal of Materials Engineering and Performance , Vol. 15, 2006, pp. 88–94. J.-C. Li et al., “Development of high damping natural rubber/butyl rubber composites compatibilized by isobutylene-isoprene block copolymer for isolation bearing,” Express Polymer Letters , Vol. 13, 2019, pp. 686–696. S. H. El-Sabbagh, M. N. Ismail, D. S. Mahmoud, and A. A. Yehia, “Investigation of natural rubber compatibility with different types of butyl rubber,” Egyptian Journal of Chemistry , Vol. 66, 2023, pp. 309–321. M. M. Eissa, S. H. Botros, and A. F. Moustafa, “Effect of triblock copolymers on homogeneity, mechanical properties and swelling behavior of IIR/SBR rubber blends,” Polymer Bulletin , Vol. 74, 2017, pp. 393–412. “Hydrogenated Hydrocarbon Resins (HHCR),” Buss-CT , Available at: www.buss-ct.com. Accessed: 2024. L. Yu, H. Colvin, J. J. Rosmus, T. E. Calabrese, and L. A. Benvenuti, “Compatibility study of hydrocarbon resins with rubber compounds for tire applications,” Rubber Chemistry and Technology , Vol. 97, 2024, pp. 145–161. S. Sugihara, “Petroleum Resin,” in Encyclopedia of Polymeric Nanomaterials , S. Kobayashi and K. Müllen, Eds., Springer, Berlin Heidelberg, 2021, pp. 1–6. C. A. Thomas and W. H. Carmody, “Synthetic Resins from Petroleum Hydrocarbons,” Industrial & Engineering Chemistry , Vol. 24, 1932, pp. 1125–1128. H.-S. Park and Y.-S. So, “KR20160131149A,” South Korea: Korean Intellectual Property Office, 2016. J. Liang, S. Chang, and N. Feng, “Effect of C5 petroleum resin content on damping behavior, morphology, and mechanical properties of BIIR/BR vulcanizates,” Journal of Applied Polymer Science , Vol. 130, 2013, pp. 510–515. P. Weng, Z. Tang, and B. Guo, “Solving 'magic triangle' of tread rubber composites with phosphonium-modified petroleum resin,” Polymer (Guildford) , Vol. 190, 2020, p. 122244. Y. Guo, J. Liu, Y. Lu, D. Dong, W. Wang, and L. Zhang, “A combined molecular dynamics simulation and experimental method to study the compatibility between elastomers and resins,” RSC Advances , Vol. 8, 2018, pp. 14401–14413. Z. Li, C. Yang, F. Zhao, Y. Wei, and S. Liao, “Molecular dynamics simulation of the influence of the trans-structure in the molecular chain structure of natural rubber on its tensile stress,” Available at: https://doi.org/10.21203/rs.3.rs-981216/v1. Accessed 2021. Y. Ma et al., “Molecular dynamic and dissipative particle dynamic simulation on the miscibility of NR/CR blends,” Polymers (Basel) , Vol. 15, 2023, p. 856. M. Gao, Y. Chen, C. Fan, and M. Li, “Molecular dynamics study on the compatibility of asphalt and rubber powder with different component contents,” ACS Omega , Vol. 7, 2022, pp. 36157–36164. Q. H. Zeng, A. B. Yu, and G. Q. Lu, “Multiscale modeling and simulation of polymer nanocomposites,” Progress in Polymer Science , Vol. 33, 2008, pp. 191-269. Y. Adamu, T. Kolawole Bello, M. Tijani Isa, and U. Shehu, “Computational dynamics study for polymer blend of polystyrene, polypropylene, and natural rubber,” The Islamic University Journal of Applied Sciences , Vol. 4, 2022., pp. 1-16. A. N. Rissanou and V. Harmandaris, “Dynamics of various polymer-graphene interfacial systems through atomistic molecular dynamics simulations,” Soft Matter , Vol. 10, 2014, pp. 2876–2888. Y. Li, Y. Wu, Y. Luo, T. W. Chan, L. Zhang, and S. Wu, “A combined experimental and molecular dynamics simulation study on the structures and properties of three types of styrene butadiene rubber,” Materials Today Communications , Vol. 4, 2015, pp. 35–41. JSOL Inc., J-OCTA 2017 , Accessed: 2017. W. L. Jorgensen, D. S. Maxwell, and J. Tirado-Rives, “Development and testing of the OPLS all-atom force field on conformational energetics and properties of organic liquids,” Journal of the American Chemical Society , Vol. 118, 1996, pp. 11225–11236. D. Van Der Spoel, E. Lindahl, B. Hess, G. Groenhof, A. E. Mark, and H. J. C. Berendsen, “GROMACS: Fast, flexible, and free,” Journal of Computational Chemistry , Vol. 26, 2005, pp. 1701–1718. H. J. C. Berendsen, D. van der Spoel, and R. van Drunen, “GROMACS: A message-passing parallel molecular dynamics implementation,” Computational Physics Communications , Vol. 91, 1995, pp. 43–56. E. Lindahl, B. Hess, and D. van der Spoel, “GROMACS 3.0: A package for molecular simulation and trajectory analysis,” Journal of Molecular Modeling , Vol. 7, 2001, pp. 306–317. G. Bussi, D. Donadio, and M. Parrinello, “Canonical sampling through velocity rescaling,” Journal of Chemical Physics , Vol. 126, 2007, p. 14101. H. J. C. Berendsen, J. P. M. Postma, W. F. van Gunsteren, A. DiNola, and J. R. Haak, “Molecular dynamics with coupling to an external bath,” Journal of Chemical Physics , Vol. 81, 1984, pp. 3684–3690. P. P. Ewald, “The calculation of optical and electrostatic grid potential,” Annalen der Physik (Leipzig) , Vol. 64, 1921, pp. 253–287. W. Humphrey, A. Dalke, and K. Schulten, “VMD - Visual Molecular Dynamics,” Journal of Molecular Graphics , Vol. 14, 1996, pp. 33–38. S. Venkatram, C. Kim, A. Chandrasekaran, and R. Ramprasad, “Critical assessment of the Hildebrand and Hansen solubility parameters for polymers,” Journal of Chemical Information and Modeling , Vol. 59, 2019, pp. 4188–4194. X. Chen, C. Yuan, C. K. Y. Wong, and G. Zhang, “Molecular modeling of temperature dependence of solubility parameters for amorphous polymers,” Journal of Molecular Modeling , Vol. 18, 2012, pp. 2333–2341. K. B. Abdan, S. C. Yong, E. C. W. Chiang, R. A. Talib, T. C. Hui, and L. C. Hao, “Chapter 6 - Barrier properties, antimicrobial and antifungal activities of chitin and chitosan-based IPNs, gels, blends, composites, and nanocomposites,” in Handbook of Chitin and Chitosan , S. Gopi, S. Thomas, and A. Pius, Eds., Elsevier, 2020, pp. 175–227. R. B. Nandeti, S. Bhadra, V. Bansal, S. Goyal, S. Nair, and N. K. Singha, “Estimating the compatibility and interaction parameter in various polymer blends by molecular dynamics simulation with J-octa,” International Rubber Conference , Bangalore, 2022. Additional Declarations The authors declare no competing interests. Cite Share Download PDF Status: Posted Version 1 posted 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. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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-6957788","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":475245072,"identity":"25c579e3-835a-4b29-800d-07a89771e3e7","order_by":0,"name":"Arpita Srivastava","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA+klEQVRIiWNgGAWjYBACCTBpwMDAxt588MEHBhCDOC0GDHw8x5INZ4C0MBOlBWiNnESOmTQPiE1Ii+S0w88+FxT8kWeTyDGQtvm1TZ6PmYHxw8cc3FqkpdOMZ88wMDBs43lWYJzbd9uwjZmBWXLmNtxa5KQTjJl5DAwY29iTNyTn9txmBGphY+bFqyX9M0iLfRtDgsFhy57b9gS1SEvngG1JbONIMWxm+HE7kaAWydk5xcwzDIyT24CBzNjbcDu5jZmxGa9fJG6nb2Yu+CNnO7+9+fiPH39ugxgHP3zEowUEEBHB2AYmG/CrR9HC8Ieg4lEwCkbBKBiBAABY2UnNJ6ZCMwAAAABJRU5ErkJggg==","orcid":"https://orcid.org/0000-0002-8022-7090","institution":"CEAT Ltd","correspondingAuthor":true,"prefix":"","firstName":"Arpita","middleName":"","lastName":"Srivastava","suffix":""},{"id":475245073,"identity":"5b89b4d9-c3ff-4d3e-b8b1-d98964c861e5","order_by":1,"name":"Debabrata Ganguly","email":"","orcid":"","institution":"CEAT Ltd","correspondingAuthor":false,"prefix":"","firstName":"Debabrata","middleName":"","lastName":"Ganguly","suffix":""},{"id":475245074,"identity":"784a7620-d368-4904-a005-05bc29c5ca89","order_by":2,"name":"Anubhav Kumar","email":"","orcid":"","institution":"CEAT Ltd","correspondingAuthor":false,"prefix":"","firstName":"Anubhav","middleName":"","lastName":"Kumar","suffix":""},{"id":475245075,"identity":"0c4e3ff3-f2b8-4f44-ac41-cff049c8eb4c","order_by":3,"name":"Sharad Goyal","email":"","orcid":"","institution":"CEAT