MODELS FOR HIGH ENERGY ION INDUCED DESORPTION OF MOLECULES FROM SURFACES

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MODELS FOR HIGH ENERGY ION INDUCED DESORPTION OF MOLECULES FROM SURFACES

S.-L. Lee, R. Lucchese

To cite this version:

S.-L. Lee, R. Lucchese. MODELS FOR HIGH ENERGY ION INDUCED DESORPTION OF

MOLECULES FROM SURFACES. Journal de Physique Colloques, 1989, 50 (C2), pp.C2-231-C2-

236. �10.1051/jphyscol:1989237�. �jpa-00229435�

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suppl6ment au n 0 2 , Tome 50, f6vrier 1989

MODELS FOR HIGH ENERGY ION INDUCED DESORPTION OF MOLECULES FROM SURFACES

S.-L. LEE and R.R. LUCCHESE

Department of Chemistry, Texas A and M University, College Station, TX 77843, U.S.A.

Resume'

-

Oe: c a l c u l s c l a s s i q u e s d e t r a j e c t o i r e s d e m o l e c u l e s d e s o r b e e s d e s u r f a c e s s o n t c o n s i d e r e s . U n e c h a l n e l l n e a l r e d ' o s c l l l a t r u r : I n h a r m o n i q u r s r s t u t i l i s P P p o u r m o d e l i s e r l e s y s t e r n e . D e s r e s u l t a t s p o u r l e m e c a n i s m e " p o p c o r n ' e t p o u r l a d e s o r p t i o n t h e r m l q u e s o n t d o n n e s . D a n s l e s d e u x c a s l e m e c a n i s m e p r i n c i p a l p o u r l a d e s o r p t i o n s ' a v e r e @ t r e l e c o u p l a g e d u m o d e d ' e x p a n s i o n d u s y s t k m e a u m o d e d e d e s o r p t i o n .

Abstract - Classical trajectory calculations of the desorption of large molecules from surfaces are considered. A linear chain of anharmonic oscillators is used to model the system. Results for the "popcorn" mechanism and for thermal desorption are given.

In both cases the main mechanism for desorption is found to be the coupling of the expansion mode of the system to the desorption mode.

1 - INTRODUCTION

The interaction of high energy ions with energies on the order of MeV's per amu and solids is known to produce a number of secondary ions which are desorbed from the surface of the solid /l/. This phenomena has been successfully exploited in the mass spectrometry of large molecules (masses in excess of 10,000 amu) where the molecule of interest is initially adsorbed on the surface of the solid and the passage of the primary ion through the solid induces the desorption of molecular ions of the molecule. The mass of the molecules can then be measured in a time-of-flight mass spectrometer /2/.

There are four processes which are important in the desorption of these molecular ions. They are (1) the initial electronic excitation of the solid by the primary ion, (2) the decay of the electronic excitation into excitation of the translational motion of the nuclei, (3) the dynamics of the nuclear motion which lead to desorption, and (4) the ionization of the molecule /3/. In this paper we will be concerned with process ( 3 ) , namely the motion of the nuclei. We will study the nuclear motion using a linear chain of anharmonic oscillators as a simple model of the systems of interest. Of particular interest will be the precise nature of the motion of the nuclei which leads to desorption, what the internal and translational energy distributions of the desorbed molecules are, and how the assumed initial distribution of the nuclear vibrational energy effects the desorption process.

We will consider two different sets of initial conditions which model differing assumptions about the ejection process. The first set of initial conditions will be used to study the

"popcorn" mechanism which has been proposed by Williams and Sundqvist / 4 , 5 / . In this model it is assumed that the molecules which are desorbed by the primary ion receive all of their vibrational excitation in a time period which is short compared to the period of the lowest frequency motion of the molecule. With this assumption we then use classical trajectories to see how the molecule responds to this sudden increase in vibrational energy. These systems are found to expand rapidly due to the anharmonic nature of the interactions and this expansion mode is strongly coupled to the desorption mode which leads to desorption of the

~nolecule from the surface in much the same manner as an exploding kernel of popcorn acquires kinetic energy when it is popped.

The second set of initial conditions corresponds to a thermal model of the desorption

process / 6 / . In such a model it is assumed that the vibrational effects due to the passage of the primary ion can be described by a local temperature which is a function of time and position. For simplicity one usually assumes that the ion passes through the solid normal to the surface so that the temperature profile has cylindrical symmetry. The temperature profile chailges in time according to the thermal diffusivity of the material. Then a molecule at some distance r from the center of the excitation, i.e. from where the primary ion passed through the solid, will feel a time dependent temperature jump T(r, t) which determines the behavior

o f the systen?. We have previously shown that experimental ~iiolecular ion yields /7/ are

consistent with this model when we assume that the desorption is an activated process and that

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1989237

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only the molecules leaving from the surface (or from only a few layers near the surface) form molecular ions. To model these conditions, we use stochastic classical trajectories which are driven by an appropriate temperature rise /8/. With this model we find that the energy transfer to the internal degrees of freedom of the molecule is very inefficient and that the primary mode of desorption is due to coupling between fluctuations in the size of the chain of anharmonic oscillators representing the surface and the desorption mode of the chain

representing the desorbing molecule.

