The second dielectric virial coefficient of a dipolar sticky hard sphere fluid

We calculate the second dielectric virial coefficient, B _?, of a fluid whose molecules are sticky hard spheres with embedded central point dipoles. The effect of stickiness is to increases B _? markedly.     

Square-well diatomics Exact low density results

Exact semi-analytical expressions are obtained for the zero density site-site distribution function and the second virial coefficient for homonuclear square-well diatomics. The diatomic molecules considered here are composed of two fused square-well spheres with hard core diameter σ, well diameter λσ, and dimer bond length L, such that 0<Lˇ-σ and 1ˇ-λˇ-1+L/σ. Very accurate, although approximate, analytical expressions are also given for these functions.     

Quantum corrections to thermodynamics of polar hard sphere fluids

The quantum corrections to the thermodynamic properties of polar hard sphere fluids and fluid mixtures are estimated taking into account the influence of dipole and quadrupole moments. Expressions are given for the second virial coefficient, free energy and pressure and results are given for different values ofμ* andϑ*. The first order quantum correction arises due to the translational contribution only. The quantum effect increases with density,μ* andϑ*. Numerical results are also estimated for binary mixtures of (i) hard spheres and dipole hard spheres and (ii) hard spheres and quadrupole hard spheres. The ‘excess’ free energy for dipole hard sphere binary mixture is also reported. It is found that the ‘excess’ quantum effect depends on the concentration and the particle diameter ratio and increases with increase ofμ* andϑ*.     

Perturbation expansions and series acceleration procedures. Part I. ε-convergence and critical parameters

A simple acceleration of convergence technique known as the ‘ε-convergence algorithm’ (ea) is applied to determine the critical temperatures and exponents. Several illustrations involving well-known series expansions appropriate to two- and three-dimensional Ising models, three-dimensional Heisenberg models, etc., are given. Apart from this, a few recently studied ferrimagnetic systems have also been analysed to emphasise the generality of the approach. Where exact solutions are available, our estimates obtained from this procedure are in excellent agreement. In the case of other models, the critical parameters we have obtained are consistent with other estimates such as those of the Padé approximants and group theoretic methods. The same procedure is applied to the partial virial series for hard spheres and hard discs and it is demonstrated that the divergence of pressure occurs when the close-packing density is reached. The asymptotic form for the virial equation of state is found to beP/ρkT ∼ (1 −ρ/ρ _c ⁻¹ for hard spheres and hard discs. Apart from the estimation of ‘critical parameters’, we have applied theea and the parametrised Euler transformation to sum the partial, truncated virial series for hard spheres and hard discs. The resulting values of pressure so obtained, compare favourably with the molecular dynamics results.     

Fluids of general hard triatomic molecules

The second, third, and fourth virial coefficients, B_i , of a fluid of general symmetric hard triatomic molecules (fused hard spheres) have been calculated both numerically and theoretically for a variety of potential parameters. It has been found that: (i) for B₂ a valency angle ω_c exists such that for ω>w_c, B ₂ is independent of ω, (ii) B ₃ is very flat for ω>w_c, and (iii) B ₄ exhibits a maximum at ω～π/2. Theoretical calculations employing an assigned convex body fit very well the second and fairly well the third virial coefficients, but fail for the fourth except in the case of a linear molecule.     

The Quantum Excess Free Energy for Two Component Plasma

The aim of this paper is to calculate the quantum excess free energy until the third virial coefficient for the two component plasma (TCP). We consider only the thermal equilibrium plasma in the case of nλ³_ab ≪ 1 where λ²_ab = (ħ²/(m_abKT)) is the thermal De Broglie wave‐length. The second and third virial coefficients are represented in forms of a convergent series expansion in terms of the interaction Parameter ξ²_ab = ((e_ae_b)/(λ_abKT)). We obtained the excess free energy until the third virial coefficient to the order ξ⁶_ab. The effects of symmetry are taken into account, also the exchange effects were taken in account. We compared our results with others. Upon comparison with Ebeling et al. one observes that the considerable contribution of the third virial coefficient in the region of high temperatures (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Explicit and implicit finiteness corrections of virial coefficients

The equation of state of finite systems deviates from thermodynamic limit. The corresponding finiteness corrections of virial coefficients are studied. Most calculations are based on the canonical ensemble with periodic boundary conditions.Explicit andimplicit finiteness corrections occur. They are displayed up to the eighth virial coefficient. These results are applied to hard spheres in one, two, and three dimensions.     

