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beef tendon in water, and Kiintzel and Doehner8 found 1.18 kcal. mole-’ for hide powder in water. The tendons used by Wijhlisch and de Rochemont, and those used by Tobolsky and co-workers as well, were not cross linked, apart from cross linkages present in the native tendon or formed adventitiously in the course of the procedure. As noted above, they determined Ts rather than T,. For these reasons we consider their stress-temperature coefficients to be unsuitable for the application of the thermodynamic equation 1 and the low value of A S reported by Tobolsky and co-workers consequently to be in error. The entropies of fusion recorded in the last column of Table V compare favorably with those for other polymers. They are not abnormally low, as claimed by Tobolsky and coworkers.13 All of the results cited, in common with those of the present paper, represent enthalpy changes per mole of peptide units present in native collagen rather than per mole of those units which are crystalline. To the extent that the native collagen may contain non-crystalline regions, correction is required to obtain the heat of fusion per mole of units which undergo melting. The percentage of crystallinity in collagen is unknown. The physical properties (e.g., elastic modulus) of the native fiber suggest that native collagen is predominantly crystalline, and hence that the mentioned correction is small, if not negligible. The diluent melting method applied by Garrett5 to the ethylene glycol-collagen system gives directly the heat of fusion per mole of crystalline polymer. Unfortunately, application of this method to the collagen-water system is fraught with difficulties posed by extensive solvolysis during the long periods of time during which the sample must be subjected to elevated temperatures. 30 For collagen-ethylene
[CONTRIBUTION FROM
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glycol, Garrett obtained A H u = 2.25 kcal. mole-’. The smaller value for A H u found by us could conceivably be due to the presence of an appreciable proportion of amorphous material in native collagen. We are inclined to reject this explanation in consideration of the evident high degree of crystallinity of native collagen. We suggest instead that the smaller value of A H u for collagen in water is attributable to an intrinsic difference in solvating effects of the two solvents. The reduction in the enthalpy of fusion by KCNS is striking. Complexing of collagen with thiocyanate evidently reduces the enthalpy in the amorphous state considerably more than in the native (crystalline) state. This is not surprising in view of the greater accessibility of functional groups in the amorphous (dissolved) state. It will be observed that whereas 3 Jd KCNS reduces A H u by a factor of nearly three, it lowers T,’ only from 333 OK. (in water) to 287 OK. The entropy change AS, accompanying melting, given in the last column of Table V, is reduced proportionately almost as much as AH,. This result is consistent with formation of ionic complexes in the amorphous state, with resultant decrease in entropy. Finally, we note the somewhat surprising observation of a decrease in exothermicity of dilution with addition of KCNS to the medium (see values of K~ in Table 11). It is as if the protein complex with thiocyanate is less hydrophyllic than the hydrate formed with water alone. More effective saturation of polar functional groups by KCNS could conceivably account for this observation. (30) L. P. Witnauer and J. G. Fee, J . Polyiiicr Sci., 26, 141 (1957), reported A H , , = 7 . 2 - 8.0 kcal./mole based on the dependence of TSi under zero stress on the concentration of water io cross-linked cowhide collageu. Again, the use of TBirather than T,’ casts doubt on t h e results.
RESEARCH A N D DEVELOPMEST DIVISION,AMERICANL’ISCOSE CORPORATION, MARCUS HOOK, PENNSYLVANIA]
Non-Newtonian Viscosity and Flow Birefringence of Rigid Particles : Tobacco Mosaic Virus BY JEN TSI YANG’ RECEIVED APRIL 18, 1960 The non-Newtonian viscosity and flow birefringence of tobacco mosaic virus (TMV) were measured over a three-decade range of shearing stress, T. The hydrodynamic lengths, L, as determined from the two methods were comparable a t high T (after due consideration of the different averages involved). A striking difference in L,however, was observed as T approached zero, where the viscosity curve went through a shallow maximum as contrasted with the sharp upward curvature for flow birefringence. The concept of equivalent ellipsoid was found applicable even for “fat” rods like TMV, although its equivalent length could differ by about 15% from the true molecular dimension.
Introduction The theories of non-Newtonian viscosities of rigid particles developed by Saito2r3and by Kirkwood and his co-workers4 afford a new method for the determination of the rotary diffusion coefficient, (1) Cardiovascular Research Institute, University of California hledical Center, San Francisco 22, California. (2) N. Saito. J . P k r s . Soc. Japaw, 6, 297 (1951). (3) H. A. Scheraga, J . Chem. Phys., B3, 1526 (1950). (4) J. G. Kirkwood, Rec. tvav. chim., 68, 649 (1949); J. G. Kirkwood and P. L. Auer, J . Chetn. P h y s . , 19, 281 (1951); J. G. Kirkwood a n d R . J. Plock, ibid.. 24, 005 (1S5G).
