1T7-1
CHEVESWALLING AND EMORENE R. BRIGGS
benzene which enters into reaction appears as phenyltrichlorosilane and diphenyldichlorosilane in the approximate molar proportion of one to three. Copper also is a catalyst for the reaction of chlorobenzene with silicon, but is not as effective as silver in the lower concentrations. In the form of a 50% copper-silicon alloy disintegrated by intergranular oxidation, the copper brings about an acceptable conversion of chlorobenzene to phenylchlorosilanes a t 430', yielding diphenyldichlorosilane as the principal product. Variations in yield have been noticed with different batches of the contact mass, possibly because of variations in the degree of oxidation and hence in the extent of disintegration. More investigation of the metallurgical changes which take place upon oxidation is necessary before an assured reactivity toward chlorobenzene can be brought about by a fixed sequence of operations. The effect of hydrogen chloride in expediting the reaction of elementary silicon and chlorobenzene could not be called catalytic, because the chlorine appears in the product. The hydrogen chloride undergoes a simultaneous reaction which attaches the chlorine to silicon atoms and in some way facilitates the reaction of the chlorobenzene. Since its use in effective proportions leads to the formation of considerable silicon tetrachloride and pheii yltrichlorosilane, hydrogen chloride could more logically be used in a direct synthesis of substituted trichlorosilanes, where extra chlorine is necessary. The separation of diphenyldichlorosilane pre-
Vol. 67
pared by direct synthesis is complicated by the necessity of removing aluminum chloride, which presumably would not be present in preparations by other methods. While the use of aluminumfree silicon would obviate the necessity of such removal, it seems easier and more economical to use the commercial grades of silicon and to carry out the filtration procedure as described. Once this has been done the phenylchlorosilanes may be distilled a t atmospheric. pressure without decomposition. In this investigation no evidence has been found to support the inference that the phenylchlorosilanes must be distilled a t reduced pressure to maintain their purity.6 Heretofore only the reduced-pressure boiling points have been given for diphenyldichlorosilane and triphenylchlorosilane. The normal boiling points for all the phenylchlorosilanes, as determined on the products from these experiments, are: C6H5SiC13, 201.5' cor. ; (CtiH&3iC12, 305.2 cor.; (CaH5),SiC1,378.0 cor.
Summary The general reaction of hydrocarbon halides with elementary silicon is applied to the direct synthesis of diphenyldichlorosilane from chlorobenzene and commercial silicon. The effects of various catalysts are described, and conditions for carrying out the reaction and for separating the phenylchlorosilanes by distillation a t atmospheric pressure are given. (6) Krause and von Grosse, "Die Chemie der Metallorganischeo Verbindungen," Borntraeger Geb., Berlin, 1937, pp. 274, 276.
SCHENECTADY, N.Y.
RECEIVED JUNE 7, 1945
[ COh'TRIBUTION FROM THE GENERAL LABORATORIES OF THE UNITED STATES RUBBERCOMPANY]
Copolymerization. 111. Systems Containing More than Two Monomers BY CHEVES WALLING AND EMORENE K. BRICGS
DBerential Equation for Copolymerization of The theory of copolymerization recently developed by Alfrey and Goldfinger,l Mayo and n Monomers.-If n monomers, A, B, C, . ., N, Lewis,2and Wall3 may be extended to the case of are allowed to copolymerize, their rates of disn monomers and the composition of product ex- appearance (making the same assumptions as in pressed in terms of the initial composition of the the copolymerization of two monomers2) are given reaction mixture and the n(n - 1) monomer re- by the system of equations activity ratios* involved. This fact has been ] - k,.[Al[A.l -I- k.b[AI[B.l-I- . . . -I- k,IAI[N-l pointed out by Alfrey and Goldfinger, who have --'[Adt developed the expression for the initial polymer (14 composition in a system of three m o n o m e r ~ . ~ = kb.[B][A.] kb,[B][B.]-k . . . f kb,[B][N*] dt This paper contains a discussion of the more --djB1 (Ib) general case of n monomers, and experimental work on combinations of styrene, methyl meth- . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . acrylate, acrylonitrile, and vinylidene chloride, --d[N] = k,.[Nl[A,] knb[N][B.] -I- . . . -I- k~~[NI~N*l dt for which the necessary monomer reactivity ratios (In) are now a ~ a i l a b l e . ~ ( 1 ) Alfrey and Goldfinger, J . Chcrtt. P h y s . , 18, 205 (1944). where [Am], [B.], . . ., [Ne] are concentrations of (2) Mayo and Lewis, THISJOURNAL, 66, 159-1 (L944). growing polymer chains ending in A, B, . . ., N (3) Wall, ibid., 66, 2050 (1944). type radicals, respectively, and k i j , in general, IS (4) Alfrey and Goldfinger, J . Chem. P h y s . , 18, 322 (1944). the rate constant for reaction of monomer I with (.il 1,ewir. Mayo and Hulse, THISJ O U R N A L . 67, 1701 (194%.
.
