Coarse-grained molecular dynamics modeling of reaction-induced phase separation

Development of a Meshless Kernel-Based Scheme for Particle-Field Brownian Dynamics Simulations

We develop a meshless discretization scheme for particle-field Brownian dynamics simulations. The density is assigned on the particle level using a weighting kernel with finite support. The system's free energy density is derived from an equation of state (EoS) and includes a square gradient term. The numerical stability of the scheme is evaluated in terms of reproducing the thermodynamics (equilibrium density and compressibility) and dynamics (diffusion coefficient) of homogeneous samples. Using a reduced description to simplify our analysis, we find that numerical stability depends strictly on reduced reference compressibility, kernel range, time step in relation to the friction factor, and reduced external pressure, the latter being relevant under isobaric conditions. Appropriate parametrization yields precise thermodynamics, further improved through a simple renormalization protocol. The dynamics can be restored exactly through a trivial manipulation of the time step and friction coefficient. A semiempirical formula for the upper bound on the time step is derived, which takes into account variations in compressibility, friction factor, and kernel range. We test the scheme on realistic mesoscopic models of fluids, involving both simple (Helfand) and more sophisticated (Sanchez-Lacombe) equations of state.

Dissipative Particle Dynamics Simulation for Reaction-Induced Phase Separation of Thermoset/Thermoplastic Blends

Reaction-induced phase separation occurs during the curing reaction when a thermoplastic resin is dissolved in a thermoset resin, which enables toughening of the thermoset resin. As resin properties vary significantly depending on the morphology of the phase-separated structure, controlling the morphology formation is of critical importance. Reaction-induced phase separation is a phenomenon that ranges from the chemical reaction scale to the mesoscale dynamics of polymer molecules. In this study, we performed curing simulations using dissipative particle dynamics (DPD) coupled with a reaction model to reproduce reaction-induced phase separation. The curing reaction properties of the thermoset resin were determined by ab initio quantum chemical calculations, and the DPD parameters were determined by all-atom molecular dynamics simulations. This enabled mesoscopic simulations, including reactions that reflect the intrinsic material properties. The effects of the thermoplastic resin concentration, molecular weight, and curing conditions on the phase-separation morphology were evaluated, and the cure shrinkage and stiffness of each cured resin were confirmed to be consistent with the experimental trends. Furthermore, the local strain field under tensile deformation was visualized, and the inhomogeneous strain field caused by the phase-separated structures of two resins with different stiffnesses was revealed. These results can aid in understanding the toughening properties of thermoplastic additives at the molecular level.

Reaction-induced morphological transitions in a blend of diblock copolymers and reactive monomers: dissipative particle dynamics simulation

The dissipative particle dynamics (DPD) method is applied to the morphological transitions of microphase-separated domains in a mixture of symmetric AB-diblock copolymers and reactive C-monomers, where polymerization and cross-linking reactions take place among C-monomers. The initial structure for the DPD simulation is an equilibrated cylindrical domain structure prepared by the density-biased Monte Carlo method with density profiles obtained from the self-consistent field theory. By introducing a cross-linking reaction among reactive C-monomers, we confirmed that the DPD simulation reproduces the morphological transitions observed in experiments, where the domain morphology changes due to segregation between A-blocks of diblock copolymers and cross-linking networks of C-monomers. When the cross-linking reaction of C-monomers is sufficiently fast compared to the deformation of the domains, the initial cylindrical domains are preserved, while the distance between the domains increases. On the other hand, when the formation of the cross-linking network is slow, the domains can deform and reconnect with each other in the developing cross-linking network. In this case, we observe morphological transitions from the initial domain morphology with a large-curvature interface to another domain morphology with a smaller-curvature interface, such as the transition from the cylindrical phase to the lamellar phase. We calculated the spatial correlations in the microphase-separated domains and found that such correlations are affected by the speed of the formation of the cross-linking network depending on whether the bridging between microphase-separated domains occurs in a nucleation and growth process or in a spinodal decomposition process.