Ltd","correspondingAuthor":false,"prefix":"","firstName":"Sharad","middleName":"","lastName":"Goyal","suffix":""},{"id":475245076,"identity":"58534959-ea11-440b-8e84-705272d3990e","order_by":4,"name":"Sambhu Bhadra","email":"","orcid":"","institution":"CEAT Ltd","correspondingAuthor":false,"prefix":"","firstName":"Sambhu","middleName":"","lastName":"Bhadra","suffix":""},{"id":475245077,"identity":"0d22baab-4627-4be9-8156-fad5ef5d0991","order_by":5,"name":"Sujith Nair","email":"","orcid":"","institution":"CEAT Ltd.","correspondingAuthor":false,"prefix":"","firstName":"Sujith","middleName":"","lastName":"Nair","suffix":""},{"id":475245078,"identity":"91b2032f-96a6-489a-95b3-54fa83781615","order_by":6,"name":"Renji Issac","email":"","orcid":"","institution":"CEAT Ltd.","correspondingAuthor":false,"prefix":"","firstName":"Renji","middleName":"","lastName":"Issac","suffix":""}],"badges":[],"createdAt":"2025-06-23 14:30:38","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-6957788/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6957788/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":85319117,"identity":"8be620f7-4e82-467e-86c8-9ef27c98789c","added_by":"auto","created_at":"2025-06-24 14:59:14","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":149550,"visible":true,"origin":"","legend":"\u003cp\u003eChemical structures of the polymers- NR, BR, SBR and IIR and the resins- DCPD, PF, C9 and C5 studied in this work.\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-6957788/v1/51d9cdd70e2e5f09183746dc.png"},{"id":85318206,"identity":"f2d5ef68-7e10-443b-99ef-e10209e73f57","added_by":"auto","created_at":"2025-06-24 14:51:14","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":44005,"visible":true,"origin":"","legend":"\u003cp\u003eTime evolution of density of pure polymeric systems to monitor equilibration in the systems.\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-6957788/v1/af7b783313aec25b579ded20.png"},{"id":85319410,"identity":"ff96660a-b79f-4933-82aa-cfe229ca5d0f","added_by":"auto","created_at":"2025-06-24 15:07:14","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":87775,"visible":true,"origin":"","legend":"\u003cp\u003eHildebrand’s solubility parameter (δ) for six different mixed polymeric systems.\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-6957788/v1/91fc9fdb58c9df047827b350.png"},{"id":85319124,"identity":"5d4ac518-c806-498f-8574-ea64c11a6db9","added_by":"auto","created_at":"2025-06-24 14:59:14","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":694103,"visible":true,"origin":"","legend":"\u003cp\u003eComparison of experimentally determined surface maps from AFM shows high uniformity in SBR-NR, , SBR-BR and BR-NR systems, moderate uniformity in BR-IIR and SBR-IIR system and completely non-uniform surface in NR-IIR system signifying high to moderate to least compatibility which is similar to the theoretically determined values of solubility parameter.\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-6957788/v1/cb5cdfef9ce4d584c8fe2196.png"},{"id":85318210,"identity":"04597d65-5302-48e1-a46c-ce67e49e6c13","added_by":"auto","created_at":"2025-06-24 14:51:14","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":63659,"visible":true,"origin":"","legend":"\u003cp\u003eThe solubility parameter lowering with an increase in the temperature from 300 K to 373 K to 433 K.\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-6957788/v1/c56d85fc1096f74cee89b47c.png"},{"id":85318215,"identity":"1b229160-b107-41b0-877e-948a28e36f92","added_by":"auto","created_at":"2025-06-24 14:51:14","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":91289,"visible":true,"origin":"","legend":"\u003cp\u003eHildebrand’s solubility parameter (δ) for twelve different mixed polymer-resin systems.\u003c/p\u003e","description":"","filename":"6.png","url":"https://assets-eu.researchsquare.com/files/rs-6957788/v1/3e36cac1b2d1046cf7c9adaa.png"},{"id":85318219,"identity":"8c0dc543-7bda-4cba-adf0-99793354f3c9","added_by":"auto","created_at":"2025-06-24 14:51:14","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":437559,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cem\u003eComparison of experimentally determined adhesion from AFM shows high uniformity in SBR system in presence of DCPD and PF resins which lowers in case of C9 system and becomes least in presence of C5 resin determining high to low compatibility of SBR with these resins- similar to that obtained in simulations.\u003c/em\u003e\u003c/p\u003e","description":"","filename":"7.png","url":"https://assets-eu.researchsquare.com/files/rs-6957788/v1/d4993bcba30b1d977c8a9000.png"},{"id":85320605,"identity":"08feb956-ce41-4749-b6b4-d39a40548135","added_by":"auto","created_at":"2025-06-24 15:23:16","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2132264,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6957788/v1/eed137db-c6ce-470f-be26-e6a16e42022f.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003eDetermination of Compatibility in Polymer-Polymer and Polymer-Resin Systems through Molecular Dynamics Simulations\u003c/p\u003e","fulltext":[{"header":"Introduction","content":"\u003cp\u003eHomogenous mixing in tyre matrix improves thermodynamic mechanical properties like flex, heat build-up, crack abrasion and durability. If two polymers and/or polymer-resin system is compatible, it will lead to homogenous composite matrix, giving improved properties and less failure due to separation among components [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e], [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e], [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e]. By improving rubber compatibility, manufacturers can develop tyre blends that not only improve performance but also extend longevity and reduce fuel consumption due to less heat build-up, ultimately leading to safer and more efficient tyres. Rubber blend technology is a key area of focus for tyre technologists, particularly the combinations of Styrene-Butadiene Rubber (SBR) with Butadiene Rubber (BR) or Natural Rubber (NR) [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e],[\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e], [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e]. Research has shown that incorporating BR into the tyre tread compound can significantly enhance wear resistance, thereby improving overall performance and longevity. This advancement highlights the importance of selecting and optimizing rubber blends to meet the demanding requirements of modern tyres. SBR-BR blends play a crucial role in high-performance tyres, primarily used in tread [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e],[\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e]. This combination leverages the strengths of both materials, offering enhanced abrasion resistance and improved wet traction. By optimizing this blend, manufacturers can create tyres that perform effectively in both dry and wet conditions, thereby enhancing safety [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eSBR-NR blends are commonly used in the tread area of tyres due to their excellent balance of elasticity, wear resistance, and grip [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e][\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e][\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e]. Natural Rubber (NR) provides superior traction and flexibility, while Styrene-Butadiene Rubber (SBR) enhances durability and resistance to aging. This combination is particularly effective in achieving optimal performance across various driving conditions, ensuring that