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

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

Flexoelectricity in Nematic and Smectic-A Liquid Crystals

Flexoelectric effects are observed in both the nematic and smectic‐A phases of p‐butoxybenzal‐p‐($\beta$‐methylbutyl) aniline (BBMBA) and p‐cyano‐benzylidine‐p‐octyloxyaniline (CBOOA). This is the first reported observation of flexoelectricity in smectic phases. The use of a symmetric interdigital electrode in the homeotropic geometry facilitated the unambiguous separation of linear and quadratic electro‐optic effects. Both the interdigital electrodes and those liquid‐crystal deformations that are quadratic in the voltage act as optical diffraction gratings with a spacing that corresponds to the repeat distance d for adjacent electrodes. In contrast linear electro‐optic effects give rise to diffraction gratings with twice this spacing since adjacent electrodes have opposite voltages. Diffraction maxima due to the linear effects are halfway between the maxima due to the other effects. Using optical heterodyne detection, the intensity of the diffraction maxima believed to arise from the linear effect are indeed observed to be linear in the applied voltage $V (\omega)$. With homodyne detection the diffracted intensity is proportional to $V (\omega)^2$. Although previous discussions of flexoelectricity in nematics have been in terms of two flexoelectric coefficients $e_{11}$ and $e_{33}$, we present theoretical arguments that as long as $\nabla \times E=0$ there is only one true volume coefficient and that the other constant can always be included in surface effects. Our measurements of the volume coefficient $f=e_{11}+e_{33}$ are an order of magnitude larger than previously obtained values for $e_{11}$ and $e_{33}$. Measured values of f are also nearly independent of temperature, in contrast to previous theoretical models, and of similar magnitude in the smectic and nematic phases. Measurements of flexoelectric signals versus the frequency of the driving voltage obtain relaxation times for splaylike nematic fluctuations and undulation‐type smectic fluctuations.Engineering and Applied Science

X-ray study of the liquid potassium surface: structure and capillary wave excitations

We present x-ray reflectivity and diffuse scattering measurements from the liquid surface of pure potassium. They strongly suggest the existence of atomic layering at the free surface of a pure liquid metal with low surface tension. Prior to this study, layering was observed only for metals like Ga, In and Hg, the surface tensions of which are 5-7 fold higher than that of potassium, and hence closer to inducing an ideal "hard wall" boundary condition. The experimental result requires quantitative analysis of the contribution to the surface scattering from thermally excited capillary waves. Our measurements confirm the predicted form for the differential cross section for diffuse scattering, $d\sigma /d\Omega \sim 1/q_{xy}^{2-\eta}$ where $\eta = k_BT q_z^2/2\pi \gamma$, over a range of $\eta$ and $q_{xy}$ that is larger than any previous measurement. The partial measure of the surface structure factor that we obtained agrees with computer simulations and theoretical predictions.Comment: 7 pages, 7 figures; published in Phys. Rev.

Raman Line Shapes in Liquid CH3ICH_3I and CD3ICD_3I

The six fundamental bands of $CH_3I$ and $CD_3I$, both as pure liquids and in solution with $CS_2$, have been studied in order to obtain information about the molecular rotational and vibrational dynamics. Emphasis was placed on the features of the spectra that can be interpreted independent of a particular model. An examination for Boltzmann asymmetry in the $A_1$ and E bands indicates that the former, being symmetric, are amenable to classical description, while the latter, being asymmetric, definitely require quantum mechanical interpretations. With respect to the validity of the assumption that rotation‐vibration coupling can be ignored, we give evidence of substantial coupling effects in a nondegenerate $A_1$ mode $(\nu1)$ as well as in the doubly degenerate E modes. We emphasize that, in attempting to obtain dynamical information, several bands of any given liquid must be studied and compared in order to decide which can be used with confidence in a detailed analysis. The consistency of the rotational diffusion model for describing the tumbling motion of the methyl iodide molecules has been confirmed.Engineering and Applied Science