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Articles 1 - 4 of 4
Full-Text Articles in Physical Sciences and Mathematics
Undulated Cylinders Of Charged Diblock Copolymers, Gregory M. Grason, Christian Santangelo
Undulated Cylinders Of Charged Diblock Copolymers, Gregory M. Grason, Christian Santangelo
Christian Santangelo
We study the cylinder to sphere morphological transition of diblock copolymers in aqueous solution with a hydrophobic block and a charged block. We find a metastable undulated cylinder configuration for a range of charge and salt concentrations which, nevertheless, occurs above the threshold where spheres are thermodynamically favorable. By modeling the shape of the cylinder ends, we find that the free-energy barrier for the transition from cylinders to spheres is quite large and that this barrier falls significantly in the limit of high polymer charge and low solution salinity. This suggests that observed undulated cylinder phases are kinetically trapped structures.
Smectic Liquid Crystals: Materials With One-Dimensional, Periodic Order, Randall D. Kamien, Christian Santangelo
Smectic Liquid Crystals: Materials With One-Dimensional, Periodic Order, Randall D. Kamien, Christian Santangelo
Christian Santangelo
Smectic liquid crystals are materials formed by stacking deformable, fluid layers. Although smectics prefer to have flat, uniformly-spaced layers, boundary conditions can impose curvature on the layers. Since the layer spacing and curvature are intertwined, the problem of finding minimal configurations for the layers becomes nontrivial. We discuss various topological and geometrical aspects of these materials and present recent progress on finding some exact layer configurations. We also exhibit connections to the study of certain embedded minimal surfaces and briefly summarize some important open problems.
Elliptic Phases: A Study Of The Nonlinear Elasticity Of Twist-Grain Boundaries, Christian Santangelo, Randall D. Kamien
Elliptic Phases: A Study Of The Nonlinear Elasticity Of Twist-Grain Boundaries, Christian Santangelo, Randall D. Kamien
Christian Santangelo
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 π/2 grain boundaries and discuss the relation of this structure to the Schwarz D surface.
Computing Counterion Densities At Intermediate Coupling, Christian Santangelo
Computing Counterion Densities At Intermediate Coupling, Christian Santangelo
Christian Santangelo
By decomposing the Coulomb interaction into a long-distance component appropriate for mean-field theory, and a non-mean-field short distance component, we compute the counterion density near a charged surface for all values of the counterion coupling parameter. A modified strong-coupling expansion that is manifestly finite at all coupling strengths is used to treat the short-distance component. We find a nonperturbative correction related to the lateral counterion correlations that modifies the density at intermediate coupling.