Flory s equation

The composition dependence of Tm is investigated for RIS models of atactic PP and random ethylene - propylene copolymers using a modified Flory s equation. 

Appendix IV. Prefactors of Eq. (14) expressed by reduced quantities using Flory s equation-of-state (15)... 

The depression of the melting point of a polymer by the presence of small amounts of comonomer is described by Flory and Eby Flory suggested that the comonomer is relegated to the amorphous regions of the polymer, its presence thus reducing the extension of the crystalline regions. Flory s equation for the melting point depression caused by comonomer B in polymer A reads ... 

The DP values are far below those anticipated from an extrapolation of linear data obtained between —35° and —100° C. Also, the DP is greatest at [M] = 0.135, which is similar to the situation found at —78° C. (16, 17). The DP values were calculated by means of Flory s empirical viscosity equation (7). Since the validity of Flory s equation in this region of high molecular weights has not been established, the molecular weights could be in error. For this reason, inherent viscosities are shown in the third column of the table. 

Calculate the sol fraction by Flory s equation to compare with the experimental Ws values. 

For d = 3, this equation coincides with Flory s equation. When N goes to infinity, the first term on the left becomes dominant with respect to the second one, and in this limit... 

For d = 3, Flory s equation which gives the swelling of an isolated chain reads (see (8.1.34),... 

Figure 35.6 Dependence of p /p° on volume fraction of polymer. Curves a, b, and c are Raoult s law, Eq. (35.11), for p = 1, 100, and 1000, respectively. Curve d is Flory s equation, Eq. (35.9). Curvee is Eq. (35.14) with w/kT = 0.38. The experimental points are for the system poly-styrene/toluene O, 25°C A, 60°C , 80°C. (Adapted from E. A. Guggenheim, Mixtures. London Oxford University Press, 1952. Data from Bawn, Freeman, and Kamaliddin, Trans. Faraday Soc. 46 677, 1950.)...

Flory s equation-of-state theory is quite complex, requiring as it does the manipulation of many interrelated parameters. Sanchez (Sanchez and Larcombe, 1978 Sanchez, 1980) has therefore developed a somewhat simpler theory based on a lattice fluid or Ising model. This approach also proceeds via... 

PVT measurements The PVT apparatus from Gnomix Research was described in detail elsewhere. The sample cell was filled with approximately 1 g polymer and mercury. The cell was closed on one end by a flexible bellows and the expansion was measured with changing temperature in order to determine the volume. In the isothermal mode volume measurements were carried out at fixed pressure intervals (10 MPa) in the range from 0 to 200 MPa. The process was repeated for temperature intervals of approximately 10 C. In order to obtain the characteristic or hard core parameteis P, Vj and T, the experimental data were fitted to Flory s equation-of-state (EOS) by using a nonlinear least squares fit... 

To get a predictive model, the reduced volumes and the external degree of freedom parameter are not calculated from Flory s equation of state, Equation [4.4.72], but from some simple approximations as given by the following relations ... 

SgConf jjig eonformational entropy per molar struetural unit at Tg h, is also given by rewriting the modified Flory s equation, which expresses the melting point depression as a function of the mole fraction of major component, X, for binary random copolymers " ... 

Fig. 12. Calculated coexistence curves in the mixture ethene -I- vinylacetate + copoly (ethene vinylacetate) applying Flory s equation-of-state (parameters see Ref [56])...

This equation coincides with Flory s one (Equations 115, 116) in the limit of large coil sizes. In Flory s approximation, coil expansion is regarded isotropic with no differences between oh 2uid Ofc (o is written without any subscript). Flory s equation has been confirmed by numerous experimental data. 

Moreover, Stockmayer has established that Flory s equation 3.1-115... 

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