tyres maintain grip and resilience. BR-NR blends are utilized in both the tread and sidewall areas, where superior resilience and dynamic properties are necessary. Butadiene Rubber (BR) enhances the tyre's ability to absorb shocks and maintain structural integrity under stress, while NR contributes to overall grip. This compatibility is vital for tyres that need to perform reliably in demanding conditions [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eApart from tread and sidewalls which are majorly composed of NR, BR and SBR, the inner liners of tubeless tyres play a crucial role in maintaining air pressure, which is vital for performance, fuel efficiency, and longevity. Various rubber blends are employed in these liners to enhance their effectiveness, particularly Isobutylene-Isoprene Rubber (IIR) in combination with other rubber types [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e][\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e], [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e]. Understanding compatibility between SBR/BR/NR with butyl is also essential to obtain better adhesion between tyre inner liner and transition liner. Ensuring compatibility helps mitigate safety risks associated with issues like layer separation. As the tyre industry faces increasing pressures for innovation and sustainability, compatibility studies pave the way for exploring new material combinations that can enhance performance while adhering to regulatory standards.\u003c/p\u003e \u003cp\u003eApart from these rubbers, resins are essential in tyre formulations as they enhance adhesion between rubber and reinforcing materials, improve grip on various surfaces, and reduce hysteresis loss, leading to better fuel efficiency[\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e]. Rubber in tyres exhibits viscoelastic properties, combining elasticity and viscosity, which affects energy recovery during rotation. Incompatible materials may cause more hysteresis loss or heat build-up, increasing tyre failure, rolling resistance and decreasing overall fuel efficiency, while also playing a key role in grip performance. The integration of hydrocarbon resins into rubber compounds can significantly alter their performance attributes, including traction in wet conditions and rolling resistance [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e]. The degree to which these properties are optimized depends largely on the compatibility between the resin and the rubber matrix. When resins do not blend well, they may cause an undesirable increase in the damping response, leading to higher rolling resistance. On the other hand, when compatibility is achieved, it allows for enhanced wet grip without compromising rolling efficiency. Lower molecular weight and similar structural features to rubber polymers often facilitate this compatibility, ensuring a more effective blend [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e] [\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eThe use of dicyclopentadiene (DCPD) and phenolic (PF) resins has become increasingly important in enhancing these properties. It is reported that DCPD-modified phenolic resins optimize the viscoelastic behavior of rubber compounds, improving traction on both wet and dry surfaces while increasing resistance to chips and cuts[\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e]. Achieving this balance is essential for developing high-performance tyres that ensure safety and efficiency across diverse driving conditions. Other synthetic resins, C9 and C5 are well reported for their significant contribution in enhancing the mechanical properties and damping performance of rubber vulcanizates [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e], [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e]. Addition of C5/C9 petroleum resins has shown to enhance the wet traction in tread compositions of passenger cars [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e]. This increasing demand in upgrading the tyre performance calls for a detailed study in a comprehensive manner to understand the driving forces regulating the compatibility between tyre components, which, in turn may guide for a better formulation for an improved performance.\u003c/p\u003e \u003cp\u003eMolecular simulation is one such rising technique for investigating both the compatibility and the properties of materials at the microstructural level without using expensive equipment and complicated experiments. In particular, atomistic molecular dynamics (MD) simulations are invaluable, as they offer detailed quantitative insights into the intrinsic characteristics of materials, including their mechanical, thermal, and chemical properties, as well as their dynamic behavior over time. Researchers increasingly rely on MD simulations to complement experimental work, especially in the study of polymers and their composites [\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e]. These simulations allow for a deeper exploration of how different components interact at the molecular level, providing a clearer picture of compatibility between materials [\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e] [\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e]. By assessing factors such as phase separation, diffusion, and mechanical stress responses, MD simulations can reveal potential challenges and synergies in material combinations [\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e], [\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e] [\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e]. The results from these simulations indicate that, when conducted with appropriate methodologies, the findings closely align with those observed in experimental samples [\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e]. This correspondence enhances our understanding of how molecular interactions influence both compatibility and overall properties, guiding the development of more effective materials for various applications .\u003c/p\u003e \u003cp\u003eThe aim of this research is to build molecular dynamics simulation model to determine the compatibility between two polymers chosen from the commonly used polymers in tyres such as NR, BR, SBR and IIR as well as compatibility of these polymers with various petroleum resins, including dicyclopentadiene (DCPD), phenolic resin (PF), and branched C9 and C5 hydrocarbon resins. Our initial step involved validating chemical parameters to ensure that the polymer densities we calculated were consistent with existing literature. In our investigation, we discovered that an interplay of various non-bonded interactions plays a pivotal role in determining the compatibility of polymer-polymer and polymer-resin mixtures. By analyzing these interactions, we assessed compatibility through Hildebrand\u0026rsquo;s solubility parameter (δ), derived from our molecular dynamics simulations. To further validate our findings, we conducted Atomic Force Microscopy (AFM) experiments, which corroborated our simulation results, providing a comprehensive understanding of how these materials behave together at the molecular level. The strong alignment between our computational and experimental data emphasizes the reliability of our approach.\u003c/p\u003e"},{"header":"Methodology","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003eComputational Modeling\u003c/h2\u003e \u003cp\u003eIn this study, we conducted all-atom molecular dynamics (MD) simulations on rubber polymer and resin systems pertinent to tyre applications. Our primary objective was to understand the compatibility between two-component systems and how temperature influences polymer interactions. The polymers under investigation include Natural Rubber (NR), Butadiene Rubber (BR), Styrene-Butadiene Rubber (SBR), and Butyl Rubber (IIR). Their respective molecular weights are detailed in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e.