58
W. J. BADGLEY AND H. MARK
VISCOSITY-MOLECULAR WEIGHT RELATIONSHIP FOR CELLULOSE ACETATE' W. J. BADGLEY
AND
H. MARK
Institute of Polymer Research, Polytechnic Institute of Brooklyn, Brooklyn, New York Received August 8 , 1946 INTRODUCTION
The problem of relating the molecular weight of a high polymer to the intrinsic viscosity of its solution has been the subject of many investigations. l'he early work of Staudinger (17) resulted in the empirical equation pap/c = KM
(1)
where K = a constant. I t must be kept in mind that this expression was obtained for polymers whose molecular weights were sufficiently low to allow for their measurement by cryoscopic experiments. The question arises as to the validity of the results obtained by the extrapolation of this equation to much higher molecular-weight ranges. During recent years, the publication of data for a rather wide variety of polymer-solvent systems (1, 4,6, 13) has indicated that a more general equation is needed. The equation suggested in 1938 (12)
[TI = KMO
'(2)
where
is found to be more applicable to describing the intrinsic viscosity-molecular weight relation for a wide variety of materials. The exponent a of equation 2 is a function of the geometry of the molecule in solution and has values between 0.5 and 2 for tightly curled and rigidly extended molecules, respectively (7). Table 1 lists values of a for various polymer-solvent systems. The wide variation in value from system to system in a molecular-weight range above about 50,000 indicates the necessity for the use of equation 2. The facts that for low-molecular-weightmaterials an a of unity is satisfactory and that for higher molecular-weight regions the a values are, for the most part, different from unity, would suggest that there may be a gradual change in the magnitude of a as one investigates the fractions of a polymer over a very wide range of molecular weight. Unfortunately there exists, at present, an insufficient amount of data t o test this possibility for the several polymers. However, it is the purpose of this paper to show, for a series of cellulose acetate fractions in acetone and in methyl cellosolve, that the linearity of the [q]-M plot and of the 1 Presented at the Twentieth Kational Colloid Symposium, which was held at Madison, Wisconsin, May 28-29, 1946.
VISCOSITY-MOLECULAR
59
WEIGHT RELATIONSHIP
log [v]-log M plot, as predicted by equations 1 and 2, does not exist except for relatively narrow ranges of molecular weight. EXPERIMENTAL
Material A sample of Waynesboro Acetate, with the following analysis Moiscure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Combined acetic acid., . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 per cent viscosity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ash. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3 . 5 per cent 54.50 per cent 360 0.03 per cent
was fractionated according to the procedure outlined by Sookne, Harris, Rutherford, and Mark (16). The first (or zero) fraction, containing a high percentage of insolubles, was discarded. In an attempt t o have each fraction as homogeneTABLE 1 a values for several systems SYSTEM
(1
Cellulose nitrateacetone . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Polyisobutylene-diisobutylene. . . . . . . . . . . . . . . . . . . . . . . . . . . . Polyvinyl acetate-acetone . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cellulose-cuprammonium oxide. . . . . . . . . . . . . . . . . . . . . . . . . . Polyvinyl chloride-cyclohexanone . . . . . . . . . . . . . . . . . . . . . . . . . .
