Structure Relaxation at Liquid–Solid InterfacesNarendra N. Roy and G. D. Halsey Jr. Citation: The Journal of Chemical Physics 53, 798 (1970); doi: 10.1063/1.1674062 View online: http://dx.doi.org/10.1063/1.1674062 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/53/2?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Measurement of the in freezing-point temperature: Effect of the liquid-solid interface structure AIP Conf. Proc. 1552, 243 (2013); 10.1063/1.4819547 The reflection of bounded inhomogeneous waves on a liquid/solid interface J. Acoust. Soc. Am. 113, 73 (2003); 10.1121/1.1523081 Experimental observations on liquid/solid interface waves J. Acoust. Soc. Am. 72, S99 (1982); 10.1121/1.2020183 The stability of gaseous nuclei at liquidsolid interfaces J. Appl. Phys. 53, 6191 (1982); 10.1063/1.331532 On Acoustic Boundary Conditions at a LiquidSolid Interface J. Acoust. Soc. Am. 44, 395 (1968); 10.1121/1.1970795

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798 S. K. SEARLES AND L. W. SIECK

involving cyclohexyl radicals and NO were proposed to account for this behavior. As indicated under Results, the relatively rapid bimolecular reaction cyclo-C6Hll++ NO-+C6HllNO+ was detected in cyclo­hexane-NO mixtures at higher pressures. Although no further reactions of this adduct with NO were ob­served under our conditions (P<O.5 torr), there is ample evidence from other laboratories8 that further incorporation of NO into CnHmNO+ adducts occurs readily at higher pressures. Since cyclo-C6Hll+ is likely to represent a major ionic intermediate in the radioly­sis of cyclohexane-NO mixtures we suggest that an ion-molecule mechanism yielding oximes and/or N 2

(either directly or following ion neutralization) is a plausible alternative to the free radical sequence proposed previously.

THE JOURNAL OF CHEMICAL PHYSICS

ACKNOWLEDGMENT

We express appreciation to Pierre Ausloos for several stimulating discussions concerning this work.

* This research was supported in part by the Atomic Energy Commission.

t NCR-NBS Research Associate, 1968-1970. 1 L. W. Sieck, S. Searles, and P. Ausloos, J. Am. Chern. Soc.

91, 7627 (1969). 2 L. W. Sieck and J. H. Futrell, J. Chern. Phys. 48,1409 (1968). 3 W. C. Lineberger and L. J. Puckett, Bull. Am. Phys. Soc.

14, 261 (1969). 'L. W. Sieck and S. K. Searles, J. Am. Chern. Soc. 92, 2937

(1970). 5 P. Ausloos, Progr. Reaction Kinetics 5, 113 (1969). 6 D. K. Bohme, R. A. Vane, F. C. Fehsenfeld, and E. E.

Ferguson, Reported at the 17th Annual Conference on Mass Spectrometry and Allied Topics, May (1969).

7 J. Milhaud, J. Chim. Phys. 64,786 (1968). 8 P. Kebarle, R. M. Haynes, and S. Searles, Advan. Chern. Ser.

58, 210 (1966).

VOLUME 53, NUMBER 2 15 JULY 1970

Structure Relaxation at Liquid-Solid Interfaces NARENDRA N. Roy AND G. D. HALSEY, JR.

Department of Chemistry, University of Washington, Seattle, Washington 98105 (Received 24 March 1970)

The high-coverage isotherms of Lando and Slutsky for neopentane and tetramethyl silane on gold films are analysed on the basis of a slab model for adsorbed layers. It is possible to fit the data to an inverse cube law for surface energy if a structure relaxation term, as proposed by Adamson and Ling, is introduced. The cube law coefficients so obtained are approximately an order of magnitude larger than the theoretical values.

Multilayer formation at a solid surface, under the influence of an energy that decays with distance from the solid-multilayer interface has been divided into two categories on the basis of an adsorption isotherm used by Singleton and Halseyl:

forms n monola yers, and Er/ k T and (w / k T) parameters that characterize the vertical and lateral interactions, respectively. The latter is roughly equal to half the energy of vaporization or sublimation of the material forming the monolayers divided by kT, that is, about five, by Trouton's rule.

In(p/ Po) = (- Er/n3kT) + (w/kT) (1- gn). (1)

Here, p/Po is the relative pressure of the adsorbate that

(0)

40

30

"-~ 20 '<

.;;--

~ '-

10

°o~--------~--------~--~

The compatibility factor gn has previously been assigned the value zero, which is the case for the

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S T Rue T U R ERE L A X A T ION A T L I QUI D - SOL I DIN T E R F ACE S 799

adsorption of liquid argon on graphitized carbon black, or a constant value gn= g< 1 for solid krypton or xenon adsorbed on the same surface. The value of 1-g reflects the degree of misfit of the two lattices when they meet at the surface, and a constant value implies that at least over the range of film thicknesses investigated, a structure distortion or fault transmits unchanged from layer to layer in the solidlike rare gas. Here, we take up the intermediate case where there is healing or relaxation of the structure, from layer to layer, which is most simply characterized by the expression used by Adamson and Ling2 in their study of contact anglE;:

1-gn = (l-g) exp[ -n/nrJ, (2)

where the constant 1-g characterizes the magnitude of the misfit at the interface, and the constant nr is the relaxation distance (in monolayer thicknesses) from the surface.