\u003c/p\u003e \u003cp\u003eTo explore compatibility, we simulated these polymers both as pure systems and in mixtures at a 50/50 wt./wt. ratio. This approach allows us to assess the interactions between different polymer components and their ability to blend effectively. Furthermore, this work delves into the compatibility of polymers (NR, BR, and SBR) with various resins, namely Dicyclopentadiene (DCPD), Phenol Formaldehyde (PF) and two branched resins, C9 and C5. The chemical structures of all the molecules studied are presented in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, offering a visual reference for their structural properties.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe simulations of pure polymers, as well as the two-component systems comprised of polymer-polymer and polymer-resin combinations, are conducted at a temperature of 300 K. To further investigate the effects of temperature on polymer interactions, we conducted additional simulations at elevated temperatures of 373 K and 433 K for the polymer mixtures. This temperature variation is crucial for understanding how thermal conditions impact the compatibility and performance of rubber formulations in practical applications. Furthermore, the compatibility between all the binary mixtures is validated by Atomic Force Microscopy (AFM) experiments which measure the phase behavior of the mixtures.\u003c/p\u003e \u003cp\u003eOverall, our research aims to provide a comprehensive understanding of the interactions within polymer-polymer and polymer-resin systems, contributing valuable insights for the development of more effective materials in tyre manufacturing and related industries.\u003c/p\u003e \u003c/div\u003e\n\u003ch3\u003eSimulation details\u003c/h3\u003e\n\u003cp\u003eThe initial configuration of the above polymers units is drawn in J\u0026thinsp;\u0026minus;\u0026thinsp;OCTA [\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e] followed by molecular mechanics (MM) calculations using OPLS-AA [\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e] force-field. Next, the final configuration of each polymer is used to simulate both pure and mixed component systems. First, we simulated pure polymeric systems having 100 chains of each polymer, randomly inserted in a cubical box. The box dimensions are presented in Table \u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. The simulations of all the systems are carried out using GROMACS [\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e], [\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e], [\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e]. In molecular dynamics, total potential energy in the system is a sum of bonded and non-bonded potential energy,\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$\\:{U}_{total}={U}_{bonded}+{U}_{non-bonded}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eThe bonded potential energy (\u003cem\u003eU\u003c/em\u003e\u003csub\u003e\u003cem\u003ebonded\u003c/em\u003e\u003c/sub\u003e) is caused by the vibrations in bond length, bond angle and dihedrals whereas the non-bonded terms (\u003cem\u003eU\u003c/em\u003e\u003csub\u003e\u003cem\u003enon\u0026minus;bonded\u003c/em\u003e\u003c/sub\u003e\u003cem\u003e)\u003c/em\u003e arise from Coulombic interactions and van der Waals interactions, modeled by 12\u0026thinsp;\u0026minus;\u0026thinsp;6 type Lennard Jones interactions. Their functional forms are given as,\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$$\\:{U}_{bonded}=\\:\\frac{1}{2}\\sum\\:{k}_{b}{\\left(r-{r}_{0}\\right)}^{2}\\:+\\:\\frac{1}{2}\\sum\\:{k}_{\\theta\\:}{\\left(\\theta\\:-{\\theta\\:}_{0}\\right)}^{2}+\\:\\sum\\:\\frac{{V}_{n}}{2}\\left[1+\\text{cos}\\left(n\\varphi\\:-\\gamma\\:\\right)\\right]$$\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$$\\:{U}_{non-bonded}=\\:\\sum\\:_{i\u0026lt;j}\\left[\\frac{{q}_{i}{q}_{j}}{4\\pi\\:{ϵ}_{0}{r}_{ij}}\\right]+\\:\\sum\\:_{i\u0026lt;j}\\left[4{ϵ}_{ij}\\left\\{{\\left(\\frac{{\\sigma\\:}_{ij}}{{r}_{ij}}\\right)}^{12}-{\\left(\\frac{{\\sigma\\:}_{ij}}{{r}_{ij}}\\right)}^{6}\\right\\}\\right]\\:$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e3\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eIn the above equations, the force constant for bond stretching is represented by \u003cem\u003ek\u003c/em\u003e\u003csub\u003e\u003cem\u003eb\u003c/em\u003e\u003c/sub\u003e whereas \u003cem\u003er\u003c/em\u003e denotes the bond length and \u003cem\u003er\u003c/em\u003e\u003csub\u003e\u003cem\u003e0\u003c/em\u003e\u003c/sub\u003e​ signifies the equilibrium bond length. For angle bending, \u003cem\u003ek\u003c/em\u003e\u003csub\u003e\u003cem\u003eθ\u003c/em\u003e\u003c/sub\u003e is the force constant, \u003cem\u003eθ\u003c/em\u003e refers to the bond angle, and \u003cem\u003eθ\u003c/em\u003e\u003csub\u003e\u003cem\u003e0\u003c/em\u003e\u003c/sub\u003e​ indicates the equilibrium bond angle. In the dihedral angle term, \u003cem\u003eV\u003c/em\u003e\u003csub\u003e\u003cem\u003en\u003c/em\u003e\u003c/sub\u003e represents the amplitude of the \u003cem\u003en\u003c/em\u003e\u003csup\u003e\u003cem\u003eth\u003c/em\u003e\u003c/sup\u003e Fourier component, \u003cem\u003en\u003c/em\u003e specifies the periodicity of the dihedral angle, \u003cem\u003eϕ\u003c/em\u003e denotes the dihedral angle, and γ stands for the phase angle. Regarding non-bonded interactions, \u003cem\u003er\u003c/em\u003e\u003csub\u003e\u003cem\u003eij\u003c/em\u003e\u003c/sub\u003e​ represents the distance between atoms \u003cem\u003ei\u003c/em\u003e and \u003cem\u003ej\u003c/em\u003e, \u003cem\u003eq\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e​ and \u003cem\u003eq\u003c/em\u003e\u003csub\u003e\u003cem\u003ej\u003c/em\u003e\u003c/sub\u003e are charges on atoms \u003cem\u003ei\u003c/em\u003e and \u003cem\u003ej\u003c/em\u003e and \u003cem\u003eϵ\u003c/em\u003e\u003csub\u003e\u003cem\u003e0\u003c/em\u003e\u003c/sub\u003e​ signifies the permittivity of free space. \u003cem\u003eϵ\u003c/em\u003e\u003csub\u003e\u003cem\u003eij\u003c/em\u003e\u003c/sub\u003e​ is the depth of the potential well in the Lennard-Jones potential for atoms \u003cem\u003ei\u003c/em\u003e and \u003cem\u003ej\u003c/em\u003e, while \u003cem\u003eσ\u003c/em\u003e\u003csub\u003e\u003cem\u003eij\u003c/em\u003e\u003c/sub\u003e​ is the finite distance at which the inter-particle potential reaches zero.\u003c/p\u003e \u003cp\u003eAll systems are energy-minimized and simulated in an NVT [\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e] ensemble for 1 ns at 300 K using a velocity-rescale thermostat to reach thermal equilibrium. Once the desired temperature is reached, NPT [\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e], [\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e] simulations are conducted for 10 ns at 1 bar pressure. The temperature and pressure of the systems are held constant velocity-rescale thermostat and Berendsen barostat with a coupling constant of 1.0 ps respectively. An integration timestep of 2 fs is followed in all the cases. The electrostatic interactions are treated with the PME [\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e] method while the van der Waals interactions are computed using cut-off method. The non-bonded interactions are cutoff at 1 nm. The convergence of the systems is confirmed by monitoring their total potential energy and density. Following this, a series of simulations are performed for mixed component systems considering a combination of two polymers in each system and along with polymer-resin combinations using the same simulation parameters as in the pure systems.