Bloembergen-Purcell-Pound expression

Rb and 1H SLR rate as a function of temperature is a very important parameter which shows the suppression of phase transition and reveals the frustration in the mixed system. Temperature dependence of Ti in any ordered system can be described by the well known Bloembergen-Purcell-Pound (BPP) type expression. However, disordered systems show deviations from BPP behaviour, showing a broad distribution of relaxation times. The magnetization recovery shows a stretched exponential recovery of magnetization following M(t)=Mo(1 — 2 exp (— r/Ti) ) where a is the stretched exponent. 

Here, K% is a constant related to the NMR coupling constant,. S 2 is the spectral density associated with the second-rank orientational correlation function g2(f). If g2(f) is an exponential function, such as in rotational diffusion, Eq. (16) reduces to the famous Bloembergen-Purcell-Pound (BPP) expression for the spin-lattice relaxation rate [81,82]. 

This was first formulated by Bloembergen, Purcell and Pound [13] and is commonly known as the BPP expression. 

The conventional, and very convenient, index to describe the random motion associated with thermal processes is the correlation time, r. This index measures the time scale over which noticeable motion occurs. In the limit of fast motion, i.e., short correlation times, such as occur in normal motionally averaged liquids, the well known theory of Bloembergen, Purcell and Pound (BPP) allows calculation of the correlation time when a minimum is observed in a plot of relaxation time (inverse) temperature. However, the motions relevant to the region of a glass-to-rubber transition are definitely not of the fast or motionally averaged variety, so that BPP-type theories are not applicable. Recently, Lee and Tang developed an analytical theory for the slow orientational dynamic behavior of anisotropic ESR hyperfine and fine-structure centers. The theory holds for slow correlation times and is therefore applicable to the onset of polymer chain motions. Lee s theory was generalized to enable calculation of slow motion orientational correlation times from resolved NMR quadrupole spectra, as reported by Lee and Shet and it has now been expressed in terms of resolved NMR chemical shift anisotropy. It is this latter formulation of Lee s theory that shall be used to analyze our experimental results in what follows. The results of the theory are summarized below for the case of axially symmetric chemical shift anisotropy. 

The temperature dependence of the spin-lattice relaxation rate Ef is usually analyzed using the simple Bloembergen, Purcell and Pound (BPP) model, which assumes a single correlation time describing non-correlated isotropic random motions. The spin-lattice relaxation expressed in terms of the spectral density function J(a>) evaluated at the NMR Larmor frequencies (Do and 2(Oo is... 

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