Convergence of distorted Brownian motions and singular Hamiltonians

We prove a convergence theorem for sequences of Diffusion Processes corresponding to Dirichlet Forms of the kind .We obtain convergence in total variation norm of the corresponding probability measures on the path space C(₊;^d) under hypotheses which, for example, are satisfied in the case of H _loc ¹ ( ^d )-convergence of the 's, but we can allow more singular situations as regards the approximating sequences. We use then these results to give a criterion of convergence for generalized Schrödinger operators in which the potential function should not necessarily exists as a measurable function. We obtain convergence not only in strong resolvent sense, but we also obtain convergence in the uniform operator topology up to sets of arbitrarily small Lebesgue measure. Applications to the problem of the approximation of ordinary Schrödinger operators by generalized ones corresponding to zero-range interactions are given.     

Classical fluids of negative heat capacity

It is shown that new parametersX can be defined such that the heat capacity C_xT(S/T)_x is negative, even when the canonical ensemble [i.e., at fixed T=(U/S)_Y and YX] is stable. This implies an extension of the classical theory of polytropes from ideal gases to general fluids. As examples of negative heat capacity systems we treat blackbody radiation and general gas systems with nonsingular _T. For the case of a simple ideal gas we even exhibit an apparatus which enforces a constraint X(p, V)=const that makes C_x<0. We then show that it is possible to infer the statistical mechanics of canonicallyunstable systems-for which even the traditional heat capacities are negative-by imposing constraints that stabilize the associated noncanonical ensembles. Two explicit models are discussed.     

The theoretical basis of column chromatography in multicomponent separations. Part 2: Peak capacity. Column systems with good selectivity

The selectivity of a column system, S, defined by equation 28, includes a variation coefficient (β) of plate number with capacity ratio which has a large influence on the peak capacity, as shown in Fig. 18. Some typical chromatograms are given. In order to predict S for a column system from Kovat's Index, equations 40 and 41 are given to calculate the constant of the carbon number rule for squalane at different temperatures or for different stationary phases. The specific retention value of heptane on squalane at different temperatures can be calculated from equation 42. The nonpolarity index, defined by equation 43, was used to calculate the retention value of heptane on various stationary phases. In liquid chromatography, the order of elution may be reversed by changing the composition of the eluent on the same chemically bonded silica (manufactured in China). The linear relations between the log retention values of different kinds of solutes or of a single solute on the silicas of different surface areas when using the same eluent are given.     

Predicting the selectivity of imprinted polymers

Summary Imprinted polymers as stationary phases for HPLC separations have been the subject of extensive investigations in recent years. In order to aid the rational design of synthetic protocols for the preparation of imprinted polymers, a series of calculations were made to assess the equilibrium concentration of templatemonomer complexes as a function of association constant (K) for the functional groups involved in the interactions and initial concentrations of reactants. This data was then used to predict the selectivity of polymers prepared under different reaction conditions and the model was tested using an experimentally determined value ofK and separation factors taken from the literature.     

Removal of H2S from Exhaust Gas by Use of Alkaline Activated Carbon

The purpose of this research was to select an activated carbon and alkaline solution blend that generated the best H₂S adsorption on alkaline-activated carbon. RB₂ (activated carbon) impregnated with NaOH solution was shown to have the optimum H₂S removal efficiency. The optimum NaOH concentration was 50 mg per gram of carbon. H₂S adsorption via RB₂-NaOH₅₀ was five times that of a corresponding fresh-activated carbon. The adsorption equivalent of H₂S is nearly 1 (mol-H₂S/mol-AOH), therefore, H₂S + AOH AHS + H₂O was the major reaction. The H₂S adsorption isotherm corresponded to the Freundlich isotherm.     