\u003c/p\u003e \u003cp\u003eThe effect of heating on the mixed polymeric systems from 300 K to 373 K to 433 K is done by using simulated-annealing method with a scan rate of 20 K ns\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e in an NVT ensemble. Once the desired temperature is reached, 1 ns NVT simulation and 10 ns NPT simulations are conducted at both 373 K and 433 K to measure the compatibility. All other simulation protocols followed for each of the systems using the above three approaches are same as that for the pure systems.\u003c/p\u003e \u003cp\u003eOnce the systems are equilibrated, the final configurations are visualized in VMD [\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e] and Hildebrand\u0026rsquo;s solubility parameter (δ) [\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e],[\u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e40\u003c/span\u003e] is computed to identify the compatibility between various polymeric mixtures. The Hildebrand solubility parameter (δ) is a critical concept in polymer science and materials chemistry that provides insight into the compatibility of different materials, particularly polymers and solvents. It is defined as the square root of the cohesive energy density (CED) [\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e41\u003c/span\u003e], which reflects the energy required to create a cavity in a solvent for a solute molecule. The solubility parameter can be expressed mathematically as:\u003cdiv id=\"Equ4\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ4\" name=\"EquationSource\"\u003e\n$$\\:{\\delta\\:}_{AB}=\\sqrt{\\frac{{E}_{coh}}{{V}_{m}}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e4\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere δ is the Hildebrand solubility parameter (in (J/cm\u0026sup3;)\u003csup\u003e1/2\u003c/sup\u003e), E\u003csub\u003ecoh\u003c/sub\u003e is the cohesive energy (in J/cm\u0026sup3;) and V\u003csub\u003em\u003c/sub\u003e is the molar volume (in cm\u0026sup3;/mol). In the context of solubility, the cohesive energy density (CED) is defined as,\u003cdiv id=\"Equ5\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ5\" name=\"EquationSource\"\u003e\n$$\\:CED=\\frac{{E}_{coh}}{{V}_{m}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e5\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eIn this work, we use the Hildebrand solubility parameter to quantify the compatibility of various polymer-polymer and polymer-resin systems. By comparing the solubility parameters of the components, we can predict their miscibility and enhance our understanding of their interactions in the context of tyre applications. To validate the compatibility obtained from the simulation models, we also compared the results with AFM experiments. The experimental results are in good agreement with the simulations, validating the suitability of our models.\u003c/p\u003e\n\u003ch3\u003eExperimental methodology\u003c/h3\u003e\n\u003cp\u003eThe respective rubbers and resins were mixed in the ratio of 50:50 wt/wt in a HAAKE internal mixer employing a mixing temperature of 130\u003csup\u003eo\u003c/sup\u003eC. The mixed compound is dumped from the internal mixer after mixing for 10 mins at 60 rpm are sheeted out using a two-roll mill. The compounds are then pressed in between two plates to form thin sheets to conduct different experiments. The AFM studies were conducted using Bruker Multimode 8 AFM employing contact mode and the surface morphologies were captured and compared along with the simulation results.\u003c/p\u003e"},{"header":"Results and Discussion","content":"\u003cp\u003eIn the initial phase of our modeling approach, we focused on simulating pure polymer systems to establish a foundational understanding of their behavior. During these simulations, we allowed the simulated box to reach a state of equilibrium, which is crucial for obtaining reliable data. The time evolution of the density for each of the pure polymer systems is depicted in Figure 2, which illustrates a clear convergence towards a stable density value over the simulation period. To quantify this convergence, we computed the average density for the last 5 ns of the simulation for each polymer. These averaged density values are presented in Table 1. The results obtained from our simulations demonstrate reasonable agreement with values reported in the literature, indicating that our modeling approach and force-field parameters are appropriate and effective.\u003c/p\u003e\n\u003cp\u003eTable 1: Details of molecular weights of polymer compositions, size of cubical box, density obtained from simulations and comparison from the density provided in literature .\u003c/p\u003e\n\u003ctable border=\"1\" cellspacing=\"0\" cellpadding=\"0\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 78px;\"\u003e\n \u003cp\u003ePolymer\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 80px;\"\u003e\n \u003cp\u003eMolecular Weight\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 77px;\"\u003e\n \u003cp\u003eBox Size (nm)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd colspan=\"2\" valign=\"top\" style=\"width: 163px;\"\u003e\n \u003cp\u003eDensity (kg/m\u003csup\u003e3\u003c/sup\u003e)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 78px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 80px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 77px;\"\u003e\n \u003cp\u003e\u0026nbsp;\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 85px;\"\u003e\n \u003cp\u003eSimulation\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 78px;\"\u003e\n \u003cp\u003eLiterature\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 78px;\"\u003e\n \u003cp\u003eNR\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 80px;\"\u003e\n \u003cp\u003e682.06\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 77px;\"\u003e\n \u003cp\u003e9.0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 85px;\"\u003e\n \u003cp\u003e0.87\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 78px;\"\u003e\n \u003cp\u003e0.92\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 78px;\"\u003e\n \u003cp\u003eBR\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 80px;\"\u003e\n \u003cp\u003e570.99\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 77px;\"\u003e\n \u003cp\u003e9.0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 85px;\"\u003e\n \u003cp\u003e0.87\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 78px;\"\u003e\n \u003cp\u003e0.91-0.92\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 78px;\"\u003e\n \u003cp\u003eSBR\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 80px;\"\u003e\n \u003cp\u003e829.35\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 77px;\"\u003e\n \u003cp\u003e11.5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 85px;\"\u003e\n \u003cp\u003e0.96\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 78px;\"\u003e\n \u003cp\u003e0.94\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 78px;\"\u003e\n \u003cp\u003eIIR\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 80px;\"\u003e\n \u003cp\u003e603.16\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 77px;\"\u003e\n \u003cp\u003e8.0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 85px;\"\u003e\n \u003cp\u003e0.87\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 78px;\"\u003e\n \u003cp\u003e0.90\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n\u003c/table\u003e\n\u003cp\u003eThis validation step is essential as it confirms the feasibility of our model. By ensuring that the simulated densities align well with established data, we can confidently proceed to model more complex two-component systems using these configurations. The successful validation of the pure systems establishes a solid groundwork, allowing us to explore interactions between different polymers and resins in subsequent simulations. By employing a reliable force-field and ensuring equilibrium, we enhance the accuracy of our predictions regarding the compatibility and behavior of polymer compositions.