A numerical method to compute exactly the partition function with application toZ(n) theories in two dimensions

I present a new method to exactly compute the partition function of a class of discrete models in arbitrary dimensions. The time for the computation for ann-state model on anL ^d lattice scales like . I show examples of the use of this method by computing the partition function of the 2D Ising and 3-state Potts models for maximum lattice sizes 10×10 and 8×8, respectively. The critical exponentsv and and the critical temperature one obtains from these are very near the exactly known values. The distribution of zeros of the partition function of the Potts model leads to the conjecture that the ratio of the amplitudes of the specific heat below and above the critical temperature is unity.     

Solvable isotherms for a two-component system of charged rods on a line

The Coulomb system consisting of an equal number of positive and negative charged rods confined to a one-dimensional lattice is studied. The grand partition function can be calculated exactly at two values of the coupling constant=q ²/k _B T (q denoting the magnitude of the charges). The exact results lead to the conjecture that in the complex scaled fugacity plane, all the zeros of the grand partition function lie on the negative real axis for<2, on the point=–1 for=2, and on the unit circle for>2. In addition, for>4, we conjecture in general and prove at=4 that the zeros pinch the real axis in the thermodynamic limit, with an essential singularity in the pressure at the reduced density 1/2.     

New Method to Calculate Thermodynamic and Transport Properties of a Multi-Temperature Plasma: Application to N2 Plasma

Multi-temperature thermal plasmas have often to be considered to account for the nonequilibrium effects. Recently André et al. have developed the calculation of concentrations in a multi-temperature plasma by artificially separating the partition functions into a product by assuming that the excitation energies are those of the lower levels (electronic, vibration, and rotation). However, at equilibrium, differences, increasing with temperature, can be observed between partition functions calculated rigorously and with their method. This paper presents a modified method where it has been assumed that the preponderant rotational energy is that of the vibrational level v=0 of the ground electronic state and the preponderant vibrational energy is that of the ground electronic state. The internal partition function can then be expressed as a product of series expressions. At equilibrium for N ₂ and N ₂ ⁺ partition functions the values calculated with our method differ by less than 0.1% from those calculated rigorously. The calculation has been limited to three temperatures: heavy species T_h , electrons T_e , and vibrational T _v temperatures. The plasma composition has been calculated by minimizing the Gibbs free enthalpy with the steepest descent numerical technique. The nonequilibrium properties have been calculated using the method of Devoto, modified by Bonnefoi and Aubreton. The ratio =T_e/T_h was varied between 1 and 2 as well as the ratio _v =T _v /T _h for a nitrogen plasma. At equilibrium the corresponding equilibrium transport properties of Ar and N ₂ are in good agreement with those of Devoto and Murphy except for T>10,000 K where we used a different interaction potential for N–N ⁺ . The effects of _v and _e on thermodynamic and transport properties of N ₂ are then discussed.     

Dependence of the rate constants on the treatment of internal rotation modes: the reaction OH + CH3SH --> CH3S + H2O as an example

The title reaction has been used as an example to test the importance of using a hindered rotor treatment instead of a harmonic oscillator model for calculating vibrational partition functions corresponding to low-frequency internal rotation modes. First, a normal-mode analysis according to the Ayala and Schlegel's algorithm has been used to identify the internal rotation modes of methanethiol and the transition state structure. Then, after calculation of the energy barrier for each internal rotation, the corresponding hindered rotor partition functions have been calculated following the CW scheme of Chuang and Truhlar. The results show that the anharmonic treatment produces a rather modest improvement of the rate constants at room temperature or below.     

Crystal Structure, Infrared Spectrum and Isotope Effect of Uranium-Crown Ether Complexes

According to the experiment results of X-ray diffraction and IR, the reduced partition function ratio (RPFR) and the contribution of various related vibration modes of uranium-crown ether complex (DCH18C6·H_3O)_2UO_2Cl_4 were theoreticallv calculated in detail. The equilibrium constant K_(eq) (that is, the single stage isotopic separation factor α) of exchange reaction for uranium isotopic chemical exchange system UO_2~(2+)(H_2O)_5—(DCH18C6.H_3O)_2UO_2Cl_4 is estimated to be 1.000746 at 12℃ and 1.000672 at 29℃, respectively, which are quite close to the experimental values 1.0010±0.0002 arid 1.0012±0.0004. Theoretical analysis shows that in the course of forming the complex of uranium with crown ether, the coordinated water of uranium is stripped, which performs a key action on the remarkable isotope effect for this system.     

