1474 INTRINSIC VISCOSITIES OF CELLULOSE AS AFFECTED BY

1474

C.

M. CONRAD,

V. W. TRIPP, .4ND T. MARES

( i ) BUSWELLASD DCDESBOSTEL: J. .4m. Chem. SOC.63, 2554 (1941). (8) D O L E :J. Chem. Phys. 16, 25 (1948). (9) EMMETTA N D BRUNAUER: J. Am. Chem. SOC.69, 1553 (1937). (10) EMMETT A N D CISES: J. Phys. & Colloid Chem. 61, 1248 (1947). (11) HEIDRICKS:J. Phys. Chem. 46, 65 (1941). (12) HENDRICKS: Ind. Eng. Chem. 37, 625 (1945). (13) HENDRICKS ASD JEFFERSON: .4m. Mineral. 23, 863 (193s). (14) HESDRICKS, S E L S O NA, N D ALEXANDER: J. Am. Chem. SOC. 62, 1457 (1949). (15) HOFMAN A N & BILKE:Kolloid-Z. 77, 238 (1936). (16) International Critical Tables, Vol. 111, p . 212. RIcGraw-Hill Book Company, Inc., Kew York (1829). (17) JOHNSOS . ~ S D LAWRENCE: J. Am. Ceram. SOC. 26, 344 (1942). (18) KEESASASD HOLMES:J. Phys. & Colloid Chern. 63, 1309 (1949). (19) K U R O NKolloidchem. : Beihefte 36, 178 (1932). (20) PAULING: The Nature of the Chemical Bond. Cornel1 University Press, Ithaca, New York (1940). (21) SIEFERTA N D HENRY:J. Am. Ceram. Soc. SO, 37 (194i). (22) TEICHNER: Compt. rend. 226, 1337 (1947). (23) THOMAS: Soil Sci. 11, 409 (1921). (24) THOMAS: Soil Sci. 17, 1 (1924). (25) WIIOA N D JUHOLA: J. Am. Chem. SOC.71,561 (1949). (26) ZOOEVA N D GAPON:Pedology (U.S.S.R.) 1943, S o . 8, 130.

INTRINSIC VISCOSITIES OF CELLULOSE AS AFFECTED BY RATE OF SHEARL CARL M. COIURAD, VERNE W. T R I P P ,

AND

TRINIDAD MARES

Southern Regional Research Laboratory: New Orleans, Louisiana Received September 14, lg60

Although considerable advance has been made in recent years in the theory and application of viscometry to high-polymer solutions, some important problems remain to be dealt with. One of these is the non-Newtonian, or rate-of-shear, effect. Previous attempts to deal with the non-Newtonian phenomena have consisted in working a t low gradients (20, 22), at which it was believed the effects were minimized; use of a “mobility ratio” (5); reference of the results to a “standard” velocity gradient (3,4, 11) ;extrapolation of the viscosities determined a t different hydrostatic pressures to zero pressure (16, 23); and extrapolation of the results to zero velocity gradient by an appropriate formula, either directly (8, 9, 19, 21) or in conjunction with the concentration extrapolation (13, 15). However, 1 Presented before the High Polymer Forum, American Chemical Society Meeting a t Detroit, Michigan, April 16-20, 1950. * One of the laboratories of the Bureau of Agricultural and Industrial Chemistry, Agricultural Research Administration, U. S. Department of Agriculture.