\u003c/p\u003e\n\u003cp\u003eOnce the force-field parameters are validated, the same molecular model is used to prepare two component systems for polymer-polymer and polymer-resin studies. The compatibility between these systems assists in determining the likability of both components as a blend. This is determined by computing the Hildebrand\u0026rsquo;s solubility parameter (\u003cem\u003e\u0026delta;\u003c/em\u003e), given in equation (4). For the mentioned polymers, we considered six compositions and computed the compatibility, shown in figure 3. A higher value \u003cem\u003e\u0026delta;\u003c/em\u003e indicates a stronger compatibility which dictates a higher cohesive energy density between the two components. From the figure, it is seen that SBR-NR and SBR- BR systems have the highest solubility parameters which makes them the most compatible systems.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThis can be attributed to the strong \u0026pi;-\u0026pi; interactions held due to the aromatic rings in SBR and the double bonds present in NR and BR polymers. These interactions cause a strong packing between the chains and increase the likeability between the two chemical units. \u0026nbsp;Next, the BR-NR systems show a moderate value for the solubility parameter. The non-polar tendency of both these hydrophobic polymers facilitates effective van der Waals interactions between them and allows for an effective blending. Thus, the hydrophobic interactions drive the miscibility in this systems.\u003c/p\u003e\n\u003cp\u003eThe trend of compatibility becomes moderate in the case of BR-IIR and SBR-IIR polymers. The IIR polymers are predominantly composed of butyl groups which cause a steric hinderance with the other polymers. In BR-IIR system, the two polymers are held together by \u0026pi;-\u0026pi; interactions present in BR and isoprene units of IIR but are the \u003cem\u003e\u0026delta;\u0026nbsp;\u003c/em\u003e lowers due to steric hinderance originating from butyl groups of IIR. In the further case of SBR-IIR systems, the \u0026pi;-\u0026pi; interactions still operate between aromatic styrene units and isoprene of IIR. But at the same time, the compatibility lowers due to the rising steric hinderance caused from butyl of IIR and bulky rings in styrene- which, is elsewise not so dominant in BR-IIR system. Thus, the competing forces in BR-IIR and SBR-IIR make these two systems moderately compatible. In the last case of NR-IIR systems, NR is primarily made of isoprene, which is less polar than SBR or BR and has limited functional groups for interaction with IIR. Moreover, the butyl groups in IIR and methyl group in NR may cause a strong steric hinderance, making these two polymers as least compatible amongst all other systems studied here.\u003c/p\u003e\n\u003cp\u003eWe further investigate the findings of compatibility from MD simulations with the AFM experiments. A blend of all the systems studied is prepared and their AFM images are presented in figure 4 [42]. A uniform surface morphology signifies systems with no phase separation and are highly compatible, whereas a non-uniform morphology and agglomeration if any components denote a phase separated system which is less compatible. As seen, the systems SBR-NR, SBR-BR and BR-NR have a clean uniform surface morphology. This indicates a strong likeability of the two components towards each other as \u0026nbsp;their surface stays even with no phase separation. This is also in-line with the high \u003cem\u003e\u0026delta;\u003c/em\u003e-value obtained from simulations. Next, the BR-IIR and SBR-IIR systems show medium uniformity in surface with a slight distinction in surface morphology. These indicate some extent of phase separation which is also reflected by their intermediate \u003cem\u003e\u0026delta;\u003c/em\u003e-value from simulations. In the last case of NR-IIR polymers, there lies a distinct difference in the surface morphology with agglomerate formation which is attributed to the localization of NR and IIR polymers on the surface indicating towards their poor compatibility. Similar findings from simulations and the weak underlying molecular interactions make this system the least compatible system amongst all. Overall, the AFM experiments are in good correlation with the \u003cem\u003e\u0026delta;\u003c/em\u003e-value obtained from simulations. This suggests the suitability of molecular simulations to study compatibility between two components which can fairly reduce the number of physical trials and experimental time.\u003c/p\u003e\n\u003cp\u003eWe have expanded our MD simulations to examine the effects of temperatures relevant to the mixing of composites and curing processes of tyres and during its service period. Specifically, we subjected the mixed polymer systems to elevated temperatures of 373 K (100\u0026deg;C) and 433 K (160\u0026deg;C) to evaluate their compatibility, as illustrated in Figure 5. We plotted the solubility parameter values as a function of temperature, revealing a systematic trend. As the temperature increases from 300 K to 373 K and further to 433 K, we observed a consistent decrease in the \u0026delta;-value (solubility parameter). This phenomenon can be attributed to several factors related to thermal energy\u0026apos;s impact on polymer interactions. The lowering of the \u0026delta;-value indicates a reduction in cohesive energy within the polymer systems. This reduction can be linked to the weakening of non-bonded interactions, such as hydrophobic forces and \u0026pi;-\u0026pi; stacking interactions, as thermal energy increases. As temperature rises, the kinetic energy of the polymer chains also increases, leading to greater molecular motion. This heightened activity disrupts the stability of non-bonded interactions, which are crucial for maintaining compatibility between different polymer systems. As cohesive energy diminishes, the networking between polymer chains weakens. This disruption can adversely affect the overall compatibility of the mixed systems. When the polymer chains are less tightly interconnected, the material properties can change, potentially leading to phase separation. The most significant observation is that the trend of compatibility between two polymers us similar- both at room temperature and at higher temperature. In a nutshell, our models provide detailed insights to deeply investigate compatibility at molecular resolution operating at nanoscales which are important for material performance. \u0026nbsp;\u003c/p\u003e\n\u003cp\u003eFurther, resins are important components in tyres as they provide bonding strength, flexibility, elasticity and strength. Thus, \u0026nbsp;it becomes an important aspect to investigate the compatibility of polymers with resin. Hence, we have simulated 12 two-component systems formed from the combination of polymers and resins shown in figure 1 and calculated their solubility parameters. As our simulation models have held good for polymer-polymer system, the polymer-resin simulations are followed in a similar manner. Figure 6 shows the \u003cem\u003e\u0026delta;\u003c/em\u003e-value of the four resins- DCPD, PF, C9 and C5 with SBR, BR and BR polymers.