Sept., 1946
1781
COPOLYMERIZATION : COMPOSITION D~STRIBUTION
in 50y0 alcohol. Using t h e curve developed by Bell and Roblinlo for correcting these values t o those in aqueous ,elution gave figures close to the 5.38 given for N1-acetplsulfanilamide itsclf. Preparation and Diazotization of 2-( o-Aminopheny1)ethene-1-sulfcnic Acid. --Hvdrolvsis and reduction of I1 \$-as carried out b y the method described for the preparation of orthauilic acid.’O Isolation of t h e product was made difficult b y thc 5urprisingly great water solubility of this aniinosulfonic acid. A m a l l amount of the aminosulfonic acid crystallized on slow evaporation of an acid solution in the cold room. It was identified by qualitative tests and analysis. Anal. Calcd. for CaHyO~SS.HyO: neut. cquiv., 217. Found: iieut. cquiv., 219, 210. A 0.35-g. sample of this aniinosulfonic acid dissolved in acid solution re:ictt.d with t h e theoretical quantity of sodium iiitiitr solution (cud-point determitied with starchiodide paper). Heating the diazoniuni solution caused a (20) Wertheim, “Organic Syntheses,” Call. Vol. 11, p. 472.
vigorous evolution of nitrogen. The mixture of salts obtained on evaporation of this solution was insoluble in organic solvents and completely soluble in water. T h e aqueous solution gave a deep blue coloration with ferric chloride solution showing the presence of a phenol.
Summary Two simple vinylogs of sulfanilamide and two of sulfacetamide have been prepared and were found to have 110 bacteriostatic activity in 1.
zlitro. 2 . Evidence has been presented to show that the ortho vinylogs have a trans configuratioii. 3 . The hypothesis of Kumler and Daniels,” concerning the relationship between the structure and activity of sulforiamidcs, has bccn criticized or1 several cc-nmts. KECEIVED DECEMHER in, im
[CONTRIBUTION FROM CELANESE CORPORATION OF AMERICA,PLASTICS DIVISIO~~ ]
Copolymerization: the Composition Distribution Curve BY IRVING SKEIST When two or more monomers are copolymer- tween A, and A is found similarly from the followized, the product is a mixture of polymer mole- ing set of equations4,j d e s which vary in composition as well AA A ( A / b a r ” B / P r b C/P”r”)(A B / a b C / a c ) as in chain lerlgth. If, e.g., the polymer - B(A/abya + B l a b y b + C / a O r b ) ( A l p s + + ~/a.) ( 2 4 first formed is richer in one component = A(A/P&Ya+ B/P&rb + c/Pra)(A B/ffb + c/ac) than the mixture, then AC C(A/acP& B/abp” C/aoOc) (A/-ya + B/yb + c)(2b) of the polymers formed subsequently must be poorer in that component than the where pa, for example, is p for the binary system original mono.mer mixture. Some mixtures of A-B, The information needed to solve these equamonomers yield a polymer aggregate of fairly tions, as well as the equations for systems involvuniform composition, while others give a product ing a greater number of monomers, can be obwhose molecules vary so widely in composition tained entirely from experiments on the binary that technical usefulness is impaired. Thus it be- systems involved. Integration of equations (1) and (2) should give comes important to know the distribution of coma relationship between the conversion, or amount positions in the polymer. At any instant, the composition of the polymer of polymer formed, and its composition. These in a binary mixture is related to the composition integrations have been performed by Xayo anti ~ in a biof the monomer according to the e x p r e s s i ~ n ~ * ~Lewis2 ~ ~ and Walling and B r i g g ~ . Even nary system, the integral is complex; in a ternary AA aAZ + A B system i t becomes nearly unmanageable. An at= aA2 + 2AB + BB2 m B tempt to simplify the integral relationship for a where A and C I are the mole fractions of the two ternary system results in an approximate exprescomponents in the monomer, AA and AB are the sion which is precise only when the polymer coinamounts (e.g., moles per unit weight) of the cor- position is close to that of the feed. It is the purpose of this paper to present a more responding components which enter the polymer in a differential time interval, A, is the mole convenient method for determining the relationfraction of the first component in the polymer ship between conversion and composition, and formed during the differential time interval, and from this the distribution of compositions, in a CY. and p are the monomer reactivitypolymer of any number of components. The CY. is k A * A / k A * B and p is k w B I k w . 4 , where kA*B, method is applicable to any system for which one for example, is the rate constant for the propaga- knows the relation between composition of monotion reaction involving the addition of B monomer mer and composition of polymer, regardless of whether the system can be described in terms of to Aradical. For a three-component system, the relation be- the monomer reactivity ratios of equations 1 and 2. (1) Alfrey and Go:dfinger, J. Chein. Phys., 12, 205 (1944).
