D. E. Sullivan

Surface tension and contact angle of a liquid–solid interface

The contact angle between a liquid film and a solid substrate is treated in the van der Waals model used previously by the author to discuss gas adsorption on solid surfaces. The model accounts for the occurrence of three types of wetting behavior, i.e., complete wetting, partial wetting, and nonwetting, as well as for transitions between these different regimes. According to this model, the contact angle depends on two parameters, namely the reduced temperature T/Tc, where Tc is the critical temperature of the liquid, and ew/kTc, where ew is the minimum in the liquid–solid interaction potential. For high‐energy surfaces, corresponding to large ew/kTc, the contact angle decreases on increasing temperature; the opposite behavior is predicted to occur on sufficiently low‐energy surfaces. With some hypotheses on how ew depends on the nature of the solid and liquid phases present, one can calculate the variation in contact angle with liquid species for a given solid at fixed temperature. The theory is compare...

Molecular interactions and interface properties of nematic liquid crystals

Molecular perturbation methods are used to derive an approximate free‐energy functional for nonuniform nematic liquids with anisotropic repulsive and attractive intermolecular forces. The free energy is simplified to a Landau–de Gennes form, providing expressions for the elastic constants and surface fields of the latter in terms of microscopic interactions. These expressions are evaluated using the Gay–Berne model potential (GB) between rigid rod‐like molecules. Short‐range attractive and repulsive components of that potential are found to give similar contributions to the Landau–de Gennes parameters, but these are strongly counterbalanced by long‐range attractive contributions. The theory is applied to orientational alignment and nematic wetting at the free liquid–vapor interface. The preferred nematic alignment is predicted to be perpendicular to the interface, due to a weak dominance by repulsive and short‐range attractive forces. It is found that wetting by the nematic phase changes from complete to ...

Evaluation of angular correlation parameters and the dielectric constant in the RISM approximation

We prove, using a projection operator method, a number of results obtained when site-site correlation functions are evaluated in the RISM approximation. In non-polar fluids, the angular correlation parameter G 2 is identically zero for any symmetric linear molecule, while G 1 is identically zero for an arbitrary linear molecule. In rigid polar fluids, the dielectric constant є is found to be given by the ideal-gas type expression є = 1 + 3y, where y = 4πβρμ2/9.

Structure of a simple fluid near a wall. II. Comparison with Monte Carlo

Monte Carlo methods are used to calculate density profiles of a dense simple fluid, interacting through a pair potential containing a hard‐sphere core and truncated Lennard‐Jones attractive tail, near a hard repulsive wall. The results are compared with integral–equation calculations based on the wall‐particle Ornstein–Zernike equation, with closure approximations such as EXP. The integral equations fail to show several features of the Monte Carlo results, namely dependence on the distance at which the Lennard‐Jones attraction is truncated, and the accumulation of conjugate vapor phase near the wall, which tends to suppress oscillations in the profiles.

Entropy-induced smectic phases in rod-coil copolymers

We present a self-consistent field theory (SCFT) for dilute solutions of semiflexible (wormlike) diblock copolymers, each consisting of a rigid and a flexible part. The segments of the polymers are otherwise identical, in particular with regard to their interactions, which are taken to be of an Onsager excluded-volume type. The theory is developed in a general three-dimensional form, as well as in a simpler one-dimensional version. Using the latter, we demonstrate that the theory predicts the formation of a partial-bilayer smectic-A phase in this system, as shown by profiles of the local density and orientational distribution functions. The phase diagram of the system, which includes the isotropic and nematic phases, is obtained in terms of the mean density and rigid-rod fraction of each molecule. The nematic–smectic transition is found to be second order. Since the smectic phase is induced solely by the difference in the rigidities, the onset of smectic ordering is shown to be an entropic effect and therefore does not have to rely on additional Flory–Huggins-type repulsive interactions between unlike chain segments. These findings are compared with other recent SCFT studies of similar copolymer models and with computer simulations of several molecular models.

