KOTES
1598
Table I Solvent
Compound
DMTF DMTF DITF DITF
Pure
407, V in o-CaH4C1, Pure 407, V in o-CsH4C12
E , kcal./mole
27.9 36.2 31.8 24.2
f 1.1 i 1.7 i2 . 8 i5 . 6
is small; and thus, they partially overlap. Since only the cheiiiical shift is averaged by fast rotation and the J splitting remains uiiaff ected, the collapse occurs between neighboring pairs of lines. (3) I n DRlTF the two closely spaced doublets of the methyl resonances collapse a t high temperature to a single doublet. The rates of rotation were obtained by the approxiiiiate procedure used4 in the similar case of dimethylforniamide. A Loreiitzian “envelope” was drawn on each of the closely separated doublets and the resulting, slightly broadened “doublet” was treated in the usual I n pure DMTF, only “ratios” were used since the collapse temperature could not be attained, whereas in solution three nieasurements were obtained from the collapsed “doublet,” using the fast exchange approximation.1 The results are summarized in Table I. All errors are probable errors calculated by least-squares fits of the lines. The number of measurements and the teniperature ranges are also given. The results show that the activation energies to hindered rotation in thionamides are much higher than the corresponding values in amides. Whereas in D I T F sonle steric hindrance due t o the bulky isopropyl groups iiiight be effective. this can be ruled out for DMTF, the corresponding E value in S,S’-diThe contrimethylformainide being 10 k~al.,/niole.~ bution of the polar form -X-C=S+, where X is oxygen or sulfur, probably determines the ralue of E . It must thus be concluded that this contribution is higher in thioiianiides than in amides. This is so in spite of the higher electronegativity of oxygen relative to sulfur. The same conclusion was reached in other studies of the carbon-sulfur double bond by means of infrared, ultraviolet, and dipole moment measurement s. It should be noted that there is a marked solvent effect for E (‘Table I) and for the chemical shifts (Fig. 1). The solvent effect has opposite direction for DITF and DJITF. This suggests that the solvent molecules are strongly associated with the thionaniides and are also involved i n the traiisition state. Similar effects were noticed for E measurements in amides and for T h e Journal of Physical Chemistry
ka, a e c . 7
(4.4 0 . 5 ) x 1013 ( 1 . 2 f 0 . 3 ) x 10*9 (8.9 f 2 . 8 ) X lOI4 ( 5 . 8 i 4 . 2 ) X 10l2
Number of measurements Temp. range, “ C .
4 7 8 6
176-1 93 141-179 162- 186 147-175
ring The nature of the association seems to be different in the two thionamides studied and thus far is not understood. All measurements were performed on a Varian A-60 n.m.r. spectrometer equipped with a V-6040 variable temperature attachment. Compounds were prepared by a method given by Walter and ;14aerten.3 Acknowledgment. A. L. and P. R. wish to thank Varian AG Research Laboratory for the kind hospitality during their summer visit. (4) G . Fraenkel and C. Franconi, J . Am. Chem. Soc., 8 2 , 4478 (1960). (5) (a) L . J. Bellamy, “Organic Sulfur Compounds,” N . Kharasch, Ed., Pergamon Press, London, 1961, p. 52; (b) C. 31. Lee and W. D. Kumler, J . O r g . Chem., 27, 2082 (1962); (c) S. C. Abrahams, Quart. Res. (London), 10, 407 (1956); (d) M .J. Janssen, Rec. traz;. chim., 8 2 , 931 (1963).
Relation between Steady-Flow and Dynamic Viscosity for Polyethylene Melts’ by Shigeharu Onogi. Tsuguo Fujii, Hideo Kato, and Sadahide Ogihara Department of Polymer Chemistry, Kyoto L’nicersity, Kyoto, J a p a n (Received December $3, 1968)
The relation between steady-flow and dynamic viscosities is an important problem which has been studied theoretically and experimentally by many investigators cited below. Enfort unately, however, the conclusions of these investigations are diverse, and we cannot know the nature of. apparent viscosity at present. In the previous paper,2 rheological properties of polyethylene melts at various temperatures were nieas(1) Paper presented at the 12th Annual Symposium on Rheology, Tokyo. Japan, September, 1963. ( 2 ) M .Horio, T. Fujii. and S. Onogi, paper presented a t the 145th National Meeting of the American Chemical Society, Xew York, K . Y . , September, 1963 (to be published).
