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
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
a
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 Staudinger and Kraemer have both correlated [ ~ 7 ] with molecular weight determinations, and unpublished work in this laboratory has indicated that i t is the best means of following the degradation of cellulose derivatives, I t s chief advantage is the fact that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 t h e faoulty of t h e 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
INDUSTRIAL AND ENGINEERING CHEMISTRY
February, 1943
I
0.2;
I
I
0.002
I
I
0.0 0 4
1
I
0.006
211
I
0.008
Ca, +c.
FIGURE1. DEPENDENCE OF OSMOTIC PRESSURE ON CONCENTRATION, FOR GUTTA-PERCHA SOLUTIONS IN TOLUENE (BLACKCIRCLES)AND IN CARBONTETRACHLORIDE (OPENCIRCLES) Data from Staudinger and Fisoher (66). The inclusion of B term (-RTCa/3Vidg) would lower the two right-hand points (at Cn = 0.008) about 0.005.
-
0.01
0.03
0.02
0.05
0.04
0.06
0.07
3. EFFECT OF THE TERM-RT,,:CiI3dS,AHj,1 EXTRAPOLATION OF CRYOSCOPIC DATATO INFINITE DILUTION, TO OBTAINMOLECULAR WEIGHTS
FIQURE ON
-
The interoepts give Mi 27,000 with this term and “ M P = 23,000 without it. Data of Kemp and Peters (12) on solutions of rubber (preparation 2, fraction 2 ) in oyolohexane. (They give “oryoacopio moleoular weights”, obtained without extrapolation, ranging from 6050 to 30,870 for this material.)
0.2 0
-*-
0
0.02
0.01
0.04
0.0 3
FIGURE 2. EFFECT OF THE TERM-RTCi/3Vld; ON EXTRAPOLATION OF OSMOTICPRESSURE DATATO INFINITE DILUTION, TO OBTAINMOLECULAR WEIGHTS
-
FIGURE 4. DETERMINATION OF pL1FROM SWELLING PRESSURE DATAOF POSNJAK (% ACCORDING I), TO EQUATION 2 0 Rubber-ether, pi
-
- -
0.55
0 Rubber-thiophene, f i i
The interoepts give MB 94,000 with this term and “ M P 102,000 without it. Data of Caspari (I) on solutiona of “fresh” rubber in light petroleum.
0.45
0 Rubber-oymeme, p i = 0.33
A plot of the left-hand member of this equation against simple thermodynamic equations to the activities of the solution components. There are thus ample data on a wide variety of systems, available for testing Equation 1. These tests have yielded such uniformly satisfactory results (9,21) that this equation must represent a close approximation to the truth. I n this paper Equation 1 will be applied to solutions of rubber.
The “Constant”
p1
The quantity pl depends in part on the heat of mixing and in part on the departure from perfect randomness of mixing of the molecules in the solution. Crudely speaking, it is a measure of the preference of each molecule (or submolecule) to have other like molecules (or submolecules) rather than units of the other kind, for immediate neighbors. Rearranging Equation 1,
V’2
should therefore give a straight line (if pl is constant) having a slope equal to pl and a n ktercept a t v2= 0 (i. e., a t infinite dilution) equal to - V1/V2 (hence, for a given solvent, inversely proportional to the molecular weight of the solute). Any accurate method for determining al as a function of concentration (bi) will thus serve to give the molecular volume (and so the molecular weight) of the solute particles and also the value of PI. If data are available on osmotic pressure (II), for example, substitution may be made into Equation 2 :
where R = molal gas law constant T absolutetempernturc i=
The value of R depends, of course, on the units in which II and VI are expressed. Also, In may be expanded:
218
INDUSTRIAL AND ENGINEERING CHEMISTRY
Vol. 35, No. 2
If the data a t hand are cryoscopic, the equations corresponding to 3,5,and 6 are
where T I , , = freezingpoint, K. A H,,, = molal heat of fusion of solvent O
FIGURE 5. DETERUISATIOS OF p i 0 Rubber-carbon disulfide,
p1 = 0.49; vapor pressure d a t a of Stamberger ( 2 4 ) A Rubber-ethylene chloride, p~ = 0 . 6 2 f 1 ) : sweiling pressure d a t a of Posnjak (90) 0 Rubber-chloroform, p l = 0.37; swelllng pressure d a t a of Posnjak (20) 0 Rubber-carbon tetrachloride, P I = 0.28; swelling pressure d a t a of Posnjak (20)
