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Randall D. Kamien

Publications and source records attributed to Randall D. Kamien.

At least 91 records · Page 5Linked to original sources
arXiv2005

Self-Consistent Field Theory of Multiply-Branched Block Copolymer Melts

We present a numerical algorithm to evaluate the self-consistent field theory for melts composed of block copolymers with multiply-branched architecture. We present results for the case of branched copolymers with doubly-functional groups for multiple branching generations. We discuss the stability of the cubic phase of spherical micelles, the A15 phase, as a consequence of tendency of the AB interfaces to conform to the polyhedral environment of the Voronoi cell of the micelle lattice.

cond-mat.soft↗
arXiv2004

Interfaces in Diblocks: A Study of Miktoarm Star Copolymers

We study AB$_n$ miktoarm star block copolymers in the strong segregation limit, focussing on the role that the AB interface plays in determining the phase behavior. We develop an extension of the kinked-path approach which allows us to explore the energetic dependence on interfacial shape. We consider a one-parameter family of interfaces to study the columnar to lamellar transition in asymmetric stars. We compare with recent experimental results. We discuss the stability of the A15 lattice of sphere-like micelles in the context of interfacial energy minimization. We corroborate our theory by implementing a numerically exact self-consistent field theory to probe the phase diagram and the shape of the AB interface.

cond-mat.soft↗
arXiv2004

Elongation and fluctuations of semi-flexible polymers in a nematic solvent

We directly visualize single polymers with persistence lengths ranging from $\ell_p=0.05$ to 16 $μ$m, dissolved in the nematic phase of rod-like {\it fd} virus. Polymers with sufficiently large persistence length undergo a coil-rod transition at the isotropic-nematic transition of the background solvent. We quantitatively analyze the transverse fluctuations of semi-flexible polymers and show that at long wavelengths they are driven by the fluctuating nematic background. We extract both the Odijk deflection length and the elastic constant of the background nematic phase from the data.

cond-mat.soft↗
arXiv2003

BPS Configurations in Smectics

It is typical in smectic liquid crystals to describe elastic deformations with a linear theory when the elastic strain is small. We extend the recent, exact solution of Brener and Marchenko to more general one-dimensional deformations, including multiple edge dislocations by relying on the Bogomol'nyi, Prasad and Sommerfield (BPS) decomposition. We introduce an approximation for the deformation profile far from a spherical inclusion and find an enhanced attractive interaction at long distances due to the nonlinear elasticity.

cond-mat.soft↗
arXiv2003

Smectic blue phases: layered systems with high intrinsic curvature

We report on a construction for smectic blue phases, which have quasi-long range smectic translational order as well as three dimensional crystalline order. Our proposed structures fill space by adding layers on top of a minimal surface, introducing either curvature or edge defects as necessary. We find that for the right range of material parameters, the favorable saddle-splay energy of these structures can stabilize them against uniform layered structures. We also consider the nature of curvature frustration between mean curvature and saddle-splay.

cond-mat.soft↗
arXiv2003

Topological Constraints at the Theta Point: Closed Loops at Two Loops

We map the problem of self-avoiding random walks in a Theta solvent with a chemical potential for writhe to the three-dimensional symmetric U(N)-Chern-Simons theory as N goes to 0. We find a new scaling regime of topologically constrained polymers, with critical exponents that depend on the chemical potential for writhe, which gives way to a fluctuation-induced first-order transition.

cond-mat.stat-mech↗
arXiv2002

Smectic Phases with Cubic Symmetry: The Splay Analog of the Blue Phase

We report on a construction for smectic blue phases, which have quasi-long range smectic translational order as well as long range cubic or hexagonal order. Our proposed structures fill space with a combination of minimal surface patches and cylindrical tubes. We find that for the right range of material parameters, the favorable saddle-splay energy of these structures can stabilize them against uniform layered structures.

cond-mat.soft↗
arXiv2002

The Geometry of Soft Materials: A Primer

We present an overview of the differential geometry of curves and surfaces using examples from soft matter as illustrations. The presentation requires a background only in vector calculus and is otherwise self-contained.

cond-mat.soft↗
arXiv2002

Nonlinear Effects in the TGB_A Phase

We study the nonlinear interactions in the TGB_A phase by using a rotationally invariant elastic free energy. By deforming a single grain boundary so that the smectic layers undergo their rotation within a finite interval, we construct a consistent three-dimensional structure. With this structure we study the energetics and predict the ratio between the intragrain and intergrain defect spacing, and compare our results with those from linear elasticity and experiment.

