Equilibrium polymerization in a solvent: Solution on the Bethe lattice

The lattice model for equilibrium polymerization in a solvent proposed by Wheeler and Pfeuty is solved exactly on a Bethe lattice (core of a Caylay tree) with general coordination numberq. Earlier mean-field results are reobtained in the limitq, but the phase diagrams show deviations from them for finiteq. Whenq=2, our results turn into the solution of the one-dimensional problem. Although the model is solved directly, without the use of the correspondence between the equilibrium polymerization model and the diluten0 model, we verified that the latter model may also be solved on the Bethe lattice, its solution being identical to the direct solution in all parameter space. As observed in earlier studies of the puren0 vector model, the free energy is not always convex. We obtain the region of negative susceptibility for our solution and compare this result with mean field and renormalization group (-expansion) calculations.     

The interface of the Ising model and the Brownian sheet

We study the limit theorem related to the interface of the three-dimensional Ising model. Dobrushin proved that the interface does not fluctuate and becomes rigid for sufficiently large. We define the random fieldX ^L (t, s), 0t, s1, on the interface, and prove that X^L(t, s) converges to the Brownian sheet as L for sufficiently large, whereL denotes the size of the system. This result does not mean that the interface itself converges to the Brownian sheet.     

Exact results for a generalized classicalO(n) matrix spin model

A generalizedO(n) matrix version of the classical Heisenberg model, introduced by Fuller and Lenard as a classical limit of a quantum model, is solved exactly in one dimension. The free energy is analytic and the pair correlation functions decay exponentially for all finite temperatures. It is shown, however, that even for a finite number of spins the model has a phase transition in then limit. The transition features a specific heat jump, zero long-range order at all temperatures, and zero correlation length at the critical point. The Curie-Weiss version of the model is also solved exactly and shown to have standard mean-field type behavior for all finiten and to differ from the one-dimensional results in then limit.     

On the critical behavior of the magnetization in high-dimensional Ising models

We derive rigorously general results on the critical behavior of the magnetization in Ising models, as a function of the temperature and the external field. For the nearest-neighbor models it is shown that ind4 dimensions the magnetization is continuous atT _c and its critical exponents take the classical values=3 and=1/2, with possible logarithmic corrections atd=4. The continuity, and other explicit bounds, formally extend tod>3 1/2. Other systems to which the results apply include long-range models ind=1 dimension, with 1/|x–y| couplings, for which 2/(–1) replacesd in the above summary. The results are obtained by means of differential inequalities derived here using the random current representation, which is discussed in detail for the case of a nonvanishing magnetic field.Research supported in part by NSF grant PHY-8301493 A02, and by a John S. Guggenheim Foundation fellowship (M.A.).     

The spherical-model limit in a random field

The spherical-model limitn of then-vector model in a random field, with either a statistically independent distribution or with long-range correlated random fields, is studied to demonstrate the correctness of the replica method in which then and replica limits limits are interchanged, provided the replica and thermodynamic limits are taken in the right order, in the case of long-range correlated random fields. A scaling form for the two-point correlation function relevant to the first-order phase transition below the lower critical dimensionality of the random system is also obtained.     

Lifshitz tails for periodic plus random potentials

We prove that the integrated density of states () for a potentialW =V _per +V has Lifshitz tails where V_per is a periodic potential with reflection symmetry andV is a random potential, e.g., of the formV =q _i ()f(x–i).research partially supported by DFG.research partially supported by USNSF under grant No. MCS-81-20833.     

Formation of Negative Hydrogen Ions in a Ne–H2 Hollow Cathode Discharge

The formation of negative hydrogen ions in a conventional hollow cathode discharge has been investigated. A mixture of Ne and H₂ proved to be more advantageous compared to pure hydrogen. The study has been performed by solving the electron Boltzmann equation, coupled with a system of balance equations for neon and hydrogen neutral and charged particles. The vibrational distribution function of hydrogen has been calculated. Our calculations show unusually high population of vibrationally excited hydrogen molecules in a Ne–H₂ mixture, which explains the high density of negative hydrogen ions under optimal conditions (total gas pressure of few Torr, hydrogen number mole fraction of 1–10% and discharge current of 10–100 mA). Line intensities originating from highly excited neon states vs. hydrogen pressure have been calculated and a comparison with existing experimental results has been made.     

C(2×2)S/Fe(001)吸附体系的SCF-Xa-MS研究

采用SCF-X_α-MS方法, 对于C(2×2)S/Fe(001)吸附体系, 选择Fe_5S和Fe_9S两种原子簇模型, 研究了该吸附体系的电子结构、吸附成键特征及其相互作用图象。结果表明, S吸附于Fe(001)单晶表面具有较强的定域性质, S原子与底物Fe原子之间的吸附相互作用主要表现为S(3p)-Fe(4s,3d)之间的轨道相互作用。通过对表面吸附键长的优化, 其结果与X.S.Zhang等的ARPEFS的实验结果一致。     

Synthesis of a new and versatile macrocyclic NADH model

A new macrocyclic NADH model 1 has been designed and synthesised. The new model consists of the same subunits as previously reported models. However, the present model is designed as such that the pyridine nitrogen of the nicotinamide units are not incorporated in the macrocyclic framework. Thus, properties such as solubility can easily be varied by alkylation with an appropriate agent. The macrocyclic framework was prepared in 7 steps. Methylation of the pyridine nitrogens followed by reduction gave the desired model. This model compound was found to reduce methyl benzoylformate stereoselectively in good yield with 48% enantiomeric excess.     

Chemischer Transport von Cr2O3 mit CrI3/I2 – Experimente und Modellrechnungen zur Beteiligung von CrOI2,g

On the Chemical Transport of Cr₂O₃ with CrI₃/I₂ – Experiments and Model-Calculations for Participation of CrOI_2,g Gaseous chromium oxyiodides that were unknown up to now cause the migration of Cr₂O₃ in the temperature gradient 1 000°C→900°C when iodine (e. g. 0.1 mmol/ml) and CrI₃ is added (eq. (1)). Transport agent for Cr₂O₃ is gaseous CrI₄. With a smaller concentration of iodine (D(I₂) ? 0.016 mmol/ml) and lower temperatures (e.g. T? = 850°C) the influence of H₂O (from the wall of the silica ampoule) becomes more important. Under these conditions the transport of Cr₂O₃ is a result from the endothermic reactions (2), (3) and (4). H_2,g has on the basis of the decomposition of HI_g a positive difference of the solubility and H_2,g should not to be considered as a transport agent. Because of the range of equilibrium-values the reaction 4 has to be taken into consideration. Estimated value of the enthalpie for CrOI_2,g is fixed more precisely by thermodynamic model calculation to Δ_fH°₂₉₈(CrOI_2,g) = ?51.4 kcal/mol. The estimated limit of error for the enthalpie of formation is smaller than ± 5 kcal/mol. Without an addition of CrI₃ is in the system Cr₂O₃/I₂ a migration of Cr₂O₃ not observable.