1475

I N T R I N S I C VISCOSITIES O F CELLULOSE

none of these techniques has proved entirely satisfactory for dealing with celluloses of a high degree of polymerizatiqn. While it has sometimes been assumed that the rate-of-shear effect becomes zero at infinite dilution (13, 15, 19, 22), this has been disputed by others (7, 14). The shear effect does, indeed, appear to approach low values at low concentrations, but it must be kept in mind that such appearances may be deceiving, in view of the fact that the effect a t low concentrations must be multiplied by the dilution factor in the calculation of intrinsic viscosity. There are observations indicating that, in spite of the trend toward disappearance at zero Concentration, the final effect is finite. Furthermore, it is not the value a t zero concentration that is desired, but only the value at such low concentration that’ neighboring molecules no longer exert any influence on the flow behavior. If an isolated molecule of cellulose, or some other “stiff” high polymer, exerts a different effect on the flow behavior depending on the alignment of its principal TABLE 1 Description of cellulose samples SATUPE OR

SAMPLE NO.

omGw OF

SAMPLE

............ Vicrcose rayon Cotton, kiered and bleached 51 . . . . . . . . . . .~2 .......... Chemical cotton 6. . . . . . . . . . . Wood pulp, purified 4 . . . . . . . .. I Linters, kiered and bleached 7. . . . . . . . . . Chemical cotton, high degree of polymerization 3 . . . . . . . Raw cotton, alcohol-extracted

.I

I

1I ~

ESTIMATED DECREE OF POLYMBRIZATION‘

495

1065 1350 1510 2000

E

* Estimated from the intrinsic viscosity determined in cuprammonium hydroxide a t a velocity gradient of 500 set.-' and multiplied by Kraemer’s factor of 260.

axis with or across the line of flow, then the non-Newtonian effect could not be expected to disappear at infinite dilution. In the present work, an attempt was made to determine the extent of the effect of uncontrolled and several selected controlled velocity gradients of flow on intrinsic viscosities of celluloses, covering a wide range of degrees of polymerizations and in two different though related solvents; it has also included a consideration of several formulas for the extrapolation of concentration and a study of the relation of velocity gradient to the concentration slope constants of the Martin (17) and the Huggins (10) equations. SAMPLES AND METHODS

Samples for the present study, consisting of seven different celluloses, are identified and described in table 1. They varied in origin and represent degrees of polymerization (D.P.) estimated to range from 500 to 5000. Several of the cottons and the linters had had a commercial treatment consisting of a hot alkaline extraction followed by light bleaching. Samples not already free of

1476

C. M. CONRAD, V. W. TRIPP, AND T. MARES

waxes were dewaxed with hot ethyl alcohol; they were then washed out with water and dried. When air-dry, the samples were paased through a Wiley mill equipped with a 20-mesh screen, and the finely reduced materials were stored in stoppered g l w bottles. Suitable portions of the samples were weighed out into small (5-mm. diameter) glass tubes for determinations of viscosity and replicate portions were taken for determinations of either moisture or cellulose content, depending on the degree of freedom from noncellulose constituents. Four to five concentrations were employed for each sample. Both cuprammonium and cupri-ethylenediamine solutions of the celluloses were studied. The cuprammonium solutions were prepared in the viscometer burets according to the techniques described by Conrad and Tripp (4). The cupri-ethylenediamine solutions of the celluloses were prepared in small bottles, very nearly according to Method B of Specification D 539-48T, A.S.T.M. (2). The only deviation consisted in using different concentrations of cellulose. For each concentration of either solvent, the fluidities (reciprocal viscosities) found for the different hydrostatic heads were plotted on log-log paper against the computed velocity gradients, and the best straight line was drawn through the points. Fluidities were read off the curves at abscissa1 values of 300,.500, and 2OOO reciprocal seconda, the required extrapolations being relatively small in most cases. In addition to the fluidities read off the curves a t selected velocity gradients, the fluidities were, computed directly from the discharge times of the viscometers without making adjustments for variations in gradient. A capillary of suitable diameter waa chosen so that an approximately constant discharge time was maintained. This naturally resulted in progressively higher velocity gradients existing during discharge as the solutions became more dilute, and the fluidity accordingly greater. The fluidities obtained at different concentrations were divided into the fluidity of the solvents to give the relative viscosities, and the ratio of the latter, minus 1, to the concentration, Le., the “reduced viscosity,” was plotted on semilog paper against concentration according to Martin’s (17, page 966, et seq.) equation, log ( d c ) = log

