Abstract:The dynamics of the layer-displacement fluctuations in smectic membranes have been studied by x-ray photon correlation spectroscopy (XPCS). We report transitions from an oscillatory damping regime to simple exponential decay of the fluctuations, both as a function of membrane thickness and upon changing from specular to off-specular scattering. This behavior is in agreement with recent theories. Employing avalanche photodiode detectors and the uniform filling mode of the synchrotron storage ring, the fast limi… Show more
“…Pronounced viscoelastic behavior may affect the dispersion relations of capillary waves, and behavior of this kind has been studied with XPCS in a variety of systems ranging from viscous free surfaces to thin polymer films and liquidcrystalline membranes [12]- [17].…”
Section: Inelastic Measurements In the Time Domain: Capillary Wavesmentioning
“…Pronounced viscoelastic behavior may affect the dispersion relations of capillary waves, and behavior of this kind has been studied with XPCS in a variety of systems ranging from viscous free surfaces to thin polymer films and liquidcrystalline membranes [12]- [17].…”
Section: Inelastic Measurements In the Time Domain: Capillary Wavesmentioning
“…The thickness can vary from two layers (about 5 nm) up to thousands of layers (tens of m) for surface areas as large as several cm 2 . X-ray photon correlation spectroscopy (XPCS) -the x-ray implementation of classical dynamic light scattering [4] -has been used to probe the fluctuation dynamics in smectic membranes [5][6][7]. In addition to simple exponential relaxation of surfacedominated overdamped fluctuations, oscillatory relaxation of the fluctuations due to inertial effects has also been observed.…”
Section: Surface and Bulk Elasticity Determined Fluctuation Regimes Imentioning
“…[1][2][3][4][5][6][7][8][9][10][11] At third-generation synchrotrons it is nowadays possible to produce intense x-ray beam with a high degree of coherence. The scattered intensity distribution of such an x-ray beam coming from a rough surface provides a speckle pattern due to destructive and constructive interference.…”
We present a rigorous description of the effects of partial coherence and detector resolution on intensity autocorrelation functions as they can be measured by x-ray photon correlation spectroscopy ͑XPCS͒. Based on the Huygens-Fresnel propagation law and on the first Born approximation, we derive a general expression for the normalized intensity autocorrelation function. We calculate how the mutual coherence function of the x-ray beam propagates from an aperture to the sample and how it propagates after the scattering process to the detector area and consequently influences the intensity autocorrelation function. We illustrate our calculation with examples of XPCS intensity autocorrelation functions of liquid surfaces calculated for grazing incidence geometry.
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