Nov., 1956
DYNAMIC MECHANICAL PROPERTIES OF AQUEOUS SODIUMDESOXYRIBONUCLEATE 1575
cathodic polarization or local activation, the higher oxide is necessarily reduced according to equation (e) and a thermodynamic calculation shows that the reaction “FeOi”
+ 2H+ + Fe++(aq) + HzO(1);
AF” = -3.4 kcal.
,
must proceed unless the ratio [Fe++]/ [H+I2exceeds 310. I n short, the inner oxide cannot exist alone in distinctly acidic solutions. Its existence necessarily depends upon maintenance of the higher oxide and the correspondingly high potential. T o summarize: the osmium and technetium experiments demonstrated that it is possible to block the metallic iron so effectively that its reaction does not disturb the oxidation-reduction system in the electrolyte. The film is sufficiently conductive for electrons, however, for the thermodynamic potential of the system to be indicated. These facts justify the conclusion that iron may be excluded as one of the reactants in the process by which the Flade potential, as an equilibrium value, is established. The present assumption of a n “abnormal” lower oxide may be compared thermodynamically with the earlier assumption of an unknown higher oxide by means of the following tabulation of the free-
energy values involved in the alternative interpretations Difference
AFO
(kcal.)
Fe, Ha, H + I/a “FeOa” ( HzO ( FeO ’/aFezOi “FeOi”
0 -30.0 -56.7 -58.4 -59.0 -73.6 -177.1 -203.8
+
I
+ Hz)/
Fez08 ( + Hz) H20 2“FeOi”
+
1
26.7
26.7
It may be pointed out that the rather large negative free-energy value of “Fe03” required to satisfy the Flade potential by a postulated reaction 6e“FeOa” 6H + e Fe 3Hz0 is irreconcilable with the powerful oxidizing power of the ferrate ion in acid solution. This is another argument against the assumption of its presence in the passive film,” since the energy of adsorption could hardly be sufficient to stabilize it to the requisite degree. This is not to say, however, that adsorption of ferrate ions may not provide the inhibition and oxidation required for the formation and stabilization of the passive film in alkaline solutions.
+
+
+
DYNAMIC MECHANICAL PROPERTIES OF CONCENTRATED SOLUTIONS OF SODIUM DESOXYRIBONUCLEATE1 BY FRANCES E. HELDERS,~ JOHND. FERRY, HERSHEL MARKOVITZ AND L. J. ZAPAS Contribution from the Department of Chemistry, University of Wisconsin, Madison, Wis., and the Melbn Institute of Industrial Research, Pittsburgh, Fa. Received Julr 16, 1966
Dynamic mechanical properties of salt-free aqueous solutions of sodium desoxyribonucleate have been studied in the concentration range from 0.38 to 18.3 X 10-8 g./ml., and a t temperatures from 5 to 35“, by the wave propagation and forced vibration torsion pendulum methods. The real parts of the dynamic rigidity and viscosity measured a t different temperatures superposed when reduced to 25’ at each concentration. The same quantities when reduced to unit concentration and g./ml. polymer) superposed except .viscosity (including some data in the presence of 0.2 M sodium chloride at 10 X for a region corresponding to the center of the plateau of the relaxation spectrum. Calculation of the spectrum from both rigidity and viscosity provided values in good agreement. The shape of the relaxation spectrum was similar to that of .a high molecular weight polyisobutylene or cellulose tributyrate in a higher concentration range, except that the plateau level was unusually low (order of 5 X los dyn/cm.*, reduced to unit concentration). The terminal zone of the spectrum was near the location predicted by the Rouse theory; the width of the plateau was 3.3 decades a t a concentration of 12 X g./ml. It is concluded that the viscoelastic properties are associated with intramolecular configuration changes just as in the case of the more familiar flexible polymers, and that such motions involve coupling with neighboring molecules, though of a somewhat different character from that observed in other polymers.
