NOTES
4150
ing pH, which shifts the helix-coil equilibrium toward higher helix content, is partially compensated by the increasing temperature, which has the opposite effect. Several experiments were carried out a t pH 11.40 and 11.50. A typical oscillogram photograph is shown in Figure 2. It can be seen that the chemical relaxstion is very fast and that the new equilibrium concentration is established in a few microseconds. To ascertain the slowest possible chemical relaxation which is hidden in the pH-jump records, the oscillograms were evaluated with the rps. Figure 3 demonstrates the use of this instrument in the evaluation of the pHjump shown in Figure 2. The exponential lines of Figure 3 are the relaxation curves generated with a heating time-constant of 4.5 psec and chemical relaxations characterized by rr = 0,2, and 5 psec, respectively. The superposition of these on the actual oscillogram (jagged lines) shows that chemical relaxation times greater than 1 or 2 psec are incompatible with the oscillogram obtained. (The seemingly small horizontal displacements are highly significant since the accuracy of the time coordinate is very high.) A similar evaluation of 20 oscillograms at pH 11.40 and at pH 11.50 indicated the same results. A limited study a t ionic strengths different from 0.2 M (i.e., 0.3-0.4M NaCI) also indicated the same behavior. Owing to the significant amount of stray light present in the ultraviolet observation beam of the temperaturejump apparatus, meaningful values for the absolute value of the change in optical density corresponding to the vertical oscilloscope beam deflections could not be obtained. Thus, the question arises as to whether the deflection seen on the oscilloscope in the first few microseconds is the entire reaction triggered by the pH jump or is only a part of the total optical densit,y change which is followed by a slow reaction not noticeable at the fast sweep rate used. The possibility of a reaction slower than 2 psec was eliminated by the following observations. (1) p H jumps recorded using a 500-psec/cm oscilloscope sweep rate indicated no further deflections in the 0.1-4-msec time range. (2) The oscilloscope trace-position gaugeg did not show voltage changes greater than those of the fast change up to a few seconds after the pH jump. (3) In the Cary 14 spectrophotometer the p H jump induced by a rapid stirring of the solution with a heated spatula did not give evidence of any further react,ion in the 1 sec-l-min range. Since no relaxation time was observed in the 2 X loe6 sec-1 min range, it appears that the chemical relaxation arising from the changes in the helix content of a partially helical poly-L-tyrosine macromolecule is characterized by a time constant of less than 2 psec. The Journal of Physical Chemistw
It is known from the studies of Hammes, Schwarz, Eigen, and Lumry that, in aqueous poly-L-glutamic acid solution, the relaxation time of the helix-coil transition is between 5 X l o + and S ~ C . ~ - Con~ sidering the bulky side chains of poly-L-tyrosine, there appear to be no reasons to believe that the helix-coil relaxation time of this polymer would be less than that of poly-L-glutamic acid. With this assumption, the relaxation time characteristic of the helix-coil transition of poly-L-tyrosine can be given as 2 X sec > r > 5 X 10+ sec. Since neither the relaxation time of the poly-L-glutamic acid nor that of poly-L-tyrosine is known sufficiently accurately, the effects of side chains on helix-coil transition rates cannot be evaluated quantitatively. It appears, however, that the similarity of the range found in the present study with that for poly-L-glutamic acid renders unlikely the possibility that side-chain effects would have a dominant role in determining the rates involved in the helixcoil transformation changes of poly-L-tyrosine or polyL-glutamic acid. Acknowledgments. Thanks are due to Mr. Gary Davenport for the construction of the rps and to Mr. Terry Troxell for help with the experimental work.
A Filter Paper Diaphragm Technique for Diffusion Coefficients’&
by Maurice 14.Kreevoy and Eugene If.Wewerka’b School of Chemistry, university of Minnesota, Minneapolis, Minnesota 66466 (Received July 6 , 1967)
The interpretation of kinetic data is often easier if certain diffusion coefficients are available. While a large number of these have been measured and collected12the possible combinations of solute and solvent are almost infinite. I n the present paper an apparatus and technique, generally applicable for the measurement of relative diffusion coefficients, is described. I n many cases, a measurement can be completed in 1 hr, the reproducibility is of the order of *2%, and the technique used is familiar to kineticists. Its application to HgI, in water and in isooctane (2,2,4-trimethyl(1) (a) Supported, in part, by the Petroleum Research Foundation through Grant P R F 1912-A3,4. (b) Los Alamos Scientific Laboratory, Los Alamos, N. M. (2) S. B. Tuwiner, “Diffusion and Membrane Technology,” Reinhold Publishing Corp., New York, N. Y., 1962, pp 369-373.
NOTES
4151
SIDE CROSS-SECTION
,.
covER4
,TRU-BORE STIRRER
rl/e”
TOP VIEW OF COVER
1
measurements a t two wavelengths. The concentration of neither the unknown nor the reference exceeded 0.2 M , so that neither influenced the bulk properties of the medium (ie., viscosity, density) appreciably. Commercial reagents, of at least reagent grade, were used throughout this work without further purification. Except where otherwise noted, Schleicher and Schuell No. 589 White Ribbon filter paper was used as the diaphragm.
Results As e ~ p e c t e d each , ~ component, in each experiment, appeared in the upper compartment according to a first-order rat,e law, shown in eq l . 4 The concentra-
c - co c-c,
“‘log{-] t--20
k-I
L
3/8’-4
- 2 3/4#-
Figure 1. The apparatus.
pentane), to iodine in isooctane, and to toluene in nhexane are described.
