Test of a simple analytic model for fluids of hard linear molecules

Lado, F.

doi:10.1080/00268978500100311

Cited by 29 publications

(6 citation statements)

References 19 publications

(28 reference statements)

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“…The angular dependence thus introduced possesses plausible characteristics just because of this coupling to a, on the other hand Lado (1985) showed that it has the deficiency of giving an isotropic value for c< 2 )(r -» 0), which is contrary to reality. Lado also tested the decoupling approximation by comparing it with the integral equation approach for hard dumbbells and found excellent agreement for the case of a separation of 0.4 times the diameter of the composing spheres.…”

Section: Integral Equation Approachcontrasting

confidence: 41%

“…behaviour at higher densities, with attractive interactions and for bidisperse systems), they do not lead to the exact result of Onsager for infinitely thin hard rods. There are also some other models based on the wormlike chain which we can only mention here: an extension of the Flory theory to wormlike chains (Ronca and Yoon 1982, 1985 and theories using a Maier-Saupe potential (Ten Bosch et al 1983, \torner et al 1985. As a last point we want to draw attention to some monographs and review papers on liquid crystals (De Gennes 1974, Stephen and Straley 1974, Chandrasekhar 1977, Luckhurst and Gray 1979, Vertogen and De Jeu 1988, Frenkel 1991 and liquid crystalline polymers (Straley 1973a, Blumstein 1978, Grosberg and Khokhlov 1981, Ciferri et al 1982, Miller 1982, Samulski and DuPré 1983, Gordon and Plate 1984, Khokhlov and Semenov 1985, Ciferri and Marsano 1987, Semenov and Khokhlov 1988, DuPré and Yang 1991, which might be helpful for the reader.…”

Section: Introductionmentioning

confidence: 99%

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Phase transitions in lyotropic colloidal and polymer liquid crystals

1992

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An overview is given of theory and experiments on liquid crystal phases which appear in solutions of elongated colloidal particles or stiff polymers. The Onsager (1949) virial theory for the isotropic-nematic transition of thin rodlike particles is treated comprehensively along with extensions to polydisperse solutions and soft interactions. Computer simulations of liquid crystal phases in hard particle fluids are summarized and used to assess the quality of statistical mechanical theories for stiff particles at higher volume fraction-like the inclusion of higher virial coefficients, y-expansion, scaled particle theory and density functional theory. Both computer simulations and density functional theory indicate formation of more highly ordered smectic phases. The range of experimental applicability is strongly widened by the extension of the virial theory to wormlike chains by Khokhlov andSemenov (1981, 1982). Finally, experimental results for a number of carefully studied, charged and uncharged colloids and polymers are summarized and compared to theoretical results. In many cases the agreement is semi-quantitative.

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Section: Integral Equation Approachcontrasting

confidence: 41%

Section: Introductionmentioning

confidence: 99%

Phase transitions in lyotropic colloidal and polymer liquid crystals

1992

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“…It has been shown moreover that for hard dumbbells [7] the ansatz provided by (4) agrees surprisingly well with the numerical solutions of the PY equation. The approximation underlying (4) is most clearly exhibited by observing [8] that when (4) is used in (2) for a nematic phase it automatically leads to a decoupling of the angular and radial variables.…”

supporting

confidence: 63%

Nematic-Smectic A and Nematic-Solid Transitions of Parallel Hard Spherocylinders from Density Functional Theory

Xu¹,

Lekkerkerker²,

Baus³

1992

Europhys. Lett.

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PACS. 64.70 -Phase equilibria, phase transitions, and critical points. PACS. 61.30B -Molecular theories of liquid crystals (inc. statistical mechanical theories). PACS. 05.70F -Phase transitions: general aspects.Abstract. -A simple density functional theory for the various liquid-crystalline phases of parallel hard spherocylinders is formulated on the basis of Pynn's ansatz for the direct correlation function of the spherocylinders. Fair agreement with the computer simulations is found.It was Onsager [1] who showed for the first time that a nematic liquid crystalline phase can be formed, above a certain density, in a system of nonspherical molecules with purely repulsive (steric) interactions. Recent computer simulations [2] have confirmed this prediction and revealed moreover that the resulting phase diagram is very sensitive to the molecular shape and includes, for certain molecular aspect ratios, also smectic phases besides the isotropic, nematic and solid phases. At present, the simplest model system known [3] to exhibit a smectic phase consists of hard spherocylinders (i.e. cylinders of length L and diameter D capped at both ends with hemispheres of diameter D), which are constrained to remain parallel one to another. At low densities such a parallel hard spherocylinder (PHSC) system is always in a nematic (N) phase, while at high densities it forms a solid (S) phase with a (close packed) face-centred cubic (f.c.c.) structure. Moreover, above a critical value of the aspect ratio, LID, a smectic A (SmA) phase forms for densities intermediate between those of the N and S phases. It is the purpose of this letter to study theoretically this competition between the N-S and N-SmA transitions of PHSC and to locate the N-SmA-S triple point in the density-aspect ratio plane.A convenient theoretical framework for the study of phase transitions in systems of hard bodies is provided by the density functional theory of nonuniform fluids [4]. In this theory the (Helmholtz) free energy, F, of a system of N spherocylinders enclosed, at a temperature T (ß = l/k B T), in a vessel of volume V is written as the sum, F = F id + F ex , of an ideal part 3 ) -1}(1)

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“…Since in this approach the influence of relative orientation is decoupled from the influence of interparticle distance, the name decoupling approximation is appropriate. It has the defect, first noticed by Lado, [165] that for r + 0 the direct correlation function is predicted to be isotropic, contrary to reality.…”

Section: (426)mentioning

confidence: 89%