2

-

^METHOD

We have modeled the desorption of a large molecule from a surface using a one dimensional chain of anharmonic oscillators where the equations of motion are of the form /8/

d 2 X.

avi. i+l avi-l. i

m i 2 = - ax. - axi for i = 1, . . a , N dt

and

where f(t) is a white-noise Gaussian random force and y is a friction coefficient which is related to f(t) through a fluctuation-dissipation theorem

where k is Boltzmann's constant and T (t) is the temperature of the surface at time t. The interacEion potentials are assumed to 2e Morse oscillators of the form

2 V. l , i+l (xi, xi+l) = [exp [-ai (xi+l- X.

-

*X. ) 1-11

1 1 ( 4 )

where a. and Di are parameters and Axi is the equilibrium separation. Note that xal= 0.

For the simulation of the popcorn mechanism, we have ignored the effects of dissipation of energy into the surface by not allowing the position of the first atom, xo, to change. In these simulations we assume some initial effective temperature of the molecule -and we assume that initially,the atoms are at their equilibrium positions. We choose the initial velocities randomly from a thermal distribution of a harmonic oscillator which has the same small

amplitude frequency as the Morse oscillator. The temperature of this distribution is that which is initially assumed for the system. Thus the initial conditions for the popcorn simulation are such that there is on average no center of mass motion but there is excitation of all of the other modes of the system.

For the thermal model a time dependent temperature profile is assumed. One choice for this profile is the Mozumder form /9/

where To is the initial temperature at the temperature of an assumed cylindrically symmetric excited region which is characterized by a radius ro, r is the distance of the molecule which is being simulated from the cent5r

of

the excited region, and 6 is the thermal diffusivity which we have taken to be 8.63

A

ps

.

This temperature profile has been used previously to describe the time and position of the vibrational excitation caused by the passage of a high energy ion /7/. An alternative temperature profile which we have used is a simple exponential form

The heating equation given in Eq. (6) has also been used previously to simulate the desorption dynamics of small systems using the stochastic trajectory method /8/.

3 - m O R N MODEL

In Figs. 1 and 2 we present the results of a simulation of the popcorn model using a chain of 40 oscillators /5/. The values of the paramefers were as follows: Do = 0.217 eV, a. 1.05 A-l , Ax ⁼2.667

A,

D. = 1.07 eV, a.= 1.20

A-

, and Ax. = 1.333

A,

mi = 150 amu, for 1 =

1, ^{0 .}, 4 8 . These paraketers yield alresonable model ofla polypeptide of mass 6000 amu. The

average initial energy per mode is 0.1 eV in these simulations. Of the trajectories run with these parameters, 7127% escape the surface in 25 ps with a mean center of mass kinetic energy of 0.13820.016 eV. The results in Fig. 1 show that the center of mass of the molecule, xcm,

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varies as a function of time in these simulations. One can see clearly by comparing Figs. 1 and 2 that the acceleration of the center of mass is accompanied by the expansion of the molecule.

The importance of the expansion to the desorption can also be seen by considering the

probability of desorption when there is no expansion. We have run a set of trajectories where the well depths have been deepened while retaining the same normal mode frequencies of the system. This leads to a nearly harmonic description of the adsorbed molecu e In these simulations the values of the parameters were Di--26.75 eV and a.

-

^0.24

^A-'

iith all other parameters as given above. As can be seen from Flg. 2 this model leads to no size expansion and is found to lead to only 2122% desorption in 25 ps.

-IS ⁰

-

⁵

Time

¹⁰

( psec

^l5

)

²⁰ ²⁵

Fig. 1

-

Time evolution of the average center of mass velocity for trajectories run using the anharmonic model for the popcorn mechanism.

0 5 10 l5 20 25

Time ( psec )

Fig. 2

-

Time evolution of the average molecular size of the popcorn model for molecular desorption. desorbed trajectories of anharmonic model;

- -

- trapped trajectories of anharmonic model; -.-v- trajectories of harmonic model.

These results can be interpreted by considering a separation of the motion of xcm.from the internal modes of the system. Using this Born-Oppenheimer type separation of variables is justified by the fact that the center of mass motion is much slower than the motion of the

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other modes. Then the initial conditions of the popcorn model correspond to an excited internal state for which the equilibrium X is somewhat larger than the value at the beginning of the trajectory which is the e88ilibrium value when there is no internal excitation. Thus from the perspective of the center of mass coordinate, the system is initially high up a potential well which is determined by the degree of internal excitation for which the minimum is at a larger value of X Then the effective force on the center of mass due to this potential well increases the c ~ ~ t e r of mass kinetic energy to such an extent that the system can break the surface bond and the molecule is desorbed. This picture is analogous to what happens when a diatomic molecule is fragmented by the absorption of a photon leading to a dissociative electronic state of the molecule.