Introduction Earlier measurements of the viscoelastic properties of several vinyl polymers3-5 and cellulose derivative&’ have delineated the relaxation spectra of these systems in their plateau and terminal zones; their dependence on temperature and concentration has been described with reduced variables, and (1) Part XXIV of a series on Mechanical Properties of Substances of High Molecular Weight. (2) General Electric Company Fellow in Chemistry, 1955-1956. (3) J. D. Ferry, I. Jordan, W. W. Evans and M. F. Johnson, J . Polymer Sci., 14, 261 (1954). (4) J. D. Ferry, M. L. Williams and D . M. Stern, THISJOURNAL, 68, 987 (1954). (5) T. W. DeWitt, H. Markovitz, F. J. Padden, Jr.. and L. J. Zapas, J. Colloid Sei., 10, 174 (1955). (6) R. F. Landel and J. D. Ferry, THISJOURNAL. 69, 678 (1955). (7) D. J. Plasek and J. D. Ferry, ibid.. 60, 289 (195G).
deviations from the theoretical spectrum of Rouse8 have been discussed in terms of molecular entanglem e n t ~ .We ~ ~now ~ report similar information for a very different polymer-the sodium salt of desoxyribonucleic acid (SDNA)-which exhibifs marked viscoelastic effects a t quite low concentrations. Some earlier rigidity measurements on solutions of SDNA in 0.2 M sodium chloride in the conceng./ml. have been tration range from 5 to 20 X published,10 but it is now apparent“ that the material (sample I) had undergone some degradation. The present measurements, on a new preparation (sample II), cover a concentration range (8) P. E. Rouse, Jr., J . Chem. Phys., 21, 1272 (1953). (9) F. Bueche, J . AppEied Phys., 26, 738 (1955). (IO) S. Kate and J. D. Ferry, J . Am. Chsm. Soo., 76, 1589 (1953). ( 1 1 ) F. E. Helders and J. D. Ferry, THISJOURNAL, 60, 1536 (1956).
1576
FRANCES E. HELDERS, JOHN D. FERRY, H. MARICOVITZ AND L. J. ZAPAS
Vol. 60
water a t frequencies between 8 and 400 cycleslsec. and temperatures 5, 15, 25 and 35", by the method of transverse wave propagation.181~4 Some of the measurements were made with an improved apparatus constructed by Mr. D. J. Plazek. Data were also obtained in 0.2 64 sodium chloride at 10.0 X 10-8 g./ml., from 5 to 35'. At two SDNA concentrations in water, 3 and 12 X 10-8 g./ml., G' and 7' were measured at 5 and 25" over a wide range of low frequencies-from 6 X lo-' to 0.6 cycles/sec.-by the forced vibration torsion pendulum of Morrisson, Zapas and DeWitt.16
Results Values of G' from wave propagation measurements at different temperatures were reduced to 25' by the formula'6 G', = G'Tocc/ Tc and are plotted in Fig. 1 against the reduced frequency 01 I I I oyToc,,/qoTc. Here To= 298°K.; 2 3 4 c, co,q and qo are the concentrations (differing from each other due only Log w reduced to 25". Fig. 1.-Dynamic rigidity reduced to 25", plotted logarithmically against to thermal expansion) and the frequency (from wave propagation). Concentrations in ascending order steady flow viscosities at tempera0.38, 0.75, 1.5, 3.0, 5.9, 11.8 and 18.3 X 10+ g./ml. Pip right, measure- tures T and To,respectively. The ments at 5"; successive 90" rotations clockwise, 15, 25 and 35". ratio 8/90 was obtained from meas5.5 I ured values extrapolated to zero I I I I shear rate" or for the more dilute solutions calculated from interpolated values of the apparent acI 9 5 I tivation energy for viscous flow. (Fig. 2, ref, 11). At each concentration all the G', values superpose within experimental error, showing that all the viscoelastic mechanisms concerned have the same temperature dependence. Earlier data of 1Cat.P on sample I fall below the present data by an order of magnitude or more, supporting the conclusion1' that sample I was partially degraded when the mechanical moperties - 5 6 7 8 9 10 were measured. Log Or. The data of Fig. 1 after further reduction to a reference state of Fig. 2.