1.00'
0.64t 0.67t 0.725 1.08
* H . Mosiman (Helv. Chim. Acta 26, 61 (1943)) and N . G r a l h (Inaugural Dissertation, Upsala, 1944) give values somewhat leas than 1.0. t P. J. Flory: J. Am. Chem. Sac. 66, 372 (1943). $ A. Matthes: J. prakt. Chem. 182, 245 (1943). # From data of GralBn: Inaugural Dissertation, Upsala, 1944. 7 D. J. Mead and R. Fuoss: J. Am. Chem. Sac. 64, 277 (1942). ous as possible, refractionation was made three times. Of the resulting thirty fractions, eight were so chosen as to represent the entire molecular-weight range. Each of the selected fractions was dissolved in acetone. The solutions were filtered through a sintered-glass filter plate and the acetate was reprecipitated with ethanol. The samples were dried in a vacuum at 55°C. for 24 hr. Solutions of 1 per cent were made up in acetone, and aliquot portions were diluted to obtain the desired concentrations. VISCOSITY
T'iscosity measurements were made in Ostwald viscosimeters at 26.5'C. =I= 0.05". The time of efflux for pure solvent at this temperature was about 80-90 sec. for all the viscosimeters. Values of [77] were obtained by plotting ~ J c versus c and extrapolating to c = 0. Data for the values of q a p for cellulose acetate in methyl cellosolve had been obtained previously at about 0.2 per cent concentration. One fraction was
60
W. J. BADGLEY AND H. bfARK
dissolved in methyl cellosolve and the k‘ for the system was determined. Assuming that the same k‘ held for all fractions, the values of [7]were calculated from the equation: = [71(1
+ k’%u)
(3) Osmotic-pressure measurements were made in a Fuoss-type osmometer a t room temperature-about 25°C. Ail measurements were made by the static method, using denitrated nitrocellulose membranes (5) These membranes were found to be satisfactory for molecular weights as low as 30,000, Le., no diffusion of solute was observed. As a check, several of the measurements were made again, using the dynamic technique (5). Agreement between the static and dynamic methods was excellent,-less than 0.02 cm. difference in all cases. Molecular weights were determined by graphical extrapolation of the ir/c-c plots to zero concentration. %P/C
I
RESULTS AND DISCUSSION
The viscosity data for the fractions are given graphically in figure 1, where hlu/c is plotted against c. Since it is to be expected (11) that divergence from linearity may result in the higher concentration ranges (particularly for the species of higher molecular weight), the measurements were made in as dilute a solution as would be favorable for reasonable precision. The linearity of the plot attests to the applicability of the Huggins equation over the concentration range investigated. Some indication of the similarity of hydrodynamic nature of the various fractions is given by the approximate constancy of k’ most of the range. The osmotic data are given in figure 2. According to the equation of Flory (3) and Huggins (9)
RT - RT 7 (0.5 - p ) ~ (5) c M Tdz it would be expected that for a series of fractions of the same thermodynamic behavior in a given solvent, the value of the slope and hence the p value should be constant. This is readily seen from the plots of figure 2. Values of p for the entire series, as calculated from the slope, are 0.42 f 0.007. Table 2 lists the value of the intercept of the n / e c plot as obtained from graphical extrapolation, together with the corresponding values for the number-average molecular weights of the fractions, M,. It must be mentioned that it is difficult to evaluate, precis&, the molecular weight of the highest fractions, since a small error in the measurement of the osmotic head constitutes a rather large percentage error in the value of r / c . This is particularly true in the regions of low concentration. ir
+
HOMOGENEITY OF FRACTIONS
Before relating the number-average molecular weight to that average obtained from viscosity measurements, it is necessary to consider the effect of hetero-
FIG.1. Viscosity data for cellulose acetate fractions in acetone a t 28.5"C. f 0.M" (according to Huggins' equation).
FIG.2. Osmotic-pressure data for cellulose acetate fractions in acetone a t room temperature (G 25'C.). 61
62
W. J. BADGLEY AND H. W R K
geneity of the samples. As has been pointed out by Kraemer (lo), the osmotic pressure gives a number average, while the viscosity measurement gives an average which is usually close to the weight average. Since the greatest contribution to the former average results from the presence of the smaller solute moleculeR while the larger molecules contribute to the latter, no satisfactory relationship may be established unless the measured samples are relatively uniform with respect to chain length. The closest approach to a sharp distribution of moleculbr weight is possible through several careful refractionations of the sample to be measured. Although it is not possible to obtain perfect homogeneity, some idea of the heterogeneity may be obtained througha comparison of the weight average as measured by light scattering or in the ultracentrifuge TABLE 2 Osmotic-pressure data for the cellulose acetate-acetone system PPACTION
la................................... lb. .................................. 2b. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4b. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14b. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23b. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31b. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40b . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
360,000 275,000 230,000 158,000 133,000 99,000 52,000 31,000
0.70 0.92 1.10 1.60 1.90 2.55 4.93 8.05
TABLE 3 Comparison of M , and M, values
8b. . . . . . . . . . . . . . . . . . . . . . . 14b. . . . . . . . . . . . . . . . . . . . . . . 18b. . . . . . . . . . . . . . . . . . . . . . .
