Monomer reactivity ratios Fineman-Ross method

The NMR analysis (21) of the chemical composition for copolymers from various monomer feed ratios at fairly low conversion are shown in Table IV. The results were then used to estimate the reactivity ratios for the diene monomers under the conditions employed. Various published methods of calculating monomer reactivity ratios have been examined. These include the once popular but now somewhat out of favor Fineman-Ross method... 

The monomer reactivity ratios could be calculated from Table A and other values by the method of Fineman and Ross (10), but owing to the narrow range of compositions studied only the value of r2 (referring to the styrene radical) was significant. A value of 0.7 was obtained which may be compared with 0.52 for styrene-methyl methacrylate, and a value of 0.41 calculated from the Q — e values for hydroxyethyl methacrylate supplied by Rohm and Haas (25). 

Fineman, M. Ross, S.D. Linear method for determining monomer reactivity ratios in copolymerization. J. Polym. Sci. 1950, 5, 259-262. Tiidos, F. Kelen, T. Foldes-Berezsnich, T. Turcsanyi, A. Evaluation of high conversion... 

The monomer reactivity ratios (r = A nn/ no and Tq = oo/ on) determined by the Fineman-Ross method are shown in Fig. 10. These values indicate a preference for the insertion of norbomene, regardless of the last inserted monomer unit. The product of the reactivity ratios (rN ro = 0.97) obtained with 4 indicates a tendency for the formation of random copolymer, whereas the products of the reactivity ratios (rj roi 2.5-3.5) obtained with 2, 3, and 5 imply a preference for the formation of the norbomene-norbomene sequence in the copolymer. 

Two types of copoly.merization, SFC and CPC, were carried out at 30°C with the catalyst system, MgCl2/TiCU/EB/Al(02115)3. For reference, homopolymerization of each olefin was conducted under similar conditiona The monomer reactivity ratios r and rp(K = ethylene, P = propylene) were calculated according to the Fineman-Ross method and Helen—Tudos method, where the necessary parameters are defined as follows ... 

The traditional method for determining reactivity ratios involves determinations of the overall copolymer composition for a range of monomer feeds at zero conversion. Various methods have been applied to analyze this data. The Fineman-Ross equation (eq. 42) is based on a rearrangement of the copolymer composition equation (eq. 9). A plot of the quantity on the left hand side of eq. 9 v.v the coefficient of rAa will yield rAB as the slope and rUA as the intercept. 

For a detailed analysis of monomer reactivity and of the sequence-distribution of mers in the copolymer, it is necessary to make some mechanistic assumptions. The usual assumptions are those of binary, copolymerization theory their limitations were discussed in Section III,2. There are a number of mathematical transformations of the equation used to calculate the reactivity ratios and r2 from the experimental results. One of the earliest and most widely used transformations, due to Fineman and Ross,114 converts equation (I) into a linear relationship between rx and r2. Kelen and Tudos115 have since developed a method in which the Fineman-Ross equation is used with redefined variables. By means of this new equation, data from a number of cationic, vinyl polymerizations have been evaluated, and the questionable nature of the data has been demonstrated in a number of them.116 (A critique of the significance of this analysis has appeared.117) Both of these methods depend on the use of the derivative form of,the copolymer-composition equation and are, therefore, appropriate only for low-conversion copolymerizations. The integrated... 

The error-in-variables method was used to estimate the reactivity ratios. This method was developed by Reilly et al. (57, 58), and it was first applied for the determination of reactivity ratios by O Driscoll, Reilly, and co-workers (59, 60). In this work, a modified version by MacGregor and Sutton (61) adapted by Gloor (62) for a continuous stirred tank reactor was used. The error-in-variables method shows two important advantages compared to the other common methods for the determination of copolymer reactivity ratios, which are statistically incorrect, as for example, Fineman-Ross (63) or Kelen-Tiidos (64). First, it accounts for the errors in both dependent and independent variables the other estimation methods assume the measured values of monomer concentration and copolymer composition have no variance. Second, it computes the joint confidence region for the reactivity ratios, the area of which is proportional to the total estimation error. 

Three different laws were used to assess the reactivity ratios rj of AN (1) and T2 of ATRIF (2) Fineman and Ross method [78], Kelen and Tiidos law [79], and the revised patterns scheme [80]. From the monomer-polymer copolymerization curve, the Fineman-Ross and Kelen-Tiidos laws (Figure 20.2) enabled to assess the reactivity ratios (r = 1-25 0.04 and = 2 = 0-93 0.05 at 70 C)... 

The relationships between the polymer composition and monomer ratio for these three copolymerizations are shown in Fig,7. Based on the polymer composition and monomer concentration data, the apparent reactivity ratios were determined according to the method of Fineman-Ross For these three copolymerization systems at 55 C in heptane, the values of reactivity ratios are listed in Table 2. 

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