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

 Title: Structure of Surfaces and Interfaces as Studied Using Synchrotron Radiation. Liquid Surfaces Author: Pershan, Peter S. Citation: Pershan, Peter S. 1990. Structure of surfaces and interfaces as studied using synchrotron radiation. Liquid surfaces. Faraday Discussions of the Chemical Society 89:231-245. Full Text & Related Files: Pershan_Structure_1990.pdf (1.134Mb; PDF) Abstract: 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. Published Version: doi:10.1039/dc9908900231 Terms of Use: This article is made available under the terms and conditions applicable to Other Posted Material, as set forth at http://nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of-use#LAA Citable link to this page: http://nrs.harvard.edu/urn-3:HUL.InstRepos:10357350 Downloads of this work: