INDUSTRIAL AND ENGINEERING CHEMISTRY
Literature Cited
Vol. 35, No. 2
(S) Lange, Phvsk'k. Z., 31, 9G4 ( 1 9 3 0 ) ; Z . physik. Client., A159, 277
Brice, Rev. Sci. Instruments, 8 , 279 (1937). Holven and Gillett, Facts About Sugar, 30, 169 (1935); E. S. Patent 2,152,645 (1939). Holven and Gillett, U. S. Patent 2,273,356 (1942). Honig and Bogtstra (tr. by Willcox), Facts About Sugar, 28,4469, 470-3, 494-6 (1928). International Critical Tables, Vol. V, p. 262, Xew York, McGraw-Hill Book Co., 1929. (6) Keane ahd Brice, IND. E N G .CHEM.,ANAL.ED., 9, 258 (1937). (7) Knowles, IND. EKG.CHEM.,17,980 (1925).
(9) (10) (11) (12) (13) (14) (15)
(1932). Meade and Harris, J. IXD. ESG. CHEM,,12, 686 (1920). Morseand McGinnis, IND.ENG.CHEM.,ANIL.ED..14,212 (1942). Muller, Ibdd., 11, 1 (1939). Nees, Ibid., 11, 142 (1939). Peters and Phelps, Bur. Standards, Tech. Paper 338 (1927). Rice, Louisiana Planter, 73,392 (1924). Wills, Facts About Sugar, 21, 1114 (1926).
PRESENTED before t h e Division of Sugar Chemistry a t the 103rd Meeting of t h e ~ M E R I C A NCEEMICAL SOCIETY, Memphis, Tenn.
Action of Light on Cellulose Viscosity-Concentration Relations of Cellulose Acetate Solutions RALPH E. MONTONNA AND C. C. WINDING' University of Minnesota, Minneapolis, Minn.
The equation qr =
1
+ kc + k1c2
which is analogous to the expanded form of the expressions derived by Einstein and by Ihnitz, describes the viscosity behavior of dilute solutions o f cellulose acetate. An easy and rapid method for obtaining the limiting specific viscosity, [VI, defined by the equation [qJ = ___ lim
('F')
c-0
is described.
EVERAL authors have derived mathematical expressions for the viscosity of colloidal dispersions, either based on experimental evidence or obtained from theoretical considerations. These equations a11 attempt to relate the relative viscosity, v., with the volume of the dispersed phase, 4, and it is generally accepted that the relative viscosity should be definitely determined by the volume of the dispersed phase alone, provided the particles are spherical in shape. Among the expressions frequently used are those of Einstein (d),
S
+ 2-56 qr = 1 + 4.56 qv =
and Hatschek
(4)
1
Equation 1 is the expanded form to the first approximation of
and Equation 2 is the expanded form of 1
Present address, Cornel1 University, Ithaoa, S. Y .
which is the relation proposed by Kunitz (6). These mathematical relations have either been developed on the assumption that the dispersed particles are approximately spherical without interference between particles, or they are empirical equations that have been determined under conditions where the above assumption was not greatly in error. However, in studying the viscosity of dispersions of cellulose acetate, we encounter conditions where the individual particles do not even approximate spherical shapes. This statement must be true whether we concede the existence of long straight-chain macromoIecules as proposed by Staudinger (11) or micelles composed of bundles of these linear molecules as suggested by McBain (7). Smoluchowski (10) and Sakurada (9) pointed out that the coefficient 2.5 of the Einstein equation includes a shape factor which is a minimum for spheres. Onsager (8) calculated the case for a suspension of rotation ellipsoids and found that the shape factor of Einstein's equation increases with the square of the ratio of major to minor axes. Eisenschita (S), by a less rigorous analysis, reached the conclusion that, as a first approximation, the shape factor would increase linearly with this ratio. It appears obvious, and in agreement with the various theoretical concepts, that coefficients for these equations derived on the assumption of the existence of spherical particles should not be applied to cases where other shapes are known to exist. Since the difficulty of determining particle shape is so great, and the hydrodynamical calculations of shapes other than spherical have not generally been worked out, i t seems logical to turn to experimental data in order to determine the true coefficients. I n order to do this, such dilute solutions must be used that the assumption of noninterference of particles is valid. A search of the literature reveals the fact that most of the work on the viscosity of dispersions of cellulose derivatives has exceeded the limit imposed by this condition since the results of this work