hl

+ K[cllc

in which c is the ooncentration in grams per deciliter (g./dl.), t ~ is, the ~ specific viscosity, [qJ is the intrinsic viscosity, and K is a constant, “Martin’s constant.” The least-squares line waa found for the points and the zero-concentration intercept computed. In a few cases at a concentration of 0.5 g./dl. it was found that the reduced viscosities fell below the straight line drawn through the points for lower concentrations. In these cases only the data falling on the initial linear part of the curve were used. The intrinsic viscosities found with cuprammonium solution were multiplied by Kraemer’s (12) factor of 260 to obtain the degrees of polymerization shown in tables 1 and 2. VIBCOSITY-CONCENTRATION CURVES FOR DIFFERENT SAMPLE8

The plots of reduced viscosity us. concentration for the different selected velocity gradients, and at uncontrolled velocity gradient, are shorn in figures 1 to

INTRINSIC VISCOSITIES OF CELLULOSE

1477

Concentrotion, Gms./dl. Fro. 1. Reduced viscosity curves for viscose rayon (degree of polymerization = 495)

7, inclusive. In each figure the results with cupri-ethylenediamine are shown in the upper panel and those with cuprammonium in the lower. The velocity wadient and the intrinsic viscosity are also indicated for each set of curves. Figure 1 shows that the curves for either cupri-ethylenediamine or cuprammonium solutions are essentially superimposed, and the intrinsic viscosities are the same, irrespective of the velocity $adient of flow. It will be noted that the

1478


values of intrinsic viscosity with cupri-ethylenediamine as solvent are slightly larger than those with cuprammonium as solvent. This effect, which becomes more pronounced as the degree of polymerization increases, will be discussed below. Figure 2 for bleached cotton of degree of polymerization about loo0 shows a beginning of separation of the curves for different velocity gradients. This is more pronounced with cupri-ethylenediamine as solvent. The zero-concentration intercepts differ slightly with velocity gradient. The curves and intercepts for the different velocity gradients are arranged below one another, and with decreasing slope, in the order of increasing gradient. I t will be noted that the dashed lines in figure 2, representing reduced viscosities without control of velocity gradient, are highest a t the higher concentrations and lowest a t the lower concentrations. Thus they cut across the other curves and, with cupri-ethylenediamine as solvent, give the lowest intercept. This effect, which becomes more pronounced as the degree of polymerization increases (figures 3 to 7), is due to the relatively large increases of velocity gradient which accompany the lowering of the concentration of the cellulose. It shows up in spite of maintenance of approximately uniform time of discharge of the viscometer through suitable selection of capillary bore. Figures 3 to 7 show an increasing divergence of the reduced viscosity-concentration curves with velocity gradient as the degree of polymerization becomes greater. The intercepts on the zero-concentration axis lie farther apart and the slopes deviate more. The divergence is always the greater for cupri-ethylenediamine as solvent; and the curve for uncontrolled velocity gradient cuts across the others and gives, invariably, the lower intrinsic viscosity. In figure 7, which represents the sample of the highest degree of polymerization studied, if the intrinsic viscosity at 500 sec.-I is used as base, the corresponding deviations in per cent a t 300 and 2000 set.+ and without control of gradient are: for cuprammonium hydroxide as solvent, +3.0, -9.7, and -22.3 per cent; for cupriethylenediamine as solvent, +5.5, - 13.6, and -22.8 per cent, respectively. In figures 3 to 5 the reduced viscosity values fall on the straight lines extended from lower concentrations, up to 0.5 g./dl. or even higher, but in figures 6 and 7 the values a t 0.5 g./dl. already fall below the straight lines and are not used in computing the intercepts, Le., the intrinsic viscosities. A treatment of the data presented by Lyons (15), according to the methods discussed above, leads to the same general effects as observed in the present study. RELATION O F SEVERAL CONCENTRATION FORMULAS

