Floiy

P. J. Floiy and M. Gordon, Advances in Polymer Science Series, Vol. 59, Spdngei-Vedag, New Yoik, 1984, p. 1. 

This equation is not particularly useful in practice, since it is difficult to quantify the relationship between concentration and ac tivity. The Floiy-Huggins theory does not work well with the cross-linked semi-ciystaUine polymers that comprise an important class of pervaporation membranes. Neel (in Noble and Stern, op. cit., pp. 169-176) reviews modifications of the Stefan-Maxwell approach and other equations of state appropriate for the process. 

The classical size-independent combinations are the Floiy parameters that combine the intrinsic viscosity, [rj], and the radius of gyration, Rg. 

The conformation of atactic polymers, with any value of the m/r ratio, must be treated as that of a copolymer, wherein the monomer unit statistics are compounded with those of the rotational states. In this case we may either refer to Monte-Carlo type procedures, as done by Floiy, Mark, and Abe (194), or to the pseudostereochemical equilibrium method used by Allegra (195) and Briick-ner (196). In the latter case the atactic polymer is formally considered as a homopolymer that may assume the conformations of either the m or r dyads, with suitable adjusted statistical weights. 

Floiy, P. J. Principles of Polymer Chemistry Cornell University Press Ithaca, 1953. 

Floiy (155) and other American writers use the opposite convention making 8 = 0° for the trans or anti conformation. As a result the numerical values of the torsion angles reported here are often different from those reported in the original literature. Differences are found in the formulas involving trigonometrical functions and in the appearance of energy maps. Specific conventions are used for vinyl polymers. 

Interaction parameter, employed in the Floiy-Huggins theory, to account for the contribution of the noncombinatorial entropy of mixing and the enthalpy of mixing to the Gibbs energy of mixing. 

The theory of Miller and Floiy is certainly more realistic than those based on Nagai s model. The latter ought to overestimate chain dimensions, but the inaccuracy will become less serious as the chain gets more helical. Further, as... 

Clark, A.H. (2000). Direct analysis of experimental tie line data (two polymer-one solvent systems) using Floiy-Huggins theory. Carbohydrate Polymers, 42, 337-351. 

The effect of intermolecular interactions is characterized by the Floiy-Huggins interaction parameter. For the polymer brush with 400 bonds, three values of the interaction parameter were selected in the calculations and the segment density profiles are plotted in Fig. 9. x 0 corresponds to a good solvent and x 0.5 to a poor one. With increasing value of x, the height of the polymer bmsb decreases. For the poor solvent ( =0.5), the chant segments tend to be more uniformly distributed (curve 3). 

In the present calculations, the interaction parameter (x or x") is the only undetermined parameter. For the PI chains-toluene interactions, x is selected 0.35, which is close to the experimental values of the Floiy-Huggins interaction parameter45 OfFH=0.32—0.36 in the concentration range temperature range 25-55 °C). For the PS chains-toluene interactions, x is taken 0.2, which is in the lower range of the experimental Floiy-Huggins interaction parameters45 (a,fh=0.04-0.67 in the concentration... 

Figure 9 shows the application of this method to the viscosity data of poly(ethyl methacrylate) obtained by Chinai and Samuels (61), where the black circles represent the theta-solvent data and the white circles represent the good-solvent data. The lines have a common intercept, leading to a single value of K independent of solvent, in contrast to the Floiy-Fox-Schaefgen plot for the same data which was shown in Fig. 1. The value of K obtained from the intercept in Fig. 9 is (49 3) 10-5, which is a little higher than the simple mean of the observed [ ]e/M ,7, values, i. e. 47.3 10-s, reflecting the very small negative slope of the best fit line for the theta solvent results. Such a...

In this connection, an interesting feature of the Floiy theory may be noted. Multiplying both sides of Eq. (25) by a2 gives... 

P. Floiy, Statistical mechanics of chain molecules, Moscow (1971) (in Russian). 

FIGURE 10-63 Schematic plot of glass transition temperature versus reciprocal molecular weight (redrawn from the data of T. G. Fox and P. J. Floiy, J. Appl Phys., 21,581 (1950)1. 

The model used (independently) by Floiy and Huggins (following an earlier suggestion by Fowler and Guggenheim) assumes a large molecule such as a polymer can be treated as a set of linked segments. Each of these segments is not necessarily equal in size to the chemical repeat unit, but defined to have a molar volume equal to that of the solvent. 

Because of these difficulties, there are various levels of approximation that have been used. The simplest result, and one that Floiy... 

Now let s look at our expressions for the entropy of mixing in more detail. We have two, one from so-called regular solution theory (Equation 11-12) and the other from the theories of Floiy and Huggins (Equation 11-13). Both have the same form and tell us that the entropy change upon mixing is positive—hence favorable (remember that the log of a fraction is a negative number). 

Huggins independently and almost simultaneously obtained a more rigorous equation for the free energy, but it is this simpler Flory expression that is most often used and which is known as the Floiy-Huggins equation. 

If we consider polymer solutions, where there is a very large mismatch in the size of the components, then we find the critical point at low polymer concentrations, as shown in some experimental data (Figure 11-23. In the Floiy-Huggins theory the con-... 

This should be a simple question, but for some reason many students erase all knowledge of the rules of differentiation as soon as they complete their last calculus class Simply derive the following equation for the chemical potential of the solvent in a polymer solution from the Floiy-Huggins equation ... 

You may recall that the temperature where % 2is what Floiy called the theta tern--perature and can now be seen to describe the situation where the second virial coefficient becomes zero (Figure 12-10). This means that at this point pair-wise interactions cancel and the chain becomes nearly ideal, as we discussed in the section on dilute solutions (Chapter 11), where we referred to the Floiy excluded volume model in which the chain expansion factor is given by Equation 12-18 ... 

Osmotic pressure of polymer solutions was discussed in detail in Section 10.3.3 because it is important to steric stabilization. The final result of that development presented here for completeness. The osmotic pressure of a polymer solution determined fiiom the Floiy-Huggins theory [22] and is given by... 

In the concentrated and marginal regimes of fig 5,3 a mean-field description, which neglects any spatial fluctuations, is appropriate. In these regimes, the solution is homogeneous and there is no chain-length dependence. Neither does the persistence p of the chains play a role since the Floiy-Huggins expressions do not contain the chain flexibility. This is so because the flexibility is assumed to be the same in the solution and in the reference state, so that p cancels in the entropy difference between the two states. 

Exactly as In lattice models, the walks are assumed to take place In a (self-consistent) field Ulz), which depends on the concentration profile

relation between U[z) and (p[z) one may use the Floiy-Hugglns theory usually in an expanded form, but other models, such as a generalized Van der Waals equation of state ) can also be taken. The most general expression for the self-consistent mean field U z) has been given by Hong and Noolandl K It has been shown ) that this expression is the continuum analogue of the lattice version of Scheutjens and Fleer, to be discussed in sec. 5.5. 

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