Experimental Section The apparatus is depicted in Figure 1. It was entirely fabricated from Teflon. I n operation, the lower, threaded cup was filled with a dilute solution containing both the unknown and the reference substance. The small lip permitted filling slightly above the flat surface so that the membrane, a piece of filtrer paper, could be wetted with the solution and placed in contact with the surface, leaving no air bubbles. Excess solution was then blotted up, the upper portion of the apparatus was screwed firmly in place, and an appropriate quantity of pure solvent was placed in the upper compartment. The lower part of the apparatus was enclosed in a thin polyethylene bag and was mounted in a constant-temperature bath. The magnetic stirring bar was driven by an air- or water-powered magnetic stirrer mounted in the bath directly beneath the apparatus. The stirrer in the upper compartment was driven mechanically at 300 rpm unless otherwise noted. Samples (3 ml) were withdrawn for spectrophotometric analysis from t8he upper compartment before stirring was begun and at appropriate intervals thereafter. Each sample was returned after the analysis and before the next was wit,hdrawn so that the volume remained approximately constant. The reference substance was chosen so that its concentration and that of the unknown could both be determined in the same sample by spectroscopic
=
tion of a solute in the upper compartment at some time, t, is C,. Typical tests of eq 1 are shown in Figure 2. The best straight lines through the points were drawn by inspection, and were used t.0 calculate values of k. The diffusion coefficient, D , is proportional to k, the proportionality constant depending on the physical characteristics of the apparatus and the d i a ~ h r a g m . ~ Thus, Dx,the diffusion coefficient of X, is given by Dx
=
Dskx/ks
(2)
where quantities subscripted with S refer to a standard substance whose diffusion coefficient is known. The derived values of DX should be independent of the volume of solvent in the upper compartment of the apparatus, the porosity of the filter paper, and the stirrer speeds.
Table I : Diffusion Coefficient of HgIz in Isooctane at 25’ Diaphragm paper
Volume, ml
cm2 sec-1
30 30 60 60
2 . 61d 2 . 53e 2.48 2.57
~@DH~IZ,
‘ Schleicher and Schuell No. 589 White Ribbon filter paper. Schleicher and Schuell No. 589 Blue Ribbon filter paper. Average Eaton Dikeman Co. No. 615 qualitative filter paper. of six determinations with average deviation from the mean of 0.05 X 10-6 em2 see-’. e Mechanical stirrer slowed from 300 t o 150.
*
(3) Reference 2, pp 39, 73. (4) A. A. Frost and K. G. Pearson, “Kinetics and Mechanism,” John Wiley and Sons, Inc., New York, N. T., 1961, p 29. ( 5 ) Reference 2, p 73.
Volume 71, Number Id
November 1967
NOTES
4152
0.10
Table I1 summarizes the diffusion coefficients obtained, all a t 25'.
0.08 0.06
i
Table 11: Diffusion Coefficients a t 25'
0.04
N
+ N
Substance 0.02
HgIz HgIz I2
a" I
8
a
CsH5CHs
Standard
1@Dx, cma sec 1
Isooctane Water Isooctane n-Hexane
CClr CH3COOH" HgIz CClPb
2.59 1.22 2.79 4.11
~
0.09
-
0.06
0.04
c
4
I
0
Solvent
0.02
Q
N
0.01
0
10
20
30
40
50
TIME, MINUTES
Figure 2. Optical densities, A , are proportional to concentration, so eq 1 was tested by plotting optical density differences, on a logarithmic scale, against t , as shown. A small correction, given by AtZ72 €Hglz240/€Hg12272has been substracted from each At240before p l o t h g , to remove the contribution of HgI2 at that wavelength. The (HpIiS are extinction coefficients of mercuric iodide. The superscripts indicate wavelengths.
Table I shows that this is true for HgIz in isooctane (2,2,4-trimethylpentane)with CCI, as a standard. (In this solvent DCCI,is 2.57 X 10-5 cmZsec-I at 25°.)2 The combined changes of variables shown in Table I resulted in changes in observed half-life of nearly an order of magnitude, from about 5 min to nearly 50 min, without appreciable change in DH~I,. The HgIz concentration used in these experiments was lov4 M ; the CC14concentration was 0.2 M . Halving the latter, to 0.1 M , gave an inappreciably different DR~I,,2.55 X 10-6 cm2sec-I.
The Journal of Physical Chemistry
a DCH~COOH in HzO a t 25' is 1.195 X 10" cm2 sec-1 (V. Vitagliane and P. A. Lyons, J. Am. Chem. SOC.,78, 4538 (1956)). * D C C Iin~ n-hexane a t 25" is 3.70 X 10" cm2 sec-1 (ref 2).
The average deviation from the mean, among a total of 11 determinations of D H ~inI ~isooctane, was 2%. This is also the order of the difference between the cm2 sec-l, present value of DcascHaand 4.21 X the value reported by Chang and Wilke.* Thus, Dx, measured by this procedure, seems to have an uncertainty of 1-274, depending on the number of replications.
Discussion None of the techniques described is new, but the present combination seems particularly suitable. The diaphragm cell was introduced by Sorthrup and AnS O ~ , and ~ J the use of filter paper diaphragms was introduced by Gage? The measurement of first-order rate constants is very well developed4 and much more reliable than dependence on just two measurements of c~ncentration.~It also does not depend on an accurate knowledge of proportionality constants if an instrumental method of analysis is used. The use of an internal standard is particularly desirable when filter paper diaphragms are used, as these may not be exactly reproducible. It also halves the time required for a determination. (6) P. Chang and C. R. Wilke, J . Phys. Chem., 59, 592 (1955). (7) J. H. Northrup and M. L. Anson, J . Gen. Physiol., 12, 543 (1929). (8) J. C. Gage, Trans. Faraday Soc., 44, 253 (1948).
