The measurements of coexistence curves and light scattering for {xC6H5CN + (1  x)CH3(CH2)6CH3} in the critical region

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Abstract

The coexistence curves and light scattering data for a critical solution of (benzonitrile + octane) have been reported. The critical exponents relating to the difference in the density variables between two coexisting phases β, the osmotic compressibility γ, and the correlation length ν have been deduced and the values are consistent with the 3D-Ising value in the range close to the critical point. The experimental results of the coexistence curves have also been analyzed to examine the Wegner correction terms and the behavior of the diameter of the coexistence curves. The light scattering data are well described by the crossover model proposed by Anisimov and Sengers, and show a monotonic crossover of the critical exponents γ and ν from its 3D-Ising value to the mean-field value as the temperature departures from the critical point. Furthermore, the dependences of the critical amplitudes on the mass of n-alkane for the binary solutions of (benzonitrile + n-alkane) have been discussed.

Introduction

The character of critical behavior in physical systems depends on the range of interactions. When a fluid approaches the critical point, the behavior of its equilibrium properties is determined by the fluctuations of the order parameter. Therefore the fluids, simple and complex, belong to the same universality, namely that of the 3D-Ising model. However, for some hydrocarbon, polymer blends, and ion solvents, the approach to universal critical behavior in such systems should be affected by a competition between the correlation length of the critical fluctuations and an additional length associated with the supramolecular structure or/and with long-range interparticle interactions. In those systems, a crossover to classical mean-field should be expected. Recently the critical crossover has attracted much attention [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11].

Near the critical point, the difference Δρ of a general density variable, such as mole fractions, refractive indices, and volume fractions, between two coexistence phases, the correlation length ξ and osmotic compressibility χ exhibit universal power-lower dependences on the reduced t {t = (T  Tc)/Tc}. The dependences may be described by the following forms:Δρ=ρ2-ρ1=Btβ,χt-γ=χ0t-γ,ξt-ν=ξ0t-ν,where ρ is the density variable, ρ1 and ρ2 are the values of the density variables in the upper and lower coexistence phases; B, χ0, and ξ0 are the critical amplitudes. The values of critical exponents β, γ, and ν are 0.327, 1.24 [12], [13], and 0.63 for 3D-Ising universality class; while they are 0.5, 1, and 0.5 from the classical mean-field theories.

The critical behaviors of chain-molecule solutions on the number N of monomer units or the molecular mass M of the chain molecule have always attracted much attention [14], [15], [16], [17], [18]. An alternative approach to the M-dependence of amplitudes for chain molecule solutions was given by An et al. [19], which derived from a Landau–Ginsberg–Wilson type model. These may be written asϕc/(1-ϕc)M-r,Bϕ(1-ϕc)-1.865M-b,ξ0(1-ϕc)0.85Mn,where ϕc is the critical volume fraction of chain-molecule component, Bϕ and ξ0 are critical amplitudes, with the universal exponent r = 0.41, b = 0.29, and n = 0.18, respectively, for the chain-molecule solutions of both small molecules and polymers. In previous work [11], [20], [21], the coexistence curves of three mixtures with one component being benzonitrile and the other being n-alkane were obtained by measurements of refractive index. This experimental results together with the data reported in this work may be used to test the validity of equations (4), (5), (6), and to determine the values of the exponent r, b, and n.

In this paper, we report the experimental results of the coexistence curves and the light scattering for the system of (benzonitrile + octane). The results are analyzed to obtain the critical exponents and critical amplitudes corresponding to (ρ2  ρ1), χ, and ξ. The experimental results of the coexistence have also been analyzed to examine the Wegner correction terms, the behavior of coexistence curves and the M-dependence of amplitudes for chain molecule solutions. Furthermore, according to the crossover theory proposed by Anisimov and Sengers, the crossover parameters were obtained and discussed.

Section snippets

Experimental

The benzonitrile, mass fraction 0.99, obtained from the Shanghai Kaiming Chemical Factory was distilled slowly under reduced pressure. The middle part of the distillate was collected and passed through a column of dried chromatographic alumina. The octane mass, fraction 0.99, supplied by Fluka Co. was dried and stored over a 0.4 nm molecular sieve.

The coexistence curves were determined by measurements of refractive indices of two coexisting phases using a technique of “minimum deviations”. The

Coexistence curves

The critical mole fraction and the critical temperature were determined to be xc = (0.464 ± 0.001) and Tc = (283.2 ± 0.2) K, respectively. The refractive indices n were measured for each coexisting phase at various temperatures. The results are listed in columns 2 and 3 of table 1 and are shown in figure 1a.

The refractive index n of a pure liquid or a mixture may be well expressed as a linear function of temperature in a certain temperature range [23]:n(T,x)=n(T0,x)+R(x)(T-T0),R(x)=xRA+(1-x)RB,where R(x

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Projects 20173024, 20473035, 20603014, 20673059), the Chinese Ministry of Education (Key Project 105074) and Committee of Science and Technology of Shanghai (Project 0652nm010).

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