173,000 135,000 77,000
(163,000)* 133,000 (75,000)
I
1.06 1.01 1.02
* Values in brackets were determined from viscosity measurements by the use of equation 6. and the number average as measured in the osmometer. For a uniform, homogeneous system, the ratio M,/M, will be unity. The more heterogeneous the system, the larger the value of the ratio. The results of some light-scattering experiments by Stein and Doty (18) on several of the fractions led to the values for the ratio given in table 3. VISCOSITY AND MOLECULAR WEIGHT
Figure 3 gives a plot of log [v] versus log M for both the cellulose acetate-acetone and cellulose acetate-methyl cellosolve systems. The straight line represents the Staudinger equation. The results in both cases indicate that the viscosity increment falls off with increasing molecular weight-the deviation
VISCOSITY-MOLECULAR
WEIGHT RELATIONSHIP
G3
occurring at a molecular weight of about 100,@00. Unfortunately, it is not possible to compare the curves for the two solvent systems, since the viscosity measurements in methyl cellosolve were made at a somewhat higher temperature. The important point is, howver, that both these curves indicate that the simple equations (1 and 2) cannot represent the [q]-M relationship over t,he entire range. Since, as has been mentioned before, there exists some doubt concerning the absolute value of the molecular weight of the highest fractions, the data in figure 3 have been plotted so that the shaded area represents the limit of error on the basis of the ability to evaluate the osmotic head to f 0.02 cm. It is seen that any values of molecular weight calculated from viscosity data by
FIG.3. Log [+log ,If plots for cellulose acetate in several solvents. Curve a , according to the Staudinger equation; curve b, experimental values for cellulose acetate in acetone; curve c, experimental values for cellulose acetate in methyl cellosolve.
means of the Staudinger equation would be much higher than observed values. It has been determined that the curve as drawn through the experimental points may be well represented by an equation of the form: [ q ] = K M a - K' M2a (6) While it is difficult to evaluate the constants precisely, owing to poor precision in the high-molecular-weight range, the following values are given tentatively: a = 1 K = 2.09 X lop6 K' = 0.315 X le1' In table 4 are listed the values of the molecular weights of the several samples, as Tvell as the observed intrinsic viscosities and those calculated from the
61
W. J . BADGLEY AND H. MARK
Staudinger equation and from equation 2, with a = 0.83 and K = 3.01 X 10-4. As would be expected, these two equations fit only certain regions of the [7]-M plot. About three or four different a and K values would be necessary to describe the entire molecular-weight range. This would adequately explain the apparent discrepancies in the a values thus' far encountered for the cellulose acetate-acetone system. From equation 7, however, it may be seen that in the range of low molecular weight the second term is relatively small and the equation reduces to that of Staudinger, which would be expected to hold, at least approximately, for the low-molecular-weight species. This is also in agreement with the recent investigations of Sookne and Harris (16), who report an a value of 1.0 for the cellulose acetate-acetone system for molecular weights up to about 130,000. With increasing molecular weight, the deviations from equation 1 become significant (compare [7]calculated from equations 1 and 2 with the observed value for molecular weight 360,000). From time to time there has been presented an TABLE 4 m d molecular-weight values for cellulose acetate In1
FRACTION
la.. . . . . . . . . . . . . . . . . . . . lb... . . . . . . . . . . . . . . . . . 2b..................... 4b..................... 14b..................... 23b..................... 31b.. . . . . . . . . . . . . . . . . . . 40b,. . . . . . . . . . . . . . . . . . . .
2ALCULATION
3.45 3.20 3.16 2.60 2.23 1.73 1.10 0.65
360,000 275,000 230,000 158,000 133,000 99,000 52,000 31,000
8.15 5.68 4.81 3.30 2.78 2.09 1.09 0.65
I
wuL%oN
5.71 4.31 3.76 2.72 2.42 1.88 1.10 0.95
11
I
C m U L A I o ~111
3.36 3.35 3.15 2.52 22.2 1.78 1.01 0.62
opportunity to check this equation against the molecular-weight value obtained from light-scattering experiments. The agreement in all cases has been very satisfactory. THE SHAPE FACTOR
Although no completely satisfactory theory has been developed t o account for the shape of long-chain molecules in solution, it is of interest to consider the results of the above experiments in terms of the shape of the solute molecules. By assuming that a molecule has a certain shape in solution, Huggins (8) has calculated the viscosity increment produced by a chain molecule made up of a certain number of hydrodynamic units. Under the conditions that the solute molecule be large, and that Brownian movement predominate markedly over the velocity gradient, he has deduced that the following relations hold: q.Jc
= kn2 for rigid rods
qr9/c = kn for random coils
(7)
(8)
VISCOSITY-MOLECULAR
65
WEIGHT RELATIONSHIP
(n = the number of hydrodynamic units per chain and hence is proportional to the molecular weight.) If it is considered that the cellulose acetate molecule is a relatively extended molecule, then from these expressions and our experiments, several conclusions may be drawn. ( I ) That the same elongated shape persists over the entire molecular-weight range. In this instance it is possible that at high values of the velocity gradient there would be an orientation of the molecule in the direction of flow, with a corresponding decrease in the value of the viscosity. This would result, on correction, in a raising of the q a p values for the low-molecular-weight species. However, since, as Lyons (11) has pointed out, the effect of velocity gradient becomes relatively negligible a t low concentrations, very dilute solutions have been used. Further, the measurements have been made in viscosimeters of small capillary diameter, so that the time of flow shall be long and hence B shall be small.* TABLE 5 Relative viscosities at several concentrations a8 a function of B w
B(sec.-l) PIACTION
II(a). . . , , . . . , . , . . . . . ,
23(c).