a
(2) Maya a n d Lewis, THISJ O U R N A L , 66, 1504 (1944). (3) Wall, i b i d . , 66, 2050 (1944).
+
+
+
+
+ +
+
(4) Alfrey and Goldfinger, J. Chem. Phys., 12, 322 (1944) ( 5 ) Walling and Briggs, THIS JOURNAL, 67, 1774 (1945).
IRVINGSKEIST
1782
Vol.
(is
Analogy between Copolymerization and DisNeglecting the product of two differentials tillation.-It is interesting t o compare copolyAdM + MdA = ApdM merization with fractional distillation. Figure 1 d M / M = dA/A, - A ) (4 gives the relationship between monomer compoM = A Ad A X sition and composition of polymer immediately (5) formed, for some binary systeins (see Table I, This is the conversion-composition equation. below). The similarity to a liquid-vapor composition diagratn is obvious ; the term “azeotrope” In combination with equation.; (1) and (a), i t has been suggested3 for the case in which both makes possible the computation of the proportion iiionomer wid polymer have the same composi- of original monomer which is still unreacted. Binary Systems.-In Fig. 1 are plotted the tion, which in our diagram would occur where the instaiitaneous monomer polymer composition recurve crosses the 45’ diagonal. lationships for styrene-methyl methacryl,tte? anti styrene-methyl acrylate.?
Lo
I V I l IAI,
by>- Component teui A 1 Styrene 2 Styrene 3 Styreue
0
0.2
0.4
0.6
0.8
1.O
A Fig. I. .--1nstaiitaneous relationship between mole fractioii of first component i n the monomer, A , a i d its inole fraction in the polymer, A,,.
In distillation, composition and yield are known to be related by the Raleigh equation6 (3)
TABLE I MONOMER C\OMPObIlION\
cumpouent n Methylmethacrylate Methyl acrylate Methyl acrylate
\Tole fr actlor,
A0 0 20 20 dU
11
XI 75 73
/i 0 5IJ
20 20
For the three original compositions indicated, the integral has been determined graphically and the percentage conversion computed from eyuation (5). In Fig. 2, conversion is plotted against instantaneous polymer composition (Ap) to give integral distribution curves. The dotted lines indicate the original tnonorner mixture. The horizontal lines indicate the portions of the curves lying between 25 and 75% conversion. The corresponding differences in polymer composition, appearing as the projections to the horizontal, may be termed the “interquartile ranges,” and are d measure of the dispersion of compositions in the polymer aggregate. 100
where L is the quantity of liquid, x is the mole fraction of the higher boiling component in the liquid, and y is the mole fraction of that component in the vapor. I t will be shown in the following that the same equation, with analogous quantities, can be derived for copolymerization. The Conversion-Composition Equation.-Consider a mixture of two monomers, of mole fractions A and B , respectively, such t h a t the polymer first formed is richer in component A than the monomer (for example, System 1 in Fig. 1). 0 0.2 0 0.2 0.8 1.0 If the total amount of both monomers is M moles, A,. then there are A M moles of the first component in the original monomer. If dM moles of monomer Fig. 2.-IntegraI distribution of compositions in polymer; conversion DS. instantaiieouq polymer composition. polymerize, t.he number of moles of component A in the polymer is A,dM. At the same time, the Not only do the three curves have very different number of moles of component A in the monomer has been reduced to ( M - dM)(A - U’I.Con- interquartile ranges, but they approach 100% conversion in markedly different manners. Curve quently, the material balance of A 1 (9% interquartile range) has a slope of unity a t A M - ( M - dM)(A - dA) = i1,d.W the finish (proceeding from the bottom toward (6) Raleigh, Phil. Mag., 8, 534 (1902).
