Scaling parameters molecular weight

In homopolymers all tire constituents (monomers) are identical, and hence tire interactions between tire monomers and between tire monomers and tire solvent have the same functional fonn. To describe tire shapes of a homopolymer (in the limit of large molecular weight) it is sufficient to model tire chain as a sequence of connected beads. Such a model can be used to describe tire shapes tliat a chain can adopt in various solvent conditions. A measure of shape is tire dimension of tire chain as a function of the degree of polymerization, N. If N is large tlien tire precise chemical details do not affect tire way tire size scales witli N [10]. In such a description a homopolymer is characterized in tenns of a single parameter tliat essentially characterizes tire effective interaction between tire beads, which is obtained by integrating over tire solvent coordinates. 

In Ref. [107] the procedure above has been employed for the measurement of the molar mass distribution of a broad molecular weight polystyrene, obtained by radical polymerization with ethylacetate as solvent. The scaling parameters for this polystyrene in this marginal solvent have been determined to be a 2.8 x 10-4 cm2/s and b 0.52 [107]. The upper curve in Figure 17 shows the resulting molar mass distribution in comparison with the one obtained by SEC. 

Now we compare the above osmotic pressure data with the scaled particle theory. The relevant equation is Eq. (27) for polydisperse polymers. In the isotropic state, it can be shown that Eq. (27) takes the same form as Eq. (20) for the monodisperse system though the parameters (B, C, v, and c ) have to be calculated from the number-average molecular weight M and the total polymer mass concentration c of a polydisperse system pSI in the parameters B and C is unity in the isotropic state. No information is needed for the molecular weight distribution of the sample. On the other hand, in the liquid crystal state2, Eq. (27) does not necessarily take the same form as Eq. (20), because p5I depends on the molecular weight distribution. 

Figure 4 compares osmotic compressibility data for isotropic schizophyllan-water solutions [63] with the scaled particle theory. The ratios of the z-average to the weight-average molecular weights of these schizophyllan samples are ca. 1.2. The solid curves, calculated with d taken to be 1.52 nm and other molecular parameters (Lc, v, and c ) estimated from Mw and the wormlike chain parameters in Table 1, are seen to come close to the data points for all samples. 

The equilibrium value of a in the nematic phase can be determined by minimizing AF. With Eq. (19) for AF from the scaled particle theory, S has been computed as a function of c, and the results are shown by the curves in Fig. 12. Here, the molecular parameters Lc and N were estimated from the viscosity average molecular weight Mv along with ML and q listed in Table 1, and d was chosen to be 1.40 nm (PBLG), 1.15 nm (PHIC), and 1.08 nm (PYPt), as in the comparison of the experimental phase boundary concentrations with the scaled particle theory (cf. Table 2). 

The Summative-Fractionation Method. To review briefly (8), in the summative-fractionation method one performs a series of small-scale single-step fractional precipitations in which increasing percentages of the total polymer are precipitated. The weight fractions x and average molecular weights Mw of all the precipitates are determined. One calculates and plots against x a parameter... 

MIF Management of information fluxes between SSCRO units. The dimensions of model parameters are coordinated the dimensions of input data are coordinated with the scales assumed in SSCRO. For instance, the formula 1 ppmv — 10 1 Mj(Ml(>) pg m 1, where M, is the molecular weight of the ith chemical element. Formulas of the type 1 pgO-s/m2 -> 0.467 x 10-7 atm-cm are also re-calculated. 

In order to test the applicability of the model to polymer-SCF systems, a hypothetical system of CC>2 and a monodisperse -mer with a monomeric unit molecular weight of 100 was simulated. Pure component parameters for the polymer, polystyrene, were obtained from Panayiotou and Vera (16). Constant values of kj< were used for the polymer system, where the degree of polymerization, , varied between 1 and 7. It was assumed that all chains had the same e, and v scaled as the molecular weight of the chain. Figure 5 shows the results of the predicted mole fraction of the -mer in the SCF phase. 

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