Semidilute regime

E. Faetibold, G. Waton. Dynamical properties of wormlike micelles in the vicinity of the crossover between dilute and semidilute regimes. Langmuir 77 1972-1979, 1995. 

Typically, scaling approaches are employed to explain the behavior in the semidilute regime. By examining static correlations near the temperature, Daoud and Jannick( ) have expressed the density-density correlation function in terms of a correlation length that is inversely proportional to concentration. Since the diffusion coefficient is inversely proportional to the correlation length it is directly proportional to the concentration. 

For now, we restrict our discussion to the 0 point, where the poly-mers in solution have a random coil distribution. Therefore, it is reasonable to say that in the semidilute regime at the 6 point the distribution of the segments in the solution is spherical. With this concept, the velocity of the diffusing segments at the 6 condition can be expressed as... 

Mechanistic Ideas. The ordinary-extraordinary transition has also been observed in solutions of dinucleosomal DNA fragments (350 bp) by Schmitz and Lu (12.). Fast and slow relaxation times have been observed as functions of polymer concentration in solutions of single-stranded poly(adenylic acid) (13 14), but these experiments were conducted at relatively high salt and are interpreted as a transition between dilute and semidilute regimes. The ordinary-extraordinary transition has also been observed in low-salt solutions of poly(L-lysine) (15). and poly(styrene sulfonate) (16,17). In poly(L-lysine), which is the best-studied case, the transition is detected only by QLS, which measures the mutual diffusion coefficient. The tracer diffusion coefficient (12), electrical conductivity (12.) / electrophoretic mobility (18.20.21) and intrinsic viscosity (22) do not show the same profound change. It appears that the transition is a manifestation of collective particle dynamics mediated by long-range forces but the mechanistic details of the phenomenon are quite obscure. 

A 13.2,2 Choice of cq. The parameter cq determines the crossover among the dilute or semidilute regimes. It is thus related to the overlap concentration c introduced in the blob model. We may determine it from an analysis of the osmotic pressure in the excluded volume limit. The scaling law reads... 

Micka et al. [169] were the first who simulated a multichain HPE system. They studied regular copolymers with alternating neutral and charged monomers (with a charge fraction of / = 1/3) in a poor solvent in the presence of monovalent counterions. The paper by Micka et al. [169] nicely demonstrated that the necklace microstructures exhibit a variety of conformational transitions as a function of polymer concentration. The end-to-end distance was found to be a nonmonotonic function of concentration and showed a strong minimum in the semidilute regime. 

For tp > 5 " the strong density fluctuations in the semidilute regime disappear, and in the marginal regime the solution may again be described by a mean-fleld theory, as discussed in 5.2c. 

The stress tensor for a semidilute solution of rods is given by Eq. (6-36), the formula for dilute solutions. However, if in a thought experiment one holds the shear rate fixed at a low value while increasing the concentration of rods from dilute to semidilute, the Brownian contribution to the stress will greatly increase, since the rotary diffusivity decreases according to (6-44). The viscous stress contribution, however, only increases in proportion to u. Thus, as Doi and Edwards (1986) argued, the ratio of viscous to Brownian stresses decreases as as the concentration increases in the semidilute regime. Hence, in the semidilute... 

Even very weak hydrodynamic interactions among fibers in the semidilute regime are enough to disturb the Jeffery orbits of individual fibers enough that a steady-state distribution of fiber orientations is obtained after long shearing times without such interactions, no steady state would ever be reached, since the initial fiber orientation would just be revisited over and over with periodicity equal to that of the Jeffery orbit. 

From Fig. 6-19, we see that this value of is low enough to be in the zero-shear regime. Hence, we can use Eq. (6-49) to obtain o in the semidilute regime ... 

Comparing this with the result for = 0.001 at the same shear rate, Eq. (A6-8), we see that a 10-fold increase in 0, from the dilute to the semidilute regime, has produced a 1000-fold increase in N]. The rate of increase is even steeper with respect to increases in the length of the rods. As an exercise, show that within the semidilute regime, at tixed 0, Pi o is proportional to L raised to the power 14 ... 

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