NOTES
1599
ured with a rotating cylinder type rheometer, and thle effects of temperature and blending were mainly studied. The rheometer used in this study enables us to measure not only the steady-flow viscosity in a wide range of rate of shear, but also the dynamic viscosity and rigidity in a wide range of frequency by a minor change in its driving s y s t e n ~ . ~Therefore, the steady-flow and dynamic properties measured with this instrument can be very favorably compared with each other in their rate of shear and frequency dependences, because they are not affected by any factor due to the difference in measuring methods. This note is concerned with the comparison of our experi-. mental results (of flow properties for polyethylene melts with the current theories and existing data on the relation between the steady-flow and dynamic viscosities.
Experimental The polyethylene samples used in this study are Dow polyethylene 544 (polymer A) and 91OhI (polymer B) and quite the same as those reported in the previous paper.2 The method of measurement is also the same as the previous one, and accurate flow curves were determined by the single-bob method proposed by Krieger and h1ar0n.~ The apparent viscosity, va, and the consistency, vo, or differential viscosity, q d , were evaluated, respectively, as S / D and dX/dD, where X and 13 represent the shearing stress and rate of shear or velocity gradient.
3 -3
-2
1
-1 . LOG D, SEC-’
1 0
I
Figure 1. Master curves of qa for polymers A (Dow polyethylene 544) and B (Dow polyethylene 910M). T h e reference temperature is 160”.
Results and Discussion
As mentioned in the previous paper,2 the rate of shear dependence curves of qa a t various temperatures can be superposed very well to give a master curve according to the usual method of t inie-temperature superposition without any correction for temperatures. Figure 1 gives master curves of va measured for polymers A and B at 140, 160, 180, and 200’. For the purpose of comparison, similar master curves of the dynamic viscosity, v’, and the dynamic rigidity, G’, for the same polymers and a t the same temperatures are reproduced in Fig. 2 . In Fig. 3 the rate of shear, D , dependence of apparent viscosity, qa, and apparent fluidity, l / q a , are compared with the angular frequency, w , dependence of dynamic viscosity, q’, dynamic fluidity, Jl’w (J” is the loss compliance) , and the absolute value of complex viscosity, 1q*1 == [vt2 (G’/(J)~]~’~, for polymer A a t 160°, assuming D = (J. Similar results for polymer B are shown in Fig. 4. According to the theory of DeWitt,5 the two curves at the top of these figures should coincide with each other, but the q’-curve decreases earlier. The same
-+
LOG Figure 2. Master curves of 7’ and G’ for polymers A and B (log w in set.?). T h e reference temperature is 160”
tendency of 7’ has been reported by several authors,6--10 and some of them stated that qa(D) is the same as ~ ’ ( c w ) when , c = 1.4--1.5,687or c = 2.2-2.3.*s10 On the (3) M.Horio, S. Onogi, and S. Ogihara, J . Japan. SOC. Testing Mater., 10, 350 (1961). (4) I. M .Krieger and S.H. Maron, J . A p p l . Phys., 2 3 , 147 (1952); 2 5 , 72 (1954). (5) T. W. DeWitt, ibid.,26, 889 (1955). ( 6 ) T. IT7. DeWitt, E-I. Markovitz, F. J. Padden, and J. Zapas, J . Colloid Sci., 10, 174 (1955). (7) H. Markovitz and B. Williamson, Trans. SOC.Rheology, 1, 25 (1957). (8) W. Philippoff, J . A p p l . Phys., 2 5 , 1102 (1954). (9) 9. Onogi, I. Hamana, and H. Hirai, ibid.,2 9 , 1503 (1958) (10) T. Arai, Chem. High Polymers, 18, 292 (1961).