+
SYSTEMS CONTAINING MORETHAN Two MONOMERS
Oct., 1945
1775
... ... steady state as.I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .-(lAl/pa [Bl/~b . . . P‘Ipn)I sumption t o each etca8 Equation (4)describes the relative rates of radical yields the auxiliary equations polymerization of each monomer (and, hence, the . . . ksn[AI[N.I = &,[A][A*] k.b[A][B.] composition of polymer formed at any instant) &,[A][A.] + kb,[B][A.] $. . , . -+ kn.[Nj[A.] (La) in terms of monomer concentrations and the kb.[B][A*] kbb[B] [Bel -I-. . . kbn[BI[N.I = n(n - 1) monomer reactivity ratios. k.b[A][~*] kbb[B][B.I+ . . . . . . k n b [ N 1 [ ~ . ](2b) ................................................... For the case of three monomers, expansion of the determinants yields kn.[N][A‘l knb[N][B.],+ . . . knn[Nl[N+l k.,[AI[N*l f kbn[Bl[hi.1 . . . I
+
+ + +
+
+
+
+
+
+ + + knn[NIIN.l (2nI
[AI([AI/Bars
+ [BI/BaYb + [Cl/Po~a)([Al+ [Bl/a~,+ [CI/ao) d[AI
As the left side of each of equations (2) is d[BI = with the right side [B]([A]/aby, [ B ] / a b ~ b [C]/ac’yb)([A]/Bsf [B] + [c]/@,) of the corresponding equation (I), d[Cl (5) substituting into (la)’ factor[B]/’yb+En [C]([ A ] a & , + [Bl/abPo + [C]/a&,)( [A]/-y. ing out [A*], etc., solving each Equation ( 5 ) is identical with that of Alfrey and equation for -dt, and equating yields G~ldfinger,~ except that the monomer reactivity ratios in keeping with the usage of Mayo, et a1.,2J are the reciprocals of the constants which Alfrey and Goldfinger employ. In the case of four or more monomers, use of equation (4)is simplified if numerical values are substituted before the determinants are expanded. , Equations (2) may be regarded as a series of n Comparison with Experiment.-In Table I homogeneous equations in n unknowns, [A*], are tabulated results on the copolymerizafion of [Be], .... [N.],so that simultaneous solution of all seven three component and one four component but one will give the ratios of each unknown to systems of the monomers styrene (S), methyl the others6 This may be accomplished most methacrylate (M), acrylonitrile (A), and vinyliconveniently by the method of determinants,’ dene chloride (V). . For calculation of the polyand the resulting determinants may then be sub- mer compositions by equations (1) or ( 5 ) the stituted into equation (3) without evaluation. In monomer reactivity ratios of Mayo, Lewis and order to use equation (3), it is then necessary to Hulses listed below were employed. replace the (at present immeasurable) rate conProbably the greatest source of error in calstants by measurable monomer reactivity ratios.2 culating polymer compositions is in the values of Let these quantities be defined as follows the monomer reactivity ratios involved, particularly (as they enter the equations as their rek d k b a = a b kss/kca = a, . . . k,/kna = an kbb/kob = Dc . . . kbb/knb = 8 n ciprocals) when these are vFry small. Thus, if we k d k s b = Pa ................................................... substitute 0.C6 for 0.04 and 0.10 for 0.15 for the monomer reactivity ratios for the acrylonitrileknnlknn = k d k b n = vb knnlkcn = yo . . . Dividing the denominator of each fraction of type radical with styrene and methyl methacrylequation (3) by kaakbbkfc . . . k n n (by dividing each ate respectively (results which are well within the column of the determinant by the appropriate k possible error of the original deterniinations6) it and the polynomial by the remaining k), and amounts to saying that an acrylonitrile-type radifactoring [A], [B], . . . . [ N ] from the successive cal, instead of preferring styrene to methyl methacrylate by a factor of 3.5 to 1, prefers it by a determinants, ,gives the desired equation factor of only 1.67 to 1. Recalculation of the data of expt. ti with these new values for the reactivity of the acrylonitrile radical changes the predicted composition of the polymer from 41.4 to 37.2% styrene, from 22.7 t o 27.7% methyl methacrylate and from 35.9 to 35.1% acrylonitrile. These changes, which are within experimental where error, are as large as the discrepancies between (6) This statement requires that the n equations are consistent. calculated and observed values found in Table I. As the determinant of their coefficients can be shown t o be equal t o In short, agreement between theory and experizero, this is so.
+
+
‘
(7) For a discussion of determinants see, for example, Ch. 111, ( 8 ) In order t o factor [ N ] from Dn it is convenient to add all the rows together giving a sum of the form - [ N ] / a . Sokolnikoff and Sokolnikoff, “Higher Mathematics for Engineers and [N]/pn Physicist*.” MrC.ritw-Hill Hook Company. Inr , New Vork. N. Y., Ih’l/a,, - . . . [N]/p,,. This w r n may lie used to replace any IU11. row r i t h o i t t altering thr K ~ I I I C nl the determinant.
