POLPMERIZATION HYDRIDETRANSFER IX PROPYLENE
July, 1959
1167
and expansion of the liquid lead to the decrease of y TABLE VI SURFACE TENSIONS OF MOLTEN FLUORIDE MIXTURES, with temperature one might speculate that the DYNES/CM.
Temp. (“C.)
LiF-NaF-KF’
NaF-ZrFP
600 (230) 128 700 (220) 120 800 (210) 112 a Surface tension of mixtures estimated from extrapolated values of surface tension of pure components11assuming additive surface tension. Surface tension measurements of this mixture have not a8 yet been made. ’ TABLE VI1 ATOMICRADIIO F NOBLEGASESg
Radius(ft.)
He
Ne
A
Xe
1.22
1.52
1.92
2.18
ionic salt would lead to a smaller standard free energy of solution and greater solubility of the gases. As the polarizability of the rare gas atoms increases in the order He, Ne, A, Xe, an ion induced dipole interaction would cause an increasing trend in the ratio (Cd/Cg)expt/(Cd/Cg)calod in this same order. The last column in Table V illOstrates t,his trend which may be a consequence of the polarization of the rare gas atom. Although the values of the solubility may be estimated in this manner, relatively large errors in the temperature coefficients of solubility can enter from even small effects which have been neglected since the derivative of a small number may be large. In the relation dy/dT is always negative. I n Table IV the standard entropy of solution of the gases listed is small. Since thermal motions of the atoms of the liquid (10) F. W. Miles and G. M. Watson, Oak Ridge National Laboratory, unpublished work. (11) F. M. Jager, 2. anow. Chem., 101, 177, 180, 185 (1917).
“surface area” of the hole created by the gas atom increases with the liquid expansion so that the product rA is relatively constant in the solvents studied. Equation 5 leads to another interesting speculation. For a non-spherical molecule dissolved in a liquid, the increase of the “surface area” of the hole created with an increase of temperature will be due not only to thermal translatory motions but will also be increased by the rotation of the gas molecules. At higher temperatures the rotation of the gas molecules becomes more free and the hole becomes larger. This would lead to a more negative entropy of solution for non-spherical molecules than for the spherically symmetric rare gases. This conclusion is consistent with observation in organic solvents.6
Conclusions The model described, in which the free energy of solution of noble gases in molten salts is equated to the free energy of formation of holes the size of the noble gas atom in a continuous fluid which has the same surface tension as the solvent, yields solubility values for the noble gases which agree with the measured values within an order of magnitude. Measurements in other solvents presently in progress a t this Laboratory will be needed to test the usefulness of this correlation. Acknowledgments.-The authors are especially indebted to Dr. P. H. Emmett who first suggested to them the surface tension model used in the present correla,tion. Many interesting and valuable discussions with Drs. F. F. Blankenship and R. F. Newton are gratefully acknowledged. We are also grateful to Mr. W. D. Harman and associates who were responsible for mass-spectrometric analysis of the many samples submit,ted.
HYDRIDE TRANSFER AND THE MOLECULAR WEIGHT DISTRIBUTION OF POLYPROPYLENE BY C. M. FONTANA~ Contributionf r o m the Research Department of the Socony Mobil Oil Company, Inc., Paulsboro, New Jerseu Received December 19, I968
Evidence is presented for the occurrence of a hydride transfer reaction in the low temperature polymerization of propylene. The theoretical molecular weight distribution assuming equilibrium hydride transfer agrees closely with the observed distribution. The results are discussed with reference to the mechanism of Friedel-Crafts reactions and the form of alkyl halide-metal halide complexes.
I n previous work on the polymerization of 1- in a formed polymer cha.in. This reaction leads to olefins with promoted aluminum bromide cata- the formation of a tree-branched polymer of wide l y s t ~ ,it~was , ~ postulated that a hydride transfer re- molecular weight distribution. The purpose of this action occurs in which the growing carbonium ion paper is to present the evidence for hydride transfer abstracts a hydride ion from a tertiary carbon atom gathered from a careful study of the molecular weight distribution of a sample of polypropylene. (1) Celanese Corporation of America, Summit Research LaboraTheoretical treatments of the molecular weight tories, Summit, New Jersey. distributions to be expected with and without hy(2) C. M. Fontana, G. A. Kidder and R. J. Herold, Ind. Eng. dride transfer under various conditions of polyChem., 44, 1688 (1952). merization are also presented and compared to the (3) C. M. Fontana, R. J. Herold, E. J. Kinney and R. C. Miller, ibid., 44, 2955 (1952). observed distribution.
