XOTES
1152
Vol. 67
However, the coefficient 6 in the exponent of (13) is temperature independent in the case of the tunneling process, whereas 6 varies as T-l in the case of flow over the barrier top. This difference makes it easy to recognize the tunneling process experimentally. AN EXTRAPOLATION METHOD FOR ESTIMATING STEADY-FLOW YISCOSITY AND STEADY STATE COMPLIAXCE FROM CREEP DBTA BY
0.5'
KA5UHIKO ~ I N O V I Y A
0
I
I
50
100
J a p a n Synthetic Rubber Co., Yokkazchr. J a p a n , and Department o f Chemzstry Universzty of Wzsconszn, M a d z s o n , Wzsconszn Recezued October $4, 198$
J(t)ss
= Je
+ (t/d
J(t)ss/i
= (Je/O
(1) Division of both sides
+ O/V)
(2)
Therefore, when J ( t )I t is plotted against l / t , the intercept a t the ordinate gives the value of l / p and the initial tangent is equal to the value of Je. The following relationship may also be introduced. lim [ d J ( t ) / d l ] = lim [mJ(t)/L]= 1/77 (3) t+ llt 0 --f
m d log J(t)/d log t The value of m appears to be less than unity and it approaches unity when steady state creep is reached. The plot of m J ( t )l t vs. l / t may be expected t o converge to l / q with much less curvature than that of J ( t )i t us. I / t so that extrapolation toward the ordinate axis would be easier for the former plot. Hence, it is suggested that mJ(t)/t os. l / t may first be extrapolated tourard the ordinate to give the intercept and then another plot may be properly smoothed to obtain the value of the initial tangent. The accuracy of Jecan never be expected to be as good as that of 7, regardless of the method of its estimation. I n practice, creep data with the value of m from 0.7 to 0.9, which are fairly removed from the steady state, may be used successfully. In most cases plots of mJ(t)/tus. l / t caii be approximated by straight lines in the region of 0.7 < m < 1 to give reasonable values for V.
To illustrate the reliability af the values of q and J,
(sec -I 1,
of extrapolation plots (polyisobutylene F5R a t 30"): 1, J ( t ) / t ; 2, nzJ(t)/t.
1.-Example
The steady-flow viscosity, p , and the steady state compliance, Je,of an amorphous polymer can be directly obtained by prolonging creep measurements into steady flow and/or by measuring the creep recovery thereafter. In practice, however, sometimes the direct method is not so desirable for several reasons, since the sample specimen may have to be kept at a rather high temperature for a considerable length of time. Therefore it would be convenient to introduce a conveiitioiial method to estimate the values of p and J , from creep data taken somewhat before attainment of steady flow. Creep compliance in shear at the steady state, de, be written in the form noted here by J ( t ) s s caii where t represents the time. in eq. 1 by t gives
I /t
I
I50
thus estiniat'ed, a comparison is made using data of Leaderman and others' 011 the shear creep of polyisobutylene samples.2 Figure 1 shows a typical example of the extrapolation method for these data. Table I compares the values of p and Je for seven samples of polyisobutylene from direct measurements extending into the steady flow stat'e, as reported by Leaderman,l with those estimated by the extrapolation method from data in advance of the steady state. TABLEI LTa4LCES O F
7 ASD
J,
FOR P O L Y I S O B U T Y L E N E SA?dPLES AT
X 10-4, poiseS,S." extrap.b
--q
Sample
S,
X
F3.s.a
30"
106, cm.Z/ciyne
extrap."
F5R
1.32 1.32 1.1 0.86 E 1.80 17.2 17 1.82 8.10 15.8 18 H 8.26 10.1 10 56.3 56.5 J K 182 5.6 6.3 185 330 330 4.36 4.6 G F2 642 3.35 3.5 641 a Obtained by Leaderman from steady-state measurements. Extrapolated by eq. 2 and 3 from data of Leaderman before the steady etate, i.e., form = 0.7 to 0.9.
The agreement between the corresponding values in Table I is very satisfact'ory. Acknowledgment.-This work was supported in part by a grant from the National Science Foundation. The author is grateful for the interest' and discussions of Professor J. D. Ferry of the University of Wisconsin, Professor H. Fujita of Osaka University, and Professor J. Furukawa of Kyoto University. (1) H. Leaderman, R. G. Smith, and L. C. Williams, J . P o l y m e r Sea., 36, 233 (1959). (2) T h e numerical data of S ( t ) as well a s 7 a n d J e for those samples were furnished through t h e kindness of Dr. H. Leaderman of t h e National Bureau of Standards.
T H E "SHAKING EFFECT" I N PRECISION CONDUCTASCE MEASUREMESTS BY J. E. PRUE' Department of Physical a n d Inorpanic Chemistry, Uniuersity of N e w E n g l a n d , A r m i d a l e , ,Yew South W a l e s , Australia Received S c v e m b e r 6 , 1962
Conductance measurements with A precision of 0.0; 9% or better are of current interest in order to test2 ne!+' theoretical equations for the dependence af molar eon:
