Solution Creeping or Dielectric Relaxation?J. O'M. Bockris, E. Gileadi, and K. Müller Citation: The Journal of Chemical Physics 47, 2510 (1967); doi: 10.1063/1.1703341 View online: http://dx.doi.org/10.1063/1.1703341 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/47/7?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Dielectric relaxation of electrolyte solutions J. Chem. Phys. 94, 6795 (1991); 10.1063/1.460257 Solution Creeping or Dielectric Relaxation? J. Chem. Phys. 47, 2509 (1967); 10.1063/1.1703340 Stress Relaxation and Creep in Dilute Polymer Solutions J. Chem. Phys. 44, 2331 (1966); 10.1063/1.1727044 On Creep and Relaxation J. Appl. Phys. 28, 906 (1957); 10.1063/1.1722885 On Creep and Relaxation J. Appl. Phys. 18, 212 (1947); 10.1063/1.1697606

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to

IP: 128.114.34.22 On: Wed, 03 Dec 2014 08:54:18

2510 LETTERS TO THE EDITOR J. CHEM. PHYS., VOL. 47, 1967

the conclusion reached by Bockris et al. is the model they use for solution creeping. Grantham2 and Leikis et al.3 used a (mathematically simple) model of a solution film of constant thickness, and Barker4 and de Levie5 discussed a film of decreasing thickness. The latter model would fit the data of Bockris et al., Le., it leads to a frequency dependence

2~ -0 InRp/o Inw~0.5, (3)

and especially to a value of - d InRp/d lnw of close to 2 for low solution resistivity, precisely in the region where the capacitive component Cp is essentially con­stant (see, e.g., Ref. 6, Fig. 6). Therefore, the data reported by Bockris et at. l could just as well be used as arguments for the presence of a tapering solution film in their measurements. At any rate, since the assumed shape of the liquid film inside the capillary determines the predicted values of d InRp/d lnw, creeping effects cannot be discarded on the basis of a single film geom­etry which happens not to fit the experimental data.

1]. O'M. Bockris, E. Gileadi, and K. Muller. ]. Chern. Phys. 44, 1445 (1966).

Z D. H. Grantham, thesis, Iowa State University, 1962; Dis­sertation Ahstr. 23, 3646 (1963).

3 D. 1. Leikis, E. S. Sevast'yanov, and L. L. Knots, Zh. Fiz. Khim. 38, 1833 (1964).

4 G. C. Barker, Anal. Chim. Acta 18, 118 (1958). 6 R. de Levie, J. Electroanal. Chern. 9,117 (1965). 6 R. de Levie, Electrochim. Acta. 10, 113 (1965).

Solution Creeping or Dielectric Relaxation?

J. O'M. BOCKRIS

The Electrochemistry Laboratory, University of Pennsylvania, Philadelphia, Pennsylvania

E. GILEADI

Institute of Chemistry, Tel-Aviv University, Ramat-Aviv, Tel-Aviv, Israel

AND

K. MULLER

Research Institttte for Catalysis, Hokkaido University, Sapporo, Japan

(Received 5 May 1967)

We appreciate the indication of a more general rela­tion (de Levie's Eq. (3)J for the effect of electrolyte penetration on pseudoresistance effects in double-layer measurements than that given in our paper. We wish to mention here criteria which may aid a distinction between the two models for double-layer resistance variation with frequency.

We have excluded by application of the experimental criterion of the variation of resistance with frequency the possibility that the effects observed by us were due to an electrolyte film of constant thickness.1- 5 It ap-

pears probable that any film present between mercury and glass does have constant thickness, for the follow­ing reasons: (a) Wetting occurs against a practically constant hydrostatic pressure of the mercury head (see below) ; (b) if any pockets of liquid are formed,3 a film of constant thickness must connect them with the bulk of the solution; (c) the mercury flows rapidly through the narrow portion of the capillary [approximately 1 m sect in the constriction (about 15 mm long), 10 em secl in the bottom section (about 4 mm long)].

In our calculations on a film model (in agreement with the treatment of the Russian authors5), 0.4-1-1 film thickness (with a capillary radius of 81-1) had to be assumed to obtain the order of magnitude of the results observed by us on a film thickness model.s This appears to be an unreasonably large value, in view of the capillary size. For a thinner film (d. de Levie's quotation7 of Melik-Gaikazyan's calculation3), we ex­pect observation of an effect only in well-conducting solutions at low frequencies, and no effect in more dilute solutions. Indeed, the deviations from the straight lines in Fig. 4 of our paper2 probably indicates such an effect. The dielectric-model conclusions of our paper are not intended to cover this deviation region.

Our capillaries were not siliconized because (a) Grantham's results with siliconized capillaries do not prove the cessation of frequency variation of the re­sistive component of the impedance; (b) Barker's paperS indicates that "water-proofed capillaries are not suitable for use with acid solutions at potentials more negative than about -0.9 V vs (Standard Calomel Electrode) ."

Our capillaries had a restriction (see above), and the mercury reservoir was 80 cm high. The probability of sucking back is thus greatly reduced.

The double-layer-dielectric water is subject to the expected behavior of dielectric materials composed of polar molecules. There is no reason to exclude applica­tion of this to a monolayer (d., Shimizu9). A depend­ence of the orientation of water at the interface, as a function of potential, has been utilized in several recent theoretical models.1o It seems to be a necessary model for the parabolic dependence on potential of the cover­age of an electrode with organic material outside the potential ranges in which oxides occur. With agree­ment that the water dipoles orient as a function of double-layer field, a dipole admittance contribution to the double layer under an ac field must occur. It depends on quantitative considerations, then, as to whether it will be observed. We have discussed the basis of the reasonable character of a distribution of relaxation times for the water molecules adsorbed, and have shown that with values TO= 10-6 sec, ~~Co= 6 I-IF cm-2, {3= 0.5, the quantitative agreement between this theory and experiment is good (d. the calculations in the test of Ref. 2 and Fig. 7 of Ref. 11).

