Quadratic Concentration Dependence Research Articles

Raman Spectral Studies of Intermolecular Coupling in Aqueous Selenious Acid Solutions

Polarized argon-ion laser and unpolarized mercury-excited photoelectric Raman spectra, and infrared spectra, were obtained for aqueous selenious acid solutions ranging in concentration from ∼1–13M at 25°C. Relative integrated Raman contour intensities, and Raman and infrared contour frequencies were obtained. Relative integrated Raman—Gaussian-component intensities, and Raman and infrared Gaussian-component frequencies were also obtained by means of a special-purpose analog computer. Relative integrated Raman contour intensities obtained with unpolarized excitation were found to fit an equation of the form I=aM2+bM for valence and deformation contours where I is the intensity, and M the stoichiometric H2SeO3 molarity. Relative integrated Raman intensities of Gaussian valence components from unpolarized spectra were also found to show the quadratic concentration dependence. Frequencies from polarized and unpolarized valence contours, as well as frequencies of Gaussian valence components from unpolarized Raman spectra, also indicated quadratic concentration dependences. Frequency differences between polarized and unpolarized valence contours, and between Gaussian valence components from unpolarized Raman spectra indicated quadratic concentration dependences as well. The quadratic intensity dependences were described by the term coupling intensification, because the molar intensities were found to increase in general with M, i.e., I/M=aM+b. The quadratic frequency dependences were described by the term coupling frequency shifting. The quadratic frequency differences constitute a splitting and they were termed coupling splitting. The use of the term coupling refers to intermolecular in-phase and out-of-phase coupling between H2SeO3 vibrations. The predominant coupling mechanism was found to involve hydrogen bonding through water between the coupled H2SeO3 molecules, as evidenced by the persistence of the characteristic out-of-phase coupled component at all concentrations.