D. N. BHATTACURYYA, C. L. LEE, J. SMID,AND M. SZWARC
612
Reactivities and Conductivities of Ions and
Ion Pairs in Polymerization Processes
by D. N. Bhattacharyya, C. L. Lee, J. Smid, and M. Szwarc Department of Chemistry, State University College of Forestry, Syracuse University, Syracuse, New York 13210 (Received September 29, 1964)
The apparent rate constants, k,, of homopropagation of living polystyrene in THF (tetraThe intercepts of such hydrofuran) were shown to be linear with l/[living p~lymer]~’~. lines give k‘S-,Mt, the propagation rate constants of ion pairs, “S-,M+; the slopes yield k’rS-(Ks-,M+)1/2, k”S- being the propagation rate constant of free wS- ion and Ks-,M+the dissociation constant of an ion pair into free ions. By studying the inhibitory effect of alkali tetraphenylborides on the rate of polymerization, the values of k”s- and K ~ - , tM could be separately determined. Thus, at 25”, k f t s - = 65,000 l./mole sec., and the values of k’S-,M+ are 160 for Li+, 80 for Na+, -60 for K+, -50 for Rb+, and 22 for Cs+ ion pairs, all given in units of l./mole sec. The free ion is therefore 400 times as reactive as the most reactive ion pair. Studies of conductivity led to an independent determination of Ks-,Mt. The agreement between these two methods is most satisfactory with the exception of a two-ended Cs+,S--.S-,Cs+. In the latter system a new phenomenon takes place. Analysis of this phenomenon showed that an ion -S*S-,Cs+ cyclizes and forms a triple 25, the equilibrium constant for cyclization was found to ion, S-,Cs+,S-. For a be -5.5, and the propagation rate constant of the triple ion was found to be 2000 l./mole sec.
-
Kinetic studies of anionic polymerization of styrene in tetrahydrofuran were reported by Geacintov, Smid, and Szwarc,l who investigated this fast reaction by a capillary flow technique. They concluded that the propagation kinetically behaves as a second-order reaction, viz., -d[S]/dt = k, [living ends] [SI, where S denotes styrene and [living ends] the concentration of growing polystyrene. The latter remains constant in the course of each experiment since this type of polymerization proceeds without termination. Although k, is constant and independent of styrene concentration in each individual run,variation of [living ends] leads to small changes in k,, its value increasing with decreasing concentration of living polystyrene. Subsequent studies of other anionic homo- and copolymerizations in THF revealed a similar behavior,2J indicating that the variation of k, is characteristic for anionic polymerizations in this solvent. Two phenomena may account for this peculiarity. It is known4 that some living polymers, e.g., “S-,Li+ The Journal of Physical Chemistry
in benzene, dimerize. The associated form is unreactive, whereas the ordinary nonassociated ion pairs grow, and in such systems the apparent k, increases on dilution of living ends. The dimerization 01” living polymers may be recognized easily. The viscosity of the associated polymer solution markedly decreases when the active terminal groups are destroyed by protonation, e.g., on adding a drop of methanol5 Such behavior is not observed in THF solutions of living polystyrene, indicating a lack of their association in this solvent. Alternatively, the increase of k, OD. dilution may arise (1) C. Geacintov, J. Smid, and M. Szwarc, J. Am. Chem. SOC.,84, 2508 (1962). (2) D.N. Bhattacharyya, C. L. Lee, J. Smid, and M. Szwarc, ibid., 85, 533 (1963). (3) M.Shima, D.N. Bhattacharyya, J. Smid, and M. Szwarc, ibid., 85, 1306 (1963). (4) D.J. Worsfold and S. Bywater, Can. J . Chem., 38, 1891 (1960). (5) H.Brody, D. H. Richards, and M. Szwarc, Chem. Ind. (London), 45, 1473 (1958).
IONS AND ION PAIRS IN POLYMERIZATION PROCESSES
from the ionic dissociation of living ion pairs, viz., -S-,Na+ 43Na+, if a free -S- ion propagates faster than its ion pair. This explanation was erroneously rejected by Geacintov, et al.,I and it is instructive to consider their reasons. The data of Geacintov, et al.,l covered a relatively narrow range of living end concentrations, namely from to 2 X M . Extrapolation to zero concentration led to k,, of 600-700 l./mole sec. Accepting thh value as the propagation rate constant of the free MS-, one can calculate the concentration of ions in the investigated solutions. For example, the experimental data led to an apparent ionic dissociation of 50% in a M solution of -S-,Na+, whereas the conductivity studies of Worsfold and Bywatere indicated only -1% dissociation. Ionic dissociation of -S-,Na+ should be depressed on adding NaC104to its solution. Therefore, the addition of this salt should slow down the polymerization if the observed increase of k , with dilution is due to ionic dissociation. Such an effect was not observed,l contradicting again the hypothesis of participation of free ions in the process. The two negative results induced us to look for more exotic explanations,’ and these appeared attractive for a while. However, further consideration of the problem forced us to return to the concept of free ions and suggested that the evidence presented by Geacintov, et aLll was not entirely convincing. The extrapolation to zero concentration of living ends could be uureliable since the data were limited to [living ends] 2 M . The effect of sodium perchlorate could be negligible if its degree of dissociation in THF is minute. It was decided, therefore, to extend the kinetic studies to much lower concentrations and to investigate the conductivities of living polystyrene and of NaC104 in THF.
613
+
Ewerimental Technique of Kinetic Studies The capillary flow technique, used in previous studies,1t2is unreliable when investigating the polymerization at concentrations of living ends lower than M because the destruction of living ends then becomes excessive. We developed, therefore, a static technique in which the progress of polymerization is followed spectrophotometrically by monitoring the absorption of styrene at 291.4 mp. At this wave length the monomer has an absorption maximum, E = 673, and its optical density obeys Beer’s law. The apparatus used for kinetic studies is shown in Figure 1. It consists of a 2-1. flask, A, filled with specially purified nitrogen at atmospheric pressure. The flask is connected though a stopcock to two con-
M
L
Figure 1* The apparatus wed for kinetic
studies of fast anionic polymerizations.
tainers, B and C. The latter are linked by a three-way Teflon stopcock, T, to an optical quartz cell, D. Three ampoules, M, L, and E, each equipped with a breakseal, are sealed to the unit. The first contains a THF solution of the monomer, while the second and third contain, respectively, a very dilute and a concentrated THF solution of living polystyrene. The whole unit, with exception of flask A, is evacuated on a high-vacuum line, flamed, and thereafter sealed off. The break-seal on ampoule E is crushed, and, by tilting the unit, the containers and the optical cell are rinsed with the concentrated solution of living polystyrene. This procedure destroys traces of water and other impurities adsorbed on the inner walls of the apparatus. The unit is turned upside down, the concentrated solution is returned to ampoule F, and, by cooling the outside walls with a pad soaked with liquid nitrogen, the solvent from F is condensed on the inner walls. This “washing” removes all the living polymer from the unit and transfers it to F. Ampoule F is then sealed off at liquid nitrogen temperature. The optical cell (optical path 1 em.) is now inserted into a spectrophotometer equipped with a recorder. Through crushing the break-seals, the solutions of styrene and of living polystyrene are transferred to the appropriate containers, B and C, which are then pres-
^ ^
(6) D. J. Worsfold and S. Bywater,
J. Chem. SOC.,5234 (1960). (7) M. Szwarc and J. Smid, “Progress in Reaction Kinetics,” Vol. 11, Pergamon Press, Inc., New York, N. Y., 1964, pp. 243-246.
VOblume 69,Number 2
February 1966
D. N. BHATTACURYYA, C. L. LEE, J. SMID,AND M. SZWARC
614
surized with the purified nitrogen while the optical cell remains evacuated, The monochromator is set at the required wave length (291.4 mp), and the recorder is switched on. Quick opening of stopcock T lets both solutions rapidly into the evacuated optical cell, and the resulting turbulence efficiently mixes the reagents. The stopcock is then closed to prevent the diffusion of the reagents into the cell. In this device the concentration of the monomer is monitored in less than 1see. after the onset of polymerization, and reactions having half-lifetimes of about 3-4 sec. may easily be investigated. The concentration of living ends is determined spectrophotometrically at the end of the experiment, but not later than 10-20 sec. after the onset of the reaction, by turning the monochromator to 340 mp, vk.,the XNM of 4 - , N a . f . The ratio of initial concentrations of the monomer to living ends was about 20: 1. In runs lasting more than 50 sec. the concentration of living polymers is determined during the experiment by turning the monochromator at regular intervals to 340 mp. This procedure is illustrated in Figure 2. Usually the concentration of living polymers remains constant during the whole course of polymerization; however, if it does not, the appropriate corrections are applied. It is important that [living ends] is determined in the polymerizing solution and not in the stock solution. This procedure eliminates any errors arising from accidental killing caused by the addition of monomer. For very slow reactions-half-lifetime of about 2 min. or more-a simplified procedure is used. The apparatus is depicted in Figure 3 which is self-exOPTICAL DENSITY
, 0
40
120 160 200 REACTION TIME ( S E W
80
240
Figure 2. A typical recorder tracing of the optical density at 291.4 mp (Aof styrene) &B a function of time. The high peaks give the optical density a t 340 mp (Am= of living polystyrene).
Ths Journal of Phvsical Chemistry
280
320
OPTICAL CELL VACUUM MONOMER SOL.
