Conformations and orientational ordering of semiflexible polymers in spherical confinement.

Semiflexible polymers in lyotropic solution confined inside spherical nanoscopic “containers” with repulsive walls are studied by molecular dynamics simulations and density functional theory, as a first step to model confinement effects on stiff polymers inside of miniemulsions, vesicles, and cells. It is shown that the depletion effects caused by the monomer-wall repulsion depend distinctly on the radius R of the sphere. Further, nontrivial orientational effects occur when R, the persistence length ℓp, and the contour length L of the polymers are of similar magnitude. At intermediate densities, a “shell” of wall-attached chains is forming, such that the monomers belonging to those chains a…

Do the contact angle and line tension of surface-attached droplets depend on the radius of curvature?

Results from Monte Carlo simulations of wall-attached droplets in the three-dimensional Ising lattice gas model and in a symmetric binary Lennard-Jones fluid, confined by antisymmetric walls, are analyzed, with the aim to estimate the dependence of the contact angle $(\Theta)$ on the droplet radius $(R)$ of curvature. Sphere-cap shape of the wall-attached droplets is assumed throughout. An approach, based purely on "thermodynamic" observables, e.g., chemical potential, excess density due to the droplet, etc., is used, to avoid ambiguities in the decision which particles belong (or do not belong, respectively) to the droplet. It is found that the results are compatible with a variation $[\Th…

Chemical and Structural Trends in the Spin-Admixture Parameter of Organic Semiconductor Molecules

Spin mixing in organic semiconductors is related to spin–orbit coupling (SOC). However, a detailed study analyzing the dependence of the spin-admixture parameter (γ) on structural and material para...

Understanding the properties of liquid-crystalline polymers by computational modeling

Abstract A topical review of recent theoretical work on the properties of lyotropic solutions and melts containing semiflexible polymers in thermal equilibrium is given, with a focus on the liquid-crystalline and smectic order of these systems in the bulk and under confinement. Starting with a discussion of single chain properties in terms of the Kratky-Porod worm-like chain model and its limitations, extensions along the lines of Onsager’s theory for the isotropic-nematic transition of solutions of hard rods are briefly reviewed. This discussion is followed by a review of recent Molecular Dynamics simulations and classical Density Functional Theory calculations. It is argued that, even in …

Phase Separation in a Binary Mixture of Semiflexible Polymers Confined in a Repulsive Sphere

Star polymers confined in a nanoslit: a simulation test of scaling and self-consistent field theories

The free energy cost of confining a star polymer where f flexible polymer chains containing N monomeric units are tethered to a central unit in a slit with two parallel repulsive walls a distance D apart is considered, for good solvent conditions. Also the parallel and perpendicular components of the gyration radius of the star polymer, and the monomer density profile across the slit are obtained. Theoretical descriptions via Flory theory and scaling treatments are outlined, and compared to numerical self-consistent field calculations (applying the Scheutjens–Fleer lattice theory) and to Molecular Dynamics results for a bead-spring model. It is shown that Flory theory and self-consistent fi…

When does Wenzel's extension of Young's equation for the contact angle of droplets apply? A density functional study.

he contact angle of a liquid droplet on a surface under partial wetting conditions differs for a nanoscopically rough or periodically corrugated surface from its value for a perfectly flat surface. Wenzel's relation attributes this difference simply to the geometric magnification of the surface area (by a factor $r_{\rm w}$), but the validity of this idea is controversial. We elucidate this problem by model calculations for a sinusoidal corrugation of the form $z_{\rm wall}(y) = \Delta\cos(2\pi y/\lambda)$ , for a potential of short range $\sigma_{\rm w}$ acting from the wall on the fluid particles. When the vapor phase is an ideal gas, the change of the wall-vapor surface tension can be co…

Stretching of Free Chains Confined in Concave Brush-Coated Nanocylinders

The structure of a free flexible macromolecule confined in a cylindrical nanopore whose wall is coated by a polymer brush is studied by Monte Carlo simulation, varying the grafting density as well as the radius of the cylindrical pore. Because of this confinement, the free chain is stretched in axial direction; while for small grafting densities of the brush the end-to-end distance increases monotonously with decreasing pore radius, a nonmonotonic variation occurs for larger grafting densities. We show that this effect is due to strong interpenetration of the free chain and the brush chains; for very narrow pores a strong layering of cylindrical shells is found, and comparison with self-con…

