ANALYTICAL SOLUTION OF THE ASSOCIATIVE MEAN SPHERICAL APPROXIMATION FOR THE ION-DIPOLE MODEL

A simple electrolyte in a polar solvent is modelled by a mixture of polar hard spheres and equal diameter charged hard spheres with the possibility of ionic dimerization. The analytical solution of the associative mean spherical approximation (AMSA) for this model is derived to its full extent. Explicit expressions for pair correlation functions and dielectric constant in terms of the AMSA are established. Some numerical calculations illustrate the role of ionic association.Простий електроліт моделюється в полярному розчиннику сумішшю полярних твердих сфер і однакового розміру заряджених твердих сфер із можливою іонною димеризацією. Подано аналітичний розв’язок асоціативного середньо-сферичного наближення для цієї моделі (АССН). Приводяться точні вирази для парних кореляційних функцій і діелектричної константи в термінах АССН. Роль іонної асоціативності ілюструється числовими результатами

Analytical solution of the associative mean spherical approximation for the ion-dipole model

A simple electrolyte in a polar solvent is modelled by a mixture of polar hard spheres and equal diameter charged hard spheres with the possibility of ionic dimerization. The analytical solution of the associative mean spherical approximation (AMSA) for this model is derived to its full extent. Explicit expressions for pair correlation functions and dielectric constant in terms of the AMSA are established. Some numerical calculations illustrate the role of ionic association.Простий електроліт моделюється в полярному розчиннику сумішшю полярних твердих сфер і однакового розміру заряджених твердих сфер із можливою іонною димеризацією. Подано аналітичний розв’язок асоціативного середньо-сферичного наближення для цієї моделі (АССН). Приводяться точні вирази для парних кореляційних функцій і діелектричної константи в термінах АССН. Роль іонної асоціативності ілюструється числовими результатами

Polynomials for Crystal Frameworks and the Rigid Unit Mode Spectrum

To each discrete translationally periodic bar-joint framework \C in \bR^d we associate a matrix-valued function \Phi_\C(z) defined on the d-torus. The rigid unit mode spectrum \Omega(\C) of \C is defined in terms of the multi-phases of phase-periodic infinitesimal flexes and is shown to correspond to the singular points of the function z \to \rank \Phi_\C(z) and also to the set of wave vectors of harmonic excitations which have vanishing energy in the long wavelength limit. To a crystal framework in Maxwell counting equilibrium, which corresponds to \Phi_\C(z) being square, the determinant of \Phi_\C(z) gives rise to a unique multi-variable polynomial p_\C(z_1,\dots,z_d). For ideal zeolites the algebraic variety of zeros of p_\C(z) on the d-torus coincides with the RUM spectrum. The matrix function is related to other aspects of idealised framework rigidity and flexibility and in particular leads to an explicit formula for the number of supercell-periodic floppy modes. In the case of certain zeolite frameworks in dimensions 2 and 3 direct proofs are given to show the maximal floppy mode property (order $N$). In particular this is the case for the cubic symmetry sodalite framework and some other idealised zeolites.Comment: Final version with new examples and figures, and with clearer streamlined proof

Thermodynamics and Dynamics of a Monoatomic Glass-Former. Constant Pressure and Constant Volume Behavior

We report constant-volume and constant-pressure simulations of the thermodynamic and dynamic properties of the low-temperature liquid and crystalline phases of the modified Stillinger-Weber (mSW) model. We have found an approximately linear increase of the effective Gaussian width of the distribution of inherent structures. This effect comes from non-Gaussianity of the landscape and is consistent with the predictions of the Gaussian excitations model representing the thermodynamics of the configurational manifold as an ensemble of excitations, each carrying an excitation entropy. The mSW model provides us with both the configurational and excess entropies, with the difference mostly attributed to vibrational anharmonicity. We therefore can address the distinction between the excess thermodynamic quantities often used in the Adam-Gibbs (AG) equation. We find a new break in the slope of the constant pressure AG plot when the excess entropy is used in the AG equation. The simulation diffusivity data are equally well fitted by applying a new equation, derived within the Gaussian excitations model, that emphasizes enthalpy over entropy as the thermodynamic control variable for transport in viscous liquids.Comment: 14 pages, 14 figure

Density of mechanisms within the flexibility window of zeolites

By treating idealized zeolite frameworks as periodic mechanical trusses, we show that the number of flexible folding mechanisms in zeolite frameworks is strongly peaked at the minimum density end of their flexibility window. 25 of the 197 known zeolite frameworks exhibit an extensive flexibility, where the number of unique mechanisms increases linearly with the volume when long wavelength mechanisms are included. Extensively flexible frameworks therefore have a maximum in configurational entropy, as large crystals, at their lowest density. Most real zeolites do not exhibit extensive flexibility, suggesting that surface and edge mechanisms are important, likely during the nucleation and growth stage. The prevalence of flexibility in real zeolites suggests that, in addition to low framework energy, it is an important criterion when searching large databases of hypothetical zeolites for potentially useful realizable structures.Comment: 11 pages, 3 figure

Theory of solvation in polar nematics

We develop a linear response theory of solvation of ionic and dipolar solutes in anisotropic, axially symmetric polar solvents. The theory is applied to solvation in polar nematic liquid crystals. The formal theory constructs the solvation response function from projections of the solvent dipolar susceptibility on rotational invariants. These projections are obtained from Monte Carlo simulations of a fluid of dipolar spherocylinders which can exist both in the isotropic and nematic phase. Based on the properties of the solvent susceptibility from simulations and the formal solution, we have obtained a formula for the solvation free energy which incorporates experimentally available properties of nematics and the length of correlation between the dipoles in the liquid crystal. Illustrative calculations are presented for the Stokes shift and Stokes shift correlation function of coumarin-153 in 4-n-pentyl-4'-cyanobiphenyl (5CB) and 4,4-n-heptyl-cyanopiphenyl (7CB) solvents as a function of temperature in both the nematic and isotropic phase.Comment: 19 pages, 9 figure