TUDO method

The TUDO method has been reinvestigated and has found wide use because of the simplicity of the experimental conditions. 

A plot ofr Vi-1 should yield a straight line with intercepts of-rBA/ a and tab at 5=0 and 5 1 respectively. A value of a corresponding to the highest and lowest values of (x /y)" used in the experiments results in a symmetrieal distribution of experimental data on the plot. Greenley " " has re-evaluated much data using the Kclcn-Tudos method and has provided a compilation of these and other results in the Polymer Handbook. ... 

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]. 

The copolymerization constants are estimated by the Mayo-Lewis method using the different means of linearization and optimization (most often the Fineman-Ross and Kelen-Tudos methods). We shall now consider the principal problems m the field of copolymerization of MCMs under the same conditions as for their homopolymerization. 

A new organotin monomer tributyltin -chloroacrylate (TCA) was synthesized in our laboratory. Detailed studies on homopolymerization and copolymerization were undertaken. Copolymerization was carried out with styrene (ST), methyl methacrylate (MMA) and acrylonitrile (AN). Both homopolymer and copolymers were characterized by IR, IF and C-13 NMR and tin analysis. Reactivity ratios were determined using Kelen-Tudos method. Reactivity ratios were r =0.500 and r = 0.170 for TCA-ST, r = 1.089 and r = 0.261 for TCA-MMA and r =1.880 and r = 0.243 for TCA-AN respectively. Micro-structures of homopolymer and copolymers were studied using C-13 NMR spectroscopy. Data obtained were compared with those of tributyltin methacrylate (TBTMA) and its corresponding copolymers. The results indicate that TCA is more reactive than TBTMA. 

Random copolymers of 4-vinylphenol with n-alkyl methacrylates were prepared by free radical copolymerisation of4-t-butyldimethylsilyloxystyrene and the corresponding alkyl methacrylates in benzene at 60C using AIBN as initiator. Reactivity ratios were determined by the Kelen-Tudos method. Selective removal of the t-butyldimethylsilyl protective group was effected by tetrabutylammonium fluoride in THE at ambient temperature. The copolymers were characterised by IR spectroscopy. 20 refs. 

Values calculated from original data using the Kelen-Tudos method as published in Ref. 164. 

Table I lists monomer feed compositions, copolymer compositions and conversions obtained in the copolymerization experiments. The copolymerization diagram of the system (Fig. 4) shows a tendency towards alternation with an azeotropic point at 70 mole % MA. Reactivity ratios for the aFS-MA copolymerization system, determined by the Kelen-Tudos method were r =0.26 and The KT-plot is shown in Figure 5. Average monomer feed compositions were used for this determination whenever the conversion was above 10 wt. percent. Almost identical values of the reactivity ratios were obtained when calculated by the Tidwell-Mortimer method. The reactivity ratio product for this copolymerization system ( MA aFS" 2) indicates a tendency for alternation.

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 ... 

Kelen and Tudos [1975] refined the linearization method by introducing an arbitrary positive constant a into Eq. 6-37 to spread the data more evenly so as to give equal weight to all... 

Even with the Kelen Tudos refinement there are statistical limitations inherent in the linearization method. The independent variable in any form of the linear equation is not really independent, while the dependent variable does not have a constant variance [O Driscoll and Reilly, 1987]. The most statistically sound method of analyzing composition data is the nonlinear method, which involves plotting the instantaneous copolymer composition versus comonomer feed composition for various feeds and then determining which theoretical plot best fits the data by trial-and-error selection of r and values. The pros and cons of the two methods have been discussed in detail, along with approaches for the best choice of feed compositions to maximize the accuracy of the r and r% values [Bataille and Bourassa, 1989 Habibi et al., 2003 Hautus et al., 1984 Kelen and Tudos, 1990 Leicht and Fuhrmann, 1983 Monett et al., 2002 Tudos and Kelen, 1981]. 

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. 

Even with the Kelen-Tudos refinement there are statistical limitations inherent in the linearization method. It has been shown [18] that the independent variable in any form of the linear equation is not really independent while the dependent variable does not have a constant variance. The most statistically sound method of analyzing the experimental composition data is the nonlinear method which involves direct curve fitting to the copolymer composition equation. 

The reactivity ratios were determined by performing a thermal polymerization at 135°C of several styrene-butylmethacrylate mixtures in which the mole fraction of styrene varied from 0.1 to 0.9 (3). Except for the mixture with a styrene mole fraction of 0.1, all mixtures showed thermal polymerization. When these mixtures had reached a conversion of 5 to 10%, the polymerization was stopped by cooling the mixture rapidly. The polymer monomer mixture was precipitated in methanol and dried in a vacuum oven. The different copolymers were analyzed by elemental analysis. The determination of the carbon and oxygen content in the copolymer gave the amount of styrene in the copolymer. The results are shown in Figure 8.4. By using the method of Kelen-Tudos (4-6), the reactivity ratios were determined at ri = 0.40 0.03 and r2 = 0.86 0.03 (styrene is monomer A). 

A convenient method developed by Tudo involves the use of dimethyl carbonate in presence of potassium carbonate (Scheme 14). 

Kelen T, Tudos, F. Analysis of the hnear methods for determining copolymerization reactivity ratios. I. A new... 

Braun, D., Czerwihski, W, Disselhoflf, G., Tudos, R, Analysis of the Linear Methods for Determining Copolymeryzation Reactivity Ratios, Angew. MakromoL Chem. 1984,125,161. 

PRINT Calculation of reactivity ratios by the method of Kelen and Tudos ... 

The experimental values of V- and M-centred triads from [ H] triads were compared with the theoretical values from Harwood s [171] statistical model using copolymerisation reactivity ratios. The reactivity ratios for free-radical solution copolymerisation of V with M were calculated using the Kelen-Tudos (KT) [172] and the nonlinear error in variables (EVM) [173] methods using the RREVM [174] program. Homonuclear H-2D-COSY and 2D-NOESY NMR of the copolymer sample were recorded for determining the interactions between different protons in the copolymer chain. 

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