Polymer Brushes on Flat and Curved Substrates: What Can be Learned from Molecular Dynamics Simulations

Semiflexible Polymers in the Bulk and Confined by Planar Walls

Semiflexible polymers in solution under good solvent conditions can undergo an isotropic-nematic transition. This transition is reminiscent of the well-known entropically-driven transition of hard rods described by Onsager’s theory, but the flexibility of the macromolecules causes specific differences in behavior, such as anomalous long wavelength fluctuations in the ordered phase, which can be understood by the concept of the deflection length. A brief review of the recent progress in the understanding of these problems is given, summarizing results obtained by large-scale molecular dynamics simulations and density functional theory. These results include also the interaction of semiflexib…

Phase Behavior of Active Swimmers in Depletants: Molecular Dynamics and Integral Equation Theory

We study the structure and phase behavior of a binary mixture where one of the components is self-propelling in nature. The inter-particle interactions in the system were taken from the Asakura-Oosawa model, for colloid-polymer mixtures, for which the phase diagram is known. In the current model version the colloid particles were made active using the Vicsek model for self-propelling particles. The resultant active system was studied by molecular dynamics methods and integral equation theory. Both methods produce results consistent with each other and demonstrate that the Vicsek model based activity facilitates phase separation, thus broadening the coexistence region.

Anomalous Fluctuations of Nematic Order in Solutions of Semiflexible Polymers

The nematic ordering in semiflexible polymers with contour length $L$ exceeding their persistence length $\ell_p$ is described by a confinement of the polymers in a cylinder of radius $r_{eff}$ much larger than the radius $r_\rho$, expected from the respective concentration of the solution. Large scale Molecular Dynamics simulations combined with Density Functional Theory are used to locate the Isotropic-Nematic ($I-N$)-transition and to validate this cylindrical confinement. Anomalous fluctuations, due to chain deflections from neighboring chains in the nematic phase are proposed. Considering deflections as collective excitations in the nematically ordered phase of semiflexible polymers el…

Influence of polymer flexibility on nanoparticle dynamics in semidilute solutions

The hierarchical structure and dynamics of polymer solutions control the transport of nanoparticles (NPs) through them. Here, we perform multi-particle collision dynamics simulations of solutions of semiflexible polymer chains with tunable persistence length lp to investigate the effect of chain stiffness on NP transport. The NPs exhibit two distinct dynamical regimes - subdiffusion on short time scales and diffusion on long time scales. The long-time NP diffusivities are compared with predictions from the Stokes-Einstein relation (SER), mode-coupling theory (MCT), and a recent polymer coupling theory (PCT). Increasing deviations from the SER as the polymer chains become more rigid (i.e. as…

Entropic Unmixing in Nematic Blends of Semiflexible Polymers

Binary mixtures of semiflexible polymers with the same chain length but different persistence lengths separate into two coexisting different nematic phases when the osmotic pressure of the lyotropic solution is varied. Molecular Dynamics simulations and Density Functional Theory predict phase diagrams either with a triple point, where the isotropic phase coexists with two nematic phases, or a critical point of unmixing within the nematic mixture. The difference in locally preferred bond angles between the constituents drives this unmixing without any attractive interactions between monomers.

B–T phase diagram of Pd/Fe/Ir(111) computed with parallel tempering Monte Carlo

We use an atomistic spin model derived from density functional theory calculations for the ultra-thin film Pd/Fe/Ir(111) to show that temperature induces coexisting non-zero skyrmion and antiskyrmion densities. We apply the parallel tempering Monte Carlo method in order to reliably compute thermodynamical quantities and the B-T phase diagram in the presence of frustrated exchange interactions. We evaluate the critical temperatures using the topological susceptibility. We show that the critical temperatures depend on the magnetic field in contrast to previous work. In total, we identify five phases: spin spiral, skyrmion lattice, ferromagnetic phase, intermediate region with finite topologic…

A new insight into the isotropic–nematic phase transition in lyotropic solutions of semiflexible polymers: density-functional theory tested by molecular dynamics

