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Accurate Measurements of Dielectric and Optical Functions of Liquid Water and Liquid Benzene in the VUV Region (1–100 eV) Using Small-Angle Inelastic X-Ray Scattering Hisashi Hayashi, and Nozomu Hiraoka J. Phys. Chem. B, Just Accepted Manuscript • Publication Date (Web): 02 Apr 2015 Downloaded from http://pubs.acs.org on April 3, 2015
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The Journal of Physical Chemistry
Accurate Measurements of Dielectric and Optical Functions of Liquid Water and Liquid Benzene in the VUV Region (1−100 eV) Using Small-Angle Inelastic X-Ray Scattering Hisashi Hayashi*,‡and Nozomu Hiraoka† ‡
Department of Chemical and Biological Sciences, Faculty of Science, Japan Women’s
University, 2-8-1 Mejirodai, Bunkyo, Tokyo 112-8681, Japan †
National Synchrotron Radiation Research Center, Hsinchu 30076, Taiwan
Keywords: optical oscillator strength distribution, energy-loss function, complex dielectric function, static structure factor, phase effects, plasmon excitation
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ABSTRACT: Using a third-generation synchrotron source (the BL12XU beam line at SPring-8), inelastic X-ray scattering (IXS) spectra of liquid water and liquid benzene were measured at energy losses of 1 to 100 eV with 0.24 eV resolution for small momentum transfers (q) of 0.23 and 0.32 a.u. with ±0.06 a.u. uncertainty for q. For both liquids, the IXS profiles at these values of q converged well after we corrected for multiple scattering, and these results confirmed the dipole approximation for q ≤ ~0.3 a.u. Several dielectric and optical functions [including the optical oscillator strength distribution (OOS), the optical energy-loss function (OLF), the complex dielectric function, the complex index of refraction, and the reflectance] in the vacuum ultraviolet region were derived and tabulated from these small-angle (small q) IXS spectra. These new data were compared with previously obtained results, and this comparison demonstrated the strong reproducibility and accuracy of IXS spectroscopy. For both water and benzene, there was a notable similarity between the OOSs of the liquids and amorphous solids, and there was no evidence of plasmon excitation in the OLF. The static structure factor [S(q)] for q ≤ ~0.3 a.u. was also deduced and suggests that molecular models that include electron correlation effects can serve as a good approximation for the liquid S(q) values over the full range of q.
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The Journal of Physical Chemistry
INTRODUCTION
Electronic excitation in molecular liquids by photons, electrons, or a combination of these particles is of fundamental importance in a variety of scientific fields, including radiation physics,1−12 radiation chemistry,5,12,13 and radiation biology.12,14 Such excitation affects the dielectric and optical properties of liquids (usually many-electron systems) and characterizes their electronic responses to incident radiation. The quantity that determines these properties is the dynamic structure factor [, ]:11,15,16
, = ∑ , ∑ exp ∙ × − − .
(1)
Here, the photon energy E and momentum q are transferred to the irradiated system, where the coordinate of the j-th electron in the system is rj. Then, the system of initial states | with energy and the corresponding probability pi is excited into its respective final states | with energy , which are allowed by the law of energy conservation: − = . For isotropic systems, such as liquids and gases, , is spherically averaged [!, = 〈, 〉$ ] and depends only on the magnitude of q (i.e., ! = ||). The q value is approximately given by ! = 4π ∙ sinθ/λ, where 2θ and λ are the scattering angle and photon wavelength, respectively. Hereafter, equations will be expressed in atomic units (a.u.) [i.e., we equate ℏ (the reduced Planck’s constant), me (the electron rest mass), and e (the elementary charge) with unity]; consequently, one atomic unit in E and q corresponds to 27.213 eV and (1/0.5292) Å-1, respectively. In atomic and molecular science, it is more common to use a quantity slightly different /0,1 1,11,15 ], /1
from !, , that is, the generalized oscillator strength distribution [
which is easily
related to !, by11,15,17
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/0,1 /1
Further,
/0,1 /1
1
=
02
!, .
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(2)
can be normalized to the number of electrons in the system (N) using the Bethe
sum rule for all values of q:1,11,15,17 3
/0,1 /1
4 = 5.
(3)
This equation transforms the scale of experimental
/0,1 /1
data into absolute values.
The imaginary part of the inverse dielectric response function (called the energy-loss function) is also directly related to !, and is given by11,15,17−19 Im 8
9:
2 ?@ 02
!, ,
(4)
where ne is the average electron density of the system. Because the complex dielectric function [ε!, = ε: !, + C !, ] depends on several optical functions of the system (as shown later in this paper), the dielectric and optical behaviors of molecular liquids are therefore dominated by their !, . Furthermore, ε!, describes the response of matter to the passage of an incident charged particle.7,8,18,20,21 Consequently, in investigations of the physical and prechemical stages of radiation interactions and energy transport in molecular liquids, these interrelated functions [i.e., !, ,
/0,1 /1
9:
, ε!, , and Im 8;0,1