(7) Alfrey. Merz and Mark, J Polymer Research, 1, 37 (194F)
Sept., 19%
COPOLYMERIZATION
:
COMPOSITION
DISTRIBUTION
1x3
the top of the :figure); curve 2 (30% range) has an infinite slope; the slope of curve 3 (1% range) is zero. Thew differences are shown more strikingly when the slopes of the curves of Fig. 2 are plotted 3 against the same instantaneous polymer compositions to give the frequency curves (differential distribution curves) of Fig. 3. The curves of systems 1 and 3 are I,-shaped with only a single peak. On the other hand, the curve of System 2 is Ushaped, indicating a decided cleavage of compositions into two very different groups. The inter1 quartile range tells us that the molecules of onefourth of the polymer aggregate differ from the inolecules of another fourth by a t least 30% in cnniposit ion. The three systems were polymerized to completion a t 00’ in the presence of 0.1 mole per cent. 1,enzoyl peroxidc. Systems 1 and 3 remained clear ; t i i d traiisparent throughout the polynierizatioii, but: system 2 developed an opalescence and was very i-xittle compared to the other speci~tieiis. ‘[his is uot surprising; i t is known that Fig 3.--Prequeiicy distributioi~uf compositioiir iri polyiiicr. polymers of differing chenlical compositions are decrease in amount of unreacted monomer is progenerally “inconipatib1e”-that is, they cannot be portional to the change in instantaneous polymer blended mechanically to give a product of good composition ; the integral distribution curve has a physical properties. slope of 1, and the frequency distribution curve One approximation is involved in Figs. 2. and has finite intercept. 3-it is Assumed that all the polymer formed a t System 2.--p = 0.2; 1112/i111 = (L4pJApl)o~zs. any instant is of the same composition. Simha The distribution curves have infinite slope at and Bransons a n d Stockmayerg have pointed out 100% conversion, consequently a n appreciable that there is :t dispersion in composition just as amount of polymer is almost pure B. The polythere is a dispdrsion in molecular weight. Thus, mer is necessarily quite mixed in composition. the polymcr formed a t any instant, while preSystem 3.-a = 0.75; 11.1~/1121 = ( B p t / B p J 3 . dominantly oi one composition, also contains The distribution curves have zero slope at 100% some polymer tllcilecules of other compositions conversion, indicating t h a t practically none of over the entire range of O-lOOx, A . Fortunately, the polymer is almost pure A. the distribution becomes sharper with increasing It is apparent that the value of 0.5 for the monochain length. The chief effect of this correction mer reactivity ratio is critical. Lower values would be to sctften the sharp edge corresponding give a polymer aggregate of widely heterogeneous t o zero conversion. composition. Monomer Reactivity Ratios and the DistribuIn each of these systems, both a! and p are less tion Curve.--The shape of the distribution curve than 1. If a is less and P is greater than or equal ccmversioii depends on the values of to 1 , die last bit of unreacted monomer is pure A, 1 he monomer reactivity ratios. and the value of a! is critical. If both a and p are From equation I , we find that as A approaches greater than 1,the last trace of monomer is neither zero, lim A,, = A ‘d. (Siniilarly, :is -4 approaches pure X nor pure B, but has the composition of an 1, lim B,, = B,a,! azeotrope. I t can be shown that, in such cases, if At the B temiinal, therefore, substitution in N = @, a value of 2 is critical. However, no sysc’q. (4) gives tem has yet been found for which both monomer d d-. l = --dA .-reactivity ratios are greater than 1. The case in which a! = 1/@,which was thought a t one time to have special significance, was investigated by Wall,lo who showed that the monomer or, since .4,,/A 3, = A?,A1 near the B terminal reactivity ratios have critical values of 0.5 and 2, respectively. It is now believed that this case has no special meaning; the value of 0.5 for a monoEquation 7 may be applied to the special cases as mer reactivity ratio is always critical, regardless of the value of the other monomer reactivity ratio. follows Ternary Systems.-When there are three or System 1.-Here /3 = 0.5 and consequentlymore components, equation (5) becomes an esM~/M= I Ap2,’Ap,. Near 10095 conversion, the pecially useful tool for relating the conversion ( 8 ) Simha and Branson, J . Chem. Phys., 1’2, 263 (1944). ~
(Y)
Stockmayer, i i w J . , 13, 199 (1945).
