761
Communications to the Editor
from the AVvalues per cross link in gel formation and the average number of H bonds in each cross link (Table I). The average value of A V for the formation of an H bond is then found to be about -5.5 ml/mol, which seems to be reasonable in comparison with the value for OH---0 bond formation, -6.0 ml/mol obtained in the dimerization of formic acid,S -4.64 ml/mol for the association of n-butyl alcohol in CS2.10
TABLE I: Slopes of Noise Spectra for Various Concentrations a n d Currentsa Concn, M
0.017
References and Notes K. Imanaga, H. Kambara, and T. Tachibana, presented at the 20th Annual Meeting of Chemical Society of Japan, Osaka, 1968, No. 22216. K. Suzuki, Y Taniguchl, and T. Enomoto, Bull. Chem. SOC.Jap., 45, 336 (1972). T. Tachibana and H. Kambara, Bull. Chem. SOC. Jap., 42, 3422 (1969). K. Serck-Hanssen, Chem. lnd. (London), 1554 (1958). J. E. Eldridge and J. D. Ferry, J. Phys. Chem., 58, 992 (1954). G. C. Pimental and A. L. McClellan, "The Hydrogen Bond," W. H. Freeman, San Francisco, Calif., 1960, p 218. R. E. Gibson and 0. H. Loeffier, J. Amer. Chem. Soc., 63, 898 (1941). K. Suzuki, Y. Taniguchi, and T. Watanabe, J. Phys. Chem., 77, 1918 (1973). E. Fishman and G. H. Drickamer, J. Chem. Phys., 24, 548 (1956).
Department of Chemistry Faculty of Science and Engineering Ritsumeikan University Kita-ku, Kyoto, 603, Japan
Yoshihiro Taniguchi* Keiro Suzuki
0 .0080
0 ,0038
96 178 70 74 82 95 119 125 43 50 62 71 95 42 49 59 89 96
fB,' Hz
1.8
0.9
5,000
2.2 1.7 1.8 1.9 1. . 6 1.7
1.3
13,000
3.0 1.7 1.6 1.5
1.3
2.1
4,500 1.4
0.9
20,000
3 1.8
2 .o 1.7 1.7 1.8
0.018
96
1.4
101
1.4 1.5 1.5 1.6 1.7 1.6 1.4 1.6
125 178 42 53 74 95 101 131
0.0019
Sir: We have, over the past several years, studied transport across cation membranes by measuring noise power spectra.l From this work, we were able to draw certain conclusions, at least for Hf ion, as to the transport mechanism.1d In our initial paper,lavb we reported some limited results on anion membranes. These results indicated that, unlike the cation membrane spectra, anion membrane spectra showed l/f noise, and sometimes l / f 3 / 2 noise. Since these results on anion membranes have not been followed by a systematic evaluation, the initial data have been left unconfirmed. Recent work by Hooge and coworkers2 has renewed interest in l / f noise, and there is a significant difference in the transport mechanism indicated by l/f noise and l/f312. For these reasons, a brief reinvestigation of the noise spectra generated by ion transport across an anion membrane seemed appropriate at this time. The technique is unchanged from that previously described,ld except that only room temperature measurements were made. The LA260V Applied Cybernetics amplifier was replaced by a Model LA460V (or by an AD-YU Model 1027C for some higher noise measurements). Solu-
C
HsPOaSpectra 0.034
0.0081.
Publication costs assisted by City Coliege of New York
bb
80
Received July 30, 1973
Noise Spectra of Ion Transport Across an Anion Membrane
a
HCI Spectra
0.024
Acknowledgment. Financial support given by the Ministry of Education in Japan is gratefully acknowledged. (1) Part of this article was presented at the 22nd International Congress of Pure and Applied Chemistry, Sydney, Australia, Aug 1969, p 104.
