The adsorption of polymers onto fluid membranes is a problem of fundamental interest in biology and soft materials, in part because the flexibility of membranes can lead to nontrivial coupling between polymer and membrane configurations. Here, we use Monte Carlo computer simulations to study the adsorption of a semiflexible polymer onto a fluid membrane vesicle. Polymer adsorption can significantly impact both the vesicle and polymer shapes, and we identify distinct classes of configurations that emerge as a function of polymer persistence length, membrane bending rigidity, adsorption strength, and vesicle size. Large-scale deformations of the vesicle include invaginations of the membrane that internalize the polymer in a membrane bud. The buds range from disk-like shapes surrounding a collapsed polymer to tubular deformations enveloping rod-like polymers. For small vesicles, polymer adsorption also induces dumbbell-like vesicle shapes with a narrow membrane constriction circled by the polymer. Vesicles with sufficiently small or large bending rigidities adopt configurations similar to those without the polymer present. We further characterize statistical properties of the membrane and polymer configurations and identify distinct classes of polymer configurations that emerge within membrane buds. Analysis of idealized polymer-membrane configurations provides additional insight into transitions between bud shapes.
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.
We propose a dynamic coarse-graining (CG) scheme for mapping heterogeneous polymer fluids onto extremely CG models in a dynamically consistent manner. The idea is to use as target function for the mapping a wave-vector dependent mobility function derived from the single-chain dynamic structure factor, which is calculated in the microscopic reference system. In previous work, we have shown that dynamic density functional calculations based on this mobility function can accurately reproduce the order/disorder kinetics in polymer melts, thus it is a suitable starting point for dynamic mapping. To enable the mapping over a range of relevant wave vectors, we propose to modify the CG dynamics by introducing internal friction parameters that slow down the CG monomer dynamics on local scales, without affecting the static equilibrium structure of the system. We illustrate and discuss the method using the example of infinitely long linear Rouse polymers mapped onto ultrashort CG chains. We show that our method can be used to construct dynamically consistent CG models for homopolymers with CG chain length N = 4, whereas for copolymers, longer CG chain lengths are necessary.
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