C. M. FONTANA
1168
Vol. 63
Experimental The preparation of the polymer sample has been previously described.8 The conditions of synthesis may be summarized briefly aa follows: Semi-continuous method, temperature -44'; continuous stage, residence time 30 minutes, HBr/AIBra (mole ratio) 0.75, C3H6/A1Br3(mole ratio) 20; batch stage, residence time 150 minutes, Cay,/ A1Br3 (mole ratio) 100. The polymer was separated 111itially into sixteen fractions by a fractional precipitation method using acetone and benzene mixed solvents. The fractionation procedure was not uniform. A fraction containing the highest molecular weight material was prepared by three successive preci itations, each time retaining the precipitate and adding t i e extract. to the remaining solution. This fract,ion then was separated into two fractions (15 and 16 in Table 11) with one additional fractional precipitation. The remaining fractions (14-1) were obtained uniformly in single precipitation steps, fraction 1 being the material finally left in solution. Subse uently, some fractions were separated into components ?mt the molecular weights of these components were not determined. These additional fractionations need not be considered for -0.2O d the urposes of the analysis. T t e molecular weights of the lower fractions (1-6) were determined by boiling point rise in benzene using the modi2.00 3.00 4.00 5.00 6.00 fied Menzies-Wright apparatus and method described by Log mol. wt. Barr and Anhorn .4 Osmotic pressure molecular weight determinations on the higher fractions (7-16) were made Fig. 1.-Relationshi of thickening power ( T P 210) to molecular iveigit for polypropylene fractions. using the apparatus and procedure described by French and Ewart.6 Toluene solvent a t 26.9' was used. The membrane material was No. 600 Cellophane obtained from Syl- Table I. The molecular weights were determined vania Industrial Corporation, Fredericksburg, Va.
TABLE I MOLECULAR WEIGHTMEASUREMENTS BY BOILINGPOINT RISE Fraqtion
THE
METHODOF
Concn. (wt. %)
Apparent mol. wt.
1
6.15 5.00 4.00 3.20 2.40
2
7.00 5.33 3.36 1.80 (0) 7.25 5.60 4.05 1.75
570 575 585 575 590 (597) 950 970 1000 1030 (1055) 1290 1350 1400 1470 (1529) 1560 1640 1750 1780 (1843) 2045 2250 2550 (2708) 2550 2870 3270 (3585)
1
(0)
(0)
6.33 4.55 2.75 1.05 (0)
7.30 4.15 2.10 (0) 7.00 4.60 2.19 (0)
Experimental Results and their Correlation The ebullioscopic measurements are given in (4) W. E. B a r r a n d V . J. Anhorn, Instruments, 20, 342 (1947). (5) D. &I. French a n d R. H. E w a r t , Anal. Chem., 19, 165 (1947).
by extrapolating a straight line obtained by the method of least squares to zero concentration, on a plot of apparent molecular weight versus concentration. The osmotic pressure measurements are given in Table 11. The molecular weights were calculated from the limiting values of h/c a t zero concentration using the method of least squares on a plot of h/c versus c . Experimental results of the fractionation are summarized in Table 111. A plot of log (TPZlo)versus log (molecular weight) is shown in Fig. 1. From Fig. 1 it is immediately apparent that a discontinuity exists between the molecular weight determinations of the two methods. As will be seen later, this is assumed to be due to the presence of low molecular weight material in the higher fractions. The method of treatment thus involves a correction to the osmotic pressure molecular weights, the correction being designed to remove error due to the diffusion of low molecular material through the membrane. A general method of treating and combining these results to yield the molecular weight distribution is that given by Beall.6 For the higher fractions the method was modified to simplify the calculations and to take into account the diffusion error in the molecular weights. I n the Beall treatment it is assumed that the molecular weight distribution of each fraction can be characterized by a binomial distribution with negative coefficients
where S is the mole fraction of total sample in the j t h fraction, X is the number of monomer-monomer bonds (DP-l), and p are the negative binomial coeficients characteristic of each fraction, and q = 1 - p. For any given separation a solubility law (6) G. Beall, J . Polymer Sei., 4, 483 (1949).
=
*
HYDRIDE TRANSFER IN PROPYLENE POLYMERIZATION
July, 1959
.
TABLE I1 OSMOTICPRESSURE MEASURE ME^fT8 Fractipn J
7
Concn., c (g./g.
sol-
v e n t X 102)
0.392 .294 .I96 .098
Height, h (om.)
