Critical Phenomena of Gels

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. 

Critical Behavior of Gels. In 1977, the critical phenomena were discovered in the light scattered from an acrylamide gel in water [18]. As the temperature was lowered, both the scattered intensity and the fluctuation time of the scattered light increased and appeared to diverge at —17 °C. The phenomenon was explained as the critical density fluctuations of polymer networks although the polymers were crosslinked [19, 20]. 

The scattered intensity increases with increasing temperature as shown in Fig. 10. The scattered intensity diverges at the spinodal temperature, Ts in this particular case Ts = ca. 34.6 °C. Experimentally such a divergence cannot be expected because a macroscopic phase separation occurs and the scattered intensity remains finite. It is worthy to note that the difference in the scattered intensities between at 34.6 °C and at 35.0 °C clearly indicates that the system undergoes a transition. The critical phenomena of the volume phase transition of non-ionic gels with respect to temperature will be discussed in Sect 5.4. 

The sol-gel transition is one of the critical phenomena of polymers (Winter and Mours 1997 Stauffer 1998 Stauffer et al. 1982 Adam and Lairez 1996 Adam et al. 1987 Dastidar et al. 2005 Hecht and Geipier 1987 Muneh et al. 1983). In order to observe the progress of the reaction during gelation, it is of great importance to... 

In addition to these technical problems, the complexity inherent to physical properties of gels is, as exemplified above, that they depend very sensitively on the preparation condition. This is because, in a formal language, a gel is a frozen system and we need two sets of statistical information, the preparative ensemble and the final ensemble , to understand its equilibrium properties [29]. Hence, a gel is by nature more complex than the usual equilibrium systems. We should clarify the dependence of the properties of gels on preparation conditions, and also on structural defects of the network before going into precise investigations such as critical phenomena associated with the phase transition. 

Percolation is widely observed in chemical systems. It is a process that can describe how small, branched molecules react to form polymers, ultimately leading to an extensive network connected by chemical bonds. Other applications of percolation theory include conductivity, diffusivity, and the critical behavior of sols and gels. In biological systems, the role of the connectivity of different elements is of great importance. Examples include self-assembly of tobacco mosaic virus, actin filaments, and flagella, lymphocyte patch and cap formation, precipitation and agglutination phenomena, and immune system function. 

Percolation describes the geometrical transition between disconnected and connected phases as the concentration of bonds in a lattice increases. It is the foundation for the physical properties of many disordered systems and has been applied to gelation phenomena (de Gennes, 1979 Stauffer et al., 1982). At just above gelation threshold, denoting the fraction of reacted bonds as p and p=Pc + A/ , pc the critical concentration (infinite cluster), the scaling laws (critical exponents) for gel fraction (5oo) and modulus E) are ... 

A closer investigation of these phenomena might be of considerable interest. It is not yet quite clear why the gels, when subjected to the special procedure of "drying referred to above, do not contract. Perhaps this is an indication that the theory discussed on p. 536, assuming that the capillary pull of the liquid menisci at the surface of the gel plays a part in the process of contraction, is correct. Beyond the critical temperature of the liquid these menisci no longer exist. 

Some models proposed by physicists are applicable to some class of material, for example, polymer gels. They are aimed to describe critical phenomena like volume phase transition[164]. The required resolution for the model is high in order to express such phenomena. 

Flory-Huggins model[166] is the start point of the models on gels. Most of the models are derivatives or extension of the model for describing critical phenomena[164, 60]. Doi et al. studied deformation process of ionic gels in electric fields[127]. They carefully extended the Flory s model in variety of conditions. Osada et al. studied cooperative binding of surfactant molecules into the ionic gels[128, 129], They are also based on Flory s model. 

These results are in line with others obtained by different - but less direct-techniques applied to unilamellar systems. For instance, ultrasound propagation and attenuation were found continuous at [12] and a critical slowing down of membrane relaxation was obseiwed [13]. Pretransitional phenomena in L, pha near are correlated to structure fluctuations in the form of gel-like domains, of finite size and lifetime, and whose existence was experimentally detected by fluorescence spectroscopy [14]. 

As discussed briefly in the previous section, gelation can generally be discussed within the framework of critical phenomena [7] by having the gel point and critical point correspond. Stauffer applied the percolation theory often used for the general theory of critical phenomena to the crosslinking reaction of polymers [8, 9],... 

Dedicated to Prof. Manfred Gordon on the occasion of his 65th birthday, who discussed critical phenomena at the gel point as early as in 1974, see Ref 1. 

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