The Fineman-Ross Plot

The Fineman-Ross method uses a more conventional plotting procedure, rearranging the copolymer equation into the following form (Equation 6-7), 

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Methylthiophene/styrene copolymers Methyl methacrylate does not homopolymerize or copolymerize if present in the monomer feed during the oxidation of 3-methylthiophene. This is the reason that its copolymer with 3-MT is prepared indirectly as described above. Its homopolymerization is generally initiated by anions or free radicals. Styrene, however, undergoes a random copolymerization when present during the chemical oxidation of 3-methylthiophene initiated with anhydrous FeCls [73]. Monomer reactivity ratios for the copolymerizations in methylene chloride and nitrobenzene at 5°C are reported, but there is considerable scatter in the Fineman-Ross plots. The proposed structure of the 3-MT/stryrene copolymer is shown in Figure 11.16, where R = H. 

If such effects occurs, the classical copolymerization equation n = (r x 1)/ r /x + 1)) gives abnormal value for, at least, one of the reactivity ratios (for instance, Tb < 0,...) and the Fineman-Ross plot is not a straight line on the whole range of monomer composition (x), but looks like the curve of Fig. 1,... 

Sometimes, it occurs that the Fineman-Ross plot shows that experiments do not fit the theoretical straight line corresponding to a penultimate effect in the extreme range of composition of monomer feed. This fact might indicate the influence of the more remote units. For instance, such an occurence is encountered when copolymerizing styrene-acrylonitrile and vinyl chloride-vinyl acetate systems. Calculations analogous to those mentionned above may be performed with the equation proposed by G. E. Ham [7] for pen-penultimate effects, which allows the determination of the reactivity ratios (with adjunction of some more assumptions). We performed these types of calculation for the two systems for... 

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. 

The experimental composition data are unequally weighted by the Mayo-Lewis and Fineman-Ross plots with the data for the high or low compositions (depending on the equation used) having the greatest effect on the calculated values of r and r2 [Tidwell and Mortimer, 1965, 1970]. This often manifests itself by different values of r and r2 depending on which monomer is indexed as Mi. 

The composition of the copolymer was determined by either NMR analysis at 90 MHz according to the equations derived by Mochel (21) or by infrared. (22) The agreement of these methods was 2% when applied to copolymer taken to 100% conversion. The reactivity ratios were calculated according to the Mayo-Lewis Plot (13,15), the Fineman-Ross Method (14), or by the Kelen-Tudos equation.(16,17,18) The statistical variations recently noted by 0 Driscoll (23), were also considered. 

Figure 7.6 Plot according to the Fineman-Ross method (data from Problem 7.7).

G is then plotted against F, or G/F against l/F, in the Fineman-Ross equations (see Figure 22-4) ... 

Using Eq. (32) and feed and terpolymer composition data, a copolymerization composition diagram can be drawn, compared with the theoretical curves, and the coefficients of the Mayo-Lewis equation, riK and / 2jK estimated (Table 10.23). Fineman-Ross plots may also be used to estimate the Mayo-Lewis coefficients. These dimensioned apparent or modified reactivity ratios deviate from the true reactivity ratio values the more greatly the equilibrium constants differ from unity. 

Several authors have calculated the E-N reactivity ratios according to the Fineman-Ross method. Examples are collected in Table 9 along with those obtained from microstmctural analysis by C-NMR spectra. McKnight and Waymouth found that four CGCs give ri values between 2.0 and 5.1. The values found are consistent with values for ethene/octene copolymerizations (ri =2.6-4) with the same catalysts and indicate a preference for the insertion of ethene over norbomene into an Mt-E active center. In no case was it possible to accurately determine T2 from the plots. However, the data were consistent with a value of T2 very close to zero. The product of the reactivity ratios for all the CGC E-N systems approaches zero, indicating a tendency toward alternation. 

Independent of the analytical methods the copolymerization parameters derived from the Mayo-Lewis equation have some major drawbacks, but do enable a part of the information contained in each copolymerization experiment to be extracted, namely the integral composition of the copolymer. A series of experiments is necessary to obtain the copolymerization parameters. Furthermore, using this approach it cannot be decided whether the application of the first-order Markov model is valid or not. One may even obtain a nearly perfect Fineman-Ross plot, where other methods show that a first-order Markov model cannot be applied. 

Using the parameters of F, G and a in Table 1—3, both Fineman—Ross and Kelen—Tiidos plots for the two types of copolymerizations are given in Fig. 1-2. The monomer reactivity ratios calculated from these plots are listed in Table 4. 

Figure 19.1 Fineman and Ross plots for copolymerization of styrene/B-styrene and the least square best-fit line.

In 1950, Fineman and Ross suggested another method called FR method or linear least square method, which is based on Eq. (7). 1 For a set of values of F and / from experiments, a plot of (1 - f)/F vs. f/F should be a straight line with the... 

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