In all the foregoing treatment the reduced viscosities were computed from actual observations a t the different concentrations. In an earlier paper (4) considerable dependence was placed upon the use of the Philippoff equation. It mas of interest to compare the present results, obtained with Martin's equation (17, page 966), with those obtained by application of Philippoffb (18) equation for extrapolation of concentration :

[VI

=

g ( G

-

l)/c

INTRINSIC VISCOSITIEB OF CELLULOSE

1479

FIQ.2. ,Reduced viscosity curves for bleached cotton (degree of polymerization = 1065)

1480

C.

M. CONRAD, V.

W. TRIPP, AND T. MARES

Fro. 3. Reduced viscosity curves for chemical cotton (degree of polymerization

-

1360)

IWFRINSIC VISCOSITIES OF CELLULOSE

Concentration, Oms. /dl. Fro. 4. Reduced viecoeity curves for purified wood pulp (degree of polymerisation

1481

-

1510)

1482


Concentration, Gms./dl. FIG.5. Reduced viscosity curves for linters (degree of polymerization

= 2000)


1483

FIQ.6 . Reduced viscosity curves for chemical cotton of high degree of polymerization (degree of polymerization = 2830).

1484

C.

M. CONRAD, V. W. TRIPP, AND T . MARES

Concentrotlon

, Oms /dl

FIQ.7. Reduced viscosity curves for raw cotton (degree of polymerisation = 5020)

as well aa the equation of Fikentscher (7) In ?I‘ = [uk2/(1 bkc) klc from which at infinite dilution can be derived the expression: [‘I]= k f 75k2

+

+


1485

The comparative results, with cupri-ethylenediamine as solvent and velocity gradient adjusted to 500 sec.-1, are presented in figure 8, plotted against intrinsic viscosity found by Martin’s equation. It will be seen that up to intrinsic viscosities of about 10-the range within which most celluloses investigated in the pa& have fallen-the deviations between the four curves were not large. However, aa the intrinsic viscosities increased the deviations became much more pronounced. The results with cuprammonium solutions were of the same nature. Thus, in spite of the theoretical equivalence of the equations a t low concentrations, the experimental results differed when celluloses of a high degree of polymerization were concerned.

RELATION OF INTRINSIC VISCOSITIES IN’ TWO SOLVENTS

As figures 1 to 7 show, a rather large difference existed between the intrinsic viscosities determined in cuprammonium hydroxide and in cupri-ethylenediamine as solvents. The intrinsic viscosities, determined in the two solvents at 500 sec.-l, are plotted in figure 9, and the least-squares line fitted through the origin. It will be seen that a rather constant ratio exists between the intrinsic viscosities in the two solvents, the intrinsic viscosity in cupri-ethylenediamine solution being 1.365 times that in cuprammonium solution. This doubtless represents differences in the nature of the two solvents (1).

1486

C. M. CONRAD, V. W. TRIPP, A N D T. MARIB

RELATION OF DEGREE OF POLYMERIZATION TO INTRINSIC VISCOSITY

In most present-day computations of degree of polymerization of cellulosea the intrinsic viscosity in cuprammonium hydroxide solutions is multiplied by Kraemer’s (12) factor of 260. This factor was derived from molecular-weight determinations in the ultracentrifuge and intrinsic-viscosity measurements on several celluloses in cuprammonium hydroxide solution ; the highest intrinsic viscosity of the samples was about 5. In view of the dependence of intrinsic viscosity of celluloses of a high degree of polymerization on the rate of shear, shown by Conrad (3), it ww evident that the factor of 260 must be applicable only at some one velocity gradient, and that for determinations made at other

INTRINSIC VISCOSITY (CUPRAMMONIUM HYDROXIDE)

