August, 1%9 drated and anhydrous salts,8 it is noted that each mole of hydrated water in a salt reduces the heat of solution approximately two to three kcal. In terms of the one gram of clay being immersed in water, and assuming that the resulting clay suspension produces a solution of the exchangeable ion, there should be about 6 cnl. less of heat evolved with each additional molecule of water associated with the exchangeable cation. Since calcium clay, preheated to 150°, gives off slightly over 12 cal. more than it does when pretreated at room temperature, then there should be two molecules of water associated with each calcium ion at room temperature. This ratio of calcium to water is also indicated in the isotherms study already reported.6 At higher temperatures, with further reduction of the 001 spacing, the heat of immersion of the calcium clay falls off because of the additional energy needed to force its way into the space between the laminae. Comparison of the present results to customary differential thermal analysis is probably not entirely valid because the samples prepared here were outgassed a.t very low pressure, and this treatment may remove the physically adsorbed and hydrated water that is usually removed a t 150 to 200' in the DTA studies. Attempts to measure the 001 spacings of the pretreated samples were not successful, primarily because of the difficulty of transferring the samples from the vacuum line to the X-ray spectrometer and, at the same time, preserving the character of the clay system. When these results are compared to other published data, such as that of Johnson2 where samples were outgassed 72 hours and presumably at room temperature, one sees the importance of the temperature of outgassing, particularly with calcium and hydrogen clays. (8) N. A. Lange, "Handbook of Chemistry." Handbook Publishers, Inc., Sandusky, Ohio, 1952,p. 1542.
TRANSLATIONAL FRICTION OF MICROSCOPIC SPHERES I N CONCENTRATED POLYMER SOLUTIONS BY STEPHEN D. MORTON AND JOHND. FERRY Department of Chemislw, University of Wisconsin,Madison, Wisconsin Received December IS, 1068
It has been recognized from experiments on diffusion1-3 and sedimentation4 that the frictional resistance for translation of a tiny particle in a matrix of flexible polymer molecules is far smaller than would be calculated from the macroscopic viscosity, and that the discrepancy is related to segmental motions of the polymer chains. There have been no systematic studies, however, of a homologous series of particles in polymer solutions (1) F. Grtln, Experientia, 3, 490 (1947). (2) Y.Nishiiiina and G . Oster, J . Polymer Sci., 19, 337 (1956). (3) 9. D. Gehman, I. Auerbach, W. R . Rliller and W. C. Kuryla, ibid., 28, 129 (1958). (4) H.IC. Sohaohman and W. F. Harrington, J . A m . Chem. Soc., 74, 3985 (1952).
NOTES
0.217
-2 0.172
0.129
-3 0
2
4
6
D m - , Fig. 1.-Logarithm of ratio of effective local viscosity in sedimentation to macroscopic viscosity, plotted against ratio of sphere diameter t o root-mean-square end-to-end distance of polymer, for three polymer concentrations identified by their weight fractions. Vertical lines represent estimated extreme error, in several cases including duplicate determinations.