The liquid-vapour interface of nematic liquid crystals

The occurrence of wetting by a nematic film at the diffuse interface between vapour and isotropic liquid is studied using a generalized van der Waals theory for liquid crystals. This contrasts with earlier studies of nematic wetting at the liquid free surface, which were based on a sharp-interface approximation. The present work also corrects several findings of an earlier study [9] on vapournematic interfaces. Variations in the wetting and alignment properties of the liquid-vapour interface are related to certain orientational symmetry-breaking terms in the model intermolecular potential. Of most relevance to experimental studies, we show that the non-monotonic variation of surface tension with temperature is a necessary consequence of the approach to complete nematic wetting.

Interfacial density profiles of a binary van der Waals fluid

The van der Waals theory of the interface between coexisting fluid phases of a binary mixture is studied. The theory can be solved analytically on making certain assumptions about the nature of the intermolecular attractive forces, most importantly, the assumption that the cross interaction parameter a12 appearing in van der Waals’ equation of state satisfies the geometric‐mean combining rule. In this case, it is found that the interfacial tensions between pairs of phases coexisting under three‐phase equilibrium conditions satisfy Antonow’s rule. The theory is not, however, a ’’one‐density’’ theory in the sense of Widom, and consequently the interfacial density profile of the more volatile component can be nonmonotonic. At three‐phase equilibrium, the location and magnitude of the nonmonotonicity is related to the proximity of two of the phases to their upper critical end point (UCEP). Which pair of phases becomes critical at the UCEP is in turn related to the type of fluid–fluid equilibrium exhibited by ...

The nematic-isotropic phase transition in semiflexible fused hard-sphere chain fluids

A density-functional theory of the isotropic–nematic phase transition in both rigid and semiflexible hard-sphere chain fluids is described. The theory is based on an exact analytical evaluation of the excluded volume and second virial coefficient B2 for rigid chain molecules, which demonstrates that B2 in these cases is equivalent to that of a binary mixture of hard spheres and hard diatomic molecules. It is assumed that the same binary-mixture representation applies to semiflexible chains, while scaled particle theory is used to obtain the properties of the fluid at arbitrary densities. The results of the theory are in very good agreement with Monte Carlo (MC) simulation data for rigid tangent hard-sphere chains, but in lesser agreement with available MC studies of rigid fused hard-sphere chains. We find that there is reasonable agreement between the theory and MC data for semiflexible tangent chains, which improves with increasing chain length. The behavior predicted by the theory for semiflexible chain...

Structure of a diatomic fluid near a wall: II. Lennard-Jones fluid

Molecular dynamics has been used to simulate a high density fluid of homonuclear diatomic molecules in the presence of a rigid planar wall. The molecular interactions were modelled by Lennard-Jones (12, 6) site-site potentials and (17, 3) wall-site potentials. The relative influence of attractive and repulsive forces on the interfacial orientational structure was studied by comparing with simulations in which the attractive components of either or both the site-site and wall-site potentials were absent. The results, presented as contour plots of the density-orientation profile ρ(z, θ), show that parallel orientation of the molecules is favoured when the centre-of-mass distance z is very close to the wall, but that perpendicular orientation is favoured at slightly larger distances. The presence of weakly attractive wall-site forces slightly increases the relative degree of parallel alignment compared with that in the absence of such forces. The presence of attractive site-site pair interactions diminishes ...

Molecular orientational structure of the water liquid/vapour interface

Theoretical and experimental results for the distribution of molecular orientations at the liquid/vapour interface of water are compared. The present calculations are based on an extended mean-field density functional theory applied to an intermolecular potential model containing dipolar and quadrupolar interactions, with parameters chosen to agree with the TIP4P model of water. The results for the orientational order parameters at the interface are used to calculate several observable quantities as functions of temperature, namely: (i) the surface electrostatic potential, (ii) the coefficient of ellipticity; (iii) the nonlinear susceptibility measured by second-harmonic generation. Comparisons are made with both the experimental and computer simulation data for water. The limitations of current methods for revealing the preferred molecular orientations at an interface are discussed.