9.31 6.52 3.66 1.69
(0) 8
0.582 .388 .194
9
0.745 .561 .373 ,190
10
1,043 0.849 .647 ,198 (0) 1.201 1.009 0.496 .438 .202
11.17 7.15 2.93
(0)
6.72 4.77 3.40 1.50
(0)
11
7.25 5.85 4.43 1.41 7.04 6.20 2.85 2.42 1.12
(0)
12
1.401 1.098 0.800 .501 .206
3.95 3.03 2.16 1.30 0.53
(0)
13
1.327 1.320 1.112 1.028 0.799 .738 .507 .474 .201 .I84
2.99 2.73 2.28 2.16 1.61 1.45 1.03 0.91 .44 .30
(0)
14
1.448 1 084 0.764 .482 .201 I
2.65 1.98 1.34 0.81 .34
(0)
15
16
1,095 ,782 ,507 .216 (0) 0.954 .669 .482 .281 .094 (0)
0.98 .67 .42 -19 0.29 .19 .I5 .08 .03
h/c
2375 2218 1867 1724 (1470) 2012 1843 1510 (1286) 902.0 850.2 911.5 789.5 (794.1)
TABLE 111 SUMMARY OF EXPERIMENTAL RESULTS O N THE FRACTIONATION OF POLYPROPYLENE Mol. wt.
Weight,'
%
TPniob
RTPb
Mol. wt.
0.441 597 0.49 3.97 ,614 1,055 .92 2 6.39 ,646 1 529 1.19 3 3.66 1.36 .667 1,843 4 5.00 1.60 ,690 2,708 5 5.00 6 3.04 1.78 ,693 3,585 ,716 17,300 2.04 7 4.62 2.24 .747 19,780 8 7.94 .787 32 ,020 2.93 9 4.64 .822 35 , 790 3.58 10 4.87 ,827 46 ,770 3.76 11 12.64 12 5.18 6.72 .866 101,200 13 9.36 7.60 ,872 136,900 10.33 .918 14 9.27 154,300 12.6 .923 300 ,000 15 4.76 829,200 16 9.66 24.6 .998 a Adjusted to 100% yield. Actual yield 97.4%. Sample weight 455.0 g. Thickening power and relative thickening power previously defined.3 1
17,300
19,780
32,020
46,770
281.9 276.0 270.0 259.5 257.3 (251.3)
1011200
89.50 85.68 82.84 87.96 (84.78) 30.40 28.40 31.12 28.47 31.91 (30.67)
Fractipn 1
695.1 689.0 684.7 712.1 (710.6) 586.2 614.5 574.6 552.5 554.5 (543.7)
225.3 206.8 205.0 210.1 201.5 196.5 203.2 192.0 218.9 163.0 (185.7) 183.0 182.7 175.4 168.0 169.2 (164.8)
1669
35 ,790
of the form Xx
=
e-ah
(2)
is assumed, where X h is the fraction of molecules of size X remaining in solution and a is a constant characteristic of the given fractionation. According to the method of moments, the three equations to be satisfied by the parameters for any given fractionation where the jth fraction is obtained, are 1 =
sj
j= 1
S[1 - Rn]
(3) (4)
j
Sj(u
+ 1 - p i ) = C S1 u [ u + 1 - p - e-5 (ue-5 + 1 - p ) R 9 j=
(5)
where j denotes the fraction numbered from that of lowest molecular weight, R = 1 p(e-" - l),u = np, and where it is understood that S, R, n, p and IL are functions of j . For the last two fractions separated, j = 1 (solution), j = 2 (precipitate), the three equations are solved for three unknowns: a! nl and n2. For each of the preceding fractions there are oiily two new unknowns, a and nj. Beall proposed that the equations to be satisfied then be equation 3
+
136,900
154 300
j
bSpj =
C
SU[I
- e-a~n-11
(6)
j=l
and 300,000 bzSjuj(uj
829 ,000
+ 1-
j pj)
=
+ 1 - p - e-a (ue-5 + 1 - p)Rn-2]
SZL[U
j- 1
(7)
where b is a new arbitrary parameter. The values of S and u are calculated readily from the experimental data from the relationships Sj =
C. M. FONTANA
1170
Wj/lcMj, k = CWj/Mj, and u = DP - 1 = Mi/ 1 42.08 - 1, where Wj is the weight of the fraction, M j is the molecular weight and IC is determined by summing over all the fractions. The Beall procedure was used for the two lowest and the two highest fractions. Because of the method of separation the two highest fractions formed an independent sample. Instead of using the Beall procedure for the higher fractions, it is possible to find values of the constants, a and nj, which satisfy equations 3 and 4 al011e.~ The procedure adopted for this calculation was as follows: for various likely values of e-a - 1 the functions j- 1
S(l - E " )
A = j=l
and j-1
Su(1 - e-aEn-l)
B = j-I