and if the solution is sufficiently dilute, all but the first two or three terms may be dropped. This leads t o the relation,
In agreement with Equation 6, graphs of Hjconcentration against concentration, for very dilute rubber solutions (as for solutions of other long-chain compounds, 9, 10, 11, 16) show a rectilinear relation (4,19). A typical example is shown in Figure 1. I n this case, the omission of the second term on the lefthand side of Equation 6 makes little difference. This is not true, however, if the data are for somewhat higher concentrations, as illustrated by Figure 2. Over the concentration range shoa.n, the agreement with a straight-line relation is not much altered. (In this case the inclusion of the second term actually results in slightly poorer agreement; more often the agreement is bettered.) There is a significant difference, IioLyever, between the intercepts (at C2 = 0) and hence between the molecular weights calculated from them. Similar remarks apply to the use of cryoscopic data to obtain molecular weights. As Figure 3 shows, somewhat different molecular weights are deduced, depending on whetliei or not the second term of Equation 9 is included. It is obvious from these figures and from Equations 6 and 9 that ‘holecular weights” computed from the limiting equations,
the second term on the left-hand side usually being negligible. Similar equations involving concentrations in other units are readily deduced. If the concentrations are in grams of solute per cc. of solution ( C 2 ) ,for example,
where dz = density of pure solute McIp = molecular weight of pure solute
v2
,
1
0
0.0 02
0.004
0.006
1
0.0 08
0.0 1 0
FIGURE 7. DETERMINATION OF A N D ; v l z FROM OSMOTIC PRESSURE DATABY STAUDINGER A N D FISCIJER (25) O N SOLUTIOSS IN TOLUENE A Rubber treated with AlzOo,
FIGURE6. DETERMINATION O F pi AND LIZ FROM OSMOTIC PRESSURE DATAOF STAUDINGER AND FISCHER (25) O N SOLUTIONS IN TOLUENE 0 Hydrorubber (less soluble fraction), PI
= 0.45, >I> = 90 000 0 Gutta-pereha (preparation II), pi = 0 36, 312 = 98 000 0 Balata (prepslation I), p , = 0.36, hI? = 84 000
*I = 0.44, Iv12 = 395,000 Masticated rubber (technical; less soluble f r a c t i o n ) , p1 = 0.46, hIz = 130,000 0 Crepe rubber I, oxidized with KMnOa, p1 = 0.43, MI = 102,000 0 Masticated rubber (technical: more soiuble fraction), p~ = 0.43, 112 = 88,000 0 Masticated rubber (more soluble fraotion), M I = 0.42, M z = 68,000 0 Cyclic rubber made with SnCla. PI = 0.46, nfz = 32,000
0
INDUSTRIAL AND ENGINEERING CHEMISTRY
February, 1943
219
V2
0 0
0.04
0.08
0.12
0.16
0.20
0.24
0.28
FIGURE 8. RUBBER-BENZENE SYSTEM 0 Osmotic pressure data (40° C.) of Kroepelin and Brumshagen (f4) Oamotic pressure data (25' C.)of Caspari ( 1 ) 0 Swelling pressure data (15-20' C.) of Posnjak (20)
or other equations equivalent to them, are true molecular weights only if the concentration is not significantly different from zero or if p1 for the particular combination of solvent and solute is close to Otherwise the so-called molecular weights are erroneous, and their use is likely to lead to false conclusions ( l a , IS,21,22),as pointed out by Gee (6). Values of the constants p1for different systems can be oomputed from the slopes of the straight lines obtained when the quantity ( II/CP) - (RTCi/3Vldi)is plotted against CPor from corresponding plots of cryoscopic data. If the data to be used are for more concentrated solutions, however-for example, Posnjak's data (20) on swelling pressures and Stamberger's (24) and Gee and Treloar's (7) on vapor pressureit is more convenient to compute In (al/vl) - 1 and plot VZ this against V2, as suggested by Equation 2; Figures 4 to 9 are examples. Table I lists values of pl,obtained from these and similar graphs, for various systems containing rubber, as well as for a few containing gutta-percha, hydrorubber, etc.
