Reactivity ratio Fineman-Ross

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. 

A simpler method for determining the reactivity ratios is that of Fineman and Ross, in which the copolymerization Eq. 3.18 is rearranged to ... 

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... 

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 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). 

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. 

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... 

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. 

Using the data in Table III, the general copolymer composition equations, and the Fineman-Ross procedure (16), the reactivity ratios were estimated at rx — 0.40 and 0.42 and r2 = 0.78 and 0.75 with mean values of 0.41 and 0.77 respectively. Values of rx = 0.406 and r2 = 0.773 were calculated by a computer program based on least squares. 

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. 

The next step in the protocol answers the question about what is the best method to estimate the reactivity ratios. Historically, because of its simplicity, linearization techniques such as the Fineman-Ross, Kelen-Tudos, and extended Kelen-Tudos methods have been used. Easily performed on a simple calculator, these techniques suffer from inaccuracies due to the linearization of the inherently nonlinear Mayo-Lewis model. Such techniques violate basic assumptions of linear regression and have been repeatedly shown to be invalid [117, 119, 126]. Nonlinear least squares (NLLS) techniques and other more advanced nonlinear techniques such as the error-in-variables-model (EVM) method have been readily available for several decades [119, 120, 126, 127]. 

Copolymer-reactivity ratios obtained from the feed and copolymer composition data with linearized equations, as in the Fineman-Ross procedure, do not allow proper weighting of the experimental data, and cannot provide a proper estimate of the precision of the parameters, which, being interdependent, have joint confidence limits. Computer-based methods for determining reactivity ratios have been summarized and non-linear least squares methods described.. Errors in the dependent variables were included by Yamada... 

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. 

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 relative reactivity of Afj and M2 can be estimated by Fineman-Ross law (G versus H). In the absence of the self-propagation of TSE monomer (k22 = 0. 2 = 0), Figure 20.9a shows that reactivity of 4FST radical toward TSE (rj) is around 0.6. The product ry x T2 is close to zero attesting a tendency to alternating structure of poly(TSE-co-4FS) copolymer. The experimental curve (i.e., the molar ratio of 4FST (Mj) units in the copolymer (Fj) versus the molar ratio of (Mj) units in the feed (fj)... 

The resulting copolymers were characterized by H, and NMR and IR spectroscopy, and SEC. Their compositions were assessed by H NMR and elemental analyses. The structure of the obtained copolymers was evidenced by the assessment of the reactivity ratio and NMR spectroscopy. From monomer-polymer composition curve and the Fineman-Ross, Kelen-Ttidos and Jenkins laws, we can conclude that the copolymers based on AN, MAN exhibit random structures, while the copolymers based on VCN with MATRIF had alternating structures. In addition, poly(TSE-co-4FST) copolymer presents an alternating structure terminated with homosequence of 4FST. 

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. 

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 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. 

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 ... 

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. 

Attempts to obtain simple reactivity ratios from composition data by various techniquesled to the conclusion that the kinetics of the styrene-MA copolymerization do not follow the classical scheme of Mayo-Lewis and/or Alfrey-Goldfinger. All systems gave rise to Fineman-Ross and... 

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. 

Using the feed and copolymer composition data and the graphical method of Fineman-Ross, it is possible to calculate numerical values for the modified reactivity ratios. Looking at the values in Table 10.24, it is easy to see that the reactivity of the styrene MA complexomer is usually more reactive than the other charge-transfer complexes. For example, the styrene-MA CTC is about 8 times more reactive than the 2-chloroethyl vinyl ether-MA complexomer. 

Subrahmanyam and co-workers [87] used H-NMR spectroscopy to determine the composition of behenyl acrylate - vinyl acetate copolymers. The reactivity ratios were evaluated by different methods and were found to be 0.021 for vinyl acetate and 1.76 for behenyl acrylate. Fineman-Ross and Kelen-Tiidos methods gave similar values. The Q and e values for behenyl acrylate were calculated as 0.25 and 0.94, respectively. The experimental copolymer composition was found to be in close agreement with calculated values. 

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