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The use of the radiotracer method to circumvent penultimate group and ceiling temperature effects in copolymerisation
Eur. Polym. J. Vol. 20, No. 2, pp. 125 127, 1984
0014-3057 84 S3.t)0+0.00 Copyright ,i: 1984 Pergamon Press [.td
Printed in Great Britain. All rights reserved
THE USE OF THE R A D I O T R A C E R M E T H O D TO CIRCUMVENT PENULTIMATE GROUP AND CEILING T E M P E R A T U R E EFFECTS IN C O P O L Y M E R I S A T I O N C. A. BARSON Department of Chemistry, The University of Birmingham, P.O. Box 363, Birmingham B I5 2TT. England (Receired 25 Mav 1983)
Abstract The radiotracer method can be used to study copolymerisations of M~ and M 2 under conditions where [MI]>>[M2]. In these circumstances, the probability of two M, units becoming adjacent in thc polymer chain during propagation is negligible. Experimentally derived reactivity ratios, obtained by a simple graphical solution of composition data, are realistic measures of relative reactivities even with systems where penultimate group effects or depropagation effects due to M2M~ diads are nora]ally significant.
When [M/]>>[M2], equation 1 simplifies to [10]
INTRODUCTION
m,
Data from copolymerisations are frequently used to obtain information about the relative reactivities of monomers towards reference polymer radicals or ions. The conventional copolymerisation equation [1-31 m~ _ d[M,] _ [M d//r~[M,] + [M2]~ /
m~
d[Md
[M2I\r2[Mq+[M,]]
m,
(I)
relates the molar ratio of the m o n o m e r feed, [Mm]/[M2], the molar ratio of the comonomers in the copolymer, m~/m2, and the reactivity ratios rL and r2; it is only valid at low conversions, when variations in [Mi] and [M:I are negligible. Some significant deviations from this "ideal" behaviour can be attributed to the influences of penultimate or even remoter units on the reactivitics of copolymer radicals or ions. If such units are taken into account, more propagation steps and therefore more reactivity ratios must be considered, resulting in more complex mathematical relationships [4]. Other deviations from "ideality" can arise when copolymerisations are carried out at temperatures near to the ceiling temperature for one of the monomers [5]. Reactivity ratios derived from equation 1 have even assumed negative values, showing that the kinetic scheme was invalid under these conditions [6]. Under conditions or for systems where penultimate or remoter units or ceiling temperatures become important, application of equation 1 to composition data will result in values for reactivity ratios which are not true measures of the relative reactivities expected from the reaction scheme. Even where the application of equation 1 is kinetically valid, its use in obtaining precise values of reactivity ratios is not easy, although some elegant solutions have been devised [7 9]. By using radiotracer techniques, many of these problems can be circumvented. Because of the very high sensitivity of the technique, the amount of a labelled comonomer, both in the feed and in the copolymer, can be determined fairly easily even at extremely small mole fractions.
-
d[M,]
[M,] - r~-d[M2] [Me]
(2)
A graphical solution of this equation, plotting m:,m~ against [M2]/[M~], was first applied to copolymerisations over 20 years ago [1 1]. The method has since been used to study the temperature effects in copolymerisation for several different systems [12]; it has also been used to determine some isotope effects in polymerisation [13]. Recently, reactivity ratios have been determined by applying equation 2 at a single composition [14]. But the advantage of the graphical solution [1 1], over a range of compositions, is that it provides evidence for the validity of the assumptions; it also gives data for assessing errors. Other advantages for the radiotracer method for copolymerisation studies are now proposed. They again result from the fact that [M2] can be maintained at extremely small values, such that [M~]>>[M2]. Under these conditions, the probability of two M, units becoming directly linked during the propagation steps is negligible. PENULTIMATE OR REMOTER GROUP EFFECTS One advantage applies to the effect of penultimate or remoter groups in copolymerisation. When the effects of penultimate groups as well as terminal groups are taken into account, the eight possible propagating steps result in the following equation [4]. mI
d[M ,]
m2
d[M2]
1 + [r,[~ =
-[M,]
I, '[M2] + ')," ~' '[M~]~] + 1
/_
(3)
-+ [M:])]
In this equation, rl = krll/k~l_,, rl = k>l kin,, r2 = k222/k22~ and r ~ - k~/k~:,. The notation lbr the
125
126
C . A . BARSON
rate constants of propagating steps follows the usual convention; the numbers in the subscript refer to each monomer type in the terminal triad, in the order in which they become incorporated by propagation. Application of the condition [Md>>[M2] to equation 3 leads to a simpler equation having the same form as equation 1. Thus m,
d[M,]
[M,]//r,[M~]+[M2]'~
(4)
