Parameters excluded volume parameter

In the classical theories of polyelectrolytes, the chain expansion is characterized by the electrostatic excluded volume parameter, zel with ... 

Fig. 3. Theoretical density profile of dendritic structures of generations 2-7 [12]. The radial volume fraction properly normalized to unity at the center of the molecule is plotted against the radial distance to the origin. All data has been calculated assuming a realistic excluded volume parameter of the segments of the dendrimer. Reproduced with permission from [12]...

Here a0 is a constant called the effective bond length of the chain, and as(z) is a dimensionless quantity called the linear expansion factor of the chain. The latter depends on long-range interactions between pairs of monomer units and chain length through the so-called excluded-volume parameter z. For details of these quantities characterizing the dimensions of random-coil polymers, the reader is referred to a recently published book by Yamakawa (40). At this place we simply note that as tends to unity in the absence of excluded-volume effect. 

As indicated, we incorporate a single overall excluded-volume parameter bxv (of order unity) to compensate for the many errors of approximating Vexcl as a simple sum of cluster volumes, neglecting, for example, cluster shape effects on interstitial packing vacancies. A nonzero bXY value brings in the complex nonlinear dependence on all cluster populations,... 

The parameter v has the dimension of volume and is called the excluded volume parameter. The above approximation of repulsive force can be apparently valid for a long macromolecule, when a very large number of subchains... 

A relation between the mean end-to-end distance of the entire chain (R2) and the mean end-to-end distance of a subchain b can be found from simple speculation. This relation includes temperature T, mean distance b between the nearest along chain particles, excluded volume parameter v and the number of particles on the chain N. When dimensional considerations are taken into account, the relation can be written in the form... 

These ratios are the most important means of quantitatively characterizing the effects of heterointeractions in copolymers, since their analytical formulas depend only on the chain composition and the cross excluded volume parameter uAB. For a particular miktoarm chain the ratio oG increases from a common good to selective and then to a common theta solvent since the intensity of heterointeractions increases. In Fig. 3 is illustrated the dependence of the chain topology as function of the length fraction of the B branch B=NB/(NA+NB). Similarly, the ratios y have higher values in a common theta than in a common good... 

Yamakawa-Stockmayer-Shimada (YSS) theory [75-77] predicts that the radius expansion factor as (=(/0)1/2) is a universal function of the scaled excluded-volume parameter z defined by... 

The parameters w and w2 reflect the change in the excluded volume parameter due to attractive interaction between the ion pair and the monomer and monomer charge and ion pair, respectively [48]. 

Kurata (268)], the intrinsic viscosity of chain molecules is expressed in a power series of the excluded volume parameter z defined by Eq. (16) ... 

Fig. 5. Concentration profile inside a grafted PDMS layer swollen by a good solvent (octane). The molecular weight of the grafted chains is 92 kg mol-1 and the surface density in the layer is a=0.011. The full line is the profile determined by neutrons reflectivity. The dotted line is the SCF result of Zhulina et al. [52] calculated for a surface density o=0.011 and an excluded volume parameter v=0.8 a3 (a is the size of the monomer, determined to be a 0.5 nm by the slope of the scaling line in Fig. 2).

In real molecules, segments on distant portions of the chain do interact because of their physical volume and short range attractions such as van der Waals forces. The excluded volume parameter... 

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