Semi-dilute solutions screening length

It is generally accepted that in semi-dilute solutions under good solvent conditions both the excluded volume interactions and the hydrodynamic interactions are screened owing to the presence of other chains [4,5,103], With respect to the correlation lengths (c) and H(c) there is no consensus as to whether these quantities have to be equal [11] or in general would be different [160],... 

It is admitted that asymptotically the coherent contribution reaches a constant limit when the transfer wave number q becomes much larger than the inverse of the correlation length of the system. This correlation length is, in dilute solutions, the size of the chains in semi-dilute solutions, the screening length. In... 

We see that this length er which tells us how the density-density correlations decrease with r is actually proportional to the size of the chains. In a semi-dilute solution, it is larger than the length e defined by (13.2.102). Of course, e is really what we usually call the screening length but the very existence of shows that, for finite chains, there is no complete screening. 

The same criterion does not apply in the semi-dilute region because, then, screening effects must be taken into account. Let us thus consider a semi-dilute solution of Brownian chains. The distance 0 between Brownian chains, the so-called overlap Brownian length , is given by (13.2.4) and, for d - 3,... 

When the concentration p increases, the screening length decreases, and this is one of the most revealing facts of the structure of good semi-dilute solutions. 

Figure 5.7. A schematic diagram of a semi-dilute solution, which may be thought of as a transient network characterised by a screening or correlation length...

In entangled solutions screening becomes effective at a characteristic distance, called the screening-length , and denoted s- Figure 3.7 provides an experimental example of the evidence. We see the scattering intensity measured for a semi-dilute solution of polystyrene in CS2, in a plot of versus 5/3 interested in the single chain structure factor in the semi-dilute... 

The adsorbed layer is well described by a self-similar picture[4] generated by a geometrical constraint on the screening length of the semi-dilute solution near the wall the only distance in the problem being the the distance z from the wall one must have i = z which leads to a concentration profile... 

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