Contraction of the polymer coil

Phenols are well known for their ability to precipitate water-soluble polymers of all kinds - natural, modified-natural (semisynthetic), and purely synthetic. This is shown most markedly by polyhydric phenols such as tannin (tannic acid). As would be expected from the preceding discussion (Section 2), precipitation is foreshadowed at lower cosolute concentrations by contraction of the polymer coil, i.e., a reduction in [tiI. ... 

The chemical structure of a polymer can also cause a contraction of the polymer coil compared to the unperturbed dimensions at theta-conditions. In this case the exponent a of the [ ]]-M-relationship shows values of a<0.5. A contraction of the coil occurs if the attractive intramolecular interactions between the polymer segments become larger than the interactions with the solvent molecules. In extreme cases, the solvent is forced out of the polymer coil and the chain segments start to form compact aggregates. The density of the polymer coil is then independent of the molar mass and the intrinsic viscosity is constant. In this case the exponent a is zero. An example is shown in Fig. 6.12 for compact glycogen in aqueous solution. 

Fig. 6.13. Different solution structure causing an expansion or contraction of the polymer coil in solution compared to the linear, flexible coil in its unperturbed dimensions...

The counterion mechanism of dielectric polarization is also in reasonable agreement with the data collected for DNA in the double-helical state as well as in the coiled denatured form. For the latter, much smaller electric increments and relaxation times are observed, indicating contraction of the polymer upon denaturation. The rotational relaxation time for helices as measured by means of flow birefringence was generally found... 

In this connection it is interesting to recall that Jordan, Kurucsev and Darskus 14) have interpreted the discontinuity observed in the physico-chemical properties of poly(4-vinyl-pyridine) in aqueous solution at around a 0.15 by assuming that at a lower charge density the contraction of the polymer to well below the expected size for a randomly coiled chain may be due to hydrophobic interactions. 

The streamlines of a converging flow field is shown in Fig. 6. In the contraction flow, the polymer coil may not have sufficient time to extend fully. The jet may reach very high speed to create cmitract flow. This technique was widely studied by Nguyen and Kausch [105-113]. 

It has been demonstrated that the excimer emission intensity from chromophores incorporated into the vinyl polymer chain have been correlated with a change in the effective volume of random polymer coil in solution, and the volume of random polymer coil was correlated with viscosity, which is dependent on temperature. But a temperature change of a polymer solution does not always lead to expansion or contraction of the chain coil it can cause conformation change to a more or less packed polymer chain and to a more or less excimer forming conformation. Both of these structural changes in a polymer chain can affect the fluorescence, but each polymer needs to be considered individually. 

The intrinsic viscosity [r ] of a polymer increases with rising solvent quality (see Solvent in Chap. 5) due to the increased solvating envelope of the polymer chain. An increased effective volume of the chain leads to an expansion of the polymer coil and therefore to an increased intrinsic viscosity (see Fig. 5.2). The solvent quality can also be seen in the exponent a of the [q]-M-relationship. In the case that the interactions of the solvent molecules with the chain are so small that the coil is not contracted or expanded, theta-conditions are reached and the coil has its unperturbed dimensions in solution. A theta solvent is referred to as a thermodynamically poor solvent. In this solution state a theoretical value for the exponent a=0.5 can be derived (the required Eqs. 8.22 and 8.33 are discussed in detail in A deeper insight into in Chap. 8). This value of a=0.5 is also experimentally observed as shown in Fig. 6.7 for the theta system poIy(styrene) in cyclohexane (T=34.5 C). 

The solution properties of polyelectrolytes in general are markedly different from those of polyelectrolyte solutions with added salts. These differences are very strikingly revealed in their viscometric behaviors. Viscosity, as pointed out in the previous section, is related to the size of polymer molecules and therefore is affected by molecular expansion. When a small amount of a simple salt, such as sodium chloride, is added to a dilute polyelectrolyte solution, the ionic strength of the solution outside of the polymer coil is increased relative to the strength of the solution inside of the coil. Consequently, some of the mobile electrolyte diffuses into the polyion coil and the thickness of the ionic atmosphere around the polymer chain is reduced. This effect produces a significant contraction of the polyion coil and is reflected in decreased values of the viscosity. 

Measurements have been made of the size of the polymer coil in miscible blends, ° using neutron scattering. Some have observed expanded coils and others contracted coils. It has been suggested that this should depend on whether the polymer is glassy or rubbery, i.e., the chain flexibility. The results are not consistent but a definitive set of experiments remains to be done. Studies on PVC show the dominant effect that the small crystalline part of this polymer can play in scattering from its blends. The crystalline regions do not mix with the other polymer and this could greatly affect the properties of PVC blends. 

At the beginning of this section we enumerated four ways in which actual polymer molecules deviate from the model for perfectly flexible chains. The three sources of deviation which we have discussed so far all lead to the prediction of larger coil dimensions than would be the case for perfect flexibility. The fourth source of discrepancy, solvent interaction, can have either an expansion or a contraction effect on the coil dimensions. To see how this comes about, we consider enclosing the spherical domain occupied by the polymer molecule by a hypothetical boundary as indicated by the broken line in Fig. 1.9. Only a portion of this domain is actually occupied by chain segments, and the remaining sites are occupied by solvent molecules which we have assumed to be totally indifferent as far as coil dimensions are concerned. The region enclosed by this hypothetical boundary may be viewed as a solution, an we next consider the tendency of solvent molecules to cross in or out of the domain of the polymer molecule. 

Our primary interest in the Flory-Krigbaum theory is in the conclusion that the second virial coefficient and the excluded volume depend on solvent-solute interactions and not exclusively on the size of the polymer molecule itself. It is entirely reasonable that this should be the case in light of the discussion in Sec. 1.11 on the expansion or contraction of the coil depending on the solvent. The present discussion incorporates these ideas into a consideration of solution nonideality. 

A plausible assumption would be to suppose that the molecular coil starts to deform only if the fluid strain rate (s) is higher than the critical strain rate for the coil-to-stretch transition (ecs). From the strain rate distribution function (Fig. 59), it is possible to calculate the maximum strain (kmax) accumulated by the polymer coil in case of an affine deformation with the fluid element (efl = vsc/vcs v0/vcs). The values obtained at the onset of degradation at v0 35 m - s-1, actually go in a direction opposite to expectation. With the abrupt contraction configuration, kmax decreases from 19 with r0 = 0.0175 cm to 8.7 with r0 = 0.050 cm. Values of kmax are even lower with the conical nozzles (r0 = 0.025 cm), varying from 3.3 with the 14° inlet to a mere 1.6 with the 5° inlet. In any case, the values obtained are lower than the maximum stretch ratio for the 106 PS which is 40. It is then physically impossible for the chains to become fully stretched in this type of flow. 

Theta conditions are of great theoretical interest because the diameter of the polymer chain random coil in solution is thenequal to the diameter it would have in the amorphous bulk polymer at the same temperature. The solvent neither expands nor contracts the macromolecule, which is said to be in its unperturbed state. The theta solution allows the experimenter to obtain polymer molecules which are unperturbed by solvent but separated from each other far enough not to be entangled. Theta solutions are not normally used for molecular weight measurements, because they are on the verge of precipitation. The excluded volume vanishes under theta conditions, along with the second virial coelTicient. 

Under theta conditions the polymer coil is not expanded (or contracted) by the solvent and is said to be in its unperturbed state. The radius of gyration of such a macromolecule is shown in Section 4.4.1 to be proportional to the square root of the number of bonds in the main polymer chain. That is to say, if M is the polymer molecular weight and A/q is the formula weight of its repeating unit, then... 

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