. .. , , . , . . . . . , . . .
1
900
CONCENTPATION
0.125 0.250 0.375 0.3 0.4 0.6
1
1500
1
1800
1
zlM)
RELATIVE VISCOSITIES
3.08
2.16 3.09
4.38
1.76 2.05 4.15
1.48 2.17 3.06
1.48 2.17 3.04
1.76 2.04
am
1.48 2.14 3.04 1.68
The dependence of relative viscosity on the mean velocity gradient has been determined for a low- and a high-molecular-weight fraction with values of 8 varying between 600 and 5800 set.-' These data are given in table 5. From the values of qrel for fraction II(a) it may be seen that the effect of the gradient up to 6 = 2100 is small and would have little effect on the value of the intrinsic viscosity as calculated from this data. The same may be said for the data for fraction 23(c) up to B = 1500 if the concentrations used are less than 0.6 g. per 100 cc. In any case, for the fractions of lower molecular weight the slope of the q a p / e c plot is sufficiently flat to allow for the extrapolation of valid [ q ] values, particularly if the q l p / c values at low concentrations (below 0.5 g. per 100 cc.) are given sufficient weight in the determination of the curve. (5') That as the molecule becomes increasingly larger, its general architecture changes, Le., branching occurs. This change in shape could adequately account for a gradual falling off of the viscosity increment provided the degree of brancha$=--
8V 3 r't
#
66
W. J. BADGLEY AiVD H. MARK
ing increased with molecular weight. It would be expected, however, that under such conditions there should also be a gradual change in the solubility characteristics of the solute as the molecular weight increased. In any case, there should be a rather marked difference in the solubility behavior of the low and high fractions. Such a difference should be reflected in the thermodynamic constant p,
P
P =
+4RT
(9)
where P = entropy contribution and (Y = heat contribution, since, while the second term in equation 9 should most probably remain constant, the entropy term, (3, would be different (2). It may be seen from a consideration of the osmotic-pressure data in figure 2 that the slo, s, and consequently the p values, are constant for all the fractions within experimentai error. (3) That as the molecule becomes larger, it becomes more and more curled up, eventually approaching a more or less spherical shape. This picture is consistent TABLE 6* Dimenszons of cellulose acetate molecules FRACTION
MOLECULAR nEIGHT
8b. . . . . . . . . . . . . . . . . . . . . 14b . . . . . . . . . . . . . . . . . . . . 1% . . . . . . . . . . . . . . . . . 32b. . . . . . . . . . . . . . . . . . . .
163,000 135,000 75,000 65,000
* R . Stein and P . Doty. J. Am. Chem.
,
ROOT-YEAN-SQUAPE DISIANCE BETWEEN ENDS
Arsummg rigid rod
1
Assuming random coil
1
1
Computed from molecular wewht
A.
A.
A.
1900 1900 1550 1550 1380
1340 1340 1120 11m 960
3100 2100 1440 1250 1000
Sac. 68, 159 (1916).
