Theories and simulations of polymers using coarse-grained models

Abstract

Full atomistic simulations of many-chain systems such as polymer melts are not feasible at present due to their formidable computational requirements. Molecular simulations with coarse-grained (CG) models have to be used instead, which interact with soft potentials that allow complete particle overlapping. One advantage of soft potentials is that it allows to simulate systems with experimentally accessible fluctuations and correlations because the invariant degree of polymerization (controlling the system fluctuations and correlations) and the polymer chain length N are decoupled using soft potentials. Another advantage is that it provides a powerful means for unambiguously and quantitatively revealing the effects of fluctuations and correlations of polymers when comparing simulation results with corresponding theoretical predictions based on the same model systems thus without any parameter fitting. Using the recently proposed fast lattice Monte Carlo (FLMC) simulations and the corresponding lattice self-consistent field (LSCF) calculations based on the same model system, where multiple occupancy of lattice sites is allowed, we studied the coil-globule transition (CGT) of one-mushroom polymeric systems and the fused-separated transition (FST) of two-mushroom polymeric systems. With soft potential, we systematically constructed the phase diagrams of one- and two-mushroom systems using LSCF theory, which neglects the interchain fluctuations and correlations. The LSCF predictions were then directly compared with the simulation results without any parameter-fitting, the fluctuation/correlation effects on these phase transitions are then unambiguously quantified. Similarly, for disordered symmetric diblock copolymers in continuum, we directly compared the thermodynamic and structural properties from fast off-lattice Monte Carlo simulations, integral equation (IE) theories (including the reference interaction site model and polymer reference interaction site model), and Gaussian fluctuation theory based on the same model systems, and unambiguously quantified the consequences of various theoretical approximations and the validity of these theories in describing the fluctuations/correlations in disordered diblock copolymers. In order to answer the questions of how to obtain the CG model and how the CG level affects the properties of CG model, we then performed systematic and simulation-free coarse graining of homopolymer melts. In this work, we proposed a systematic and simulation-free strategy for structure-based coarse graining of homopolymer melts, where each chain of Nm monomers is uniformly divided into N segments, with the spatial position of each segment corresponding to the center-of-mass of its monomers. We used integral-equation theories, instead of molecular simulations, to obtain the structural and thermodynamic properties of both original and CG systems, and quantitatively examined how the effective pair potentials between CG segments and the thermodynamic properties of CG systems vary with N. Our coarse-graining strategy is much faster than those using molecular simulations and provides the quantitative basis for choosing the appropriate N-values. Taking the simple hard-core Gaussian thread model (K. S. Schweizer and J. G. Curro, Chem. Phys. 149, 105 (1990)) as the original system, we demonstrated our strategy and compared in detail the various integral-equation theories and closures for coarse graining. Our numerical results showed that the effective CG potentials using various closures can be collapsed approximately onto the same curve for different N, and that structure-based coarse graining cannot give the thermodynamic consistency between original and CG systems at any N < Nm. The CG potential from structure-based coarse graining can further be used to parameterize CG potentials with a given analytic functional form containing finite number of parameters, which is much more convenient to use in molecular simulations than the numerically tabulated CG potentials from structure-based coarse graining. In this work, we applied our systematic and simulation-free strategy to the recently proposed relative-entropy-based coarse graining, which minimizes the information loss quantified by the relative entropy. The values of relative entropy obtained from relative-entropy-based coarse graining with different CG potential functional forms can further be compared to determine the appropriate functional form or number of parameters. Note that the ideal-chain conformations were used in both structure-based and relative-entropy-based coarse-graining strategies, which is not valid for systems with strong pair interactions or small invariant degree of polymerization, self-consistent integral equation theory can be used to obtain more accurate intrachain pair correlations. In order to improve the quality of coarse graining, our proposed systematic and simulation-free coarse-graining strategy can be further combined with the self-consistent integral equation theory. This work will be remained for future researchers.