FIG.9. Ratio of intrinsic Viscosities in two solvents

gradients, other factors must be required. From the constants of the viscometers employed by Kraemer,a it was ascertained that the intrinsic viscosities on which his ratio was based were determined a t velocity gradients of about 1000 set.-' Since he worked on celluloses whose maximum intrinsic viscosity did not exceed 5, and at concentrations as low as 0.05 g./dl., in consequence of which the rateof-shear effect was negligible (see below), it follows that the ratio used by Kraemer may be taken as a reference point. It may be applied to the viscosities of celluloses found in cuprammonium hydroxide solvent and reported in the present paper, as a relative measure of degree of polymerization, pending a more exact 3 Data kindly furnished through a private communication with Dr. J. B. Kichols and hlr. E . D. Bailey, E. I. du Pont de Nemours and Company.

1487


determination. If we accept this factor tentatively aa being suitable for transforming intrinsic viscosities determined in cuprammonium hydroxide solution into values of degree of polymerization, then the proper factor for making the comparable conversions with cupri-ethylenediamine solutions may be computed from the results of the preceding section. We have

D.P.

= 260[~1cu,m=

260/1.365 [V]C.E.D. = 1 9 0 . 5 [ 9 1 ~ . ~ . ~ .

where the subscripts CuAm and C.E.D. stand for cuprammonium and cupriethylenediamine, respectively.

K It has been pointed out by Huggins (10) that in Martin’s equation (17, page 966) the K is equivalent to the k‘ of his own (Huggins’) equation, if we multiply the former by the factor 2.3 to convert it for natural logarithms. Lyons (15) had raised the question as to whether the k‘ of Huggins and the K of Martin MARTIN’S

SLOPE CONSTANT,

TABLE 2 Marlin’s K-values at different dearees of. .pol , Leriralion and velocity gradients DEGREE OF POLYMERIZATION OF SAMPLE

495 1065 1350 1510

m 2835

Mrn

c O?

G OF CUPPAMHONIUM 300

0.115 0.112 0.106 0.122 0.091 0.096 0.072

iw ___0 114 0 113 0 109 0 130 0096 0 091 0 064

~

,

2Mx)

-G

CUPPI-ETHYLENIDI*IIINE

3w

500

ZOO0

0.121 0.091 0.105 0.104 0.079 0.093 0.055

0.122 0.092 0.105 0.108 0.080 0,089 0.048

0.125 0.098 0.103 0.097 0.084 0.071 0.026

-G

~

0 0 0 0 0 0 0

120 119 118 118 106 098 038

0.127 0.125 0.143 0.137 0.132 0.140 0.107

-

0.124 0.116 0.132 0.140 0.127 0.122 0.089

are actually insensitive to differences in velocity gradient, and had suggested this as a subject needing further study. It was therefore of interest, in the present investigation, to determine how K behaved at different velocity gradients as the degree of polymerization of the cellulose changed. The slopes of the curves in figures 1 to 7 represent the products of K with the.intrinsic viscosities. Therefore, to isolate K we must divide the slopes of the curves in those figures by the appropriate intrinsic viscosities. From the data in table 2 a t controlled velocity gradients, it will be noted that the K-values were moderately uniform, irrespective of gradient or solvent a t the lower degrees of polymerization. However, as the degree of polymerization increased, the K-values decreased and were generally less for the higher gradients ; this latter is especially true for the cupri-ethylenediamine solvent. Where the velocity gradient was not controlled the K-values nere the same as at the controlled velocity gradient for the lowest degree of polymerization. They did not change with increasing degree of polymerization until the very highest degree of polymerization was reached, when they dropped suddenly for both solvents.

1488

C. M. CONRAD, V. W. TRIPP,

A N D T. MARIB

The extent of the drop is entirely too large to be accounted for by experimental error.

