GEL FORMATION IN ADDITION POLYMERIZATION
Starch, 1945
215' was then distilled several times under reduced pressure. The final product had a boiling point of 6949.5' at
-, nim.
Steroids.-
M. p., 'C.
1. Cholestanediol-38,7a 9 . Cholestanediol-38,719
167-168 152-153 164-165 168-169
3. CholestanolS~-one-7 4. Ib-Cholestenol-3,9-one-7 A. Testosterone = A4-androstenol-170one-3 154-155 6. &-Testosterone = A'-androstenol178-one-3 220-221 7 . Y-Androstenediol-3~,17a 182-183 8. 1\6-Androstenediol-38,178 198.0-198.5 9. Androsterone = etio-allo-cholanol3a-one-17 182.5-183.5 10. @-Androsterone= etio-allo-cholanol3 pone- 17 171.4-173 11. i14-Androstenedione-3,17= A4-etioallo-cholene-dione-3,17 173-174 15. Dehydroandrosterone = As-androstenol-3@-one-17 135-137 Compounds 1-4 were obtained from Dr. 0. Wintersteiner of the Squibb Institute for Medical Research, compounds 5-11 from Dr. C. R. Scholz, of Ciba Pharmaceutical Products, Inc., and compound 12 from Professor Byron Kiegel of Northwestern University.
Acknowledgment.-The authors take pleasure in acknowledging the cooperation of Dr. 0. Wintersteiner, Dr. C. R. Scholz and Professor Byron Riegel in supplying the steroids which made this study possible. They also wish to thank Dr. I. F. Halverstadt, Dr. C. R. Scholz and Professor Byron Riegel for their comments and discussions.
summary The dipole moments of eight androstane derivatives, four sterols, and isophorone have been
[CONTRIBUTION FROM THE
44 1
measured in dioxane solution. The moments of the compounds are as follows : cholestanediol3@,7cy, 2.31 ; cholestanediol-3@,7/3, 2.55; cholestanol-30-one-7, 2.98; A5-cholestenol-3@-one-7, 3.79; androsterone, 3.70; @-androsterone,2.95; A6-androstenediol-3@, 17a, 2.89; A5-androstenediol-3@,17@, 2.69; A5-androstenol-3@-one-17,2.46; testosterone, 4.32; cis-testosterone, 5.17; A4androstenedione-3,17, 3.32; isophorone, 3.96. The moments of four of these compounds fall outside the range calculated for free rotation of the hydroxyl groups, from which it is concluded that the 30- and 170-hydroxyl groups do not have freedom of rotation. A ketone group conjugated with a double bond in a six-membered ring has a moment about 1 unit higher than a simple ketone. The dipole moment of isophorone indicates that the compound exists chiefly in a form with the double bond conjugated with the ketone group. A double bond in the sterol nucleus that is not conjugated decreases the moment of the compound by 0.49 unit in the one case studied. Two explanations are discussed. Sterols with two polar groups and differing only in respect to the position of a hydroxyl group on the same carbon atom have different moments. The difference in moments of the members of any epimeric pair depends somewhat on the moment of the other polar group in the molecule. There appears to be no correlation between the dipole moments of the sex hormones and their physiological activity. SANFRANCISCO, CALIF.
