Entropy-driven enhanced self-diffusion in confined reentrant supernematics

We present a molecular dynamics study of reentrant nematic phases using the Gay-Berne-Kihara model of a liquid crystal in nanoconfinement. At densities above those characteristic of smectic A phases, reentrant nematic phases form that are characterized by a large value of the nematic order parameter S?1. Along the nematic director these "supernematic" phases exhibit a remarkably high self-diffusivity, which exceeds that for ordinary, lower-density nematic phases by an order of magnitude. Enhancement of self-diffusivity is attributed to a decrease of rotational configurational entropy in confinement. Recent developments in the pulsed field gradient NMR technique are shown to provide favorable conditions for an experimental confirmation of our simulations.     

Intrusion of fluids into nanogrooves

We study the shape of gas-liquid interfaces forming inside rectangular nanogrooves (i.e., slit-pores capped on one end). On account of purely repulsive fluid-substrate interactions the confining walls are dry (i.e., wet by vapor) and a liquid-vapor interface intrudes into the nanogrooves to a distance determined by the pressure (i.e., chemical potential). By means of Monte Carlo simulations in the grand-canonical ensemble (GCEMC) we obtain the density ρ(z) along the midline (x = 0 of the nanogroove for various geometries (i.e., depths D and widths L of the nanogroove. We analyze the density profiles with the aid of an analytic expression which we obtain through a transfer-matrix treatment of a one-dimensional effective interface Hamiltonian. Besides geometrical parameters such as D and L , the resulting analytic expression depends on temperature T , densities of coexisting gas and liquid phases in the bulk ρ^g,l _x and the interfacial tension γ . The latter three quantities are determined in independent molecular dynamics simulations of planar gas-liquid interfaces. Our results indicate that the analytic formula provides an excellent representation of ρ(z) as long as L is sufficiently small. At larger L the meniscus of the intruding liquid flattens. Under these conditions the transfer-matrix analysis is no longer adequate and the agreement between GCEMC data and the analytic treatment is less satisfactory.     

Drinfeld modules and torsion in the Chow groups of certain threefolds

Let E B be an elliptic surface defined over the algebraic closureof a finite field of characteristic greater than 5. Let W bea resolution of singularities of E x _B E. We show that the l-adicAbel–Jacobi map from the l-power-torsion in the secondChow group of W to H³(W, _l(2)) _l/_l is an isomorphism for almostall primes l. A main tool in the proof is the assertion thatcertain CM-cycles in fibres of W B are torsion, which is provenusing results from the theory of Drinfeld modular curves.     

Surface acidity and basicity of functionalized silica particles

Tetraethoxysilane has been co-hydrolyzed with functionalized organosilanes in a modified Stöber process to produce silica particles with amino, carboxylate or dihydroimidazole groups on the surface. The effects of reaction conditions and the loading of the functionalized organosilane on particle size was examined by TEM. Fluorescence spectroscopy of the surface amino groups covalently modified with fluorescamine, and the surface carboxylate groups with 4-bromomethyl-6,7-dimethoxycoumarin, demonstrated that these functional groups were accessible for further reaction. Changes in surface acidity and basicity caused by the presence of functional groups (amine, dihydroimidazole, carboxylate) on the particle surface were determined using an indicator titration technique. Particles with surface imidazole and amine groups and particles with surface carboxylate groups have enhanced basicity and acidity, respectively. Dihydroimidazole-modified silica had greater surface basicity than the amine-modified silica. The effect on basicity and acidity increases as the amount of added functionalized silane increases. However, this increase is nonlinear with respect to the increase in added functionalized silane. Particles with both surface dihydroimidazole and carboxylate groups demonstrated reduced surface basicity and acidity.     

Finite-size scaling analysis of isotropic-polar phase transitions in an amphiphilic fluid

We present Monte Carlo simulations of the isotropic-polar (IP) phase transition in an amphiphilic fluid carried out in the isothermal-isobaric ensemble. Our model consists of Lennard-Jones spheres where the attractive part of the potential is modified by an orientation-dependent function. This function gives rise to an angle dependence of the intermolecular attractions corresponding to that characteristic of point dipoles. Our data show a substantial system-size dependence of the dipolar order parameter. We analyze the system-size dependence in terms of the order-parameter distribution and a cumulant involving its first and second moments. The order parameter, its distribution, and susceptibility observe the scaling behavior characteristic of the 3D Ising universality class. Because of this scaling behavior and because all cumulants have a common intersection irrespective of system size we conclude that the IP phase transition is continuous. Considering pressures 1.3 ≤ P ≤ 3.0 we demonstrate that a line of continuous phase transitions exists which is analogous to the Curie line in systems exhibiting a ferroelectric transition. Our results are qualitatively consistent with Landau's theory of continuous phase transitions.