Liquid–solid disk extraction followed by supercritical fluid elution and gas chromatography of phenols from water

A method combining the techniques of liquid – solid disk extraction (LSDE) and supercritical fluid elution (SFE) has been developed for the phenols regulated by the Clean Water Act. LSDE uses a disk or membrane made of polytetrafluoroethylene (PTFE) fibrils impregnated with small particles, e.g. styrene divinylbenzene (SDB) resin, to extract phenols from water. After disk extraction the retained analytes are eluted from the disk using SFE. SFE is used as an alternative to liquid solvent elution with an organic solvent. Analytes are separated, identified, and quantified using gas chromatography – ion trap detector mass spectrometry (GC-ITDMS). The method is capable of sub parts per billion detection limits, and precision of 5–28% RSD. Evaluation of various disks or membranes, such as C₁₈-silica disks, SDB disks, and ion exchange membranes, has also been performed for the extraction of phenols from water. The results obtained from the in-situ aqueous acetylation of phenols and extraction of their acetates are quantitative. The utilization of LSDE and SFE techniques has proven to be a more effective approach than liquid – liquid extraction in minimizing air pollution and solvent waste.     

Specific and non-specific interactions of hydropseudohalic acids with water and organic solvents

Partition coefficients P of the HNCS, HNCO and HN₃ hydropseudohalic acids between a number of organic solvents and water were determined. It has been found that log P increases with pKa of the acid and with the basicity of the solvent, but the effect of pKa on P is the smaller the more basic is the solvent. The relationships have been explained in terms of hydrogen bond formation between undissociated acid and solvent molecules. H-bonding between the pseudohalic acids and organic solvents has been confirmed by IR spectra on the example of HN₃ in benzene. Association constants for H-bonding between the three acids and water, benzene, dibutyl ether and tri-n-butyl phosphate were determined from partition data. It has been found that H-bonding increases with the strength of the acid, whereas the contribution to partition from non-specific interactions with water and organic solvents depends on the molecular surface area of the acid molecule.     

COSMO-RS: A novel view to physiological solvation and partition questions

Both, dielectric continuum solvation models as well as surface or group based methods using polarity and lipophilicity parameters have been proven to be useful tools for the analysis of solvation and partition questions. For the first time, COSMO-RS provides an integrated theory, which combines the aspects of continuum solvation and surface interactions, and which ends up with chemical potentials of molecules in almost arbitrary solvents and mixtures. Due to its sound theoretical basis, COSMO-RS does not only provide a new quantitative access to solvation and partition properties in well defined solvents, but it also opens a novel view and gives a better understanding of the general problem of solvation. Finally, this allows for a generalisation of COSMO-RS to sophisticatedphysiological partition problems involving as complex phases as blood, brain, or cell membranes. The use of COSMO-RS for drug discovery and design is demonstrated by applications to blood-brain partition coefficients, and water solubility.     

疏水分配常数用于反相液相色谱保留值的预测

在反相液相色谱保留值基本方程log k_′=a+_cC_B的基础上,描述了采用疏水分配常数及氢键作用能来预测a、c参数的方法,并系统讨论了疏水分配常数对参数a、c的影响,借此对反相液相色谱宽浓度范围内的保留值进行了预测。     

AN/St悬浮共聚体系中AN在水/油两相间分配及其对共聚物组成的影响

研究了丙烯腈/苯乙烯(AN/St)悬浮共聚体系中AN在水/油两相间的分配及其对AN/St共聚物组成的影响.结果表明,AN分配于水/油两相间,使油相AN的含量低于相同单体配料比的本体聚合,导致生成的AN/St共聚物组成偏离本体共聚.为了准确预测进而控制AN/St悬浮共聚物的组成,提出了在考虑AN相分配的基础上计算AN/St悬浮共聚物组成的模型.计算结果与实验值一致,计算中用到的油相实际竞聚率与本体聚合相同,但该悬浮聚合的表观竞聚率随水/油比的变化而发生较大改变.