Semiflexible polymers in solution are studied for a wide range of both contour length L and persistence length lp as a function of monomer concentration under good solvent conditions. Both density-functional theory (DFT) and molecular dynamics (MD) simulation methods are used, and a very good agreement between both techniques is observed for rather stiff polymers. Evidence for a new mechanism of order parameter fluctuations in the nematic phase is presented, namely collective deformations of bundles of wormlike chains twisted around each other, and the typical wavelengths and amplitudes of these modes are estimated. These long wavelength fluctuations cause a reduction of the order parameter…

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 …

Interactions between polymer brush-coated spherical nanoparticles: the good solvent case.

The interaction between two spherical polymer brushes is studied by molecular dynamics simulation varying both the radius of the spherical particles and their distance, as well as the grafting density and the chain length of the end-grafted flexible polymer chains. A coarse-grained bead-spring model is used to describe the macromolecules, and purely repulsive monomer-monomer interactions are taken throughout, restricting the study to the good solvent limit. Both the potential of mean force between the particles as a function of their distance is computed, for various choices of the parameters mentioned above, and the structural characteristics are discussed (density profiles, average end-to…

Spherical polymer brushes under good solvent conditions: molecular dynamics results compared to density functional theory.

A coarse grained model for flexible polymers end-grafted to repulsive spherical nanoparticles is studied for various chain lengths and grafting densities under good solvent conditions, by Molecular Dynamics methods and density functional theory. With increasing chain length the monomer density profile exhibits a crossover to the star polymer limit. The distribution of polymer ends and the linear dimensions of individual polymer chains are obtained, while the inhomogeneous stretching of the chains is characterized by the local persistence lengths. The results on the structure factor of both single chain and full spherical brush as well as the range of applicability of the different theoretic…

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 oc…

Capillary Nematization of Semiflexible Polymers

emiflexible polymers under good solvent conditions confined by two planar parallel repulsive walls are investigated for a wide range of monomer concentrations and distances between the walls, for a case where persistence length and contour length of the macromolecules are almost equal. Chain conformations and local nematic ordering near the walls are studied by both molecular dynamics methods and density functional theory, putting it in perspective with the recent work where the isotropic phase of semiflexible polymer solutions in the vicinity of a single repulsive wall in semi-infinite geometry is considered. Profiles of the total density of monomers as well as densities of end- and middle…

Effect of the solvent quality on the structural rearrangement of spherical brushes: coarse-grained models

A coarse-grained model for flexible polymers end-grafted to repulsive spherical nanoparticles is studied for various polymer lengths, grafting densities, and nanoparticle sizes by molecular dynamics simulations, considering variable solvent quality in the framework of an implicit solvent treatment. Below the theta point, the tuning of the temperature strongly influences the coverage of the nanoparticle surface by collapsed single chains or clusters of several chains. The shape and size of the aggregates depend on the number of monomers and surface density of the polymers. Specifically we analyzed the effect of the solvent quality on the density profiles and radius of gyration of the single …

Controlling the Interactions between Soft Colloids via Surface Adsorption

By employing monomer-resolved computer simulations and analytical considerations based on polymer scaling theory, we analyze the conformations and interactions of multiarm star polymers strongly adsorbed on a smooth, two-dimensional plane. We find a stronger stretching of the arms as well as a stronger repulsive, effective interaction than in the three dimensional case. In particular, the star size scales with the number of arms $f$ as $\sim f^{1/4}$ and the effective interaction as $\sim f^{2}$, as opposed to $\sim f^{1/5}$ and $\sim f^{3/2}$, respectively, in three dimensions. Our results demonstrate the dramatic effect that geometric confinement can have on the effective interactions and…

Activity mediated phase separation: Can we understand phase behavior of the nonequilibrium problem from an equilibrium approach?

