Statistical thermodynamics evaluation of polymer–polymer miscibility

The Simha and Somcynsky (S–S) statistical thermodynamics theory was used to compute the solubility parameters as a function of temperature and pressure [δ = δ(T, P)], for a series of polymer melts. The characteristic scaling parameters required for this task, P*, T*, and V*, were extracted from the pressure–temperature–volume (PVT) data. To determine the potential polymer–polymer miscibility, the dependence of δ versus T (at ambient pressure) was computed for 17 polymers. Close proximity of the δ versus T curves for four miscible polymer pairs: PPE/PS, PS/PVME, and PC/PMMA signaled the usefulness of this approach. It is noteworthy, that the tabulated solubility parameters (derived from the solution data under ambient conditions) propounded the immiscibility of the PVC/PVAc pair. The computed values of δ also suggested miscibility for polymer pairs of unknown miscibility, namely PPE/PVC, PPE/PVAc, and PET/PSF. In recognizing the limitations of the solubility parameter approach (the omission of several thermodynamic contributions), these preliminary results are auspicious because they indicate a new route for estimating the miscibility of any polymeric material at a given temperature and pressure. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 2909–2915, 2004     

Computation of confined coflow jets with three turbulence models

A numerical study of confined jets in a cylindrical duct is carried out to examine the performance of two recently proposed turbulence models: an RNG-based K-? model and a realizable Reynolds stress algebraic equation model. The former is of the same form as the standard K-? model but has different model coefficients. The latter uses an explicit quadratic stress-strain relationship to model the turbulent stresses and is capable of ensuring the positivity of each turbulent normal stress. The flow considered involves recirculation with unfixed separation and reatachment points and severe adverse pressure gradients, thereby providing a valuable test of the predictive capability of the models for complex flows. Calculations are performed with a finite volume procedure. Numerical credibility of the solutions is ensured by using second-order-accurate differencing schemes and sufficiently fine grids. Calculations with the standard K-? model are also made for comparison. Detailed comparisons with experiments show that the realizable Reynolds stress algebraic equation model consistently works better than does the standard K-? model in capturing the essential flow features, while the RNG-based K-? model does not seem to give improvements over the standard K-? model under the flow conditions considered.     

An Analytical Study of Molecular Transport in a Zeolite Crystallite Bed

Analytical solutions of the diffusion equations to obtain the diffusant concentrations in the macro- and micropores which constitute the pore system of a zeolite bed are presented. The parameter which determines the influence of each pore type on the evolution of the adsorbate/adsorbant system towards the equilibrium state is described. Examples are given to illustrate a qualitative and quantitative study based on the curves obtained from these equations.     

Retention of ionizable compounds on HPLC. Modelling retention for neutral and ionizable compounds by linear solvation energy relationships

Summary A global LSER model that relates HPLC retention to mobile phase composition and pH is tested for a varied group of solutes, both neutral and ionizable, in a polymeric column and methanol-water mobile phases. It is compared to the local LSER model developed only for a given mobile phase, i.e., a fixed organic modifier content, and to the global LSER model set only for neutral solutes. The global LSER model for neutral and ionizable solutes requires a few supplementary parameters over the other models tested, but it accounts for retention under any experimental conditions for a given column and methanol-water mobile phases, describing properly the interactions established in the HPLC system (hydrophobicity, hydrogen-bond acidity and basicity, dipolarity/polarizability…). This paper is number 13 of a series with the same general title: “Retention of Ionizable Compounds on HPLC” published in various journals.     

Stationary states of crystal growth in three dimensions

A new Markov process describing crystal growth in three dimensions is introduced. States of the process are configurations of the crystal surface, which has a terrace-edge-kink structure. The states are continuous along edges but discrete across edges, in accordance with the very different rates for the two types of captures of particles. Stationary distributions, describing steady crystal growth, are found in general. To our knowledge, these are the first examples of stationary distributions for layered crystal growth in three dimensions. The steady growth rate and other quantities are obtained explicitly for two interacting edges. For many interacting edges, growth behavior is determined (a) in various asymptotic regimes including thermodynamic limits, (b) via simulations, and (c) using series (cluster) expansions in the slope of the surface, the first three coefficients being computed. The theoretical growth rates show a marked dependence on surface dimensions. This may contribute to the size dependence and dispersion in the observed growth rate of small crystals.     

The Influence of the Flow-Pattern on Column Leaching Experiments: Formulation and Measurement by Radiotracer

The leaching of microconstituents from granular solid wastes is often studied by column experiments. The underlying assumption is that the flow is of the one-compartment or “backmix” type. The influence of small deviations from this ideal situation on the outcome of the leaching experiment depends slightly on the specific mass-transfer function of the trace involved. The deviation itself may be measured by a simple separate radiotracer experiment.     

Excitation of the Characteristic K Series Radiation,Coherent and Incoherent Scatter of Low Energy Gamma Rays

On the basis of a simplified mathematical model there is calculated the probability of a photon of characteristic K series radiation excited by a photon of low energy gamma radiation hitting the detector. There are also included the probabilities for coherently and incoherently scattered primary radiation considering electron binding energies.     

Exclusion process and droplet shape

We use a mathematical isomorphism between the one-dimensional exclusion process and the two-dimensional stochastic Ising model in the low-temperature limit to describe the typical instantaneous shape of a supercritical droplet. We derive, specifically, the exact asymptotic distribution of the boundaries of a (+1) spin region, confined to Z ₊ ² and subjected to a positive magnetic field. In an appropriate scaling, the boundary distribution converges to a deterministic continuum limit.On leave at the EPFL, CH-1015 Lausanne, Switzerland.     

Extremality and the global Markov property II: The global markov property for non-FKG maximal Gibbs measures

We give a condition on a Gibbs measure for an attractive Markov specification, which assures extremality and the global Markov property. As an example of application we consider the class of attractive Markov specifications defined on a compact configuration space over a two-dimensional lattice by the interaction Hamiltonians (assumed to have a finite set of periodic ground configurations) satisfying Peierl's condition. We prove that each extremal Gibbs measure for such a specification, at sufficiently low temperature, has the global Markov property.On leave of absence from the Institute of Theoretical Physics, University of Wrocaw, Poland.