1750 Macromolecules 1995,28, zyxwvu 1750-1753 Determination of Reactivity Ratios in Radical Copolymerization: zy A Comparison of Methods for a zyx MethacrylatelN-Vinylpyrrolidone System G6rard Bauduin* and Bernard Boutevin Laboratoire de Chimie Appliquke, URA zyxwv CNRS 1193, Ecole Nationale Supkrieure de Chimie de Montpellier, 8 rue Ecole Normale, 34053 Montpellier Cedex 1, France Mohammed Belbachir and Rachid Meghabar Laboratoire de Chimie des Polym&es, Institut de Chimie, Universitk d'Oran es Senia, BP 1524 El Menaouar, DZ 31000 Oran, Algeria Received September 14, 1994; Revised Manuscript Received November 23, 1994@ ABSTRACT: To determine the reactivity ratios in the radical copolymerization of the reaction product of acetylsalicyclicacid with 2,3-epoxypropyl methacrylate and N-vinylpyrrolidone,all available methods are used and compared. Using as criteria the accuracy of the confidence interval and the impossibility of obtaining in any case negative values for a reactivity ratio, the Tidwell-Mortimer method is recommended. Introduction To prepare water-soluble polymeric derivatives of acetylsalicyclic acid (ASA), we copolymerize a meth- acrylate containing an ASA moiety with N-vinylpyrroli- done zyxwvutsrqpo (NVP). The synthesis and the characterization of the methacrylate 1 obtained by reacting 2,3-epoxypropyl methacrylate with ASA will be described elsewhere. To control the copolymer composition, it is first necessary, to know the reactivity ratios rl of monomer 1 (meth- acrylate) and r2 of monomer 2 (NVP). I The determination of rl and r2 gives us the op- portunity to compare the different evaluation methods, which are based on the analysis of reactants or copoly- mer at the beginning of the reaction. Experimental Section NVP is distilled under nitrogen before use, and concentra- tions of methacrylate 1 are (2-3) zyxwvuts x mo1.L-l. Initiator concentration is 1% of the total concentration of both mono- mers. The copolymerization reactions are carried out in acetoni- trile at 80 "C in the presence of azobis(isobutyronitri1e) (AIBN) as initiator. Each solution is prepared with a given molar fraction f1 of monomer 1, and equal volumes are placed in several (10-15) sealed tubes. The tubes are put in an oil bath at 80 "C and stirred magnetically. Every 2 or 3 min, a tube is taken out of the bath and rapidly cooled. A given quantity of chlorobenzene is then added as an internal standard, and the solution is analyzed using high-pressure liquid chromatog- raphy (standard CIS column; eluant: acetonitrile). The con- sumption curves of each monomer are plotted, and the molar fraction F1 of monomer 1 in the copolymer at the beginning of the reaction is calculated from the slopes of the curves at the origin of time. @Abstract published in Advance ACS Abstracts, February 1, 1995. Table 1. Experimental Results: Molar Fractions of Monomer 1 in the Feed fi and in the Copolymer F1 fi F1 0.10 0.30 0.50 0.70 0.90 0.219 0.452 0.514 zyx 0.762 0.901 Five different compositions of the feed solution are studied, regularly chosen over the whole range of variation of f1. Results and Calculation The experimental results are given in Table 1. De- spite the extent of the experimental error in 3'1, three significant digits (as written in Table 1) are taken into account for the calculations. The methods to determine the reactivity ratios from experimental results can be separated into four groups.' (i) The approximate methods constitute the first group. They will not be used here because, as they are based on approximate kinetic equations or approximate calculations, they are expected to give biased values of rl and r2. (ii) The second group includes the straight-line inter- section methods. The Mayo-Lewis method is the oldest one.2 However, it difficult to apply, because the values of rl and r2 can be given by each of the n(n - 1)/2 intersections (10 in our case) of the n (5 in our case) straight lines plotted from the n experimental couples of values. Lewis and Mayo do not indicate any particu- lar means to choose between these numerous possibili- ties. Fortunately, Joshi and Kapul3 and subsequently Joshi and Joshi4 proposed two different ways to find the most representative intersection point. The Joshi- Kapur (JK) method takes into account all the interaction points between any couple of straight lines. Each point is weighted by multiplying rl and r2 values by the tangent value of the angles of both lines (the lines are more clear-cut when the angle is near a right angle than when it is close to zero). Then the most probable values of rl and r2 are the average values of all the weighted intersections. The calculation of the confidence interval in the Joshi-&pur method will be discussed in a forthcoming paper. The Joshi-Joshi (JJ) method chooses 0024-929719512228-1750$09.00/0 0 1995 American Chemical Society