PROPERTIES OF THE SYSTEM CELLULOSE TRINITRATE-ISOPHORONE
Mar., 1956
aqueous solution. Thus available thermodynamic datasJ' indicate that the following reactions (19) Hg++(aq) H) +H e 2H+(aq) and
+ Hgz++(aq) + H2
----f
+ 2HgO + 2H+(aq)
289
0
(20)
involving the formation of free Hg atoms, are exothermic by about 27 and 12 kcal./mole, respectively (neglecting solvation of the uncharged Hz molecules and Hg atoms). It thus appears possible that reactions (19) and (20) represent the ratedetermining processes in the present system and that the reducing intermediates which are formed (designated as X and Y in equations 6 and 7), are essentially free Hg atoms. Alternatively, it is possible that the electron-transfer process in the ratedetermining step is not complete and that hydrogen-carrying intermediates such as (Hg . . H2)++and (Hg, Hz)++are formed, which are stabilized by electron sharing and which react directly with Hg++, Hgz++ or with metallic Hg to form the observed reaction products. Provided that the secondary reactions are all fast, these various possibilities cannot be distinguished kinetically. It is of interest that the values of ICl reported here for perchlorate solutions are about ten times higher than those found earlier for the corresponding reaction of mercuric salts with HZin acetate solutions, where the mercuric ion is presumably present largely in the form of acetate complexes.lO On the other hand it has been shown2c,dthat addition of acetate increases the rate of reaction of Cu++ with HZ up to 120 times. The reason for the opposite
..
(9) G. Sohwarzenbach and G. Anderegg, Helu. Chim. Acta, S 1 , 1289 (1954);
(10) P. Mahapatra, 8. Aditya and B. Prasad, J . Ind. Chem. Soc., So, 509 (1963).
-0.5 4.
d
-P I
4
-
-1.0
E
-3
e-
- 1.5
-2.0 2.8 2.9 3.0 lOOO/T, OK. Fig. 3.-Arrhenius plots showing the temperature dependence of kl and k2. 2.6
2.7
influences of acetate in the two systems is not clear a t this point. Acknowledgment.-Support of this work through a grant from the National Research Council of Canada is gratefully acknowledged.
VISCOSITIES AND DYNAMIC MECHANICAL PROPERTIES OF THE SYSTEM CELLULOSE TRINTTRATE-ISOPHORONE' BY D. J. PLAZEK AND JOHND. FERRY Contribution from the Department of Chemistry, Uniuersity of Wisconsin, Madison, W i s . Received J u l y 96, 1066
Concentrated solutions of a cellulose trinitrate fraction ( M , = 145,000) in isophorone have been studied by the capillar and falling sphere methods to determine steady flow viscosities, and by the wave propagation and single transducer methodjls to determine dynamic rigidities and viscosities in thc audio frequency region. The ranges of concentIration and temperatl.re covered were 2.00 to 18.17% and 0 t o 60'. The dependence of viscosity on concentration was similar to that observed for vinyl polymers. The apparent activation energy for viscous flow increased linearly with concentration after a very rapid increase over that of the solvent at low concentrations. The dynamic data, when reduced to unit concentration and viscosity by the usual method of reduced variables, all superposed to give single composite curves of dynamic rigidity and viscosity aa functions of reduced frequency. From each of these curves, the distribution function of relaxation times was cal-. culated, the two sources giving results in good agreement. The terminal zone of the distribution is close to the location predicted by the Rouse theory. The plateau zone has a slope of -0.15 on a logarithmic plot, and is intermediate in character between those of cellulose tributyrate and of vinyl polymers of comparable molecular weight in concentrated solutions.
Introduction Recent measurements~ of the dynamic rigidity and viscosity of concentrated cellulose tributyrate (CTB) soJutiollshave showll that their dependence (1) Part XXI of a series on Mechanical Properties of Substances of High Molecular Weight. (2) R. F. Landel and J. D. Ferry, THISJOURNAL, sa, 658 (1955).
