Molecular Dynamics Study of Nanoparticle Collision with a Surface – Implication to Nanoparticle Filtration

Collision dynamics of nanoparticles with a surface was studied by classical molecular dynamics simulations. Silver, nickel and silica were selected as the particle materials, and silver as the surface material. Particle sizes ranged approximately from 0.5 to 2 nm. The results indicate that particles with thermal energy at room temperature do not bounce off a surface, even when a very weak interaction potential between the particles and the surface is assumed. The loss mechanisms of the center-of-mass energy of nanoparticles colliding with a surface were also investigated. The findings indicate that energy losses to the surface and the rotational degree of freedom are important. The loss to the surface is significant when a harder particle hits a softer surface. This is because the center-of-mass energy is mainly transferred to the surface as elastic energy, and the energy is not effectively transferred back to the particle. Non-spherical silica particles were found to lose more energy than the other types of particles. This phenomenon is due to a large energy transfer to the rotational degree of the freedom upon collision.


INTRODUCTION
The collision of nanoparticles (particles smaller than approximately 50 nm in diameter) with surfaces is relevant to many practical applications.Examples are the nanoparticle collection after they are synthesized in chemical reactors or emitted from mobile/stationary combustion sources, micro-contamination control in semiconductor processes, and worker protection in industrial hygiene.Filtration is a typical technique for particle control and removal.According to the traditional single-fiber theory the filtration of nanoparticles is an easy task due to the high diffusion coefficient of nanoparticles.On the other hand, it is a fact that filters cannot remove air molecules.In order to bridge the gap between particle and molecule sciences, Wang and Kasper (1991) argued that nanoparticles smaller than certain sizes might penetrate filters by bouncing off the filter surfaces due to their thermal velocity (thermal rebound).It could represent a serious problem because more evidence indicates that nanoparticles have serious adverse health effects (Donaldson, et al., 1998).The main motivation of this study is to assess the possibility of nanoparticle penetration through filter media.
The stickiness of nanoparticles on a filter medium surface depends on the loss of center-ofmass energy of the incident particles due to the collision.The energy loss mechanisms include the transfer of incident energy to the rotation, vibration, and deformation of the particle, and energy transfer to the impact surface.The significance of each mechanism is thought to depend on parameters, such as the incident energy, particle-surface interaction, elastic properties of particle and surface, and particle characteristics.Such energy loss mechanisms are, however, not yet well understood in the incident velocity ranges of interest (up to a few hundred meters per second).
The impact of micron-sized particles with a surface for a relatively low incident velocity (typically less than 100 m/s) has been studied for years.Several macroscopic models have been proposed to explain energy loss mechanisms upon the collision.Many studies have attributed the main energy loss to the plastic deformation of a particle and/or a surface (Bitter, 1963;Rogers and Reed, 1984;Reed, 1989;Wall et al., 1989Wall et al., , 1990;;Tsai et al., 1990;Xu and Willeke, 1993;Andres, 1995).Tsai et al. (1990) also included the energy loss due to the plastic deformation of surface asperities and showed that this energy loss can be significant.On the other hand, Brach and Dunn (1995) and Li et al. (1999) argued that the strain rate due to such a collision is too high for the plastic deformation and suggested a completely different model based on the model Hunt and Crossley (1975).Their model assumes that energy is mainly dissipated in the heat forms during the collision.In all the models described above fitting parameters were usually included and determined by the comparison with experiments.The ratio of the rebound particle velocity to the initial velocity was the main quantity measured in experiments (for instance, Dahneke, 1972Dahneke, , 1973Dahneke, , 1975;;Wall et al., 1990;Dunn et al., 1995;Li et al., 1999).A typical behavior of the ratio as a function of the incident velocity is that after the incident velocity exceeds the critical value for rebound the ratio increases rapidly with the increase of the initial velocity and then levels off.Particularly interesting is that this behavior can be explained by two completely different models: the model by Brach and Dunn (1995) and, say, the one by Wall et al. (1990).This seems partly because the quality of existing experimental data is not good enough to determine the main energy loss mechanism.On the other hand, one can also argue that any of the existing models are not comprehensive.
For nanoparticle filtration or bounce, several experimental studies have been reported.Otani et al. (1994) measured the particle penetration through a wire screen and a circular tube using silver particles with a size down to 1 nm.They observed that the penetration of particles of 2 nm or smaller through the tube was larger than that predicted by Gormley and Kennedy (1949), while the penetration through the wire screen agreed well with the prediction by Cheng and Yeh (1980).
They attributed the discrepancy to the thermal bounce of particles from the tube's inner surface.Alonso et al. (1997) also performed a similar experiment using particles as small as 2 nm and ions (1.36 nm).Their results, however, agreed well with the theoretical prediction given by Gormley and Kennedy (1949) and Cheng and Yeh (1980).They argued that the seemingly higher penetration observed by Otani et al. (1994) was probably caused by the unreliable sizing of test particles.
As just described, particle-surface collision dynamics is not yet well understood for a wide range of particle sizes.In this study, the collision dynamics of nanoparticles (0.5-2 nm) with a surface was investigated using the classical molecular dynamics simulation.The incident velocity of particles was in the range of 10-1000 m/s.The microscopic approach was employed because macroscopic approaches may not be appropriate when phenomena occurring in the nanometer scale are described.There are two primary objectives in this study.The first one is to explore the possibility of the thermal rebound when nanoparticles are impacted on a surface.The second is to study the main energy loss mechanisms of nanoparticles during the collision.Detailed information obtained by the simulation facilitates understanding the collision dynamics of nanoparticles and exploring the possibility of particle thermal rebound.

