MASATAMI TAKEDA AND RYUICHI ENDO
1202
Vol. 60
VISCOSITY OF DILUTE POLYVINYL CHLORIDE SOLUTION BY MASATAMI TAKEDA~ AND RYUICHIENDO Tokyo College of Science, Tokyo, Japan Received March 6. 1966
It is shown that ~ f . ~ /for c a polyvinyl chloride fraction in cyclohexanone decreases linearly as the concentration is lowered from 4 to 1 g./L and then increases as the concentration is lowered further. This increase in v s p / c is well explained by the theory of Ohrn which proposes the adsorption of polymer to the wall of the capillary of the viscometer. The equation for analysis of this phenomenon is derived and using this equation the dependence of the minimum concentration of qsp/c,Cor;$, with molecular weight and temperature is discussed.
Introduction In our previous report2 some experimental results were reported in which an upturn in q8,/c with decreasing concentration of polyvinyl chloride was indicated. We carried out further experimental study of this unexpected phenomenon in viscometric behavior of dilute solutions of the non-electrolyte polymer. In the course of our study, Streeter and Boyer3reported the same tendency on the curve of qgp/c us. Concentration of polystyrene and they ascribed this phenomenon to an expansion of the individual coil in very dilute solution. However, recently Ohrn4 showed that the anomalous dilute solution data are well explained by an adsorption of polymer on the wall of the capillary. I n this paper several experimental results in the viscometric behavior of polyvinyl chloride solution are reported apd some considerations are given according to Ohrn's point of view. Experimental Part \Ve used Ubbelohde's viscometer with a capillary of 0.27 mm. in radius and 12.15 cm. in length. Flow time for cyclohexanone was 824 ==! 0.1 second a t 30". We also used the double capilla.ry viscometer according to 0hr11 and it has radii of 0.22 and 0.6 mm. The constant temperature bath was kept within the deviation of 3=0.002" a t 15-30' and 10.01" a t 50 -60". The solutions were made by two different methods. In method A all solutions are prepared by dissolving weighed polyvinyl chloride in cyclohexanone a t 90" for 3 hr. The volume change during this time due t o evaporation of the solvent from closed flask was corrected by adding new solvent to that flask in a constant temperature bath of 20". In method B concentrated solutions which were .made by method A are diluted by pipett,ing this solution into pure solvent. Fractions of polyvinyl chloride used in this experiment are fractionated from industrial polymer Fractions I and I1 were fractionated froin C-46 of Mitui Chemical Co. Fractions 111, IV and V were fractionated from Geon 101 of Japan Geon Co. One per cent. polymer solution in cyclohexanone was fractionated with the addition of purified methanol. Solutions of fraction I and I1 were made by method A and solutions of fraction 111, IV and V were made by method B for measurement. Approximate molecular weights are estimated from [TI using the following equation
KM.
(1) where [1f1 is the intrinsic viscosity and M is the osmotic molecular weight. The values of the constants which were determined from the work of Staudinger and Narberleb (Y = 0.925. are K = 7.2 X [q] =
(1) Fulbright a n d Smith-Mundt Exchange Research Scholar, 1955. Department of Chemistry and Chemical Engineering, University of Illinois. (2) RI. Takeda and E. Turuta, Bull. Chem. Soc. Japan, 2 6 , 80 (1952). (3) D.J. Streeter and R. F. Boyer, J . Polymer Sei., 14,5 (1954). (4) 0.E.b h r n , i b i d . , 17,137 (1955). ( 5 ) H.Staudinger a n d M. Harberle. Makromol. Chem., 9, 35 (1953).
I
I
I
I
I
-
Ob-
03t
c I 0.03
I
I
01
03
,
i I
I
3
cf/L.
'
Fig. 1.-Typical results showing tendency for the upturn in v a p / cplots a t low concentration of polyvinyl chloride fractions in cyclohexanone. Fraction I (0); 11, (a); 111, ( 1; Ccrit (-1.
