Excluded volume screening

Unfortunately, there is no accurate theoretical estimate of the strength of hydrodynamic interaction or the extent of hydrodynamic screening of polydisperse branched polymers. Hydrodynamic screening usually correlates well with excluded volume screening. As was demonstrated... 

In other words a labelled polymer in dilute solution in a good solvent would experience opposing effects on cyclization as the concentration of matrix chains is increased Excluded volume screening would lead to an... 

In both poor and good solvents, one expects the screening of hydrodynamic interactions to increase the net friction felt by the chain, causing the mean cyclization rate to decrease. In good solvents, this retardation is compensated by excluded volume screening. From the net increase in Ie/Im for I in THF, it appears that the latter effects predominate. In contrast to the results for Py-polystyrene Py, here the cyclization rate is quite sensitive to the molecular weight of matrix chains. In addition, there seems to be no simple explanation at this time for the more complicated behavior of I + PVAc in a poor solvent. 

Fig. 21(a) that, in contrast to the case of polymer melts where the screening of excluded volume interactions leads to 1/2, in the porous medium... 

Thus we can see that a combination of van der Waals treatment of hard sphere excluded volume and Debye-Huckel treatment of screening with a minor generalization to account for hole correction of electrostatic interactions yields quite accurate bulk thermodynamic data for symmetrical salt solutions. 

The range of semi-dilute network solutions is characterised by (1) polymer-polymer interactions which lead to a coil shrinkage (2) each blob acts as individual unit with both hydrodynamic and excluded volume effects and (3) for blobs in the same chain all interactions are screened out (the word blob denotes the portion of chain between two entanglements points). In this concentration range the flow characteristics and therefore also the relaxation time behaviour are not solely governed by the molar mass of the sample and its concentration, but also by the thermodynamic quality of the solvent. This leads to a shift factor, hm°d, is a function of the molar mass, concentration and solvent power. 

However, this is true only for good solvent conditions, where (c) is also the correlation length, beyond which both the excluded volume and the hydrodynamic interaction are screened and self-entanglements (intramolecular... 

Under -conditions the situation is more complex. On one side the excluded volume interactions are canceled and E,(c) is only related to the screening length of the hydrodynamic interactions. In addition, there is a finite probability for the occurrence of self-entanglements which are separated by the average distance E,i(c) = ( (c)/)1/2. As a consequence the single chain dynamics as typical for dilute -conditions will be restricted to length scales r < (c) [155,156],... 

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],... 

Muthukumar and Winter [42] investigated the behavior of monodisperse polymeric fractals following Rouse chain dynamics, i.e. Gaussian chains (excluded volume fully screened) with fully screened hydrodynamic interactions. They predicted that n and d (the fractal dimension of the polymer if the excluded volume effect is fully screened) are related by... 

Muthukumar [44] further investigated the effects of polydispersity, which are important for crosslinking systems. He used a hyperscaling relation from percolation theory to obtain his results. If the excluded volume is not screened, n is related to df by... 

In the case of full screening of excluded volume he obtained... 

Fig. 9. Relation between relaxation exponent n and fractal dimension d for a three-dimensional network. In case of complete screening of excluded volume, values of 0 < n < 1 are possible if d is chosen between 1.25 and 2.5...

The fractal dimension measures how open or packed a structure is lower fractal dimensions indicate a more open system, while higher fractal dimensions indicate a more packed system (22). Theories relating the fractal dimension to the relaxation exponent, n, have been put forward and these are based on whether the excluded volume of the polymer chains is screened or unscreened under conditions near the gd point (23). It is known that the excluded volume of a polymer chain is progressively screened as its concentration is increased, the size of the chain eventually approaching its unperturbed dimensions. Such screening is expected to occur near the... 

In scenario (c) corresponding to semidilute solutions, polyelectrolyte chains interpenetrate. Under these circumstances, there are three kinds of screening. The electrostatic interaction, excluded volume interaction, and the hydro-dynamic interaction between any two segments of a labeled polyelectrolyte chain are all screened by interpenetrating chains. Each of these three interactions is associated with a screening length, namely, and These screening... 

Under the conditions of screening of electrostatic interactions between polyions, as occurs at high ionic strength (say, / > 0.1 mol dm- ), or in solutions containing neutral (non-ionic) polymers, the excluded volume term is the leading term in the theoretical equation for the second virial coefficient. In this latter type of situation, the sizes and conformation/ architecture of the biopolymer molecules/particles become of substantial importance. 

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