The validity of the theories were confirmed experimentally in previous publication^.^ These earlier studies, however, were designed to cover as wide a range of shearing stresses as possible (up to l o 5 dynes a t the expense of precision. For very elongated or flattened particles this is neither necessary nor practical, and it seems desirable, therefore, to further explore this subject by using
0.
( 5 ) J. T. Yang, J . A m . Chem. Soc., 80, 1783 (1958); ibid.. 81, 3902 (1939).
NON-NEWTONIAN VISCOSITY OF RIGIDTOBACCO MOSAIC VIRUS
March 20, 1961
Ubbelohde-type vis'cometers which adequately cover the shear range of interest. Until recently the flow birefringence technique was the only convenient method for determining the 6 of rigid particles. With the development of the viscosity method, it is now possible to study the molecular shapes of rigid particles with either technique. It seems also of interest to compare the effect of polydispersity on these hydrodynamic measurements. I n a recent paper6 i t has further been suggested that the intrinsic viscosity a t zero shear can be determined by a combination of the two methods without extrapolation of the viscosities to zero shear. Complications due to polydispersity that would be expected to arise have still not been investigated. It is now generally recognized that the mathematical models used in the hydrodynamic calculations do not necessarily resemble the actual molecules in size and/or shape. A further examination of the extent to which the interpretations of hydrodynamic properties in terms of these models can be trusted seems highly desirable. It is with these objectives in mind that we have made a more detailed study of the non-Newtonian viscosity and flow birefringence of tobacco mosaic virus. The actual characterization of this protein has already been excellently described by Boedtker and Simmons.'
Experimental A. Material.-The
tobacco mosaic virus (TMV) solution was obtained through the courtesy of Dr. N. S. Simmons of the Atomic Energy Project, University of California a t Los Angeles. All the chemicals were of reagent grade. The phosphate buffer was made up with 0.008 M NatPOd and 0.002 M NaHzPOr, containinrr M Versene (adjusted t o pH 7.4). . The finalpH was 7.2; B. Viscosity Measurements. (a) Viscometers.-Three Ubbelohde-type viscometers were specially designed t o cover a wide range of shearing stresses, 7 . One was modified after Hermans and Hermans* with a precision-bore tubing attached t o the capillary, which constitutes a continuously varying pressure head when filled with the solution. Usually about thirty experimental points were taken for each solution. The other two were multi-gradient viscometers having four and five bulbs, respectively. In Table I are listed the relevant geometrical data of the three
TABLE I DIMENSIONS OF VISCOMETERS
Type Continuously varying pressure head 4-bulb
Capillary Radius, Length, R,cm. L , cm.
0.02651 ,02156
5-bulb
a
282.0 25.40
3.610
Volume of flow, V ,ml.
0.1242 per cm. (1) 1.000 (2) 1.495 (3) 2 . 0 1 ~ (4) 3 . 0 0 8 (1) 0 . 9 9 8 (2) 1.510 (3) 1.996 (4) 2.507 (5) 3 . 0 2 0
Range of shearing stress" r , dynes cm.-z
0.05-1.10 3.132
6.180 9.416 11.84
14.98 24.97 35.78 47.13 58.02
Based on water a t 25.0'.
(6) J. T. Yang, J. Phys. Chem., 63,894 (1958). (7) H. Boedtker and N. S. Simmons, J . A m . Chem. Soc., 80, 2550 (1958). (8) J. Hermans, Jr., and J. J . Hermans, Proc. Koniitkl. N e d . A k o d . Wetenschap., B61, 324 (1958).