Critical temperature of infinitely long chains from Wertheim's perturbation theory

Wertheim's theory is used to determine the critical properties of chains formed by m tangent spheres interacting through the pair potential u(r). It is shown that within Wertheim's theory the critical temperature and compressibility factor reach a finite non-zero value for infinitely long chains, whereas the critical density and pressure vanish as m ^-1.5. Analysing the zero density limit of Wertheim's equation or state for chains it is found that the critical temperature of the infinitely long chain can be obtained by solving a simple equation which involves the second virial coefficient of the reference monomer fluid and the second virial coefficient between a monomer and a dimer. According to Wertheim's theory, the critical temperature of an infinitely long chain (i.e. the Θ temperature) corresponds to the temperature where the second virial coefficient of the monomer is equal to 2/3 of the second virial coefficient between a monomer and dimer. This is a simple and useful result. By computing the second virial coefficient of the monomer and that between a monomer and a dimer, we have determined the Θ temperature that follows from Wertheim's theory for several kinds of chains. In particular, we have evaluated Θ for chains made up of monomer units interacting through the Lennard-Jones potential, the square well potential and the Yukawa potential. For the square well potential, the Θ temperature that follows from Wertheim's theory is given by a simple analytical expression. It is found that the ratio of Θ to the Boyle and critical temperatures of the monomer decreases with the range of the potential.     

New results for virial coefficients of hard spheres inD dimensions

We present new results for the virial coefficientsB _k for κ<- 10 for hard spheres in dimensionsD = 2,..., 8.     

The thermodynamic functions of molecular liquids in the interaction site model

The excess Helmholtz Free Energy (H.F.E.) of the hard molecule liquid with respect to the perfect gas (point-like non-interacting molecule) is obtained; the Equation of State (E.S.) is then derived.

The site-site and molecular correlation functions involved in both the excess H.F.E. and the E.S. are determined in the framework of a modified Reference Interaction Site Model. For a symmetric diatomic molecule the exact value g ₁₁(r = σ⁺) = 1/4 of the site-site correlation function and the exact second virial coefficient is obtained.     

A Light and X‐Ray Scattering Study of Aqueous Micellar Solutions of a Diblock Copolymer of Propylene Oxide and Ethylene Oxide with Solubilized Alkylcyanobiphenyl Liquid Crystals

Abstract

The temperature and concentration dependences of the physicochemical properties of aqueous solutions of the diblock copolymer P₄₃E₃₁₂ (P = oxypropylene, E = oxyethylene) with solubilized liquid crystal (LC) have been studied using static and dynamic light scattering (SLS and DLS), small‐angle x‐ray scattering (SAXS), and ultraviolet (UV) spectroscopy. Relaxation time distributions from DLS obtained from inverse Laplace transformation of intensity correlation functions are multimodal, where the two fastest modes are attributed to diblock copolymer unimers and micelles, respectively. The remaining modes at longer decay times reflect the presence of free LC with hydrodynamic radii (R _h) of hundreds of nm. The R _h of both unimers and micelles were independent of temperature (T), while the hydrodynamic virial coefficient k _D and the second virial coefficient, A ₂, decreased with increasing T. The UV spectroscopy measurements showed that there is a reduction in the amount of solubilized LC per gram of copolymer (c _s) as the copolymer concentration (c _p) is increased. The SAXS results agree well with a model of a homogeneous system of polydisperse interacting hard spheres. In solution, both the effective micellar radius of interaction (R _eff) and the hard‐sphere micellar radius (R¯_s) increase in the presence of LC due to solubilization of the latter in the hydrophobic micellar core. Both SAXS and SLS results show that intermicellar interactions become important at c _p > 1% (w/w) at high temperatures [T > the critical micelle temperature (cmt)].     

Second virial coefficient of homonuclear two-centre Lennard-Jones molecules

A semiempirical expression based on numerical values of the second virial coefficient of the two-centre Lennard-Jones molecules and on the theoretical expression for hard dumbells is given. The resulting expression possesses the form developed formerly for the second virial coefficient of the Kihara non-spherical molecules and reproduces fairly well the correct limits at high temperatures. It allows the prediction of the second virial coefficient at reduced temperatures T*≧0·5.     

Smectic phases in hard particle mixtures: Koda's theory

Mixtures of parallel linear particles and spheres tend to demix upon compression. The linear species usually concentrates in regular layers, thus forming a smectic phase. With increasing concentration of spheres this ‘smectic demixing’ transition occurs at ever lower packing densities. For the specific case of hard spherocylinders and spheres Koda et al. [T. Koda, M. Numajiri, S. Ikeda, J. Phys. Jap., 65, 3551 (1996)] have explained the layering effect in terms of a second virial approximation to the free energy. We extend this approach from spherocylinders to other linear particles, namely fused spheres, ellipsoids and sphero-ellipsoids.     