MODELS FOR THERMAL REBOUND BY WANG AND KASPER (1991)
As mentioned in the previous section, many experimental studies show that there is a critical velocity for particle bounce, below which all particles stick to a surface.Many models have been proposed in order to predict the critical velocity.Wang and Kasper (1991) derived the following equation: where V cr is the critical velocity, E ad the adhesion energy of a particle with a surface, m p the particle mass, and e the coefficient of restitution.The coefficient of restitution was defined as: where KE cm,i is the initial center-of-mass energy of the particle, and L the energy loss in the impact.
For the adhesion energy, two different types were used.One is the Bradley-Hamaker (B-H) adhesion energy, which considers the van der Waals energy between the particle and the surface, and is proportional to the particle diameter, d p .If this adhesion energy is assumed, the critical velocity will become inversely proportional to the particle diameter for a spherical particle.The other type of adhesion energy is based on the JKR theory (Johnson et al., 1971), which considers deformation of the particle.According to the theory, the adhesion energy is proportional to d p 4/3 .
Therefore, substituting the adhesion energy into Eq. 1 leads to the critical velocity proportional to d p -5/6 .
On the other hand, the mean thermal particle velocity is proportional to the square root of the particle mass, namely, proportional to d p -1.5 for spherical particles.The mean thermal velocity increases more rapidly with decreasing diameter than the critical velocity above.Wang and Kasper (1991) thus argued that it is possible for the thermal velocity to exceed the critical velocity in the nanometer size range.This situation is illustrated in Fig. 1.

General description
In this study, the classical molecular dynamics (MD) simulation was used to study nanoparticle-surface collision dynamics.A typical particle-surface system is shown in Fig. 2 (a).
It is not our intension, however, to study the collision dynamics for a particular particle-surface combination.Instead, the purpose is to gain a general knowledge of the nanoparticle-surface collision.In order to achieve this goal, a hypothetical interaction potential between a particle atom and a surface atom was employed.This choice will be explained later in detail.
Fig. 2(a).An Ag55 particle (consisting of 55 silver atoms) and a silver surface (1440 atoms) used for the molecular dynamics simulations.
In the MD simulation, the following quantities as a function of time were extracted from the trajectories of atoms: (1) the particle trajectory; (2) the kinetic energy of nanoparticle and surface (including translational, rotational, and random motion energy); (3) the potential energy of the particle and surface; (4) the potential energy between the particle and surface.These quantities were investigated in this study as functions of the particle incident velocity, particle size, interaction potential between particle and surface atoms, particle and surface materials, and the system temperature.Special attention was paid to identify the favorable conditions for particle recoiling from the surface.Furthermore, the following assumptions were made in the simulation: (1) the impact occurs at a right angle relative to the surface; (2) the surface and particle are electrically neutral before and after the impact; and (3) the surface is smooth and free of contamination before the impact.