Figure 3. The apparatus used for kinetic studies of slower anionic polymerizations.
planatory. The solutions of the monomer* and the polymer are sealed in the appropriate ampoules, and, through crushing the break-seals, they are admitted to the respective arms of a V-shaped reactor which previously was purged with a concentrated solution of living polymer. The contents are then vigorously shaken, the mixture poured into the attached optical cell by turning the unit upside down, the cell placed in the spectrophotometer, and the recorder switched on. This procedure takes about 15 sec. The length of the optical cell used for such kinetic studies depends on the dilution; l-cm. cells were used for higher concentrations, ([43-,M+] M), whereas for diluted solutions M or less) 5- or 10-cm. cells had to be employed. The initial concentration of styrene was usually 10 to 20 times that of the living ends. The extremely diluted THF solutions of living polystyrene are relatively unstable, and -S-,Li+ seems to be the least stable alkali salt of living polystyrene. Therefore, it is advisable to store a more concentrated solution in the respective ampoule; then, by crushing the break-seal and tilting the unit, a fraction of it may be transferred into the appropriate reservoir and diluted by distilling in the THE' from the remaining concentrated solution. The dilution is accomplished a few minutes prior to the actual experiment. The rate of decay of M solutions of living polystyrene is about a few per cent per minute; the twoended wS-,Cs+ is, however, exceptionally stable. It appears that the decay is due to a reaction of the free -Sions with THF leading to the formation of S (CHJ 4 0 -. The results are calculated by plotting {log (O.D., -
-
My
(8) It is more convenient t o introduce into the ampoule a pure, undiluted monomer; this minimizes the extent of killing.
615
IONS A.ND ION PAIRS IN POLYMERIZATION PROCESSES
in a blue tint of the solution which eventually becomes black. Properly prepared solutions show only one fairly sharp absorption peak (for wS-,Cs+, A,, 345 mp). The living 43-,Cs+ having only one growing end per chain was prepared by slowly adding a THF solution of styrene to the stirred solution of cumyl-,Cs+. The resulting polymer of a 25 shows an absorp341 mp. The slight difference in the tion at X, absorption spectra of the two-ended and one-ended cesium polystyrenes may indicate the intramolecular association of the former polymer; i e . , its structure may be [S-,Cs+,S-],Cs+. The problem of intramolec-
t hCS+ J kp
= 218 I. mol-'
[L.EJ =
-I 5
\
5
*
seC.-'
2.6 x I O - ~ M ~ ~
p+ym&&
-
0
4
8
12
16
18
TIME (Sec.)
Figure 4. Plot of log (O.D.$ - O.D.,)
= log D vs. time.
O.D.,>)/[living ends] us. time as shown in Figure 4. The term O.D., corrects for the absorption of living polystyrene at 291.4 mp. The plots remain linear even if the reaction is followed for 3 or 4 half-lifetimes of the process. Preparation of Living Polymers. Living polystyrenes endowed with two growing ends and possessing Na+ or IC+ counterions were prepared in a conventional way from living a-methylstyrene dimers or tetramers (see ref. 1 for further details). The T P of the resulting polymer was usually between 20 and 25. Living polystyrene with Li+ counterion was prepared by treating ethyllithium recrystallized from benzene with an excess of styrene in THF. It was checked that all the ethyllithium reacted, and none was left in the solution. Notice that such polymers have only one living end per chain. Polymers having Rb+ or Cs+ counterions were prepared by slowly adding a THF solution of styrene to the respective alkali metals. Cesium and rubidium were prepared by heating the respective chlorides with metallic calcium and distilling the liberated metal under high vacuum into the reaction flask. It was found desirable to have a slight excess of cesium and to filter the solution 10-15 min. after the onset of the reaction when some free cesium fs stiU present. A prolonged contact with the metal results
-
u
ular association of ~ s - , C s +ends will be discussed at length in a later part of this paper. A solution of cumyl-,Cs+ is prepared by adding to a stirred dispersion of metallic cesium in THF a THE' solution of methyl cumyl ether. The blue color of the Cs solution disappears instantly and, gradually, a yellow coloration appears which eventually turns to a deep red. As the reaction proceeds, cesium methoxide precipitates. The reaction is continued overnight; then the mixture is cooled to -80" to enhance the sedimentation of the precipitate, and after 2 hr. the clear solution is decanted through a glass sinter plate. The absorption spectrum of cumylcesium shows a maximum at 345 mp, and by titrating the solution, the extinction coefficient was determined to be -1.8 X lo4. Conversion exceeds 90%, but a much longer exposure to the metal is not recommended since it leads to some side reactions which are manifested by the appearance of new absorption peaks. Extinction Coe@cients of Living Polymers. In the kinetic studies, as well as in studies of conductivities which will be described in a later part of this paper, we determined the concentration of living polymers from their optical densities. It was necessary, therefore, to determine accurately their extinction coefficients. The following device, shown in Figure 5, was used for this purpose. Ampoule A, containing an aliquot of concentrated living polymer solution (-1-2 X M), and ampoule F, having a small amount of dry and deaerated methyl iodide, are sealed to the left arm of the apparatus. This consists of an optical quartz cell, B, having a 2-mm. optical path, equipped with a 1.9mm. spacer, C, a flask, D, with a calibrated narrow neck which serves to determine accurately the total volume of the solution, and a round-bottom flask, E, with a magnetic stirrer in which the titration of living polymers is accomplished. The apparatus is evacuated through the connected tube, flamed under high vacuum, and eventually sealed off at constriction PI. The break-seal on ampoule A is crushed, and the concenVolume 69,Number 2 Febrwlry 1966
D. N. BHATTACHARYYA, C. L. LEE, J. SMID,AND M. SZWARC
616
A
poule containing an exactly weighed amount of deaerated water or other suitable protonating agent is attached to flask E. The amount of water should not be sufficient to destroy all the living ends, and, thus, after its contents are introduced into the flask, the optical density of the remaining polymer may be r e determined. The difference in optical densities, in conjunction with the known amount of the “killing” agent, gives the extinction coefficient. The values of the extinction coefficients determined in this laboratory are listed in Table I. The validity of Beer’s law was
E
UD
Figure 5. Apparatus used for determining extinction coefficients of living polymers.
