Dynamic Self-Consistent Field Approach for Studying Kinetic Processes in Multiblock Copolymer Melts

Abstract

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 a recent study, one of us and coworkers have developed a method to systematically construct mobility functions from reference fine-grained simulations. Here we focus on melts of linear chains in the Rouse regime and show how the mobility functions can be calculated semi-analytically for multiblock copolymers with arbitrary sequences without resorting to simulations. In this context, an accurate approximate expression for the single-chain dynamic structure factor is derived. Several limiting regimes are discussed. Then we apply the resulting density functional theory to study ordering processes in a two-length scale block copolymer system after instantaneous quenches into the ordered phase. Different dynamical regimes in the ordering process are identified: at early times, the ordering on short scales dominates; at late times, the ordering on larger scales takes over. For large quench depths, the system does not necessarily relax into the true equilibrium state. Our density functional approach could be used for the computer-assisted design of quenching protocols in order to create novel nonequilibrium materials.

Dynamic coarse-graining of polymer systems using mobility functions

“…Additionally shown is the result from traditional simulations (black dashed line), and the theoretical results for Rouse polymers from our previous paper, Ref. [56] (black solid line).…”

“…However, the approach also has limitations. This becomes apparent when looking at the partial mobility functions for chain blocks, which is important for dynamical studies of block copolymer ordering and disordering [55,56]. To illustrate this, we split our ultrashort chain (N = 4) in two symmetric blocks A and B of length N = 2 (see Sec.…”

“…In a previous publication [56], we have derived an expression for the single-chain mobility function of ideal infinitely long chains in the Rouse regime. The result was lengthy and shall not be repeated here.…”

“…The reason why the mobility of the finite chain at large (qR G ) differs from that of the infinite chain can be rationalized as follows: In the regime 1 (qR G ) (qR G ) c , the local mobility is dominated by the collective motion of whole chain portions with a locally scale invariant conformations. The effective friction of such a "wad" is reduced, compared to that of a monomer, and can be calculated from its local self-similar structure [56]. On the other hand, on ultra-short length scales with (qR G ) c (qR G ), the effect of chain connectivity becomes negligible and monomers diffuse individually.…”

“…The generalization to block copolymers is straightforward [55,56]. In our previous work, we have shown that a DDFT (1) based on this approach can accurately reproduce the kinetic evolution of block copolymer melts after sudden changes of the χ-parameter, when compared to fine-grained reference simulations.…”