Self-Consistent-Field Theory of Viscoelastic Behavior of Inhomogeneous Dense Polymer Systems

Alignment of Copolymer Morphology by Planar Step Elongation during Spinodal Self-Assembly

Using simulation and numerical self-consistent field theory of an unentangled diblock copolymer melt, we study the interplay between relaxation of molecular conformations from a highly stretched, nonequilibrium state and structure formation of the local, conserved density during self-assembly from a disordered state. We observe that the planar elongation of molecular conformations in the initial, disordered state results in an alignment of lamella normals perpendicular to the stretch direction during the subsequent self-assembly. Although thermodynamically the parallel orientation is favored, the alignment of the lamella normal perpendicular to the stretch direction is characterized by the larger growth rate of composition fluctuations during the spinodal ordering process.

Simulating the Flow of Entangled Polymers

To optimize automation for polymer processing, attempts have been made to simulate the flow of entangled polymers. In industry, fluid dynamics simulations with phenomenological constitutive equations have been practically established. However, to account for molecular characteristics, a method to obtain the constitutive relationship from the molecular structure is required. Molecular dynamics simulations with atomic description are not practical for this purpose; accordingly, coarse-grained models with reduced degrees of freedom have been developed. Although the modeling of entanglement is still a challenge, mesoscopic models with a priori settings to reproduce entangled polymer dynamics, such as tube models, have achieved remarkable success. To use the mesoscopic models as staging posts between atomistic and fluid dynamics simulations, studies have been undertaken to establish links from the coarse-grained model to the atomistic and macroscopic simulations. Consequently, integrated simulations from materials chemistry to predict the macroscopic flow in polymer processing are forthcoming.

Interfacial slip in sheared polymer blends

We have developed a dynamic self-consistent field theory, without any adjustable parameters, for unentangled polymer blends under shear. Our model accounts for the interaction between polymers, and enables one to compute the evolution of the local rheology, microstructure, and the conformations of the polymer chains under shear self-consistently. We use this model to study the interfacial dynamics in sheared polymer blends and make a quantitative comparison between this model and molecular dynamics simulations. We find good agreement between the two methods.

Dynamic self-consistent field theory for unentangled homopolymer fluids

We present a lattice formulation of a dynamic self-consistent field (DSCF) theory that is capable of resolving interfacial structure, dynamics, and rheology in inhomogeneous, compressible melts and blends of unentangled homopolymer chains. The joint probability distribution of all the Kuhn segments in the fluid, interacting with adjacent segments and walls, is approximated by a product of one-body probabilities for free segments interacting solely with an external potential field that is determined self-consistently. The effect of flow on ideal chain conformations is modeled with finitely extensible, nonlinearly elastic dumbbells in the Peterlin approximation, and related to stepping probabilities in a random walk. Free segment and stepping probabilities generate statistical weights for chain conformations in a self-consistent field, and determine local volume fractions of chain segments. Flux balance across unit lattice cells yields mean field transport equations for the evolution of free segment probabilities and of momentum densities on the Kuhn length scale. Diffusive and viscous contributions to the fluxes arise from segmental hops modeled as a Markov process, with transition rates reflecting changes in segmental interaction, kinetic energy, and entropic contributions to the free energy under flow. We apply the DSCF equations to study both transient and steady-state interfacial structure, flow, and rheology in a sheared planar channel containing either a one-component melt or a phase-separated, two-component blend.

Numerical simulation of polymer nanocomposites using self-consistent mean-field model

Clay-containing polymeric nanocomposites (PNC) are mixtures of dispersed clay platelets in a polymeric matrix. These materials show enhancement of physical properties, such as modulus, strength, and dimensional stability, as well as a reduction of gas permeability and flammability. The performance is related to the degree of clay dispersion (i.e., intercalation or exfoliation) and the bonding between the clay and the matrix. The main goal of this work has been to map the degree of dispersion as a function of independent variables (viz., magnitude of the interaction parameters, molecular weights, composition, etc.). In this paper, we present the results of the numerical analysis of the equilibrium thermodynamic miscibility using one- and two-dimensional (1D and 2D) models based on the self-consistent mean-field theory. In the limit, the 2D model reproduced the 1D model published results. The adopted 2D model considers the presence of four PNC components: solid clay platelets, low molecular weight intercalant, polymeric matrix, and end-functionalized compatibilizer. The simulations, with realistic values of the binary interaction parameters, were analyzed for potential exfoliation of PNC with a polyolefin as the matrix. The simulation results show that intercalation and exfoliation is expected within limited ranges of the independent variables. The presence of a bare clay surface (e.g., generated by thermal decomposition of intercalant or extraction by molten polymer) has a strong negative effect on the dispersion process. The simulation successfully identified the most influential factors, e.g., optimum ranges of the compatibilizer and the intercalant concentration.