(10) Wall, T H IJ~ O U R N A L , 63, 18G2 (1941).
P. H. EMMETT
1784
to the distribution of polymer compositions. For a ternary system, the method is as follows: The computation makes use, alternatingly, of equations (2) and (5), evaluating the total in consecutive steps. The polymer compositions corresponding to the initial monomer compositions are calculated from equation ( 2 ) . This gives a value of ( A , - A ) , (Fig. 4) which is assumed to be constant for limited variations in A . Equation ( 5 ) gives the per cent. conversion for such a variation d.4. FI-om A1 ( = A dA), and the corresponding B1 and C1, the new polymer compositions are calculated from equation ( 2 ) , thus giving ( A , - A)l, which is used for the next conversion calculn tiori according to equation ( 5 ) .
+
STYRENE
-
AGRYLON l T R l LE
5 0
0
100 Conversion to polymer, 70 Fig. 4 .-Compositions of monomer and polymer us. conversion, for an equimolar mixture of acrylonitrile, methyl methyacrylate and styrene.
If (A, - .4)is found to vary over the interval dA, a more suitable value for ( A , - A ) can be
chosen (for example, the average of ( A , - A ) , and ( A , - A ) l ) , and the conversion recalculated. To reduce the number of calculations this preferable value for ( A , - A ) is anticipated from the
Vol. G8
trend of the curves. In regions where ( A , - A ) is changing rapidly, precision is maintained by calculation over smaller intervals. Figure 4 shows the conversion-composition relationship obtained by this method for an equimolar mixture of acrylonitrile, methyl methacrylate and styrene.11s5 The first polymer is richer in styrene and poorer in acrylonitrile than the monomer ; consequently the monomer is depleted of styrene and enriched in acrylonitrile. As polymerization proceeds, compositions of both unreacted monomer and instantaneous polymer change; but the change in the latter is less. Thus, up to 70% conversion, the polymer aggregate is fairly uniform in composition. At that point, however, the changes become more marked. At 90% conversion, the styrene is virtually gone; and the last 1%of polymer is almost pure acrylonitrile. I n a technical process, if uniformity of polymer composition were desired, the polymerization could be stopped a t approximately io% conversion. For systems of more than three components, computation of instantaneous monomer-polymer relationships becomes more tedious, but with this accomplished, the calculation of the conversion from equation (5) is just as easy as for a ternary or binary system. Acknowledgment.-The author wishes t o thank Dr. Ernest P. Irany for helpful discussion and criticisms. Summary A new method of computation of the composition distribution of copolymers is proposed which permits evaluation of systems containing any number of components. NEWARK, N. J.
RECEIVED'~ APRIL 17, 1946
(11) Lewis, Mayo and Hulse, THIS JOURNAL,67, 1701 (1943). (12) Presented before the High Polymer Forum nt the Atlantic City meeting of the American Chemical Society, April, 19tG
[CONTRIBUTION FROM MELLONINSTITUTE
O F INDUSTRIAL
RESEARCH]
Multilayer Adsorption Equations BY P. H. EMMETT Brunauer, Emmett and Teller' have suggested that, if low temperature adsorption data are plotted according to the equation --P
(C
1 __
-
1) 1.
(1) Ti,c po a straight line is obtained over a relative pressure range extending from about 0.05 to 0.35. Vm, in this equation, represents the volume of adsorbate required to form a monolayer over the solid ad-
u(Po
- P)
v,c
+
(1) Brunauer, Emmett and Teller, THISJ O U R N A L , 60, 310 (1938).
sorbent. v is the volume of gas adsorbed a t relative pressure p / p o ; and C is a constant. A simple multiplication of the number of adsorbed molecules corresponding to Vm, by their average crosssectional area, would then yield an absolute value for the surface area of the solid being measured. This equation has been applied successfully t o a large number of finely divided and porous solids. Recently, Harkins and Jura2j3have published a ( 2 ) Harkins and Jura, r b t d , 66, 919 (1944) (3) Harkins and Jura, rbrd , 66, 1366 (1944)