on temperature and concentration can be described over a corisiderable range by reduced variables, just in Of polymers* These measurements have provided relaxation distribution functions for three CTB fractions. The CTB distribution function exhibits a longer and flatter plateau than those Of Vinyl polymers O f comparable
D. J. PLAZEK AND JOHND. FERRY
290
Vol. 60
molecular weight,a indicating a stronger tendency the container was very slowly rotated between the poles of a large permanent magnet and warmed to about 45' by an to intermolecular coupling by entanglement. lamp. After measurements of viscosity and dyWe have now obtained similar data for another infrared namic mechanical properties a t various temperatures, adcellulose derivative, the trinitrate (CTN). Meas- ditional solvent was added and the mixing process was reurements of steady flow viscosity, dynamic rigid- peated. This sequence was followed through nine successive dilutions. Care was taken to avoid contamination with ity and dynamic viscosity are reported here. metal ions, though in the course of mechanical measurements the solutions were a t times in contact with stainless steel or, Materials The CTN was specially prepared for this study at the Allegany Ballistics Laboratory by Drs. Seymour Newman and Paul Drechsel. Purified cottonseed hull shavings were nitrated with nitric acid and phosphorus pentoxide at 20°, washed, neutralized with sodium bicarbonate, and repeatedly washed with water followed by methanol. The nitrogen content was not determined but on the basis of similarly prepared materials was probably 13.8%. A rough fractionation was made on several successive batches by precipitation with n-heptane from a 1% solution in acetone. High and low molecular weight cuts of approximately 25% each were discarded; the central portions were combined for subsequent measurements. The resulting sample had an intrinsic viscosity in ethyl acetate a t 25" of 5.1 dl./g. From osmotic pressure measurements in ethyl acetate a t 25", its number-average molecular weight was calculated to be 145,000. The thermodynamic coefficient A2 was 1.2 X 10-8 cm.3 mole g.-2, in reasonable agreement with values of 0.9-1.0 X 10-3 found for similar cellulose nitrates by Newman.4 The weight-average molecular weight was estimated from light scattering6; the scattered intensity at 90" together with a measured 45/135 dissymmetry of 1.45 provided a value of 145,000 also. However, this figure is probably too low, in view of the expected polydispersity6J of a rough fraction prepared as this was. The solvent chosen for mechanical properties was isophorones (3,5,5-trimethyl-2-cyclohexen-l-one,GH,C( CH&-
_____ 1
CHtC(CH3): CHC: 0), in which fairly concentrated solutions can be prepared without gelation, and which is relatively high-boiling. It was redistilled at 5-10 mm. and 80". Before preparation of solutioons, the fractionated CTN The most concentrated was dried in vacuo 15 hr. a t 45 solution (18.2%) was mixed first. A Teflon-covered piece of magnetized iron was imbedded in the mixture, while
.
Fig. 1.-Photomicrograph between crossed Nicole of a sample of solution (wz = 0.1448) after melting at 60" and holding a t room temperature 2 days, showing spherulites; magnification X 168. (3) L. D . Grandine, Jr., and J. D. Ferry, J . A p p l . Phys., 24, 679 (1953). (4) S. Newman, L. Loeb and C. M. Conrad, J . Polymer Sci.. 10, 463 (1953). (5) We are niuch indebted to Dr. Sidney Katz for these measurements. (6) A. M. Holtzer, H. Benoit and P. Doty, THISJOURNAL. (1954).
58, 624
(7) 5. Newman, private communication. (8) We are indebted to Mr. A. K. Doolittle, Carbide and Carbon Chemicals Company, for advice on the properties of solvents, and for generously supplying the isophorone.
very briefly, nickel. Concentrations were determined in two ways: from the original weights of the components, and by gravimetric analysis, precipitating the CTN from a diluted aliquot with petroleum ether. Densities ( p ) of all solutions were measured, using in most cases a small cupshaped pycnometer with a flat ground glass cover. They followed the relation 1/p = 1.088 - 0.498 we,where w2 is weight fraction of polymer; this was used to check the concentrations of the more dilute solutions. At the end of the dilution sequence, which covered a period of 18 months, the intrinsic viscosity in isophorone was measured and compared with that of a portion ,Of the original 18.2% solution which had been stored a t -5 . The values were 3.76 and 4.27 dl./g., respectively, indicating that a small amount of degradation had occurred during the exposure of the Sam le, at various dilutions, to temperatures as high as 60". t h i s change throws some uncertainty on the concentration dependence of the steady flow viscosity, but none on the dynamic properties reduced to a standard reference state, as explained below. Even in as effective a solvent as isophorone, crystallization occurred at high concentrations or low temperatures. When a2 18.2% solution was stored at any temperature below 42 , transmitted light eventually revealed a rippled structure of discontinuities of the order of 1 mm. in size, recognizable between crossed polaroids as spherulites (e.g., Fig. 1). Measurements of wave propagation and viscosity could be made for a brief period below this temperature before the crystallization progressed appreciably; later, abnormally high viscosity values were obtained, and eventually the birefringence of the spherulites completely prevented measurements of wave propagation by the strain double refraction method. At lower concentrations, the measurements could be carried t o lower temperatures; below 9%. no crystallization occurred even at 0".
