Clusters,metastability, and nucleation: Kinetics of first-order phase transitions

We describe and interpret computer simulations of the time evolution of a binary alloy on a cubic lattice, with nearest neighbor interactions favoring like pairs of atoms. Initially the atoms are arranged at random; the time evolution proceeds by random interchanges of nearest neighbor pairs, using probabilities compatible with the equilibrium Gibbs distribution at temperatureT. For temperatures 0.59T_c, 0.81 T_c, and 0.89T _c, with density of A atoms equal to that in the B-rich phase at coexistence, the density C₁ of clusters ofl A atoms approximately satisfies the following empirical formulas: C₁ w(1 –)³ andC ₁, (1 –)⁴Q₁w¹ (2 l 10). Herew is a parameter and we defineQ _l = _K e ^–E(K) , where the sum goes over all translationally nonequivalentl-particle clusters andE(K) is the energy of formation of the clusterK. Forl > 10,Q ₁ is not known exactly; so we use an extrapolation formulaQ _l Aw _s ^–l l ^– exp(–bl ), wherew _s is the value ofw at coexistence. The same formula (withw > w _s) also fits the observed values of C, (for small values ofl) at densities greater than the coexistence density (forT=0.59T_c): When the supersaturation is small, the simulations show apparently metastable states, a theoretical estimate of whose lifetime is compatible with the observations. For higher supersaturation the system is observed to undergo a slow process of segregation into two coexisting phases (andw therefore changes slowly with time). These results may be interpreted as a more quantitative formulation (and confirmation) of ideas used in standard nucleation theory. No evidence for a spinodal transition is found.Supported by AFOSR Grant No. 73-2430D and by ERDA Contract No. EY-76-C-02-3077*000.     

Transport properties of the Lorentz gas: Fourier's law

We investigate the stationary nonequilibrium (heat transporting) states of the Lorentz gas. This is a gas of classical point particles moving in a region gL containing also fixed (hard sphere) scatterers of radiusR. The stationary state considered is obtained by imposing stochastic boundary conditions at the top and bottom of , i.e., a particle hitting one of these walls comes off with a velocity distribution corresponding to temperaturesT ₁ andT ₂ respectively,T ₁ <T ₂. Letting be the average density of the randomly distributed scatterers we show that in the Boltzmann-Grad limit,,R 0 with the mean free path fixed, the stationary distribution of the Lorentz gas converges in theL ¹-norm to the stationary distribution of the corresponding linear Boltzmann equation with the same boundary conditions. In particular, the steady state heat flow in the Lorentz gas converges to that of the linear Boltzmann equation, which is known to behave as (T ₂-T ₁)/L for largeL, whereL is the distance from the bottom to the top wall: i.e., Fourier's law of heat conduction is valid in the limit. The heat flow converges even in probability. Generalizations of our result for scatterers with a smooth potential as well as the related diffusion problem are discussed.Research supported in part by NSF Grant no. Phy 77-22302.On leave of absence from the Fachbereich Physik der Universität, München. Work supported by a DFG fellowship.     

Growth of clusters in a first-order phase transition

The results of computer simulations of phase separation kinetics in a binary alloy quenched from a high temperature are analyzed in detail, using the ideas of Lifshitz and Slyozov. The alloy was modeled by a three-dimensional Ising model with Kawasaki dynamics. The temperature after quenching was 0.59T _c, whereT _c is the critical temperature, and the concentration of minority atoms was=0.075, which is about five times their largest possible single-phase equilibrium concentration at that temperature. The time interval covered by our analysis goes from about 1000 to 6000 attempted interchanges per site. The size distribution of small clusters of minority atoms is fitted approximately byc ₁(1-)³ w(t),c ₁ (1–)⁴ Q _l w(t)^l(2l10); wherec _l is the concentration of clusters of sizel;Q ₂,...,Q ₁₀ are known constants, the cluster partition functions;t is the time; andw(t)=0.015(1+7.17t ^–1/3). The distribution of large clusters (l20) is fitted approximately by the type of distribution proposed by Lifshitz and Slyozov,c _l ,(t)=–(d/dl) [lnt+p (l/t)], where is a function given by those authors and is defined by(x)=C _o e–x-C ₁ e ^–4x/3-C ₂ e ^–5x/3;C ₀,C ₁,C ₂ are constants determined by considering how the total number of particles in large clusters changes with time.Supported by the U.S. Air Force Office of Scientific Research under Grant No. 78-3522 and by the U.S. Department of Energy under Contract No. EY-76-C-02-3077*000.     