In conclusion, the variation of resistance of the dou-

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to

IP: 128.114.34.22 On: Wed, 03 Dec 2014 08:54:18

J. CHEM. PHYS., VOL. 47, 1967 LETTERS TO THE EDITOR 2511

ble layer which we have reported is more likely to be due to dielectric relaxation effects than to a solution­creeping model because: The explanation in terms of dielectric relaxation involves a model consistent with, and necessary for the explanation of, a number of other experimental phenomena. The model of solution creep­ing, however, demands a model of a relatively thick tapered film between metal and solution which seems to be qualitatively and quantitatively improbable in a streaming-mercury si tua tion.

1 R. de Levie, J. Chem. Phys. 47, 2509 (1967), preceding comment.

2 J. O'M. Bockris, E. Gileadi, and K. Miiller, J. Chem. Phys 44, 1445 (1966).

3 R. de Levie, J. Electroanal. Chem. 9,117 (1965). 4 D. H. Grantham, disseration, Iowa State University, 1962;

Dissertation Abstr. 23, 3646 (1963). 6 E. A. Ukshe, N. G. Bukun and D. I. Keikis, Dokl. Akad.

Nauk SSSR 135, 1183 (1960); Zh. Fiz. Khim. 36, 2322 (1962); Electrochim. Acta 9,431 (1964); D. I. Leikis. E. S. Sevast'yanov and L. L. Knots, Zh. Fiz. Khim. 38,1833 (1964).

6 K. Miiller, dissertation, University of Pennsylvania, Philadel-phia, Pa., 1965; Dissertation Abstr. 26, 7064 (1966).

7 R. de Levie, Electrochim. Acta 10, 113 (1965). 8 G. C. Barker, Anal. Chim. Acta 18, 118 (1958). 9 M. Shimizu, J. Chem. Soc. Japan 74, 587 (1953); 75, 887

(1954) . 10 N. F. Mott and R. J. Watts-Tobin, Electrochim. Acta 4, 79

(1961); R. J. Watts-Tobin, Phil. Mag. 6, 133 (1961); J. O'M. Bockris, M. A. V. Devanathan, and K. Miiller, Proc. Roy. Soc. (London) A274,55 (1963); J. R. Macdonald and C. A. Barlow, J. Chern. Phys. 39, 412 (1963).

11 K. Miiller (unpublished).

Comment on "Heat Capacity of Polyethylene from 2.50 to 300 K"*

J. A. MORRISON AND D. M. T. NEwsHAMt

Division of Pure Chemistry, National Research CouncU of Canada, Ottawa

(Received 11 May 1967)

Tucker and Reesel have recently published heat­capacity data on three different specimens of poly­ethylene. Basically, their aim was to make deductions from the thermodynamic results about the dependence of the vibrational structure of the polymers on their degree of crystallinity. A similar strategy has been used in discussing the low-temperature thermodynamic properties of vitreous and radiation-damaged sub­stances.2- 4 As with these latter substances, there appears to be an "excess" heat capacity5 associated with the amorphous parts of the polyethylene specimens. However, in deriving the "excess" heat capacity, Tucker and Reesel have used specific models. If, instead, a more general basis is used for the interpre­tation, it is possible to show that their data support their general thesis very much better than they sup­posed.

.-'", ..

.022

.020

.018

\ .016

'" 'E ~ .014

u

.012

o

LO

(8;§-

-- --MI ---

~8'-~~

4·K

10 20

FIG. 1. A plot of Cp/T3 against P. for three polyethylene spec­imens. 0- experimental data (Ref. 1). For an explanation of the curves, see the text.

In their Fig. 2, Tucker and Reesel demonstrate that the quantity Cp jT3 depends linearly on the degree of crystallinity of the polyethylene and, by extrap­olation, find that Cp jT3=0.00819 m] cm-3·deg-4 for 100% crystalline polyethylene in the region T< lOOK. While this cannot be an exact result because of the effect of dispersion of the lattice waves through this region,6 it is probably acceptable to 1% or 2% for T < 4 OK. Tucker and Reesel then proceed to describe the heat capacities of their specimens as the sum of a term in T3 plus a single Einstein term, the latter representing a contribution of the amorphous structure. But the coefficients taken for the terms in T3 vary from 0.010 to 0.017 m] g-l·deg-4, a variation that seems rather too large, as the following argument indicates.

The coefficients are simply the limiting values of Cp jT3 as T-?()°K and, although they are inde­pendent of the detailed structure,6 they will depend on the volume through an appropriate Griineisen param­eter.7 In particular, we may write

where p is the density, 'Yo the limiting low-temperature value of the Griineisen parameter, and the subscript 100 refers to 100% crystalline polyethylene. The quantity 'Yo has not been determined for polyethylene. However, the heat-capacity data can be analysed consistently if the limiting values of Cpj1'3 are taken to be inversely proportional to the density. This implies that 'Yo=i which is a reasonable value.8

Figure 1 is a plot of Cp/1'3 against T2 for the low-

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to

IP: 128.114.34.22 On: Wed, 03 Dec 2014 08:54:18