of different concentrations. A few rough measurements of this sort are reported here. The particles were polystyrene spheres in the forin of aqueous latices obtained through the generosity of the Dow Chemical Company,' of diameters 880, 1380 and 1880 A. The polymer was an unfractionated polyacrylic acid, generously furnished by Rohm and Haas Company; its intrinsic viscosity in dioxane a t 30" was 0.48 dl./g., its viscosityaverage molecular weight calculated from the equation of Newman, et al.,6 was 315,000, a n d t h e unperturbed rootmean-square end-to-end distance ( r 0 2 ) ' / 2 was 440 A. The acid was 55% neutralized with sodium hydroxide so that both particles and polymer were negatively charged, and all solutions contained 0.2 M sodium chIoride t o minimize electrostatic effects. The polymer concentrations (made up by weight, allowing for a 9.7% moisture content in the lyophilized acid as determined by titration) were 12.9, 17.2 and 21.7010, expressed as weight fraction of unneutralized acid. The particle concentrations were of the order of O.O5%--enough t o give a slight opalescence whlch vented light transmission in a n ultracentrifuge cell. was no evidence of aggregation; the angular dependence of scattered light, viewed visually, was not highly asymmetric for suspensions either in the polyacrylic acid, in 0.2 M aqueous sodium chloride, or in distilled water. Sedimentation coefficients of the particles were measured in the Svedberg oil turbine ultracentrifuge by following the (upward) motion of the opaque boundary. Because the supernatant solution was not perfectly clear, it was difficult to make good photographs and the displacement was measuFed visually on the projected image, with rather poor precision. Using Stokes' la^, the effective local viscosity ve was then calculated for each experiment. Since the density of the polystyrene? is 1.05 and those of the solutions ranged from 1.09 to 1.15, the Archimedes factor was also very uncertain, and the accuracy of the h a 1 values cannot be better than f25'%. This is sufficient, however, to show a n enormous difference between the macroscopic viscosity and the effective local viscosity. The values of the latter ranged from 0.008 poise (essentially that of the solvent) t o 2-poises.
TRl:;
(5) E. B. Bradford and J. W. Vanderhoff, J . A p p l . Phys., 26, 804 (1955). ( G ) S. Newman, W. R. Krigbaum, C. Laugier and P. J. Blow, J . Polymer N r i . . 14,451 (1954). (7) T.Ci. F o x , Jr., and P. J . E'lory, J . A p p l . P h y s . , 21, 581 (1950).
NOTES
1336
The macroscopic viscosity, q , was measured over a range of polymer concentrations and temperatures by the conventional falling ball methods with glass spheres of the order of 1 mm. diameter. Values were then interpolated on a logarithmic plot for the concentrations and temperatures of the ultracentrifuge experiments (the temperatures ranged from 22 to 28'). At 2 5 O , log q for the three polymer concentrations cited above was 0.93, 1.56 and 2.33, respect,ively. Presumably an important quantity determining the ratio of qe to q is the ratio of particle diameter ( D ) to some characteristic dimension of the polymer coil; clearly, as the latter ratio becomes large, q e / q mustapproach unity. As a measure of coil size, we have used (ro2)1/2, even though we are dealing with a charged polyelectrolyte; it probably does not deviate much from the 8-solvent configuration in our concentrated solutions, where there is a high density of counter ions as well as added neutral salt. In Fig. 1, log q e / q is plotted against D/(ro2)'/2. The latter size ratio lies in the range from 2 to 4.3: the local effective viscositv is tremendoudy smaller than 'the steady flow viscosity, b"y a factor of 80 t o 1400. Log q e / q increases with increasing 0 / ( 6 ? ) ' / 2 as expected. Moreover, it increases M ith increasing polymer concentration. The latter dependence is probably related to the role of entanglement coupling in determining the viscosity,g which suggests that the average distance between entanglemAnt points, (rT)Ih,is the important dimension rather than (rq2)'/2. The average distance between entanglements certainly decreases with increasing concentration, though the functional relation is uncertain,'O and hence the data of Fig. 1 might fall on a sing& composite curve if log qe/q could be plotted against D/(re2)l/z. The accuracy of the present data is insufficient, however, for a more detailed analysis. Data of this sort are potentially valuable in clarifying the frictional resistance encountered by polymer segments themselves in translation, as reflected in time-dependent mechanical properties." This, too, is of course very much smaller than would correspond to the steady-flow viscosity, and in some diluted systems the local viscosity encountered by the polymer segments appears to be of the same order of magnitude as that of the solvent.12
VOl. 63
ratio of HSA to SDS (HSA/SDS) is between 100/0 and 70/30, there are three kinds of complexes, AD,-ADI2, AD, and AD2, (A: HSA, D:SDS, and n = 105/2). In the mixing ratio region between 70/30 and 45/55 the complex ADzn changes continuously to AD,,. Measuring diffusion coefficient and intriiisic viscosity of the system HSASDS, Neurath and Putnam3 found that the formation of AD, occurs without detectable changes in molecular shape and the formation of AD2n involves an increase in the molecular asymmetry of the protein. This time an ultracentrifugal study was carried out a t p H 6.8. The results are reconciled with those by diffusion and viscosity. Experimental Horse serum albumin and sodium dodecyl sulfate used were the same as used previously.1 Experiments were conducted a t room temperature at 59,780 r.p.m. using a Spinco Model E ultracentrifuge. Ionic strength of the phosphate buffer was 0.10 and the sum of concentrations of HSA and SDS was 1.0%. Ultracentrifugal drive was continued for 60 minutes.
