Flory equation

Povodyrev et aJ [30] have applied crossover theory to the Flory equation ( section A2.5.4.1) for polymer solutions for various values of N, the number of monomer units in the polymer chain, obtaining the coexistence curve and values of the coefficient p jj-from the slope of that curve. Figure A2.5.27 shows their comparison between classical and crossover values of p j-j for A = 1, which is of course just the simple mixture. As seen in this figure, the crossover to classical behaviour is not complete until far below the critical temperature. 

The olefin distribution in the catalytic processes, on the other hand, tends to foUow the Schultz-Flory equation, where equals the number of moles of olefins having carbon number N, X equals the moles of olefins having two carbon numbers lower, andis a constant depending on the reaction conditions can range from 0.4—0.9 but usually equals 0.6—0.8. 

The production of hydrocarbons using traditional Fischer-Tropsch catalysts is governed by chain growth or polymerization kinetics. The equation describing the production of hydrocarbons, commonly referred to as the Anderson-Schulz-Flory equation, is ... 

These researchers have pointed out that the basic principles of polymer physics apply to tackified elastomers, such as natural rubber. Thus the Tg relationship provided by the Fox-Flory equation applies ... 

Both extrapolated lines meet on the A axis at the same point, and this corresponds to 1/M. Other solution properties of the polymer may also be determined once the Zimm plot has been prepared. Along the line of 0 = 0, A = 1/M (1 + 2T2 c +. ..). Hence the slope of this line is 2T2/M, from which r of the Flory equation may be evaluated. 

The data show that calcium chloride is 20 times more effective on a concentration basis in compacting hydrolyzed copolymers than is sodium chloride. Radii of gyration shown in Table 4 are calculated with the Flory equation,... 

The product distribution frcm the Fischer-Tropsch reaction on 5 is shown in Table I. It is similar but not identical to that obtained over other cobalt catalysts (18-21,48, 49). The relatively low amount of methane production (73 mol T when compared with other metals and the abnormally low amount of ethane are typical (6). The distribution of hydrocarbons over other cobalt catalysts has been found to fit the Schulz-Flory equation [indicative of a polymerization-type process (6)]. The Schulz-Flory equation in logarithmic form is... 

Schrock alkylidyne catalysts, 26 948-949 Schrodinger s equation, 16 734-735 Schultz-Flory distribution, 20 156 Schultz-Flory equation, 17 714 Schulze—Hardy rule, 7 289, 10 121 Schweizer, M. E., 11 248 Schwenzfeier process, 3 641 Science... 

Much easier, and with higher precision, on-line intrinsic viscosity measurements are possible. Unfortunately, new problems arise from the insufficiently well known interdependence between g and g. The relationship between the intrinsic viscosity and the radius of gyration is fairly well settled for linear chains [3,71] and is satisfactorily described by the Fox-Flory equation (Eq. 21), but for the branched chains the 0-factor for branched chains may be different. In general one has [49]... 

When is the Flory equation similar to the Mark-Houwink equation ... 

The relationship between Tg and molecular weight, M, is often described by the Fox and Flory equation 266 Tg = T/XJ - K/M, where T/XJ is the glass transition temperature of the polymer with infinite molecular weight and K is a constant characteristic of the polymer. For the malto-oligomer series, a double reciprocal plot of... 

Flory polymerization kinetics (4). Henrici-Olive and Olivd (5) proposed the use of the related equation of Schulz (6). Over the last decade the Flory equation has been used frequently to describe product distributions in FT synthesis. The Friedel-Anderson (i) or Flory (4) approaches apply when the rates of propagation and termination are independent of carbon number. We do not attempt here to discuss all previous research on FT product distributions except to say that the literature contains many examples of product distributions that obey Flory kinetics within relative narrow carbon number ranges and many that do not. 

Bogdanic, G., Fredenslund, A. Revision of the Group-Contribution Flory Equation of State for Phase Equilibria Calculations in Mixtures with Polymers. 1. Prediction of Vapor-Liquid Equilibria for Polymer Solutions. Ind. Eng. Chem. Res. 1994,33 1331-1340. 

To calculate the two-dimensional mixing entropy, the following generalized Flory equation, proposed by Donohue and PrausnitzJ17] is employed ... 

The F-T synthesis typically follows polymerization kinetics. The Anderson-Schulz-Flory equation describes the product distribution ... 

The Oishi-Prausnitz model cannot be defined strictly as a lattice model. The combinatorial and residual terms in the original UNIFAC and UNIQUAC models can be derived from lattice statistics arguments similar to those used in deriving the other models discussed in this section. On the other hand, the free volume contribution to the Oishi-Prausnitz model is derived from the Flory equation of state discussed in the next section. Thus, the Oishi-Prausnitz model is a hybrid of the lattice-fluid and free volume approaches. 

The Flory equation of state does not reduce to the ideal gas equation of state at zero pressure and infinite volume. Flory and his coworkers derived the equation of state specifically for liquid polymer solutions and were not concerned with the performance of the equation in the vapor phase. Poor vapor phase performance of an equation of state causes considerable difficulty, however, when one tries to apply the equation to higher pressure, higher temperature situations. The Chen et al. equation of state was developed in order to remedy this deficiency of the Flory equation of state. 

Holten-Andersen et al. (1987) modified the Flory equation of state in order to develop an equation that is applicable to the vapor phase, to make it more applicable to associating fluids, and to introduce a group contribution approach. Chen et al. (1990) revised and improved the equation of state. The final model takes the following form. 

The procedure is based on the group contribution equation of state by F. Chen, Aa. Fredenslund, and P. Rasmussen, "A Group-Contribution Flory Equation of State for Vapor-Liquid Equilibria" Ind. Engr. Chem. Res., 29, 875 (1990). 

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