INTRAPARTICLE DIFFUSION EFFECTS IN FISCHER-TROPSCH SYNTHESIS Ⅰ. MODELING OF DIFFUSION AND REACTION

IntroductionCatal}ticrcactionsaffcctcdb}'diffosionaIlimitationincatal}'stporcshavcbccnextensive1}dcaltx`ithinlit.rat.rcll~5I.Scvcraltcchniqucsonthcspccialcase0fFischcr-Tropschs}'nthcsis(FTS)t\crcapplicdtocxplorcthebchaviorofthiscatal}ticrcactionundercxpcrimcntalandopcrationaIconditionsI3~5l.It`"ouldbeofvaluctoindicatchcrcthatthcseinvcstigationsx"ercmainl}'bascdonthesimplcstkineticsofthcfirstordcrinH2proposedbyAndersonl6]attheearIystages.However-thesetboents,striCtlyspeaking,areinvalidfor…     

Borel summability of the perturbation series in a hierarchical λ(▽φ)4 model

We prove Borel summability of the perturbation series for the dielectric constant and the free energy density for the hierarchical ()⁴ lattice model. Our methods are based on nonperturbative renormalization group analysis of the model.On leave from the Department of Mathematical Methods of Physics, Warsaw University, Poland.Supported in part by the Center for Interdisciplinary Research, Bielefeld University, Germany.     

Effect of disorder on relaxation in the one-dimensional Glauber model

We study the long-time relaxation of magnetization in a disordered linear chain of Ising spins from an initially aligned state. The coupling constants are ferromagnetic and nearest-neighbor only, taking valuesJ ₀ andJ ₁ with probabilitiesp and 1–p, respectively. The time evolution of the system is governed by the Glauber master equation. It is shown that for large timest, the magnetizationM(t) varies as [exp(–₀ t](t), where ₀ is a function of the stronger bond strengthJ ₀ only, and (t) decreases slower than an exponential. For very long times, we find that ln (t) varies as –t ^1/3. For low enough temperatures, there is an intermediate time regime when ln (t) varies as –t ^1/2. The results can be extended to more general probability distributions of ferromagnetic coupling constants, assuming thatM(t) can only increase if any bond in the chain is strengthened. If the coupling constants have a continuous distribution in which the probability density varies as a power law near some maximum valueJ ₀, we find that ln (t) varies as –t ^1/3(lnt)^2/3 for large times.     

An intermediate spherical model of a ferromagnet

A one-parameter family of partition functions is considered which for zero value of the parameter reduces to the spherical model of a ferromagnet. The model for > 0 is closer to the usual discrete lattice spin model of a ferromagnet than is the spherical model. The first four terms in of the limiting value of the partition function are calculated above and below the critical temperature for arbitrary interactions using the saddle point method to calculate certain correlation functions for the spherical model. These calculations indicate that the critical temperature is independent of for small and certain interactions.Part of this research appeared in the author's doctoral thesis.⁽³⁾     

Dispersion state of CuO on CeO2

XRD and XPS are used to study the dispersion state of CuO on ceria surface. The dispersion capacity values of CuO measured by the two methods are consistent, which are of 1.20 mmol CuO/100 m² CeO₂. In addition, the results reveal that highly dispersed Cu²⁺ ions are formed at low CuO loadings and that increasing the CuO content to a value higher than its dispersion capacity produces crystalline CuO after the surface vacant sites on CeO₂ are filled. The atomic composition of the outermost layer of the CuO/CeO₂ samples has been probed by using static secondary ion mass spectroscopy (SSIMS), and the ratim of Cu/Ce are found to be 0.93 and 0.46 for the 1.22 and 0.61 mmol CuO/CeO₂ samples respectively. Temperature-programmed reduction (TPR) profile with two reduction peaks at 156 and 165°C suggests that the reduction of highly dispersed Cu²⁺ ions consists of two steps and is easier than that of CuO crystallites, in which the TPR profile has only one reduction peak at about 249°C. The above experimental results are in good agreement with the prediction of the incorporation model. Project supported by the National Natural Science Foundation of China.     

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.     

The size distribution for theA g RB f−g Model of polymerization

This paper gives the equilibrium distribution of polymer sizes for Flory'sA _g RB _f–g model of polymerization. In this model, the polymers are composed of structural units withg functional groups of the typeA and (f-g) functional groups of the typeB. Reaction is subject to three conditions: (1) Functional groups of the typeA react only with those of typeB, and vice versa. (2) Intramolecular reactions do not occur [and therefore only branched-chain (noncyclic) polymers and formed]. (3) Subject to conditions (1) and (2), all functional groups are equally reactive. The derivation employs Stockmayer's statistical mechanical method (first used on Flory'sRA _f model), coupled with a recursion giving the number of distinct polymers which may be assembled fromk units of theA _g RB _f–g type. We also give distributions for a limiting case of theA _g RB _f–g model, the so-calledA _g RB model. This paper completes the solution of the Smoluchowski coagulation equation (monodisperse case) for the kernelsa _ij =A + B(i +j)+ Cij. The proof will be given in another publication.     

A generalization of the Rouse-Zimm model

The idea of consistently averaging the hydrodynamic interaction and its various consequences for Hookean dumbbells are reviewed. For long chains this idea can be used to generalize the Rouse-Zimm model for polymer solutions. Unlike the usual Rouse-Zimm model, the new model for steady shear flow predicts a nonzero second normal stress coefficient and shear rate dependent material functions. In the limit of long chains, the viscosity and the normal stress coefficients are universal functions of the reduced shear rate.This paper was presented at the Frühjahrstagung des Fachausschusses Polymerphysik der Deutschen Physikalischen Gesellschaft at Kaiserslautern (West Germany), March 12–14, 1986.     

Inverse relaxation-model and relation to recovery internal friction

Inverse relaxation is studied for hard elastic polypropylene (HEPP), rubber and non-elastic polypropylene. The results show that contractive stress, stress, and internal friction are three essential factors related to the phenomenon. A three-element model in which each element has a definite meaning is proposed to describe this phenomenon. The results also show that, in the first cyclic deformation, relaxation time increases with the increase of recovery for all the materials, which indicates that recovery viscosity increases with the increase of recovery, but the stress rising amplitude (SRA) of inverse relaxation has a maximum in the recovery range. Analysis indicates that SRA equals recovery internal friction (RIF) for ideal material in which stress is solely a function of strain, independent of paths, and approximately equals RIF for non-ideal material at a given strain. From this principle it is found that the order of the work counteracted by RIF for the four materials is the same as that of their second hysteresis loop, and the RIF of HEPP has a sudden increase at the later recovery range.     

Preparation and Characteristics of Porous Silica Films by a Modified Base-Catalyzed Sol-Gel Process Containing PVA: II. Film Preparation

Porous SiO₂ films were successfully deposited on silicon substrates by a modified base-catalyzed Sol-Gel process (MBCP) containing polyvinyl alcohol (PVA). The process conditions, such as the gelation time, the synthesis temperature, the stabilizing agent of the precursor solution and the spin coating speed, the heat-treatment, the annealing temperature of the film on the microstructure and porosity of porous SiO₂ films were systematically investigated by SEM, XRD and ellipsometry techniques. This study provides a novel preparation technique for the porous SiO₂ film. Using this process, the resultant film can reach a thickness of 3.6 m for one layer, a porosity of 25–50%, a low thermal conductivity of 0.11 W/m·K. This film will be used as a low dielectric layer, an thermal-insulating layer and a low refractive index layer.