were calculated. From these, values of R' = ue-aA/B were determined with corresponding values of n' obtained from the relationships R' = 1 p'(e-a - 1) and u = n'p'. Using the values of A and n', the values of the function R" = (A/S)'-"', are determined. The functions €2' and R" are plotted against e-a - 1 and the point of intersection gives the true value of e-= - 1. Values of R were then found by linear interpolation of R' and the corresponding values of p and n were determined. The final values were checked by equations 3 and 4 in the form
+
j=1
and i
j- 1
Xu = j=l
Sue-"Rn-' j=l
pressure. This critical size is assumed constant for all higher molecular weight fractions through j = 14. For the higher fractions, starting with j = 8, the procedure was as follows: Three or four reasonable values of M (assumed) were taken. For each of these values the parameters and the distributions were obtained as in the foregoing procedure, again using the same value of k. Values of M(ca1cd.) then were determined by
0
M(ca1cd.) = (1 - F)Bm
where
Values of M(ca1cd.) and M(assumed) were plotted against n and the intersectioe of the two curves fixed both Mc and n. From Mc the paramet,ers S, u, n, p and e-a - 1 were determined readily as before. Finally, a new value of k was determined for the whole sample using values of Mc in order to determine values of S, such that CSj = l . The final
.
j
values of the parameters, S, u, n, p , 1 - e-a and 2, are summarized in Table IV. The distribution functions for each sample were calculated and summed to about 200 terms in the series
+
(A
-
€)(A
- E - 1). . . .(1 - € ) 2 A XI
(11)
+
2 XRn
S = j-1
Vol. 63
(9 1
where E = n 1 and II: = -p/(l - p ) , by means of the International Business Machines' "Card Programmed Calculator." Each term multiplied by S ( l - p)" gives the value of cpX a t any given A. Values of the function cpX a t high X values were calculated by
T o treat the higher fractions involving diffusion error in the osmotic pressure molecular weights, the following procedure was used: For the first such fraction ( j = 7) the true molecular weight was approximated by extrapolating from lower molecular weight values in Fig. 1. This value (mol. wt. = where a and @ are the absolute values of n and p and 4,876) was used to obtain the distribution c p ~for 'l is the gamma function, The distributions are fraction 7, using S and u values calculated by means shown in Fig. 2, together with the over-all sample of the same value of k as used previously. The distribution (circles) obtained by summing the measured and corrected molecular weights are re- fraction distributions. It may be observed from Fig. 2 that the number distribution follows closely lated by an inverse square law with increasing molecular weight over the range of DP from 20 to about 20,000. Theoretical Molecular Weight Distributions.where is the corrected number average molecular weight and M , is the molecular weight meas- Theoretical molecular weight distributions were ured by osmotic pressure. From this relationship derived for two extreme cases (1) assuming no the value c = 129 was determined. This is the hydride transfer and (2) assuming hydride transfer critical value of X corresponding to a molecular to be sufficiently rapid that the carbonium ion weight of 5470 and corresponds to the largest size carbon may be considered to be statistically dismolecule capable of diffusing through the mem- tributed over all polymer molecules. Both treatbrane in order to account for the observed osmotic ments presume a slow growth of many polymer chains throughout the reaction time, a picture con(7) An alternative procedure would be to generalize the solubility law to include two arbitrary constants and uae equations corresponding sistent with the results of a previous kinetic study of the polymerization of propylene with promoted to (31, (4)and ( 5 ) .
.
