Relaxation, viscous liquids

Usually, nuclear relaxation data for the study of reorientational motions of molecules and molecular segments are obtained for non-viscous liquids in the extreme narrowing region where the product of the resonance frequency and the reorientational correlation time is much less than unity [1, 3, 5]. The dipolar spin-lattice relaxation rate of nucleus i is then directly proportional to the reorientational correlation time p... 

Cole and Davidson s continuous distribution of correlation times [9] has found broad application in the interpretation of relaxation data of viscous liquids and glassy solids. The corresponding spectral density is ... 

FIG. 23 A schematic illustration of the molecular motions and associated T2 relaxation curve behavior for the three major domains in foods—liquid, viscous liquid, and solid (crystalline and glassy). Typical H T2 NMR relaxation time values observed in these domains, and values specific for water in liquid and crystalline domains, are listed. 

Thus, even when the elongation rate, as defined by equation 3.76, is constant, the separation of two material points increases exponentially with time. As stress relaxation occurs exponentially, it is clear that at high elongation rates the stress will increase very rapidly. In a purely viscous liquid the stress relaxes instantaneously and consequently this high resistance to stretching does not occur. 

Whether a viscoelastic material behaves as a viscous liquid or an elastic solid depends on the relation between the time scale of the experiment and the time required for the system to respond to stress or deformation. Although the concept of a single relaxation time is generally inapplicable to real materials, a mean characteristic time can be defined as the time required for a stress to decay to 1/e of its elastic response to a step change in strain. The... 

Spin-spin relaxation of nuclei is accelerated when the nuclei participate in a dipolar bond (O — H, N — H, 13C—1H). Spin-spin relaxation involving dipole-dipole interaction is very effective in solids and viscous liquids with slow molecular motion, since the magnetic fields caused by slowly tumbling dipoles change very slowly. 

As shown in Chapter 10, molecular dynamics in polymers is characterized by localised and cooperative motions that are responsible for the existence of different relaxations (a, (3, y). These, in turn, are responsible for energy dissipation, mechanical damping, mechanical transitions and, more generally, of what is called a viscoelastic behavior - intermediary between an elastic solid and a viscous liquid (Ferry, 1961 McCrum et al., 1967). 

In a fluid system, the rotational freedom of the particles affects the susceptibilities in two ways (1) the applied field (either AC or DC) deforms the orientational distribution function of the easy axes, which can never happen in a solid system with its fixed distribution of the particle axes and (2) if out of equilibrium, in a magnetic fluid the orientational diffusion of the particle axes works as an additional channel of magnetic relaxation that is, besides intrinsic processes, the magnetic moment can achieve equilibrium by rotating together with the particle in the suspended viscous liquid. Expressing the reference... 

The most advanced theories of relaxation phenomena in a system of entangled macromolecules is based on the dynamics of a single macromolecule. Dynamics of the tagged macromolecule is simplified by the assumption that the neighbouring macromolecules can be described as a uniform structureless medium and all important interactions can be reduced to intramolecular interactions. The dynamic equation for a macromolecule can be written as a modification of equation (2.1) for dynamics of macromolecule in viscous liquid... 

These equations describe the reptation normal relaxation modes, which can be compared with the Rouse modes of the chain in a viscous liquid, described by equation (2.29). In contrast to equation (2.29) the stochastic forces (3.47) depend on the co-ordinates of particles, equation (3.48) describes anisotropic motion of beads along the contour of a macromolecule. 

These are exactly the known results (Doi and Edwards 1986, p. 196). The time behaviour of the equilibrium correlation function is described by a formula which is identical to formula for a chain in viscous liquid (equation (4.34)), while the Rouse relaxation times are replaced by the reptation relaxation times. In fact, the chain in the Doi-Edwards theory is considered as a flexible rod, so that the distribution of relaxation times naturally can differ from that given by equation (4.36) the relaxation times can be close to the only disentanglement relaxation time r[ep. 

Abstract Macromolecular coils are deformed in flow, while optically anisotropic parts (and segments) of the macromolecules are oriented by flow, so that polymers and their solutions become optically anisotropic. This is true for a macromolecule whether it is in a viscous liquid or is surrounded by other chains. The optical anisotropy of a system appears to be directly connected with the mean orientation of segments and, thus, it provides the most direct observation of the relaxation of the segments, both in dilute and in concentrated solutions of polymers. The results of the theory for dilute solutions provide an instrument for the investigation of the structure and properties of a macromolecule. In application to very concentrated solutions, the optical anisotropy provides the important means for the investigation of slow relaxation processes. The evidence can be decisive for understanding the mechanism of the relaxation. 

Because all tissues are viscoelastic this means that their mechanical properties are time dependent and their behavior is characterized both by properties of elastic solids and those of viscous liquids. The classic method to characterize a viscoelastic material is to observe the decay of the stress required to hold a sample at a fixed strain (stress relaxation) or by the increasing strain required to hold a sample at a fixed stress (creep) as diagrammed in Figure 7.1 and explained further in Figure 7.2. Viscoelastic materials undergo processes that both store (elastic) and dissipate (viscous)... 

Brawer S (1985). Relaxation in Viscous Liquids and Glasses American Ceramic Society, Columbus, OH. 

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