Kelen-Tiidos method

A plot ofr vs should yield a straight line with intercepts or-rBA/a and rAB at =0 and = 1 respectively. A value of a corresponding to the highest and lowest values of (V y)l 5 used in the experiments results in a symmetrical distribution of experimental data on the plot. Greenley18,i i,1 has re-evaluated much data using the Kelen-Tiidos method and has provided a compilation of these and other results in the Polymer 1 landbook.18... 

Copolymerization Procedures. The copolymerization kinetics runs were made using azobis(isobutyronitrile) (AIBN) as the initiator, at [M][I] = 15, a total monomer concentration of 14 wt % in water, at 60 °C under N2. Polymers were isolated by precipitation in acetone. The initial rate of polymerization (Rp) was determined by measuring the initial slope of time vs. conversion plots. Analysis of reactivity ratio data was performed by using the Kelen-Tiidos method (13, 14). 

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. 

These problems were addressed by Tidwell and Mortimer117 118 who advocated numerical analysis by non-linear least squares and Kelen and Tiidos110 1"0 who proposed an improved graphical method for data analysis. The Kelen-Tiidos equation is as follows (eq. 43) ... 

Copolymerization reactions Copolymerization experiments with styrene and MMA employed molar fractions of 20, 40, 60, and 80% comonomers, which were reacted in ethanol 1,2-dichIorethane 60 40 (by volume) mixtures and benzoyl peroxide as catalyst. Polymerizations were carried out at 70°C. The reactions were quenched by the addition of methanol as non-solvent, and the copolymer was isolated by centrifugation. Copolymer analysis employed UV spectroscopy for copolymers with MMA, and methoxyl content determination according to a procedure by Hodges et al. (16) in the case of styrene copolymers. Reactivity ratios were determined in accordance with the method by Kelen-Tiidos (17) and that by Yezrielev-Brokhina-Roskin (YBR) (18). Experimental details and results are presented elsewhere (15). 

Oehme et al. used the catalyst NdO/TEA/DEAC for the BD/IP-copolymer-ization and determined the reactivity ratio of BD and IP by the method of Kelen-Tiidos pbd = 1-09 and np = 1-32. This is the only study in which Dp > pbd [168]. Studies on the copolymerization of BD and IP with the catalyst system NdO/TIBA/EASC performed by the same group showed that the cis- 1,4-content of the BD units decreases with increasing content of incorporated IP [163]. A higher content of incorporated IP results in a lower PDI of the copolymer. The dependence of Tg on copolymer composition indicates a random distribution of BD and IP units in the copolymer. 

Copolymerizations of BD with 1-alkenes such as 1-octene and 1-dodecene aim at short chain branching of BR. Kaulbach et al. used the ternary catalyst system NdO/TIBA/EASC (htiba/ Nd = 25, nci/nNd = 3) for the respective copolymerizations of BD/l-octene and BD/l-dodecene [508]. These authors showed that only small amounts of 1-alkenes are incorporated and that no neighboring 1-alkene moieties are present in the copolymer. The copolymerization parameters have been determined by the method of Kelen-Tiidos rBD = 25 and ri-octene 0 rBD = 18 and r dodecene = 0.1. With increasing amounts of 1-alkene in the monomer feed catalyst activity decreases drastically. The cis- 1,4-contents of the BD units in the copolymer were around 90% and were barely affected by increases of the 1-alkene content in the monomer feed. 

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)... 

Good linearity was obtained for Pineman-Ross plots as well as Kelen-Tiidos plots. Both plotting methods provided almost the same reactivity ratios. The propylene reactivity ratio in SFC is about two times larger than that in CPC. This is... 

Kapur and Brar [179] prepared acrylonitrile-ethyl methacrylate (A/E) copolymers of different monomer concentrations in bulk by free radical initiation. Copolymer composition was determined by nitrogen analysis and the comonomer reactivity ratios were determined by the method of Kelen-Tiidos. C-NMR spectra of several A/E copolymers are discussed in terms of their triad monomer sequence and cotacticity. Terminal and penultimate reactivity ratios were calculated using the observed monomer triad sequence distribution determined from C-NMR spectroscopy for individual samples. Triad sequence distribution was used to calculate dyad concentrations, probability parameters, number average sequence lengths, and the comonomer mole fractions in the copolymers. The configurational sequence distributions in terms of all the 10 A-centred and 10 E-centred triad cotactic sequences have been determined and found to be in excellent agreement with those obtained using various cotactic probability parameters. 

Because Eq. 3.26 is based on the differential form of the copolymerization equation, it is strongly valid only for infinitely low conversions, but this cannot be realized in real life. For higher conversions one has to start with an integrated form of the copolymerization equation. Fortunately, Kelen and Tiidos developed an elegant method of iteration. It allows the use of the earlier suggested method without the loss of graphical clearness. 

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... 

There are a few methods for determining rt and r2 by using a modified versions of Eq. (15-2). Recently, the method of Kelen and Tiidos 2 3,4) has received increased attention and is more frequently used than the earlier methods of Fineman and Ross 5), Mayo and Lewis 1, and Ezrielev, Brokchina and Roskin 6). Most of these methods are applicable only for low conversion data (for exceptions see Ref.3>). 

Kelen, T., Tiidos, R Analysis of the linear methods for determining copolymerization reactivity ratios. 1. New improved linear graphic method. 1. Macromol. Sci. Pure Appl. Chem. A9(l), 1-27 (1975)... 

Although frequently used, the Finemann-Ross method is not accurate for low values of [A]/[B] (or [B]/[A]) and is not suitable for a wide range of concentrations. The method described by Kelen and Tiidos is often preferred it consists of dividing all the terms of the Finemann-Ross equation by (a + F), with the value of the constant a being taken equal to (Fmin/ max) ... 

Linear Methods Mayo and Lewis (2), Fineman and Ross (8), Kelen and Tiidos (9)... 

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