TABLE IV VALUESOF CONSTANTS CALCULATED FROM 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
THE
EXPERIMENTAL DATA
S
11
-n
-P
0.2773 .2525 .09981 .1131 .07606 .03535 .03950 .04438 .01560 .01177 .01971 ,004445 .005035 .003410 .0006617 .0004857
13.18 24.07 35.34 42.80 63.35 84.19 114.9 176.3 293.8 409.2 634.7 1,154 1,841 2,693 7,128 19,704
2.207 3.542 0.9653 1.699 0.5844 ,5609 .4478 .4446 .2661 .3253 .3705 .1910 .2235 .3553 .9751 1.925
5.972 6.796 36.61 25.19 108.4 150.1 256.6 396.5 1,104 1,258 1,713 6,042 8,238 7 ,580 7,310 10,238
aluminum bromide at low temperatures.8 Both treatments also imply no chain termination or other chain transfer mechanism. (a) Without Hydride Transfer.-Consider the statistical distribution of N molecules of monomer among c growing chains, the probability for any given monomer adding to a given chain being l / c . I n a batchwise polymerization, the probability of obtaining the nth-mer, which is the resulting mole fraction of nth-mer in the polymer, is given by Bernouilli's theorem
(:), ('+)""
p* = nl(NN! -n)~
P, =
en -8 v
42rn
(i)"
(14)
For a continuous polymerization stage (CFSTR), the distribution may be obtained from equation 14 by multiplying by e-8/8'/s' and integrating over s, where s' is the olefin-to-catalyst mole ratio. The result is S In
+ 1)"f'
Pn' =
n
P,-,.P,' = r=o
=
+
(s
r=O
(n
-
Ma
597
1,055 1,529 1,843
2,708 3,585 4,876 7,460 12,405 17,260 26,750 48,600 77,500 113,350 300,000 829 ,200
-1
-2
-3
-4
-5
5
-2
-6 -7
-8
-9
- 10 -11
e-t,p-rsr T N S -I- 1Y+1
5 Ar/T! + 1)"+lr=0
- e-")
(15)
If the continuous stage is followed by a batch stage (semi-continuous method) the filial distribution is n
(1
40.84 40.84 8.76 7.28 3.78 1.45 1.40 1.303 0.387 .261 .373 ,0712 .0730 .0433 ,5908 .5908
(13)
where n is the degree of polymerization. Applying the Stirling approximation to the facand letting torials in the form n! = nne-V%%, N -t a,c -+ m , and N / c = s, (the olefin-to-catalyst ratio) the resulting distribution function becomes
P," =
1171
HYDRIDE TRANSFER IN PROPYLENE POLYMERIZATION
July, 1959
1 2 3 4 5 log DP = log (1 1). Fig. 2.-The distributions: circles represent the most probable experimental distribution obtained by summing the individual probable distributions of the fractions.
0
(16)
where A = t(s l)/s, tis the ratio of olefin-to-catalyst in the batch stage and s is the ratio of olefin to catalyst in the continuous stage. The distribution (16) was calculated using the parameters corresponding to the experimental con( 8 ) C. M. Fontana and G. A. Kidder, J . Am. Chem. SOC.,TO, 3745 (1948).
+
ditions t = 133.3, s = 26.67 and the results are given in Fig. 2 as curve A. (b) With Equilibrium Hydride Transfer.-In a continuous flow reactor under conditions of equilibrium with respect to hydride transfer, there are n/s carbonium ion ca~bonsM?BCK&ed With the pn, nth-mers. At steady-state conditions
C. M. FONTANA
1172
where IC1 is the rate constant for the addition of monomer, and IC4 is the rate const,ant for removal of macromolecules (= rate constant for addition of catalyst). The distribution function is the solution of equation 17, or A pn
= m
where A is a normalization constant ( A = 1for
P,
1
= 1).
If the continuous stage is followed by a batch stage, the differential equation to be solved is and its solution is
+
where y = s/(s t ) , s and t are the olefin-to-catalyst ratios in the continuous and batch stages, respectively, and A is a normalization constant ( A = m
1 for
C P,
= 1). This is the distribution function
Vol. 63
the prior removal of small molecules in the stripping operation. Thus, assuming that the partial pressure of any one component is no greater thari about 1 mm. a t 250°, the mole fraction of each component in the finished polymer would be limited approximately to curve C (Fig. 2). This result is strongly suggestive that the observed maximum in the molecular weight distribution was caused by removing the polymer product. If it is assumed that the distribution of unremoved polymer is correctly given by the distribution law (equation 24) with A = 1 a t the low end, and that low molecular weight components were removed under the conditions described above, the amount of polymer removed can be calculated readily. The result shows that 45.5 mole % or 3.1 weight % of the original polymer could have been removed in this way. This would account for the observed discrepancy a t the low molecular weight end. It is instructive to compare the observed average degree of polymerization with the experimental monomer-to-catalyst ratio. From the results in Table IV, @ = Em, = 99.1. Assuming
a
(m)
j
the original distribution to be given by equation 20
1
for semi-continuous polymerization assuming equilibrium hydride transfer. Discussion Following its initial discovery,g the hydride transfer reaction is now generally recognized in various high temperature carbonium ion reactions such as catalytic cracking, isomerization and conjunct polymerization of hydrocarbons.10 In alkylation it forms an essential step of the carbonium-ion mechanism. Recently, it has been postulated to occur a t low temperatures (-80") in the self-alkylation of isobutane in the system HF-BF3.l1 However, its occurrence in low temperature polymerization with promoted aluminum bromide appears to be unique and forms the basis for the synthesis of some novel polymers from l - o l e h ~ . Heretofore, ~~~ the evidence for the occurrence of hydride transfer in low temperature polymerization, although convincing, has been mainly qualitative. In this paper more quantitative evidence is considered. On comparison of the theoretical curve A, assuming no hydride transfer, with the experimental distribution it is found that this theory is wholly inadequate to account for the wide molecular weight distribution observed. Moreover, it is difficult to find reasonable reactions, other than hydride transfer, which can account for such a high poly-dispersity. The theoretical curve B, assuming equilibrium hydride transfer, agrees very well with the observed distribution except at very low and a t very high molecular weights. The discrepancy a t the low molecular weight end (which results in A = 2 instead of A = l ) , can be largely accounted for by (9) P. D. Bsrtlett, F. E. Condon and A. Schneider, ibid., 66, 1531 (1944). (10) For a recent review see L. Schmerling, Ind. Eng. Chem., 46, 1447 (1953). (11) C. K. Donne11 and R . M. Kennedy, J . Am. Cham. Soc., 1 4 , 4162 (19521, and previous papers of this series.
