Krigbaum

We shall devote a considerable portion of this chapter to discussing the thermodynamics of mixing according to the Flory-Huggins theory. Other important concepts we discuss in less detail include the cohesive energy density, the Flory-Krigbaum theory, and a brief look at charged polymers. 

To apply these ideas to solution nonideality, we consider a theory developed by Flory and Krigbaum. This is only one of several approaches to the problem, but it is one which can be readily outlined in terms of material we have already developed. We shall only sketch the highlights of the Flory-Krigbaum theory, since the details are complicated and might actually obscure the principal ideas. 

The objective of the Flory-Krigbaum theory is to find a quantitative expression for the placement probability n(d) of the two coils as a function of their separation d. There are three stages to the derivation ... 

The full Flory-Krigbaum theory results in the following expression for the excluded volume ... 

The complicated form of the final result makes it clear why we have skipped over the details of the Flory-Krigbaum derivation ... 

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. 

Figure 8.13 n/c2 versus C2 for polyiosbutylene in benzene at the temperatures shown. [Reprinted with permission from W. R. Krigbaum and P. J. Flory,/. Am. Chem. Soc. 75 5254 (1953), copyright 1953 by the American Chemical Society.]... 

Figure 10.8 Light-scattering data plotted to give slope-intercept values which can be interpreted in terms of M and B. (a) Polystyrene in methyl ethyl ketone. [From B. A. Brice, M. Halwer, and R. Speiser,/. Opt. Soc. Am. 40 768 (1950), used with permission.] (b) Polystyrene in cyclohexane at temperatures indicated. Units of ordinates are given in Example 10.4. [Reprinted with permission from W. R. Krigbaum and D. K. Carpenter,7. Phys. Chem. 59 1166 (1955), copyright 1955 by the American Chemical Society.]...

A. Cifferi, W. R. Krigbaum,and R. B. Meyer (eds.), Polymer Liquid Crystals, Academic Press, New York (1982). 

Intrinsic viscosity measurements revealed a conformational transition upon heating from 26 to 40 °C, while the UV absorbance of the solution was insensitive to the change. The entropy parameters for PA were also discussed in light of the Flory-Krigbaum correlation between the second virial coefficient and theta temper-... 

A more realistic model of this solution was developed in 1950 by Rory and Krigbaum, and assumes that the polymer consists of approximately spherical clusters of segments. These clusters have a maximum density of segments at their centre and this density decreases with distance from the centre in an approximately Gaussian distribution. 

The approach of Rory and Krigbaum was to consider an excess (E) chemical potential that exists arising from the non-ideality of the polymer solution. Then ... 

This involves the Flory-Huggins parameter x and hence assumes the same limitation as the rest of the Flory-Huggins approach, i.e. a moderately concentrated solution. Flory and Krigbaum rewrote this equation in terms of some other parameters, i.e. 

In a sufficiently poor solvent at a given temperature, the condition where a = 1 can be achieved, and the chain attains its unperturbed dimensions. This turns out to be the 6 temperature of Rory and Krigbaum previously described in Section 5.5 of this chapter. 

In 1933, Bernal and Crowfoot [1] reported on the solid state polymorphism of p-azoxyanisole. They found two crystalline modifications of this compound, a stable yellow form and an unstable white polymorph. Krigbaum et al. [31 reexamined the crystal structure of the stable yellow form. The compound shows an imbricated structure which is the basic packing required for nematic behaviour according to Gray [132]. 

Fig. 38.—Plots of w/c against c for a series of polyisobutylene fractions M =38,000 to 720,000) in cyclohexane ( ) and in benzene (O), both at 30°C. The osmotic pressure tz is expressed in g./cm. and c in g./lOO cc. Curves have been calculated according to Eq. (13). (Krigbaum. )...

Fig. 40.—Plots of y/ /c against c according to the method of Berglund. The data are those of Krigbaum, for polyisobutylene fractions in cyclohexane ( ) and in benzene (O) previously shown in Fig. 38. Units are the same as there given.

Fig. 117.—Log (RTA2) for polyisobutylene fractions in cyclohexane at 30°C plotted against log M. The filled circles represent the initial slopes RTA2) of the curves shown in Fig. 38. The open circles are from earlier results on the same system. Dashed line calculated as described in text. (Krigbaum ).

Fig. 118.—Plot of log (RTA2) against log M for polystyrene fractions in toluene. Filled circles represent slopes of the curves shown in Fig. 116. Open circles are from the results of Frank and Mark. i Dashed line calculated as described in text. (Krigbaum.29)...

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