Fox-Flory relation

Of course, the observed behavior could result from some combination of these effects. The first possibility given above cannot be expected to explain the observed effect alone unless the BBB chain behaves in a far different way than other linear polymers for which v does not exceed ca. 0.80 6,7). Calculation of the Stokes diameter D8 from the data for [77], and M in Table I yields values of the order 5 A., which seems too low to be meaningful. Calculation of < from the Fox-Flory relation (13)... 

Intrinsic viscosity is related to the linear size of the coil R and the molar mass M by the Fox-Flory equation ... 

Polymer-solvent interactions have been examined by viscometric studies of polymer-solvent-non-solvent mixtures in dilute solution84 86). The Fox-Flory model which relates the molecular parameters of the unperturbed dimension and the linear expansion coefficient to the total sorption parameter has been used. The latter can be obtained by the simultaneous solution of several Equations when the intrinsic viscosities of the mixtures are known. This method is in an early stage of development and pro-... 

The Flory-Fox equation relates the number average molecular weight Mn to the glass transition temperature Tg of a polymer as (40)... 

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,... 

The Fox-Flory equation (Eq. 8.33) in combination with the square root relation of the molar mass (Eq. 8.22) and the calculation of the radius of gyration from the end-to-end distance (Eq. 8.14) allows for a derivation of the [/j]-M-relationship for theta conditions ... 

The thermodynamic linear expansion factor has been related to Flory or thermodynamic interaction parameter, %, and the entropy of dilution parameter, Xs, through the Flory-Fox [10] equations. 

Although in the discussion presented above we assumed, either explicitly or implicitly, the existence of a parallel relationship between [> ] and for interrupted helices, no definitive answer to the validity of this assumption is as yet known. As is well known (40), the [q] and of randomly coiled macromolecules are fairly accurately related to each other by the Flory-Fox empirical equation... 

In GPC, the product [77] M, (or the hydrodynamic radius Re) has been widely accepted as a universal calibration parameter. In the Ptitsyn-Eizner modification of the Flory-Fox equation the quantity 4>, which relates the dimensional parameters to the above product, is taken as a variable. The value of < depends upon molecular expansion in solution as represented by a function f(e). Because of this dependence polymeric species having the same [77] M value cannot have the same statistical dimensions (radius of gyration or end-to-end distance) unless they have the same e value. Thus, if [77] M is a universal calibration parameter, the statistical parameters cannot be used as such. A method is presented for obtaining the Mw/Mn ratio from GPC data even though universal calibration is used. 

The ratio (Re/R)3 = (I)3 is thus implicit in the value of in the Flory-Fox equation and has a value of 0.49, corresponding to the Flory-Fox value of 2.1 X 1023. It is clear from Equations 1, 2, and 3 that [77] M cannot be related to the statistical polymer dimensions h and R without a knowledge of , i.e., < , which varies with solvent for a given polymer. It follows, that if all species having the same [77] M elute together from the GPC columns, then only Re can be the universal parameter, since will not be the same for all solute-solvent pairs and h and R will not be equally correct for universal calibration. 

Fox, T. G., and P. J. Flory Second-order transition temperatures and related properties of polystyrene. I. Influence of molecular weight. J. Appl. Phys. 21, 581 (1950). 

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. 

The effect definitely depends on the use of Eq. (58) instead of the Flory-Fox relation, Eq. (9). The value of K obtained in a mixed and quite polar theta-solvent (see Table 13 in the Appendix) is very close to that for acetone. 

Le rapport de rjjij, est certainement trfes different pour des homo-polymeres de masse moleculaire, M, elevee. En effet, on sait que la viscosite de cisaillement de ces corps varie selon la relation = f[T) M3>4, ou f(T) ne depend que de T (Fox et al., 1956). D autre part, comme la temperature de transition vitreuse des polym res lineaires est pratique-ment independante de M, si la chaine comporte plus d une centaine d uni-tes monom res (Fox et Flory, 1950 Beevers et White, 1960), il... 

In the first case, characteristic viscosity of the fraction, r ], with the known molecular mass in ideal -solvent was measured. This method is based on the known Flory-Fox relation [38], The second method represents measurements of the fraction [r ] in good thermodynamic solvents and extrapolation of experimental data in accordance with the known techniques [39 - 41], Because in the cur-rent work [36] all measurements were performed in good thermodynamic solvent, unperturbed di-mensions of macromolecules, , were determined by graphical extrapolation in accordance with the Shtockmayer-Fixman, suggested by the authors for flexible macromolecules, in [t ] M1/2-M12 coordinates (Figure 6). 

In the various theoretical attempts to explain the relation between [77] and the molar mass M, a relation derived by Flory and Fox for random coil molecules is often applied to interpret viscometric measurements for even more general polymer structures. Although applicable to a broader range of polymers than the MHS equation, the Flory-Fox relation has its own shortcomings. Nevertheless, its frequent use and good correlation with experimental data over a... 

In 1950, Fox and Flory (1950) observed that the Tg of homopolymers such as glucose polymers was related to their molecular weight (AL). The value for Tg was reported to decrease linearly with the increase in M. 

Equations that relate T to the presence of plasticizers, organic liquids, and monomerf in polymers have been proposed by a number of Investigators. Among the first was the equation proposed by Fox and Flory In 1954 (19) ... 

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. 

A polymer molecule moving in a dilute solution undergoes frictional interactions with solvent molecules due to its motion relative to the surrounding medium. The effects of these frictional interactions are related t6 the size and shape of the polymer molecule. Thus, the chain dimensions of polymer molecules can be evaluated from measurements of their frictional properties (Flory and Fox, 1950). 

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