W. A. Mukatir and Temple Ohll Bradley University Peoria, Illinois 61606
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Reactivity Ratios from Copolyinet5~cltionKinetics A quantitative gas-liquid chromatography experiment
Polymers have a fascination because their properties are dependent not only on their monomer composition but also on their size and shape. Polyethylene polymerized in the high pressure, free radical process has more branched chains than the Ziegler-Natta variety. As a consequence, the latter is stiffer, stronger, more heat resistant and has a higher density (1). Copolymers have an additional intriguing dimension over homopolymers in that properties of the former are determined not only by monomer composition and chain length but also by the distribution of monomers along the chains. Natural polymers, such as enzymes and DNA, dramatically illustrate the importance of monomer distribution along the chain. For or-chymotrypsin, a pancreatic proteinase, the conversion of one particular serine residue to a dehydroalanine moiety results in complete inactivation of the enzyme (9). I n the case of DNA, the arrangement of four purine and/or pyrimidine bases in sets of three along a polymer chain literally determines whether its host is a frog, a dog, or a hog (3). The situation is not as dramatic for synthetic polymers; however, here also properties are modified by the arrangement of molecules along the chain. For a copolymer containing two monomers A and B one can conceive of two limit cases (1) aperfectly alternating copolymer-(A-B)f (2) & copolymer containing long blocks of variable length of each monomer -Az-Bv-AcB,-ArBr where z,y,z,w,r,s >> 1.
can certainly be neglected here because the radicals are extremely reactive and the induction period very short. Basically the rate equations for copolymerization of two monomers can be written as (6) Rate kll
A.+A-A.
k~[A.l[Al
(1)
+B
k ~ [ A .[B] l
(2)
k,r[B.][AI
(3)
kz,[B.][B]
(4)
A.
'Supported by a grant from the Bradley University Committee on Faculty Research.
B.
k,
B.+A-A. B.
kw
+B-B.
where A and B . represent growing polymeric radicals with a unit of A or B.respectively on the growing end. From the scheme above one can write for the rate of disappearance of monomers A and B respectively Rate of disappearance of A
=
- d[Al - = kn[A,] [A] + dl k,,[B.I [A1 (.5)
and Rate of disappearance of B
= -
+
d[Bl = kdA.1 [B] dt k d B ; l [Bl
(6)
If one now introduces the steady-state assumption that (after a very short interval) the rate of appearance of either radical is eqnal to its rate of disappearance then one can write for A. kdA.lIBI ~
Measurement of the copolymer reactivity ratios (to be defined and discussed later) provides a means of approximately determining the monomer distribution in the polymer. Polymer properties can then be related to monomer distribution. I n order to define reactivity ratios some relatively simple kinetics need be understood, including the concept of the steady state for high energy intermediates (4). It is rather easy to rationalize the steady-state assumption to a sophomore by reasoning that if the rate of destruction of a high-energy (low-concentration) intermediate does not rapidly become eqnal to its rate of production, then in a short time that intermediate will build up and become detectable and isolatable or, by definition, low energy. The fact that the steady-state concentration, after reaching a maximum very slowly decreases is normally neglected (4) and
LIP
~~
~
=
k~~lB.l[Al
(7)
since A. disappears in eqn. (2) and reappears in eqn. (3). By dividing eqn. ( 5 ) by eqn. (6) and using eqn. (7) for simplifying, one obtains the following expression (5)
where R1 = k~r/ks
and R*
=
b*lk,
R1and R1 are called reactivity ratios. These ratios of rate constants give an excellent indication of monomer distribution in the polymer. Assume for the moment equal concentrations of monomers. Then one can see that R1 is a measure of how well a growing polymer radical, A , , prefers to add another monomer unit A as compared to a molecule of B. Thus, if R1>> 1, a polymer radical A. will greatly prefer A over B. This will result in long blocks of A in the chain. Similarly if Rz>> 1 then when a B molecule finally Volume 49, Number 5, May 1972
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367
