New Monte Carlo method for the self-avoiding walk

We introduce a new Monte Carlo algorithm for the self-avoiding walk (SAW), and show that it is particularly efficient in the critical region (long chains). We also introduce new and more efficient statistical techniques. We employ these methods to extract numerical estimates for the critical parameters of the SAW on the square lattice. We find=2.63820 ± 0.00004 ± 0.00030=1.352 ± 0.006 ± 0.025v=0.7590 ± 0.0062 ± 0.0042 where the first error bar represents systematic error due to corrections to scaling (subjective 95% confidence limits) and the second bar represents statistical error (classical 95% confidence limits). These results are based on SAWs of average length 166, using 340 hours CPU time on a CDC Cyber 170–730. We compare our results to previous work and indicate some directions for future research.     

Semiclassical study of collision-induced predissociation: Comparison of the Landau-Zener model with the method of analytic continuation

Semiclassical calculations are carried out by two methods for the problem of collision-induced predissociation of electronically excited I₂. The first method is that of surface-hopping with the Landau-Zener model. The second method is similar to surface-hopping, except that analytic continuation of the adiabatic potential energy surfaces replaces the Landau-Zener model. Results of the calculations by the two methods compare favorably with each other and with experiment. The possible advantages of the second method are discussed.Camille and Henry Dreyfus Teacher-Scholar, Alfred P. Sloan Research Fellow.     

The molecular and crystal structures of two diastereomeric 3,4-dihydropyrromethenones

The molecular and crystal structures of the two racemic diastereomeric 3,4-dihydropyrromethenone derivatives1 and2 of configurations (Z) and (E) were determined at 93 K (1, 2) and at room temperature (1). From an analysis of the crystallographically observed temperature coefficients a pseudorotation flexibility of the pyrrolidinone ring in the crystal is deduced. In both compounds a nearly orthogonal arrangement between the two heterocyclic ring systems is observed, which is ascribed to the steric bulk of the substituents in positions 1 and 3 of the pyrrolidinone ring.Herrn Prof.Josef Schurz zum 60. Geburtstag gewidmet.     

Optical Properties of Model Compounds of Polyaniline

The UV and visible spectra of six model compounds were studied. These compounds can be considered as models of polyaniline in the reduced, cation radical, partially oxidized and oxidized forms. After treatment of a mixture of equal molar quantities of the reduced form (DPPD) and the oxidized form (QDIM) with acid, the following reaction was observed: DPPD(I)+QDIM(III)+2H⁺=2DPPD⁺(II) After similar treatment of the partially oxidized form (V) with acid, the radical cation salt formed. The UV and visible spectra of polyaniline in the reduced form, oxidized form and conductive form are similar to the spectra of DPPD, QDIM and DPPD⁺ or radical cation salt of V respectively. We propose that the polyaniline synthesized by chemical oxidation of aniline consists of oxidized and reduced repeat units. Upon protonation a redox reaction (or electron rearrangement) occurs and forms delocalized radical cations (polarons) in the polymer chain which are highly conductive.     

Dynamics of the formation of two-dimensional ordered structures

The growth of ordered domains in lattice gas models, which occurs after the system is quenched from infinite temperature to a state below the critical temperatureT _c, is studied by Monte Carlo simulation. For a square lattice with repulsion between nearest and next-nearest neighbors, which in equilibrium exhibits fourfold degenerate (2×1) superstructures, the time-dependent energy E(t), domain size L(t), and structure functionS(q, t) are obtained, both for Glauber dynamics (no conservation law) and the case with conserved density (Kawasaki dynamics). At late times the energy excess and halfwidth of the structure factor decrease proportional tot ^–x, whileL(t) t ^x, where the exponent x=1/2 for Glauber dynamics and x1/3 for Kawasaki dynamics. In addition, the structure factor satisfies a scaling lawS(k,t)=t ^2xS(kt^x). The smaller exponent for the conserved density case is traced back to the excess density contained in the walls between ordered domains which must be redistributed during growth. Quenches toT>T _c, T=T_c (where we estimate dynamic critical exponents) andT=0 are also considered. In the latter case, the system becomes frozen in a glasslike domain pattern far from equilibrium when using Kawasaki dynamics. The generalization of our results to other lattices and structures also is briefly discussed.     

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…     

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.     

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.