Determination of Partial Molar Volumes of EPA and DHA Ethyl Esters in Supercritical Carbon Dioxide

The use of supercritical fluids (SCFs) as solvents has been attracting widespread interest in the research and commercial applications. The study of partial molar volumes of solutes at infinite dilution in the near-critical region is of considerable fundamental importance, as these data reflects the interactions occurring between the solute and the solvent. Experimental measurements of partial molar volumes may be divided into two categories: direct and indirect methods. The direct methods…     

Chemical equilibrium model for the thermodynamic properties of mixed aqueous micellar systems: Application to thermodynamic functions of transfer

Mixed micelles can be formed in water between various pairs of hydrophobic solutes such as surfactants, alcohols and hydrocarbons. These systems can often be studied through the thermodynamic functions of transfer of one of the solutes, usually kept near infinite dilution, from water to an aqueous solution of the other solute. When mixed micelles are formed, these functions change significantly, and often go through extrema, in the region where the binary system micellizes or undergoes some microphase transition.Three main effects are responsible for the observed trends: pair-wise interactions between both solutes in the monomeric form, a distribution of the reference solute between the aqueous and micellar phases and a shift in the monomer-micelle equilibrium in the vicinity of the reference solute. Simple equations can be derived for these three effects which can account for the sign and magnitude of the observed trends using parameters which are derived for the most part from the two binary systems.     

Group contributions to the thermodynamic properties of non-ionic organic solutes in dilute aqueous solution

The thermodynamic properties G _h ^o,H _h ^o, and C _p,h ^oassociated with the transfer of non-ionic organic compounds from gas to dilute aqueous solution and the limiting partial molar properties C _p ^o ,2 and V₂ ² of these compounds in water are described through a simple scheme of group contributions. A distinction is made between groups made only of carbon and hydrogen, and functional groups i.e. groups containing at least one atom different from carbon and hydrogen. Each group is assigned a contribution, for each property, through a least squares procedure which utilizes only molecules containing at most one functional group. Finally, for compounds containing more than one functional group, correction parameters are evaluated as the differences between the experimental values and those calculated by means of the group contributions. The different behavior of hydrophilic compared with hydrophobic groups is discussed for the various properties. A rationale for the correction parameters, i.e. for the effects of the interactions among hydrophilic groups on the thermodynamic properties, is attempted.     

Reversible Melting of Semi-Crystalline Polymers 2. Annealing Near to the Melting Point

Annealing experiments have been carried out at a few degrees below the melting point of different polyethylenes (LDPE, LLDPE, HDPE), of polypropylene (PP) and of Nylon-6. The heat capacities decrease during the annealing, within a 2-4 min time scale, to a lower value which corresponds to the extrapolated heat capacity values obtained for the cooling cycle when the polymer is cooled from the melt. Heat capacities in the heating cycle following the cooling cycle of PP, Nylon-6 and HDPE have the same value as during the cooling section. This is not the case for LDPE and LLDPE. Exothermic total heat flow in the cooling section following the annealing indicates that the crystallisation takes place during the cooling rather than during the annealing period. The total melting enthalpy measured before and after the annealing cycle is the same. The reversing heat flow shows an excellent fit to the change of the crystallinity measured by small angle scattering of synchrotron radiation during a heating cycle at temperatures below the melting peak. A coupled thermodynamic interaction of the crystalline and the amorphous phases is concluded from this study. This kind of interaction is possible at the lateral end of polymeric chains incorporated into the crystalline phase. This is an indication of the portion of tie molecules in the system, i.e. the portion of fringed micelle type of crystalline morphology with respect to that of folded chain lamellae. This revised version was published online in July 2006 with corrections to the Cover Date.     

Electrochemical characterization of negative electrodes consisting of surface-modified Zr0.9Ti0.1(Ni1.1Co0.1Mn0.5V0.2Cr0.1)x Laves-phase alloys

Laves-phase hydrogen storage alloy has a high potential for use as negative electrode material as alternative for the misch-metal-based material. In order to improve the energy density and the rate capability of negative electrode, chemical and mechanical modification of Lavesphase alloy with different stoichiometric ratios was carried out. Discharge capacity and high-rate dischargeabilty was evaluated by electrochemical methods and the characterization of Laves-phase alloy was made by X-ray diffraction, SEM observation and PCT measurement. The best result in discharge capacity could be obtained for stoichiometric Laves-phase alloy with a composition of Zr_0.9Ti_0.1Ni_1.1Co_0.1Mn_0.5V_0.2Cr_0.1 by boiling in 10 M KOH solution. On the other hand, the high-rate dischargeability was increased remarkably by introducing mechanical grinding before alkali treatment. The cause for improved performance was discussed on the basis of thermodynamic stability of metal hydride and changes in crystal structure and surface morphology influencing on diffusion coefficient and diffusion path length of hydrogen.