with the idea of a molecule with a relatively high rotational restriction between adjacent segments. This change in over-all shape from an elongated, quite rigid, rod-like particle to one which, at sufficiently high molecular weight, would be matted, would account for the falling off of the viscosity increment, since after a sufficiently matted particle had been formed, an increase of molecular weight would effect little change in the over-all shape and hence mould result in a variation of the value of the exponent in equation 2 toward zero. Some corroborating evidence for the change in shape as a function of molecular weight may be obtained from the experiments of Stein and Doty (18) on the angular dependence of light scattering. They have measured five of the above fractions over the molecular weight range 52,000 t o 163,000. From the ratio of the forward and backward angle scattering they have determined that a t about 80,000 molecular weight, the cellulose acetate molecules take on a less extended shape. The data are given in table 6. I t may be seen that values for the three low-molecular-weight fractions correspond within experimental error to the calculated values, while values for
VISCOSITY-MOLECCIR
G7
WEIGHT REL.iT IOSSHIP
samples 8b and 14b are considerably less than that for the completely stretchedout molecule. This change a t about 80,000 corresponds remarkably well to the point a t which deviation from the Staudinger equation begins (see figure 3). In an attempt to place the evaluation of the shape factor on a somewhat more quantitative basis, Simha (14) and Kraemer (10) have developed equations of a semiempirical nature, relating the intrinsic viscosity to the axial ratio (length/diameter) of the molecule. Although the basic assumption (Le., that the molecules, in solution, may be considered comparable to an ellipsoid of revolution which, hydrodynamically, produces the same effect as the molecule) is such as to disallom,a comparison of different solute species, it seems quite reasonable that this treatment may give some semiquantitative information concerning the relative shape of a series offractions of the same material. In the following treatment of the viscosity data we have used the curve of Simha relating axial ratios to intrinsic viscosity under the condition that there existed complete Brownian movement. It should be stated that over the range of TABLE 7 Dimensions of cellulose acetate molecules in acetone, f r o m viscosity measurements FILACTIOR
i I
40b. . . . . . . . . . . . . . . . . . . . . 31b.. .................... a b . .. . . . . . . . . . . . . . . . . . . . 14b.. ..................... 4b. . . . . . . . . . . . . . . . . . . . . ..I 2b. ..................... lb. .................... l a . .....................
1
1~1.
0.97 1.58 2.53 3.28 3.86 4.60 4.83 5.00
LENGTE (X-RAY)
595 loo0 1910 2560 3040 4430 6920
LENGTS
’
DIAKETER
A.
A.
434 628 938 1130 1285 1556 1676 1861
12.4 13.4 15.1 15.7 16.3 17.9 18.8 20.4
observed intrinsic viscosities, the value of the axial ratio, f , mould be somewhat larger if Brownian movement were not complete. In the calculation of the viscosity in terms of volume concentration of solute, Kraemer’s (10) value of 0.68 for the partial specific volume of cellulose acetate in acetone was used. From, the equation it may be deduced that the length, I , of a molecule with an axial ratio f = l / d may be expressed as
where 11.1 = molecular weight, N , = Avogadro’s number, and p = density. Table 7 lists the various observed and calculated values for the series of fractions in acetone. Similar values are given in table 8 for the cellulose acetatemethyl cellosolve system.
68
W. J. BADGLEY AND E. MARK
?PACTION
40b ...................... 31b...................... 23b...................... 14b...................... 4b. ..................... 2b......................
[nl.
0.88 1.38 2.28 2.46 2.58 3.06
LEHGTB (X-XAY)
LZNGTB
A.
A.
A.
595 loo0 1910 2560 3040 4430
415 582 890 1025 1090 1315
12.6 13.8 15.4 17.1 17.6 19.3
DfAKEtEP
FIG.4. Plot of the apparent diameter of the cellulose acetate molecule (calculated from viscosity values in acetone) as a function of the molecular weight. revolution the ratio of whose major and minor axes is about 0.14 that of the completely extended molecule, while for molecular weight 31,000 the ratio of curled to fully extended is greater than 0.5. Although, as has been mentioned before, the temperature at which the viscosity measurements were made on' the cellulose acetate-methyl cellosolve system was about 5°C. higher than that for the acetone system, a comparison of the values of 2 and d indicates that the shape of the solute molecule does not change mark: edly when one passes from a good solvent (p = 0.43 for acetone) to a poorer one
VISCOSITY-MOLECULAR
WEIQHT RELATIONSHIP
69
( p = 0.49 for methyl cellosolve),Le., for fraction 14b of molecular weight 133,000, 2 equals 1130 A. in acetone and 1025 A. in methyl cellosolve. This observation has been made by Doty (18) during an examination of the shape of the vinylite VYNW molecule in several solvents, as determined by light-scattering measurements. On this basis it would appear that the differences in viscosity are due to a marked degree to the extent of solvation or desolvation of the solute molecule. In figure 4 are plotted the values of the diameter of the cellulose acetate molecule, in terms of the hydrodynamically equivalent ellipsoid of revolution versua the number-average molecular weight. While it is realized that the Simha equation holds only for axial ratios above E 10, it is rather surprising to note that the curve may be extrapolated to zero molecular weight, yielding a value of d equal to about 11 A, which, according to the x-ray experiments, is a reasonable value for the diameter of the monomer unit.
