Swollen phase

This is a virial expansion form of the osmotic pressure analogous to the van der Waals fluid. Dusek and Patterson examined this equation and predicted the presence of two phases, i.e. collapsed and swollen phases. % is temperature dependent and is given by,... 

However, it remains unknown how heterogeneities affect the phase transition itself. In fact, the perturbation scheme used to derive Eq. (4.52) breaks down near the spinodal point. We can well expect that domains of a shrunken (or swollen) phase are created and pinned around heterogeneities with higher (or lower) crosslink densities. 

Below, I will first describe the observation on thin cylinders because the phase coexistence can most clearly be observed in these samples and, moreover, samples of this shape are most frequently used in various experiments. The results of the observation are depicted schematically in Fig. 12. As the temperature was increased from the swollen phase, the sample gradually shrunk following the swelling curve (Fig. 7) and the onset of the transition region was manifested by the appearance of a nucleus of the high-temperature (shrunken) phase at the end of the cylinder. We denote this temperature as Tt. As long as... 

Fig. 12. Process of the first-order transition observed on an ionized NIPA gel rod on heating. The phase-coexistence starts at temperature T, and ends at T2. Between these temperatures, the volume fraction of the swollen (shrunken) phase decreases (increases) with temperature, and the gel never becomes homogeneous. On cooling from the shrunken to the swollen phase, the process similar to the above occurs in the reverse direction. This time, the nuclei of the swollen phase appear at both ends of the shrunken rod and grow towards the center...

Most challenging are the systems that have ionic surfactants and are free of electrolyte. In this case it is possible to obtain a swollen phase, by the addition of a mixture of cosurfactant and oil.2,28 24 The thickness of the water lamellae, evaluated from the composition of the liquid crystal and the repeat distance, is about 17 A.2 If... 

Figure 12.2. Sketch of the maximal number of contacts that a short, compact tube can make as a function of X, the dimensionless ratio of the tube thickness to the range of the attractive interaction. When X is large compared with 1, one obtains a swollen phase. At the other extreme, when X 1, one finds a highly degenerate compact phase. The twilight zone between these two phases occurs in the vicinity of X 1 and is characterized by marginally compact structures. The figure shows typical tube conformations in each of the phases.

The picture we have developed based on the tube-protein hypothesis has several attractive features. First, as noted before, protein structures he in the vicinity of a phase transition to the swollen phase, which confers on them exquisite sensitivity to the effects of other proteins and ligands. The flexibility of different parts of the protein depends on the amount of constraints placed on them from the rest of the protein [40]. From this point of view, it is easy to understand how loops, which are... 

There are two other fixed points (0.254037, 0.022159, 0.07098) and (0.2000, 0.0666, 0.0666) on the line separating the basins of attraction of the fixed points corresponding to the collapsed and the swollen phases. These are purely repulsive, and cannot be reached starting with our choice of initial condition. These correspond to higher order multicritical points( tetra critical). 

Figure 15. Schematic representation of the different phases of a linear cliain with selfattraction on the Sierpinski gasket with at most two visits per site allowed (a) the swollen phase (b) branched polymer phase with branches made of the doubled-up chain (c) the collapsed phase...

For u < Uc 2 the random - animal fixed point corresponding to the swollen phase of the polymer is reached. Linearizing around the fixed point one finds only one relevant eigenvalues Aj = 3.14069. With this eigenvalue one finds i/ = log 2/ log Ai = 0.60566, and 9 = 0.75667. 

In this case, we have three phases possible the desorbed swollen(DS), the desorbed collapsed (DC) and the adsorbed swollen (AS) phases. The fixed points corresponding to the desorbed phases have S = C = E = 0, and A, B equal to the value for the 4-simplex at the S or C fixed point ( section 6.2). The fixed points corresponding to the polymer adsorbed on the surface, on the other hand, have A = B = C = B = 0 and S equal to the value corresponding to the swollen phase fixed point on the 3-simplex surface ( section 3.1). The phase boundaries, determined numerically by finding the basins of attraction of these fixed points are shown in Fig. 18. 

Fig. 14 The bi-continuous structure of PVA hydrogels obtained by freeze-thaw cycles with a PVA-rich phase and a PVA-poor phase. The fine structure of the polymer-rich region, including PVA crystallites and a swollen phase, is tilso indicated...

Different phase separated morphologies can be found in different polymer solvent systems. The pattern formation consists of several stages. In the initial stage, phase separation results in a layered morphology of the two solvent swollen phases. As more solvent evaporates, this double layer is destabilized in two ways (1) capillary instability of the interface, and (2) surface instability. Each of the mechanisms results in different morphological length scales. Core shell spherical domains in phase-separated ternary systems have also been found. The shell thickness can be a few nanometers. 

Ions diffuse into the polymer with a distinct boundary between a fully reduced/ swollen phase and a fully oxidized/contracted phase. The boundary is very sharp on the first reduction cycle but is broader on subsequent cycles. This type of diffusion behaviour is typical of solvent diffusion in polymers that causes a softening phase change and is called Type II (non-Fickian) behaviour [49]. This process occurs in... 

In discussing solution polymerizations of vinyl chloride we must recall that poly(vinyl chloride) is insoluble in its monomer as well as in many common solvents. Therefore we have to distinguish between true solution polymerizations, /.e., systems in which the monomer, the added solvent, and the polymer are truly in solution and pseudo-solution polymerizations, i,e, systems in which the monomer is in true solution but from which the polymer separates as a swollen phase. Among the true solvents are tetra-hydrofuran (THF) chlorobenzene 1,2-dichloroethane diethyl oxalate 2,4,6-trichloroheptane and many plasticizers. Examples of pseudo-solvents are methanol, aliphatic hydrocarbons, and cyclohexane [22]. 

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