cond-mat.soft↗
arXiv2001

Maximizing Entropy by Minimizing Area: Towards a New Principle of Self-Organization

We propose a heuristic explanation for the numerous non-close-packed crystal structures observed in various colloidal systems. By developing an analogy between soap froths and the soft coronas of fuzzy colloids, we provide a geometrical interpretation of the free energy of soft spheres. Within this picture, we show that the close-packing rule associated with hard-core interaction and positional entropy of particles is frustrated by a minimum-area principle associated with the soft tail and internal entropy of the soft coronas. We also discuss these ideas in terms of crystal architecture and pair distribution functions and analyze the phase diagram of a model hard-sphere--square-shoulder system within the cellular theory. We find that the A15 lattice, known to be area minimizing, is favored for a reasonable range of model parameters and so it is among the possible equilibrium states for a variety of colloidal systems. We also show that in the case of short-range convex potentials the A15 and other non-close-packed lattices coexist over a broad ranges of densities, which could make their identification difficult.

cond-mat.soft↗
arXiv2001

Dislocation Geometry in the TGB-A Phase: Linear Theory

We demonstrate that an arbitrary system of screw dislocations in a smectic-A liquid crystal may be consistently treated within harmonic elasticity theory, provided that the angles between dislocations are sufficiently small. Using this theory, we calculate the ground state configuration of the TGB-A phase. We obtain an estimate of the twist-grain-boundary spacing and screw dislocation spacing in a boundary in terms of the macroscopic parameters, in reasonable agreement with experimental results.

cond-mat.soft↗
arXiv2000

Order and Frustration in Chiral Liquid Crystals

This paper reviews the complex ordered structures induced by chirality in liquid crystals. In general, chirality favors a twist in the orientation of liquid-crystal molecules. In some cases, as in the cholesteric phase, this favored twist can be achieved without any defects. More often, the favored twist competes with applied electric or magnetic fields or with geometric constraints, leading to frustration. In response to this frustration, the system develops ordered structures with periodic arrays of defects. The simplest example of such a structure is the lattice of domains and domain walls in a cholesteric phase under a magnetic field. More complex examples include defect structures formed in two-dimensional films of chiral liquid crystals. The same considerations of chirality and defects apply to three-dimensional structures, such as the twist-grain-boundary and moire phases.

cond-mat.soft↗
arXiv2000

Soap Froths and Crystal Structures

We propose a physical mechanism to explain the crystal symmetries found in macromolecular and supramolecular micellar materials. We argue that the packing entropy of the hard micellar cores is frustrated by the entropic interaction of their brush-like coronas. The latter interaction is treated as a surface effect between neighboring Voronoi cells. The observed crystal structures correspond to the Kelvin and Weaire-Phelan minimal foams. We show that these structures are stable for reasonable areal entropy densities.

cond-mat.soft↗
arXiv1999

Chiral Interactions and Structures

The chiral structure of liquid crystalline phases arises due to the intrinsic chirality of the constituent mesogens. While it is seemingly straightforward to quantify the macroscopic chirality by using, for instance, the cholesteric pitch or the optical rotatory power, it is not as simple to quantify the chirality of a single molecule. I will discuss a systematic quantification of molecular chirality and show how the resulting chiral parameters may be used to predict macroscopic chiral structure.

cond-mat.soft↗
arXiv1999

Poisson Bracket Formulation of Nematic Polymer Dynamics

We formulate the dynamical theory of nematic polymers, starting from a microscopic Poisson bracket approach. We find that the Poisson bracket between the nematic director and momentum depends on the (Maier-Saupe) order parameter of the nematic phase. We use this to derive reactive couplings of the nematic director to the strain rates. Additionally, we find that local dynamics breaks down as the polymers begin to overlap. We offer a physical picture for both results.

cond-mat.soft↗
arXiv1999

Molecular Chirality and Chiral Parameters

The fundamental issues of symmetry related to chirality are discussed and applied to simple situations relevant to liquid crystals. We show that any chiral measure of a geometric object is a pseudoscalar (invariant under proper rotations but changing sign under improper rotations) and must involve three-point correlations which only come into play when the molecule has at least four atoms. In general, a molecule is characterized by an infinite set of chiral parameters. We illustrate the fact that these parameters can have differing signs and can vanish at different points as a molecule is continuously deformed into its mirror image. From this it is concluded that handedness is not an absolute concept but depends on the property being observed. Within a simplified model of classical interactions, we identify the chiral parameter of the constituent molecules which determines the macroscopic pitch of cholesterics.

cond-mat.stat-mech↗