Free energy calculations by molecular simulations of deformed polymer glasses

Breemen, Lambèrt C.A. van; Theodorou, Doros N.; Hütter, Markus

doi:10.1016/j.cpc.2019.107008

Cited by 10 publications

(67 citation statements)

References 102 publications

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“…The protocol of generating the glassy configurations, and the united-atom model governing the atomistic interactions have been described in detail in ref ( 8 ). Following the generation of equilibrated reverse-mapped configurations in the melt state, it entails quenching by Molecular Dynamics (MD) 63 at a rate of 0.1 K/ns down to 300 K. The applied quenching rates in the simulations are orders of magnitude faster compared to those employed experimentally.…”

Section: Methodsmentioning

confidence: 99%

“…The inclusion of higher-order (anharmonic) terms to the free energy is certainly possible; they can be rigorously derived by following our work on obtaining second- and third-order analytical derivatives of the potential energy. 8 …”

Section: Methodsmentioning

confidence: 99%

“… 64 At temperatures higher than the Debye temperature of glassy atactic polystyrene, θ D ≃ 100 K, 70 the classical vibrational partition function is also a reasonable approximation. Furthermore, we can split the Helmholtz energy as A = U – TS , where S is the entropy of the microscopic system, 71 , 72 and U is the internal energy, 8 The latter is independent of temperature and can be calculated from the potential energy of the IS and the vibrational frequencies.…”

Section: Methodsmentioning

confidence: 99%

“…This is accomplished by maximizing the potential energy along the walking (parallel to the canyon floor) direction while requiring minimum of the potential energy with respect to all other lateral directions, hence walking along the “stream bed”, which runs in the direction of uphill movement. The minimization in the lateral directions is accomplished by projecting the gradient 29 and employing it in the framework of a minimization algorithm (either conjugate gradient 29 or a limited-memory Broyden–Fletcher–Goldfarb–Shanno algorithm as implemented in our previous work 8 ).…”

Section: Methodsmentioning

confidence: 99%

“…All steps of the procedure are greatly facilitated by a unified analytical treatment of the local slopes (gradients) and curvatures (Hessians) of the energy landscapes of classical molecular force fields, presented in our earlier work. 8 For the discovered transition states, the distribution of (free) energy barriers separating the connected minima are studied and the corresponding rate constants are calculated by applying multidimensional transition-state theory (TST). Finally, insightful connections to theoretical models of the glass phenomenology are drawn, allowing us to predict from first-principles important parameters entering macroscopic models.…”

Section: Introductionmentioning

confidence: 99%

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Structural Transitions in Glassy Atactic Polystyrene Using Transition-State Theory

2021

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Transition pathways on the energy landscape of atactic polystyrene (aPS) glassy specimens are probed below its glass-transition temperature. Each of these transitions is considered an elementary structural relaxation event, whose corresponding rate constant is calculated by applying multidimensional transition-state theory. Initially, a wide spectrum of first-order saddle points surrounding local minima on the energy landscape is discovered by a stabilized hybrid eigenmode-following method. Then, (minimal-energy) “reaction paths” to the adjacent minima are constructed by a quadratic descent method. The heights of the free energy, the potential energy, and the entropy barriers are estimated for every connected triplet of transition state and minima. The resulting distribution of free energy barriers is asymmetric and extremely broad, extending to very high barrier heights (over 50 k B T ); the corresponding distribution of rate constants extends over 30 orders of magnitude, with well-defined peaks at the time scales corresponding to the subglass relaxations of polystyrene. Analysis of the curvature along the reaction paths reveals a multitude of different rearrangement mechanisms; some of them bearing multiple distinct phases. Finally, connections to theoretical models of the glass phenomenology allows for the prediction, based on first-principles, of the “ideal” glass-transition temperature entering the Vogel–Fulcher–Tammann (VFT) equation describing the super-Arrhenius temperature dependence of glassy dynamics. Our predictions of the time scales of the subglass relaxations and the VFT temperature are in favorable agreement with available experimental literature data for systems of similar molecular weight under the same conditions.

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Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Structural Transitions in Glassy Atactic Polystyrene Using Transition-State Theory

2021

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Microscopic Carriers of Plasticity in Glassy Polystyrene

Mols

Vogiatzis

Breemen

et al. 2021

Macro Theory & Simulations

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The relevant parts of the microstructure participating in the plastic deformation of glassy polystyrene are identified. This is achieved by performing quasi‐static deformation simulations of an atomistic representation of polystyrene, within a thermodynamic framework, under experimentally realistic boundary conditions (controlled compressive strain, atmospheric pressure in the lateral directions, and room temperature). In particular, it is shown that discontinuities in the free energy in the course of deformation are representative of microscopic plastic events, which are strongly correlated with the heterogeneous non‐affine deformation of the phenyl‐rings. However, despite the induced anisotropy during deformation, the phenyl‐rings do not show any preferred orientation during deformation. The rearrangements of the microstructure during the discontinuities are analyzed further in terms of a local best‐fit deformation gradient tensor (a modified version of the procedure introduced by Falk and Langer in 1998) as well as the stretch‐ and rotation‐components of the local deformation of clusters of atoms that show significant non‐affine deformation. This analysis shows that the local deformation is highly heterogeneous, and locally the strains and rotations can be orders of magnitude larger than the imposed deformation, giving rise to plastic deformation of the material.

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Molecular dynamics inferred transfer learning models for finite‐strain hyperelasticity of monoclinic crystals: Sobolev training and validations against physical constraints

Vlassis

Zhao

et al. 2022

Numerical Meth Engineering

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We present a machine learning framework to train and validate neural networks to predict the anisotropic elastic response of a monoclinic organic molecular crystal known as β$$ \beta $$‐HMX in the geometrical nonlinear regime. A filtered molecular dynamic (MD) simulations database is used to train neural networks with a Sobolev norm that uses the stress measure and a reference configuration to deduce the elastic stored free energy functional. To improve the accuracy of the elasticity tangent predictions originating from the learned stored free energy, a transfer learning technique is used to introduce additional tangential constraints from the data while necessary conditions (e.g., strong ellipticity, crystallographic symmetry) for the correctness of the model are either introduced as additional physical constraints or incorporated in the validation tests. Assessment of the neural networks is based on (1) the accuracy with which they reproduce the bottom‐line constitutive responses predicted by MD, (2) the robustness of the models measured by detailed examination of their stability and uniqueness, and (3) the admissibility of the predicted responses with respect to mechanics principles in the finite‐deformation regime. We compare the training efficiency of the neural networks under different Sobolev constraints and assess the accuracy and robustness of the models against MD benchmarks for β$$ \beta $$‐HMX.

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Free energy calculations by molecular simulations of deformed polymer glasses

Cited by 10 publications

References 102 publications

Structural Transitions in Glassy Atactic Polystyrene Using Transition-State Theory

Structural Transitions in Glassy Atactic Polystyrene Using Transition-State Theory

Microscopic Carriers of Plasticity in Glassy Polystyrene

Molecular dynamics inferred transfer learning models for finite‐strain hyperelasticity of monoclinic crystals: Sobolev training and validations against physical constraints

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