-Dynamic rigidity from wave propagation reduced to reference state of unit concentration and viscosity. Pip right, 0.38 x 10-3 unit viscosity and concentration16 g./ml.; successive 90" rotations clockwise, increasing concentrations as are plotted in Fig. 2, where G', = listed under Fig. 1. Black circles, 10.0 X g./ml. in 0.2 M sodium G ! T ~ / and T ~ Or = w q ~ o / ~ cThe . chloride. points fall reasonably on a single from 0.38 to 18 X 10-3 g./ml. in salt-free solution, curve, indicating that in this range themechanisms g./ml. in 0.2 all have the same concentration dependence. A with additional data at 10 X similar plot for the reduced dynamic viscosity, q'r, M sodium chloride. was also somewhat scattered but could be repreMaterials and Methods sented within experimental error by qtr = 0.20 The preparation and characterization of the SDNA have correspondingto an approrcimately constant been described.11 Its molecular weight and radius of gyration were 5.8 X 106 and 2170 A., respectively, compar- damping index Over the whole range, x/zO = 0*63* Values of G' and q' from torsion pendulum ing well with current preparations in other laboratories.'* Solutions were prepared as described previously.11 Their measurements at 5" were reduced to 25" and cornpH was always between 6.45 and 7.0, usually near 6.75; at 250 as shown in Fig. 3. the mechanical properties are expected to be insensitive to bined with measurements
I
I
~
pH in this range. The dynamic rigidities, G', and dynamic viscosities, TI', were measured over the entire concentration range in (12)
M . E. Reichmann, 9. A. Rice, C. A. Thomas and P. Doty, J .
A m . Ch.em, Sop., 1 6 , 3634.7 ( 1 9 5 4 ) .
j
~
/
~
~
,
(13) J. N. Ashworth and J. D. Ferry, ibid., 71, 622 (1949). (14) F. T.Adler, W. M. Sawyer and J. D. Ferry, J . Applied Phys., 20, 1036 (1949). ( 1 5 ) T. E. Morrisson, L. J. Zapas and T. W. DeWitt, Rm. Sci. Instruments, 26, 357 (1956). ( 1 6 ) J. D. Ferry, J. A m . Cliem. SOC., 72, 3746 (1850).
a
Nov., 1956
1577 DYNAMIC MECHANICAL PROPERTIES OB AQUEOUSSODIUMDESOXYRIBONUCLEATE
4 4 The coincidence of these more precise data shows clearly the identity of temperature dependence for mechanisms extending over a range 3 of time scale of three logarithmic decades. Although the two types of measurements do not overlap, 2 a reasonable interpolation provides 4 curves extending over six decades Ug e4 for these two SDNA concentra- 8 -Y tions. Their shapes are qualita- % 1 tively similar to those of cellulose .a 3 r ho derivatives6.' and polyi~obutylene~ 3 of high molecular weight in a con- 3 siderably higher concentration 2 0 g./ml. range of 50 to 250 X I n Fig. 3 are also shown plots of the non-Newtonian apparent 1 -1 viscosity in steady flow, qa, against rate of shear, from measurements a t the Mellon Institute quoted in a n earlier paper." These lie quite close to'the corresponding -2 -1 0 1 2 3 4 curves of q ' ( w ) , as would be ex-3 Log w reduced to 25". pected from the theory of DeWittl7- they are, however, some- Fig. 3.-D namic rigidity (1, 2) and viscosity (3, 4) reduced to 25", plotted what io the right of the corre- ogarithmica& against circular frequency. Circles from torsion pendulum, open a t 25", black at 5"; solid curves a t right from wave propagation. Dashed .'pending dynamic viscosities, as curves (5, 6) denote apparent viscosity ax a function of rate of shear (reference found also by DeWitt for P o b ~ o -11). Concentrations: 1, 3, 5 are 3.0 x 10-3 g./ml.; 2, 4, 6 are 12.0 x 10-8. butylene solutions.! Relaxation Distribution Functions.