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
February, 1943
indicate that, even for the relatively low viscosity cellulose acetates used, this limit is in the neighborhood of 0.5 gram per 100 cc. of solution. The value of characterizing the viscosity properties of solutions by the limiting specific viscosity, [VI, defined by lim
1111 =
(
V
G
(3)
)
was discussed by Kraemer (5) and Dobry ( I ) , and is substantiated by this work. The equations of Einstein and Kunitz can be expanded to include a term involving 62; and since 4 is equal t o cu/lOO where u is the partial specific volume and c is the concentration in grams per 100 cc., a general equation 11?. =
1
4
3 JlJ
2
+ kc f k'c*
(4) may be written. I n this equation k and kl are constants containing a shape factor and a specific volume term, both of which are constant for any given material. Rearranging,
If the value (qr - l)/c is plotted against concentration c, a straight line of slope k1 and intercept k should result. I n addition, the intercept k is the value of (7. - l ) / c a t infinite
I
J
OO
A
Experimental The cellulose acetate used in this work consisted of ten samples of commercial material manufactured and furnished by the Eastman Kodak Company, E. I. du Pont de Nemours and Company, Inc., and the American-British Chemical Supplies, Inc. Grateful acknowledgment is made for their use. The acetyl contents of the various types were as follows:
10
5
Manufacturer's Type Designation High viscosity Medium viscosity Medium viscosity High viscosity Medium viscosity Medium viscosity Low viscosity Medium viscosity Medium viscosity L o w viscosity
Acetyl Content, yo
40.6 41.6 42.2 39.5 39.1
41.4
40.0 38.4 38.7 38.6
To purify the acetone used as a solvent, it was stored over calcium chloride for a t least 48 hours; potassium permanganate was then added, and the mixture was allowed to stand and was finally distilled through a 90-cm. column, packed with glass tubing, in 2-liter batches. The first 500 cc. coming over were arbitrarily discarded, and the distillation was stopped after 1.5 liters had distilled over. The intermediate fraction of 1 liter was saved and used. This fraction distilled a t a constant temperature. The cellulose acetate was dried in a desiccator over P205 for 48 hours and dispersed in the proper solvent; the solution was analyzed for the cellulose acetate content and placed in calibrated 50-cc. volumetric flasks. Pipets, calibrated to hold either 10 or 25 cc., were used to remove samples for viscosity determinations. By this means a definite volume was removed for each determination after temperature adjustments had been made. At least 24 hours were allowed between determinations after the addition of solvent to permit complete dispersion. Viscosities were determined by Ostwald pipets of approximately the proper dimensions, a t 30" * 0.1" C. Various pipets were used so that in no case was the time of flow less
1.2
.8
C FIGURE 1
dilution and is equal to the previously defined "limiting specific viscosity" [VI.
Sample No. 21 12 50 101 102 107 108 15
215
than 100 seconds. The volume of flow varied from approximately 4 t o 8 cc., depending on the pipet used. I n any one case check runs were made with different pipets. The concentration was varied from 1.6 down t o 0.02 gram per 100 cc. The resulting viscosity-concentration data were first plotted on large graph paper so that curves for vr against c were obtained; 25 to 50 points were taken for each type of acetate, and the best curve was drawn through them. The values of vr and c in Figure 1 were obtained by reading from this curve. This method tended t o smooth out slight inaccuracies in the viscosity determinations and gave good average values for the viscosity a t any one concentration. Figure 1 shows typical curves obtained by plotting c us. (v? - l)/c for dispersions of various types of cellulose acetate in acetone. I n all cases a straight-line relation is obtained up to a concentration of approximately 0.5 gram. At this point the higher viscosity cellulose acetates give a curve which begins to deviate from a straight line. Table I gives the values for the intercept, k , and the slope, kl,for dispersions of various types of cellulose acetate in acetone. The duplicate values are the results of check runs.
