Flory relation

A somewhat similar equation has been given by Ptitsyn (219) on the basis of related arguments, and the deviations from the Flory relation are in the same direction. Thus there seems to be general agreement that some modification in the Flory expression for the long-range interaction effects on chain dimensions is needed. 

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)... 

In dilute solutions the polymer molecule is coiled and swollen (water is a good solvent for PEO). The radius of gyration of a flexible neutral chain in good solvent is given by Flory relation [219,220] ... 

For example. If the well-known Flory relation (16) Is assumed and the Intrinsic and reduced viscosities are considered comparable at low concentrations, then the solution viscosity may be roughly approximated by... 

The values for xanthan gum were also reported in an earlier work (7). The molecular sizes were obtained by using the Flory relation (8). There are alternate discussions as to what the configuration and the size of xanthan gum molecules in solution are. Whitcomb, Ek, and Macosko have presented an interpretation of the intrinsic viscosity data assuming a cylindrical rod conformation (9). The K-j and a values for Pusher are given by Lynch and Mac-Williams (10). It should be noted that a range of Kj and a values for polyacrylamides can be found in the literature (11). 

As the reported values of the thermodynamic parameters indicate, the largest pool of data is based on the Huggins-Flory relation. This is only to be expected since the theory and related to it concept of the binary interaction parameters, either B or was introduced to polymer science more than a half century ago, in 1941 to be precise. Even their well-recognized complexity of functional dependence, viz. B = B(T, P, ( ), MW, MWD, molecular stmcmre, stresses,...), does not discourage efforts to continue using this approach against all odds. 

It is customary to discuss blend miscibility starting with the Huggins-Flory relation [1] ... 

With the establishment of the characteristics of the fusion process of random copolymers the melting temperature-composition relation of such copolymers can be examined. To analyze the problem distinction must again be made as to whether the crystalline phase is pure or if the B units enter the crystallite, either on an equilibrium basis or as a defect. Merely establishing the liquidus is not sufficient to resolve this problem. The Flory relation is only applicable to an ideal system whose crystalline phase is pure. Deviations from this relation can be due to lack of ideality, with either the raising or lowering of the expected equilibrium melting temperature. On the other hand the B units can be entering the lattice. This... 

The Flory relation, for random sequence distribution, then becomes... 

In this section and the last, we have examined the lattice model of the Flory-Huggins theory for general expressions relating AHj and ASj to the composition of the mixture. The separate components can therefore be put together to give an expression for AGj as a function of temperature and composition ... 

More fundamental treatments of polymer solubihty go back to the lattice theory developed independentiy and almost simultaneously by Flory (13) and Huggins (14) in 1942. By imagining the solvent molecules and polymer chain segments to be distributed on a lattice, they statistically evaluated the entropy of solution. The enthalpy of solution was characterized by the Flory-Huggins interaction parameter, which is related to solubihty parameters by equation 5. For high molecular weight polymers in monomeric solvents, the Flory-Huggins solubihty criterion is X A 0.5. 

In Fig. 21(a) we plot the variation of R with increasing system density Cobs 3.nd, for comparison, also give the respective change for a system of moving medium (dynamic host matrix) of equal density. This result is in good agreement with recent predictions [89]. If one defines an effective Flory exponent from the scaling relation Rg oc it is then evident from... 

However, Szabo-Rethy293) showed that Flory s assumption leads to wrong values of rate constants and that the error can be as high as 15 to 35%. This author gave a method of calculation which takes into account the elimination of water. Similar relations have been used recently by Lin and Hsieh270) but in our opinion erroneously. 

In several works published after Flory (e.g. Tang and Yao7)) elimination of water is not taken into account either in the calculation of the conversion or in the general kinetic relation. However, these two approximations cancel each other and the final relation is correct. 

The global rate of the process is r = rj + r2. Of all the authors who studied the whole reaction only Fang et al.15 took into account the changes in dielectric constant and in viscosity and the contribution of hydrolysis. Flory s results fit very well with the relation obtained by integration of the rate equation. However, this relation contains parameters of which apparently only 3 are determined experimentally independent of the kinetic study. The other parameters are adjusted in order to obtain a straight line. Such a method obviously makes the linearization easier. 

In the Flory-Huggins picture, the interchain interaction parameter should be related to the intersegment interaction parameter by... 

There Is a large body of experimental literature relating to polymer fractionation In liquid-liquid equilibria. In addition, numerous authors have analyzed polymer fractionation using Flory-Huggins theory. We have considered use of the corresponding states theory to model polymer fractionation for the ethylene/ polyethylene system at reactor conditions (18). Results of the... 

Find the standard deviation of the Flory distribution as given by Equation (13.26) and relate it to the polydispersity. Extend the calculations in Problem 13.5 to /X3. Find the kurtosis of the distribution in the limit of high conversion. 

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. 

Cations can be seen as acting as ionic crosslinks between polyanion chains. Although this may appear a naive concept, crosslinking can be seen as equivalent to attractions between polyions resulting from the fluctuation of the counterion distribution (Section 4.2.13). Moreover, it relates to the classical theory of gelation associated with Flory (1953). Divalent cations (Zn and Ca +) have the potential to link two polyanion chains. Of course, unlike covalent crosslinks, ionic links are easily broken and re-formed under stress there could therefore be chain slipping and this may explain the plastic nature of zinc polycarboxylate cement. 

Further disagreement with the Flory theory is found in the magnitude of 2Cj and 2Cj + 2C2 in Figure 1. These results are quantified In terms of the structure factors A and A2. Aj and A2 relate the small and large-strain moduli to the number of... 

The above phenomenon is due to the pronounced polydispersity of these products in their chemical size l described by the Flory exponential distribution. Because the composition of each macromolecule of the sample under investigation is unambiguously related to its degree of polymerization l, the Flory distribution for l in a polymer sample is responsible for its significant composition inhomogeneity. 

An important source of experimental and theoretical studies of equilibria in ring formation is represented by the field of so-called macrocyclisation equilibria (Flory, 1969). Interest in this field appears to have been restricted so far to chemists conventionally labelled as polymer chemists. Experimental evidence of cyclic oligomer populations of ring-chain equilibrates such as those obtained in polysiloxanes (Brown and Slusarczuk, 1965) may be delated to the statistical conformation of the corresponding open-chain molecules (Jacobson and Stockmayer, 1950 Flory, 1969). In these studies experimental results are expressed in terms of molar cyclisation equilibrium constants Kx (14) related to the x-meric cyclic species Mx in equilibrium with the... 

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