The refractive index of colorless liquids in the visible and infrared: Contributions from the absorption of infrared and ultraviolet radiation and the electronic molar polarizability below 20 500 cm−1

Abstract

This paper addresses the separation of the contributions to the visible refractive index of colorless liquids from electronic ͑ultraviolet͒ and vibrational ͑infrared͒ absorption. The goal is to find the most accurate infrared values of n el (), the refractive index that results solely from electronic absorption, by fitting and extrapolating currently available visible refractive index data. These values are needed, interalia, to improve the accuracy of infrared real refractive index spectra calculated by the Kramers-Kronig transform of infrared imaginary refractive-index spectra. The electronic molar polarizability ␣ el () is calculated from the values of n el () at wave numbers between 20 500 and 0 cm Ϫ1 . The methods are applied to ten liquids: H 2 O, D 2 O, CH 3 OH, CH 3 COOH, CH 3 CN ͑CH 3 ͒ 2 CO, CH 2 Cl 2 , C 6 H 6 , C 6 H 5 Cl, and C 6 H 5 CH 3 . The visible refractive indices are expressed as power series in wave number, by expansion of the Kramers-Kronig integral. Terms in ϩ2m , mϭ1,2, are due to the electronic contribution and terms in Ϫ2m are due to the vibrational contribution. The vibrational contribution to the visible refractive index is also calculated from experiment by Kramers-Kronig transformation of the known infrared imaginary refractive index spectrum of the liquid. It is shown that the vibrational absorption contributes у0.001 to the visible refractive index only for the four hydrogen-bonded liquids, and that, for all ten liquids, at least 25% of the vibrational contribution arises from absorption below 2000 cm Ϫ1 . If the vibrational intensities are not known, the available visible refractive indices yield the most accurate infrared values of n el for all liquids except H 2 O if they are fitted to the equation nϭa 0 ϩa 2 2 ϩa 4 4 . A similar equation, with the additional term a 2 Ϫ2 , is theoretically superior because the latter term adequately describes the vibrational contribution to the visible refractive indices, but only for H 2 O are the currently available visible refractive indices sufficiently accurate and sufficiently extensive to allow the four coefficients in the equation to be determined with useful accuracy. For H 2 O, D 2 O, CH 3 OH, CH 2 Cl 2 , C 6 H 6 , C 6 H 5 Cl, and C 6 H 5 CH 3 , corrections are given to slightly improve the accuracy of the previously published infrared real refractive-index spectra.

Organic aerosol and global climate modelling: a review

“…7 by solid circles. The temperature dependence of the refractive index in this wavelength range is reported to be in the order of dn/dT=−5×10 −4 K for all the investigated pure organic components (Bertie and Lan, 1995;El-Kashef, 1998;Li et al, 1994). Various other studies of the refractive index, n(λ), of organic liquids report values at one single wavelength, 590 nm, and some of them are relevant to atmospheric conditions (Aminabhavi et al, 1996;Cases et al, 2001;De Lorenzi et al, 1997;Gomez-Diaz et al, 2001;Ritzoulis and Fidantsi, 2000;Segade et al, 2003).…”

“…Consequently, the effect of the individual organic compounds in the aerosols on the incoming solar radiation is characterized by a large uncertainty. Whereas data on the complex index of refraction of mixtures of organic components relevant to atmospheric aerosols is sparse, there are several studies of pure organic liquids and their absorption index and/or refractive index in the short wavelength region at a single selected wavelength or in a wider region (Bertie and Lan, 1995;El-Kashef, 1998;Jacobson, 1999;Li et al, 1994;Marsh, 1987;Räty et al, 1999). Figures 7a, b summarize the absorption and refractive indices, respectively, of organic components relevant to the troposphere.…”

“…Figures 7a, b summarize the absorption and refractive indices, respectively, of organic components relevant to the troposphere. These figures include the optical constants of some pure organic liquid components (Bertie and Lan, 1995;El-Kashef, 1998;Jacobson, 1999;Li et al, 1994;Marsh, 1987;Räty et al, 1999), the absorption and refractive index of lignin dissolved in water (Räty et al, 1999), and selected optical constants of aqueous organic acids present in tropospheric aerosols, and fog samples (Myhre and Nielsen, 2003;Myhre and Nielsen, 2004). Finally, a typical literature value of soot (Liu et al, 2002) is indicated by solid star in this figure to show the optical constants of an aerosol component, which is known to strongly absorp in the atmosphere.…”

“…Li et al (1994) have measured the refractive index of liquid n-hexane and toluene at 632.8 nm at 7 temperatures ranging from 15-45 • C. Their results for toluene are in excellent agreement with those of Marsh (1987) and their value for n-hexane is shown in the figure by an open start. Bertie and Lan (1995) calculated the refractive index of pure acetic acid, methanol, acetone, dichloromethane, benzene, chlorobenzene and methylbenzene in the UV-Visible region by extending the KramersKronig transformation of absorption indices obtained in the infrared region. The results are presented in Fig.…”

Highly sensitive and simple method for refractive index sensing of liquids in microstructured optical fibers using four-wave mixing

“…(1). The refractive index data for water are therefore obtained from the expression found in [20] using some additional terms:…”