Exduded-volume effect

Note that the eiqiansion coefBdent R )INb does not depend on N. This is essentiaUy different from the situation in dUute solutions, and indicates the screening of the exduded volume effect. Flory first conjectured that the conformation of a polymer in concentrated solutions and melts becomes Gaussian, and the present theoretical calculation is that given by Edwards. 

Figure 20 shows with extensive data for a variety of flexible polymers " " " that a, is a universal function ofz as predicted by the QTP theory and is accurately described by eqn [85]. For stiff chains, the theta condition is hardly observed, and in most cases, [>/]o must be obtained from [>/] data at low M in a given solvent. For example, we may evaluate a, for CTC (in Figure 19) as the measured [>/] relative to the theoretical curve at a given Al. In Figure 21, the a, values thus obtained for various semiflexible polymers " " are shown in comparison with eqn [85] the data cover the range of 2 from 7.8 to 82 nm. The dose fit of the theoretical line substantiates that the Barrett equation in the QTP scheme describes exduded-volume effects on [>/] of a variety of stiff polymers. In condusion, the QTP theory is capable of quantitatively explaining a, data for both flexible and stiff polymers. 

Equation [156] underestimates the ratio of Rh/Rg by about 15% ° when compared with the experimental one at the 6 temperature. Similar calculations can be made for Gaussian chains with other architectures. In real chains, the expansion of chain dimension by exduded-volume effects brings about an expansion of the hydrodynamic radius. ... 

As a consequence of the screening, the distribution of the conformation of the test polymer becomes Gaussian. Indeed given the effective exduded volume potential v(r), it is easy to calculate the mean size of the polymer by use of the method described in Section 2.5. For example, the straightforward perturbation calculation gives (see Appendix 5.m)... 

The manifestation of the excluded-volume effects in a polymer coil (swelling) depends on the quality of a particular low-molecular-weight solvent (solvent strength) for a given polymer and on the chain length. The effective monomer-monomer exduded-volume parameter depends on the balance of repulsion arising due to geometrical exduded volume... 

In the vicinity of the 0 temperature, both x(T) and v(T) vary linearly as a function of relative deviation z= (T-0)/T5 1 from the 0 temperature. The second virial coefficient v can be approximated as v Vqt, where Vo is geometrical (bare) exduded-volume parameter, v—>Vo at T>0. Assuming that the effective chain thickness is on the order of the monomer unit length a, one finds Vo = a. For semiflexible polymers, the second virial coefficient for a statistical segment can be estimated at p = f/fl S 1 as Vp s zi a=za p. ... 

On the other hand, the crossover from dilute to semidilute regime in solutions of randomly branched polymers is strongly affected by size and shape polydispersity. In particular, at moderate concentrations, large dusters are overlapped, whereas the smaller ones still behave as in the dilute regime, penetrate the larger ones, and contribute to screening of the intramolecular exduded-volume repulsions. The concentration effects in semidilute solutions of polydisperse randomly branched polymers were analyzed in detail in Reference 158. 

Solvent also changes the density distribution ftmction of the end-to-end vector r for linear polymer of x rmits (Wx(r)), influendng in this way directly the ring-chain equilibria. In a good solvent, this effect, assodated with the exduded volume, change the power law of the dependence of Kx on the ring size X, making this dependence steeper instead of -2.5 (K x" ) values -2.8 or even -2.9 are observed. ... 

Anisotropic nanopartides in a polymer matrix can be aligned by shear forces that are typical in standard polymer processing methods. Filler orientation also has a significant effect on the percolation threshold in networks of anisotropic partides. The exduded volume of the rodlike partides varies depending on their relative orientations, thereby impacting the percolation threshold. Filler alignment also has a considerable effect on the... 

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