It will be convenient to rewrite Eq. (1) and in­corporate Eq. (2), with the adsorption characterized by the actual film thickness, d:

In(p/ Po) = (-Kt/d3) + Kr exp( -d/dr). (3)

This extension of the earlier treatment has been stimulated by the recent work of Lando and Slutsky3

who have studied the adsorption of neopentane and tetramethyl silane on gold films at room temperature. At high coverages, where the data are stated to be especially accurate, these authors find that an inverse square law fits the data, whereas, a simple cube law, as in Eq. (1), does not.

We have fitted these data to Eq. (3). We have used the bulk liquid density and a roughness factor of unity to compute the film thickness. The fit is shown in Figs. l(a) and l(b) and 2(a) and 2(b), and constants required for the fit are given in Table I. For purposes of comparison, a rough monolayer thickness dm has been estimated from the liquid density and close packing, and approximate experimental values of El/kT have been calculated. The constants used in these calculations are given in Table II. Where polarizability is not available, it has been calculated from index of refraction or dielectric constant. The Kirkwood-Mueller (K-M) energy coefficient is calculated from the expression4 •5

7rmc2 [N10il 0i2 1 ]

Kl(K-M) = d3kT (0it/Xl)+(Oidx2) -7j(N20i2X2)

(4)

and the Lennard-Jones (L-J) coefficient is calculated from the expression4-6

Kl(L-J) = (mc2jd3kT) [h2-t(7rN20i2X2)]. (5)

Both calculations are grossly too small to account for the adsorption energy coefficient derived from the data. If the K-M energy, which depends on the electrons of the gold ions, and the L-J contribution which depends on the conduction electrons were added, it would

~ I

'Cl o V}

'c: .... N

o '" o

.... '" V}

0-N

t-

N V}

o o

t­V}

N

o

'Cl .... '" o

o

'" ....

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800 N. N. ROY AND G. D. HALSEY, JR.

30 (0) o 70

20 80

~ ~

10 100

150

a 0.005 0.010 In Pol P

150

100

50

00

00 000

... -.. .. .--0.5

PIPo

0 0

1.0

FIG. 2. (a) Plot of l/d' against InPo/ P for tetramethylsilane according to Eq. (3) at 19°C. d is the film thickness in angstroms. e, Experimental points at 19°C (data of Lando and Slutsky). (b) Adsorption isotherm for tetramethyl­silane according to Eq. (3). e, Experi­mental points at 19°C (data of Lando and Slutsky).

TABLE II. Constants used for calculating K-M and L-J energy coefficients.

Diamagnetic Polarizability susceptibility Density

X 10'4 Molecule (cm"/mol)

Neopentane 9.97-Tetramethylsilane 12.670

Gold (Au+) 1.883-

"Handbook of Chemistry and Physics (Chemical Rubber. Cleveland Ohio. 1966--1967). 47th ed.

b G. Foex, Cons/antes Selectionnee's Diamagnetisme et Paramagnetisme (Masson. Paris. 1957).

require a roughness factor of the order 2 to produce agreement.

In addition, if the lower coverage measurements are considered, there is a great qualitative difference be­tween the sort of type III isotherm actually encountered and the very strong binding implied by the extrapola­tion of the high coverage results to low coverage by means of Eq. (3). This behavior could conceivably be explained by a grossly dirty surface.

We conclude, therefore, that it is possible to fit the high-coverage data of Lando and Slutsky to a modified cube law, but that the coefficient required is so large that it must decay at distances close to the surface, comparable to two or three monolayers. An attempt was made to fit the high-coverage data to an equation of the form

In (p/Po) = - (1/d3) [K1+ (K2-K1) exp( -d/dr')],

(6)

X 1029

(cm'/mol)

1O.48b

12.27d 10.790

Density (gcm-a)

0.6135-0.6480-

19.3"

in molecules (cm-3 XlO-2')

0.5121 0.4424 5.901

o A. P. Altshuller and L. Rosenblum. J. Am. Chern. Soc. 77, 272 (1955). d K. Frei and H. J. Bernstein, J. Chern. Phys. 37, 1891 (1962). e J. H. VanVleck. The Theory of Electric and Magnetic Susceptibilities

(Oxford U. p .. London. 1932). p. 225.

which implies a change from a short-range K2 to the long-range K 1• The result was a large negative value of K2 of the order of 20X103 for the neopentane data. It would take further terms to fit the data properly, and this type of equation was not explored further. Alter­natively, we may conclude that the cube law is not valid over the large range of distances investigated.

ACKNOWLEDGMENT

We are indebted to Professor Leon J. Slutsky, who kindly made his data available to us prior to publication.

1 J. H. Singleton and G. D. Halsey, Jr., Can. J. Chern. 33, 184 (1955).

2 A. W. Adamson and I. Ling, Advan. Chern. 43, 57 (1964). aD. J. Lando and L. J. Slutsky, J. Chern. Phys. 52, 1510

(1970). 4 J. G. Kirkwood, Z. Phys. 33, 57 (1932). 5 A. Muller, Proc. Roy. Soc. (London) A154, 624 (1936). 6 J. E. Lennard-Jones, Trans. Faraday Soc. 28, 333 (1932).

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