Excluded volume effects screening

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. 

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... 

Finally, it is interesting to note that the value of a for the poly-(metaphosphate) chain [Strauss and Wineman (241 )] has the same order of magnitude as those of non-electrolyte chains with substituents of comparable size. Under the observed theta-solvent conditions (0.415 M aqueous NaBr), the screened long range electrostatic interactions are just balanced by the various other contributions to the excluded volume effect, but there is no reason to expect a simultaneous obliteration of short-range electrostatic effects1. 

A major difference of branched molecules from chain molecules is that more units are bound together and compressed into a very narrow space around the center of gravity. Hence, an immediate supposition is that in order for the monomer-monomer interaction to balance with the monomer-solvent interaction and the entropy force, and for the excluded volume effects to vanish, more attractive force between monomers are needed than is the case of chain molecules. Now we will focus our attention on concentrated systems such as non-solvent systems. An interesting idea is the influence of solvenf size on the osmotic pressure (screening effect) [19]. 

The state of a statistical fractal in which the excluded volume effect is compensated by the screening effect is referred to as the compensated state. For this state. Family has found that ... 

Thus, the fractal dimension D increases near the compensation point this is due either to the geometric screening of the excluded volume effect or to the enhancement of the attractive interaction. Big clusters near the critical point in thermally induced phase transitions and polymers at the 0-point are examples of statistical fractals in the... 

For chains with a low molecular weight (unentangled case), the Rouse theoiy (Adachi and Kotaka 1993 Rouse 1953) can be employed to describe it because excluded volume effects and hydrodynamic interactions are screened out (de Gennes 1979). 

A local correlation length f(x) was defined (the length over which excluded volume effects are screened), the polymer layer at the interface then resembling a network of variable mesh size (x). When the hydrodynamic equation is integrated up to a distance correspjonding to the longest mesh size Rp (the Flory radius of polymers in solution), it is found that the hydrodynamic thickness scales... 

When the chain is seen as a whole with blobs as the structural repeat unit, the excluded-volume effect by monomer interaction is screened by the presence of the blobs of other chains, and hence considered to behave as an ideal chain. If we assume such a screening effect, the radius of gyration is given by... 

It is important to keep in mind (see the Introduction ) that the GGS approach provides a rather simple description of polymer systems it does not take into account interactions such as the excluded volume effects or entanglements. til some special cases (such as for polymer melts or dry polymer networks) the excluded volume interactions may be screened [2,4]. The entanglement effects, in turn, are quite small for sufficiently short polymer chains [3]. Also, our GGS treatment here does not account for hydrodynamic... 

Assume that we are dealing with polymers in good solvents and in the semidilute solution. If r is a scale to measure, then the chain entanglement shows the following properties. At r >, that is, outside the blob, the repulsive interactions between monomers are screened out by other chains in the solution so that the whole chain is composed of blobs connected in an ordinary random walk without excluded volume effect. Overall, the chain follows Gaussian statistics. At r <, that is, within the blob, the chain does not interact with other chains, but there is a strong excluded volume effect. 

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