Interaction between a disclination and a uniaxial-isotropic phase interface in a nematic liquid crystal

We consider the interaction between a disclination line of strength +/-1/2 and an interface between the uniaxial and isotropic phases of a nematic liquid crystal. We apply a recently developed set of interface conditions including a configurational force balance which generalizes the Gibbs-Thomson equation to account for the curvature elasticity of the uniaxial phase and the orientation dependence of the interfacial free-energy density. We consider a rectangular vessel containing both phases and a disclination. We formulate a relevant free-boundary problem and use numerical methods to determine equilibrium shapes of the interface. When the interfacial free-energy is constant, the shape of the interface is insensitive to whether the strength of the defect is +1/2 or -1/2 and to rotations of the director field consistent with the boundary conditions. Accounting for the dependence of the interfacial free-energy density on the angle between the interfacial unit normal field and the director field eliminates these degeneracies. In particular, when such dependence is taken into account, different solution branches are found, indicating the presence of a bifurcation. We find also that, depending on the magnitude of the anisotropic contribution to the interfacial free-energy density, the interaction between the disclination and the interface may be repulsive or attractive. When the interaction is repulsive, the disclination line positions itself at an energetically optimal distance adjacent to the interface. Otherwise, the uniaxial phase expels the disclination to the interface where a cusp forms.     

Incompatible strains associated with defects in nematic elastomers

In a nematic elastomer the deformation of the polymer network chains is coupled to the orientational order of the mesogenic groups. Statistical arguments have derived the so-called neoclassical free energy that models this coupling. Here we show that the neoclassical model supplemented by the usual Frank energy predicts incompatible network strains associated with the formation of standard nematic textures. The incompatibility is measured by the Riemann curvature tensor, which we find to be nonzero for both radial hedgehog defects and escaped disclinations of strength +1 in circular cylinders. Analogous problems for conventional nonlinearly elastic solids do not possess solutions with such incompatibilities. Compatibility in nematic elastomers would require either more complicated nematic textures in elastomers than in conventional (polymeric and low molecular weight) liquid crystals or a free-energy density more complicated than the neoclassical expression.     

First principles simulation of a superionic phase of hydrogen fluoride (HF) at high pressures and temperatures

We have conducted ab initio molecular dynamics simulations of hydrogen fluoride (HF) at pressures of 5-66 GPa along the 900 K isotherm. We predict a superionic phase at 33 GPa, where the fluorine atoms are fixed in a bcc lattice while the hydrogen atoms diffuse rapidly with a diffusion constant between 2 x 10(-5) and 5 x 10(-5)cm(2)s. We find that a transformation from asymmetric to symmetric hydrogen bonding occurs in HF at 66 GPa and 900 K. With superionic HF we have discovered a model system where symmetric hydrogen bonding occurs at experimentally achievable conditions. Given previous results on superionic H(2)O [Goldman et al., Phys. Rev. Lett. 94, 217801 (2005)] and NH(3) [Cavazzoni et al., Science 283, 44 (1999)], we conclude that high P, T superionic phases of electronegative element hydrides could be common.     

Improved wood–kirkwood detonation chemical kinetics

We report an improved implementation of the Wood–Kirkwood kinetic detonation model based on a multi-species Buckingham exponential-6 equation of state (EOS) and multiple reaction rate laws. The exp-6 EOS allows for treatment of chemical systems at a statistical mechanics level, instead of an atomistic level. Finite global rate laws are used for the slowest chemical reactions. Other reactions are given infinite rates and are kept in constant thermodynamic equilibrium. The global rates do not necessarily correspond to a specific physical process, but rather to the sum total of slow physical processes. We model ideal and non-ideal composite energetic materials. We find that using the exp-6 non-ideal model improves the accuracy. The detonation velocity as a function of charge radius is also correctly reproduced. Contribution to the Mark S. Gordon on 65th Birthday Festschrift Issue.     

Gradient nanoscale polycrystalline elasticity: Intergrain interactions and triple-junction conditions

Using the principle of virtual power, we develop general balance equations, interface conditions, triple-junction conditions, and boundary conditions for second-grade nanocrystalline elastic materials undergoing infinitesimal deformations. We further develop thermodynamically consistent constitutive equations and provide a weak formulation of resulting boundary-value problems that automatically yields internal conditions such those that hold across interfaces and at triple junctions.     

Free-energy density functions for nematic elastomers

The recently proposed neo-classical theory for nematic elastomers generalizes standard molecular-statistical Gaussian network theory to allow for anisotropic distributions of polymer chains. The resulting free-energy density models several of the novel properties of nematic elastomers. In particular, it predicts the ability of nematic elastomers to undergo large deformations with exactly zero force and energy cost—so called soft elasticity. Although some nematic elastomers have been shown to undergo deformations with unusually small applied forces, not all do so, and none deform with zero force. Further, as a zero force corresponds to infinitely many possible deformations in the neo-classical theory, this non-uniqueness leads to serious indeterminacies in numerical schemes. Here we suggest that the neo-classical free-energy density is incomplete and propose an alternative derivation that resolves these difficulties. In our approach, we use the molecular-statistical theory to identify appropriate variables. This yields the choice for the microstructural degrees of freedom as well as two independent strain tensors (the overall macroscopic strain plus a relative strain that indicates how the deformation of the elastomeric microstructure deviates from the macroscopic deformation). We then propose expressions for the free-energy density as a function of the three quantities and show how the material parameters can be measured by two simple tests. The neo-classical free-energy density can be viewed as a special case of our expressions in which the free-energy density is independent of the overall macroscopic strain, thus supporting our view that the neo-classical theory is incomplete.