Relaxation network density

These results clearly indicate that the multi-frequency dynamic analysis method allows us to estimate the contribution of different relaxation mechanisms during curing of elastomers, and the changes in chemical and physical networks densities can be studied separately. 

A major focus of this chapter is the effect of network formation and network density on the relaxation times of the H and 13C nuclei in the NMR experiment. The changes in relaxation times can be exploited to obtain information about crosslink density and chain motion, and must be taken into account in the design of experiments to determine changes in chemical structure. In this section we examine how crosslinking changes the transverse (T2) relaxation times of nuclei, and how this information can be of use. Two different approaches have been taken in the literature, namely changes in T2 can be used to estimate crosslink density, or used to develop and verify models of chain motion. 

While the network density v is more or less given by the concentration of the surfactant, the relaxation time can depend on many parameters such as surfactant concentration, temperature, type of counterions or ionic strength. 

It is interesting to note that the useful properties of supercritical water arise from the breakdown of the extensive HB network that is at least partly responsible for many of the anomalies of liquid water. We have discussed how the use of the idea inherent in the Widom line helps in understanding the large-scale fluctuations observed in supercritical water. Because of the large separation of timescales between vibrational relaxation and density relaxation, the vibrational line widths are influenced significantly by the transient density inhomogeneity present near the critical temperature. 

FIGURE 13.3 The dependences of elasticity modulus E on entanglements cluster network density n, in tests with constant strain rate (1), strain discontinuous change (2) and on stress relaxation (3) for PASF [1]. 

Figure 3.21 Results from measurements of continuous stress relaxation of nitrile rubber (low network density). Data from Bjork (1983).

Pal Majumder T, Mitra M, Roy SK (1994) Dielectric relaxation and rotational viscosity of a ferroelectric liquid crystal mixture. Phys Rev E 50(6) 4976-4800 Petit M, Daoudi A, Ismaili M, Buisine JM (2006) Electroclinic effect in a chiral smectic-A liquid crystal stabilized by an anisotropic polymer network. Phys Rev E 74 061707 Petit M, Hemine J, Daoudi A, Ismaili M, Buisine JM, Da Costa A (2009) Effect of the network density on dynamics of the soft mode and the Goldstone modes in short-pitch ferroelectric liquid crystals stabihzed by an anisotropic polymer network. Phys Rev E 79 031705 Pirs J, Blinc R, Marin B, Pirs S, Doane JW (1995) Polymer network volume stabilized ferroelectric liquid crystal displays. Mol Cryst Liq Cryst 264 155-163 Polyanin AD, Zaitsev VF (2003) Handbook of exact solutions for ordinary differential equations, 2nd edn. Chapman Hall, Boca Raton... 

It is of interest that the phenomena discussed above are most clearly manifested for linear polymers. When passing over to cross-linked polymers (eg copolymers of styrene and divinylbenzene), the effect of the surface on the relaxation time becomes less perceptible as the network density increases. This is due to the fact fiiat the reduction in the mobility of large segment of the chains caused by cross-linking excludes them from participation in the relaxation process, thus leveling the effect of the surface on their mobility. 

Later we will describe both oxidation and reduction processes that are in agreement with the electrochemically stimulated conformational relaxation (ESCR) model presented at the end of the chapter. In a neutral state, most of the conducting polymers are an amorphous cross-linked network (Fig. 3). The linear chains between cross-linking points have strong van der Waals intrachain and interchain interactions, giving a compact solid [Fig. 14(a)]. By oxidation of the neutral chains, electrons are extracted from the chains. At the polymer/solution interface, positive radical cations (polarons) accumulate along the polymeric chains. The same density of counter-ions accumulates on the solution side. 

The above models describe a simplified situation of stationary fixed chain ends. On the other hand, the characteristic rearrangement times of the chain carrying functional groups are smaller than the duration of the chemical reaction. Actually, in the rubbery state the network sites are characterized by a low but finite molecular mobility, i.e. R in Eq. (20) and, hence, the effective bimolecular rate constant is a function of the relaxation time of the network sites. On the other hand, the movement of the free chain end is limited and depends on the crosslinking density 82 84). An approach to the solution of this problem has been outlined elsewhere by use of computer-assisted modelling 851 Analytical estimation of the diffusion factor contribution to the reaction rate constant of the functional groups indicates that K 1/x, where t is the characteristic diffusion time of the terminal functional groups 86. ... 

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