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThe compatibility and performance of SBR-DCPD, BR-DCPD, and NR-DCPD resins are significantly influenced by their distinct chemical structures and features. SBR has both non-polar butadiene segment with a polar styrene segment, introducing functional groups that facilitate favorable van der Waals interactions. On the other side, DCPD possesses double bonds due to its bicyclic structure. This results in homogeneity with enhanced interactions, making SBR-DCPD highly compatible. In contrast, BR, primarily composed of non-polar polybutadiene, lacks polar characteristics necessary for effective interactions with DCPD. Consequently, BR-DCPD may exhibit limited mixing and increased phase separation due to weaker dispersive interactions and lower cohesive energy density compared to SBR-DCPD. NR, primarily consisting of polyisoprene, also presents compatibility challenges due to its non-polar nature. The absence of polar functional groups in NR results in significant phase separation and reduced interfacial adhesion when blended with DCPD.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eWith PF resins, the compatibility lowers from BR to NR to SBR. This can be connected with the structure of PF resin, shown in figure 1. As this resin is larger in size, the steric repulsions between SBR and PF due to their aromatic counterparts dominate. This leads to an ineffective interactions sights and hence causes SBR to be least compatible with PF-resin. NR polymer, on the other hand, does not have bigger side groups as in the case of SBR. This permits a better van der Waals interaction between PF and NR and causes an improvement in the \u003cem\u003e\u0026delta;\u003c/em\u003e-value for compatibility. The \u0026delta;-value\u003cem\u003e\u0026nbsp;\u003c/em\u003eis highest for BR-PF combination which is again an outcome of the chemical framework. The polybutadiene in BR supports stronger \u0026pi;-\u0026pi; interactions with aromatic sings of PF-resin. Alongside, an absence of any hinderance from the side chain effectively improves the compatibility between these two molecules, reflected from their high \u003cem\u003e\u0026delta;\u003c/em\u003e-value.\u003c/p\u003e\n\u003cp\u003eThe C9 resin is a branched molecule having benzene rings substituted in the parent chain. Thus, the polymers exhibit an obvious trend in compatibility, moving from SBR to BR and then to NR. The high compatibility with SBR is credited to the favorable \u0026pi;-\u0026pi; interactions in SBR and C9 aromatic rings, favored by the smaller and more flexible size of C9. The lower polarity in BR than SBR causes a lowering in BR-C9 compatibility. The lowest \u003cem\u003e\u0026delta;\u003c/em\u003e-value in NR-C9 is caused due to the least favorable interactions due to non-polar isoprene units of NR which are held poorly with C9 resins.\u003c/p\u003e\n\u003cp\u003eThe overall lowering in \u003cem\u003e\u0026delta;\u003c/em\u003e-value of polymers with C9 \u0026nbsp;as compared to DCPD and PF is caused due to the steric factors. The C5 resin branch makes it sterically unfavorable along with its aliphatic feature makes it highly non-polar as well. Thus, all the polymers are least compatible with C5 resin as compared to other resins.\u003c/p\u003e\n\u003cp\u003eWe confirmed our findings for SBR-resin system using AFM experiments in a similar manner as done for polymer-polymer systems, shown in figure 7. \u0026nbsp;As high degree of uniformity in the surface for SBR-DCPD and SBR-PF shows that they in well mixed and compatible with each other. The SBR-C9 system shows an uneven distribution of components, indicating a lower compatibility. In SBR-C5 system, a clear distinction between the two components can be seen. This shows a localization of the two entities within the system, where they prefer a phase-separated behavior. This entire experimental observation of SBR-resin systems is in good correlation with the solubility parameter values obtained from molecular dynamics simulations.\u003c/p\u003e\n\u003cp\u003eOverall, the varying degrees of compatibility among these resin systems arise from their structural and chemical differences and SBR-DCPD system is the most compatible system among all the polymer-resin systems investigated.\u003c/p\u003e"},{"header":"Conclusion","content":"\u003cp\u003eIn this work, we have performed MD simulation for different pairs if polymers from the commonly used polymers in tyres such as, Natural Rubber (NR), Butadiene Rubber (BR), Styrene-Butadiene Rubber (SBR), and Isobutylene-Isoprene Rubber (IIR) as well as compatibility of these polymers with commonly used resins such as dicyclopentadiene (DCPD), phenolic resin (PF), and C9 and C5 resins. Our approach involved analyzing these materials both as pure systems and in binary combinations, focusing on polymer-polymer and polymer-resin compatibility through molecular dynamics simulations. To establish a standardized baseline for our chemical parameters, we first simulated the pure systems, which yielded polymer densities that closely match those reported in the literature. This validation ensured the accuracy of the force-field parameters and directed towards our subsequent modeling of binary systems, allowing us to effectively explore and understand their compatibility behaviors.\u003c/p\u003e\n\u003cp\u003eIn examining the binary mixtures, we identified that the interplay of molecular-level non-bonded interactions-such as π-π stacking, polar and non-polar interactions, and steric effects have an underlying role in determining the compatibility of the two components. This compatibility is quantified through the solubility parameter (\u003cem\u003eδ\u003c/em\u003e), with higher values indicating greater likelihood of miscibility. Among all the polymer pairs studied, the compatibility trend is SBR-NR \u0026gt; SBR-BR \u0026gt; BR-NR \u0026gt; BR-IIR \u0026gt; SBR-IIR \u0026gt; NR-IIR and for polymer-resin systems compatibility trend with SBR/BR/NR rubbers is DCPD \u0026gt; PF \u0026gt; C9 \u0026gt; C5. Additionally, we characterized the compatibility through Atomic Force Microscopy (AFM) experiments, which well supported our simulation findings.\u003c/p\u003e\n\u003cp\u003eThe alignment of our simulation results with experimental data reinforces the reliability of our modeling approach, suggesting that our computational framework is robust and accurate. Looking ahead, these molecular simulations will facilitate a deeper understanding of the intricate interactions within multi-component systems, particularly the forces that govern compatibility in tyre materials which in turn will help to select most suitable polymers or resins through MD simulations. By minimizing the need for extensive physical trials, these models enable us to save time and costs associated with experimental work while also predicting innovative recipe designs in material formulation. This research has the potential to significantly enhance the development of advanced tyre compounds, optimizing their performance and durability through informed design choices based on molecular insights.