Relaxation times and diffusion

The time it takes for the chain to diffuse out of the original tube of average length (L) is the reptation time  

3) was used for the average contour length of the tube. The reptation time Trep is predicted to be proportional to the cube of the molar mass. The experimentally measured scaling exponent is higher than 3  

We will discuss the possible reasons for the disagreement between the simple reptation model and experiments in Section 9.4.5. 

Reptation steps (a) formation of a loop at the tail of the snake and elimination of the tail segment of the confining tube  

The first part of the final relation of Eq. (9.8) is the Rouse time of an entanglement strand containing Ae monomers  

---

In situ NMR measurements can be made in conjunction with down-hole fluid sampling [5, 6]. The NMR relaxation time and diffusivity can be measured under high-temperature, high-pressure reservoir conditions without loss of dissolved gases due to pressure depletion. In cases when the fluids may be contaminated by invasion of the filtrate from oil-based drilling fluids, the NMR analysis can determine when the fluid composition is approaching that of the formation [5, 6]. 

Diffusivity correlates linearly with the ratio of temperature and viscosity. Therefore the diffusivity can also be expected to correlate with relaxation time because the latter correlates with temperature and viscosity according to Eq. (3.6.1). Figure 3.6.3 illustrates the correlation between relaxation time and diffusivity with the gas/oil ratio as a parameter [13]. The correlation between diffusivity and relaxation time extends to hydrocarbon components in a mixture and there is a mapping between the distributions of diffusivity and relaxation time for crude oils [17]. 

Fig. 3.6.3 Correlation of relaxation time and diffusivity with gas/ oil ratio (GOR, m3 m-3) as a parameter [13]. The solid line is for zero GOR. The dashed lines are for the indicated GOR.

We have applied the discrete-exchange model to these data. An exchange between Na ion under a particular slow-motion condition and in the extreme narrowing limit is assumed. Transverse relaxation time and diffusion coefficient are written as follows ... 

Entangled polymer dynamics 9.5.1 Relaxation times and diffusion... 

Consider a molecule made out of two /-arm stars with Kuhn segments per arm with junction points connected by a central linear strand of Abb Kuhn monomers. This molecule is called a pom-pom polymer. If/= 1, this molecule is linear, while the H-polymer corresponds to /=2. Estimate the /-dependence of relaxation time and diffusion coefficient of a melt of monodisperse pom-pom polymers for /> 1. Consider only single-chain modes and assume that the coordination number of an entanglement network is z. 

The rate dependence of the inverse relaxation time and diffusivity D exhibited a non-trivial scaling D I/t Such power-law fluid scaling contrasts... 

The investigation of relaxation times and diffusion coefficients requires the determination of the eigenvalues of the matrix corresponding to the system of algebraic equations obtained from Eqs. (18) after Fourier-Laplace transformation (s, Laplace transform of time q, Fourier transform of the space coordinate). The roots of the secular equation are... 

In many polymer systems, polydispersity is a feature that must be accounted for in analysing the results of PGSE NMR measurements. Allowing for both relaxation time and diffusion coefficient dependence on molar mass, the echo attenuation expression in equation (9.6) must be modified to read... 

STRAFI spectroscopy resembles normal spectroscopy except that the chemical shift and dipolar interactions are too small to perturb the signal appreciably. Studies are therefore confined to the study of relaxation times and diffusion. For heterogeneous solid samples, or liquids in solids, discrimination between different motional components is possible, the contributions for components with fast motions being dominant for the last echoes in a long sequence. 

---