Refined semi-empirical formula for liquid–vapour critical point exponent δ and its relevance to the random field Ising model

Recent work in D.J. Klein and N.H. March, Phys. Lett. A 372, 5052 (2008) has considered, by a semi-empirical approach, the critical exponent δ at the liquid–vapour critical point as a function of dimensionality D. Here we first refine δ(d′), again semi-empirically, but with better results for other critical exponents, especially η(d′). The resulting form of δ(d′) is then utilised to discuss the random field Ising model. Systems with random fields are expected to exhibit drastically modified critical properties. We discuss the relation between a d-dimensional spin system in a random field with a d′-dimensional spin assembly in a zero magnetic field. A further matter focused in here concerns effective reduced dimensionality and hyperscaling relations. We conclude by assessing the way in which the available experimental results relate to the issues raised above.     

The liquid–liquid coexistence curves of {benzonitrile + n-pentadecane} and {benzonitrile + n-heptadecane} in the critical region

Liquid + liquid coexistence curves for the binary solutions of {benzonitrile + n-pentadecane} and {benzonitrile + n-heptadecane} have been measured in the critical region. The critical exponent β and the critical amplitudes have been deduced and the former is consistent with the theoretic prediction. It was found that the coexistence curves may be well described by the crossover model proposed by Gutkowski et al. The asymmetries of the diameters of the coexistence curves were also discussed in the frame of the complete scaling theory.     

The liquid–liquid coexistence curves of {x dimethyl adipate + (1 − x) n-octane} and {x dimethyl adipate + (1 − x) n-nonane} in the critical region

The liquid–liquid coexistence curves of (dimethyl adipate + n-octane) and (dimethyl adipate + n-nonane) have been determined within about 10 K from the critical temperatures, from which the critical amplitudes and the critical exponents are deduced. The critical exponents corresponding to the coexistence curve β are consistent with the 3D-Ising values. The experimental results have been analyzed to determine Wegner-correction terms and to discuss the asymmetric behaviour of the diameters of the coexistence curves by the complete scaling theory. Molar mass-dependences of the critical amplitude and the critical volume fraction have been shown to be consistent with the theoretical prediction.     

The liquid–liquid coexistence curves of {x dimethyl adipate + (1 − x) n-hexane} and {x dimethyl adipate + (1 − x) n-heptane} in the critical region

The liquid–liquid coexistence curves for (dimethyl adipate + n-hexane), (dimethyl adipate + n-heptane) have been measured, from which the critical amplitudes and the critical exponents are deduced. The critical exponent β corresponding to the coexistence curves are consistent with the 3D-Ising value. The experimental results have also been analyzed to determine the critical amplitudes of Wegner-correction terms when β and Δ are fixed at their theoretical values, and to examine the asymmetry of the diameters for the coexistence curves.     

Effects of the alkali-metal cation size on molecular and extended structures: formation of coordination polymers and hybrid materials in the homologous series [(4-Et-C6H4OM)·(diox)n], M = Li, Na, K, Rb, Cs

The complete series of group 1 metal 4-ethylphenoxide (4-Et-C(6)H(4)O(-)) networks have been synthesized using 1,4-dioxane (diox) as a neutral linker. [{(4-Et-C(6)H(4)OLi)(4)·(diox)(2.5)}·diox](∞) (1) and [{(4-Et-C(6)H(4)ONa)(6)·(diox)(3)}(∞)] (2) form 2D and 3D networks, respectively, composed of discrete aggregates linked by diox. Compound 1 forms a hexagonal layered structure with Li(4)O(4) cubanes acting as nodes, whereas compound 2 forms a primitive cubic network (pcu) with Na(6)O(6) hexameric nodes. [{(4-Et-C(6)H(4)OK)(3)·diox}(∞)] (3), [{(4-Et-C(6)H(4)ORb)(2)·(diox)(0.5)}(∞)] (4), and [{(4-Et-C(6)H(4)OCs)(2)·(diox)(0.5)}(∞)] (5) are composed of isostructural 1D inorganic rods that are linked through diox to form pcu-type networks. Compound 5 is the first example of a network built from cesium inorganic rods.     

Measurement and correlation of the (p, ρ, T) relation of liquid cyclohexane,toluene, and ethanol in the temperature range from 233.15 K to 473.15 K at pressures up to 30 MPa for use as density reference liquids

Comprehensive (p, ρ, T) measurements on cyclohexane, toluene, and ethanol were carried out in the homogeneous liquid phase for temperatures from 233.15 K to 473.15 K at pressures up to 30 MPa. The measurements were performed by using an accurate single-sinker densimeter based on the Archimedes’ buoyancy principle. The total uncertainty of the measurements in density was estimated to be 0.015% (level of confidence 95%). Based on the experimental results, accurate correlation equations for the density of the three liquids have been established; their uncertainty is 0.020%. Comparisons with previous results of other experimentalists and with values calculated from current equations of state are presented. In this context it is also shown that the density of a liquid can vary slightly depending on the batch of the liquid used for the measurements. The purpose of this work was to provide accurate correlation equations for the densities of the three selected liquids so that these liquids can be used as density reference liquids for the calibration of densimeters and, in particular, for the calibration of vibrating-tube densimeters.