Richard P. Sear

Thermodynamic perturbation theory for association with bond cooperativity

A simple model of a hydrogen‐bonding molecule is considered, each model molecule can bond to two other molecules. This bonding is not, in contrast to previous work, taken to be pairwise additive. The association energy contains a three‐body term which either increases or decreases the strength of the bonds in chains of three or more molecules, i.e., it makes the bonding cooperative. Motivation for this form of the intermolecular potential is provided by the behavior of hydrogen fluoride: the bond strength of a hydrogen fluoride dimer is considerably less than the bond strength in chains of three or more molecules. An analytical theory for the free energy of this model molecule is derived via a new approach which is sufficiently general to accommodate the non‐pairwise additive interaction. Calculations are performed which show the effect of the cooperative bonding on vapor–liquid coexistence.

Theory for the phase behavior of a mixture of a rodlike colloid and a rodlike polymer

A suspension of rodlike colloidal particles and rodlike liquid crystalline polymers is modeled as a mixture of thick (colloidal) and thin (polymeric) rods. The model mixture is studied by means of an Onsager type theory, the colloidal particles are represented by hard rods and the polymer by hard rods with zero diameter. Extensive immiscibility is observed for the colloid plus polymer model mixture and if the polymer is more than 3 times as long as the colloid coexistence between two isotropic phases is observed. For all polymer lengths phase separation into an almost pure ideal gas of polymer and a dense nematic phase of colloid is observed at high polymer fugacity. The phase separation is driven by excluded volume effects; the volume available to the polymer is maximized by separating from the colloid.

Theory and computer simulation of hard-sphere site models of ring molecules

A previous theory for hard-sphere site models of non-spherical molecules, the bonded hard sphere (BHS) theory, is reviewed and a generalization is proposed to extend the theory to ring-like molecules. New simulation data are presented for rigid ring molecules formed from three, four and five tangent hard spheres of equal size, and the results are compared with the predictions of the generalization. In all, four models are studied consisting of hard spheres at the corners of an equilateral triangle, a square, a regular tetrahedron, and a regular pentagon, respectively. Good agreement between the exact Monte Carlo data and the approximate theory is found. The two approximations made in the BHS theory and in its generalization are discussed, as is the extent of their validity. Theories of this type, based on the bonding of spheres into the desired molecules, require distribution functions for three or more spheres; the problem of estimating these functions given only the pair radial distribution function is ...

Bonded hard-sphere theory and computer simulations of polyatomic hard-sphere models of alkanes and their derivatives

The equation of state of the first two members of a homologous series of model alkane-like molecules which incorporate the identities of the backbone and substituent atoms as hard-sphere sites is examined. These polyatomic molecules are formed from tangentially bonded hard spheres with diameters σ1 and σ2, where spheres of type 1 make up the backbone of the chain, and spheres of type 2 represent the substituent atoms. The spheres are bonded together in a tetrahedral geometry so that all of the bond angles are ω = 109°; for the second and higher homologues dihedral angles χ about the 1–1 bonds also have to be specified. In order to test the predictions of a recent bonded hard-sphere (BHS) theory, isothermal-isobaric Monte Carlo (MC-NPT) simulations are undertaken for methane- and ethane-like molecules with different diameter ratios σ2/σ1 over a range of densities in the fluid state. In the case of the ethane-like molecules trans (χ = 30°) and freely rotating geometries are examined. The simulation data are...

Thermodynamic perturbation theory for association into doubly bonded dimers

A theory is proposed for model molecules which may form one or two bonds with other molecules. These molecules may therefore be in one of four states: unbonded, bonded to one other molecule via one bond, bonded to one other molecule via two bonds, and bonded to two other molecules. This model has been extensively studied using a formalism developed by Wertheim but the third state has always been neglected. This neglect is reasonable if the molecule forms bonds in such a way that the two bonded molecules lie on opposite sides of the central molecule. However, if this is not the case, dimers with the molecules bonded together by two bonds can also form. The necessary theory, within Wertheims formalism, is proposed here. Two specific models are considered: a sphere with two association sites mediating the two bonding interactions, and a chain of spheres with a site on each of the end spheres. According to the model, two approximation schemes are proposed for the additional association graph required to acco...