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-
-
1776
CHEVES
W A L L I N G AND
EMORENE R. BRIGGS
Vol. 67
TABLEI Substituting these values into equations (1) and ( 2 ) yields as the condition for the formation of THREEAND FOUR COMPONENT POLYMERIZATIONS OF STYRENE(S), METHYLMETHACRYLATE (M), ACRYLONI-an azeotropic copolymer, the system of equations TRILE (A) AND VINYLIDENE CHLORIDE (V) AT 60" Feed Polymer 1 - = [AI [BI/(Yb -k [ C ] / L Y , . . . f Mole Mono- Time, Yield, Polymer (mole %) Expt. yo mers hr. wt. % analyses, % ' Found Calcd. [N]/cY. = 0 (6a) 1 31.24 S 16 18.2 43.4 44.3
(
2
3
4
5 6
7
8
31.12 37.64 35.10 28.24 36.66 34.03 34.49 31.48 35.92 36.03 28.05 53.23 26.51 20.26 28.32 28.24 43.44 27.76 52.06 20.18 25.21 25.48 25.40 23.91
M V M A V S A V S M A S M A S
12
C, 6 8 . 5 3 C1,12.01
68.79 39.4 12.13 1 7 . 2
N, 4 . 6 0
28.3 20.9 52.8 36.7 10.5 44.7 26.1 29.2 52.6 20.2 27.2 38.4 23.0 38.6 36.4 40.6 23.0 40.7 25.5 25.8 8.0
50.8
18.1
8
C1,17.24
17.17
S, 6.02
6.12 8.83
16.5 C1, 8 . 7 8
3.5
13.6
C, 7 8 . 3 5 7 8 . 8 6 N, 4 . 6 7 4 . 6 9 5 , 7 5 1 5 . 4 C, 80.99 8 1 . 9 0 N, 4 . 2 2 4 . 3 2 4.5
18.4
M
C, 7 7 . 3 8 77.46
A
N, 6 . 4 7
S: M A S M A V
6.48
5.75
17.2
8.5
C, 74.51 7 4 . 4 5 N, 3.52 3.62 1 8 . 9 C , 7 3 . 1 8 73.27 N. 4 . 0 2 4 . 0 1 C1, 6 . 3 9 . 6 . 3 9
Monomer radical S S .. M 0.50 .4 0.04 V 0.14
M 0.50 .*
A 0.41 1.20
0.15 0.24
0.37
41.2 14.5 54.3 29.7 16.0 52.4 40.5 7 1 43.6 20.2 26.2 52.9 23.2 23.9 41.4 22.7 35.9 36.8 43.8 10,4
41.0 27.3 24.8 6.9
V 2.00 2.53 0.91
..
.. ment is as good as can be hoped for a t this time, and indicates that the theory of copolymerization can be satisfactorily extended to systems of more than two monomers. The LLAzeotropicCopolymer" of n Components.-An "azeotropic copolymer" has been defined by Wall3 as one in which the polymer being formed contains the same ratio of monomers as the feed, and both he and Alfrey and Goldfinger :have determined the conditions in two monortier systems under which such a copolymer may be formed. It is of interest to determine whether such a copolymer can occur in multicomponent systems. If Equation (2a) is substituted into (la), (2b) into (lb), etc., the resulting set may be solved for [As], [Be] .... etc., as ratios of determinants. Since the condition for the formation of an azeotropic copolvmer is that -a-41 =-= ~ [ B I = _ dA'N1 _ the results may be ' * . [N ]dt' [Aldt [Bldt finallv exmessed (after dividing the ith column of eaGh de'terniinant by Kii) in t h i form kaa [A.] = .
2)
[AI/Pa
+
+
+ (1 - D$) [Bl + [Cl/So f . . . 4- [Nl/Bn = 0 (6b)
...................................................
As equations (6) are linear, for any set of monomers only one composition is capable of yielding an azeotropic copolymer, regardless of the number of monomers p r e ~ e n t . ~Furthermore, as no concentrations or monomer reactivity ratios may be negative if the result is to have physical significance, all determinants must have the same sign. In the case of a two component system, this reduces to the condition, found by Wall, that for an azeotropic polymer to be possible the two monomer reactivity ratios must both be larger or both be smaller than unity.1° Substitution of the monomer reactivity ratios of Lewis, Mayo and Hulse5 into the determinants phows that azeotropic copolymers are not possible with any of the possible three or four component systems of styrene, methyl methacrylate, acrylonitrile or vinylidene chloride as in none of them do all the determinants have the same sign. Integration of the Copolymerization Equation. -If polymer compositions in multicomponent systems are desired a t high extents of reaction, integration of equation (4) is necessary. Although this integration has not been accomplished in closed form, a simple approximation which appears to give quite accurate results is possible, and any higher degree of precision is possible by means of series expansion. Let there be a series of quantities u, v , w , . . . such that u = ln[A]/[Ao], v = In [B]/[Bo], . . ., where subscript zeros refer to initial concentrations. It follows that [A] = [&]e-", [B] = [B0]eP',. . . and du = d[A]/[A], dv = d[B]/B, . . . . Substituting these quantities into equation (4) and multiplying each denominator by euiVwi * . yields
