The Concentrated Regime

At the upper limit of the ci range, v decreases to a minimum as the molecules are progressively immobilized, effectively making good and poor solvents functionally indistinguishable. In this regime, viscosity merges into elasticity, P becomes independent of c, and the dispersion simulates the behavior of a molten polymer. 

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Few studies in the literature concern the structure of concentrated phases of extractant in diluent. Recently, Bauduin et al. (125) have investigated the structure of DMDBPMA-dodecane and DMDBTDMA-dodecane solutions in the concentrate regime. Figure 7.21 clearly shows the difference in the microstructure of the... 

With Increasing concentration the and terms of [5.2.15] become more Important. When v is small we can ignore the quadratic term. In the concentrated regime the term is the dominant contribution to or FI (see fig. 5.3). The transition between the ideal dilute (1) and concentrated (c) regimes occurs at a volume fraction

functional dependencies, we ignore numerical coefficients of order unity. 

Figure 3.95. Same system as in fig. 3.94 but now plotted double logarithmically for the concentrated regime.

Consider a PDMS network prepared in the dry state that swells to an equilibrium swelling ratio of 2 = 4 in the concentrated regime (0-like swelling). Estimate the dry modulus of the network at room temperature. Compare your result with Fig. 7.17 and estimate the numerical prefactor in Eq. (7.91). 

In Fig. 6.18 this distance dependence is plotted for several sphere diameters. The effective ranges of several interaction forces is also indicated. We see that the mean distance becomes of the order of the interaction range at a volume fraction of about 0.2 for particles of 50 nm and about 0.5-0.6 for particles of 1000 nm. Below these volume fractions the suspension can be considered as diluted or semi-diluted and above these volume fractions as concentrated. It appears that the smaller the particle size, the lower the volume fraction for the transition to the concentrated regime. 

In the concentrated regime, the concentration of the polymer is fairly even. Nevertheless, a correlation length can be defined, and it is proportional to 1 /cp. For most food polymers, this regime will be reached at fairly high polymer concentrations, say above 3%, unless [j is very small. 

Note For several polymers, there is a limited concentration region where the slope gradually changes from small to large and one takes as the critical concentration that where the steepest slope begins, often denoted c. Possibly, the concentrated regime then has been reached. 

For example, it was demonstrated [110] that the most dramatic changes in reaction efficiency induced by nonrandom arrangements of multiplets on a d = 2 lattice of hexagonal symmetry occur in the concentration regime ... 

Narasimhan and Peppas [61] analyzed the dissolution mechanism of rubbery polymers by dividing the penetrant concentration field into three regimes which delineate three distinctly different transport processes. The swollen rubber was defined as the concentrated regime. The existence of a diffusion boundary layer adjacent to the rubbery-solvent interface, S, was proposed. This was defined as the semi-dilute regime. When the polymer is fully dissolved, the disentangled chains move freely in the solvent and exhibit Brownian motion ( dilute regime. Fig. 30). 

The entire concentration field is divided into three regimes. We define the swollen polymer (i.e. the region R < x < S in Figure 1) as the concentrated regime. We postulate the existence of a diffusion boundsuy layer adjacent to the rubl iy -solvent interface, S, through which the disentangled chains diffuse. The diffusion... 

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