m~ - d [ M 2 ] - [M:] [\ M ~ +, ] / - -"" where r~ is analogous to r2 in equation 1. However, this equation can be further simplified by reapplication of the above monomer feed condition, resulting in equation 2. Thus r, can be obtained graphically as before. If a plot of experimental data shows no deviation, within experimental errors, from the simple linear relationship of equation 2, the unimportance under these conditions of the reactivity ratio r~ in equation 4 is demonstrated; the only significant reactivity ratio is r~. This conclusion is confirmed by considering the propagation sequences involved in the reactivity ratio r~. In this ratio, the numerator, k~22, refers to the step ,,~MIM2* + M : ~ ~,~MtM2M2* Since such a process is highly improbable when [M,]>>[M2], this particular reactivity ratio is unimportant. By reversing the labelling, such that [Mz]>>[M~], r2 can also be obtained from a simple linear plot; in this case, the magnitude of r; is unimportant. It is concluded that, even in systems where penultimate group effects are normally quite large, such effects can be ignored when using radiotracer techniques under the conditions [Md>>[M2]. The measured reactivity ratio in these circumstances is a valid estimate of the relative reactivities of the monomers towards a specific polymer radical or ion. Similar arguments can also be applied to the effect of the groups preceding the penultimate groups. The propagating species to which r~ refers in this method can therefore be safely assumed to contain a sequence of several Mt units in the terminal group; this means that it should be kinetically indistinguishable from a homopolymeric radical or ion of M/. If the labelling is reversed to obtain r2, this ratio refers to a propagating species which is kinetically indistinguishable from homopolymeric radicals or ions of M2. DEPROPAGATION EFFECTS
The radiotracer method can also be used to advantage under conditions where reversible propagation occurs, for example, near to the ceiling temperature of one of the monomers. As ceiling temperatures are approached under the usual conditions of copolymerisation, changes in the magnitude of reactivity ratios with temperature can be larger than would be expected if equation 1 were still valid [5]. Lowry [15] postulated three different cases when depropagation could accompany growth to some extent; each category depended on the composition of the terminal group of monomer units in the growing polymer. Except for differences in the values of the reactivity ratios, no distinction needs to be made
between radical and ionic mechanisms. In Lowry's Case 1, a reversible propagation step is significantly probable only if the terminal diad in the growing polymer species is M~M2M2*, but not if it is ~M2M~* or ,~,AM1Mt*; thus m 2 d[M2] [M:][1/(1-~)] m, d[Md r,[Md +[M2] -
-
-
-
(5)
where ~ = [(rn2),+~*]/[(rnz),*] and 0 < n < or. The symbol [(rn2)n*] denotes an active species containing n units of M2, immediately preceded by one or more units of M~, at the active end of the growing polymer. If [M~]>>[M2], the probability of n having a value greater than 1 is negligible. Thus a = 0 and equation 5 reduces to equation 2. If a terminal triad of ,,~M2M2M2* is required before depropagation can occur (Case 2), the equation derived by Lowry again reduces to equation 2 when [Md >>[M2]. Case 3 requires the presence of the terminal triads N~M2M2M,* or ~,AM2M2M2* for depropagation to occur. As the formation of the diad ~'~M2M2* in any propagation step is highly improbable when [M1]>>[M2], similar conclusions are reached about the unlikelihood of depropagation influencing the kinetics under these conditions; equation 2 is again valid. When [M~]~>[M2] and at temperatures near to the ceiling temperature of M2, reactivity ratios determined using equation 1 are invalid and are not true measures of relative reactivity. This invalidity disappears when [MI]>>[M2] and the reactivity ratios obtained by the radiotracer method may be safely used to compare reactivities. CONCLUSION
If penultimate group effects or depropagation are prevalent in copolymerisation, mathematical solutions of composition data to give true reactivity ratios can be extremely complex. Yet, unless these effects can be satisfactorily taken into account, studies involving the finer variations in reactivity ratios, such as temperature effects, are pointless. The advantage of the radiotracer method is that the solution is just as simple as if the effects did not exist. However, it is necessary to keep conversions to low levels, so that m~/m2 = d[Md/d[M2]; since radioactive assays can be carried out on quite small samples, this usually presents no problems. It is also important to avoid significant kinetic isotope effects; since labelling is often possible at a point remote from the active site in the monomer, any resulting secondary isotope effects are usually negligible. REFERENCES
1. F. R. Mayo and F. M. Lewis, J. Am. chem. Soc. 66, 1594 (1944). 2. T. Alfrey and G. Goldfinger, J. chem. Phys. 12, 205 (1944). 3. F. T. Wall, J. Am. chem. Soc. 66, 2050 (1944). 4. G. E. Ham, J. Polym. Sci. 45, 169 (1960). 5. J. C. Bevington and B. W. Malpass, Eur. Polym. J. 1, 19 (1965). 6. M. Izu and K. F. O'Driscoll, 9". Polym. Sci. A-1 8, 1687 (1970). 7. M. Fineman and S. D. Ross, J. Polym. Sci. 5, 259 (1950).