GENERAL LABORATORIES OF THE UNITED
RECEIVED NOVEMBER 27, 1944
STATES RUBBER COMPANY]
Gel Formation in Addition Polymerization' BY CHEVES WALLING When a polymerization is carried out in the presence of a polyfunctional component which permits the three-dimensional growth and crosslinking of chains, there is, a t some stage in the reaction, a rather abrupt transition from the liquid to the gel state. In 1931 Carothers pointed out that such a gel is the result of the linking together of polymer molecules into a three-dimensional network of indefinitely large size.2 In 1941 Flory outlined a general method for determining the extent of reaction at which such a network becomes possible, and carried out the detailed calculations for the case of polycondensation reaction~.~ His results were in good agreement with experiment, and he indicated that a similar (1) Presented before the Physical and Inorganic Section a t the N e w York meeting of the American Chemical Society, September 12, 1944. ( 3 ) W. H. Carothers, Chrm. Rev., 8, 402 (1931). ( 3 ) P T Florv. TITIS JVITYNAL. 85. 3083 (1041)
method might be applied to addition polymeriza tions. Recently, Stockmayer*has applied Flory's procedure to a mixture of polyfunctional components with a generalized distribution of functionality and has obtained an expression which should predict the gel-point in both vulcanization reactions and addition polymerizations in which all functions have equal reactivity. In this paper, calculated and observed gelpoints are compared for the systems methyl methacrylate-ethylene dimethacrylate and vinyl acetate-divinyl adipate. Observed extents of reaction a t the gel-point are, in general, found to be several times those calculated, particularly in experiments in which very early gel-points are anticipated. This discrepancy is discussed from the point of view of the discontinuous nature of dilute polymer solutions. (4)
W
H Stockmawr J Chem P h v ~ 11. I 2 5 flOJ4)
4.12
Vol. 67
CHEVES mfALL1NG
Flory's" iiiethcd oi' cdculating the gel-l)oiiiti i ! a polyiiierizing systciii is it statistical tilie, a i i d consists in tlcterniiiiing the conctit ions iinctcr which t h e esistciice of :LII iiitlefinitcly large iiiolrcule twconies possible. StLitctl i i i the iiiost gciieral tvrii~s,this possibility arises whcii t he csl)cctc.ti riuniber of additiounl elcnicnts to which R r:mctuinlv selected elenient, 1i11ow11oiily to be coniiected to a single other eleiiient or s!-steni ctf eleiiittits, is attached exceecls iiiiity . A\ccordingl!.-, the point in a reaction whcrib this cqic.cl:ition conies unity is drfincd as the gcl-i)oii~t.> 'Niis 1-ondition for the formnticm of infinite iv..twc:rks .~i)pliesregardless of whether inonoilier units i n jicncral, polyfuiwtiorial braiiching ceiitcr-s, (ir whole polymer chains are choscii 21s tlie elenicnts t o be considered. Pnralleling Flory's treatriicrit of polycoi~densat Io11 reactions, the gel-point in tlie addition polyiiierizatiori of ;F mixture of mono- and divinyl iiiunoiners6 in which all vinyl groups have the s;tnie reactivity may be calculatecl as follows. Choosing as the elements in the polyiner the iiionoiiier units regardless of the nunibcr of re:~ctedvinyl groups which they contain, let I/ equal the probability that a given vinyl group tins reacted, (I, that a reacted vinyl group ends a chain, % i n t i r , that a unit contains two viriyl groups (re:Lcted or unreacted). That p a n d r are iritleiwritlerit probabilities, as the treatment requires, follows froni the assuniption that all vinyl groups have ecpal reactivity. The independence of q requires, as well, that the ratio of rates of chain growth to chain transfer or termination i s indeiwndctit of chain lengtl, and that each chain is iornied by a single active center. In the case of catalyzed polymerizations, where chain transfer with solvent is appreciable, or where termination is by disproportionation rather than coupling, both requirements are probably met satisfactorily. Employing these symbols, the gel condition may he written down as ( 1 - r ) ( l - q\ + r [ ( I - q ) Zp ( 1 - q ) ] = 1 (1) which siniplies to h
i
-
+
2 p r = y!(l
-
Q)
(2)
The first product in ( I ) is the expectation of additional attachments arising from the selection of a inonovinyl unit, (1 - q), times the probability that such a unit was chosen, (1 - r ) . The second product is the expectation arising from the selection of a divinyl unit, (1 - q) from the other end of the reacted vinyl group by which it is known to be already connected, plus p(l - 4) from the other vinyl group which may or may not have re(5) For an excellent and detailed discussion of the reasoning behind these statements, thc reader is referred to Flory's original paper.' (6) Because, in general. the reaction of n vinyl group in an addit i o n polymerization results in thc attachment of the monomer unit t < r two other units, an n-vinyl mononier (i.e . , one containing n reurtive vioyl groups) corresponds to a Sn-functional unit in the polyctmdeneations discwssed hy Flory. However, as will be seen I,!tcr. in any ,*tatistical consiclerntirrn of tlie polymers. these fnnctiom i l i n r i l d be thoiiyht < i f as reacting in wairi.