Simple and convenient mapping of molecular dynamics mechanical property predictions of bisphenol-F epoxy for strain rate, temperature, and degree of cure

It is well-known that all-atom molecular dynamics (MD) predictions of mechanical properties of thermoset resins suffer from multiple accuracy issues associated with their viscoelastic nature. The nanosecond simulation times of MD simulations do not allow for the direct simulation of the molecular conformational relaxations that occur under laboratory time scales. This adversely affects the prediction of mechanical properties at realistic strain rates, intermediate degrees of cure, and elevated temperatures. While some recent studies have utilized a time-temperature superposition approach to relate MD predictions to expected laboratory observations, such an approach becomes prohibitively difficult when simulating thermosets with a combination of strain rates, intermediate degrees of cure, and temperatures. In this study, a phenomenological approach is developed to map the predictions of Young's modulus and Poisson's ratio for a DGEBF/DETDA epoxy system to the corresponding laboratory-based properties for intermediate degrees of cure and temperatures above and below the glass transition temperature. The approach uses characterization data from dynamical mechanical analysis temperature sweep experiments. The mathematical formulation and experimental characterization of the mapping is described, and the resulting mapping of computationally-predicted to experimentally-observed elastic properties for various degrees of cure and temperatures are demonstrated and validated. This mapping is particularly important to mitigate the strain-rate effect associated with MD predictions, as well as to accurately predict mechanical properties at elevated temperatures and intermediate degrees of cure to facilitate accurate and efficient composite material process modeling.

Addressing diffusion behavior and impact in an epoxy-amine cure system using molecular dynamics simulations

To deepen understanding of diffusion-controlled crosslinking, molecular dynamics (MD) simulations are carried out by taking the diffusion image of 3,3'-diamino diphenyl sulfone (3,3'-DDS) and polyethersulfone (PES) with epoxy resin varying temperatures from 393.15 to 473.15 K over crosslinking conversion of 0-85%. The diffusion of PES and 3,3'-DDS into the bulk increased with increasing the temperature as a result of enhanced mobility of the molecules when the difference between the glass-transition temperature (T_g) and the curing temperature. Beyond the onset points of the converged crosslinking conversion ratio of 3,3'-DDS and PES, their diffusion properties are obviously restricted with crosslinking conversion ratio. At low crosslinking conversion ratios (> 10%), the diffusion coefficients of triglycidyl p-aminophenol (TGAP) were 1.1 times higher than those of diglycidyl ether of bisphenol F (DGEBF) because of the lower molecular weight of TGAP. On the other hand, the diffusion coefficients of TGAP decreased when the crosslinking ratio was up to ~ 60% because, compared with DGEBF, it had more functional groups available to react with the curing agent. At higher crosslinking ratios, the diffusion coefficients of both resins converged to zero as a result of their highly crosslinked structures.

Simulation of polymerization induced phase separation in model thermosets

Polymerization induced phase separation (PIPS) in a three component thermoset is studied using molecular dynamics simulations of a new coarse-grained thermoset model. The system includes two crosslinker molecules, which differ in their glass transition temperatures (T_g) and chain length and thus have the potential for phase separation. One crosslinker has a high T_g corresponding to a rubbery behavior, and simulations were performed for a short length (4 beads) and a long length (33 beads). The resin and other crosslinker have low T_g. A coarse-grained model is developed with these features and with interaction parameters determined so that for either rubbery crosslinker length, the system is in the liquid state at the cure temperature. For sufficiently slow reaction rates, the long rubbery molecule exhibits PIPS into a bicontinuous array of nanoscale domains, but the short one does not, reproducing recent experimental results. The simulations demonstrate that the reaction rates must be slow enough to allow diffusion to yield phase separation. Particularly, the reaction rate corresponding to the secondary amine must be very slow, else the structure of crosslinked clusters and the substantially increased diffusion time will prevent PIPS.