The Fox-Flory Theory

The exponent v is a measure for the solvent quality or the solution structure and is correlated to the exponent a of the [q]-M-relationship (see Table 6.6 and The Fox-Flory theory below) ... 

A theoretical approach for the determination of a I Q-M-relationships is possible from the viscosimetry, if vis calculated from the exponent a of the [q]-M-rela-tionship according to Eq. (8.26) and the constant Krq according to the Fox-Flory theory via Eq. (8.42) from the constant K[j y... 

The importance of viscosimetry as an independent area in the field of polymer analytics becomes clear through the Nobel prices awarded for two works in this area. The name of the 1953 honored Prof. Hermann Staudinger for his proof of the existence of polymers is still used in viscosimetry in the intrinsic viscosity (German "Staudingerindex ) (see "Intrinsic viscosimetry in Chap. 4). In 1974, Prof. Paul J. Flory was honored with the Nobel price for his groundbreaking works on the conformation of polymers in solution and his name is conserved for posterity in the Flory constant (see "The Fox-Flory theory in Chap. 8). 

In summarizing the intrinsic viscosity relations presented in this section, it must be admitted that they represent nothing more than rather small semi-empirical refinements of the Flory excluded volume theory and the Flory-Fox viscosity theory. For a large fraction of the existing body of experimental data, they offer merely a slight improvement in curve-fitting. But for polymers in good solvents it is believed that a more transcendental result has been achieved. The new equations permit more reliable assessment of unperturbed chain dimensions in such cases, and in some instances (e. g., certain cellulose derivatives see Section III B) they offer possible explanations of heretofore paradoxical solution behavior. 

Based on the Kirkwood-Riseman theory, if polymer chains are nondraining, it follows [Kirkwood and Riseman, 1948 Auer and Gardner, 1955] that intrinsic viscosity data can be related to the radius of gyration, Rg, of flexible polymers. This can be expressed in an equation of the form [Flory and Fox, 1951]... 

Over the past 30 years a number of theories have been developed to account for the variation in the glass transition temperature (Tg) of polymeric materials as a function of molecular weight (MW). Three of the most notable of these approaches have included the straight line technique of Fox and Flory and the statistical mechanical theories of Gibbs and Gibbs-DiMarzio (G-DM). Because of the universal applicability claimed for the latter approach, the G-DM theory has received considerable attention. " ... 

Fig. 5. Scatter diagram for PS using the G-DM theory with n = 1.80 and r 1.05 A, Enns et al. A, Fox and Flory andu Glandt et al. on blends A, Krause and Iskan-...

From these findings, the free volume theory shows that between atoms and molecules there is nothing but free volume. The free volume was first defined by Fox and Flory at temperatures above the transition temperature as the specific volume above the transition temperature minus the solid specific volume extrapolated to the same temperature above the transition temperature. This early definition implies that the free volume at... 

Theory must account for these properties of fluids, their temperature dependence, the glass transition, and the properties of the amorphous solid. The two most widely accepted theories are the entropy theory, as formulated by Gibbs and Di Marzio (1958), Gibbs (1960), and Adam and Gibbs (1965), and the free-volume theory as developed by Eyring (1936), Fox and Flory (1950), Williams, Landel and Ferry (1955), Cohen and Turnbull (1959), and Turnbull and Cohen (1961, 1970). 

After the Krikwood-Riseman theory [12], there are many theories that have been developed by other researchers, such as the dependence of intrinsic viscosity on molecular weight by Flory and Fox [13,7], and by Yu and Stockmayer [14],... 

Flory-Fox theory (or Fox-Flory) n. This theory is relates viscosity to molecular dimensions by treating the polymer molecule as a hydrodynamic sphere. In a 0-solvent in which the molecular coU is compact, these authors write the intrinsic viscosity as,... 

Fig. 143.—The intrinsic viscosity of a polyisobutylene fraction of high molecular weight plotted against temperature in four solvents cyclohexane, diisobutylene (DIB), toluene and benzene. The lines shown have been calculated according to theory. (Fox and Flory. )...

Meyerhoff (182)] but also in the short-chain region [Marzolph and Schulz (176)]. The decrease in the slope of the double-logarithmic plot at low molecular weights is naturally and faithfully reproduced. This would be equally true of the Flory-Fox theory, as represented by Eqs. (5) to (8). There seems to be absolutely no evidence for partial draining of the solvent through the polymer coils, such as would be predicted by the theories of Brinkman (45 ), Debye and Bueche (79), Kirkwood and... 

Cohen and Turnbull [87] generalized somewhat the theoretical concepts of the relationship between diffusion and self-diffusion of liquids modelled by assemblies of rigid spheres and obtained on the basis of the theories of Frenkel and Eyring, Fox and Flory [88] and Williams, Landell and Ferry [89] the equation ... 

Before becoming too optimistic about the possibility of evaluatii unperturbed macroion dimensions from the procedure outlined above, we must recall two serious objections advancal by Flory 49), First of all. extrapolations of intrinsic viscosity data for the graphical evaluation of K, as required by equations (2) and (3), as well as by the equation of Flory and Fox [50), are extrapolations into a region in which approximate theories of pol5nner solutions are no longer tenable. Secondly, Flory indicates that there is at least one case which clearly shows that the application of equation (3) leads to physically irrational conclusions, namely the case of hydroxyethylcellulose in aqueous solution. Flory s original paper must be consulted for a clearer appreciation of the two important objections indicated above. The first objection is of basic importance and it is perhaps worthwhile to digress briefly and to try... 

Fig. 4 Molecular weight dependences of and T of the monodisperse PS, which were determined by DSC and LFM, respectively. The arrow beside the ordinate shows the room temperature. The dotted curve 2 traces the T variations with M as deduced by Mayes scaling theory. The dashed curve 1 is drawn on the basis of the empirical equation established by Fox and Flory. The solid curve is drawn in the context of the power law analysis...

The relationship, based on Flory-Fox theory, can be used also for branched polymer characteristic [5] ... 

The 3.4 power law for melt viscosity, eq 5.1, is of surprising generality, well compared to the Houwink-Mark-Sakurada relation for intrinsic viscosity. Thus its derivation by molecular theory has been one of the central themes in polymer physics since it was proposed in 1951 by Fox tind Flory [63]. Despite many efforts no real success has as yet been achieved. The reader is advised to consult Graessley s review [64] in 1974 concerning the earlier theories. 

When a size-exclusion chromatograph is calibrated correctly, one can know the molecular weight of a polymer just based on the time it takes to pass, or elute through the column. From Fox and Flory s theory of solution viscosity one can learn that the size of a solvated macromolecular coil is directly correlated with its solution viscosity. The correlation is ... 

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