The decrease of K with the degree of polymerization of the sample at controlled velocity gradient was quite surprising. Since K is an interaction quantity,


1489

it might be expected, in line with the discussion of Eirich and Riseman (6),to remain constant rather than to decrease with increasing intrinsic viscosity. A better picture of the situation may be secured by plotting the K-values of table 2 (except those for uncontrolled gradient, which obviously were subject to the accidental conditions existing experimentally, and could not be expected to be entirely reproducible) against intrinsic viscosity (figure 10). The open and filled circles, referring to results with cuprammonium and cupri-ethylenediamine solutions, respectively, seemed to lie on straight lines for each velocity gradient, without respect to type of solvent involved. Least-squares straight lines were therefore fitted to the data, as shown. The intercepts of these lines on the ordi-

VELOCITY ORADIENT, seoa-’

FIG.11.

Relation of the slopes of Martin’s K-valuea with intrinsic viscosity to velocity

gradient.

nate differed slightly with velocity gradient, being 0.120, 0.124, and 0.136 for velocity gradients of 300, 500, and 2000 sec.-l, respectively. It is evident that when the velocity gradient is held constant the K-values are not constants, as in Martin’s (17, page 966) experience, nor as expected by Eirich and Riseman (6). On the contrary, they decrease apparently linearly with the intrinsic viscosit,y and vary in slope with the velocity gradient existing during measurement of the viscosity. To this extent they confirm the contention of Eirich and Riseman as to the complexity of the factors grouped together in k‘, Le., 2.3 K . The slopes of the straight lines in figure 10 were computed and were found to be -0.232, -0.287, and -0.480 X lo-*, respectively, for 300, 500, and 2000

1490

C. M. CONRAD, V. W. TRIPP, AND T.

MARES

sec.-’ When these slopes were plotted against velocity gradient, the curve shown in figure 11 was obtained. Evidently, this slope is no simple function of the velocity gradient. I t does not seem to be a simple parabola, although the data are too scanty and inexact to permit any reliable test of this possibility. Further work will be required to resolve this problem. SUMMARY AND CONCLUSIONS

Data have been presented on the application of Martin’s equation for determining intrinsic viscosity to a series of seven celluloses, representing an extreme range of degrees of polymerization. In each case the viscosity determinations were made in both cuprammonium and cupri-ethylenediamine solvents and the results read off from curves a t velocity gradients of 300, 500, and 2000 set.-' For comparison, the intrinsic viscosities were also computed from viscometer readings taken without regard to velocity gradient. It was shown that for a cellulose of low degree of polymerization (viscose rayon) the intrinsic viscosity was unaffected by the velocity gradient. However, as the degree of polymerization of the cellulose increased to about 1000, the intrinsic viscosities began to vary progressively with the velocity gradient, and to decrease as the velocity gradient increased. In all cases where the results showed dependence upon gradient, the Martin’s plot of log nBp/cvs. c for observations a t uncontrolled gradients had higher slopes with concentration and crossed the family of curves, representing controlled gradients, thus yielding the lowest intrinsic viscosities. This effect has its cause for any particular cellulose jointly in the natural variation of velocity gradient with concentration and in the selection of suitable flow times for the viscometers. The maximum range of intrinsic viscosities resulting from the choice or nonchoice of velocity gradient occurred in the cellulose of highest degree of polymerization and amounted to 25 per cent for cuprammonium and 28 per cent for cupri-ethylenediamine solvents. It was shown that the Philippoff and Fikentscher equations for determinations of intrinsic viscosities, when applied in the range of high degree of polymerization (above [n] = IO), lead to much lower intrinsic viscosities than does Martin’s equation. The intrinsic viscosities in cupri-ethylenediamine and cuprammonium solutions, determined a t 500 set.-', were found to be linearly related, with the ratio of the former to the latter being 1.365. Thus, if Kraemer’s factor of 260 is used for cuprammonium hydroxide solutions, for cupri-ethylenediamine a factor of 190 should be used for converting intrinsic viscosities to degree of polymerization. Finally, it was shown that Martin’s slope constant, K , a t the different velocity gradients studied, is not constant but is inversely related to the intrinsic viscosity, with increasingly greater slope as the velocity gradient increases. The relation of the slope to the velocity gradient appears to be complex. The authors wish to express their appreciation to Miss Hilda M. Ziifle, who made the statistical calculations and drew the figures.