The radiotracer method in copolymerisation 8. A. I. Yezrielev, E. L. Brokhina and Ye. S. Roskin, Vysokomolek. Soedin. A l l , 1670 (1969); Polym. Sci., U.S.S.R. 11, 1894 (1969). 9. T. Kelen and F. Tfid6s, J. Macromol. Sci. Chem. A9, 1 (1975). 10. E. M. Hodnett and A. W. Jensen, J. Polym. Sci. 43, 183 (1960). 11. C. A. Barson, J. Polym. Sci. 62, S128 (1962).
127
12. C. A. Barson and D. K. Burns, Eur. Polvm. J. 14, 497, 733 (1978). 13. C. A. Barson and D. K. Burns, Eur. Polvm. J. 14, 357 (1978). 14. D. R. Burfield and C. M. Savariar, J. Polvm. Sci., Polym. Lett. Ed. 20, 515 (1982). 15. G. G. Lowry, J. Polym. Sci. 42, 463 (1960).
0014-3057 84 S3.t)0+0.00 Copyright ,i: 1984 Pergamon Press [.td
Printed in Great Britain. All rights reserved
THE USE OF THE R A D I O T R A C E R M E T H O D TO CIRCUMVENT PENULTIMATE GROUP AND CEILING T E M P E R A T U R E EFFECTS IN C O P O L Y M E R I S A T I O N C. A. BARSON Department of Chemistry, The University of Birmingham, P.O. Box 363, Birmingham B I5 2TT. England (Receired 25 Mav 1983)
Abstract The radiotracer method can be used to study copolymerisations of M~ and M 2 under conditions where [MI]>>[M2]. In these circumstances, the probability of two M, units becoming adjacent in thc polymer chain during propagation is negligible. Experimentally derived reactivity ratios, obtained by a simple graphical solution of composition data, are realistic measures of relative reactivities even with systems where penultimate group effects or depropagation effects due to M2M~ diads are nora]ally significant.
When [M/]>>[M2], equation 1 simplifies to [10]
INTRODUCTION
m,
Data from copolymerisations are frequently used to obtain information about the relative reactivities of monomers towards reference polymer radicals or ions. The conventional copolymerisation equation [1-31 m~ _ d[M,] _ [M d//r~[M,] + [M2]~ /
m~
d[Md
[M2I\r2[Mq+[M,]]
m,
(I)
relates the molar ratio of the m o n o m e r feed, [Mm]/[M2], the molar ratio of the comonomers in the copolymer, m~/m2, and the reactivity ratios rL and r2; it is only valid at low conversions, when variations in [Mi] and [M:I are negligible. Some significant deviations from this "ideal" behaviour can be attributed to the influences of penultimate or even remoter units on the reactivitics of copolymer radicals or ions. If such units are taken into account, more propagation steps and therefore more reactivity ratios must be considered, resulting in more complex mathematical relationships [4]. Other deviations from "ideality" can arise when copolymerisations are carried out at temperatures near to the ceiling temperature for one of the monomers [5]. Reactivity ratios derived from equation 1 have even assumed negative values, showing that the kinetic scheme was invalid under these conditions [6]. Under conditions or for systems where penultimate or remoter units or ceiling temperatures become important, application of equation 1 to composition data will result in values for reactivity ratios which are not true measures of the relative reactivities expected from the reaction scheme. Even where the application of equation 1 is kinetically valid, its use in obtaining precise values of reactivity ratios is not easy, although some elegant solutions have been devised [7 9]. By using radiotracer techniques, many of these problems can be circumvented. Because of the very high sensitivity of the technique, the amount of a labelled comonomer, both in the feed and in the copolymer, can be determined fairly easily even at extremely small mole fractions.