FIGURE 10. ACTIVITY AS A FUNCTION OF MOLE FRACTION FOR RUBBER-BENZENE SYSTEM (PI = 0.43) Heavy curve: molecular weight = 300,000 Light curve: molecular weight = 1,000
the chemical treatment undergone by the various samples studied. As Figure 9 shows, a constant value of p l , represented by the straight line, agrees with the experimental observations on the rubber-benzene system over the whole range of composition, within or nearly within the probable experimental error. (The scattering of the experimental points a t high values of is due partly to the impossibility of reading the coordinates of the points on the published graphs accurately; the numerical data were not published. One might expect slightly low values a t high rubber concentrations, however, as a result of failure t o obtain equilibrium.) The value of p1 would be expected to vary somewhat with the temperature. I n the case of the rubber-benzene system, this variation is very slight, as indicated by the fact that experimental results obtained at three different temperatures agree reasonably well with the same straight line (Figure 8). From Gee and Treloar's measurements of osmotic pressure a t 30.6' and at 8.8-9.95' C., one can compute an average
vz
TAHLE
I.
VALUES OF
System
FOR VARIOUS SY0TEMS PI
0.26
FIGURE 9. RUBBER-BENZENE SYSTEM(25" C.), GEE AND TRELOAR (7) 0 Osmotic pressure
FROM
DATA OF
A Equilibrium against triolein 0 Direct manometric method McLeod gage method
The value of p l is apparently independent of molecular weight, as it is for other high-polymer systems studied. The slight differences in slope shown in Figure 7 are probably due in part to experimental error; on the other hand, minor differences in the chemical nature of the molecules (and so in their attractions for one another and for the solvent, resulting in differences in pJ would be expected from the differences in
Light petroleum Acetylene dichloride Toluene Bennene Chlorobenzene Thiophene Carbon disulfide Amyl acetate Benzene 15% CHaOH Ether Ethylene chloride fhrtta-n nhara _r .-ICarbon tetrachloride Toluene Benzene Balata-toluene Hydrorubber-toluene
+
Tzmp., C. 25
0.28 0.29 0.33 0.33 0.36 0.37 0.38 0.43 0.43 0.43-0.44 0.43-0.44 0.44 0.45 0.49 0.49 0.50 0.55 0.621
15-20 180 15-20 6.5 15- 20 15-20 15-20
0.28
27 27 25 e7 27
0.36 0.52 0.36 0.45
Citation
~
25
15-20 27 7-40 7 15-20 25 25 25 15-20 15-20 (25) (25) (1) ($6) 06)
220
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
Vol. 35, No. 2
Activity Curves for Rubber-Benzene System
0.2
0
0.4
0.6
v2
0.8
Figure 10 shows, for the rubber-benzene system, the enormous departure of the activity-mole fraction curve from Raoult’s law. I n addition to the heavy curve, drawn for a (number-average) molecular weight of 300,000, corresponding approximately to ordinary unfractionated rubber solutions, a curve is shown for a fraction of very lorn molecular weight (1000). Figure 11 gives the corresponding curves for the activity as a function of volume fraction. Similar curves can be readily drawn for other molecular weights and for other systems, once ,u1 has been determined. Figure 12 shows the activity us. volume fraction curves for certain arbitrary values of p1, with the size of the “solute” molecules (component 2) assumed to be infinitely large relative t o the size of the solvent molecules. (This state of affairs may be assumed to exist in any gel.) As previously pointed out ( 3 , I O ) the curves corresponding to values of ,ul greater than 0.5 have a double inflection, indicating a separation of phases. Except when ,ul is very close t o the limiting value, one phase is practically pure solvent; the other consists of the high-molecular-weight component (rubber) containing an amount of the low-molecular component determined by the concentration a t which its activity equals unity.