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cdiv class=\"Heading\"\u003e\u003c/div\u003e \u003cp\u003eWe confirmed our findings for SBR-resin system using AFM experiments in a similar manner as done for polymer-polymer systems, shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e. As high degree of uniformity in the surface for SBR-DCPD and SBR-PF shows that they in well mixed and compatible with each other. The SBR-C9 system shows an uneven distribution of components, indicating a lower compatibility. In SBR-C5 system, a clear distinction between the two components can be seen. This shows a localization of the two entities within the system, where they prefer a phase-separated behavior. This entire experimental observation of SBR-resin systems is in good correlation with the solubility parameter values obtained from molecular dynamics simulations.\u003c/p\u003e \u003cp\u003eOverall, the varying degrees of compatibility among these resin systems arise from their structural and chemical differences and SBR-DCPD system is the most compatible system among all the polymer-resin systems investigated.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eIn this work, we have performed MD simulation for different pairs if polymers from the commonly used polymers in tyres such as, Natural Rubber (NR), Butadiene Rubber (BR), Styrene-Butadiene Rubber (SBR), and Isobutylene-Isoprene Rubber (IIR) as well as compatibility of these polymers with commonly used resins such as dicyclopentadiene (DCPD), phenolic resin (PF), and C9 and C5 resins. Our approach involved analyzing these materials both as pure systems and in binary combinations, focusing on polymer-polymer and polymer-resin compatibility through molecular dynamics simulations. To establish a standardized baseline for our chemical parameters, we first simulated the pure systems, which yielded polymer densities that closely match those reported in the literature. This validation ensured the accuracy of the force-field parameters and directed towards our subsequent modeling of binary systems, allowing us to effectively explore and understand their compatibility behaviors.\u003c/p\u003e \u003cp\u003eIn examining the binary mixtures, we identified that the interplay of molecular-level non-bonded interactions-such as π-π stacking, polar and non-polar interactions, and steric effects have an underlying role in determining the compatibility of the two components. This compatibility is quantified through the solubility parameter (\u003cem\u003eδ\u003c/em\u003e), with higher values indicating greater likelihood of miscibility. Among all the polymer pairs studied, the compatibility trend is SBR-NR\u0026thinsp;\u0026gt;\u0026thinsp;SBR-BR\u0026thinsp;\u0026gt;\u0026thinsp;BR-NR\u0026thinsp;\u0026gt;\u0026thinsp;BR-IIR\u0026thinsp;\u0026gt;\u0026thinsp;SBR-IIR\u0026thinsp;\u0026gt;\u0026thinsp;NR-IIR and for polymer-resin systems compatibility trend with SBR/BR/NR rubbers is DCPD\u0026thinsp;\u0026gt;\u0026thinsp;PF\u0026thinsp;\u0026gt;\u0026thinsp;C9\u0026thinsp;\u0026gt;\u0026thinsp;C5. Additionally, we characterized the compatibility through Atomic Force Microscopy (AFM) experiments, which well supported our simulation findings.\u003c/p\u003e \u003cp\u003eThe alignment of our simulation results with experimental data reinforces the reliability of our modeling approach, suggesting that our computational framework is robust and accurate. Looking ahead, these molecular simulations will facilitate a deeper understanding of the intricate interactions within multi-component systems, particularly the forces that govern compatibility in tyre materials which in turn will help to select most suitable polymers or resins through MD simulations. By minimizing the need for extensive physical trials, these models enable us to save time and costs associated with experimental work while also predicting innovative recipe designs in material formulation. This research has the potential to significantly enhance the development of advanced tyre compounds, optimizing their performance and durability through informed design choices based on molecular insights.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eL. Wang and S. 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Hao, \u0026ldquo;Chapter 6 - Barrier properties, antimicrobial and antifungal activities of chitin and chitosan-based IPNs, gels, blends, composites, and nanocomposites,\u0026rdquo; in \u003cem\u003eHandbook of Chitin and Chitosan\u003c/em\u003e, S. Gopi, S. Thomas, and A. Pius, Eds., Elsevier, 2020, pp. 175\u0026ndash;227.\u003c/li\u003e\n\u003cli\u003eR. B. Nandeti, S. Bhadra, V. Bansal, S. Goyal, S. Nair, and N. K. Singha, \u0026ldquo;Estimating the compatibility and interaction parameter in various polymer blends by molecular dynamics simulation with J-octa,\u0026rdquo; \u003cem\u003eInternational Rubber Conference\u003c/em\u003e, Bangalore, 2022.\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"CEAT Ltd","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Molecular Dynamics Simulations, Compatibility, Polymer, Resins, Solubility Parameter","lastPublishedDoi":"10.21203/rs.3.rs-6957788/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6957788/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eTyre is a complex composite comprising of various rubber compounds, metal cords and fabrics having dynamic utility. The rubber compounds are further composed of various components such as polymers, fillers, resin and antioxidants. For homogeneous mixing of ingredients, compatibility between two polymers and/or polymer-resin is very essential which in turn improves the thermodynamic mechanical properties of the rubber vulcanizate and reduces tyre failure. This study focusses on understanding compatibility between polymer-polymer and polymer-resin systems through molecular dynamics (MD) simulations. For this study, we have selected commonly used rubbers in tyre compounds such as Natural Rubber (NR), Butadiene Rubber (BR), Styrene-Butadiene Rubber (SBR), Isobutylene-Isoprene Rubber (IIR) as well as compatibility of these polymers with commonly used resins in tyres, such as dicyclopentadiene (DCPD), phenolic resin (PF), and C9 and C5 which are branched hydrocarbons resins.\u003c/p\u003e \u003cp\u003eIn simulations, we quantified compatibility using Hildebrand\u0026rsquo;s solubility parameter (\u003cem\u003eδ\u003c/em\u003e) and experimentally characterized it via Atomic Force Microscopy (AFM) experiments, which confirmed our simulation results. Our findings indicate that competing non-bonded interactions such as π-π stacking, polar and non-polar interactions, and steric effects play a critical role for compatibility in both polymer-polymer and polymer-resin mixtures.\u003c/p\u003e \u003cp\u003eThe alignment between our computational and experimental findings underscores the robustness of our modeling approach. These simulations offer valuable insights into the interactions within two-component systems, aiming to further understand multi-component systems by reducing physical trials and costs along with enlightening towards innovative tyre formulations.\u003c/p\u003e","manuscriptTitle":"Determination of Compatibility in Polymer-Polymer and Polymer-Resin Systems through Molecular Dynamics Simulations","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-06-24 14:51:10","doi":"10.21203/rs.3.rs-6957788/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"5e0b9622-a4eb-4d81-81c7-6f4b052ddef7","owner":[],"postedDate":"June 24th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":50462969,"name":"Computational Chemistry"},{"id":50462970,"name":"Polymer Science"}],"tags":[],"updatedAt":"2025-06-24T14:51:10+00:00","versionOfRecord":[],"versionCreatedAt":"2025-06-24 14:51:10","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-6957788","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6957788","identity":"rs-6957788","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}