Fineman-Ross method

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. 

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... 

Fig. 19. Determination of copolymerization parameters by the Fineman-Ross method, a = y, b = n.

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

Both the Mayo-Lewis and the Fineman-Ross methods rely on linearizing the copolymer equation. It has been shown that... 

B. Given the molecular weight of vinyl phenol is 120 and styrene is 104, calculate the reactivity ratios describing this copolymerization using the Fineman-Ross method. 

By Fineman-Ross method and confimed by the Mortimer-Tidwell (22) non-linear least square computed method. 

Determine rj and V2 for the monomer pair by the Fineman-Ross method. Answer ... 

In the aforesaid Mayo-Lewis and Fineman-Ross methods, the experimental composition data are unequally weighted as, for example, at low [M2] in Eq. (7.28) or low [Ml] in Eq. (7.29) the experimental data have the greatest influence on... 

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

Kelen and Tudos (1975, 1990) modified the Fineman-Ross method by introducing an arbitrary positive constant a into Eq. (7.28) so as to spread the data more evenly thereby giving equal weightage to the data points. Their modification is expressed in the form... 

By Fineman-Ross method and confirmed by the Mortimer-Tidwell (22) non-linear least square computed method. b By assuming that the product of reactivity ratio equals unity and using the relationship rj = Fi fp/Fp fi where Fj and / denote the mole fractions of isobutylene in the copolymer and charge, respectively, and Fp and fp those for (3-pinene. c By Fineman-Ross method. 

Early methods such as the Intersection, " and Fineman-Ross" methods do not give equal weighting to the experimental points such that there is a non-lincar dependence of the error on the composition. Consequently, these methods can give en oneous results. 

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 ... 

Detailed reviews of the methods used are given in (2). We mention here the very popular graphical Fineman-Ross method (28), the simple and convenient analytical method (29% and some precis methods ba on ideas of linear programming (20) and curve fitting (30,3 i). 

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. 

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