Methods Steady-flow viscosities were measured by the capillary and falling ball methods, as described in earlier p a p e r ~ . ~ J ~ Stainless steel balls were used. The container for falling ball measurements was sometimes the rectangular cell used in wave propagation measurements; in this case, the effective container radius used in the Faxen formula for viscosity was taken as the reciprocal mean of the reciprocal half-length and half-width of the cell. The single transducer method of Smith, Ferry and Schremp,ll in which the mechanical impedance of a needle vibrating along its axis in the solution is determined from measurements of the electrical impedance of the driving coil producing the motion, was used over the concentration range from 3.8 to 8.9% to determine the real part of the dynamic viscosity ( 7 ' ) . Measurements were made from 160 to 400 cycles/sec. at 20 and 35". The associated measurements of the dynamic rigidity ( G ' ) were unsatisfactory, probably because of their greater sensitivity to inertial effects and other errors. T h e wave propagation method1aJ3was used over the concentration range from 8.9 to 18.2%. Photoelastic measurements of wave length and damping of a transverse vibration set up in a rectangular cell were made between 250 and 3200 cgcles/sec. a t temperatures from 0 to 60". Values of G' and v' were calculated by equations previously given.12J3 (9) J. D. Ferry, E. L. Foster, G. V. Browning and W. M. Sawyer, J . Colloid Sci., 6, 377 (1951). (10) J. D. Ferry, L. D. Grandine, Jr., and D. C. Udy, ibid., 8 , 529 (1953). (11) T. L. Smith, J. D. Ferry and F. W. Schremp, J . A p p l . Phus., 2 0 , 144 (1949). (12) J. N. Ashworth and J. D. Ferry, J . Am. Chsm. Soc.. '71, 622 (1949). (13) F. T. Adler, W. M. Sawyer and J. D. Ferry, J. A p p l . Phys., 2 0 , 1036 (1949).
PI~OPEHTIES OF THE SYSTEM CELLULOSE TRINITRATE-ISOPHORONE 291
Mar., 1956
Results Viscosity.-The steady flow viscosity results are given in Table I and plotted logarithmically
not affect the temperature dependence, expressed logarithmically, a t any one concentration, but it will exaggerate the apparent concentration dependence. The relative viscosities interpolated at 35 " are TABLE I plotted against concentration (c, in g. polymer per STEADY FLOW VISCOSITIES cc. solution) in Fig. 3 both as measured and also Capillary method for wp = 0, 0.0200, 0.0232 and 0.0384; approximately corrected for the effect of degradafalling ball method for all others. tion. For the latter purposes, a logarithmic corTemp., T:mp.. log rection has been added, assuming that log g changed WZ OC. log 7 WI C. 0 25.0 -1.606 0.0887 0.0 3.075 due t o degradation by an equal amount with each 30.0 -1.654 20.1 2.543 successive dilution. Figure 3 also includes two 35.0 -1.702 40.2 2.107 points a t low concentrations (at 25") from intrinsic 0.0200 25.0 0.116 59.9 1.729 viscosity measurements. r)
0.0232
25.0 35.0
0.301 0.114
0.0384
15.0 20.0 25.0 30.0 35.0 5.0 20.0 35.0
1.145 1,053 0.952 0.854 0.761 1,778 1.441 1.137
5.0 20.0 35.0
2.392 2.031 1.717
22
against the reciprocal absolute temperature in Fig. 2. The plots deviate somewhat from linearity, as expected from results on other polymers.1°
I
0.0686
I
I
0.1448
0.1770
0.1817
I
19.5 39.3 59.7 9.5 19.5 39.3 59.7 29.5 39.2 49.7 59.7 40.8 48.8 58.1
6
3.246 2.783 2.382 4.187 3.854 3.340 '2.906 4.167 3.902 3.658 3.429 3.992 3.809 3.606
0.0471
0.1151
5
4 15 e
.
ln m
v)
Pn
c
Gi3
6
c'
F
10
u
0
5
I
0
0
0.05
0.10
0.15
0 0
c, q./cc. Fig. 3.-Logarithm of relative viscosity a t 35" (open circles) and apparent activation energy for flow a t 35' in kcal. (black circles) plotted against concentration (a. polymer per cc. solution). Horizontal bars denote viscosities before approximate correction for degradation. First two open circles are values a t 25".