SUMMARY
Experimental values for intrinsic viscosity and molecular weight for the cellulose acetate-acetone and the cellulose acetate-methyl cellosolve systems, over a wide molecular-weight range, show that the simple equations relating these two quantities are inadequate. An empirical equation is suggested, which represents the data with an average deviation of 3 per cent over the entire molecular-weight range. The constants K and K’ and the exponent a have tentatively been evaluated as 2.09 X lo+, 0.315 x and 1, respectively. An attempt has been made to relate these measurements with the work of Simha and Kraemer on the axial ratios of molecules. The results indicate that in the regions of lower molecular weight the molecule is rather rigidly extended, but that as the molecular weight increases the molecule takes on a more spherical shape. Calculation of the diameter of the hydrodynamically equivalent ellipsoid of revolution yields reasonable values. REFERENCES
(1) BARTOVICS, A., A N D MARK,H . : J. Am. Chem. SOC.66, 1901 (1943). (2) DOTY,P . M.:Private communication. (3) FLORY, P . J.: J . Chem. Phys. 9, 660 (1941);10,51 (1942). P.J.: J . Am. Chem. SOC.61, 372 (1943). (4) FLORY, (5) Fuoss, R . , AND MEAD,D . J.: J. Phys. Chem. 47, 59 (1943). (6) GRALBN,N.: Inaugural Dissertation, Upaals, 1944. (7) HUGGINS, M. L.: J. Phys Chem. 49, 911 (1938);4% 439 (1939). (8) HUGGINI,M. L.: In CeELuZose and Cellulose Derivatives, Emil Ott (Editor). Interscience Publishers, Inc., New York (1943). M.L.: J. Phys. Chem. 46, 151 (1942). (9) HUGGINS, (10) KRAEYER, 0.: J. Franklin Inst. 181, 1 (1941). (11) LYONS,W.:J. Phys. Chem. 13, 43 (1945). (12) MARK,H . : Diefeste Kbrper, page 103. S. Hirsel, Leipsig (1938). (13) &YER, K.:Helv. Chim. Acta 99, 1063 (1940). (14) SIXHA,R.:J. Chem. Phys. 13, 188 (1945).
70
PER-OLOF KINELL
AND HARRIS,M.: Ind. Eng. Chem. 37, 475 (1945). (16) SOOKNE, A,, HARRIS, X, RUTHERFORD, H. A,, AND MARKH . : J. Research Natl. Bur. Standards 29, 123 (1942). (17) STAUDIKGER, H. : Die hochmolekularen organischen Verbindungen. J. Springer, Berlin (1932). (18) STEIK,R., A N D DOTY, P . : J. Am. Chem. SOC. 68, 159 (1916).
(15) SOOKNE, A,,
ELASTICITY MEASUREMENTS O S POLYCHLOROPRENES' PER-OLOF KINELL
Universzty of Upsala, Upsala, Sweden Received August 8 , 1946
During the last fifteen years great interest has been directed toward the physicochemical behavior of synthetic high-molecular compounds; this is perhaps especially true of rubber-like materials. The main problem here is to get a proper understanding of the factors which determine the specific property of high elasticity. Many investigations have appeared in this field, and a short review of the modern theories is given below. It seems, however, that comparatively little attention has been devoted to the influence of the different sizes of the macromolecules on the network structure in the polymer and to the extent to which the molecular weight determines the elastic properties. The purpose of this paper is to give a brief account of some preliminary attempts to study the building up of network structures by means of molecular-n eight determinations and especially to establish the relation between the size of the macromolecules in solution and the constants characterizing the netffork structure. The most fundamental difference betn-een the elastic properties of ordinary solid bodies such as metals and of rubber-like materials is that on isothermal stretching at constant volume in the case of solids the change in entropy is zero but for rubbers the change in internal energy is zero. This means that in solids the stress causes a deformation of the molecular structure in such a manner that the ordered state is not disturbed. In rubber-like materials there is no deformation of chemical bonds or valence angles but only a rearrangement of the segments in the molecular chains as a result of free rotation about single carboncarbon bonds. It must, however, be emphasized that these conditions, Le. (aAS/tJAl)
=
0 and
(aAE/aAl)
= 0
( S = entropy, E = internal energy, 1 = length of specimen, and T = absolute temperature) are valid only for ideal substances. In real matter the changes in free energy are due to changes both in entropy and in internal energy. It is a I\ ell-knonm fact that high-molecular compounds with thread-shaped 'Presented a t the Tn entieth National Colloid Symposium, which was held a t Madison, Wisconsin, Mag 2&29, 1946
