1IICH.IEL IV-ILES U e p r c h ~ i e n ot j C h c ~ ~ ~ i c iZ l +y I. I ~ ~s i 1 1 1 ‘11 l l v z s r o i i ~ i r i ,l r t d 7 ~ 0 1 1 .Ti ? , s c o ~ l s l t l 1Zcceiwtl -1otenrbc, 26, 1941
The object of this paper is to review home experimental data on flow birefringence (4) with the purpose of exploring the possibilities of flow birefringence measurements as a secondary method of determining the molecular weights of high polymers. This method appears particularly attractive, since it gives two different types of average molecular weight, instead of one as with the intrinsic viscosity. One average is obtained from measurements of the extinction angle, the other from the birefringence. The types of average obtained will he later discussed. It has been shown (1G) that for polydisperse systems of any type, with no interaction be tween component5 sin 2\21;
~i
tan 2 9 =
-5
A L cos 2 9 ,
and A, cos 2\k,)’
A’ =
+ (EA, sin 2\21,)’ i
where is the estinction angle and A is equal t o ne - no, the difference in principal refraction indices for the birefringent solution. These equations have heen esperimentally tested ( l i ) ,the agreement being excellent for a mixture of cellulose acetates in cyclohexanone, but only fair for mixtures of methyl cellulose and 3odiiim thymonncleate in water, at finite concentrations. The various quantities in equations 1 and 2 have been espressed in ternis of molecular constants for the case of rigid ellipsoidal particles by Hoeder ( l ) , Peterlin (13), and Peterlin and Stuart (14). These equations have been used to interpret the data for various protein holutions (7). They will be modified for the case of threadlike polymers. tan 2Q.i -li
=
=
G
-
ai
(ne -
These relationships hold for values of 01’
’
ti =-
8;
hich are not excessively large. Here 0,= (Ob) the 1otaiy diffusion conitant of species z TI ith major a& a , and minor axis 6. G is the velocity gradient. yl - g, is a function of the particle h a p e and of the refractive indice.. of the particle and of the .elution. Foi d h c i e n t l y long particle> it 1. [sonstant For@, (12)
11
(61 'I'hc symliol 7 refers througlioiit t o the i.iscw.ity of the solution. For the case of rigid ellipsoidal molecules it then folloivs that for long molecules at low gradients and concentration.
where I', 13 a weight fraction. This equation i5 a s accurnte as equations 3-6 for particle. having the same f = a / b ; for very long particles it is also true when all particles have the same minor asis but varying major axis. For the LansingIcraemer (10) and Schiilz (18) distribution function.. thi.; expression is equal to
13y the use of the birefringence
For the equation of Scliulz this is
n-here
For the equation of Lansing and Kraemer this becomes equal to up. It can be noiv seen that flon- hirefringenee results can be expected to give very high n-eighting of the molecular length. If .f = a,% is constant, equations 7 and 9 yield JI, and A[,,, respectively. for the average molecular weight. If 2, i. constant while a varies. the averaging of the molecular Jreight and length is the same. It is proposed that the qumtities
be defined in analogy to the intrinsic viscosity.
Here w =
P ~
4
- q. These quan-
923
MICHAEI, WALES
tities have previously been discussed in terms of n theoretical model by TI*. TCuhn and H. Kuhn (9), although no extrapolations to zero concentration and gradient Jvere made. The use of these quantities in characterizing colloidal materials would eliminate questions of the correctness of equations 1 and 2 at finite conccntrations and the dependence of w on G at high rates of shear except as this affected the extrapolation to C: = 0. For the rigid ellipsoidal model [A] = zvi11 vary slightly with the molecular weight (2) and in addition liill not be necebmrily equal to 3/2. IY, Kuhn and H. Buhn (9) have deduced that the exponents in expressions I3 and 14 are equal to 1 and 2, respectively, for flexible chain molecules with restricted rotation. If the behavior of the intrinsic viscosity as a function of molecular weight is any criterion, probabl>r the exponents will lie unequal and range from 1 to 3, for various materialh. Hence, for high polymers over not too wide a range of molecular 11eighti: [A] = zLIRT
Flow birefringence data from the literature are briefly revieived. It is shou n that flow birefringence data can be used as a secondary method of molecular n-eight determination, in analogy to the intrinsic. viscosity. Two different arerage molecular ]\-eights are obtained from f l o ~birefringence, in contr intrinsic viscosity. l‘lie type of average obtained iq discussed. $
The author u-isheb t o tlinnk Professor ,J. IT.IYilliams for suggesting thiz prublem. His continued intereqt and aid have been most T nluable. 11EFF: 111,:S C 1,: S (1) I < o e u m , l’.: % . l’h,~~sik 75, 25s (1038). ( 2 ) I~J;RYE P., : P a p e r prcscsrited at t h c Chicago 11ccting of tlic Aiiicrirnn C’hemiral Society, Scptemher, 1946; c j . also ,J. Chem. I’hys. 14, 636 (1946).