;ic.tctl, ti1iic.s tlic 1mb:ibility r that a divinyl unit w t s cliuscn. 'l'lie iiiaiiiier in which p appears in the equation is a result of the fact that addition i~olytiierizutiorisare rapid chain reactions, so that i i i these coiisideratic~ns,when one e n d of ; I vinyl group has reacted, Lhc possibility that the other has not niay be iieglected. This rapidity of cliaiii growth is iri direct contrast to the behavior of Ij"1ycoiicleiisatio~i reactions a n d its conse(ltie1ices will bc culisitlercd again in this paper i n tiic tliscussioii of experiinental result$. I I' 1 4 aiid 13 :ire thc concentrations of unreacted iiiotio- and cliviiiyl monomers, A0 and 13, their initial coiiceiitratiotis, and all vinyl groups we consitiercd to have the s;tiiie reactibity, p = I - Airlo (or 1 - (UjUo)'/2 by virtue of the fact that W will enter the polyiner proportionally twice as fast as A ) , ant1 r = 2130/(A0 2230). Noting that q = 1/X, the average kinetic chain length in the polymerization (i. e., the average degree of polymerization if all bifunctional units were cut in two between the functions, or the average number of chain growth steps occurring between :i transfer or disproportionation reaction) , these quantities may be substituted into (2) to yield as the gel-point equation.
+
If the weight average numbcr of units i n a kinetic chain is equal to 2X - 1 (the calculated relationshii) if chain termination is independent of chain length, and each chain is produced by only one active center'), Equation (8) is equivalent to that derived by Stockmayer,* employing as branching units the kinetic chains rather than the individual monomer unitsR Equation ( 3 ) states that the extent of reaction a t the gel-point, :IS measured by 1 - A/Ao, varies inversely with both the amount of crosslinking agent and the average chain length of the polymerization. I n order to test this hypothesis, methyl methacrylate and vinyl acetate have been polymerized in the presence of small amounts of ethylene dimethaerylate and divinyl adipate, respectively. These systems were chosen because it was felt that, in each, the reactivities of all functiotis should be similar, and because data were available on the viscosity-niolecular weight relationship for polymers of both rnonofunctional tiionomers. Experimental Materials.-Methyl methacrylate and vinyl acetate were commercial materials, fractionated shortly before (73 Schulz. Z. p k y s i k . C h m . , B30, 379 (1936).using approximations valid only for large values of ?,. has obtained 2 X for the weight average number of units. However, when the actual summations are carried out. the above value results. (8) While the niethod outlined above stresses the detailed mechanihm o f addition polymerization with which we are here concerned, the niethod of Stockmayer seems more xcneral and more elegaut i n that i t Ureclicts the amount o f raudomly distributed cross-linkinc necessary to produce gelation in any system when the weipht I I V C ~ ~ X P number o f units per chain is k n o w n .
March, 1945
GELFORMATION IN ADDITION POLYMERIZATION
use (the former under reduced pressure) and stored in the refrigerator. Ethylene dimethacrylate was prepared by the alcoholysis of methyl methacrylate with ethylene glycol, followed by vacuum distillation. Its physical constants were: b. p. 1 mm., 83-85', n% 1.4533. Divinyl adipate was prepared from vinyl acetate and adipic acid.@ The product boiled a t 89.5-89.7' at 0.5 mm. and hadD'n '1.4544. Solvents were c. P. materials, used without further purification. Determinations of gel-points were carried out on approximately 5-cc. samples in 12 X 75 mm. test-tubes, flushed out with nitrogen, corked securely, and placed in a 60" thermostat. From 0.10 to 1.00 g. of benzoyl peroxide per mole of monomers served as catalyst, and gelation occurred in one-half to fifteen hours, depending upon the system. The extent of reaction was followed by index of refraction measurements, the relation being assumed identical with analogous systems containing only the monovinyl monomer, where it was found to be linear. For two experiments containing over 5% of divinyl monomer, the extent of reaction a t the gel-point was determined by actual isolation and weighing of the polymer. With the exception of some of the vinyl acetate experiments which showed appreciable induction periods, rates of reaction in any one system were approximately constant and independent of the amount of cross-linking agent. The viscosities of the solutions were determined by inverting the tubes from time to time, and the gel-point taken as the point when a bubble would no longer rise in the solution. The suddenness with which the viscosity rises as the gelpoint is approached, particularly when it occurs a t a low extent of reaction, is shown in Fig. 1where the variation in time of bubble rise with extent of reaction is plotted for one of the methyl methacrylateethylene dimethacrylate systems. Duplicate experiments usually agreed to better than 10% of the measured values. Molecular weight determinations by viscosity measurement were carried out on polymer samples prepared by polymerizing pure methyl methacrylate and vinyl acetate under the same conditions as the gelation experiments in order to obtain the values of the average chain length, A, to use in Equation (3), it being assumed that the small amounts of cross-linking agent employed had no effect on the kinetic chain length. For polymethyl methacrylate in chloroforni the relation for unfractionated material determined by Schulz and Dinglingerlo was used, and for vinyl acetate i n acetone that of Staudinger and Warth." Solutions yielding relative viscosities, qrei, of 1.5-2.0 were employed, and the intrinsic viscosity, [ q ] , calculated by the equation In qrsl/Cv = [ q ] . The value at 60" of [ q ] and several values of qrel for the polymer samples in media corresponding to the appropriate reaction mixtures were also measured for calculations which will be discussed below.