= 54.8 (nt = 30,000). Correcting the observed distribution for loss of light materiacas above, the corrected value for the original polymer becomesDP = 55.7. Thus, while the average degree of polymerization is somewhat uncertain, due to the uncertainties in the distribution a t the low end, the more probable figure is about 55. This is nearly onethird the monomer-to-catalyst (promoter-limited) ratio used experimentally. (This means that possibly three macromolecules were formed per promoter-catalyst couple). This may indicate a slow inactivation of randomly situated carbonium ions due to the formation of resonating carbonium ions of the type H CH, H CHa H CHa
R--&-(!k.d!hL-=(!k/7
I
tic
6+
AlBr46f
H
a process which requires two proton transfers (presumably to monomer, starting a new chain) for each catalyst-promoter couple inactivated. It is also indicated that other proton transfer reactions are not predominant under t,hese conditions of polymerization. The discrepancy between theory and experiment a t the high molecular weight end of the distribution is believed to be due to failure to establish equilibrium with respect to hydride transfer during chain growth. Since the hydride transfer reaction is one between macromolecules, the rate of reaction must decrease with increasing size as a result of steric effects. At some size the rate of hydride transfer will not be sufficiently high to enable the macromolecule to accumulate its equilibrium portion of carbonium ions. This should result in a slight positive deviation from theory a t molecular weights below a critical limit and a large negative deviation
c
July, 1959
HYDRIDETRANSFER IN PROPYLENE POLYMERIZATION
above this limit. This is approximately what is observed. The extent of isomerization of carbonium ions during chain growth in this polymerization system remains an open question. Certain limitations in the rate of isomerization, however, are indicated. Thus it may be seen readily that a catalyst which isomerizes sufficiently rapidly during chain growth so as to eliminate all tertiary hydrogens, could not subsequently promote an intermolecular hydride transfer reaction and would not yield polymers of this type. The present picture of polymer growth, if accepted, does lead to some interesting conclusions with respect to the nature of carbonium ion complexes in hydrocarbon media. It is clear that no appreciable concentration of free carbonium ions is allowed, otherwise equilibration with respect to hydride transfer would involve a very different distribution due to the accumulation of positive charge on a single molecule. Of course, energetic considerations alone rule out this possibility in hydrocarbon media. The requirement of random distribution of carbonium ion complexes can be met if it is assumed that the complexes exist either as ion pairs or as coordinated complexes, or both. However, if more than one form of the complex exists and it is assumed that only one form reacts, then it is necessary that a reasonably rapid rate of interconversion exists, otherwise the postulate of random addition of monomer could not possibly be valid. If the two forms are assumed to be essentially a t equilibrium, the picture is inconsistent with the previous kinetic results.8 The kinetics of polymerization are explained on the basis of a rapid and reversible association of monomer with complex, followed by an unimolecular, rate-determining rearra,ngement step. The sum of the concentration of complex and monomerassociated complex is assumed constant. This sum will not be constant if the active complex is in equilibrium with an appreciable amount of a non-reactive complex. One is thus led to examine the validity of the postulate, commonly assumed, that alkyl halide-aluminum halide complexes exist in two forms. From a theoretical standpoint, FairbrotheP considered the question of the existence of the transition of covalent alkyl halide to ionic alkyl halide brought about by electrophilic metal halides. I n considerations of this kind it is generally assunied that if the hypothetical potential energy curve for the ionic state is lowered sufficiently by solvation so that it crosses the hypothetical potential energy curve for the covalent state, there exists the possibility of two states with a potential energy hump between them. These theoretical considerations all seem to be inconclusive because it apparently is impossible to determine whether or not the resonance interaction between the hypothetical states will be high enough to yield only one minimum in (12) F. Fairbrother, J. Chem. Soc., 503 (1945).