Two-stage Off-Gel isoelectric focusing: protein followed by peptide fractionation and application to proteome analysis of human plasma

This paper presents the recently introduced Off-Gel electrophoresis (OGE) technology as a versatile tool to reproducibly fractionate intact proteins and peptides into discrete liquid fractions. The coupling of two stages of OGE, i.e., the separation of intact proteins in a first-stage followed by fractionation of peptides derived from each protein fraction after proteolysis in a second stage, results in an array of 15 x 15 fractions that are directly amenable to additional peptide fractionation like reverse-phase liquid chromatography (RPC). The analysis of all second-stage peptide fractions from only the first-stage protein fraction representing pH 5.0 -5.15 by on-line reverse-phase LC-tandem mass spectrometry resulted in the identification of 53 proteins (337 peptides), of which 10 were on different immunoglobulin (Ig) chains, with an input of only 1.5 mg human blood plasma proteins. Increasing the protein load to approximately 12 mg increased the number of identified proteins in the same protein fraction to 73 proteins (449 peptides), of which 15 were Ig-related. Immunodepletion of six of the most abundant proteins (albumin, transferrin, haptoglobin, IgG, IgA, and alpha-1-antitrypsin) prior to first-stage OGE with an input of 1.5 mg of protein (equivalent to approximately 10 mg nondepleted plasma) resulted in the identification of 81 proteins (660 peptides), of which three were still Ig fragments. The pI-based separation of peptides appears to be nonuniform based on the theoretically determined pI values of identified peptides. This observation specifically accounts for the neutral zone (pI 5-8) and can be accounted for by the physicochemical properties of the peptides given by their amino acid composition. The power of OGE separation of proteins and peptides is discussed with a focus on the use of the knowledge about the pI of proteins and peptides that assist the validation of correct identifications together with the retention time of peptides on RPC.     

Conformation-dependent reaction thermochemistry: study of lactones and lactone enolates in the gas phase

Gas-phase acidities (Delta H degrees (acid)) of lactones with ring sizes from four to seven have been measured on a Fourier transform ion cyclotron resonance mass spectrometer. Electron affinities (EAs) of the corresponding lactone enolate radicals were measured on a continuous-wave ion cyclotron resonance mass spectrometer, and the bond dissociation energies (BDEs) of the alpha C-H bonds were derived. In order of increasing ring size, Delta H degrees (acid) = 368.7 +/- 2., 369.4 +/- 2.2, 367.3 +/- 2.2, and 368.3 +/- 2.2 kcal/mol and BDE = 99.4 +/- 2.3, 94.8 +/- 2.3, 89.2 +/- 2.3, and 92.8 +/- 2.4 kcal/mol for beta-propiolactone, gamma-butyrolactone, delta-valerolactone, and epsilon-caprolactone, respectively. For their corresponding enolate radicals, EA = 44.1 +/- 0.3, 38.8 +/- 0.3, 35.3 +/- 0.3, and 37.9 +/- 0.6 kcal/mol. All of these lactones are considerably more acidic than methyl acetate, consistent with a dipole repulsion model. Both BDEs and EAs show a strong dependence on ring size, whereas Delta H degrees (acid) does not. These findings are discussed, taking into account differential electronic effects and differential strain between the reactant and product species in each reaction.     

Ab initio global potential-energy surface for H5(+) --> H3(+) + H2

An accurate global potential-energy surface (PES) is reported for H5(+) based on more than 100,000 CCSD(T)/aug-cc-pVTZ ab initio energies. This PES has full permutational symmetry with respect to interchange of H atoms and dissociates to H3(+) and H2. Ten known stationary points of H5(+) are characterized and compared to previous ab initio calculations. Quantum diffusion Monte Carlo calculations are performed on the PES to obtain the zero-point energy of H5(+) and the anharmonic dissociation energy (D0) of H5(+) --> H3(+) + H2. The rigorous zero-point state of H4D+ is also calculated and discussed within the context of a strictly classical approach to obtain the branching ratio of the reaction H4D+ --> H3(+) + HD and H2D+ + H2. Such an approach is taken using the PES and critiqued based on the properties of the quantum zero-point state. Finally, a simple procedure for adding the long range-interaction energy is described.     

