Inversion three-parameter fitting

Natural abundance 13c spectra were obtained using quadrature detection modified Bruker HX-270 and HFX-90 spectrometers operating at 67.9 and 22.6 MHz, respectively. Free induction decays were accumulated using 4K/4K data points and a 3kHz spectral window. A fast inversion recovery (FIRFT) pulse sequence (21) was employed to measure T] s T] s were calculated using a nonlinear three parameter fitting procedure(22). 

To test equation 7 one needs to know F either from experiment or from theory. If we use experiment there will be a two-parameter fit rather than a three-parameter fit as in the VF equation. There is a general consensus diat the specific heat above the glass transition, Cp, ., varies approximately inversely with temperature (43). We therefore use as an approximation to the experimental situation the form... 

One consequence of this situation is that the FFC relaxation curves cannot be analyzed assuming any fixed starting or ending value. For example, under the mono-exponential hypothesis, the relaxation rate R (inverse of the relaxation time) must be estimated by fitting the three-parameter formula... 

Spin-lattice relaxation times were measured by the fast inversion-recovery method (24) with subsequent data analysis by a non-linear three parameter least squares fitting routine. (25) Nuclear Overhauser enhancement factors were measured using a gated decoupling technique with the period between the end of the data acquisition and the next 90° pulse equal to eibout four times the value. Most of the data used a delay of eibout ten times the Ti value. (26)... 

A three-parameter non-linear procedure for fitting inversion recovery measurements for spin-lattice relaxation times," J. Magn. Resonance 26, 533-536 (1977). 

Because the inverse Debye length is calculated from the ionic surfactant concentration of the continuous phase, the only unknown parameter is the surface potential i/io this can be obtained from a fit of these expressions to the experimental data. The theoretical values of FeQx) are shown by the continuous curves in Eig. 2.5, for the three surfactant concentrations. The agreement between theory and experiment is spectacular, and as expected, the surface potential increases with the bulk surfactant concentration as a result of the adsorption equilibrium. Consequently, a higher surfactant concentration induces a larger repulsion, but is also characterized by a shorter range due to the decrease of the Debye screening length. 

Similar to the PDF model, and in contrast to some of the more complex nonUnear models, all three models (monoexponential, logistic, and kinematic) for isovolumic relaxation characterization can generate parameters by fitting the pressures, the equivalent of solving the inverse problem. The clear advantage of invertible (i.e., linear) models is their ability to provide unique quantitative parameters. 

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