Michael C. Weinberg

Molecular rotation and reorientation: Microscopic and hydrodynamic contributions

The relative roles of microscopic and hydrodynamic contributions to molecular rotation and reorientation are examined within the framework of the microscopic boundary layer theory recently proposed by the authors. The theory is applied to rough spheres, for which computer simulation data are available and to experimental results on spherical top molecules. Attention is focused on rotational diffusion constants, the kappa parameter introduced by Kivelson et al., and orientational relaxation times. It is shown that, while collective effects are present and often nonnegligible, the motion of small molecules is dominated by its microscopic aspects. Experimental trends which can incorrectly suggest dominance by hydrodynamic contributions are discussed in some detail. Finally, the transition to the regime where collective effects are dominant is considered.

Molecular theory of translational diffusion: Microscopic generalization of the normal velocity boundary condition

A simple molecular theory is presented for the diffusion constant D for a test hard sphere translating in a hard sphere solvent. It is argued that there is a breakdown of the applicability of hydrodynamics in the neighborhood of the test particle due to collisional effects. It is shown that, as a consequence, the traditional hydrodynamic boundary condition (BC) on the particle–solvent normal relative velocity is incorrect for molecular motion. An approximate replacement for this BC is constructed from collisional considerations. With this new BC and the usual hydrodynamic equations, D is found to have two additive contributions. The first is the microscopic, collisional Enskog diffusion constant; the second is of the hydrodynamic Stokes–Einstein form. It is shown how the standard hydrodynamic Stokes–Einstein relation for D can hold numerically to a good approximation despite the dominance of (or significant contribution to) the motion by microscopic collisional contributions. Observed trends of D with siz...

A test of classical nucleation theory: crystal nucleation of lithium disilicate glass

For several inorganic glasses predictions have been made of the homogeneous crystal nucleation rate using classical nucleation theory. However, in none of these cases were comparisons made with experiment, due primarily to the inability of being able to guarantee homogeneous conditions. Evidence has been provided that crystalline formation in Li2O · 2 SiO2 glass may initiate by a homogeneous mechanism. Thus, we have computed the nucleation rate curve of lithium disilicate crystals in this glass. It is found that not only do all forms of the classical theory predict nucleation rates many orders of magnitude smaller than those observed, but also that the temperature dependence of the theoretical rate is quite different from that observed.

Microscopic boundary layer effects and rough sphere rotation

A calculation of the rough sphere angular velocity correlation function is presented which takes into account the presence of both the microscopic boundary layer and outer hydrodynamic regions around the test particle. The boundary layer region is approximately accounted for by the slip boundary condition while generalized hydrodynamic equations (frequency dependent transport coefficients plus fluid spin variables) are used to describe the outer region. The approximate calculation of the slip coefficient and the use of the slip coefficient to account for processes occurring in the boundary layer are discussed in the context of kinetic theory results. Since a description of both regions is incorporated, the present theory contains both microscopic and collective effects. The structure of the result is compared in some detail to a recent renormalized kinetic theory calculation on the same system and various levels of approximation are examined. The results are in good agreement with the molecular dynamics c...

Slip boundary condition for rough sphere rotation

Abstract Microscopic boundary layer effects for rough sphere rotation are considered via a slip boundary condition. Predictions for diffusion constants are compared with molecular dynamics results. The slip coefficient is discussed.

Crystallization of Na2OSiO2 gel and glass

Abstract The crystallization behavior of a 19 wt% soda silica gel and gel-derived glass was compared to that of the ordinary glass of the same composition. Both bulk and ground glass samples were utilized. X-ray diffraction measurements were made to identify the crystalline phases and gauge the extent of crystallization. It was found that the gel crystallized in a distinctive manner, while the gel glass behavior was not qualitatively different from that of the ordinary glass.

The preparation and characterization of a lithium borate glass prepared by the gel technique

The preparation of an amorphous lithium borate gel by the metal organic procedure is described. In addition, a preliminary evaluation of the behaviour of the gel upon heating is given. In particular the crystallization tendency of the gel is studied with the aid of DTA and X-ray diffraction, and the structural changes in the gel are monitored with the aid of IR spectroscopy. The glass produced from the lithium borate gel is compared to both the gel precursor material and a glass of similar composition prepared by conventional techniques. Specifically, the relevant water contents, crystallization behaviour, and structural features are contrasted.

The crystallization behavior and kinetics of a barium fluorozirconate type glass

Abstract An investigation of the crystallization behavior of a Zr-Ba-La-Al-F glass which is subjected to isothermal heat treatments is presented. The number and nature of the crystalline phases which form and their nucleation sites are determined at three temperatures. Also, the growth rate and volume fraction of crystals which nucleate internally in the glass, when heated at 320°C, are determined as a function of time.

Surface tension effects in gas bubble dissolution and growth

Abstract The influence of surface tension upon the dissolution and growth of a stationary, isolated gas bubble in a fluid is examined. It is demonstrated that for small gas undersaturation of the liquid, surface tension corrections for bubble dissolution are significant for nearly the entire period of bubble dissolution. Also, it is shown that for slight supersaturation of the liquid, when bubble growth occurs, surface tension corrections are non-negligible too. Furthermore, comparisons are made with the quasi-stationary results which seem to indicate that surface tension corrections are of greater significance than convective corrections for small undersaturations. In the case of large undersaturations surface tension corrections are only of importance when the radius of the bubble is small.

Crystallization of barium fluorozirconate based glasses

Abstract The crystallization behavior of glass in the barium fluorozirconate family is examined. In particular, the number and type of crystalline phases which form upon isothermal heat treatment is studied. In addition, the sequence of crystallization events, and the nature of the potential crystallization sites are discussed. Finally, the random (non-reproducible) nature of the crystallization behavior is described and analyzed.