VISCOSITIES O F SOME MIXED GASES

1491

REFERENCES

1) ALFREY,T., BARTOVICS, A., A N D MARK,H.: J. Am. Chem. SOC.64, 1557 (1942). (2) AMERICAN SOCIETY FOR TESTING MATERIALS: A.S.T.M. Standards on Teztile Materials (with related information). American Society for Testing Materials, Philadelphia, Pennsylvania (1948). (3) CONRAD, C. M.: Ind. Eng. Chem., Anal. Ed. 13, 526 (1941). (4) CONRAD, C. M.,A N D TRIPP, V . W.: Textile Research J. 16,275 (1946). (5) D E WAELE,A , , A N D DINNIS,G.: Physics 7,426 (1936). (6) EIRICH,F., A N D RISEMAN, J.: J. Polymer Sci. 4,417 (1949). (7) FIKENTSCHER, H.: Cellulosechemie 13, 58, 71 (1932). (8) Fox, T. G, JR.:Personal communication. (9) Fox, T . G, Fox, J . C., A N D FLORY, P . J.: Paper presented before the High Polymer Forum, American Chemical Society Meeting, Detroit, Michigan, April 16,1950. (10) HUGGING, M.L.:J. Am. Chem. SOC.64,2716 (1942). (11) JELINEK,V. C . : Ind. Eng. Chem., Anal. Ed. 16, 172 (1944). (12) KRAEMER, E. 0.: Ind. Eng. Chem. 30, 1200 (1938). J. G., AND WHITWELL, J. C.: Textile Research J. 1%253 (1949). (13) KRIEBLE, (14) LAUFFER,M. A.: Chem. Revs. 31, 561 (1942). (15) LYONS,W.J.: J. Chem. Phys. 13, 43 (1945). (16) MEAD,D. J., A N D Fuoss, R. M.: J. Am. Chem. SOC.64,277 (1942). (17) Om, E.: Cellulose and Cellulose Derivatives. Vol. V . High Polymers. Interscience Publishers, Inc., New York (1946). (18) PHILIPPOFF, W.: Cellulosechemie 17, 57 (1936). (19) PHILIPPOFF, W.: Viskositdt der Kolloide. Theodor Steinkopff, Dresden (1942). (20) SCHULZ, G. V.: Z. Elektrochem. 43, 479 (1937). (21) SIMHA,R.: High Polymer Physics. A Symposium, page 411. Remsen Press Division, Chemical Publishing Company, Brooklyn, New York (1948). (22) STAUDINGER, H . : Die hochmolekularen organischen Verbindungen. J . Springer, Berlin (1932). (23) WEHR,W.: Kolloid-2. 88, 185 (1939).

VISCOSITIES O F SOME MIXED GASES J . W . BUDDENBERG

AND

C. R. WILKE

Department of Chemistry and Chemical Engineering, University of California, Berkeley, California Recezued September 20, 1960

In connection with the development of general equations (3, 26) for the estimation of viscosities of gas mixtures from properties of the pure components, experimental measurements of viscosity were made on several systems which had not been studied previously. These experiments will be described briefly in order that the results may be evaluated in relation to quality of materials and limitations of experimental technique. A completely detailed account of these experiments is available elsewhere (2). APPARATUS AND PROCEDURE

An apparatus similar to that described by Rankine and Smith (15) was constructed for measurement of viscosities relative to nitrogen. This equipment is

1474 INTRINSIC VISCOSITIES OF CELLULOSE AS AFFECTED BY

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