trated solution of living polymers ( ~ 1 - 2X 10-2 M ) is introduced into E. Ampoule A is washed by chilling its walls with a pad soaked in liquid air, then the wash solution is frozen in E, and A is sealed off at constriction Pz. By rinsing the apparatus with the living polymer solution all the impurities and any residual moisture adsorbed on the walls are removed. All the contents are then collected in E, and the remaining parts of the equipment are washed by chilling the walls and condensing the solvent. From E the liquid is quantitatively transferred into D and brought to the desired temperature; its volume is measured by determining the position of the meniscus in the narrow neck. The solution is then introduced into optical cell B; it is mixed well by being poured in and out a few times, and eventually its spectrum is recorded. Thence, it is again quantitatively transferred into E, chilled, and magnetically stirred. The break-seal on the methyl iodide ampoule, F, is crushed, and, as soon as the red color disappears, the distillation of methyl iodide is interrupted by chilling F. Flask E is then cut off; the solvent and the slight excess of methyl iodide are evaporated; the residue containing the killed polymer and sodium iodide is dissolved in distilled water and titrated for inorganic iodide, following a conventional analytical procedure. To secure complete solution of the salts in water, a small amount of benzene is added to dissolve any polymer. The titration of a concentrated solution of living polymer with methyl iodide is reliable although difficulties are encountered in titrating very dilute solutions. The procedure may be improved by eliminating all the difficulties of analysis arising from the uncertainty in the end-point determination. Instead of ampoule F containing an excess of methyl iodide, a small amThe Journal of Physical Chemistry
Table I : Decimal Extinction Coefficients of Salts of Living Polystyrene at 25’ Counterion
Solvent
Li + Li + Na + Na + K+ K+ Rb + Rb + Cs + (two-ended) Cs + (one-ended) Cs + (two-ended)
THF Dioxane THF Dioxane THF Dioxane THF Dioxane THF THF Dioxane
,A,
mp‘’
337 (338) 336 342 (343) 339 343 (346) 340 340 341 345 341 342
e
X
10-4‘
1.00 1.02 1.20 (1.18) 1.21 1.20 1.21 1 . 2 (?) 1.23 1.3 (?) 1.25 1.24
a The values in parentheses are those of S. Bywater, A. F. Johnson, and D. J. Worsfold, Cun. J. Chem., 42,1255 (1964).
established by using a procedure similar to that described in the section dealing with the conductivity measurements.
Results The results of the kinetic experiments are summarized in Tables I1 and 111. The sodium salt of living polystyrene was most extensively studied, its apparent k, values being determined for [living ends] ranging from to lod2 M . The kinetics of polymerization of other salts, viz., those of Li+, K+, Rb+, and CS+, were studied at sufficiently low concentrations to establish unequivocally the functional dependence of the respective k, values on [living ends]. Let us assume that ion pairs, “S-,M+, and free -S- ions participate in the propagation, their respective rate constants of growth being ? c ‘ ~ - , ~ +and k f f s - . If fraction x of living polymers is dissociated into ions, then the observed k, is given by the equation IC, = (1 - x ) ~ ’ s - , M + xk”s-. For x 0.05, the approximations (1 - x ) = 1 and x = (Ks-,M+)”’/ are valid and, thus, k, = k ’ s - , ~ + [living IC”S-(KS-,M+)’/*/ [living ends]’/‘. In this equation
+
