Gels critical dynamics

Let us examine the critical dynamics near the bulk spinodal point in isotropic gels, where K + in = A(T — Ts) is very small, Ts being the so-called spinodal temperature [4,51,83-85]. Here, the linear theory indicates that the conventional diffusion constant D = (K + / )/ is proportional to T — Ts. Tanaka proposed that the density fluctuations should be collectively convected by the fluid velocity field as in near-critical binary mixtures and are governed by the renormalized diffusion constant (Kawasaki s formula) [84],... 

Tanaka T (1985) Critical dynamics, kinetics and phase transitions of polymer gels. Polym Preprt 27(1) 235... 

Critical dynamics of a nematic liquid crystal in silica gels, as observed by the... 

Material properties at a critical point were believed to be independent of the structural details of the materials. Such universality has yet to be confirmed for gelation. In fact, experiments show that the dynamic mechanical properties of a polymer are intimately related to its structural characteristics and forming conditions. A direct relation between structure and relaxation behavior of critical gels is still unknown since their structure has yet evaded detailed investigation. Most structural information relies on extrapolation onto the LST. 

Fig. 12. Dynamic moduli master curves of PBD 44 precursor (p = 0) and PBD 44 critical gel [60]. The entanglement and glass transition regime is hardly affected by the crosslinking. Open symbols correspond to G, filled ones to G"...

Dynamic mechanical data near the gel point allow easy determination of the parameters of the critical gel, Eq. 1-1. Tan 8, as shown in Fig. 26, gives the relaxation exponent n... 

The dynamic mechanical properties of elastomers have been extensively studied since the mid-1940s by rubber physicists [1], Elastomers appear to exhibit extremely complex behavior, having time-temperature- and strain-history-dependent hyperelastic properties [1]. As in polymer cures, DMA can estimate the point of critical entanglement or the gel point. 

Critical phenomena of gels have been studied mainly by dynamic light scattering technique, which is one of the most well-established methods to study these phenomena [18-20]. Recently, the critical phenomena of gels were also studied by friction measurement [85, 86] and by calorimetry [55, 56]. In the case of these methods, the divergence of the specific heat or dissipation of the friction coefficient could be monitored as a function of an external intensive variable, such as temperature. These phenomena might be more plausible to some readers than the divergence of the scattered intensity since they can observe the critical phenomena in terms of a macroscopic physical parameter. 

Here we describe briefly the recent studies of the critical phenomena of gels by dynamic light scattering, friction coefficient measurement, and calorimetry. Some of the latest results by neutron scattering are also given. 

Fig. 25a, b. a. Collective diffusion coefficient D of a NIPA gel as determined by the kinetics of volume change, as a function of temperature. It diminishes at the critical point, b. collective diffusion coefficient as determined from the density fluctuations by use of photon correlation spectroscopy. The agreement between the results obtained from dynamics of microscopic fluctuations and from kinetics of macroscopic volume change is excellent considering the difficulty in the dynamic experiments... 

Here, the spatial derivatives on and p are taken with respect to the real position X. The first term in Eq. (3.13) is of the well-known form in the dynamical model of fluid binary mixtures near the critical point [34, 35]. This ought to be the case because our model reduces to that of fluids for v0 = 0. The last term in Eq. (3.13) is the elastic contribution, AT(jco) being a function of the original position jc0- If the gel is in mechanical equilibrium, we should require = 0 within the gel. 

The use of photon correlation spectroscopy to study the dynamics of concentration fluctuations in polymer solutions and gels is now well established. In bulk polymers near the glass transition there will be slowly relaxing fluctuations in density and optical anisotropy which can also be studied by this technique. In this article we review the development of the field of photon correlation spectroscopy from bulk polymers. The theory of dynamic light scattering from pure liquids is presented and applied to polymers. The important experimented considerations involved in the collection and analysis of this type of data are discussed. Most of the article focuses on the dynamics of fluctuations near the glass transition in polymers. All the published work in this area is reviewed and the results are critically discussed. The current state of the field is summarized and many suggestions for further work are presented. 

Table 13.3 presents the expressions for the rate constants applied in this work. The parameters are taken mostly from the work of Xie et al. [6], A distinctive feature of the numerical simulation of the influence of gel effect on the termination in the polymer-phase is described by a relation proposed by Kipparisides et al. [5], This combination of parameters gives realistic results on modeling both the reaction dynamics and the development of the molecular-weight distribution, reproducing closely experimental data (see Figure 13.6). The subscript 1 refers to the monomer phase, 2 to the polymer phase, and 22 to the polymer-phase after the critical conversion Xf. In addition, Table 13.4 presents first-order constants for usual initiators. 

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