Current density, A/m2
42 61 71 78 119 42 50 55 59 71 77
1.1
1.8
9,000
1.4 1.7 1.1 1.o
1.2 1.6
1.9
4,500 1.7
1.8 2.6
8,000
15,000 15,000 20,000 15,000
1.5 1.1
2 .o 3 .O 2.6 3 .O
20,000
1.3
2.3
15,000
1.1
>
Slopes as -d log power/d log f. *For values of fa 104 Hz, the b slopes are based on a small number of points, and have a relatively large error. Frequency at which curves of two slopes meet, &tZO%.
tions of HsP04 were prepared as follows: solution 1, 0.034 M ; solution 2, 0.018 M, solution 3, 0.0081 M , solution 4, 0.0019 M . Also, solutions of HC1 were prepared: solution 1, 0.1024 M , solution 2, 0.017 M , solution 3, 0.0080 M , solution 4, 0.003 M . The anion membrane was Ionac Type MA 3236, with an exposed surface of 8.4 x 10-6 m2. The spectra were taken, as before, with a Tektronix 3L5 spectrum analyzer in the frequency range 300-80 kHz; in this work, the center frequency settings were checked with an IEC Model F34 function generator. No other changes in procedure were made from the previous work.ld The results are summarized in Table I. As can be seen, two types of spectra exist: those in which an approximate f-3/2 slope was found, and those in which an f - I slope was found a t lower frequencies, with an approximate f - 2 a t higher frequencies. It is relatively simple to deal with the -1.5 slope cases, as these are normally characteristic of diffusion.3 Furthermore, with cation membranes at low current densities, diffusion appears to dominate the The Journal of Physical Chemistry, Vol. 78, No. 7, 1974
Communicationsto the Editor
762
noise.ld It is probably safe to conclude that for the more concentrated H s P O ~solutions, this is equally true. However, the other form of spectrum is not comparable to any found with the cation membranes. Here, l / f noise does appear over an appreciable frequency range. The fact that a steeper slope appears a t higher frequencies gives a strong hint as to the source of the noise, however. I t has long been known that a distribution of relaxtion times could produce l / f noise between the lower and upper frequency limits of the distribution, and that, above the ~ is upper frequency limit, f - 2 noise should r e ~ u l t .This fairly close to the behavior observed here. The fact that, even in the more dilute solutions, single slope spectra which are usually between 1.5 and 2.0 occur suggests that the relaxation processes do not exclude the simultaneous presence of diffusion. If the two contributions are of similar magnitude (as is indicated by the fact that either one may be found with only a relatively small change in conditions) it is possible for them to combine so as to produce a spectrum which takes this form, within experimental error. Current-voltage curves for anion membranes do not produce clearly defined plateaus a t a critical current density, as cation membranes do;la this behavior was found again in this system. Of the systems studied here, only the most concentrated HaPOl solution remains ohmic in its behavior throughout the range of current densities in which noise spectra were taken. This solution gave only diffusion spectra. No spectra showing two slopes appeared a t current densities less than that a t which non-ohmic behavior began (within experimental error, 1 8 A/m2), although single slope spectra, as in the case of the least concentrated HCl solution, appeared well above this point.
The Journal of Physical Chemistry, Vol. 78,
No. 7, 1974
Above the critical current density, cation membranes show a spectrum fairly close to two straight lines of slope -3, -5, and this could be interpreted as due to turbul e n ~ e . l d ,Although ~ the anion membrane spectra sometimes showed a steeper spectrum following a less steep one, and a -1 slope can appear between -3 and -5, the steeper slope for the anion case did not approach -5, and no evidence of a -3 slope was found a t low frequency. Therefore, it appears that turbulence does not occur with anion membranes as it does with cation membranes. The following conclusions can be drawn. (1) At current densities lower than that for the start of non-ohmic behavior, the noise spectra are dominated by diffusion noise. (2) At higher current densities, the spectra often are of a type which would be characteristic of a distribution of relaxation times. (3) In contrast to cation membranes, these spectra show no evidence of turbulent flow.
References and Notes (a) M. E. Green and M. Yafuso, J. fhys. Chem., 72, 4072 (1968); (b) ibid., 73, 1626 (1969); ( c ) M. Yafuso and M. E. Green, ibid., 75, 654 (1971): (d) S.H. Stern and M. E. Green, ibid., 77, 1567 (1973). (a) F. N. Hooge and J . L. M . Gaal, fhillps Res. Rep., 26, 77 (1971); (b) F. N. Hooge, fhys. Lett., 33A, 169 (1970); (c) F. N. Hooge, fhysica, 45, 386 (1969). M. Lax, Rev. Mod. Phys., 32, 25 (1960). R. H. Kingston and A. L. McWhorter, fhys. Rev., 103, 534 (1956). C. M. Tchen, Phys. Rev. A , 8,500 (1973).
Department of Chemistry The City College of the City University of New York New York, New York 10031 Received December 10, 1973
Michael E. Green
