Entropic Unmixing in Nematic Blends of Semiflexible Polymers

Phase behavior of polymer dispersed liquid crystals, comparison between mean-field theory, and coarse-grained molecular dynamics simulations

We report a simulation methodology to quantitatively predict the thermodynamic behaviour (phase diagrams) of polymer mixtures, that exhibit phases with broken orientational symmetry. Our system consists of a binary mixture of short oligomers (NA = 4) and long rod-like mesogens (NB = 8). Using coarse-grained molecular dynamics (CGMD) simulations we infer the topology of the temperature-dependent free energy landscape, from the probability distributions of the components for a range of compositions. The mixture exhibits nematic (N) and smectic phases (Sm-A) as a function of two temperature scales, Tc, that governs the demixing transition, and TNI the nematic-isotropic temperature. Thus in addition to the isotropic (I), a nematic (N) phases observed in simulations of similar systems earlier we report the formation of a new entropy-stabilized phase separated smectic-A (Sm-A) phase with alternating mesogen-rich and oligomer-rich layers. Using the mean-field free energy for polymer-dispersed liquid crystals (PDLCs), with suitably chosen parameter values, we construct a mean-field phase diagram that matches those obtained from CGMD simulations. Our results are applicable to mixtures of synthetic and biological macromolecules that undergo phase separation and are orientable, thereby giving rise to the liquid crystalline phases. Our proposed methodology has a distinct advantage over other computational techniques in its applicability to systems with complex molecular interactions and in capturing the coarsening dynamics of systems involving multiple order parameters.

Mixing Linear Polymers with Rings and Catenanes: Bulk and Interfacial Behavior

We derive and parameterize effective interaction potentials between a multitude of different types of ring polymers and linear chains, varying the bending rigidity and solvent quality for the former species. We further develop and apply a density functional treatment for mixtures of both disconnected (chain-ring) and connected (chain-polycatenane) mixtures of the same, drawing coexistence binodals and exploring the ensuing response functions as well as the interface and wetting behavior of the mixtures. We show that worsening of the solvent quality for the rings brings about a stronger propensity for macroscopic phase separation in the linear-polycatenane mixtures, which is predominantly of the demixing type between phases of similar overall particle density. We formulate a simple criterion based on the effective interactions, allowing us to determine whether any specific linear-ring mixture will undergo a demixing phase separation.

Dispersion and orientation patterns in nanorod-infused polymer melts

Introducing nanorods into a polymeric matrix can enhance the physical and mechanical properties of the resulting material. In this paper, we focus on understanding the dispersion and orientation patterns of nanorods in an unentangled polymer melt, particularly as a function of nanorod concentration, using molecular dynamics simulations. The system is comprised of flexible polymer chains and multi-thread nanorods that are equilibrated in the NPT ensemble. All interactions are purely repulsive except for those between polymers and rods. Results with attractive vs repulsive polymer-rod interactions are compared and contrasted. The concentration of rods has a direct impact on the phase behavior of the system. At lower concentrations, rods phase separate into nematic clusters, whereas at higher concentrations more isotropic and less structured rod configurations are observed. A detailed examination of the conformation of the polymer chains near the rod surface shows extension of the chains along the director of the rods (especially within clusters). The dispersion and orientation of the nanorods are a result of the competition between depletion entropic forces responsible for the formation of rod clusters, the enthalpic effects that improve mixing of rods and polymer, and entropic losses of polymers interpenetrating rod clusters.

Surface enrichment and interdiffusion in blends of semiflexible polymers of different stiffness

A model for a mixture of two kinds of semiflexible polymers (A and B) with the same chain length (N_A = N_B = 32), but different persistence lengths, confined between parallel planar repulsive walls in a common good solvent is studied by molecular dynamics simulations. In the isotropic phase at low polymer concentrations, both polymers are repelled by the walls, and the system is anisotropic near the walls over a range controlled by the polymer linear dimensions. Close to the concentrations where in the bulk nematic order sets in, precursors of thick nematic layers at the walls are observed, strongly enriched by a stiffer component, which hence is depleted in the center of the slit pore. At larger concentrations, where in the bulk a uniformly mixed nematic phase occurs, the enrichment of B-chains at the walls is rather minor, extending over the scale of the transverse correlation length of concentration fluctuations, which is of the order of a few monomeric diameters only for the present model. In this ordered phase, both self-diffusion and interdiffusion of chains (in the direction perpendicular to the director) are found to be significantly slowed down in comparison to dilute solutions. Since equilibration times scale with the square of the slit thickness, incomplete equilibration is predicted when polymeric coatings on substrate containing polymers differing in stiffness are produced.