-The log- left end of the plateau, though they diverge in the arithmic relaxation spectrum, aP,was calculated center. This lack of superposition is not infrom the data of Fig. 3 by the usual second approxi- consistent with the successful superposition of G'r mation formulas18for both concentrations, and the shown in Fig. 2. Values of ar calculated from the results are plotted in Fig. 4. The agreement latter, as well as from the associated plot of B'r, between the calculations from G' and q' is excellent are also shown in Fig. 5 as vertical lines (the top except for the shortest time a t the higher concen- and bottom of each line representing the calculatration (wave propagation data) where the result tion from G' and q', respectively). At the right, from G' is probably more reliable. where GI, is obtained from wave data on dilute These spectra show the three zones characteristic solutions, derived therefrom agrees with curve 1, of linear polymers of high molecular weight in from torsion pendulum data on a dilute solution. concentrated solution-the beginning of a transi- Since there are no wave data on concentrated tion at the left, a broad plateau, and a terminal solutions in this region of reduced time scale, the region at the right. I n contrast t o a number of superposition failure is not apparent from the wave other polymers, however, the shapes are not quite data alone.21 the same a t different concentrations; at 3 X Discussion g./ml. the plateau is flat as observed especially Comparison with Rouse Theory.-According to there is in cellulose derivatives,E while a t 12 X a minimum and maximum as observed in undiluted the theory of Rouse,* the relaxation spectrum of a flexible linear polymer depends on cooperative polyi~obutylene~~ and polyvinyl acetate.20 For reduction to unit concentration and viscosity, modes of Brownian motion of the polymer chain the curves of Fig. 4 were shifted by plotting log and not on details of structure; if, in concentrated @r (i.e,, log @ / c ) against log T C / q . Here log q solutions, the interlacing with other molecules a t 25" was estimated by extrapolating q' to zero retards all such motions to the same extent13then frequency, giving 2.25 and 3.91, respectively, only the molecular weight is needed for an explicit though the former is somewhat higher than that calculation of the reduced spectrum ar. The reported previouslyll from direct measurement. function calculated in this manner23 is compared As seen in Fig. 5, the terminal zones now coincide (21) The divergence between the two curves at different concentraexactly, showing that the slowest relaxation tions cannot be removed by substituting e* for c in the reduced varimechanisms have the same concentration de- ables, as introduced by Hatfield22 and DeWitt6 for synthetic polymers pendence14 and the curves approach again at the at high concentrations. I n such a plot, the maximum divergence in
-
0
:.
"
(17) T. W.DeWitt, J. Applied Phye. 26, 889 (1955). (18) M. L. Williams and J. D. Ferry, J . Polymer Scsci., 11, 169 (1953). (19) R. S. Marvin, Proc. 2nd Intern. Congress Rheology, 1954, p. 156. (20) K. Ninomiya and H. Fujita, J . Colloid Sci., in press.
the center of the d o t is over-corrected. (22) M. R. Hatfield and G. B. Rathmann, J. Applied Phvs., 26,
1082 (1954). . . (23) The theory actually predicts a discrete terminal relaxation time, = BMM/a3RT. The tail of the spectrum shown a t the right is a fictitious continuous curve which would be calculated by our approxi-
mation methods18 from dynamic viscosity.