Volume 68, Number 6 June, 1964
NOTES
1600
polymer B with increasing D or w. This means that or q’ curves cannot be superposed by asimpleshift along the abscissa to coincide with each other. However, in the case of polymer B, in which the change in viscosity is rather small, the viscosity curves appear to be superposed fairly well by shifting either of the two by a factor of about 1.5. Pao’s theoryL3requires l/va(D) to be the same as J”w(w). Our result in Fig. 3 (middle) does not satisfy this requirement, especially a t higher rates of shear or frequencies, while that in Fig. 4 (middle) does very well. The reason why such a difference arises between two polymers is not clear. Sext, Cox and i\Ierz14-16 have found empirically that qa(D)is equal to /q* (w)for melts of polystyrene and polyethylene, and Williams and Birdll have showed that qa(D) should be the same as lq*((kw),where k is a constant varying from 0.91 to 1.12. The above experimental studies by Cox, et aE., suggest that k = 1. As seen from Fig. 3 and 4 (bottom), qa(D) for polymers A and B coincides very well with [ q* (w), indicating that k = 1here also. Recently, Strella17 has discussed the same problem of the relation between the steady-flow and dynamic viscosities, and derived the empirical law originated by Cox and Merz on the basis of a Voigt element. According to him, the consistency qc(D) or differential viscosity qd(D) should be the same as q’(w),and hence qa = qo (G’/u), when k = 1. I n Fig. 5 , qc is com(G’/w)] for polymer A pared with q’ and qa with [qc a t 160’. It is clear from this figure that qc is much lower than 11’ a t intermediate rates of shear or frequencies. It coincides with q’ very well only a t very low and high rates of shear or frequencies. On the other hand, [qo (G’/w)] is several per cent higher than qa or lq*I a t most frequencies except for the middle region. When one allows for the experimental errors in the measurements and in the time-temperature superposition, one may have to conclude that [qc (G’/w)] is the same as qa within experimental errors. However, the former shows a much different tendency from the latter, as is seen by comparing the curves in the figure. I n conclusion, the relation between the steady-flow and dynamic viscosities for polyethylene melts can be l a
..
I
01 0.001
I
I
I
0.01
0.I D OR W, SEG-’
I
I IO
Figure 3. A comparison of steady-flow properties with dynamic ones for polymer A a t 160”.
1
+
+
+
+
Figure 4. A comparison of steady-flow properties with dynamic ones for polymer B a t 160”.
other hand, Williams and Birdll haye recently derived c = 1.24 theoretically on the basis of the three-constant
Oldroyd modeLL2 According to our results shown in Fig. 3 and 4, however, c is not a constant and increases from 1 to about 3.1 for polymer A and to about 2.7 for T h e Journal of Physicat Chemistry
(11) M. C. Williams and R. B. Bird, Phya. Fluids, 5 , No. 9 (1962). (12) 5. G. Oldroyd, Proc. R o y . SOC.(London), A245, 278 (1958). (13) Y. H. Pao, J . A p p l . Phys., 28, 591 (1957). (14) W . P. Cox and E. H. Mers, J . Polymer Sci., 28, 619 (1958). (15) W. P. Cox and E. H. R‘ferz, Am. Sac. Testing Muter., 247, 178 (1958). (16) W. P. Cox, O f i c . Dig.,Federation Sac. P a i n t Technot., 32, 2 (1960). (17) S. Strella, J . Polymer Sci.. 6 0 , S9 (1962).
XOTES
1601
librium constant at 21 O was determined in thislaboratory from near-infrared measurements and found to be 59 f 5. The effect of ring substitution in phenol on the equilibrium constant was also investigated. Only limited data, primarily dealing with substituted pyridines,' have appeared in the literature concerning this reaction. A correlation of the hydrogen-bonding equilibrium constants with the Hammett substituent parameters was obtained. Apparently this effect has not been studied or has not appeared in the literature prior to this investigation. 0.001
0.01
0.I
I
IO
D OR 0 ,SEC-' Figure 5 . A comparison of qc with 11' as well as of [qa ( G ' / w ) ] with q . or 1q*1 for polymer A. at 160'.