Epigenetic-structural changes in X chromosomes promote Xic pairing during early differentiation of mouse embryonic stem cells

X chromosome inactivation center (Xic) pairing occurs during the differentiation of embryonic stem (ES) cells from female mouse embryos, and is related to X chromosome inactivation, the circadian clock, intra-nucleus architecture, and metabolism. However, the mechanisms underlying the identification and approach of X chromosome pairs in the crowded nucleus are unclear. To elucidate the driving force of Xic pairing, we developed a coarse-grained molecular dynamics model of intranuclear chromosomes in ES cells and in cells 2 days after the onset of differentiation (2-day cells) by considering intrachromosomal epigenetic-structural feature-dependent mechanics. The analysis of the experimental data showed that X-chromosomes exhibit the rearrangement of their distributions of open/closed chromatin regions on their surfaces during cell differentiation. By simulating models where the excluded volume effects of closed chromatin regions are stronger than those of open chromatin regions, such rearrangement of open/closed chromatin regions on X-chromosome surfaces promoted the mutual approach of the Xic pair. These findings suggested that local intrachromosomal epigenetic features may contribute to the regulation of cell species-dependent differences in intranuclear architecture.

Mathematical model of chromosomal dynamics during DNA double strand break repair in budding yeast

During the repair of double-strand breaks (DSBs) in DNA, active mobilizations for conformational changes in chromosomes have been widely observed in eukaryotes, from yeast to animal and plant cells. DSB-damaged loci in the yeast genome showed increased mobility and relocation to the nuclear periphery. However, the driving forces behind DSB-induced chromatin dynamics remain unclear. In this study, mathematical models of normal and DSB-damaged yeast chromosomes were developed to simulate their structural dynamics. The effects of histone degradation in the whole nucleus and the change in the physical properties of damaged loci due to the binding of SUMOylated repair proteins were considered in the model of DSB-induced chromosomes based on recent experimental results. The simulation results reproduced DSB-induced changes to structural and dynamical features by which the combination of whole nuclear histone degradation and the rigid structure formation of repair protein accumulations on damaged loci were suggested to be primary contributors to the process by which damaged loci are relocated to the nuclear periphery.

Blends of Semiflexible Polymers: Interplay of Nematic Order and Phase Separation

Mixtures of semiflexible polymers with a mismatch in either their persistence lengths or their contour lengths are studied by Density Functional Theory and Molecular Dynamics simulation. Considering lyotropic solutions under good solvent conditions, the mole fraction and pressure is systematically varied for several cases of bending stiffness κ (the normalized persistence length) and chain length N. For binary mixtures with different chain length (i.e., NA=16, NB=32 or 64) but the same stiffness, isotropic-nematic phase coexistence is studied. For mixtures with the same chain length (N=32) and large stiffness disparity (κB/κA=4.9 to 8), both isotropic-nematic and nematic-nematic unmixing occur. It is found that the phase diagrams may exhibit a triple point or a nematic-nematic critical point, and that coexisting phases differ appreciably in their monomer densities. The properties of the two types of chains (nematic order parameters, chain radii, etc.) in the various phases are studied in detail, and predictions on the (anisotropic) critical behavior near the critical point of nematic-nematic unmixing are made.

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.

Phase Separation and Nematic Order in Lyotropic Solutions: Two Types of Polymers with Different Stiffnesses in a Common Solvent

The interplay of the isotropic-nematic transition and phase separation in lyotropic solutions of two types of semiflexible macromolecules with pronounced difference in chain stiffness is studied by Density Functional Theory and Molecular Dynamics simulations. While the width of the isotropic-nematic two-phase coexistence region is narrow for solutions with a single type of semiflexible chain, the two-phase coexistence region widens for solutions containing two types of chains with rather disparate stiffness. In the nematic phase, both types of chains contribute to the nematic order, with intermediate values of the order parameter compared to the corresponding single component solutions. As the difference in bending stiffness is increased, the two chain types separate into two coexisting nematic phases. The phase behavior is rationalized by considering the chemical potentials of the two components and the Gibbs excess free energy. The geometric properties of the chain conformations under the various conditions are also discussed.