We present results for structure and dynamics of mixtures of active and passive particles, from molecular dynamics (MD) simulations and integral equation theory (IET) calculations, for a physically motivated model. The perfectly passive limit of the model corresponds to the phase-separating Asakura-Oosawa model for colloid-polymer mixtures in which, for the present study, the colloids are made self-propelling by introducing activity in accordance with the well known Vicsek model. Such activity facilitates phase separation further, as confirmed by our MD simulations and IET calculations. Depending upon the composition of active and passive particles, the diffusive motion of the active specie…

Structural properties of concave cylindrical brushes interacting with free chains

We present a self-consistent field theoretical study of the microstructure of concave cylindrical brushes as a function of the cylinder radius, grafting density, grafted chain length, and the solvent quality. We show that the results for the radial monomer density profile and the distribution of the free ends are in good agreement with the corresponding molecular dynamics results. Part of the investigation is focused on the conformational behavior of a free macromolecule in a cylindrical brush. A central result is the observed non-monotonous variation of the size of a free chain in a brush-coated tube when the tube radius is systematically changed. An interpretation of this behavior which d…

Disentangling the Role of Chain Conformation on the Mechanics of Polymer Tethered Particle Materials

[Image: see text] The linear elastic properties of isotropic materials of polymer tethered nanoparticles (NPs) are evaluated using noncontact Brillouin light spectroscopy. While the mechanical properties of dense brush materials follow predicted trends with NP composition, a surprising increase in elastic moduli is observed in the case of sparsely grafted particle systems at approximately equal NP filling ratio. Complementary molecular dynamics simulations reveal that the stiffening is caused by the coil-like conformations of the grafted chains, which lead to stronger polymer–polymer interactions compared to densely grafted NPs with short chains. Our results point to novel opportunities to …

The escape transition of a compressed star polymer: Self-consistent field predictions tested by simulation

The escape transition of a polymer "mushroom" (a flexible chain grafted to a flat non-adsorbing substrate surface in a good solvent) occurs when the polymer is compressed by a cylindrical piston of radius $R$, that by far exceeds the chain gyration radius. At this transition, the chain conformation abruptly changes from a two-dimensional self-avoiding walk of blobs (of diameter $H$, the height of the piston above the substrate) to a "flower conformation", i.e. stretched almost one-dimensional string of blobs (with end-to-end distance $\approx R$) and an "escaped" part of the chain, the "crown", outside the piston. The extension of this problem to the case of star polymers with $f$ arms is c…

Critical adsorption of a single macromolecule in polymer brushes.

The adsorption of long flexible macromolecules by polymer brush-coated surfaces is studied by molecular dynamics simulations and by calculations using density functional and self-consistent field theories. The case of repulsive interactions between the substrate surface and the monomers of both the brush polymers and the extra chains that can get absorbed into the brush is considered. Under good solvent conditions, critical absorption can occur, if the interaction between the monomers of the brush polymers and the extra chain is (weakly) attractive. It is shown that it is possible to map out the details of the critical absorption transition, if the chain length and/or the grafting density o…

Densely packed semiflexible macromolecules in a rigid spherical capsule

The ordering of semiflexible polymers with persistence length lp and contour length L confined in a sphere of radius R is studied by molecular dynamics simulations of a coarse-grained model. Monomer densities are chosen where the corresponding bulk lyotropic solution or melt is a well-ordered nematic, and purely repulsive walls of the rigid confining sphere are considered. It is found that polymers close to the walls are bent according to the curvature of the confining spheres with all their monomers in a few layers parallel to the sphere surface, whereas the remaining macromolecules closer to the sphere center have one chain end and their center of mass far from the surface. The latter cha…

Adsorption and structure formation of semiflexible polymers on spherical surfaces

Abstract Rigid spheres with a short-range attractive potential are taken as a coarse-grained model of vesicles, which contain a solution of semiflexible polymers in their interior. Assuming good solvent conditions with an implicit description of the solvent, effective monomers experience bond-length and bond-angle potentials as well as excluded-volume interaction. Due to the attractive vesicle surface, phase separation occurs between a thin shell of adsorbed monomers at the surface and a rather dilute, and therefore, disordered polymer solution in the sphere interior. While at a planar attractive surface the wormlike chains would exhibit liquid crystalline (nematic and smectic) order, the c…

Entropic Unmixing in Nematic Blends of Semiflexible Polymers.