The concentration dependence of the viscosity is very marked, as in all concentrated solutions of polymers; g is roughly proportional to c5, an empirical relation which has also been found for polyisobutylene. 14 The apparent activation energy for viscous flow, Q, ( = R d In T/d(l/T)), calculated from tangents to the curves of Fig. 2 drawn a t 35", is given in Table I1 and also plotted in Fig. 3 against volume 0.0232 concentration. It increases linearly with c, as I. ,H I I I previously found for other polymers; however, it is 3.0 3.2 3.4 3.6 notable that the linear plot extrapolates to an intercept of 7.1 kcal. a t c = 0, considerably higher I OOO/T than that of the solvent (4.0 kcal.). For the vinyl Fig. 2.-Logarithm of steady flow viscosity plotted against reciprocal absolute temperature for nine solutions. polymers which we have in several Figures denote weight fraction of polymer. different solvents, such plots extrapolate rather The degradation detected a t the close of the dilu- closely into the respective purc solverit values. tion sequence from intrinsic viscosity measurements The abnormally high intercept seen here has been was also apparent from a comparison of the vis- found alsoi5for solutions of cellulose tributyrate in cosity of the final 2.00% solution with that of a 1,2,3-trichloropropane, and may be characteristic similar solution freshly diluted from the 18.2% of cellulose derivatives. (14) M . F. Johnson, W. W. Evans, I. Jordan and J. D. Ferry, J . stock which had been stored a t -5". The former Scd.. 7 , 498 (1952). was lower by a factor of 0.49. The gradual change Colloid (15) R. F. Landel, J. W. Berge and J. D. Ferry, unpublished experiover the total elapsed time of the experimcllts would ments.
.
D. J. PLAZEK AND JOHND. FERRY
292
Vol. 60
TABLE I1 APPARENT ACTIVATION ENERQY FOR VISCOUSFLOWAT 35' (KcAL.) QS
Wf
0 0.0232 ,0384 .047 1 ,0686
4.03 7.85 7.91 8.33 8.60
w1
Q11
0.0887 .1151 .1448 .1770
9.20 9.75 10.30 11.21
I
z6.0 P
-
S
W &.5
-
0
Dynamic Properties.- Values of G' and q' are not reported directly,ls but have been reduced to standard reference states." Wave propagation values of G' a t different temperatures were reduced to 35" for each concentration by the formula G', = G'Toco/Tc and are plotted in Fig. 4 against the reduced frequency wqToco/qoTc. Here To = 308°K.; c, CO, q and qo are the concentrations (differing from each other due only t o thermal expansion) and the steady flow viscosities a t temperatures T and TO,respectively. All the values a t each concentration superpose within experimental error, showing that all the viscoelastic mechanisms concerned have the same temperature dependence.
I
"E
I
I
I
5.0 .
5
I
I
I
I
1
6
7
8
9
IO
Log w,.
Fig. 5.-Real part of dynamic rigidity, reduced to unit viecosity and concentration at 35", plotted logarithmically against reduced frequency: pip left, weight fraction of polymer 0.0887; successive 90" rotations counterclockwise, 0.1151, 0.1448 and 0.1817.
reduced t o unit viscosity and concentration, depend on molecular weight only to a very minor degree in the range of time scale covered here.2si8 C
I
I
. L
c w.i
J 0
4.0 2.5
I
3.0
I I I 3.5 4.0 4.5 W reduced t o 3 5 '
I
5.0
Loq Fig. 4.-Real part of dynamic rigidity reduced to 35" and plotted loyarithinically against reduced frequency for solutions with the following weight fractions of polymer: 1, 0.0887; 2, 0.1151; 3, 0.1448; 4, 0.1817.. Key to temperatures: pip right, 0"; successive rotations clockwse, 20, 35, 40, 50 and 60".