-
d[M,]
[M,] - r~-d[M2] [Me]
(2)
A graphical solution of this equation, plotting m:,m~ against [M2]/[M~], was first applied to copolymerisations over 20 years ago [1 1]. The method has since been used to study the temperature effects in copolymerisation for several different systems [12]; it has also been used to determine some isotope effects in polymerisation [13]. Recently, reactivity ratios have been determined by applying equation 2 at a single composition [14]. But the advantage of the graphical solution [1 1], over a range of compositions, is that it provides evidence for the validity of the assumptions; it also gives data for assessing errors. Other advantages for the radiotracer method for copolymerisation studies are now proposed. They again result from the fact that [M2] can be maintained at extremely small values, such that [M~]>>[M2]. Under these conditions, the probability of two M, units becoming directly linked during the propagation steps is negligible. PENULTIMATE OR REMOTER GROUP EFFECTS One advantage applies to the effect of penultimate or remoter groups in copolymerisation. When the effects of penultimate groups as well as terminal groups are taken into account, the eight possible propagating steps result in the following equation [4]. mI
d[M ,]
m2
d[M2]
1 + [r,[~ =
-[M,]
I, '[M2] + ')," ~' '[M~]~] + 1
/_
(3)
-+ [M:])]
In this equation, rl = krll/k~l_,, rl = k>l kin,, r2 = k222/k22~ and r ~ - k~/k~:,. The notation lbr the
125
126
C . A . BARSON
rate constants of propagating steps follows the usual convention; the numbers in the subscript refer to each monomer type in the terminal triad, in the order in which they become incorporated by propagation. Application of the condition [Md>>[M2] to equation 3 leads to a simpler equation having the same form as equation 1. Thus m,
d[M,]
[M,]//r,[M~]+[M2]'~
(4)
m~ - d [ M 2 ] - [M:] [\ M ~ +, ] / - -"" where r~ is analogous to r2 in equation 1. However, this equation can be further simplified by reapplication of the above monomer feed condition, resulting in equation 2. Thus r, can be obtained graphically as before. If a plot of experimental data shows no deviation, within experimental errors, from the simple linear relationship of equation 2, the unimportance under these conditions of the reactivity ratio r~ in equation 4 is demonstrated; the only significant reactivity ratio is r~. This conclusion is confirmed by considering the propagation sequences involved in the reactivity ratio r~. In this ratio, the numerator, k~22, refers to the step ,,~MIM2* + M : ~ ~,~MtM2M2* Since such a process is highly improbable when [M,]>>[M2], this particular reactivity ratio is unimportant. By reversing the labelling, such that [Mz]>>[M~], r2 can also be obtained from a simple linear plot; in this case, the magnitude of r; is unimportant. It is concluded that, even in systems where penultimate group effects are normally quite large, such effects can be ignored when using radiotracer techniques under the conditions [Md>>[M2]. The measured reactivity ratio in these circumstances is a valid estimate of the relative reactivities of the monomers towards a specific polymer radical or ion. Similar arguments can also be applied to the effect of the groups preceding the penultimate groups. The propagating species to which r~ refers in this method can therefore be safely assumed to contain a sequence of several Mt units in the terminal group; this means that it should be kinetically indistinguishable from a homopolymeric radical or ion of M/. If the labelling is reversed to obtain r2, this ratio refers to a propagating species which is kinetically indistinguishable from homopolymeric radicals or ions of M2. DEPROPAGATION EFFECTS