The gas, liquid, and solid phases of dimerizing hard spheres and hard-sphere dumbbells

The complete phase diagram of a model associating molecule is determined, including the gas, liquid, and solid phases, the regions of coexistence between these three phases, and the location of the critical and triple points. The model molecule is a hard sphere with two very different attractive interactions, one a short ranged and directional attraction and the other a mean field. The first interaction only forms dimers as a molecule can only interact in this way with one other molecule. This saturable attraction mimics hydrogen and chemical bonding. The second interaction is an approximation for the dispersion forces between molecules. Thermodynamic functions for the liquid and gas phases of this model molecule are obtained from an existing theory for associating fluids but a new theory is developed for the solid phase. This is believed to be the first microscopic theory of a model associating molecule in the solid phase. In the low temperature limit no monomers are present; the system is then a fluid o...

Theory for hydrogen-bonding nematic liquid crystals

A theory for highly anisotropic hydrogen-bonding molecules in the nematic and isotropic phases is presented. The theory is applied to a very simple molecular model: a hard spherocylinder which is able to form a dimer with another such molecule. In the dimer the two molecules are constrained to be positioned end-to-end and nearly parallel. The phase diagram of this model, within the approximations of the theory, is calculated and the effects of hydrogen bonding discussed. Unsurprisingly, the bonding enhances the stability of the nematic phase, but in a small range of densities a system heated at constant volume will start in the nematic region then enter the nematic-isotropic coexistence region before returning to the nematic region. This is a type of re-entrant behaviour. It is also shown that the hydrogen bonding is enhanced by the orientational ordering in the nematic phase and that there is significant hydrogen bonding in the nematic phase at temperatures too high for bonding in the isotropic phase. In...

The liquid crystalline phase behavior of dimerizing hard spherocylinders

The phase behavior of dimerizing (associating) rigid particles is studied by both theory and computer simulation. The model molecule comprises a hard spherocylinder of length L and diameter D with a terminal square well bonding site embedded in one of the hemispherical caps. This model mimics the properties of simple hydrogen bonding mesogens; for example, mesogens with a carboxylic acid end group which are capable of forming dimers. A recently proposed theory of the isotropic (I)-nematic (N) phase transition for long hard spherocylinders with an attractive site at one end [R. P. Sear and G. Jackson, Mol. Phys. 82, 473 (1994)] is extended to shorter molecules. In the original theory the free energy is truncated at the level of the second virial coefficient. We now include the higher virial coefficients in an approximate manner with a Parsons type scaling. The accuracy of the theory is demonstrated by comparison with novel Monte Carlo simulation data for the same model. Excellent agreement is found for den...

THE RING INTEGRAL IN A THERMODYNAMIC PERTURBATION THEORY FOR ASSOCIATION

Molecules which associate forming both inter- and intramolecular bonds have recently been considered by R.P. Sear and G. Jackson (1994, Phys. Rev. E., 50, 386) and by D. Ghonasgi and W.G. Chapman (1995, J. chem. Phys., 102, 2585). The same free energy expression was proposed in both these studies, and both considered associating chains of hard spheres, but whereas Sear and Jackson proposed a simple analytical approximation to the ring graph contribution to the free energy, Ghonasgi and Chapman evaluated it by computer simulation. The original Sear and Jackson approximation is improved and compared with the simulation data, with good agreement. It is concluded that the theory is a simple and accurate treatment of intramolecular association.

STABILITY OF THE NEMATIC PHASE OF A MIXTURE OF ALIGNED CYLINDERS WITH RESPECT TO THE SMECTIC AND COLUMNAR PHASES

The theory for the stability of the nematic phase of parallel cylinders due to Mulder [Phys. Rev. A 35, 3095 (1987)] is generalized to binary mixtures. It is shown that adding cylinders of a different length to a one‐component nematic phase of cylinders postpones the nematic–smectic A transition, enhancing the range of the nematic. This is a result of the two different length scales each favoring a density modulation of a different wavelength. When the ratio of the lengths of the cylinders is large a cusp appears in the limit of stability of the nematic phase. This cusp corresponds to a large jump in the wavelength of the density modulation from a wavelength characteristic of ordering of the short rods to that characteristic of the longer rods. The cusp is, however, masked by a transition to a columnar phase unless the diameters of the two species of rod are significantly different. The limit of stability with respect to the smectic phase bears a striking resemblance to the phase behavior of a mixture of two mesogens studied some time ago by Sigaud et al. [J. Phys. (Paris) Colloq. 40, C3 (1979)]. Their results have hitherto only been described by Landau theory and via lattice ‘‘analogs’’ which have no obvious connection with the underlying behavior at the molecular level. In contrast, theories of specific model molecules such as the cylinders studied here offer insight into behavior at the molecular level.