Log-log plot of the time-domain OKE signal decay for NMA. All signals have been normalized to the signal peak at zero delay. The inset details the decay at on a log-linear scale, showing that after it follows a simple exponential decay (dashed line).
High-resolution OKE data for NMA at shown up to on a log-log plot and (inset) up to on a linear plot. The fit is mostly indistinguishable from the data. The (fitted) -autocorrelation function is shown in both plots as a dashed curve. The fit parameters are given in Table I.
Temperature-dependent OKE data for NMA and the fits (dashed lines) as described in the text. All traces except that at are vertically offset. The temperatures and relaxation-mode parameters are given in Table II.
Fit to the data for NMA shown in the frequency domain. The three relaxation modes are shown as heavy lines accompanied by the librational modes, which all peak above . The shaded area shows the difference in the Cole–Cole function due to the modification to include the rise time and the termination. The inset compares the three fitted relaxation modes to the data in the time domain.
Parameters for the fits shown in Fig. 3. and refer to the amplitude and Cole–Cole exponent for the intermediate relaxation, and is the amplitude of the Debye relaxation.
The temperature dependence of the time constants for the relaxation, , and the intermediate relaxation, . The data for are fitted by an Arrhenius dependency [Eq. (15)], while a line of the same activation energy is drawn through the data for .
OKE signal for water and the fit of the sum of a Cole–Cole function and five Brownian oscillators (solid and dashed lines, where the dashed refers to the fit that includes the termination). The inset is the frequency-domain representation including the fit (dashed) that includes the termination. The fit has also been decomposed to show the -relaxation mode and the first two Brownian oscillators and . The shaded part shows the modification to the Cole–Cole function by the inertial rise and termination. The fit parameters are given in Table III.
The result of the modifications to the Cole–Cole function [Eq. (4)] by the rise function [Eq. (A1)] and the termination. The extent of the shaded areas represents the unmodified functions with the Cole–Cole exponents of 1, 0.8, and 0.5. The frequency scale is normalized to . The solid lines are the modified functions for and .
Parameters returned by the fit to the data for NMA shown in Fig. 2 for the modes fitted by nine Brownian oscillators [Eq. (11)]. Values obtained from Raman spectra of crystalline NMA at in Ref. 39 are given for comparison.
Parameters for the fits shown in Fig. 3, , and refer to the intermediate Cole–Cole relaxation; and the Debye relaxation. The fast relaxation was held fixed with and , and the inertial rise was fixed at . The librational modes cannot be fitted quantitatively.
Parameters for the fit to water shown in Fig. 7. is the relaxation mode modeled as a Cole–Cole function and are the Brownian oscillators [Eq. (11)] representing the librational modes. The fitted rise time parameter . The parameters with a prime superscript refer to the alternative fit where the termination is included. is close to the upper limit of the spectrum, and the parameters for the librational modes are approximate.
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