Computer simulation of physisorption on a heterogeneous surface

Surface Science 199 (1988) L395-L402 North-Holland, Amsterdam

L395

JAN and William A. STEELE Department of Chemistry, The Pennsylvcq. ic S!czte University, University Park, PA 16802, USA

Received

19 February

1988; accepted for publication

9 March 1988

The technique of molecular dynamics was used to determine the structures of krypton physisorbed on a simple heterogeneous surface. The solid was modelled as at: infinite set of straight square-walled grooves cut into an otherwise flat surface. The computed local densities show that the atoms adsorb as one-dimensionally ordered rows near the walls of the grooves. This order decays with increasing distance from the walls. Also, the atoms adsorbed on the steps exhibit little order at the simulation temperature of 110 K.

M.J. Bojan, W.A. Steet’e / Computer simulation of physisorption

L396

length in the x-direction and with an infinite rectangular saw-toothed profile in the y-direction. Within the confines of this simple model, one still has many adjustable parameters for e heterogeneity, including the de of the grooves, as well as spacing between them. The interaction potential between a krypton atom and the surface is modelled by taking the total energy to be a pair-wise sum of Lennard-Jones 12-C I&-C atom interactions with parameters selected to give agreement with low-coverage (Henry’s Law) measurements on a homogeneous sohd [3]. The pairwise sum for the gas is transfolrmed into the usuai Fourier series representation, with a leading term given by a sum over planes of the Kr-surface averaged interaction [a]. For reasons of mathematical convenience, periodic terms in this gas-solid interaction potential are omitted. (Specifically, the hexagonally-symmetric periodic terms could not be easily included when one has straight-edged groove walls.) In fact, this approximation to the potential lends itself well to the modelling of a grooved surface, since one can build up the steps betw(een the grooves merely by attaching parallel strips of these surface-averaged carbon planes to the flat surface of the homogeneous substrate. The overall height of the spacers is determin planar strips added. Their vertical separation ia t interplanar spacing in bulk gr te. The comple the strips and the spacing between them in determined by setting the width plicit expressions for t

lane

0

ntials are obtaine

M.J. Bojan, W.A. Steele / Computer simulation 01’physisorption

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where u,,,(z$

*I2 y*) = %256 i

Y” y*2+z*2

8

-I-

zz”( y*2 + r/r,,,(z,*, y*) =

l/2 m

(

F

((

g’)’

>

-+1/2

1

7

+

Y*

Y *2+t,*q

1

zm*‘(y*2 +

ii

zz2)”

1

2+

e4m

(3)

7

z*2 m

t y*2

+

2;“)

1

l

ne retrieves the usual result for an infinite plane y letting y* --f* 00, which makes y*/(~*~ + zz2) * & 1. In this case, all terms in the curly

3.6 3.6 3.5

li3jW) H pairs)

M.J. Bojan, W.A. Steele / Computer simulation of physisorption

L398

1. Atomic

trajectoriesfor

ite-like

surfaceare

s

ealized contour for the surface in the y-dir *Lo LLIL

,,,.h,pter rQr.-t

genera!rs

the random

a wpe

motions for a fluid ora step-groove wall.

groove near the

M..?. Bojan, W.A. Steele / Computer simulation of physisorption

Fig. 2. SaPneas fig. 1, hue for 196 atoraasadsorbe

rep surfaces

ES”s

L400

M.J. Bojan, U/A. Steele / Computer simulation of physisorption

’

-25-15

I

-5

I

I

I

5 15 25 ‘II Mb

Fig. 3. The local density of atoms in layer P and in layer as the average number o oms in a given layer and x-direction and width Q.246 A in the y-direction, divided obtained from table 2 by multip results for the smallest groove respectively.

i

i

.

i

P II -7

I

35 -25 -15 -5

2 is shown here. The d in an area of length by the area. (Avera area and surm-ning are for grocrde wicit

I

5

15 25 35

M.J. Bojan, W.A. Steele / Computer simulation of physisorption

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Fig. 4. Time-dependence of the number of atoms adsorbed in the fir?: idyer and in the second layer are shown in the top two panels for the surface wit ized groove. Note t the two plots add up to 144 minus the number of thir ue to a spontaneous transfe e third panel shows tbe changes in population

L402

M.J. Bojan, WA. Steele ,/ Computer simulation of physisorption

with correlation length y, = 6.0 + 0.2 A. Finally, the spacing between the peaks is not given by 21/6uKr_ti = 4.C4 A as one might expect, but by okr_kr. In future work, both the surface coverage and the temperature will be varied and thermodynamic properties such as average potential energy (local and global) and chemical potential will be reported. In this way, we expect to produce a much more detailed picture of the adsorption on these simple heterogeneous surfaces. Support for this work was provided by grant National Science Foundation.

MR 84-19261 from the

[I] D. Nicholson and N.G. Parsonage. Computer Simulation and the Statistical Adsorption (Academic Press, New York, 1982). [2] h4. .?arcniec and P. BrZuer, Surface Sci. Rept. 6 (1986) 65. [3] V. Bhethanabotla and W.A. Steele, J. Phys. Chem., in press. [4] W.A. Steele, Surface Sci. 36 (1973) 317.

Mechanics

of