Effects of Thermal Roughness on X-ray Studies of Liquid Surfaces

The effects of thermal roughness on X-ray studies of liquid surfaces will be discussed. In contrast to solid surfaces, for which the surface height–height correlation function remains finite at large distances, for liquid surfaces thermal fluctuations induce a logarithmic dependence for distances smaller than a gravitationally induced cutoff that is of the order of mm. As a result of this there is no true specular X-ray reflectivity liquid surfaces. Theory and measurements explaining this phenomena will be presented.Engineering and Applied Science

Liquid and Liquid Crystal Surfaces

Engineering and Applied Science

Structure of Surfaces and Interfaces as Studied Using Synchrotron Radiation. Liquid Surfaces

The use of specular reflection of X-rays to study the structure of the liquid/vapour interfaces along the direction normal to the surface is described. If $R_F(\theta)$ is the theoretical Fresnel reflection law for X-rays incident on an ideal flat surface at an angle $\theta$, and $R(\theta)$ is the measured reflectivity from the true surface, the ratio $R(\theta)/R_F(\theta)$ is a measure of the electron density along the surface normal; i.e.$\frac {R(\theta)} {R_F(\theta)} \approx \mid \frac {1} {p_\infty} \int \frac {\partial〈p(z)〉} {\partial z} exp (iQ_zz) dz\mid^2$ where $p_{\infty}$ is the electron density far from the surface, $\partial〈p(z)〉/\partial z$ is the gradient of the average electron density along the surface normal and $Q_z=(4\pi/\lambda) sin (\theta)$. For simple liquids $p^{–1}_\infty \partial〈p〉/\partial z \approx [1/\sqrt (2\pi \sigma^2)] exp (–z^2/2\sigma^2)$, and $R(\theta)/R_F(\theta)\approx exp (–Q^2\sigma^2)$, where $\sigma^2$ is dominated by the mean-square average of thermally excited fluctuations in the height of the surface. For liquid crystals and for lyotropic miceller systems temperature-dependent structure in $R(\theta)$ is due to surface-induced layering in $〈p(z)〉$. Other experimental results from thin layers of liquid $^4He$ and monolayers, of amphiphathic molecules on the surface of $H_2O$ will be described. The possibility of complementing specular reflectivity measurements of surface roughness by studying diffuse scattering at small angles off of the specular condition will also be illustrated with results from the $H_2O$ surface.Engineering and Applied Science

Amphiphilic Molecules and Liquid Crystals

A brief description of the essential features of amphiphillic molecules will be presented. This will be followed by a discussion of specific physical phenomena and their relation to a number of contemporary research areas. Foremost amongst these is the possible application of amphiphillic monolayers to the physics of two-dimensional systems. Specific experimental and theoretical examples will largely be drawn from studies of synthetic phosphatidylcholine (e.g., lecithin) type lipids. Recent experimental results from our laboratory will be mentioned.Engineering and Applied Science

Dislocation Effects in Smectic-A Liquid Crystals

A method for calculating stress‐strain fields around edge dislocations in smectic‐A samples is discussed. In large part the method is isomorphic with the formalism for calculating magnetic fields around lines of electric current. The force law between dislocations that follows from the analogy is equivalent to the accepted force law between dislocations in crystals. In addition to rederiving the expression for the strain field surrounding an isolated edge dislocation that was first given by de Gennes, we present the solutions for the stress‐strain fields surrounding dislocations near one or two boundaries and also the strain field surrounding an edge dislocation that is curved to form a circular loop. The stress‐strain fields surrounding other defects with the same symmetries and boundary conditions can be expressed in terms of the above‐mentioned solutions using Green's function techniques. The relative stability of dislocations in samples with different types of boundaries and also the effects of dislocations on the elastic properties of smectic samples are also discussed in some detail. We comment briefly on the relation between the analogy discussed here and an earlier one developed by de Gennes.Engineering and Applied Science

Irradiation Damage and Semiconducting Properties of CdF2:EuCdF_2:Eu

$Eu^{3+}$ in the insulating $CdF_2$ host. Optical absorption and EPR measurements of semiconducting $CdF_2:Eu$ are the bases of a model of this semiconductor.Engineering and Applied Science

Continuous Crystallization in Hexagonally-Ordered Materials

We demonstrate that the phase transition from columnar-hexagonal liquid crystal to hexagonal-crystalline solid falls into an unusual universality class, which in three-dimensional allows for both discontinuous transitions as well as continuous transitions, characterized by a single set of exponents. We show by a renormalization group calculation (to first order in $\epsilon = 4-d$) that the critical exponents of the continuous transition are precisely those of the XY model, which gives rise to a continuous evolution of elastic moduli. Although the fixed points of the present model are found to be identical to the XY model, the elastic compliance to deformations in the plane of hexagonal order, $\mu$, is nonetheless shown to critically influence the crystallization transition, with the continuous transition being driven to first order by fluctuations as the in plane response grows weaker, $\mu \to 0$.Comment: 4 pages, 2 figures (revised version

Landau Theory of the Reentrant Nematic-Smectic A Phase Transition

The reentrant, nematic to smectic A phase transition is shown to follow from the Landau theory if one assumes the existence of an optimum density for smectic ordering. The shape of the coexistence line in the P-T plane is fit exactly by this theory. The effects of concentration on reentrant behaviour are also explained.Engineering and Applied Science

Dislocation and Impurity Effects in Smectic-A Liquid Crystals

The effects of dislocations and impurities on the macroscopic elastic properties of smectic‐A liquid crystals are discussed. The first conclusion is that smectics behave like linear elastic media only so long as the stresses are smaller than some critical value that is analogous to the critical velocity of a superfluid. Below the critical stress, smectics can store elastic energy without flowing and consequently without any dissipative processes in analogy with the fact that, below a critical velocity, superfluids store kinetic energy without any dissipation. For most practical samples the critical smectic stress is that value for which pinned dislocation will grow unstable; however, for ideal samples, initially free of dislocations, the critical value is determined by the condition of unstable growth of thermally generated dislocation loops. In the linear elastic region both dislocations and impurities modify the macroscopic elastic properties such that the effective elastic constant is smaller than the value for an ideal sample. This is a sort of diaelasticity and can be discussed in the same way as diamagnetism. Impurities are shown to act as sources of stress fields analogous to the way magnetic dipoles and magnetic monopoles are sources of magnetic fields. The result is to predict long‐range elastic interactions between impurities in smectic systems. Since biological systems like chloroplasts and retinal rods have lamellarlike structures that are similar to the smectic structure, there is the possibility that long‐range elastic interactions may play some role in biological function.Engineering and Applied Science