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Biomedical subjects

Randall D Kamien

Publications and source records attributed to Randall D Kamien.

13 recordsLinked to original sources
PubMed2006

Elliptic phases: a study of the nonlinear elasticity of twist-grain boundaries.

We develop an explicit and tractable representation of a twist-grain-boundary phase of a smectic-A liquid crystal. This allows us to calculate the interaction energy between grain boundaries and the relative contributions from the bending and compression deformations. We discuss the special stability of the pi/2 grain boundaries and discuss the relation of this structure to the Schwarz D surface.

Biomechanical Phenomena↗
PubMed2006

Geometry of proteins: hydrogen bonding, sterics, and marginally compact tubes.

The functionality of proteins is governed by their structure in the native state. Protein structures are made up of emergent building blocks of helices and almost planar sheets. A simple coarse-grained geometrical model of a flexible tube barely subject to compaction provides a unified framework for understanding the common character of globular proteins. We argue that a recent critique of the tube idea is not well founded.

Computer Simulation↗
PubMed2005

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 the tendency of the AB interfaces to conform to the polyhedral environment of the Voronoi cell of the micelle lattice.

Journal Article↗
PubMed2005

Entropically driven helix formation.

The helix is a ubiquitous motif for biopolymers. We propose a heuristic, entropically based model that predicts helix formation in a system of hard spheres and semiflexible tubes. We find that the entropy of the spheres is maximized when short stretches of the tube form a helix with a geometry close to that found in natural helices. Our model could be directly tested with wormlike micelles as the tubes, and the effect could be used to self-assemble supramolecular helices.

Colloids↗
PubMed2004

The foam analogy: from phases to elasticity.

By mapping the interactions of colloidal particles onto the problem of minimizing areas, the physics of foams can be used to understand the phase diagrams of both charged and fuzzy colloids. We extend this analogy to study the elastic properties of such colloidal crystals and consider the face-centered cubic, body-centered cubic and A15 lattices. We discuss two types of soft interparticle potentials corresponding to charged and fuzzy colloids, respectively, and we analyze the dependence of the elastic constants on density as well as on the parameters of the potential. We show that the bulk moduli of the three lattices are generally quite similar, and that the shear moduli of the two non-close-packed lattices are considerably smaller than in the face-centered cubic lattice. We find that in charged colloids, the elastic constants are the largest at a finite screening length, and we discuss a shear instability of the A15 lattice.

Journal Article↗
PubMed2004

Elongation and fluctuations of semiflexible polymers in a nematic solvent.

We directly visualize single polymers with persistence lengths l(p), ranging from 0.05 to 16 microm, dissolved in the nematic phase of rodlike fd virus. Polymers with a 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 the semiflexible polymers and show that at long wavelengths they are driven by the fluctuating nematic background. We extract the Odijk deflection length and the elastic constant of the background nematic phase from the data.

Actins↗
PubMed2003

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.

Journal Article↗
PubMed2003

Geometric theory of diblock copolymer phases.

We analyze the energetics of spherelike micellar phases in diblock copolymers in terms of well-studied, geometric quantities for their lattices. We argue that the A15 lattice with Pm3;n symmetry should be favored as the blocks become more symmetric and corroborate this through a self-consistent field theory. Because phases with columnar or bicontinuous topologies intervene, the A15 phase, though metastable, is not an equilibrium phase of symmetric diblocks. We investigate the phase diagram of branched diblocks and find that the A15 phase is stable.

Journal Article↗
PubMed2003

Bogomol'nyi, Prasad, and Sommerfield configurations in smectics.

It is typical in smectic liquid crystals to describe elastic deformations with a linear theory when the elastic strain is small. In smectics, certain essential nonlinearities arise from the requirement of rotational invariance. By employing the Bogomol'nyi, Prasad, and Sommerfield decomposition and relying on boundary conditions and geometric invariants, we have found a large class of exact solutions. 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, confirmed by numerical minimization.

Journal Article↗
PubMed2002

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.

Journal Article↗
PubMed2002

Foam analogy in charged colloidal crystals.

We model charged colloidal suspensions using an analogy with foams. We study the solid-solid phase transitions of these systems as a function of particle volume fraction and ionic strength. The screened-Coulomb interaction is replaced by an interaction between walls of the Voronoi cells around each particle. We fit the surface charge to reproduce the phase diagram for the charged suspension studied by Sirota et al. [Phys. Rev. Lett. 62, 1524 (1989)]. With this fit parameter we are able to calculate the elastic moduli of the system and find good agreement with the available data.

Journal Article↗