Landau and Lifshitz [1] and Buckingham and Raab [2] have related these fields to the electric and magnetic multipole moments of the system. If A IS the wavelength of the incident ray, use the well-known result. For non-interacting molecules, the intermolecular fields arising at any molecule due to the permanent and induced multipole moments of the other molecules in the assembly are negligible.
The insight gained from the preceding discussion can now be used in the specific case of the depolarization ratio p of Raleigh-scattered light. Now that we have found the expression for the field FP(I) at molecule 1, the expression for the corresponding field gradient must be FP~I). found. However, the experimental measurement of the depolarization ratio p is performed in the space-fixed axis system oriented with.
The average projection of the molecule's tensor properties into the space-fixed axes is obtained by (i) referring the molecular property tensors to molecule-fixed axes, (ii) projecting these tensors into the space-fixed axes, and (iii) the average of the projection over the orientational motion of the molecule. Here the probability P('T) at'T is related to the intermolecular potential energyU. where .Q = I~II fd1' is the integral over the orientation coordinates of the neighboring. R is the displacement between the two molecular centers, and is initially chosen to lie along the z-axis of the space-fixed axes for convenience.
The analysis is very similar to the treatment of the linear and quasi-linear molecules. The induction energy arises from the distortion of the electronic structure of a molecule due to the permanent electrical moments on the neighboring molecule. The London dispersion energy arises from interactions of the electric moments due to fluctuations in the charge distributions of the two molecules.
The Light-scattering Apparatus
The optical system used to measure the depolarization ratio p of the light scattered by dimethyl ether. Second, the intensity of Rayleigh scattered light is inversely proportional to the fourth power of the wavelength of the incident beam. The use of stainless steel and aluminum and Teflon O-rings as seals ensured that the cell would be inert to many of the corrosive chemical gases that can be used to measure s.
A visual test to determine that the gas sample was dust-free was to increase the power of the incident beam to its full 0.8 W and observe the 90° scattered beam with a traveling microscope. The 90° scattered light emanating from the cell was passed through the analyzer prism to allow selection of the vertical or horizontal polarized component of the scattered light. Accurate measurements of these scattered signals are key to measuring the depolarization ratio p, which is typically of the order of 10-2.
The vernier scale allowed angle settings with a precision of 2' of arc. The analyzer prism was connected to the 90° exit window of the scattering cell via a light-tight tube to prevent scattered light from interfering with the scattered light signal. Clearly, successful measurement of the depolarization ratio p is dependent on accurate measurement of the intensity components of the 90° scattered light beam. Since the vertical component of the scattered light is typically a hundred times that of the horizontal component, its count rate generally falls in the nonlinear region.
The attenuation factor of the filter was precisely measured to use this value in the p measurements made in this work. An IBM-compatible PC was used to install a Thorn EMI C660 counter/timer board, effectively turning the computer into a high-performance pulse-counting instrument for recording the output of the 9128B photomultiplier when operating in photon-counting mode. Data collection and storage and analysis of the depolarization ratio p could be efficiently achieved.
For example, a computer program written by us in BASIC accesses data files containing measured count rates of the 90° scattered light, and directly calculates the depolarization ratio p and its statistical uncertainty. The density dependence of the depolarization ratio P is best described by the viral expansion, as given by equation (2.30) of Chapter 2: . Bp Cp P= Po. Our measurement of the pressure dependence of the depolarization ratio p of dimethyl ether was performed at room temperature without direct temperature control on the cell. However, our laboratory does not have windows to ensure a well-insulated environment: consider the significant temperature dependence of Bp.
The Kerr Effect
Introduction
Theory
A Kerr cell with spatially defined axes (x, y, z), where z is the direction of propagation of the light beam, x is the direction of the applied electric field, and y is perpendicular to the field. The molecular Kerr constant Km is defined as [5]. where Ex is the applied electrostatic field, V is the molar volume of the studied gas, and na and Cr are the refractive index and relative permeability of the medium in the absence of the field, respectively. Piijand Yiijj are the first and second hyperpolarizability tensors, while I.l~O) is the constant dipole moment of the molecule under study.
The relative magnitudes of the different contributions to BK from dimethyl ether calculated at T= 292.12 K and A= 632.8 nm. The experimental uncertainties of the measured data are reported to be in the range of ±10% to ±20%, and the calculated curve is found to be within the error bars of the experimental points over almost the entire temperature range. During 1999, Dr. Couling and honors student Ms. Jean McKenzie developed a device to measure the density dependence of the molar Kerr constant, as reported in [15].
Pockels glass windows are located on either side of the glass tube to contain the liquid and allow unobstructed passage of the incident beam. The output of the secondary coil was connected to the high voltage input of the Kerr cell. The signal was fed directly into a frequency doubler at 500 mV rms, the 50 mV rms output going into the current feed combined with a phase shifter to provide an AC signal to the 100 turn coil of the Faraday cell which is set to be exactly in antiphase with the Kerr signal.
To obtain results from the optical cascade, the signal from a photodiode placed at the end of the cascade was fed into a Lock-In Amplifier (LIA) Princeton Applied Research EG&G model 5210. The LIA output voltage is then proportional to the light intensity which is modulated to the desired frequency and read by an HP 3478A precision digital multimeter connected to an HP 86 microcomputer which recorded and averaged the readings. It is useful to introduce the parameterization KO' defined as [12]. where v, 1/ is the molar volume of the gas and Eoi is the amplitude of the applied electric field.
This leaves 8, the phase change, which is the quantity we wish to measure experimentally so that n,Ko can be determined. As already mentioned, the quantity we wish to measure is the induced phase difference 8, which will allow the calculation of nXo. The monochromatic light beam from the He-Ne laser passes through the polarizer with its transmission axis set at 45° to the electric field. We plan to make the Kerr cells temperature dependent during the year 2000 and hope to measure the temperature dependence of the BK.
Conclusion
We can conclude that provided molecular symmetry is fully taken into account, the dipole-induced dipole model reliably accounts for the contribution made by interacting pairs of molecules to a wide range of molecular-optical phenomena.
Appendix A
Electric Multipole Moments
Various definitions have been adopted for electric multipole moments of higher order than the dipole. This form of quadrupole moment is often used by molecular physicists because it vanishes for a spherically symmetric distribution of electric charge and is therefore intuitively appealing. However, Raab [2] cautioned against the widespread use of multipole moments without traces and emphasized the existence of electrodynamic situations where primitive definitions of multipole moments must be preserved.
Appendix B
Appendix C
Appendix D
An Example of a Fortran Program to Calculate Contributions to Bp