1173
the potential energy curve as a function of carbonhalogen distance. On the other hand, all the experimental evidence of which this author is aware is consistent with the view that only one form exists for any given complex. Fairbrother12 interpreted the substantial increase in polarization of ethyl bromide upon addition of aluminum bromide in cyclohexane solution to be due to the formation of a relatively small percentage of ion pairs. Alternately, these results could be interpreted by assuming the formation of a substantial amount of a less polar complex. Fairbrother and W r i g h P find the trityl bromide-stannic bromide complex to be mainly ionic. There was no evidence for the covalent complex, although a relatively small amount was considered possible. Bentley and Evans14report the trityl chloride-mercuric chloride complex to be mainly ionic. From an examination of the properties of 1: 1 complexes of gallium chloride and aluminum halides with primary alkyl halides, Brown, et aZ.,l6 conclude these addition compounds exist primarily in non-ionic form and undergo ionization only slowly, if at all. However, in this same paper, two different mechanisms of alkylation of aromatic hydrocarbons are proposed, based essentially on the premise that two types of alkyl halide-metal halide complexes exist. The existence of only one such complex would clearly result in one mechanism of alkylation, a mechanism identifiable with Swain’s concerted displacement mechanism.l6 After about seventeen more papers on the catalytic halides, Brown, et aE.,l? still have not found positive evidence for the existence of two distinct forms of the metal halide-alkyl halide complexes. More recently, the idea of two separate forms of certain complexes has been invoked more generally. For example, Winstein’s18formulation into classes I (covalent) and I1 (internal ion pair) is analogous to the above. The same question is also involved in controversial mechanisms of s u b ~ t i t u t i o na~t~ a saturated carbon atom. However, further discussion of this question is beyond the scope of this paper. On the basis of presently available evidence, it is believed that, in general, only one form of a metal halide-alkyl halide complex exists, a form which is neither purely ionic, nor purely coordinated, but a resonance hybrid of these two extremes. This view is consistent with the previously expressed views on the nature of carbonium ion-anion bonds discussed in connection with the mechanism of hydride t r a n ~ f e r . ~ (13) F. Fairbrother and B. Wright, {bid., 1058 (1949). (14) A. Bentley and A. G. Evans, Research, 6, 535 (1952). (15) H.C. Brown, H. W. Pearsall, L. P. Eddy, W. J. Wallaoe, M. Grayson and K. L. Nelson, Ind. Eng. Chem., 46, 1462 (1Q63), and previous papers. (16) C. G. Swain and W. P. Langsdorf, Jr., J . A m . Chem. rSoc., 7 8 , 2813 (1951), and previous papers of this series. (17) F. R. Jensen and H. C. Brown,J . A m . Chem. Soc., 80, 3039 (1958). (18) S. Winstein, E. Clippinger, A. H. Fainberg and G. C. Robinson, Chemistry and Industry, 664 (1954). (19) E. P. Hughes, C. K. Ingold, S. F. Mok, 8. Patai and Y. Pocker, J. Chem. Soc., 1265 (1957) and related papers.
JOHN WALKLLEY AND JOEL H. HILDEBRAND
1174
Vol. 63
PARTIAL VAPOR PRESSURE AND ENTROPY OF SOLUTION OF IODINE BY JOHN WALKLEY AND JOEL H. HILDEBRAND Contribution from the Department of Chemistyy, University of California, Berkeley, California Received December 90, 1868
Measurements of the partial vapor pressure of iodine a t 25" from its solutions in CClr and CS2 are reported giving values for ( b In p 2 / b In x2)rof 0.98 and 0.86, respectively. These are combined with values of R( b In x 2 / bIn 2') from solubility to give for the entropy of solution of solid iodine, 21.5 and 16.2 cal. deg.-l mole-', respectively. These values are independent of the assumptions contained in regular solution theory, including extrapolated properties of liquid iodine.
