Semidilute solutions mesh size

In semidilute solution, the average mesh size, , of the polymer is... 

In the semidilute regime, the molecules cannot distribute themselves at random over the volume. The polymer concentration fluctuates with a wavelength equal to the correlation length. The system can be seen as a kind of network with mesh size comparable to The network continuously changes conformation due to Brownian motion. Over distances along the polymer chain < , which implies short time scales for molecular motion, polymer sub-chains behave as in a dilute solution interactions between two... 

Thin liquid films made from the mixed solutions below CAC exhibit a stratification phenomenon, with a stratum thickness corresponding to the mesh size of the polymeric network, i.e. the distance between overlap points of two polymer chains. The oscillatory forces are particular to polyelectrolytes and disappear when the electrostatic forces are screened with salt. The study of freely suspended films gives new useful insights into the structure of semidilute polymer solutions which are presently the object of numerous speculations. 

In a semidilute solution there are three different, and in principle, independent length scales the mesh size the... 

Fig. 1 Illustrations of the different concentrations regimes encountered in wormUke micellar solutions with increasing concentration. is the mesh size of the entangled network in the semidilute regime and d denotes the average distance between colinear micelles in the concentrated isotropic, nematic and hexagonal phases. An estimate of d can be gained from the position of the structure peak in the scattering function...

Contrary to the earlier beliefs, dynamical properties of semidilute solutions at the theta temperature are much more difficult to comprehend than properties of good-solvent solutions. Here, without going either into the details of the experimental determination or theoretical considerations, we will review different experimental results obtained on polystyrene solutions. Our aim is to show that, at the theta temperature, the mesh size of the transient gel is not proportional to the correlation length of the concentration fluctuations. The coexistence of these two characteristic lengths explains why some dynamical properties do not obey scaling laws at the theta temperature. 

Why the change from the one to the other limit must take place around is intuitively clear, essentially corresponds to the distance between entanglement points, as these are the points where monomers interact with other chains, which is the cause for the alteration of the chain structure. In the literature, is therefore often addressed as mesh-size, in order to emphasize that it can also be interpreted as the diameter of the meshes of the entanglement network built up by the chains in a semidilute solution. It is furthermore plausible to assume that approximately equals the distance r, where g(r) comes down to values in the order of the mean monomer density in the sample... 

We repeat here an argument due to de Gennes [36]. The main idea is to assume that the relation Eq. (38) holds locally 0(z) = [ (z)/u] , where (z) is the local mesh size of the semidilute polymer solution. Since there is no other length scale in the... 

The dynamics of concentration fluctuations expressed by eqn [161] (or eqn [34]) of the Omstdn-Zemike type exhibits the diflrrsion coeflrdent D =feT/(6nj 0), eqn [72], which can also be derived from fluctuations of gel-like networks with screening of hydrodynamic interactions. Thus, it is often rderred to as the gd mode. A decrease in mesh size increases the rdaxation rate of the gel mode. Experimentally, DLS for semidilute solutions rrsually exhibits another mode of motions with a very slow decay rate. This slow mode may be assodated with some inhomogeneity depending on solvent quality and sample preparation, or may be rdated to the translational... 

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