The same data further reduced to a reference state of unit viscosity and concentration are plotted in Fig. 5, where G', = G'To/Tc and Wr = w ~ T ~ / T The c . points fall fairly well on a single curve, showing that all the mechanisms have the same concentration dependence. This is further demonstrated by the plot of reduced dynamic viscosity, q'/g, in Fig. 6. Here both wave propagation and transducer data are included; all the points fall quite satisfactorily along a single composite curve. The data reduced in this way should not be perceptibly affected by the slight degradation apparent from the comparison of intrinsic and steady flow viscosities at the end of the dilution sequence. The actual measured viscosities were used in the reduction process; and dynamic properties, when (16) The original data will appear in the Ph.D. Thesis of D. JI Plarek. University of Wisconsin, 1956. (17) J. D. Ferry, J . Am. Chem. Soc., 79,3746 (1950).
Fig. 6.-Real part of dynamic viscosity, reduced to unit viscosity and concentration at 35", plotted logarithmically against reduced frequency: open circles, wave propagation data; black circles, single transducer data.
Relaxation Distribution Function.-The logarithmic distribution function of relaxation times, %,was calculated from the data of Figs. 5 and 6 by the usual second approximation formula^.'^ The results are plotted in Fig. 7. The agreement between values from G' and from q' is excellent. The theoretical distribution function calculated from the Rouse theory,20Bi8for calculation of which (when reduced t o the standard reference state) only the molecular weight is required, is also plotted in Fig. 7. The location of the terminal zone at the right appears t o be correctly predicted by the theory, as it is in cellulose tributyrate solutions.2 However, as usual in concentrated solutions, the remainder of the function within the time scale covered is a rather flat plateau instead of being proportional t o T - ' / - as provided by theory. (IS) J. D. Ferry, I. Jordan, W. W. Evans and M. F. Johnson. J . Polymer Sci., 14,261 (1954). (19) J. D. Ferry and M. L. Williams, J . Colloid Sci.. 'I, 347 (1952). (20) P. E. Rouse, Jr., J . Chsm. Phhys., 91, 1272 (1953).
.
PROPERTIES OF THE SYSTEM CELLULOSE TRINITRATE-ISOPHORONE 293
Mar., 1956
I
I
I
I
I
-10
-9
-8
-7
-6
-5
Lo9 7 In SPC. Fig. 7.-Relaxation distribution function reduced to unit viscosity and concentration at 35": cjrclee top black, calculated from 0';bottom black, from 7 . Dashed line is the prediction of the Rouse theory.
Gelation Phenomena.-Some of the above data were obtained below the gel points of the solutions, by taking measurements soon after attainment of thermal equilibrium, before the slow crystallization processes had progressed appreciably. In one experiment, however, a 14.5% solution was kept below its gel point for 24 hours and wave propagation measurements were made repeatedly after gelation. The solution was cooled from 60 t o Z O O , reaching thermal equilibrium within 0.5 hr. Wave propagation measurements over a frequency range from 300 to 2000 cycles/sec. at this point showed G' increasing with frequency from 1.5 to 1.8 X lo6 dyne/cm.2, in accordance with the dispersion shown in curve 3 of Fig. 4. At 4.5 hr. after changing the temperature! gelation had occurred; G' was now somewhat hgher-3.4 X 106 dyne/cm.2-and independent of frequency. With further storage at 20°, G' increased linearly with time t o 7.8 X lo6 dyne/cm.2 (Fig. 8), remaining independent of frequency. The transverse waves appeared to be damped in this gel to an extent (damping index12h/xOof the order of 1) incompatible with the absence of dispersion of G'. It is believed that the observed damping is spurious, due t o the effect of the walls of the container as expectedla when the inherent damping is small. The same effect has been observed in other gels.21.22 The absence of dispersion within experimental error means that 9 < lo4dyne/cm.2 over a range of (unreduced) time scale from 10-2.6 t o 10-a.3 see., in contrast to its value of 4 X lo4 in this solution before gelation. In this time range, which corresponds just t o the middle of the reduced curve i n Fig. 7, the elastic contributions are believed t o be due t o cooperative motions of groups of molecules coupled fairly tightly to each other by occasional entanglements. l8 Gelation evidently sharply depresses these contributions as neighboring molecules become still more tightly coupled by crystallite cross-links. The cooperative motions may be modified by the fact that the coupling is tighter or by a different spatial distribution of linkage points or both. After gelation, G' as measured is probably not much different from the equilibrium modulus representing the rubber-like elasticity of the crosslinked network. Its increase with time no doubt reflects the lateral growth of crystallites. A linear (21) J. D. Ferry and J. E. Eldridge. THISJOURNAL, I S , 184 (1949). (22) G. E. Heckler, Ph.D. Theaia, University of Wisconsin, 1952.