Editorial

Using coupled cluster singles and doubles linear response theory and the d-aug-cc-pVTZ basis set extended with a 3s3p2d1f1g set of midbond functions, the interaction induced electric dipole polarisability surface of the CO–Ar van der Waals complex is computed. Combining this surface with accurate intermolecular potential energy and electric dipole surfaces, the pressure and dielectric second virial coefficients of the complex are calculated by a classical statistical approach. Excellent agreement with experimental results (to within the experimental error bars) is obtained for the pressure second virial coefficient over a range of temperatures. No previous experimental or theoretical investigations have been carried out for the dielectric second virial coefficient, B _ε(T), which is estimated to be about 1.9 cm⁶ mol^??1 at room temperature. This value results from a balance of terms due to the interaction induced electric dipole polarisability (predominant at high temperatures) and orientational electric dipole contributions.     

Analytic Calculation of B 4 for Hard Spheres in Even Dimensions

We exactly calculate the fourth virial coefficient for hard spheres in even dimensions for D = 4, 6, 8, 10, and 12.     

Monte-Carlo integration for virial coefficients re-visited: hard convex bodies,spheres with a square-well potential and mixtures of hard spheres

Techniques to adapt the hit-and-miss Monte-Carlo numerical integration are proposed with the aim to determine virial coefficients up to eighth order in fluids of hard convex bodies, hard spheres with an attractive square-well potential and a two-component mixture of hard spheres. These algorithms make use of look-up tables of all the blocks contributing to the coefficients. Each type of block is represented in the tables by several entries. These correspond to all possible topologically equivalent graphs that can be generated by the Monte-Carlo process. This rendered the Monte-Carlo method statistically more efficient. In the case of a two-component system the look-up tables had to have representations of blocks having two sorts of vertices. The reported data are: improved values of the seventh and eighth virial coefficients for hard spheres, the sixth, seventh and eighth coefficients of spheroids, spherocylinders and cutspheres, fifth virial coefficient of spheres with a square-well potential of relative range 1.25; 1.5; 1.75 and 2.0 and the partial contributions of the sixth virial coefficient for a mixture of hard spheres with the size ratio 0.1.     

Stability of the H2–(He,Ne, Ar) fluid mixtures

A theory of mixtures based on a statistical mechanical perturbation scheme is used to compute the excess free energy of mixing, the excess entropy of mixing and the concentration fluctuations in the long wavelength limit as functions of composition (c) over a wide range of temperature (T = 150 to 350 K) and pressure (p = 10 MPa to 10 GPa). This has been utilized to investigate the effects of c, T and p on the solubility of H₂ (the first element of the periodic table) to He, Ne and Ar (the first three elements of the last group) and the thermodynamic stability of the mixture. The long-range correlations among the constituent species are included through the double Yukawa potential which acts as a perturbation to the hard sphere reference mixture. The non-additivity of the potentials of the constituent species is linked to the second virial coefficients which can be determined from the experimental data. Necessary corrections to the equation of state for dimerisation of H₂ molecule and quantum effects are included. At a given T = 150 K and p = 100 MPa, H₂–Ar mixture exhibits greater thermodynamic stability than H₂–Ne and H₂–Ar.     

Equations of state for the hard disk fluids

By using the published accurate new virial coefficients B₁₁～B₁₄ for the hard disk fluids [C. Zhang and B.M. Pettitt, Mol. Phys., 2014, 112, 1427], we here propose a new updated version of Tian-Gui-Mulero equation of state [J.X. Tian, Y.X. Gui and A. Mulero, Phys. Chem. Chem. Phys., 2010, 12, 13597]. Compared with other proposals, the new version stands strongly to be the only which can reproduce the known virial coefficients B₂～B₁₃ at the same time that can describe the relation of the compressibility factor versus the packing fraction for the hard disk fluids with high accuracy.     

Self-diffusion of spheres in a concentrated suspension

We calculate the concentration-dependence of the short-time self-diffusion coefficient D_s for spherical particles in suspension. Our analysis is valid up to high densities and fully takes into account the many-body hydrodynamic interactions between an arbitrary number of spheres. The importance of these many-body interactions can be inferred from our calculation of the second virial coefficient of D_s.