Upturn of qsp/c curve increases with increasing molecular weight and decreases with increasing temperature. The minimum of osp/c curve which is called the critical concentration, Ccrjt, in Boyer and Streeter's paper6 is determined from the curve where gSp/c is the ordinate and c is the abscissa. The values of C c r i t are shown in Table I and on Fig. 1. Coritdecreases with increasing molecular weight and decreases with increasing temperature. TABLE I CRITKALCONCENTRATION, C.,it A N D THICKNESS OF THE ADSORBEDLAYEROF POLYMER IN Ccritra(C,,it) OF POLYVINYL CHLORIDE FRACTIONS Temp. of
Mol. wt.
Fraction
I
104
meas.__
urernent, "C
[?I,
Corit,
I./g.
&/l.
a(Corid X
0.071 50 0.7 20 ,076 .76 I11 6.6 30 ,094 .55 15 ,100 .G .loo .8 7.0atb 30 IV 30 .loo .5 .115 .8 v 8.OQrb 30 ,115 30 .5r .4 I 10.4 50 ,136 ,145 30 ,45 a From the measurement of 0.22 mm. capillary. the measurement of 0.60 mm. capillary. 4.9
103,A.
0.9
1.1 0.9 1.3 1.9 2.5 2.4 3.1 1.1 1.5 * From
(G) R. F. Boyer and D. J. Streeter, J . Polymer Sei.,17, 154 (1955).
VISCOSITY OF DILUTEPOLYVINYL CHLORIDE SOLUTION
Sept., 1956
The results of experiments using the viscometer which has two different capillaries are shown in Fig. 2. It is seen that the dependence of the phe-
T H I C K N E SOFS
THE
1203
T A B L EI1 ADSORBED LAYEROF POLYMER, a(c) A T
VARIOUS CONCENTRATIOK Fraction 11‘ Concn., g./L
x
(ca)
0.01 .03 .05
103,
A.
Fraction Y
1.40 2.06 2.20 2.11 2.31 1.92
.07 .1 :5
x 108, A. 1.84 2.65 3.20 3.10 3.31 2.20
a(c)
viscosity of dilute polyvinyl chloride solution. Huggins7presented the following equation vap/c =
O
L
I
01 I
003 I
=
Fig. 2.-Experimental results of double capillary viscometer showing the effect of capillary size. Fraction IV, radius of capillary 0.22 mm. (e); 0.6 mm. (A). Fraction V, radi;s of capillary 0.22 mm. ( 0 ) ; 0.6 mm. ( 0 ) . Corit (-+), 30 .
nomena on capillary size iseverystriking and these results are very similar to Ohrn’s experimental results. considering the adsorption of polymer, Ohrn derived the following equation. =
? W C
?ap/C
+ 4a(c)(tl.,/c +- l/c)/r
(2)
where qsp/c is the true value, q*sp/c is the observed value, a(c) is the thickness of the adsorbed polymer a t some concentration and r is the radius of the capillary. If vsp/c is negligible to l/c, equation 2 becomes q * d c = qsp/c
+ 4a(c)/cr
(3)
I n Fig. 3 the agreement of experimental results with equation 3 is shown. In Table I1 we give the
r t
1
I
I
p
1
1 - T - l 0.OlCP/a
J &mni
1
Fig. 3.-Relation
2 1
3 1
4 1
5
i?lZ c
(4)
where [v] is intrinsic viscosity and IC’ is an independent constant from molecular weight. When this equation is combined with equation 2, we obtain
’-
.
+ k‘
[VI
8
7
of observed qap/c to l / r a t various conceiitration; fraction IV, 30”.
