Incorporating fluctuations and dynamics in self-consistent field theories for polymer blends

Self-consistent field theory (SCFT) is one of the useful methods to simulate phase separated structures of multi-component polymer systems. In this article, we propose an SCFT for semiflexible polymer melts, where the basic equations for the SCFT are derived by introducing a bending stiffness into a flexible Gaussian bead-spring model and taking its continuous limit. Our SCFT is described by a coupled modified diffusion equations for the statistical weight of the chain confor...

A generalized self-consistent field approach for polymer networks with fixed topology is developed. It is shown that the theory reproduces the localization of crosslinks which is characteristic for gels. The theory is then used to study the order-disorder transition in regular networks of endlinked diblock copolymers. Compared to diblock copolymer melts, the transition is shifted towards lower values of the incompatibility parameter $\chi$ (the Flory- Huggins parameter). More...

There exists a generic relationship between the thermodynamics of a continuous polymer with a generic self-interaction and the two-point function of an interacting field-theory. In addition, the (2N)-point function of the resulting field theory is similarly related to a system of N interacting polymers. In the present paper, this relation is explored for the special case of a polyelectrolyte, characterized by a screened Coulomb pair potential. The corresponding field theory...

We introduce $\infty$-dimensional versions of three common models of random hetero-polymers, in which both the polymer density and the density of the polymer-solvent mixture are finite. These solvable models give valuable insight into the problems related to the (quenched) average over the randomness in statistical mechanical models of proteins, without having to deal with the hard geometrical constraints occurring in finite dimensional models. Our exact solution, which is sp...

We study a solution of interacting semiflexible polymers with curvature energy in poor-solvent conditions on the d-dimensional cubic lattice using mean-field theory and Monte Carlo computer simulations. Building upon past studies on a single chain, we construct a field-theory representation of the system and solve it within a mean-field approximation supported by Monte Carlo simulations in d=3. A gas-liquid transition is found in the temperature-density plane that is then int...

The self-consistent field theory is a popular and highly successful theoretical framework for studying equilibrium (co)polymer systems at the mesoscopic level. Dynamic density functionals allow one to use this framework for studying dynamical processes in the diffusive, non-inertial regime. The central quantity in these approaches is the mobility function, which describes the effect of chain connectivity on the nonlocal response of monomers to thermodynamic driving fields. In...

We introduce a finite-volume numerical scheme for solving stochastic gradient-flow equations. Such equations are of crucial importance within the framework of fluctuating hydrodynamics and dynamic density functional theory. Our proposed scheme deals with general free-energy functionals, including, for instance, external fields or interaction potentials. This allows us to simulate a range of physical phenomena where thermal fluctuations play a crucial role, such as nucleation ...

The dynamics of polymer-nanoparticle (NP) mixtures, which involves multiple scales and system-specific variables, has posed a long-standing challenge on its theoretical description. In this paper, we construct a microscopic theory for polymer diffusion in the mixtures based on a combination of generalized Langevin equation, mode-coupling approach, and polymer physics ideas. The parameter-free theory has an explicit expression and remains tractable on pair correlation level wi...

In theory, there exist two extreme forms of substances: pure form and single-molecule mixture form. Single-molecule mixture form contains a mixture of molecules that have molecularly different structures. This elusive form has not yet been explored. Herein, we report a study of single molecule mixture state by a combination of model construction and mathematical analysis, and a series of interesting results were obtained. These results provide theoretical evidence that single...

We briefly discuss our recent field-theoretic study of polyelectrolyte complexation, which occurs in solutions of two oppositely charged polyelectrolytes. Charged systems require theoretical methods beyond the mean-field (or self-consistent field) approximation; indeed, mean-field theory is qualitatively incorrect for such polyelectrolyte solutions. Both analytical (one-loop) and numerical (complex Langevin) methods to account for charge correlations are discussed. In particu...