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Multiscale Prediction of Polymer Relaxation Dynamics via Computational and Data-Driven Methods

Nguyen T. T. Duyen, Ngo T. Que, Anh D. Phan

TL;DR

The paper tackles predicting polymer glass transition dynamics in scenarios with limited experimental $T_g$ data. It develops a multiscale pipeline that combines MD-based $T_g$ estimation, Gaussian Process Regression Tg predictions from SMILES fingerprints, and ECNLE theory with a thermal mapping to predict $ au_ ext{α}(T)$, $D(T)$, and dynamic fragility. MD-derived $T_g$ values agree with experimental data within about $10$–$15$ K, while ML-derived $T_g$ overestimates slightly but yields accurate fragility predictions; ECNLE predictions using these inputs reproduce broadband dielectric spectroscopy results across temperature representations. The approach offers a practical, high-throughput framework for predicting polymer glassy dynamics without adjustable parameters, enabling design and screening when experimental data are scarce.

Abstract

We present a multiscale modeling approach that integrates molecular dynamics simulations, machine learning, and the Elastically Collective Nonlinear Langevin Equation (ECNLE) theory to investigate the glass transition dynamics of polymer systems. The glass transition temperatures (Tg) of four representative polymers are estimated using simulations and machine learning model trained on experimental datasets. These predicted Tg values are used as inputs to the ECNLE theory to compute the temperature dependence of structural relaxation times and diffusion coefficients, and the dynamic fragility. The Tg values predicted from simulations show good quantitative agreement with experimental data. While machine learning tends to slightly overestimate Tg, the resulting dynamic fragility values remain close to experimental fragilities. Overall, ECNLE calculations using these inputs agree well with broadband dielectric spectroscopy results. Our integrated approach provides a practical and scalable tool for predicting the dynamic behavior of polymers, particularly in systems where experimental data are limited.

Multiscale Prediction of Polymer Relaxation Dynamics via Computational and Data-Driven Methods

TL;DR

The paper tackles predicting polymer glass transition dynamics in scenarios with limited experimental data. It develops a multiscale pipeline that combines MD-based estimation, Gaussian Process Regression Tg predictions from SMILES fingerprints, and ECNLE theory with a thermal mapping to predict , , and dynamic fragility. MD-derived values agree with experimental data within about – K, while ML-derived overestimates slightly but yields accurate fragility predictions; ECNLE predictions using these inputs reproduce broadband dielectric spectroscopy results across temperature representations. The approach offers a practical, high-throughput framework for predicting polymer glassy dynamics without adjustable parameters, enabling design and screening when experimental data are scarce.

Abstract

We present a multiscale modeling approach that integrates molecular dynamics simulations, machine learning, and the Elastically Collective Nonlinear Langevin Equation (ECNLE) theory to investigate the glass transition dynamics of polymer systems. The glass transition temperatures (Tg) of four representative polymers are estimated using simulations and machine learning model trained on experimental datasets. These predicted Tg values are used as inputs to the ECNLE theory to compute the temperature dependence of structural relaxation times and diffusion coefficients, and the dynamic fragility. The Tg values predicted from simulations show good quantitative agreement with experimental data. While machine learning tends to slightly overestimate Tg, the resulting dynamic fragility values remain close to experimental fragilities. Overall, ECNLE calculations using these inputs agree well with broadband dielectric spectroscopy results. Our integrated approach provides a practical and scalable tool for predicting the dynamic behavior of polymers, particularly in systems where experimental data are limited.
Paper Structure (7 sections, 8 equations, 7 figures, 2 tables)

This paper contains 7 sections, 8 equations, 7 figures, 2 tables.

Table of Contents

  1. Introduction
  2. THEORETICAL BACKGROUND
  3. The ECNLE theory
  4. Molecular dynamics simulation
  5. Machine learning models
  6. Results AND Discussion
  7. Conclusion

Figures (7)

  • Figure 1: (Color online) Schematic illustration of the dynamic free energy in the ECNLE theory. Key length and energy quantities are defined.
  • Figure 2: (Color online) Distribution of actual and predicted glass transition temperatures of polymers for (a) training data and (b) test data.
  • Figure 3: (Color online) Temperature dependence of the simulated volume from MD simulations for (a) PPS, (b) PI, (c) PPG, and (d) PB. Blue squares indicate raw data at each temperature step, while black circles indicate averaged values used for analysis. Linear fits to the low-temperature and high-temperature regimes are shown as brown and black lines, respectively. The intersection of these two lines corresponds to the predicted $T_g$ of the polymer.
  • Figure 4: (Color online) Temperature dependence of the structural relaxation time for (a) PPS, (b) PI, (c) PPG, and (d) PB calculated using Eqs. (\ref{['eq:1']}-\ref{['eq:6']}) and (\ref{['eq:11']}). The $T_g$ used in the thermal mapping (Eq. (\ref{['eq:11']})) is obtained from MD simulations, ML predictions, and experimental data in Ref. 25. Experimentally, the molecular weights obtained were 44000 g/mol for PPS, 1040 g/mol for PI, 192 g/mol for PPG, and 777 g/mol for PB. In contrast, the corresponding values derived from MD simulation were 631, 683, 656, and 570 g/mol, respectively.
  • Figure 5: (Color online) The logarithm of structural relaxation times as a function of $T_g/T$ for (a) PPS, (b) PI, (c) PPG, and (d) PB from the same data as in Fig. \ref{['fig3']}.
  • ...and 2 more figures