01
I
I
I
0
10 20 Time in hours at 20". Fig. €$.-Increase in real part of dynamic rigidit with time for 14.5% gel at 20". Vertical bar at left ¬es range of G' between 300 and 2000 cycles/sec. before gelation.
increase of modulus with time has also been observed by B i s s ~ h o p in s ~gels ~ of polyacrylonitrile. Discussion I n Fig. 9, the relaxation distribution function of cellulose trinitrate is compared with those of several other cellulose derivatives: three fractions of cellulose tributyrate dissolved in 1,2,3-trichloropropane2 and a cellulose acetate dissolved in dioxane (calculated bySmith2' from data of Philippoff 26). The other derivatives exhibit quite horizontal plateaus, while the plateau for cellulose trinitrate is inclined, with a slope of about -0.15. Vinyl polymers of comparable molecular weights3 exhibit slopes of about -0.3, all thus deviating from the prediction of the simple Rouse theory of -0.5. Such deviations from the Rouse slope are attributed t o entanglement coupling, and with respect to the latter cellulose trinitrate thus appears to be intermediate between cellulose tributyrate and vinyl polymers in character.2s Without a more pre(23) (24) (25) (26)
J. Biaschops, J . Polymer Sci., 12, 583 (1954); 17, 89 (1955). T. L. Smith, J . Polymer Sci., 14, 37 (1954). W. Philippoff, P h y d k . 2.. 86, 900 (1934).
Another phenomenon in concentrated solutions has been attributed to entanglementa by Hatfield and Rathmann" and by DeWitt,-namely. an exaggerated concentration dependence of the magnitude of contributions to the relaxation spectrum, which makes it necessary to replace c by C* in the usual definitions for reduced variablw-above a critical value of C. It should be emphasized that the Hatfield-DeWitt entanglements are not the same as the entanglements responsible for a plateau in the relaxation spectrum. In vinyl polymers:lla aa well 88 in cellulose derivatives,' plateaus appear in the spectra of moderately ooncentrated solutions where the usual definitions for reduced variablea give accurately superimposed composite curves. For example, the critical concentration for appearance of a plateau in solutions of polyisobutylene of molecular weight 1od is about 1%, as calculated from the average molecular weight between coupling entanglements in the undiluted polymerm and its anticipated inverse proportionality to concentration.a But the critical concentration for the onset of the e* concentration dependence observe by DeWitt is 8%. (27) M. R. Hatfield and G. B. Rathmann, J . A p p l . Phus., 26, 1082 (1954). (28) T. W. DeWitt, H. Markovits. F. J. Padden, Jr.. and L. J . Zapas. J . Colloid Sei.. 8. 174 (19551. (29) J. D. Ferry, R. F. Landel and M. L. Williams. J . A p p l . Phys., 46. 359 119551. (30) F. Bueche. ibid., 46, 738 (1955).