+
explained by none of the current linear theories cited above: the constant c appearing in the theory of Williams, et al., varies with D or w , and ~ ' ( w is ) not the same as r c ( D ) in contrast to the prediction of thie theory by Strella. Very recently, Yamamoto'* has presented a new phenomenological theory for nonNewtonian flow on the basis of the three-dimensional nonlinear model and compared theoretical curveis for r,(D) with that for ~ ' ( w ) . His result also shows that the constant (* increases with increasing D or w, in general. Therefore, we are inclined to ascribe the above lack of agreement of our observations with the linear theories to a n essential difference between the steady-flow and dynamic behavior: the latter is linear while the former is nonlinear.
--
(18) M. Yamamoto, paper presented at the 12th Annual Symposium on Rheology, Tokyo, Japan, September, 1963 (to be published).
Pyridine Interactions with Phenol1 and
Experimental The phenols and pyridine were purified by recrystallization and/or distillation in vacuo prior to use. The carbon tetrachloride was Matheson Coleman and Bell Spectroquality grade and used with no further treatment, All measurements were performed with a Beckman DK I1 ratio recording spectrophotometer a t 21 f 1'. Matched silica cells 5 cm. in length were used. All solutions were measured with an equivalent concentration of pyridine in the reference cell. Absorbance measurements a t 1.4 p were utilized in the evaluation of the equilibrium constants. This overtone of the fundamental hydroxyl group vibration was selected since no interfering absorption was encountered a t this wave length. The molar absorptivities of the pure phenols were determined under conditions where Table I : Equilibrium Constant Values a t 21", l./mole" PMePhenolb Methylb Methylb thoxyb Q-
65.6 59.2 61.7 54.6 56.0 54.1 52.8
Substituted Phenols by Jerome Rubin, Bernard Z. Senkoviski, Gilbert S. Panson Chemistry Department, Rutgers University, Newark, New Jersey (Received January 7, 1964)
Several investigations have appeared in the literature describing hydrogen bonding of Phenol in the Presence of pyridine. 'ITa1ues reported for the Constant at 20' obtained under different experimental conditions were 42,' 55 f 64,3and 88.4 The equi-
59 i 5
112-
Q-t-
Butyl*
PIodoC
mChloro'
PChlorob
47.8 48.5 34.8 148 192 145 48.1 46.2 45.1 38.7 151 182 142 46.0 44.2 43.4 41.8 152 166 124 42.7 42.6 39.4 146 183 123 40.6 40.2 41.8 39.5 40.0 176 128 140 41.2 41.6 38.7 140 167 116 40.1 40.0 40.5 39.4 38.2 129 160 116 40.3 42.5 41.1 40.4 38.9 128 112 40.0 41.3 39.5 39.2 38.8 47.0 42.0 42 & 2 43 i 3 42 2 39 & 2 142 f 8 175 i 9 126 & 10
*
a The phenol concentrations in all solutions was 0.025 M . All solutions studied, except p-iodo- and m-chlorophenol, contained pyridine at concentrations from 0.01 t o 0.10 M . ' I n t h e case of p-iodo- and m-chlorophenol, the pyridine concentration varied from 0.020 t o 0.040 M .
(1) A. Halleux, B ~ L aOc. L . chim. ~ e l g e s6, 8 , 381 (1959). (2) N. Fuson, et al., J . Chem. Phys., 5 5 , 454 (1958). (3) G. Aksnes and T. Gramstad, Acta Chem. Scand., 14, 1485 (1960). (4) A. K. Chandra and 9. Banerjee, J . P h y s . Chem., 66, 952 (1962).
Volume 68, Number 6 June, 1964