4

-

^THERMAL^MODEL

For trajectory models appropriate to thermal desorption we wish to emphasize the relative frequencies of the different oscillators so that we will specify the model by giving the the force constants of interaction potential V-+1

.

in terms of the frequencies in wave numbers of an isolated oscillator with this po$enti&l energy and with particles with the same mass as is used in the full model. These frequencies are related to the a's by

where for the thermal models all the masses will be taken to be 15 amu.

Here we are interested in two aspects of the thermal model for high energy ion induced desorption of molecules. The first aspect we will consider is how do the internal modes of a molecule become excited when the molecule is adsorbed to the surface. We will assume that the molecule is weakly bound to the surface in comparison to the internal bonds of the molecule.

At the same time we will assume that the weak surface bond also has a smaller force constant which leads the motion associated with the surface bond being of low frequency. In Fig. 3 we

oscillator gpains where we have taken D- = 10. eV, eV, v = 95 cm , Ax ⁼2.667, and D.= 4.163 eV,

, 3 9 0 The teypera@ure profile of the random force

with To = 10 K and r = 2.5 r

.

The value of -y of results given in Fig. 3 illusgrate the general behavior of weakly coupled systems /8/. The surface atom, i.e. the atom at xo, heats up rapidly and in general closely follows the time dependent temperature given in Eq. (5) which is used to compute f(t) in Eq. (2). The internal vibrational temperature is seen to respond only slowly to the excitation of the surface atom. Thus as long as the desorption mechanism is rapid compared to this relatively slow internal excitation, the internal energy of the molecule can be much cooler than the temperature of the surface at the time of desorption.

0.00

0 50 100

Time (

PS

)

Fig. 3 - Typical temperature profile of a linear chain of anharmonic oscillators coupled to a Mozumder temperature jump. Solid and dotted histograms are the kinetic energy of the surface atom and the mean kinetic energies of the rest of the atoms in units of To. The smooth dotted curve is the driving temperature given by Eq. (5).

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atoms interacting by Morse potentials. The first 5 atoms repfesent the surface and are governed by the potential parameters D. = 10 eV, Li--2776 cm a , Ax

-

3.0 Alfor i = -1,-*.,3.

The interface bond has the parameters h4= 0.217 eV, v4= 178 cm-' o$ 600 cm

,

and

Ax4= 2.667

A.

The molecule has the potential parameters D. = 4.163 eV, vi= 2000 cm -1

,

and Axi= 1.333

A,

for i = S,**-,44. The temperatyre jump was koverned by Eq. (6) with parameters To = 30,000 K and t

-

l ps. With 178 cm- we found'that the mean kinetic energy of the desorbing m lecules was 3.35 eV and the mean internal excitation was 0.08 eV per mode. With v = 600 cm-' we found that the mean kinetic energy of the desorbing molecules was 2.19 eV and tke mean internal excitation was 0.16 eV per mode. The differing levels of internal

excitation show that the lower frequency interface bond couples the molecule to the surface less well than the higher frequency interface bond. This is in agreement with an exponential gap law for the energy transfer process /10/. The trend in the center of mass kinetic energies can be qualitatively understood by reversing the argument we have given for the trend in the internal excitations. Thus the lower the frequency of the interface bond the better the motion of the surface will couple to the low frequency center of mass motion of the molecule.

In Fig. 4 we give the time dependence of the variables x4 and x5 in the time interval during which the molecule acquires the center of mass kinetic energy needed to desorb. The

trajectory plotted here is typical trajectory using the parameters given in the preceding paragraph with

C4 -

^{l78 cm-'}

.

One can see from this figure that the size of the surface is

subject to large fluctuations particularly at -2.8 ps and -3.5 ps. In response to these size fluctuations of the surface, the adsorbed molecule is pushed away from the surface and acquires enough kinetic energy to desorb.

2.5 3.0 3.5

Time ( ps )

Pig. 4

-

Thermal desorption trajectory for 45 atom model system with i4 = 178 cm-'.

-

^x5;

a . . .

X4.

5

-

CONCLUSIONS

We have seen that the underlying mechanism for both the popcorn model and the thermal model for high energy ion induced desorption of large molecules is the efficient coupling between size fluctuations of extended systems and the mode for desorption of the large molecule. In both cases the anharmonicity of the underlying oscillators provides an efficient coupling mechanism between the energy in the high frequency modes and the low frequency expansion modes. Further studies will need to consider what the length scale of the size fluctuations is which determines the desorption dynamics and what the effects are of going to three dimensions from one dimension which is used in the model studies reported here.

ACKNOWLEDGEMENTS

Acknowledgement is made to the Dow Chemical Company Foundation, to the Monsanto Company, and to the Celanese Chemical Company for partial support of this research. This research is based upon work in part supported by the National Science Foundation under Grant CHE-8351414.

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/5/ Lee, S.-L. and Lucchese, R.R., Surf. Sci.

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/7/ Lucchese, R.R., J. Chem. Phys.

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/8/ Lucchese, R.R. and Tully, J.C., J. Chem. Phys. 81 (1984) 6313.

/9/ Mozumder, A., Adv. Radiat. Chem.

1

(1969) 1.

/10/ Zare, R.N. and Levine, R.D., Chem. Phys. Lett. 136 (1987) 593.