Particle and surface materials, and interatomic potentials
Silver material was selected as the primary particle and surface materials.This choice is partly because silver particles have normally been included in experimental studies on nanoparticle filtration, and partly because the interatomic potential for silver is well-established (Cleri and Rosato, 1993).The potential form was originally derived using quantum mechanics (e.g., Gupta, 1981), and parameters included in the potential were determined by experiments (Cleri and Rosato, 1993).The potential, called a tight-binding (TB) potential, is expressed as: The equation indicates the potential energy of an atom i by the surrounding atom j.In the equation, r ij is the distance between atoms i and j, and r 0 is the first-neighbor's distance in a lattice of a metal.The parameters, ξ q, A t , and p are different for different transition or noble metals.The values for silver and nickel are given in Table 1.The forces exerted on atoms are obtained by taking the derivative of Eq. ( 3).The tight-binding potential is non-linear in nature.
As proposed by Cleri and Rosato (1993), surrounding atoms up to the 5 th neighbors were considered in the potential calculations.
The same tight binding potential could be used between a particle atom and a surface atom.
However, for the reason described above, a hypothetical Lennard-Jones (LJ) type potential was used instead: where ε is the energy parameter, σ the length parameter, and r ij the distance between atoms i and j.The potential has a minimum of ε at r ij = 2 1/6 σ The potential energy of an atom i is obtained by summing up V LJ (r ij ) over surrounding atoms, j.The choice of this potential made it possible to study the dependence of collision dynamics on the strength of the interaction force between the particle and surface.To reduce the simulation time, it is a common practice to truncate the LJ potential at a distance of 2.5σ.However, the truncated LJ potential and force will have a discontinuity at 2.5σ, causing numerical instabilities.In order to overcome this difficulty, the following shifted-force L-J potential (Allen and Tildesley, 1987) was used: where V LJ (r ij ) is the LJ potential defined in Eq. ( 4), and r c the cut (truncated) distance (r c =2.5σ).
In addition to silver, nickel and silica were used as particle materials in our study.For nickel, the TB potential with parameters shown in Table 1 was used.An empirical interatomic potential developed by Tsuneyuki et al. (1988) and Guissani and Guillot (1996) was used for silica.
Between a nickel (or silica) particle atom and a silver surface atom, the hypothetical potential given by Eq. ( 5) was again used.

Parameters studied in the simulation
The ranges of parameters involved in the simulation and the particle/surface materials are summarized in Table 2.As for the surface direction, the Ag(111) surface was employed.For reference, an energy parameter of 0.02 eV is about the same as the one between Xenon atoms, and the parameter of 0.125 eV is of the same order as that between metal atoms (Blömer and Beylich, 1999).The length parameters, σ, in the LJ potential for each particle-atom/surface-atom combination are given in Table 3.For the silver/silver and nickel/silver combinations, the σ's were determined so that the potential has a minimum at the average of the nearest neighbor distances of the particle and surface materials in a bulk phase.For the oxygen/silver and silicon/silver combinations, the σ's were obtained from the van der Waals radii proposed by Huheey et al. (1993).
The silver and nickel particles used have an icosahedral structure, which is one of the stable structures of these particles in the size range studied.The shape of a silica particle was obtained by cooling the particle rapidly from its liquid phase.It is non-spherical, as shown in Fig. 2 (b).