The senior authorl1 in 1952, called attention to the straight lines obtained by plotting log x2, where x2 is the solubility of a non-polar solid, such as iodine, against log T, instead of the usual 1/T, and he and Scott2 in the same year discussed the entropy of solution of the solid as given by the purely thermodynamic relation
a denotes activity referred to pure liquid solute as standard state. The factor, d In az/b In 5 2 was estimated by aid of the regular solution equation In a2
- In xz + v2+1~(6~ - 8J2/RT
( 2)
vzdenotes molal volume of the solute as supercooled liquid; the 6's are solubility parameters. This factor is unity when Henry's law is obeyed, which is practically the case where the solubility is small. We calculated 0.96 in CC4, 0.98 in C7H1,3 and 0.998 in C7F16. I n CS2,however, it fell to 0.81. Hildebrand and Glew* found that a plot of R(b In x2/bIn T) against -log x2 for iodine solutions gives a straight line, beginning with CSZ, through a tenfold range in x2. The linear range was later extended to 50-fold by Shinoda and Hildebrand.4 The present study was undertaken in order to convert R(d In a2/b In T)sat to entropy in the case of the CS2solution by a direct, experimental evaluation of the Henry's law factor. For this, we replace b In az/bIn x2 by a In p 2 / aIn x 2 ,where p2is the partial vapor pressure of iodine from its solution. Experimental The partial vapor pressure of iodine was determined by extracting and titrating the iodine vapor from a large flask, 3.126-liters capacity, connected by a wide neck with a small bulb, 200 cc., holding the solution. The latter was immersed in a thermostat maintained at 25.000 f O.O0lo; the flask was above the water in an air thermostat held at 26.00 f 0.05' to prevent condensation upon its walls. This difference of 1" was found to be adequate. The two vessels were connected by a ground-glass joint, sealed vacuum tight with Apiezon wax. Both vessels were thoroughly cleaned and dried. A solution was placed in the lower one; the two vessels were connected and sealed; the solution was frozen in a Dry Ice-alcohol bath, and the apparatus was evacuated through a capillary tube in the (1) J. H. Hildebrand, J . Chem. Phgs., 20, 190 (1952). (2) J. H.Hildebrand and R . L. Scott, ibid.. 20, 1520 (1952). (3) J. H. Hildebrand and D. N. Glew, THISJOURNAL, 60, 618 (1956). (4) K6z5 Shinoda and J. H. Hildebrand, ibid., 62, 292 (1956).
neck, which was then sealed off. The apparatus was placed in position in the double thermostat. After about 24 hours, with frequent &ation, e uilibrium was reached. The apparatus was removed, and &e bulbs quickly separated. The mole fraction of iodine in the solution waa determined by titration in the usual manner. The vapor of iodine was absorbed in KI solution, using successive portions until there was no further coloration. The va or pressure of iodine was calculated upon the assumption tfat at these dilutions it obeys the ideal gas law. The validity of this assum tion is attested by the fact that our value for the saturatecf solution, 0.305 mm., agrees well with the vapor pressure of solid iodine, 0.309 mm., determined by Gillespie and Frazer? using a flexible diaphragm. We made preliminary measurements with CCl, solutions, and also with solutions in CHBrs. The results in the latter were somewhat scattered, possibly on account of ins& bility of the solvent, and were not sufficiently reliable for our purpose. The data for the other two solutions are given in Table I.
TABLE I PARTIAL VAPORPRESSURES AND MOLEFRACTIONS OF IODINE AT 25" PZ (mm.)
0.076 ,138 .181 .234 .305
CClr
100x2
0.271 .518 .679 .893 1.148
1.38 2.29 3.22 4.63 5.00 5.46
0.086 ( .172)
.191 .264 .282
.305
A plot of log pz against log x2 gives a curved line in the case of the CSn solution, but log ( p 2 / z 2 )against XP gives a straight line with a slope of 0.60. All points except the one in parentheses in Table I fall closely upon this line. From this we calculate a In p z / a In x2 = 0.86, with which the earlier, indirect figure, 0.81, is in fair agreement. Table I1 gives the entropy of solution of Rolid iodine as determined from these data. TABLE I1 ENTROPY OF SOLUTION OF SOLIDIODINE AT - 25" st
Solvent
CC14
cs2
(-ET 0.98 0.86
. ( %b- E In? T) eat
21.9 18.8
-
82,
ca1.deg.mole-'
21.5 16.2
We defer discussion of these values of entropy till we have the results of a study nearly completed which will enable us to take into account the contribution of expansion to entropy of solution in these and other cases.
This research has been supported by the National Science Foundation. (5) L. J. Gillespie and L. H. D. Brazer, J . Am. Chem. Soc., 68, 22GO (1936).