Diminished Respirative Growth and Enhanced Assimilative Sugar Uptake Result in Higher Specific Fermentation Rates by the MutantPichia stipitis FPL-061

A mutant strain ofPichia stipitis, FPL-061, was obtained by selecting for growth on L-xylose in the presence of respiratory inhibitors. The specific fermentation rate of FPL-061, was higher than that of the parent,Pichia stipitis CBS 6054, because of its lower cell yield and growth rate and higher specific substrate uptake rate. With a mixture of glucose and xylose, the mutant strain FPL-061 produced 29.4 g ethanol/L with a yield of 0.42 g ethanol/g sugar consumed. By comparison, CBS 6054 produced 25.7 g ethanol/L with a yield of 0.35 gJg. The fermentation was most efficient at an aeration rate of 9.2 mmoles O₂ L^-1 h^-1. At high aeration rates (22 mmoles O₂ L^-1 h^-1), the mutant cell yield was less than that of the parent. At low aeration rates, (1.1 to 2.5 O₂ L^-1 h^-1), cell yields were similar, the ethanol formation rates were low, and xylitol accumulation was observed in both the strains. Both strains respired the ethanol once sugar was exhausted. We infer from the results that the mutant, P.stipitis FPL-061, diverts a larger fraction of its metabolic energy from cell growth into ethanol production.     

“Short-bite” ligands in cluster synthesis

The short-bite ligands CH₂(PR ₂)₂ or CH(PR ₂)₃ (R = Me, Ph),RN(PX ₂)₂ (R=H, Me, Et;X = F, OR (R= Me, Et, i-Pr, Ph), Ph),RE(CH₂ ER₂)₂ (E = P, As;R = Me, Ph ), Ph₂ P(2-C₅H₄N) and related species are particularly versatile for the synthesis of di- and polynuclear complexes which frequently possess metal-metal bonds. In addition to homometallic products, these ligands often permit the directed synthesis of heterometallic complexes. Selected aspects of the chemistry of these complexes are also reviewed.     

Cyano-bridged hexanuclear Fe4M2 (M = Ni, Co, Mn) clusters: spin-canted antiferromagnetic ordering of Fe4Ni2 cluster

Heterobimetallic hexanuclear cyano-bridged complexes, [{Fe(Tp)(CN)3}4{M(MeCN)(H2O)2}(2)].10H2O.2MeCN [M = Ni (1), Co (2), Mn (3); Tp = hydrotris(1-pyrazolyl)borate], have been synthesized in H2O-MeCN solution. Complexes 1-3 are isostructural and hexanuclear with [{Fe(Tp)(CN)3}4{M(MeCN)(H2O)2}2] units linked by hydrogen bonds to form a 2D-structure in the solid state. Complex 1 is a canted antiferromagnet that undergoes a field-induced spin-flop-like transition at approximately 1 T and 2 K. At 4.45 K 1 has a transition to paramagnetic state of noninteracting S = 4 magnetic clusters. However, 2 and 3 show antiferromagnetic intracluster coupling. Facile loss of solvent from 2 alters the local symmetry resulting in changing the intracluster interaction from antiferro- to ferromagnetic.     

A group additivity approach for the estimation of heat capacities of organic liquids and solids at 298 K

A group additivity method is described which provides heat capacity estimates of the condensed phase. The data base consists of 810 liquids and 446 solids. Group values for carbon in various common substitution and hybridization states and for 47 functional groups are provided. The standard error of estimation using this approach on this data base is 19.5 (liquids) and 26.9 J/ (mole K) (solids). This can be compared to typical experimental uncertainties of 8.12 and 23,4 J/ (mole K) associated with these measurements, respectively. Experimental uncertainties were estimated from the numerical differences obtained for a given substance from multiple independent literature reports.