Raman differential

Hug and Surbeck 35) have proposed the use of Ada. = daL — daR, the difference of the Raman differential scattering cross sections in left and right circularly polarized incident light. This is the Raman equivalent of the circular dichroism Ae = el — eR, where s is the decadic molar extinction coefficient and, unlike the measured (but not the theoretical) IR — IL which depends on both sample and instrumental factors, is solely a molecular parameter. They introduced a chirality number q defined by... 

Thus, the respective absolute trace and anisotropy Raman differential cross sections are functions of a single polarizability invariant derivative only... 

Direct determination of absolute Raman differential cross sections is quite difficult and tedious work often leading to incorrect results. It is easier to measure cross sections relative to some standard. The absolute differential Raman scattering cross sections of the sample can then be straightforwardly obtained. 

The more conventional, energy domain fonnula for resonance Raman scattering is the expression by Kramers-Heisenberg-Dirac (KHD). The differential cross section for Raman scattering into a solid angle dD can be written in the fomi... 

Measurement of the total Raman cross-section is an experimental challenge. More connnon are reports of the differential Raman cross-section, doj /dQ, which is proportional to the intensity of the scattered radiation that falls within the element of solid angle dQ when viewing along a direction that is to be specified [H]. Its value depends on the design of the Raman scattering experiment. 

Flere we examine the viewing angle dependence of the differential Raman cross-section for the cases of... 

State or vibrational energies. If the current across the metal-insulator-metal sandwich is recorded as a function of applied voltage, the current increases as the threshold for each state or vibrational mode is crossed. The increases in current are in fact very small, and for improved detectability the current is double-differentiated with respect to voltage, thereby providing, in effect, a vibrational spectrum that can be compared directly with free-molecule IR and Raman spectra. 

The Raman measurements provide values directly for P)mn, the coefficients of the Legendre expansion related to coordinates axes chosen with respect to the principal axes of the differential polarizability tensor, hence the superscript r. The coefficients Pimn for the orientation of the units of structure must then be obtained by further calculation from the P)mn. 

It can readily be appreciated that in the absence of any knowledge regarding the differential polarizability tensor, it is a difficult exercise to obtain precise information from the Raman measurements. However, if r is known, Equations (19) are six linear simultaneous Equations in the six quantities (ot2I0N0) 1, P)0o> P220) PIoo> P420 and... 

Surface-enhanced Raman scattering (SERS) and differential capacitance methods have been used to study the interfacial solvent structure and... 

Radio tracer studies, and adsorption of perchlorate ions on copper, 94 Raman s scattering, and differential capacitance, 80... 

About one decade ago Bass et al. [13,14] proposed first that such approach could help in exploring the structure of water dissolved silicates. Following this initiative, recently we critically evaluated how the published FTIR and Raman assignments could be adopted for differentiating between the molecular structures of some commercially available sodium silicate solutions [7-9,15], In this paper we present comparative structural studies on aqueous lithium and potassium silicate solutions as well. According to some NMR studies, the nature of A+ alkaline ion and the A+/Si ratio barely affects the structural composition of dissolved silicate molecules [5], In contrast, various empirical observations like the tendency of K-silicate solutions to be less tacky and more viscous than their Na-silicate counterparts, the low solubility of silica films obtained from Li-silicate solutions compared to those made from other alkaline silicate solutions, or the dependence of some zeolite structures on the nature of A+ ions in the synthesis mixture hint on likely structural differences [16,17]. It will be shown that vibrational spectroscopy can indeed detect such differences. 

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