adds to a growing A. radical, the new radical, B . , will prefer monomer B over A. Hence, a. long block of B will be incorporated. The resulting polymer for R1>> 1 and Rz >> 1 can be approximated by -A,-B,-A.B,-A,-B,where x,y,z,w,r,s >> 1. Let us look a t one more combination of reactivity ratios, RI >> 1 and Rz > 1 and y,w,s 2 1. The main reason that the above representations are only approximations is because equal concentrations of monomers were assumed. If the two reactivity ratios are different, one monomer must be used up faster than the other. Thus, polymer formed later in the reaction will have a different composition from that formed a t the beginning. In this latter case just discussed ( R 1>> 1, R2> 1, R2>> 1). Table 1 . Monomer Distribution in a Copolymer for Different Reactivity Ratios and Equimolar Concentrations of . A ond B 151
.-,
~
Reactivity Ratios
Rz >> 1, Rz >> 1 Rl >> 1, R2 1 R, O min. Gas chromatograph injection samples in the range of 1.0-1.i pl are suggested. Each sample should be injected a t least twice into the chromatograph and the results averaged. One student may operate the gas chromatograph while the other is collecting samples. The order of peak elution is: CHCh, MMA, CeHaCI, and styrene. If the samples withdrawn from the polymerization mixtures at later times are too viscous to drew up into the microsyringe they may bediluted with CHCL. After two runs the culumu should be taken out and the inlet and column front rinsed with hot benzene (syringe) several times to remove polymer which begins to build up. The column should then he heated a t around 150°C to drive off residual benzene. The polymer in the inlet is easily washed out and in no way damages the column. Data T~ealrnent. Peak height ratios (PHRs) of MhlA/ C6HG1and styrene/CnH5CLare plotted versus time as shown in Figure 2. These PHRs have been normalized to 1.0 so that the concentration at m y time can be obtained by multiplying the ordinate value by the initial monomer concentration. If polymerization hits not exceeded about 20%, straight line slopes may usually he drawn by eye or by s. least squares procedure. If the line is not straight a smooth curve is drawn and the initial slope obtained. T h i ~e m he done very simply using the method outlined by Hoare (10). This involves using a glass rod placed over Volume 49, Number 5, May 1972
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369
Altenzate Systems. Two other systems heve been investigated preliminarily to find proper gas chromatographic conditions for separation of peaks and reasonable initial wncentrations. They me (1) MMAlbutyl acylate (BA). This system may he run on the same column with tbutylheneene (TBB) as the internal standard. Peaks are eluted in the order CHCb, MMA, BA, snd TBB. For BA/MMA on a 50/50 mole basis the following quantities are suggested: CHCL, 22.00 ml; BA, 10.45 ml; MMA, 7.95 ml, and TBB, 16.00 ml. Chromatographic temperatures are the same as suggested for the MMA-styrene system. (2) Butyl awlate (BA)/stme. This system may he run on the same column with tetrschloroethane (TCE) as the internal standard. Peaks are eluted in the order: CHCI. BA, styrene, and TCE. For BA/sty on a 50/50 mole basis the following quantities are suggested: CHCla, 22.00 ml; BA, 10.45 ml; styrene, 8.55 ml; TCE, 12.00 ml. Temperatures are: injector, 155'C; column, 125'C; and detector, 200°C.
0
20 TIME
40
(MINI
Figure 2. Rota of disappearance of styrene (solid circles) and methyl methacrylde ( d i d triangles1 in one copolymorimtion run. The initial mole ratio i s 70130 for the rtyrene/methyl methacrylote mixture.
the curve to obtain the tangent. The glass rod is placed over the curve at the point a tangent is desired and approximately perpendicular to it. The rod is moved until the ourve appears unbroken when viewed through the rod. A perpendicular to the curve may then he drawn along theedge of the rod. The initial slopes are converted to concentration/time units. After two (or more) runs eqn. (8)is solved for RI and Ra.
370
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Journal of Chemicol Educofion
Literature Cited
,.-,,"~
R ~ PR., , AND L Y ~EE ..Hioh P,durn., XX ( ~1).t 1 , (1965). W ~ m s nH . . . WAITB.W . N.. H OARE, D. G . , A N D KOSHLAND, D . E. JR., 3. Ama.Chem.Soc..88.3851 lLrool. 08.80 (1963). letiol and Mechanism." (2nd n e y a u o n s i n o . . ~ e r vy o n . 1961,~.172. .. P n r o ~ W. . A., "Free Radioab." MoGraw-Hill Gook C o m ~ n n y ,New York.1966, pp. 2 4 2 4 . X w * m H . , BROADBENT. H. 8.. AND BIRTLETT.P . D.. J . Amer. Cham. Soc.. 72, lo60 (1950). HAW,G . E.. High Polym.. XVm, Ioteraoisnoe Publishera, New Y o r k 7 ,."e", ,.a"=,. B R ~ D R OJ.P AND IXMERLIOT E . H.. "Polymer Handbook " Interscienoe Publishers. New York. 1967. pp. 11-210 andII-211. M c N A ~H . . M . . m o BONELLI. E. J.. "Bmic Gas Chromatoaraphu," Varisn Aerograph. 1968, pp. 137-67. Hoam. J. P., J. Cmesl. Enuo.,38,570 (1961).
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