Stable multi-sets

In this paper we introduce a generalization of stable sets: stable multi-sets. A stable multi-set is an assignment of integers to the vertices of a graph, such that specified bounds on vertices and edges are not exceeded. In case all vertex and edge bounds equal one, stable multi-sets are equivalent to stable sets.  For the stable multi-set problem, we derive reduction rules and study the associated polytope. We state necessary and sufficient conditions for the extreme points of the linear relaxation to be integer. These conditions generalize the conditions for the stable set polytope. Moreover, the classes of odd cycle and clique inequalities for stable sets are generalized to stable multi-sets and conditions for them to be facet defining are determined.  The study of stable multi-sets is initiated by optimization problems in the field of telecommunication networks. Stable multi-sets emerge as an important substructure in the design of optical networks. Received: February 14, 2001/Revised version: September 7, 2001     

Electrokinetic characterization of poly(dimethylsiloxane) microchannels

This paper characterizes the basic electrokinetic phenomena occurring within native poly(dimethylsiloxane) (PDMS) microchannels. Using simple buffers and current measurements, current density and electroosmosis data were determined in trapezoidal, reversibly sealed PDMS/PDMS and hybrid PDMS/glass channels with a cross-sectional area of 1035.5 microm(2) and about 6 cm length. This data was then compared to that obtained in an air-thermostated 50 microm inner diameter (1963.5 microm(2) cross-sectional area) fused-silica (FS) capillary of 70 cm length. Having a pH 7.8 buffer with an ionic strength (I) of 90 mM, Ohms's law was observed in the microchannels with electric field strengths of up to about 420 V/cm, which is about twice as high as for the FS capillary. The electroosmotic mobility (micro(EO)) in PDMS and FS is shown to exhibit the same general dependences on I and pH. For all configurations tested, the experimentally determined micro(EO) values were found to correlate well with the relationship micro(EO) = a + b log(I), where a and b are coefficients that are determined via nonlinear regression analysis. Electroosmotic fluid pumping in native PDMS also follows a pH dependence that can be estimated with a model based upon the ionization of silanol. Compared to FS, however, the magnitude of the electroosmotic flow in native PDMS is 50-70% smaller over the entire pH range and is difficult to maintain at acidic pH values. Thus, the origin of the negative charge at the inner wall of PDMS, glass, and FS appears to be similar but the density is lower for PDMS than for glass and FS.     

Surface characterization of industrial fibers with inverse gas chromatography

Inverse gas chromatography (IGC) was applied for the determination of the surface characteristics of Tenax carbon fibers and Akzo Nobel Twaron fibers. Furthermore, IGC procedures for the determination of dispersive and acid-base interactions were validated. The data show that too high values for the dispersive component of the surface energy are obtained when the adsorption area occupied by a single adsorbed n-alkane molecule is estimated from parameters of the corresponding liquid. Comparable values are obtained when the Doris-Gray methodology (area per methylene unit) or measured probe areas are employed. For the fibers studied in this work meaningful Gibbs energy values of the acid-base interaction were only obtained with the polarizability approach. When the dispersive interaction of the polar probes with the fiber surface was scaled to the n-alkane interaction via surface tension, the boiling point, or the vapor pressure of the probes often negative acid-base interaction energies were found. From the temperature dependence of the Gibbs energy, the enthalpy of the acid-base interactions of various probes with the carbon and Twaron aramid fibers was determined. However, from these enthalpy values no meaningful acid-base surface parameters could be obtained. Generally, the limited accuracy with which these parameters can be obtained make the usefulness of this procedure questionable. Also the Gibbs energy data of acid-base interaction can provide a qualitative basis to classify the acidity-basicity of the fiber surface. This latter approach requires only a limited data set and is sufficiently rapid to enable the use of IGC as a screening tool for fibers at a production site. For several polar probes significant concentration effects on carbon fibers were observed. At very low probe loadings the interaction with the fiber surface suddenly increases. This effect is caused by the heterogeneity of the interaction energy of the active sites at the surface. A simple procedure to measure the adsorption isotherm at infinite dilution was developed. The determination of the concentration dependence of the interaction of an n-alkane, an acidic and a basic probe was incorporated in the IGC screening procedure of carbon fibers to monitor this heterogeneity.     

Exchange Phenomena in Radical-Anions of Cyclopentadithiophenones and Dithienothiophene-Dioxides

During electron spin resonance studies of radical-anions¹ of the thiophene analogues of fluorenone (cyclopentadithiophenones, I_A-VI_A) and dibenzothiophene-dioxide (dithienothiophene-dioxides, I_B-VI_B) deuteriumhydrogen exchange phenomena were observed.     

What is 'unfreezable water', how unfreezable is it,and how much is there?

Water that remains unfrozen at temperatures below the equilibrium bulk freezing temperature, in the presence of ice, is sometimes called unfreezable or bound. This paper analyses the phenomenon in terms of quantitative measurements of the hydration interaction among membranes or macromolecules at freezing temperatures. These results are related to analogous measurements in which osmotic stress or mechanical compression is used to equilibrate water of hydration with a bulk phase. The analysis provides formulas to estimate, at a given sub-freezing temperature, the amount of unfrozen water due to equilibrium hydration effects. Even at tens of degrees below freezing, this hydration effect alone can explain an unfrozen water volume that considerably exceeds that of a single 'hydration shell' surrounding the hydrophilic surfaces. The formulas provided give a lower bound to the amount of unfrozen water for two reasons. First, the well-known freezing point depression due to small solutes is, to zeroth order, independent of the membrane or macromolecular hydration effect. Further, the unfrozen solution found between membranes or macromolecules at freezing temperatures has high viscosity and small dimensions. This means that dehydration of such systems, especially at freezing temperatures, takes so long that equilibrium is rarely achieved over normal experimental time scales. So, in many cases, the amount of unfrozen water exceeds that expected at equilibrium, which in turn usually exceeds that calculated for a single hydration shell.     

Visualization of liquid-solid interface morphologies in gallium subject to natural convection

Melting and solidification of pure gallium is studied using real-time radioscopy methods. Sharp contrast between melt and solid phases with a 3% density difference is illustrated. The interfacial shape reflects convective flow in the liquid phase. Comparisons are made between real-time non-intrusive X-ray observations and results gained from probing techniques and numerical simulations reported in the literature. Similar qualitative trends in temperature distribution, yet discrepancies in interfacial location and shape, are exhibited.