Discussion of Results Although this method of presenting viscosity-concentration relations is admittedly approximate and applies only to very dilute solutions, it does illustrate the fact that the theoretical equations developed can be correlated with experimental data, provided the fundamental assumptions are modified to apply to the particular system under consideration. Table I presents the values of the coefficients a and b in the equation: llT=
1
+ a6 + b@
(6)
These values were obtained, using a partial specific volume of 0.66 for cellulose acetate. Since 4 = cv/lOO, a = - - - - - - looand b
k' X 10,000 V2
At first glance these values appear to be surprisingly large, but if a shape factor of 100 were substituted in place of unity in the original equations, a would be 250 in Equation 1 or 450 in Equation 2. Corresponding values of b would be 30.000
INDUSTRIAL AND ENGINEERING CHEMISTRY
216
OF EQUATIONS 4 AND 6 TABLE I. COEFFICIENTS TYPES OF CELLULOSE ACETATE
Sample No. 5 10 12 15 21 50 101 102 107 108
Viscosity Type
Low
Medium Medium Medium High Low High Medium Medium Low
-Equation
IC
0.86-0.90 1.10-1.16 1.10-1.12 1.19-1.20 1.66 0.76-0.77 1.30 0.96-1.06 1.16-1.23 0.57-0.62
4-
kl
FOR
.--Equation a
0.64-0.50 0.99-0.98 1.04-1.02 1.18-1.06 1.25 0.46-0.31 1.08 0.94-0.80
1.24-1.13 0.36-0.34
136 171 168 182
252
115
197 151 182 91
VARIOUS 6--b 13,100 21,500 23,700 25,300 28,700 9,000 24,800 20,000 27,200 6,300
and 100,000. According to Onsager (8) a factor of this magnitude would be necessary if the ratio of major to minor axes was 10. Even with micellar structures, a ratio of this magnitude would be expected, while long, single-chain macromolecules of the Staudinger type might have ratios varying from 10 to over 1000. These theoretical speculations are interesting and indicate that the effect of shape of particles must be considered, but the most important discovery of this work is the ease with which the “limiting specific viscosity” [the value of (7. - l ) / c a t infinite dilution] can be obtained. By this method it is necessary only t o make two viscosity determinations at two different concentrations below 0.5 gram per 100 cc., and [77] can be obtained assuming only the validity of the linear relation between (7. - l)/c and c in this concentration range. S o available experimental data invalidate
Vol. 35, No. 2
this assumption. This value is slowly coming into general use as a means of characterizing the properties of this type of colloidal solution. Staudinger and Kraemer have both correlated [ ~ 7 ] with molecular weight determinations, and unpublished work in this laboratory has indicated that i t is the best means of following the degradation of cellulose derivatives, I t s chief advantage is the fact that thixotropic effects seem to be eliminated as infinite dilution is approached. The very satisfactory check runs in different pipets are an indication of this fact. The constancy of this value, coupled with its ease of determination, should ultimately lead to its use t o designate viscosity types of cellulose acetate in place of the falling-ball viscometer.
Literature Cited (1) Dobry, J. chim. phys., 31, 568 (1934). ( 2 ) Einstein, Ann. Physik, 19, 289 (1906); Ann., 34, 591 (1911). (3) Eisenschitz, 2. physik. Chem., 158, 78 (1931); Kolloid-Z., 6 4 , 184 (1933). (4) Hatsohek, Kolloid-Z., 7, 301 (1910). (5) Kraemer and Lansing, J. Phys. Chem., 39, 153 (1935). (6) Kunitz, J . Gen. Physiol., 9, 715 (1926). (7) McBain and Scott, IND.ENO.C H E W , 28, 470 (1936). (8) Onsager, Phys. Rev., 40, 1028 (1932); see also, Jeffery, Proc. Roy. SOC.(London), A102, 161 (1922). (9) Sakurada, Kolloid-Z., 64, 195 (1933). (10) Smoluchowski, Ibid., 18, 191 (1916). (11) Staudinger, Trans. Faraday SOC.,29, 18 (1933). ABSTRACTED from a thesis submitted b y C. C . Winding to the faoulty of the Graduate School of the University of Minnesota, in partial fulfillment of the requirements for the degree of doctor of philosophy.
Properties of Rubber Solutions and Gels
MAURICE L. HUGGINS Kodak Research Laboratories, Rochester, N. Y.
The writer’s theory of the thermodynamic properties of solutions of longchain molecules is shown to be applicable to rubber solutions. Each rubbersolvent system is characterized by a constant which determines the dependence of the activity (and, therefore, of various properties derived from the activity) on concentration. The theoretical equations hold over the whole range of composition, for the rubber-benzene system at least. Theoretically sound equations for the determination of molecular weights from osniotic pressure and cryoscopic data are presented; the errors inherent in the use of other equations are pointed out.
R
UBBER solutions, like other solutions of long-chain molecules in small-molecule solvents, show large deviations from Raoult’s law even when the heat of mixing is small. As Meyer (17, 18) pointed out, this can be attributed to a large entropy-of-mixing effect, a result of a randomness of orientation of each segment of the solute molecule chain relative t o the adjacent segments. This conception has been put on a quantitative basis by the writer (9, 10, 11) and, independently, by Flory (3). Combining his theoretical equation for the entropy of mixing with an approximate expression, due to van Laar (15), Scatchard (23), and Hildebrand (8),for the heat of mixing, the writer deduced the following equation for the thermodynamic activity of the small-molecule component:
(1)
where
activity vl,v2 = thermodynamic volume fractions
v,, v2 = partial molal volumes of components (for present purpose assumed equal to actual molal volumes, ,u1 =
VI and Vs of pure components) a constant (approximately), characteristic of a
given solute-solvent system at a given temperature
The corresponding equation for In a2 is like Equation 1, except for the interchange of all subscripts. Such properties as vapor pressures, osmotic pressures, freezing-point depressions, and solubilities are related by