443
quantitatively with those calculated from t h e measured chain lengths and amounts of crosslinking agent, agreement is poor, and i t seems reasonable to re-examine the assumptions upon which such derivations are based. I I 20 .
& &0 ( 1
9 I
'I
2
4
f
P
6
8
10
yo Reaction. Fig. 1.-Effect of presence of ethylene diniethacrylate upon viscosity (measured by time required for bubble to rise in reaction tube) during polymerization of methyl methacrylate a t 60" in presence of 0.1% BurOt, 1.0% methallyl chloride.
First, if Equation (3) is otherwise correct, observed gel-points should occur slightly later than calculated, because no account has been taken of the occasional formation of cyclic structures. However, there seems to be no a priori reason to assume that the effect would be larger than in the case of polycondensation reactions where i t is of minor importance and insufficient to account for discrepancies of the magnitude observed here. Second, the initial assumption that all functions have the same reactivity might be in error. If this were the case, as has been pointed out by Stockmayer, the net result (at least a t low extents of reaction) would be merely to introduce a constant before one side of the equation, so that the Discussion of Results Results of gelation experiments in which the ratio of observed to calculated gel-points would amount of divinyl monomer is varied between maintain a constant value. In the last column 100 and 0.05%, the average chain length be- this ratio is calculated. While the ratio for any tween 400 and 5000, and the amount of solvent amount of cross-linking agent is rather roughly from 0 to 67 weight yo are listed in Table I. constant (for example, for gel experiments in the Under thcse conditions, the gel-point varied from presence of 0.05 cross-linking agent i t averages 1.0 to 45% reaction, and inspection indicates that 1.62 with an average deviation of 0.55) it varies results are in qualitative agreement with Equa- widely with the amount of cross-linking agent, tion (3), with the exception of Experiments l and and a t 5% has risen to an average of 13.2. The 2, which will be discussed later. Thus, there is a ratios appear also to be increased somewhat by the pronounced delay in the gel-point with decreasing presence of solvent. Apparently, the equation, amounts of divinyl monomer (compare for ex- although predicting the gel-point of these systems ample Expts. 3-6) and with decreasing chain reasonably well when they contain only very length (compare Expts. 3-6 with 7-10). How- small amounts of cross-linking agent, becomes inever, when the observed gel-points are compared creasingly inaccurate as the amount of crosslinking agent is increased. ;he discrepancy in (9) Toussaint and MacDowell, U. S. Patent 2.299.862 (1942). Experiments 1 and 2 containing 100 and 20%) (10) Schulz and Dinglinger, J. prokl. C k e m . , 168, 1.76 (1941) wnw-linking agent i s particularly striking. Al(1 1) Stnudinerr and Warth. i h i d , 166. 27R (1040)
CHEVESWALLING
14 k
Vol. 67
TABLEI SYSTEMS METHYLMETHACRYLATE-ETHYLENE DIMETHACRYLATE AND VINYLACETATE-DIVINYL ADIPATE All at 60' in the presence of 0.10 g. benzoyl peroxide/mole unless otherwise noted. Mole % divinyl --___ % Reaction at gel-point
CALCULATED A X D OBSERVED GEL-POINTS FOR
Expt.
CVt
1
2 3 4 5 6 7" 8" 9" 10" 11 12 13 11
15 Iti
i0tK
XOIl(~
Uone YOllt
Sone None T