10 .
FIGURE 11. ACTIVITYAS A FUNCTION OF VOLUME FRACTION FOR RUBBER-BENZENE SYSTEM (pi = 0.43) Heavy curve: moleoular weight = 300,000 Light curve: molecular weight = 1,000
Conclusion value of d,ul/dT of about -0.0002. The higher the temperature, the smaller the value of pl. Considerably larger values of the temperature coefficient would be expected for many other systems. The swelling pressure data on rubber gels containing ethylene chloride indicate an increasing value of p1 with increasing concentration (Figure 5 ) . This may perhaps be real; it seems more likely, however, that the experimental data are in error. The swelling pressure is over 5 atmospheres a t the highest concentration.
10 .
Aclmowledgment The writer takes pleasure in acknowledging the assistance of Dorothy Davis and Kuan Han Sun with the calculations involved in the preparation of this paper.
Literature Cited
bi 0.9
0.0
I
I
I
Although the data presented suffice t o show the general applicability of our theoretical equations to rubber systems, large gaps in our knowledge obviously remain. I n particular, it would be deEirable to have more data on systems having large pClvalues.
0.7 I
0.6 I
0.5 I
0.4 I
0.3
0.2
0.1
I
I
I
0
I
(1) Caspari, W. A., J . Chem. Soc., 105, 2139 (1914). (2) Fikentscher, H., see Meyer, K. H., and Mark, H., Ber., 61B, 1939 (1928). (3) Flory, P. J., J . Chem. Phys., 10, 51 (1942). (4) Gee, G., Trans. Faraday Soc., 36, 1162 (1940). ( 5 ) Ibid., 36,1171 (1940). Ibid., 38, 109 (1942). Gee, G., and Treloar, L. R. G., Ibid., 38, 147 (1942). Hildebrand, J. H., J . Am. Chem. Soc., 57, 868 (1938). Huggins, & L., I.Ann. N . Y . Acad. Sci., 41, 1 (1942). Huggins, M . L., J . Am. Chem. Soc., 64, 1712 (1942). Huggins, M. L., J . Phys. Chem., 46, 181 (1942). Kemp, A. R., and Peters, H., IND.ENG. CHEM.,33, 1283 (1941). Ibid., 34, 1097, 1192 (1942). Kroepelin, H., and Brumshagen, W., Ber., 61, 2441 (1928). Laar, J. 3 . van, 2. phgsik. Chem., A137, 421 (1928). Mark, H., “Physical Chemistry of High Polymeric Systems”, D. 241. New York. Interscience Publishers, 1940. (17) Meyer, K. H., Helv. Chim. Acta, 23, 1063 (1940). (18) Meyer, K. H., 2. physik. Chem., B44, 383 (1939). (191 Mever. K. H., Wolff, E., and Boiseonnas, C. G., H e h . C h i m Acta, 23,430 (1940). (20) Posnjak, E., Kolloidchern. Beihefte, 3,417 (1912). (21) Pummerer, R., Andriessen, A., and Giindel, W., Be?., 62, 2628 (1929). (22) Pummerer, R., Nielsen, H., and Giindel, W., Ibid., 60, 2167 (1927). (23) Scatchard, G., Chem. Rev., 8, 321 (1931). (24) Stamberger, P., J . Chem. SOC.,1929, 2318. (25) Staudinger, H., and Fischer, K., J . prakt. Chem., 157, 19 (1940). .
FIGURE 12. ACTIVITYAS A FUNCTION OF VOLUME FRACTION “SOLUTE”(E, G., RUBBER) OF INFINITE MOLECULAR WEIGHT(A GEL),FOR DIFFERENT VALUESOF PI
FOR A
I
PRESENTED before t h e Division of Rubber Chemistry at the 104th Meeting of t h e AMBRICAN CHEXICALSOCIETY,Buffalo, N. Y. Communication 881 from Kodak Researoh Laboratories.