values of a(c) calculated from the slope of the line in Fig. 3 and a(c) of fraction V which are obtained by the same analysis. These results suggest that the general applicability of adsorption correction for the treatment of
tl*ap/~
=
([VI
+ k‘
[?I2
C)
(1
+ 4 d c ) l r ) + 44c)/rc
(5)
From this equation we can derive the relation between Ccrit and other quantities. From the definition of C c r i t , it is clear that
(a ?*sp/C/aC)c+Ccrit
= 0
(6)
If we combine equation 5 with 6, and assume that a ( C c r i t ) near Ccritfor simplicity, we obtain
a(c) is a constant k
’[912 (I
+ 4a(c)/r)
- 4a(c)/rcz = 0 a t c =
Grit
(7)
Now we consider 1 >> 4a(c)/r, equation 7 becomes u
(Corit)
+ 1/4 k ’[?I2
C’crit
(8)
From equation 8 we can estimate the thickness of adsorption a t C c r i t , a( C c r i t ) from the observed value of Ccrit and [v]. Using this method a ( C , , i t ) are calculated and shown in Table I. The agreement of a(C,,.it) for sample I V and V with the value of a(c) near Ccritin Table I1 is not bad. In this calculation we used the value of 0.52 as k‘ from Breitenbach, Forster and Renner’s worka It is seen that equation 8 can cover the observed dependence of C c r i t with molecular weight and temperature, if we assume reasonable a ( C c r i t ) values. However, a ( C c r i t ) value for sample I is about of a(c) value in lower concentration which was roughly estimated from experimental value of vsp/c in Fig. 1. Even if we consider the tendency of slight decrease of a(c) in higher concentration which is seen in Table 11, this disagreement is too large and it might be due to too simple assumption of a ( C c r i t ) = const. Boyer and Streeter6suggested that C c r i t might be increasing with increasing molecular weight, if a ( C c r i t ) increases with increasing molecular weight. However, this is not always true, from equation 8 C*orit a a(Ccrit)/[vl2
and from equation I
[VI
a
Ma
(7) M. L. Huggins, J . A m . Chem. Soc., 64, 2716 (1942). (8) J. W. Breitenbach, E. L. Forster and A . J. Renner, Kolloid Z., 137, 1 (1952).
JOHNG . BUZZELL AND CHARLES TANFORD
1204
Therefore Ccrit might increase with increasing molecular weight when a(C,it) MB 2 CI < B When 2a > p, we might have the decrease of Ccrit with increasing molecular weight which is the case observed in this experiment. Batzerg found that branched polyvinyl chloride showed a maximum in qsp/c a t low concentration, whereas less branched polyvinyl chlorides have a (9) H.Batzer, Makromol. Chcm., 12, 145 (1954).
Vol. 60
straight line plot in ~ ~ and~ c curve. / c This experiment may be explained by assuming different adsorption character of samples. We can conclude that the adsorption theory of Ohrn is the most reliable explanation for present anomalous viscometric behavior of dilute polyvinyl chloride solutions. It is also noted that equation 5 might be useful for exact determination of [ q ] from viscosity data, when the correction term due to adsorption is not negligible in higher concentrations like 1g. 2 g./l.
-
THE EFFECT OF CHARGE AND IONIC STRENGTH ON THE VISCOSITY OF RIBONUCLEASE1 BY JOHNG . BUZZ ELL^ AND CHARLES TANFORD Contribution from the Department of Chemistry, State University of Iowa, Iowa City, Iowa Received Februarv 24, 1966
T h e intrinsic viscosity of ribonuclease near its isoionic point is 3.30 cm.a/g., Le., 0.033 dl./g. This is one of the lowest values reported for any protein, indicating that the ribonuclease molecule is very com actly folded. When the molecule acquires a charge there is only a small increase in intrinsic viscosity: the maximum vayues observed over the range of pH 1 to 11 lying between 3.5 and 3.6. Thus the ribonuclease particle appears t o undergo no a preciable deformation when charged. The observed changes in [ 7 ] are, however, slightly greater than those predicted by 800th for the pure electrovisccus effect in solutions of charged spheres. The slopes, d (vSp/c)/dc, of viscosity lots increase sharply with increasing charge (2)and decreasing ionic strength ( p ) . Empirically, the equation q,,/c = ( K I Kz.Z2/ps/*) [q]2cfits the present data, as well a those previously reported for serum albumin, with K I equal to 1.9 in both cases. This value is close t o that predicted by Guth and Gold for uncharged spheres.