Boundary conditions for surface domain
The surface domain for the simulation was composed of ten or more atomic layers, each of them containing a few hundred atoms.The numbers of layers and atoms in each layer depended on particle size.Periodic boundary conditions were used in the directions parallel to the surface.
In the perpendicular direction, three bottom layers were fixed at the equilibrium position of the bulk material and served as the cell boundary.The sizes of simulated surfaces were chosen so that its further increase would not change the simulation results.The size of the surface domain is summarized in Table 4.

Simulation procedure
The equations of motion were integrated numerically with a typical time step of 2 femtoseconds (fs).The Verlet velocity algorithm (Allen and Tildesley, 1987) was used for the integration.The choice of time step depended on the system studied.The time step is determined to ensure the energy of the system is conserved (the fluctuations of total energy were typically less than 1 ppm).
In the simulation, the particle and surface were first equilibrated independently at a certain temperature (mainly 298 K).After the equilibration, the particle's initial orientation was chosen randomly, and its initial position parallel to the surface was chosen randomly in the unit cell located at the center of the surface.In the vertical direction, particle was initially placed outside the interaction range from surface atoms.The initial velocity of the particle was then assigned.
The direction of the initial velocity was normal to the surface.No rotational motion was initially given to the particle.The position and velocity of the atoms of the particle and surface were recorded during the entire simulation period.The obtained data were then analyzed to archive the desired information; e.g., the particle trajectory, the kinetic and potential energies.
For a given particle and surface system, ten microscopically initial states were prepared.At least ten runs were performed for each simulation condition using these states.The bounce probability as the function of simulation parameters was obtained from these multiple runs.The particles were considered to stick to the surface if the particle velocity normal to the surface changed its sign (or direction) twice.The critical velocity (or energy) for particle bounce was defined as the velocity (or energy) for 50% bounce probability.