The radiotracer method can also be used to advantage under conditions where reversible propagation occurs, for example, near to the ceiling temperature of one of the monomers. As ceiling temperatures are approached under the usual conditions of copolymerisation, changes in the magnitude of reactivity ratios with temperature can be larger than would be expected if equation 1 were still valid [5]. Lowry [15] postulated three different cases when depropagation could accompany growth to some extent; each category depended on the composition of the terminal group of monomer units in the growing polymer. Except for differences in the values of the reactivity ratios, no distinction needs to be made
between radical and ionic mechanisms. In Lowry's Case 1, a reversible propagation step is significantly probable only if the terminal diad in the growing polymer species is M~M2M2*, but not if it is ~M2M~* or ,~,AM1Mt*; thus m 2 d[M2] [M:][1/(1-~)] m, d[Md r,[Md +[M2] -
-
-
-
(5)
where ~ = [(rn2),+~*]/[(rnz),*] and 0 < n < or. The symbol [(rn2)n*] denotes an active species containing n units of M2, immediately preceded by one or more units of M~, at the active end of the growing polymer. If [M~]>>[M2], the probability of n having a value greater than 1 is negligible. Thus a = 0 and equation 5 reduces to equation 2. If a terminal triad of ,,~M2M2M2* is required before depropagation can occur (Case 2), the equation derived by Lowry again reduces to equation 2 when [Md >>[M2]. Case 3 requires the presence of the terminal triads N~M2M2M,* or ~,AM2M2M2* for depropagation to occur. As the formation of the diad ~'~M2M2* in any propagation step is highly improbable when [M1]>>[M2], similar conclusions are reached about the unlikelihood of depropagation influencing the kinetics under these conditions; equation 2 is again valid. When [M~]~>[M2] and at temperatures near to the ceiling temperature of M2, reactivity ratios determined using equation 1 are invalid and are not true measures of relative reactivity. This invalidity disappears when [MI]>>[M2] and the reactivity ratios obtained by the radiotracer method may be safely used to compare reactivities. CONCLUSION
If penultimate group effects or depropagation are prevalent in copolymerisation, mathematical solutions of composition data to give true reactivity ratios can be extremely complex. Yet, unless these effects can be satisfactorily taken into account, studies involving the finer variations in reactivity ratios, such as temperature effects, are pointless. The advantage of the radiotracer method is that the solution is just as simple as if the effects did not exist. However, it is necessary to keep conversions to low levels, so that m~/m2 = d[Md/d[M2]; since radioactive assays can be carried out on quite small samples, this usually presents no problems. It is also important to avoid significant kinetic isotope effects; since labelling is often possible at a point remote from the active site in the monomer, any resulting secondary isotope effects are usually negligible. REFERENCES
1. F. R. Mayo and F. M. Lewis, J. Am. chem. Soc. 66, 1594 (1944). 2. T. Alfrey and G. Goldfinger, J. chem. Phys. 12, 205 (1944). 3. F. T. Wall, J. Am. chem. Soc. 66, 2050 (1944). 4. G. E. Ham, J. Polym. Sci. 45, 169 (1960). 5. J. C. Bevington and B. W. Malpass, Eur. Polym. J. 1, 19 (1965). 6. M. Izu and K. F. O'Driscoll, 9". Polym. Sci. A-1 8, 1687 (1970). 7. M. Fineman and S. D. Ross, J. Polym. Sci. 5, 259 (1950).
The radiotracer method in copolymerisation 8. A. I. Yezrielev, E. L. Brokhina and Ye. S. Roskin, Vysokomolek. Soedin. A l l , 1670 (1969); Polym. Sci., U.S.S.R. 11, 1894 (1969). 9. T. Kelen and F. Tfid6s, J. Macromol. Sci. Chem. A9, 1 (1975). 10. E. M. Hodnett and A. W. Jensen, J. Polym. Sci. 43, 183 (1960). 11. C. A. Barson, J. Polym. Sci. 62, S128 (1962).
127
12. C. A. Barson and D. K. Burns, Eur. Polvm. J. 14, 497, 733 (1978). 13. C. A. Barson and D. K. Burns, Eur. Polvm. J. 14, 357 (1978). 14. D. R. Burfield and C. M. Savariar, J. Polvm. Sci., Polym. Lett. Ed. 20, 515 (1982). 15. G. G. Lowry, J. Polym. Sci. 42, 463 (1960).