Extended capillary wave theory and the ellipsometric coefficient

1998 ◽  
Vol 109 (12) ◽  
pp. 5002-5007 ◽  
Author(s):  
J. Stecki
Keyword(s):  
1982 ◽  
Vol 60 (2) ◽  
pp. 137-153 ◽  
Author(s):  
Luis de Sobrino ◽  
Jože Peternelj

We use van Kampen's expression for the partition function of a van der Waals gas to investigate the effect of noncritical fluctuations on the interface of an inhomogeneous fluid. Such a procedure combines in a consistent manner the results of mean field theory and of capillary wave theory and, in addition, uncovers contributions due to fluctuations of the interface profile. Although the latter add negligibly to the interfacial width, they result in corrections to the mean field surface tension comparable to those resulting from capillary fluctuations. The effect of the walls in limiting the fluctuations is explicitly taken into account.


1989 ◽  
Vol 177 ◽  
Author(s):  
M. L. Schlossman ◽  
D. K. Schwartz ◽  
E. H. Kawamoto ◽  
G. J. Kellogg ◽  
P. S. Pershan ◽  
...  

ABSTRACTX-ray specular reflectivity is used to study the liquid-vapor interface of pure water and of fatty acid and polymer monolayers at that interface. For the pure water surface the reflectivity was measured for three different spectrometer resolutions and simultaneous fits with only one free parameter to all of the data are in excellent agreement with the prediction of capillary wave theory for the RMS surface roughness. Diffuse scattering away from the specular condition, at wavevectors corresponding to those of the capillary waves, yields intensities and line shapes in agreement with theory with no significant adjustable parameters. Reflectivity from separate monolayers of co-poly 1,2-butadiene/butyl alcohol (50% random substitution) and lignoceric acid (CH3(CH2)22COOH) at the water/vapor interface are interpreted to obtain profiles of the average electron density ρ(z) as a function of distance z along the surface normal. For the polymer monolayer we find the following: 1) a local maximum in the electron density approximately 10% larger than that of the bulk polymer and 2) the RMS roughness of the vapor/polymer interface agrees with capillary wave theory predictions for the lower surface pressures. For the highest surface pressure the RMS roughness exceeds the value predicted by the capillary wave model. Measurements of reflectivity from a lignoceric acid monolayer, as a function of surface pressure throughout an isotherm (near room temperature), reveal the following behavior: 1) the overall thickness of the monolayer increases with increasing pressure and 2) the head groups occupy a progressively larger region along the surface normal as the pressure increases, indicating that they rearrange normal to the interface.


1986 ◽  
Vol 33 (1) ◽  
pp. 614-616 ◽  
Author(s):  
J. R. Henderson

1999 ◽  
Vol 590 ◽  
Author(s):  
Mark L. Schlossman ◽  
Ming Li ◽  
Dragoslav M. Mitrinovic ◽  
Aleksey M. Tikhonov

ABSTRACTWe present our recent progress in using synchrotron x-ray surface scattering techniques to study several different aspects of ordering at liquid-liquid interfaces. (1) We present measurements of the interfacial width at the water-alkane interface for a series of different chain length alkanes. The width for the shortest chain length studied is in agreement with capillary wave theory. However, significant deviations occur for longer chain lengths, indicating the presence of molecular ordering at the interface. (2) Under appropriate conditions, a surfactant monolayer forms at the interface between water and a hexane solution of a fluorinated surfactant. Reflectivity measurements that probe the electron density profile normal to the interface provide information about the surfactant ordering. This monolayer undergoes a solid to gas transition as a function of temperature. Diffuse scattering near the transition reveals the presence of islands. (3) Equilibrium interfaces between two aqueous phases containing PEG (polyethylene glycol) and potassium phosphate salts can be studied. We present studies of coherent capillary wave fluctuations between two interfaces of a thin film of this biphase system. We also demonstrate that biological macromolecules can be trapped and studied at this aqueous-aqueous interface.


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