(3, DI: I ~ O S ; S EAT., J . : .J. Chem. Phys. 9 , 766 (1941’1.
I ,T. . : In A d m i i c e s in C ~ l l c ~ i,Science, tI 1-01.I! p , 260. ( 4 ) (a) E I E ~ ~ L6.
Interscience I’ubl i s h n s , h i c . . Sc,n- l*orl.c (1943). (1)) Eus.~LI,. J . : I n l’,,ofeir{s, Aliriino .l(.itis c c ~ dl’epliiles, p. 506, Reinhold Publishing C‘orporatioii. Srn- Yo1.1.; (1043j. l?evic\vs. ( 5 ) I’:DSALL, .J. T.! GORDOX]C . G , , 11~111.. J . I T . , SVHICISBERG, 11.) ASD XIAXS, D. R.: Rev. Sci. I n s t i u m r n t s 16, 243 (1944). (6) ( a ) EYRISG,H.: Phys. Ilcv. 39, 746 (1932‘1. ( b ) C.f. L.~SKO\YSKI. I,.,.\SD BI-RK!R . 15.: .J. Cliem. 1’1iys. 7 , 465 (1939). ( 7 ) F O S T E R , J . F., .%SD XIIS.\ J . T . : J . Am. Chcni. So(:. 67, 617 (1945). (8) FREY-\VISSI,IS(:, .\., .\SD E R E R , E . : llclv. Chini. A c t a 24, 278 (1941). (9) (a) KL-HS,W,, .\SI) Kcris. 13.: Helv. C h i n . A c t a 29, 71 (1946). (ti) KIXS, W., ..\SI) Kr-ns, €1.: Hclv. Chini. Acta 26, 1394 (19433. , 11...mi) KR.WNER: E. 0 . :J . :\m. Chrm. Soc. 67, 1369 (1935j. H . : Helv. Chirn. A c t a 26, 369 (1943). (12) PERRIN, F . : ,J. phys. radium [ i ]6, 497 (l’X3-1.).
SEI)IlIES‘I’~Y~IOS EQUILIBKI~IOF I’O1,YDISPERSE SOS-IDE.4L SOLITES
EXPLRIMIA I v i v i i 1 1 , ~w A u , c h .,J IV. WILLLUIS, J
o
TIIOMPSO‘~, . i \ D
R II LWART
of 11*zrconaiti. lIndisot1. 1f7zsconsm atid the L ( i / ) r ~ i ~i ct s~ i 1 7 i / / t i d8Sintes R i t b b e ~ ( 1 0 1 t i p ~ i t i i / . Ptrssriic. .Yeir J e i ?e//
1 ) ~ p ( i t / t i i ~ 1 o1i /
(‘heittisti 11. I - J i i i e i , i t t /
frenpinL7
1 Z e c r r i d -Yo1 e i t i b t i 28, 1947
I n a previous communication (14), n theory of the equilibrium behavior of high-polymer solutions in a centrifugal field was developed. In this article, reSiilts are presented n hich substantiate the theory and show that the sedimentation-equilibrium method offers a reliable means for the characterization of high polymers. I t s great adrantage over other methods lies in the fact that it is possible not only to determine an average molecular weight, but also a molecularweight distribution curve, if the polymer is known to have a “continuous” distribution of molecular weights. I n addition, only milligram quantities of material are required for an experiment. Polystyrene was selected as the polymeric material to be studied in this investigation, since it is easily prepared under reproducible conditions and because some fractionated samples were available which had had weight-average molecular weights determined b y the light-scattering technique. Butanone was selected as a solvent, since it forms solutions with polystyrene which deviate less from ideality than those with any other pure solvent known to the authors. The slope of the reduced osmotic pressure curve, which determines the value oi this non-ideality correction factor, was also knon-n to be independent of molecular