[,y+
+
This paper reports a study of the viscosity of content was determined by drying t o constant weight at aqueous solutions of the protein ribonuclease be- 107’. The more concentrated solutions used for viscosity tween pH l and pH ll, essentially the entire pH measurement were prepared from such stock solutions by range over which this protein is stable. As in a addition of appropriate amounts of standard HC1, KOH, previous similar study of bovine serum a l b ~ r n i n , ~KCI and conductivity water. The more dilute solutions usually prepared by weight dilution of more concenour major interest lies in the effect of charge and were trated solutions. All solutions were filtered through fritted ionic strength, both on intrinsic viscosity and on the Pyrex glass funnels immediately before determination of further increase in specific viscosity with concen- their viscosities. Measurement of Density and Viscometer Flow T h e . tration. The principal difference between ribo- The viscosity is determined from measurements of flow time nuclease and serum albumin is that the former be- in a capillary viscometer and of density in a pycnometer. haves as an essentially undeformable solid particle All measurements were made at 25.0’. The apparatus throughout its range of stability, whereas serum used and the proc,edure for measurement were the same as previously described for serum albumin.3 Two modificaalbumin does so only between p H 4.3 and 10.5. tions of the procedure were found desirable. (1) It was found that visconieters were more difficult t o clean atter use with ribonuclease than they had been after use with Ribonuclease.-Crystalline ribonuclease, of bovinc. wi- serum albumin. Hot concentrated “01 was found to be gin, lots 381-059 and 381-062, was obtained from Arlnour the most effective cleaning agent, and was used in place of and Co. The two lots used differ in the relative content of the sulfuric acid-dichromate solution employed in the work the two major chromatographic components. The differ- with serum albumin. (2) It was found that smooth curves ence between these components, however, is only the of tldP/c Z I E T S ~ L S concentration, for isoionic ribonuclease substitution of a free carboxyl group for a n amide group‘ solutions, could not be obtained when Cannon-Fenske viscomand the physical properties appear t o be unaffected by this eters were used. Instead a break appeared, a t a protein difference, except t h a t there is a small difference in the concentration about 1.5 g./100 ml., very similar t o that c h a r g e p H relationship. No experimentally significant dif- observed for ovalbumin by Bull.6 Bull ascribed this effect ference between the two lots used could be detected in to a difference in the wetting of the glass surface (below a the resent study. critical concentration) hy the falling and rising menisci of &e protein was dissolved in water and the solutions were the liquid. We did not attempt t o confirm this explanation passed down an ion-exchange column of the type designed direct,ly. However, the effect wits completely eliminated by Dintziss for serum albumins. The resultin stock solu- by use of TJbbelohde “suspended level” viscometer^,^ &xis were assumed salt-free and isoionic. +heir protein in which surface tension plays a less important role than it does in the Cannon-Fenske viscometers. Accordingly, (1) Presented at the 30th National Colloid Syinposium, Madison, v i r t d l y all the results reported, including all of those at Wisconsin. June 18-20, 105F. tile isoionic point, were obtained using Ubbelohde viscom(2) Abstracted in p a r t from the Ph.D. TlLcsis of John G . B ~ ~ z s r l l , eters. The effect here described did not occur in acid State liniversity of Iowa, August, 1955. solutions, and a few of the results reported for acid solutions (3) (a) C. ‘I’anfordand J. C . BIIZRPII, THISJ O U R N A L . 60,225 (105G): were ohtained using Cannon-Fenske viscometers. (I,) C:. Tanford,, I . G . Diirscll, D. C . Rands xnd S. A . Swanson. J . A m . Units of Concentration and of Viscosity.-It haR been Chem. Soc.. 77,6421 (1955). customary in viscosity experiments t o express concentration
Experimental
( 4 ) t. Tanford and J. D. H a i i e n s w i n . Llzocb~m.8 i o p h y s . Acta. 19, 535 (19.56). ( 5 ) 11. hl. Dintzis, 1’h.D. Thesis, Ifarvard University, 1952.
.
.
. . .,
.
..__I.
-. .^.
(G) H. B. B d l , J. B i d . Chem., 133,39 (1940). (7) L. Ubbelohde, I n d . Ene. Chem., A n d . Ed.. 9,85 (1937).