1578
FRANCIS E. HELDERS, JOHNTI. FERRY, H. MARKOVITZ AND L. J. ZAPAS
VOl. 60
there is evidence for such entanglements from several source^,^^^^^ their nature is only vaguely understood. It is remarkable that SDNA with its . 2 far greater extension and stiff structure, which rg could hardly be expected to kink by doubling back rn 0 on itself, for example, manifests much the same d 1 coupling behavior as the more flexible polymers. lfk" Of course, this appears a t much smaller concen3 trations than usual; a t 3 X g./ml., for exI4 0 ample, polystyrene of the same molecular weight shows no evidence of coupling a t all,27the entanglement probability corresponding to fewer than two -1 coupling points per molecule.9 Moreover, the -3 -2 -1 0 1 2 3 level of the plateau for SDNA is lower by an order Log 7 at 25". of magnitude than the usual range of 0.6 to 3.0 X Fig. 4.-Relaxation spectra a t 25" calculated from Fig. 3. lo5 dyn/cm.2 (reduced to unit concentration). Curve 1, 3.0 X 10-8 g./ml., 2, 12.0 X lob3. Circles top The level is not related directly t o the number of black calculated from G', bottom black from 7 ' . entanglements, but is believed to depend on their distribution and the nature of the coupling process. The width of the plateau is approximately related to the distance between entanglements by the formulaz4A = ( B - 1) log (M/2Me), where B is the exponent describing the dependence of viscosity on molecular weight, and Me the average molecular weight between entanglements. As measured from the theoretical Rouse line with a slope of -I/Z to the corresponding rise in the experimental curve for 12 X g./ml. with the same slope at the left, -10 -9 -8 -7 -6 -5 -4 -3 A = 3.3 decades. If B is 3.4, as it is for many Log r r . Fig. 5.-Relaxation spectra reduced to reference state synthetic polymers,28 M e = 1.2 X lo5 at this of unit concentration and viscosity. Curves 1 and 2 corconcentration. respond to those in Fig. 4. Vertical lines denote calcul% Terminal Zone of the Spectrum.-The tail of the tions from G', in Fig. 2 (top bar) and corresponding reduced spectrum a t the right drops much less steeply and dynamic viscosity data (bottom bar) from wave propagation measurements. ROUSE, Rouse theory for M = extends to longer times than it should for a linear polymer homogeneous with respect to molecular 5.8 x 106. weight. Similar behavior in other polymers3e6J with the experimental result in Fig. 5 . The has been attributed to molecular weight heterolocation of the terminal zone where drops steeply but this does not seem so likely in the case is predicted rather successfully, as it is for vinyl geneity, of SDNA. The relaxation mechanisms in this polymer^^.^ and cellulose derivative^.^.' The diver- region reflect cooperative motions of groups of gence a t shorter times is also seen in other polymers molecules coupled by entanglements. Even if the of high molecular weight, and its origin is dis- molecules are all of the same length, the gradual cussed below. The close similarity of SDNA to decrease in coupling through sequences of entangleother polymers in these respects is strong evidence m e n t ~should ~ ~ broaden the spectrum. Further that the viscoelastic properties, like the non- examination of the terminal zone may clarify the Newtonian flow,l' are governed in these concen- nature of the entanglement coupling. trated solutions by configurational rearrangements Acknowledgments.-The experiments a t Wisof the molecules. Even though in very dilute consin were supported in part by the Office of solution the SDNA molecule is rather stiff, it evidently possesses some flexibility; and when Naval Research, United States Navy, under interlaced with its neighbors the rate of its re- Contract N7onr-28509, and by the Research arrangements is determined primarily by the Committee of the Graduate School of the Univerresistance of its environment rather than its own sity of Wisconsin from funds supplied by the Wisconsin Alumni Research Foundation. Those at the internal stiff ness. Mellon Institute were supported by the Rubber Plateau of the Relaxation Spectrum.-The Research Group of the National Science Foundaexistence of a plateau, diverging from the linear portion of the theoretical spectrum with a slope of tion. The fellowship of the General Electric - '/z on a logarithmic plot, has been attributed in Company is also gratefully acknowledged. We other polymers to coupling of neighboring mole- are indebted to Dr. Sidney Kats for supervising cules by some sort of occasional entanglements preparation of the SDNA. which severely retard the slow relaxation mecha(25) A. V. Tobolsky and E. Catsiff, J . Polymer Sei., 19, 111 (1956). (26) F. Bueche, J . Chem. Phys., 20, 1959 (1952). nisms without affecting the rapid o n e ~ . ~ Though J~ (27) P. E. Rouse, Jr., and K. Sittel, J . A p p l i e d P h y s . , 24, 690
I '
I
I
I
I
e
+
(24) J. D. Ferry, R. F. Landel and M. L, Williama, J . Applied Phys., 26, 359 (1955).
(1953). (28) T. G. Fox and S. Loshaek. ibid., 26, 1080 (1955).
&