Binary mixtures of semiflexible polymers with the same chain length, but different persistence lengths, separate into two coexisting different nematic phases when the osmotic pressure of the lyotropic solution is varied. Molecular Dynamics simulations and Density Functional Theory predict phase diagrams either with a triple point, where the isotropic phase coexists with two nematic phases or a critical point of unmixing within the nematic mixture. The difference in locally preferred bond angles between the constituents drives this unmixing without any attractive interactions between monomers.

Semiflexible polymers confined in a slit pore with attractive walls: two-dimensional liquid crystalline order versus capillary nematization

Semiflexible polymers under good solvent conditions interacting with attractive planar surfaces are investigated by Molecular Dynamics (MD) simulations and classical Density Functional Theory (DFT). A bead-spring type potential complemented by a bending potential is used, allowing variation of chain stiffness from completely flexible coils to rod-like polymers whose persistence length by far exceeds their contour length. Solvent is only implicitly included, monomer-monomer interactions being purely repulsive, while two types of attractive wall-monomer interactions are considered: (i) a strongly attractive Mie-type potential, appropriate for a strictly structureless wall, and (ii) a corrugat…

Semiflexible polymers under good solvent conditions interacting with repulsive walls.

Solutions of semiflexible polymers confined by repulsive planar walls are studied by density functional theory and Molecular Dynamics simulations, to clarify the competition between the chain alignment favored by the wall and the depletion caused by the monomer-wall repulsion. A coarse-grained bead-spring model with bond bending potential is studied, varying both the contour length and the persistence length of the polymers, as well as the monomer concentration in the solution (good solvent conditions are assumed throughout, and solvent molecules are not included explicitly). The profiles of monomer density and pressure tensor components near the wall are studied, and the surface tension of…

Antiferromagnetism-Induced Spin Splitting in Systems Described by Magnetic Layer Groups

Phase behavior of flexible and semiflexible polymers in solvents of varying quality.

The interplay of nematic order and phase separation in solutions of semiflexible polymers in solvents of variable quality is investigated by density functional theory (DFT) and molecular dynamics (MD) simulations. We studied coarse-grained models, with a bond-angle potential to control chain stiffness, for chain lengths comparable to the persistence length of the chains. We varied both the density of the monomeric units and the effective temperature that controls the quality of the implicit solvent. For very stiff chains, only a single transition from an isotropic fluid to a nematic is found, with a phase diagram of "swan-neck" topology. For less stiff chains, however, also unmixing between…

Nematic order in solutions of semiflexible polymers: Hairpins, elastic constants, and the nematic-smectic transition

Coarse-grained models of lyotropic solutions of semiflexible polymers are studied by both molecular dynamics simulations and density functional theory calculations, using an implicit solvent bead-spring model with a bond-angle potential. We systematically vary the monomer density, persistence length, and contour length over a wide range and explore the full range from the isotropic-nematic transition to the nematic-smectic transition. In the nematic regime, we span the entire regime from rigid-rod like polymers to thin wormlike chains, confined in effective straight tubes caused by the collective nematic effective ordering field. We show that the distribution of bond angles relative to the …

Interaction Between Polymer Brush-Coated Spherical Nanoparticles: Effect of Solvent Quality

The interaction between two spherical polymer brushes in solvents of variable quality is studied by molecular dynamics simulation and by self-consistent field theory, varying both the radius of the spherical particles and their distance, as well as the grafting density and the chain length of the end-grafted flexible polymer chains. Both the potential of mean force between the particles as a function of their distance is computed, for various choices of the parameters mentioned above, and the structural characteristics are discussed (density profiles, average end-to-end distance of grafted chains, etc.) It is found that for rather short chain lengths and not too large grafting densities, is…

Semiflexible polymer brushes and the brush-mushroom crossover.

Semiflexible polymers end-grafted to a repulsive planar substrate under good solvent conditions are studied by scaling arguments, computer simulations, and self-consistent field theory. Varying the chain length N, persistence length lp, and grafting density σg, the chain linear dimensions and distribution functions of all monomers and of the free chain ends are studied. Particular attention is paid to the limit of very small σg, where the grafted chains behave as "mushrooms" no longer interacting with each other. Unlike a flexible mushroom, which has a self-similar structure from the size (a) of an effective monomer up to the mushroom height (h/a ∝ N(v), ν ≈ 3/5), a semiflexible mushroom (l…