Results and Discussion All the patterns in the weight ratio region HSA/SDS = 100/0 - 45/55 had a single boundary. One of the patterns is shown in Fig. 1.
Acknowledgments.-This work was supported in part by the Research Committee of the Graduate School of the University of Wisconsin from funds supplied by the Wisconsin Alumni Research Foundation. We are greatly indebted to Dr. J. W. Vanderhoff of Dow Chemical Company and Dr. F. J. Glavis of Rohin and Haas Company for supplying materials, and to Mr. E. M. Hanson for operating the ultracentrifuge. (8) J. D. Ferry, L. D. Grandine, Jr., and D. C. Udy, J. Colloid Sci.9 8, 529 (1953). (9) R. F. Landel, J. W. Berge ana J . D. Ferry, ibid., 12, 400 (1957). (10) P. R. Saunders, D. hl. Stern, S. F. Kurath, C. Sakoonkim and J. D. Ferry, ibid., in press. (11) 6. D. Ferry and R . F. Landel, Kolloid-Z., 148, 1 (1550). (12) J. D. Ferry, D.J. Plazek and G. E. Heckler, J. chim. p h y s . , 66, 152 (1958).
ULTRACENTRIFUGAL STUDY OF HORSE SERUM ALBUMIN-SODIUM DODECYL SULFATE INTERACTION BY KOICHIRO AOKI Contribution from the Chemistry Laboratory, Napoya Cilu Uniusrsify. Mixuho-ku, Nagoya, Japan Received December 16,1368
It has been found by electrophoretic studies on the system horse serum albumin (HSA) and sodium dodecyl sulfate (SDS) that various complexes are formed a t p H G.8.192a When the weight mixing (1) K. Aoki, J. Am. Chem. Xoc., 80, 4904 (1958). (2) (a) F. W. Putnam and H. Nerirath, J. Biol. Chem., 169, 155 (1945); see also, (b) J. T. Yang and J. F. FoRter, J . Am. Chem. Soc., 76, 6560 (1953); ( 0 ) &I. J. Pallansch and D. R. Briggs, i b i d . , 76, 1390
(1954).
Sedimentation coefficients ~ ~ calculated 0 , ~ are shown in Fig. 2. These values are not those extrapolated to zero concentration. The ~ 2 0 value , ~ of 0.3% HSA solution was 4.4 8,agreeing wlt'h the value found in the l i t e r a t ~ r e . ~Values of the partial specific volume (6) were determined by sinlply assuming that all the SDS used was bound to HSA to form a complex and by measuring the density of the mixture a t 25.00'. It was found that V was TABLE I WEIGHTMIXINGRATIOREGIONAND THE COMPOSITION OF COMPLEX FORMED HSA/SDS
100/0-95/5 95/5-80/20 80/20-70/30 70/30-45/55
Complex formed
ADi-ADI? A D l 2and A D , AD, and ADw AD2n-ADan
(3) H . Neurath and F. W. Putnam, J . Biol. Cham., 160, 357 (1945) P. A. Charlwood and A. Ens, Can. J . Chem., 86, 99 (1957). (6) P. A. Charlwood, J . A m . C h e n . Sac.. 79, 770 (1957). (4)