RORERT F. LANDEL .4~n JOHN D. FERRY
294
Vol. 60
viscosity parameter derived by KuhnS2 for the resistance of the chain itself t o deformation is much smaller for cellulose derivatives than for polystyreiie. The differences in monomer structure must be responsible not only for the characteristic plateau shapes in Fig. 9 but also for other contrasting mechanical properties, such as the activation ener"3& 4 01 gies for viscous flow (Fig. 5 ) and the shapes of re1 laxation spectra in the transition region between rubber-like arid glass-like consistency, which will I I I 1 be further discussed in later comrnuni~ations.~~,~3 -4 -9 -8 -7 -6 -5 Acknowledffment.-This work was part of a proLoq In 5 e c . Fig. 9.-Comparison of relaxation distribution functions gram of research on the physical structure and of cellulose derivatives: CTN, cellulose trinitrttte (Fig. 7 ) ; properties of cellulose derivatives and other polyCTB, cellulose tributyrate (reference 2), molecular weights of 55,000 (L), 152,000 (R2), and 300,000 (H); CA, cellulose mers supported by the Allegany Ballistics Laboratory, Cumberland, Maryland, an establishment acetate (references 23, 24). cise concept of the nature of the entanglement cou- owned by the United States Navy and operated by pling, however, it is difficult to interpret these dif- the Hercules Powder Company under Contract ferences. The CTB chain is certainly far more ex- NOrd 10431. I t was also supported in part by a tended than those of vinyl polymers,3l and the grant from Research Corporation and by the ReCTN chain appears to be even more SO.^ But search Committee of the Graduate School of the there is some evidence that the cellulose units are University of Wisconsin from funds supplied by the actually more mobile than those of vinyl polymers, Wisconsin Alumni Research Foundation. We are a feature perhaps associated with the free-draining indebted to Mrs. J. C. Alexander and Mrs. Garrett character of the cellulose hai in.^ Thus, the internal Droppers for assistance with calculations. (32) W. Kuhn and H. Kuhn, HeEu. chim. acto, !29, 609 (1946). (31) L. Mandelkern and P. J. Flory, J . Am. Chem. Soc., 7 4 , 2517 I
I
I
1
I
1
0
(1952).
(33) R. F. Landel and J . D. Ferry, T H I B JOURNAL, 60, 294 (1956).
DYNAMIC MECHANICAL PROPERTIES OF THE SYSTEM CELLULOSE TRIBUTYRATE-DIMETHYL PHTHALATE' BYROBERTF. LANDELAND JOHN D. FERRY Contribution from the Department of Chemistry, University of Wisconsin, Madison, Wis. Received August IO, 1966
The real and imaginary components of the complex compliance, J' and J", have been measured between 30 and 4500 cycles/sec. for three gelatinous compositions of cellulose tributyrate ( M n = 300,000) and dimethyl phthalate containing 20.4, 42.6 and 57.5% polymer. The temperature range was from 25 to -52". Data for the 20.4% gel were combined by the method of reduced variables to give composite curves of J' and J" reduced to a standard temperature. Data for the 42.6% gel were similarly combined above -25" and separately below -25'; near -25" there was a change in properties attributable to a structural modification, probably increased crystallinity. Data for the 57.5% gel could not be combined by reduced variables, since there were progressive changes with decreasing temperature, attributable also to increases in crystallinity. Where reduced variables were applicable, the temperature shift factors followed a recently proposed equation of Williams, Landel and Ferry. The equilibrium rigidity ap roached at low frequencies a t 25" was proportional to the 2.8 power of polymer concentration. The loss tangent passed tgrough a maximum with increasing frequency; with increasing concentration (at constant temperature) this maximum became lower and broader and shifted to lower frequencies. The retardation distribution functions exhibited maxima whose heights were directly proportional to the equilibrium compliances. Increased crystallinity evidently depresses the retardation distribution, especially at long times; depresses J"; and depresses J' somewhat less, at the same time flattening the slope of the latter. The relaxation distribution function of the 20.4% gel followed the slope rescribed by the Rouse theory remarkably well. The more concentrated gels showed somewhat flatter slopes in a region wEere vinyl polymer systems show steeper slopes than that predicted by the Rouse theory.
Introduction Recent studies of the dynamic rigidities and viscosities, at audiofrequencies, of concentrated solutions of cellulose tributyrate in trichloropropane2 and of cellulose trinitrate in isophorone3 have delineated the relaxation distribution functions of these systems in the plateau zone of soft viscoelastic consistency. These investigations provided no information, however, about the transition from soft t o (1) Part XXII of a series on Mechanical Properties of Substances of High Molecular Weight. (2) R . F. Landel and J. D. Ferry, THIS JOURNAL,19, 658 (1955). (3) D. J. Plazek and J. D. Ferry, ibzd., 19, 289 (1956).
glass-like consistency which appears in shorter regions of time scale. The transition zone can be made accessible to audiofrequency methods by increasing the solvent viscosity and lowering the temperature. Measurements of dynamic mechanical properties in the transition zone are now reported for solutions of cellulose tributyrate in dimethyl phthalate. Such sohtions are partly crystalline, and hence crosslinked (Le., gelatinous), at the temperatures of measurement. When the concentration of polymer is not too high (e.g., 20%), the crystallinity does not interfere with interpretation of the results, but a t
