Good solvent domains

SANS Studies of Polymers in Organic Solvents and Supercritical Fluids in the Poor, Theta, and Good Solvent Domains... 

Fig.6 shows that PDMS may tdso enter the good solvent domain at a theta temperature Te = 65 5 C, as observed in PS-CH solutions [21]- However, unlike organic solvents, diis transition can also be made to occur at a critical tiieta pressure (P - 52 4 MPa) in COj, as illustrated in the inset in Fig.6. To our knowledge, this is die first time that the existence of a theta pressure has been demonstrated experimentally and a more detailed description of tilts phenomenon is given in reference [22].

In a good solvent, the end-to-end distance is greater than the 1q value owing to the coil expansion resulting from solvent imbibed into the domain of the polymer. The effect is quantitatively expressed in terms of an expansion factor a defined by the relationship... 

Although the emphasis in these last chapters is certainly on the polymeric solute, the experimental methods described herein also measure the interactions of these solutes with various solvents. Such interactions include the hydration of proteins at one extreme and the exclusion of poor solvents from random coils at the other. In between, good solvents are imbibed into the polymer domain to various degrees to expand coil dimensions. Such quantities as the Flory-Huggins interaction parameter, the 0 temperature, and the coil expansion factor are among the ways such interactions are quantified in the following chapters. 

For high molecular weight polymers in good solvents, fo] exceeds fo]0 because of coil expansion under nondraining conditions that is, as more solvent enters the coil domain than would be present under 0 conditions, Equation (92) continues to apply, with R replacing R2gfi. Using Equation (90) to quantify this expansion effect, we obtain... 

Toluene Swelling. All samples swell substantially when immersed in toluene. It is assumed that toluene, a good solvent for polybutadiene, with a low dielectric constant (e—2.38 at 25°C) is absorbed preferentially in the hydrocarbon polymer phase and excluded from the ionic domains. Swelling is then equivalent to changing the distance between domains. 

Finally, we may say that polymers in solution interact with one another and that this interaction which is observed by osmotic pressure in the dilute concentration domain, in good solvents, is related to the chain size. We shall later examine this relation in detail, and we shall also see that it extends to the semi-dilute regime (see Chapter 13). 

Let us finally remark that the screening length e can be defined even in cross-over domains. In good solvents (Kuhnian chains), the length and the length k = d which measures the distance between Kuhnian chains,... 

Consequently, the shape of the demixtion curve is not simple. Moreover, as we noticed, it seems that two dimensionless parameters (y and z) are needed to characterize the chains in this domain whereas only one dimensionless parameter (z) is sufficient in good solvent. In these conditions, it is not surprising that we still lack good theoretical descriptions of the properties of the system. Of course, various approaches exist but they are not very consistent. 

The distinction between poor and good solvent was introduced in the 1950s by Fox and Flory after experimental studies of the intrinsic viscosity of polymer solutions. These authors recognized that the viscosity varies in relation to the dependence of the chain sizes on temperature the poor solvent state is the state of a solution in which the chains have quasi-Brownian configurations. Systematic experiments have been made in this domain, for instance to determine the Flory temperature, but they have never given very precise results. Physicists are just now beginning to overcome the experimental and theoretical difficulties. Experiments have been made to show the existence of a collapse of the polymer chain, and certain authors have been prone to compare it with the coil-globule transition in proteins. 

We shall assume that this expression remains valid when it is extrapolated to the poor solvent domain. Thus, b 0 for T = TF (34.0 °C) and b < 0 for T < TF. This does not really mean that the true two-body interactions vanish for T = TF and that at T = TF there are only three-body interactions. Actually, the interaction b is a bare interaction but is nevertheless an interaction which is additively renormalized (see Chapter 14, Section 6) and its value depends partly on the true three-body interactions. Incidentally, this remark also applies to good solutions for this reason, if b is measured in good solvent, it is legitimate to extrapolate the result thus obtained to determine the value of b in poor solvent. Thus, in perturbation theory, when the diagram contributions are calculated by dimensional regularization, we may say that b = 0 for T = TF ... 

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