Adsorption and structure formation of semiflexible polymers on spherical surfaces

Effects of self-avoidance on the packing of stiff rods on ellipsoids

Using a statistical-mechanics approach, we study the effects of geometry and self-avoidance on the ordering of slender filaments inside nonisotropic containers, considering cortical microtubules in plant cells, and packing of genetic material inside viral capsids as concrete examples. Within a mean-field approximation, we show analytically how the shape of the container, together with self-avoidance, affects the ordering of the stiff rods. We find that the strength of the self-avoiding interaction plays a significant role in the preferred packing orientation, leading to a first-order transition for oblate cells, where the preferred orientation changes from azimuthal, along the equator, to a polar one, when self-avoidance is strong enough. While for prolate spheroids the ground state is always a polar-like order, strong self-avoidance results with a deep metastable state along the equator. We compute the critical surface describing the transition between azimuthal and polar ordering in the three-dimensional parameter space (persistence length, eccentricity, and self-avoidance) and show that the critical behavior of this system is in fact related to the butterfly catastrophe model. We calculate the pressure and shear stress applied by the filament on the surface, and the injection force needed to be applied on the filament in order to insert it into the volume. We compare these results to the pure mechanical study where self-avoidance is ignored, and discuss similarities and differences.

Adherent Moving of Polymers in Spherical Confined Binary Semiflexible Ring Polymer Mixtures

Based on the coarse-grained model, we used molecular dynamics methods to calculate and simulate a semiflexible long ring–semiflexible short ring blended polymer system confined in a hard sphere. We systematically studied the distribution and motion characteristics of the long ring chain. The results show that when the short ring is short enough (Lshort < 20), the long ring (Llong = 50) is separated from the blend system and then distributed against the inner wall. As the length of the short ring increases (Lshort ≥ 20), the long ring can no longer be separated from the blending system. Moreover, we found that the long ring demonstrates a random direction of adherent walking behavior on the inner surface of the hard sphere. The velocity of the long ring decreases with the increase in the short ring length Lshort. Specifically for Lshort ≥ 20, the system does not undergo phase separation and the speed of the long ring decreases sharply along with the long ring distributed inside the confined bulk. This is related to the inner wall layer moving faster than the inside bulk of the restricted system. Our simulation results can help us to understand the distribution of macromolecules in biological systems in confined systems, including the restricted chromosome partitioning distribution and packing structure of circular DNA molecules.

Computational Reverse Engineering Analysis for Scattering Experiments (CREASE) on Vesicles Assembled from Amphiphilic Macromolecular Solutions

In this paper we present the development and validation of the "Computational Reverse-Engineering Analysis for Scattering Experiments" (CREASE) method for analyzing scattering results from vesicle structures that are commonly found upon assembly of synthetic, biomimetic, or bioderived amphiphilic copolymers in solution. The two-step CREASE method takes the amphiphilic polymer chemistry and small-angle scattering intensity profile, I exp(q), as input and determines the vesicles' structural features on multiple length scales ranging from assembled vesicle wall's individual layer thicknesses to the monomer-level packing and distribution of polymer conformations. In the first step of CREASE, a genetic algorithm (GA) is used to determine the relevant vesicle dimensions from the input macromolecular solution information and I exp(q) by identifying the structure whose computed scattering profile best matches the input I exp(q). Then in the second step, the GA-determined dimensions are used for molecular reconstruction of the vesicle structure. To validate CREASE for vesicles, we test CREASE on input scattering intensity profiles generated mathematically (termed as in silico I exp(q) vs q) from a variety of vesicle sizes with known dimensions. We also test CREASE on in silico I exp(q) vs q generated from vesicles with dispersity in all relevant dimensions, resembling real experiments. After successful validation of CREASE, we compare the CREASE-determined dimensions against those obtained from the traditional approach of fitting the scattering intensity profile to relevant analytical model in SASVIEW package. We show that CREASE performs better than or as well as the core-multishell analytical model's fitting in SASVIEW in determining vesicle dimensions with dispersity. We also show that CREASE provides structural information beyond those possible from traditional scattering analysis using the core-multishell model, such as the distribution of solvophilic monomers between the vesicle wall's inner and outer layers in the vesicle wall and the chain-level packing within each vesicle layer.

Cylindrical confinement of solutions containing semiflexible macromolecules: surface-induced nematic order versus phase separation

Solutions of semiflexible polymers confined in cylindrical pores with repulsive walls are studied by Molecular Dynamics simulations for a wide range of polymer concentrations. Both the case where both lengths are of the same order and the case when the persistence length by far exceeds the contour length are considered, and the enhancement of nematic order along the cylinder axis is characterized. With increasing density the character of the surface effect changes from depletion to the formation of a layered structure. For binary 50 : 50 mixtures of the two types of polymers an interplay between surface enrichment of the stiffer component and the isotropic-nematic transition is found, and a phase separated structure with cylindrical symmetry occurs, with the isotropic phase located around the cylinder axis. For melt densities the mixed nematic phase forms at the wall a layer with a screw-like structure of a tilted smectic phase. The observed behavior is tentatively interpreted in terms of the competition of the chain orientational entropy with entropy of mixing and excluded volume due to the wall.

Phase Behavior of Lyotropic Liquid-Crystalline Polymers under Varying Solvent Conditions: Effect of External Fields on the Phase Diagram

In this work, we report a Density Functional Theory based study of phase behavior of lyotropic liquid-crystalline polymers under both good and varying solvent conditions in the presence of external electric or magnetic field. Our microscopic model for the good solvent case is based on the tangent hard-sphere chain with bond-bending potential to account for the chain stiffness; the variable solvent quality is modeled by adding attractive monomer-monomer interactions. The phase diagrams are constructed in three intensive variables (temperature, pressure, and field strength), and are characterized by the presence of critical and triple lines, which originate from the critical and triple points of the corresponding zero-field case. The merging of critical and triple lines results in the appearance of the "double critical" and "critical triple" points, already known from the earlier studies of the phase behavior of spin fluids in magnetic fields. The important difference of the present model from the spin fluids is due to the finite stiffness of the polymer chains (characterized by their persistence length), which adds an additional parameter controlling the morphology of the phase diagrams.

Self-assembly of semiflexible polymers confined to thin spherical shells

Confinement effects are critical for stiff macromolecules in biological cells, vesicles, and other systems in soft matter. For these molecules, the competition between the packing entropy and the enthalpic cost of bending is further shaped by strong confinement effects. Through coarse-grained molecular dynamics simulations, we explore the self-assembly of semiflexible polymers confined in thin spherical shells for various chain lengths, chain stiffnesses, and shell thicknesses. Here, we focus on the case where the contour and persistence length of the polymers are comparable to the radius of the confining cavity. The range of ordered structures is analyzed using several order parameters to elucidate the nature of orientational ordering in different parameter regimes. Previous simulations have revealed the emergence of bipolar and quadrupolar topological defects on the surface when the entire cavity was filled with a concentrated polymer solution [Phys. Rev. Lett., 2017, 118, 217803]. In contrast, spherical shell confinement restricts the appearance of a bipolar order. Instead, only the extent of the quadrupolar order changes with chain stiffness, as evidenced by the relative motion of topological defects. In the case of monolayers, we observe a nematic to smectic transition accompanied by a change in the nematic grain-size distribution as the contour length was decreased.