Spinodal Decomposition of Polymer-Solvent Systems: Theory and Simulation

Abstract

The unmixing dynamics of a polymer-solvent system is investigated via computer simulation of a mesoscopic model. The polymer component is represented by a bead-spring model where the quality of the solvent can be varied by adjusting the attractive component of the pair interaction. The polymers are dissipatively coupled to a Lattice-Boltzmann solvent background in order to include hydrodynamic interactions. The project’s overarching goal is to compare the present model to a continuum model that is being investigated in a collaborating group and perform a parameter matching. The fact that the available macroscopic models were found to be lacking a comprehensible connection to microscopic physics motivated the creation of a novel continuum theory from scratch. This theory is derived from microscopic principles, always keeping the numerical implementation in mind and at the same time making sure that it is compatible with the GENERIC formalism and fundamental symmetries. Thus, all parameters have a well-defined meaning with respect to the computer model. Numerical simulations of the mesoscopic model are performed using a coupled Lattice Boltzmann/Molecular Dynamics approach which at the same time provides the basic picture used in the derivation of the continuum model. The attraction strength corresponding to the theta solvent is estimated for two-dimensional systems. Three-dimensional systems are simulated at various densities. The results are used to estimate the parameters of the analytically determined Van der Waals equation of state. The coarsening dynamics during phase separation is examined by calculating the dynamic structure factor for both two- and three-dimensional systems. Comparison to a simple fluid reveals that in the viscoelastic case dynamic scaling is violated, meaning that the phase-separation dynamics of the present computer model is indeed non-standard. First comparisons are made to a macroscopic model which was simulated by a collaborating group. Furthermore, the use of Minkowski functionals for analyzing the dynamics of the emerging structures’ geometrical properties is explored. In parallel, a procedure for calculating Lattice Boltzmann weights based on the numerical solution of the Maxwell-Boltzmann constraints has been developed and implemented in a Python script. The script determines whether or not a valid model corresponding to the user-supplied parameters exists and calculates its weights if this is the case. A procedure to obtain particular models even when there are infinitely many solutions to the problem is available. Furthermore, the script provides a function to determine the validity of a solution, which can be used to verify existing models from the literature.