Ward's identity in critical dynamics

We consider the relaxation of an order-parameter fluctuation of wave numberk in a system undergoing a second-order phase transition. In general, close to the critical point, wherek ^{–1 –1} (the correlation length) the relaxation rate has a linear dependence on/k of the form (k, ) = (k, 0)x(1–a/k). In analogy with the use of Ward's identity in elementary particle physics, we show that the numerical coefficienta is readily calculated by means of a mass insertion. We demonstrate, furthermore, that this initial linear drop is the main feature of the full/k dependence of the scaling functionR ^–x (k,), wherex is the dynamic critical exponent andR=(k²+ ²)^1/2 is the distance variable.     

磷脂酰胆碱水溶液CMC的测定

磷脂酰胆碱水溶液ＣＭＣ的测定陈鲁生周武姜云生（山东师范大学化学系济南２５００１４）关键词磷脂酰胆碱临界胶束浓度磷脂酰胆碱是一种天然生物两性表面活性物质，也是一种重要的生命物质，具有广泛的用途［１］，由于磷脂酰胆碱的水溶性较差，所以较长时间以来对其溶液...     

拟合粘度曲线法研究高聚物的长链支化

本文介绍了用计算机试误法拟合粘度曲线,讨论支化参数的方法,本法可以同时确定支化临界分子量和支化程度,在此基础上可以同时得到支化参数及平均分子量、分子量分布.以聚乙烯标准参考物:SRM 1475(线型)、1476(支化物)及镍催化顺式聚丁二烯为对象介绍了上述方法.     

The mean spherical model in a random external field and the replica method

We provide a quick elementary solution of the mean spherical model in a random external field. This also allows an immediate proof of the self-averaging property of the free energy. We calculate the free energy by means of the replica method, i.e., for any (not necessarily integer) replica numbern, and show that when a phase transition occurs the limits andn 0 are not interchangeable.     

High-density percolation: Exact solution on a Bethe lattice

A new percolation problem is posed where the sites on a lattice are randomly occupied but where only those occupied sites with at least a given numberm of occupied neighbors are included in the clusters. This problem, which has applications in magnetic and other systems, is solved exactly on a Bethe lattice. The classical percolation critical exponents=gg=1 are found. The percolation thresholds vary between the ordinary percolation thresholdp _c (m=1)=l/(z – 1) andp _c(m=z) =[l/(z – 1)]¹/(z–1). The cluster size distribution asymptotically decays exponentially withn, for largen, p p _c .Supported in part by National Science Foundation grant DMR78-10813.     

The solubilization of alcohols in micellar solutions

The specific conductivities of dodecyldimethylbenzylammonium bromide (C12BBr) have been determined in aqueous butanol and aqueous benzyl alcohol solutions in the temperature range of 5-40°C. From these data the temperature dependent critical micelle concentration (cmc) was determined. The molar fraction of alcohol in the micelle was estimated using the theory suggested by Motomura et al. for surfactant binary mixtures. The thermal properties such as standard Gibbs free energy, enthalpy and entropy of solubilization of alcohols in the micelles were estimated for the phase separation model. The change in heat capacity upon solubilization of alcohol in the micelle has been estimated form the above properties. This revised version was published online in July 2006 with corrections to the Cover Date.     

Comparative analysis of blue‐shifted hydrogen bond versus conventional hydrogen bond in methyl radical complexes

Methyl radical complexes H₃C…HCN and H₃C…HNC have been investigated at the UMP2(full)/aug‐cc‐pVTZ level to elucidate the nature of hydrogen bonds. To better understand the intermolecular H‐bond interactions, topological analysis of electron density at bond critical points (BCP) is executed using Bader's atoms‐in‐molecules (AIM) theory. Natural bond orbital (NBO) analysis has also been performed to study the orbital interactions and change of hybridization. Theoretical calculations show that there is no essential difference between the blue‐shift H‐bond and the conventional one. In H₃C…HNC complex, rehybridization is responsible for shortening of the N? H bond. The hyperconjugative interaction between the single electron of the methyl radical and N? H antibonding orbital is up to 7.0 kcal/mol, exceeding 3.0 kcal/mol, the upper limit of hyperconjugative n(Y)→σ*(X–H) interaction to form the blue‐shifted H‐bond according to Alabugin's theory. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Re-Evaluation of the Activity Coefficients of Aqueous Hydrochloric Acid Solutions up to a Molality of 2.0 Using Two-Parameter Hückel and Pitzer Equations. Part II. Results from 0 to 95°C

Simple two-parameter Hückel and Pitzer equations were used for the calculation of the activity coefficients of aqueous hydrochloric acid at temperatures 0–60°C up to a molality of 2.0 mol-kg^–1. The data obtained by Harned and Ehlers^(2,3) on galvanic cells without a liquid junction were used in the parameter estimations of these equations. These data consist of sets of measurements at the temperature intervals of 5°C. It was observed that all estimated parameters follow very simple equations with respect to temperature. They are either constant or depend linearly on the temperature. The values for the activity coefficient parameters calculated by these simple equations are recommended here. The recommended parameter values were tested by predicting the data of Gupta, Hills, and Ives,⁽⁵⁾ consisting of cell measurements from 5 to 45°C and molalities up to 1.0 mol-kg^–1, and the data of Bates and Bower,⁽⁴⁾ which extend to 95°C but measurements were only made on molalities less than about 0.1 mol-kg^–1. The activity coefficients obtained by the new equations were also compared to those calculated by the Pitzer equations with the parameter values determined by Saluja, Pitzer, and Phutela⁽⁶⁾ from calorimetric data. The agreement observed was excellent up to a molality of 1.5 mol-kg^–1 at temperatures from 0 to 60°C.     

Field-theoretic approach to second-order phase transitions in two- and three-dimensional systems

We review the physical principles which are at the basis of recent field-theoretic computations of the critical exponents in two- and three-dimensional systems. We concentrate on those points that do not show up explicitly in the more standard-expansion: they must be discussed with care if one uses a perturbative approach at fixed space dimensions (the loop expansion). We present in detail simple computations of the critical exponents, while we summarize the results of longer and more accurate computations.     

Radiation polymerization of thermo-sensitive poly (N-vinylcaprolactam)

Temperature-sensitive poly (N-vinylcaprolactam) both in water-soluble state and in gel was prepared by γ-radiation polymerization. The effects of radiation dose, radiation dose rate and monomer concentration on polymerization and the low critical solution temperature characteristics of the polymer were studied. The results show that the polymer prepared within certain radiation dose (beyond 2 kGy) and dose rate range (2–14 Gy/min) has good temperature sensitivity and uniformity.