964
COMMUNICATIONS TO T H E EDITOR
COMMUNICATIONS TO THE EDITOR FLEXIBILITY OF NITROCELLULOSE MOLECULES I N ACETOSE
It has been previously reported (R. M. Badger and R. H. Blaker: J. Phys. & Colloid Chem. 63, 1056 (1949)),largely on the basis of light-scattering, viscosity, and diffusion measurements, that the hydrodynamic equations for flexible macromolecules of Kirkwood and Riseman (J. G. Kirkwood and J. Riseman: J. Chem. Phys. 16,565 (1948); J. Riseman and J. G. Kirkwood: J. Chem. Phys. 17, 442 (1949)) offered promise as being applicable to solutions of cellulose and its derivatives possessing degrees of polymerization, 2, greater than 100. This writer would like to mention that he had considered the applications of the Kirkwood-Riseman theory to cellulose nitrate in acetone, employing published sedimentation data, and had similarly concluded that for large molecular weights the theory might serve, at least to a first approximation, as a satisfactory formalism interrelating translational and rotatory diffusion, viscosity, and sedimentation. The validity of the theoretical equations in the case of polystyrene has been experimentally demonstrated (J. G. Kirkwood and J . Riseman: Zoc. eit.; S. Sewman, J. Riseman, and F. Eirich: Rec. trav. chim. 68, 921 (1949)). Because of the greater precision of sedimentation measurements as compared to those of diffusion, and because of the convenience of the former in computing the molecular parameters b, the effective bond length, and f , a frictional coefficient, which appear in the Kirkmood-Riseman theory, we had considered the sedimentation data of H. Mosimann (Helv. Chim. Acta 26, 61 (1943)) and I. Jullander (Arkiv Kemi, Mineral. Geol. 21A, 1 (1945)) on nitrocellulose in acetone. It was found, upon neglecting small differences in the degrees of esterification, that for five fractions (hlosimann) the sedimentation constants extrapolated to infinite dilution bore, to a good approximation, the following relation to the degree of polymerization:
so= 2.2 x Solving for b and
10-13
+ 0.58 x 10-13
2 0 6
r from the equation' So = Mo(1 - P p ) [ l Xo = < / ( ~ s ~ ) O vob .~
+ (8X0/3)2~~~1/rzV
where ;Mois the relative monomer weight, X is Avogadro's constant, (1 - v p ) is the buoyancy factor, and v o is the viscosity coefficient of the solvent, we have obtained t,he values reported in table 1. For comparison, the results of Badger and Blaker from diffusion and light scattering on samples of somexhat higher nitrogen content are included. Values of the parameters calculated from sedimentation data of Jullander for unfractionated samples containing approximately 12.5 per cent nitrogen lead to substantially the same results as t'hose of Mosimann, which contain approx1 The original published equation (J. G. Kirkwood and J . Riseman: J. Chem. Phys. 16, 565 (1948)) contains a typographical error.
965
COMMUNICATIOiiS TO THE EDITOR
imately 12.0 per cent nitrogen. The samples of Badger and Blaker were nitrated to slightly more than 13 per cent nitrogen. We have computed with the Kirkwood-Riseman equations the intrinsic viscosity of the samples of Badger and Blaker, using the b- and {-values calculated from sedimentation data and reported above, and have compared them with the experimental intrinsic viscosity values (see table 2). Considering sample inhomogeneity and differences in degrees of nitration, a satisfactory agreement between observed and calculated values is noted. This agreement suggests that of the range of values for b reported by Badger and TABLE 1
Molecular parameters for nitrocellulose in acetone
I
XLTHOD
b
A.
g./rcc.
30 46 32-57
11.9 8.0
~
Sedimentation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Diffusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Light-scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . TABLE 2
,
Comparison of observed and calculated intrinsic viscosities SAMPLE
I MOLECULAR WEIGHT
s-4,3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . s-3,4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .I S-1,14 .............................. 1 P-3,2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . P - 4 , 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ,~ ~
9,400 35,000 50,000 93,000 319,000
I, I
1
I N T R I N S I C VISCOSITY
Calculated
Observed
0.30 1.30 2.22 2.98 6.86
1 ~
,
(0.51) 1.50 1.98 3.14 7.45
Blaker, the lowest ones approximating those x e have used would seem to be more appropriate for the samples they have studied and which are discussed here. While the agreement noted in table 2 may be fortuitous, we believe rather that for high molecular weights there is sufficient “bending” in the molecule to permit an approximate application of the Kirkwood-Riseman theory, even though it was not intended for so “stiff” a molecule. Coordinate measurements on homogeneous samples are required for a quantitative study of the limits of applicability of the theory in its present state. Since it is postulated that for a rod-like molecule SOis proportional to log 2,* and for the Sedimentation data cited here such a plot approaches linearity only for 2 < 100, we had tentatively concluded that a theory based on a flexible
* Private communication
from Dr. J. Riseman.
966
COMMUNICATIONS TO THE EDITOR
macromolecule would be inapplicable in this lower range; this confirms the conclusions of Badger and Blaker. SEYMOUR NEWMAN. Southern Regional Research Laboratory Agricultural Research Administration U. S. Department of Agriculture New Orleans, Louisiana February 2, 1950
A METHOD FOR DETERMISING T H E PROPERTIES OF MICELLES We have found it possible to obtain thermodynamic and kinetic data about micelles formed by association colloids by “tagging” the micelles with a minute amount of a solubilized material such as a dye. In aqueous solutions of soap, for example, water-insoluble dyes are taken up by micelles alone (J. W. McBain: Frontiers in Colloid Chemistry, Interscience Publishers, Inc., New York (1950)) and the movement of the dyes, and therefore of the micelles, may be observed under the influence of various forces. Thus the self-diffusion coefficient of the micelle (or a t least of the average solubilizing micelle), its electrophoretic mobility, sedimentation equilibrium, etc. may be determined. These lead by wellknown methods (Alexander and Johnson : Colloid Science, Oxford University Press (1949)) to an estimate of the molecular weight, charge, and approximate shape of the micelle. The method is generally applicable to solubilizing particles in both aqueous and nonaqueous solutions and may be used with any solventinsoluble tracer as well as with dyes. In preliminary experiments we have estimated the electrophoretic mobility and the diffusion constant of the micelle in 5 per cent potassium laurate containing 4 mole per cent potassium hydroxide on the soap, using Sudan IV, a water-insoluble dye, as a tracer. We have also observed the sedimentation in a centrifugal field of micelles of sodium lauryl sulfate containing Sudan IV. The electrophoretic movement of ascending and descending boundaries between the tagged and the dye-free solutions of the same concentration was observed in a standard Tiselius apparatus made available through the kindness of Dr. E. Jameson. Owing to the absence of density differences, a parabolic boundary is obtained. Diffusion was observed between two similar solutions in an unstirred sintered-glass diaphragm cell made available by Professor A. Adamson. Sedimentation was observed qualitatively in a McBain-Ford airdriven opaque centrifuge. The values obtained were D = 0.04 cm.*/day and u = 2.3 X crn.l/volt sec. The only comparable, although differently interpreted, measurement is D = 0.06 cm.Z/day obtained by Dean and Vinograd (J. Phys. Chem. 46, 1091 (1942)) for Yellow AB in Aerosol OT.
