Linear susceptibility, determination

An important aspect of reliable susceptibility measurements is the calibration of the magnetometers with respect to field and temperature a number of high-purity compounds exist to calibrate (1) the applied field via measurement of the susceptibility (palladium metal, HgCo(NCS)4), (2) the temperature linearity via determination of the Curie constant of (NH4)2Mn(S04)2-6H20, or (3) the absolute values of the sample temperature that are especially important for low-temperature measurements and for which the critical temperatures of pure-element low-7 c superconductors can be used, for example, lead (7.20 K) or indium (3.41 K).11... 

The frequency dependence of the linear susceptibility (4.102) is determined by a superposition of the Debye relaxation modes as... 

From the results of MD simulations, the non-linear susceptibility, Xs p. can be calculated for each interfacial species of water molecule as a function of distance along the simulation cell (see Figure 2.13) to determine how each species contributes to the SF signal and to the depdi that SF intensity is generated. Although this representation is only a first approximation of the SF probe depth, it is the most relevant measure of interfacial thickness for SF experiments because it indicates the depth to which water molecules are affected by the presence of the interface. To make a direct comparison to experiment, the contribution from each OH oscillator to the total xisp is multiplied by a factor, linear in frequency, that accounts for the IR vibrational response dependency on frequency. For example, an OH vibration at 3400 cm is approximately 12 times stronger in SF intensity than the free OH. 

In this section, we investigate the relations between the macroscopic susceptibilities and the molecular polarizabilities. Consistent microscopic interpretations of many of the non-linear susceptibilities introduced in Section 2 will be given. Molar polarizabilities will be defined in analogy to the partial molar quantities (PMQ) known from chemical thermodynamics of multicomponent systems. The molar polarizabilities can be used as a consistent and general concept to describe virtually all linear and non-linear optical experiments on molecular media. First, these quantities will be explicitly derived for a number of NLO susceptibilities. Physical effects arising from will then be discussed very briefly, followed by a survey of experimental methods to determine second-order polarizabilities. 

The general microscopic expression for the nth-order susceptibility contains n + 1 dipole moment matrix elements, involving n intermediate states. For the linear susceptibility there is only one intermediate state, and if the latter is a hybrid one, the corresponding dipole matrix elements are determined mainly by the Frenkel component of the hybrid state. Thus, the linear susceptibility of the hybrid structure contains the factor (dp/ap)2, as is seen from eqn (13.77). For the second-order nonlinear susceptibility x one must have two intermediate states or three virtual transitions. One of them may be a hybrid one, and as long... 

The poled polymer acts as a uniaxial medium with the optical axis along the poling axis. The complex linear susceptibility x P determines the refractive index n as well as the absorption coefficient a of the material as can be seen from the following equations ... 

As with the evaluation of the linear susceptibility, one can determine the properties of the nonlinear susceptibility tensor from Eqs. 2 and 3. In regions of low dispersion the x ifk tensor exhibits special symmetry properties that are referred to as Kleinman... 

The zero-field and field-induced optical second harmonic generation (SHG) was investigated for the nematic and smectic A phases of various liquid crystals. The components of the cubic non-linear susceptibility tensor were measured for substances with different molecular structure. The phase-matched SHG was observed for all the compounds investigated. The directions of the phase synchronisms as well as the corresponding non-linear susceptibilities were determined for the ee-o and oe-o interactions. The zero-field phase-matched SHG was observed for the oe-o interaction. It was accounted for by a multipolar mechanism. 

Ishikawa etal. proposed an approach for the determination of the ligand-field (LF) parameters of a set of isostructural lanthanide complexes. This method consists of a simultaneous fit of the temperature dependence of magnetic susceptibilities and NMR spectra for the whole isostructural series [18]. In order to avoid over-parametrization a key restriction is imposed each parameter is expressed as a linear function of the number of f electrons, n ... 

Static charge-density susceptibilities have been computed ab initio by Li et al (38). The frequency-dependent susceptibility x(r, r cd) can be calculated within density functional theory, using methods developed by Ando (39 Zang-will and Soven (40 Gross and Kohn (4I and van Gisbergen, Snijders, and Baerends (42). In ab initio work, x(r, r co) can be determined by use of time-dependent perturbation techniques, pseudo-state methods (43-49), quantum Monte Carlo calculations (50-52), or by explicit construction of the linear response function in coupled cluster theory (53). Then the imaginary-frequency susceptibility can be obtained by analytic continuation from the susceptibility at real frequencies, or by a direct replacement co ico, where possible (for example, in pseudo-state expressions). 

Salt Transport. The effects of ozone on membrane permeability can also be assessed by estimating salt leakage from treated tissue. In one study, susceptible bean plants were allowed to take up RbCl for 24 hr prior to ozone exposure. After exposure, leaf discs were placed in a desorption solution containing 0.5 M CaSOi and 2 mM KCl and the rate of Rb leakage into the desorption solution was determined. The initial loss was indistinguishable between treated and untreated plants and we assume that it represented exchange from free space. Then, for an extended period, treated tissue exhibited a linear loss of... 

Structural Effects and Solvent. The effect of solvent on the equilibrium of Reaction 4 can be first discussed in terms of effects on the susceptibility to substituent effects. The values of pK2, characterizing this equilibrium, are a satisfactorily linear function of the Hammett constants correlation coefficient r (Table VI). The values of reaction constant p are practically independent of the ethanol concentration (Table VI), as was already indicated by the almost constant value of the difference (A) between pK2(H20) and p 2 (mixed solvent) for a given composition of the mixed solvent (Table I). The same situation is indicated for DMSO mixtures (Table II) by the small variations in A for any given solvent composition. In this case, the number of accessible p 2 values was too small to allow a meaningful determination of reaction constants p. The structural dependence for various water-ethanol mixtures is thus represented by a set of parallel lines. The shifts between these lines are given by the differences between the pK2H values (p 2 of Reaction 4 for the unsubstituted benzaldehyde) in the different solvent mixtures. 

When the data in Fig. 3.2 are fit to Eq. (3.10), the results yield A = 0 and f (y) = sin 3 y/ for I (11, ) [67, 68]. Using p-polarized input and output, the data fits to A/B = 1 and f y/) = cos 3 // for I (11, 11). With appropriate choices of the input and output polarizations and separate SH phase measurements, combinations of the four independent surface susceptibility elements and the bulk susceptibilities y and C contributing to A and B for this system were also determined. There is inherent difficulty in separating the bulk surface susceptibilities such that the bulk susceptibility y is always measured in a linear combination with a surface susceptibility element for any experimental geometry [82-84]. 

Although the rotational anisotropy scans are informative, considerably more information can be obtained by separate determination of changes in the isotropic and anisotropic components of the surface susceptibility tensor as done by Koos et al. [122]. The experiments consist of monitoring the SH intensity at a fixed angle of 0 = 30° where / oc a 2 and Tj a b0) 2. The results shown in Fig. 5.16 are displayed in terms of thallium coverage. The data has been fitted to a simple linear Langmuir isotherm model of Heinz [79] where the adsorbate contribution to x(2) varies linearly with coverage such that... 

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