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instruments which were calibrated with mercury. For the 5-bulb viscometer, where kinetic energy and end effects were no longer negligible, the viscosities were calculated from the equation q = at - p / t = Here a and p are two constants characteristic of the gcometrical dimensions of the viscometer and also of the solution used. In all cases the constants, as determined with water a t two temperatures, were found in excellent agreement with those calculated from the capillary dimensions. (b) Calculations.-Details of the calculations of the maximum shearing stresses a t the capillary wall and the nominal rates of shear for the multi-gradient viscometers have already been described elsewhere.6 With the concentrations used in this paper corrections t o the rates of shear due to inhomogeneous flow were found to be negligible in all cases. All the intrinsic viscosities a t constant shearing stress6 were calculated according t o the Huggins' equation. No corrections due t o the density difference between solution and solventg were applied, since they wcre quite insignificant in this case. The viscosities as measured under a continuously varying pressure head were treated according to Hermans aiirl Hermans' equation* 1 d In Ah d* In Ah [4 ( 7 + (d*h)(1?)1 ) -7 -4$ : ( 21 7 = viscosity of the solution or solvent Ah = ht - h m = distance between the meniscus and the equilibrium position t = flowtime R and L = radius and length of the capillary, respectively S = cross-section area of the wide precision-bore tubing containing the solution or solvent d = density of the solution or solvent g = acceleration of gravity In most cases, in particular with very dilute solutioas, tlit last term in equation 2 may be omitted without introduci ig significant errors. Thus we have n (solution) - (d In Ah/dt)eoi,.enJ ( 3) c (solvent) (d In Ah/dt)aolution at any choseri pressure head, Ah. The differentials in equation 3 can be determined from a In Ah versus t plot. Or better, the experimental data can be programmed into an equation which assumes the first three terms of a power series t = a0 a1 In Ah a2 (In Ah)2 (4 1 where ao, al and a2 are constants characteristic of the solution used. Thus the d l n Ah/dt at any chosen pressure head, Ah, can be computed with great ease. Needless to say, the last term in equation 4 drops out for the solvent viscosity. (Strictly speaking, the solution of equation 4 is by no means unique, but i t should be quite adequate for our purposes.) To use equation 4 one must first know precisely the h values, for example, with a high-precision cathetometer. For solvent alone the equilibrium position, h m , a t infinite time can be located automatically by the computer so as t o give a constant slope of dlnAh/dt throughout the entire range of Ah. I t turned, however, that the computed h m always differed slightly from the observed hm . In the present case hm (computed) - hm (obsd.) = 0.080 out of a total pressure head of about 24 cm., presumably due to the surface tension, drainage and other errors. This discrepancy cast some doubt on the calculated viscosities of the solutions, for which the hm could not be computed because of the presence of non-Newtonian viscosity and therefore the value for the solvent was employed for all the calculations. T o what extent hm for the solution was different from that for the solvent could not be determined. The error introduced should be negligible so long as Ah is very large, but it certainly can become very serious when Ah reduces to, say, below 5 cm. I t is noted that any small error in Ah and, in turn, the relative viscosity could be manifested several times in the final specific viscosities. C. Flow Birefringence Measurements.-Both the extinction angles and birefringences were measured in a Rao
+
+
(9) C . Tanford, J. Phys. Chem., 69, 798 (1955).
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I I
h
TSIYANG
I
x
Vol. 83
*ooop
1 FLOW
BIREFRINGENCE
'4
t :om
~
-
&
-
-
ZJ
-
Sb-IAHV
~
l
-
q SIEIVMG
+
A STRESS. T
-
l
Fig. 3.-Hydrodynamic 50
60
c i '
-
~
~
1 .
STFFSi
T
0""e'
1
43
~
50
1
60
rm e
lengths of tobacco mosaic virus
as calculated from non-Newtonian viscosity ( 0 ) and flow birefringence (0).
Fig. 1 . S h e a r dependence of the intrinsic viscosities of tobacco mosaic virus, including the calculated values of [ ~ ] + / F ( X ) ~See , ~text . for detail.
are summarized in Fig. 1. The marked drop in [q]+ with increasing shearing stress, 7 , was what would have been expected for rigid particles.6 I The intrinsic extinction angles, XO, as a function 45 of the r are shown in Fig. 2, where the smooth curve was made possible by the use of equation 5 which greatly minimized the scattering of the experimental points. Also included in Fig. 2 are the birefringence increments, An/C, at one concentration. The shape of the curve, which appeared to approach saturation at high shear, clearly indicated that TMV is comprised of rigid particles. B. The Mean Hydrodynamic Lengths.-From the results in Figs. 1 and 2 the CY values at various shears can be calculated by using the theoretical , tables~~6~12 and assuming an approximate axial 0 10 20 30 40 ratio (in this case, p = 25). Here CY is defined as Shearing stress, 7 ( = Dm dynes cm. -2) the ratio of the rate of shear, D ,to the rotary difFig. 2.-Intrinsic extinction angles and birefringence fusion coefficient, 8, from which the lengths, L (=2u), can be determined by means of equaincrements of tobacco mosaic virus as a function of shearing tion 6. In Fig. 3 are shown the results from both stress. the viscosity and the flow birefringence methods. Flow Birefringence Instrument, Model 4-B. The methods The viscosity-average length at zero shear was of operations have been described elsewhere.lO The intrinsic extinction angles, XO, were calculated from an em- estimated in the following way: By definition pirical equation10 the intrinsic Viscosity is cot 2x = cot 2x, KC (5) [ q ] = N V e v/100 M (74 where x is the extinction angle for concentration, C, a t or, for a prolate ellipsoid constant rate of shear, D,and K is a constant. For TMV (7b) [TIM = (4r N / 3 0 0 ) (4(vlp') solutions in the concentration range studied (
