Microscopic Dynamics and Viscoelasticity of Vitrimers

Abstract

We implement a hybrid molecular dynamics/Monte Carlo simulation to study the microscopic dynamics and the macroscopic rheology of vitrimers with a fast bond exchange rate. We show that the linear viscoelastic properties and mean squared displacement of the vitrimers collapse onto master curves by applying the same shift factors that follow the Williams−Landel−Ferry equation at low temperatures and Arrhenius-like behavior at high temperatures. The linkage between the microscopic dynamics and the linear rheology of vitrimers is established using the generalized Stokes−Einstein relationship, which efficiently extends the timescale of simulations and predicts the viscoelasticity. The values of the shift factors are related to the characteristic decay time of the intermediate scattering function, which is accessible in scattering experiments. The same results hold in the case of an all-atom model of an ionic liquid. Our methodology provides a microscopic basis for the time-superposition principle and predicts the macroscopic rheology of thermo-rheologically simple vitrimers.

Creep and Recovery Behavior of Vitrimers with Fast Bond Exchange Rate

“…This is different from the temperature behavior of the a T values (shift factors obtained from TTS) reported in experiments and simulations where two distinct temperature regimes for the vitrimer a T s are observed. [ 30,66 ] A WLF behavior at low temperatures, while an Arrhenius one at high temperatures. [ 28,43 ] However, it is important to remember that the enhanced creep displayed by the vitrimer is a direct manifestation of the stress and not temperature‐induced bond exchange reactions.…”

“…[ 41 ] It is important to note that we refer to the dynamics at work in this class of vitrimer as diffusion‐limited model, implying that in the current algorithm, there is a limited thermal activation barrier to prevent the bond exchange from taking place. Our prior study showed that the current model incorporates an activation energy barrier of 5.7 kJ mol −1 , [ 30 ] which is smaller than the experimental range of 30–90 kJ mol −1 [ 20,42,43 ] and corresponds to a fast bond exchange rate. This type of behavior has also been reported experimentally.…”

“…These include using MD in conjunction with Mode-Coupling Theory, [24] three-body potential algorithm, [25][26][27] and MD-Monte Carlo (MC) methods. [28][29][30] In our recent work using the MD-MC method, [30] we showed that the dynamics of vitrimers in the melt state are solely determined using the lifetime of dynamic bonds. Furthermore, the temperature dependence of the relaxation time of the vitrimer followed an Arrhenius-like temperature dependence in the regime the bond exchanges were active, while this dependence changed to the Williams-Landel-Ferry (WLF) [31] equation form at lower temperatures.…”

Linear and Nonlinear Viscoelasticities of Dissociative and Associative Covalent Adaptable Networks: Discrepancies and Limits

“…The comparison of G ( t ) and MSD clarifies each size of motion unit and its relaxation time. A quantitative relationship can be found in ref …”

“…Shao et al in our group then extended it to a dual-network system. Wu et al and Perego et al , studied the influence of temperature and kinetic activation energy on bond exchange reactions (BERs) of Asso-CANs independently. Olsen et al studied the walking and hopping diffusion through the intermediate scattering function using Brownian dynamics simulations.…”