Collision of Ag particles with an Ag surface
This section presents the simulation results of a particle consisting of 55 silver atoms (Ag55) colliding with a silver surface at 298 K.The Ag55 particle and the surface are shown in Fig. 2 (a).
Fig. 3 shows an example of the particle trajectory in the direction perpendicular to the surface.It is for a particle with the initial velocity (V cm,i ) of 170 m/s and with an energy parameter (ε) of 0.05 eV.Since the z-axis (vertical to the surface) points from the surface to the particle, the particle has a negative velocity initially.Clearly, the particle bounces in this case.The magnitude of the particle final velocity is less than that of initial velocity, indicating that a part of the centerof-mass energy was lost.The bounce probability of Ag55 particle from the silver surface as the function of initial velocity is shown in Fig. 4. For the case of ε = 0.125 eV, the particle sticks to the surface regardless of its initial velocity.For the case of ε = 0.02 eV, there is the velocity below which the particle sticks to the surface.Above the velocity, the bounce probability increases rapidly, reaching unity at approximately V cm,i = 100 m/s.This behavior is similar to that reported for micron-sized particles (e.g., John, 1995).The bounce probability for ε = 0.05 eV shows strange behavior.For initial velocities less than 170 m/s, the bounce probability shows similar behavior as that for ε = 0.02 eV; however, the bounce probability decreases as the initial velocity increases beyond 170 m/s.In order to investigate this strange behavior, the energy changes of the particle and the surface throughout the simulation period were examined.The kinetic and potential energies of the particle for V cm,i = 170 m/s and ε = 0.05 eV as the function of time are shown in Fig. 5 (a).The kinetic energy is divided into four components: the center-of-mass energy (translation energy) in the vertical direction, KE cm ; the center-of-mass energy in the horizontal direction, KE cm,h ; the rotational energy, KE rot ; and the random-motion and vibration energy, KE rand,vib .KE rand,vib is defined as: where KE p is the total kinetic energy of the particle.As seen in the figure, the center-of-mass energy (in the vertical direction) becomes zero at the elapsed time (t) of about 3700 fs, then goes up and down, and eventually reaches a constant value.The particle potential energy, PE p , has a temporal increase at t = 3000 -4500 fs, coinciding with the time of the collision.The potential energy increase is attributed to particle deformation due to the collision.The subsequent decrease indicates that the particle regains its original shape after the collision.A case for V cm,i = 500 m/s and ε = 0.05 eV is now addressed.The particle and surface energies as the function of elapsed time are shown in Fig. 6 (a) and (b), respectively.In this case, the center-of-mass energy of the particle eventually becomes zero; namely, the particle sticks to the surface.The distinct difference from the previous case is that the particle potential energy increases by the collision and remains the same afterward.This behavior indicates that the particle deforms permanently.It is also seen that the random-motion and vibration energy increases.Fig. 6(b) also shows that surface vibration is excited due to the collision.It is clear from the results that the decrease in the bounce probability for ε = 0.05 eV is due to energy consumption caused by permanent particle deformation and surface excitation.111) surface (from Kleyn, 1997).
In order to understand the collision dynamics in detail, the energy loss mechanism was investigated.It has been found that a relatively large amount of energy is lost to the horizontal and rotational degrees of freedom, even though the particle does not originally have energies in these degrees of freedom.The energy transfer to the rotational degree is the largest for the largest particles (Ag309).It can account for as much as 60% of the total energy loss.This energy transfer occurs partly because the surface is not completely flat in the atomic scale, and partly because the particles are not completely spherical.
It has also been found the energy loss of the Ag13 particles is mostly due to the energy transfer to the surface, which is not significant for the Ag55 and Ag309 particles.To understand why the Ag13 particles lose more energy to the surface, the energy changes during collision are plotted in Fig. 8 (a) and (b) for the Ag13 and Ag55 particles, respectively.The plots show typical results for each particle size when little permanent deformation of the particle occurs.In the figures, the "particle internal" refers to the particle total energy minus the particle rotational and center-ofmass energies (namely, the sum of the random-motion, vibration, and deformation energy).The "surface" stands for the surface total energy.Except for the vertical center-of-mass energy, the changes from the initial values are shown.As can be seen in Fig. 8 (a), the center-of-mass energy of the Ag13 particle is mainly transferred to the surface as elastic energy upon collision, and that only a small portion of it is recovered when the particle rebounds.The less energy transfer to the particle internal energy is probably due to the fact that the Ag13 particle does not have many internal degrees of freedoms, compared to the surface or the other particles.In other words, the Ag13 particle behaves like a "spring" with a larger spring constant: the center-of-mass energy is mainly stored as the elastic energy of the surface that has a smaller "spring constant."In the rebound phase, the energy stored in the surface was not completely recovered because of the incompatibility of the "spring constants" (i.e., differences in frequencies of vibration motion).
The explanation using the imaginary springs seems justified by the results for the Ag55 particles.
As can be seen in Fig. 8 (b), the surface energy and particle internal energy increase by almost the same amount upon collision.Most of these energies are recovered in a similar manner when the particle rebounds.This observation can again be explained using the concept of imaginary springs: the Ag55 particle has enough internal degrees of freedom so that it behaves like a spring whose spring constant is the same as that of the surface.

Particle material dependence (a) Ni particles
If the imaginary spring description proposed in the previous section is valid, particles harder than a surface should lose a relatively larger amount of energy by the collision.In order to test this hypothesis, the collision of nickel particles (Ni13, Ni55, and Ni309) on a silver surface was simulated.The bounce probability as the function of the ratio of initial kinetic energy to the adhesion energy (KE cm,i / E ad ) is shown in Fig. 9.All of the probability curves of the Ni particles are positioned to the right of the curve for the Ag55 particle, which indicates more energy losses for the Ni particles.

(b) Silica particles
The impaction of a silica particle on an Ag surface was also simulated.The silica particle consisted of 36 oxygen atoms and 18 silicon atoms (Silica54).The particle has a non-spherical shape as shown in Fig. 2 (b).Therefore, the possible effects of a non-spherical shape on the collision dynamics can be investigated in this simulation.
The bounce probabilities of the silica particle for ε = 0.008 eV, and 0.02 eV are shown in Fig. 11.The bounce probability curves are positioned to the far right of that for the Ag55 particle, indicating larger energy losses.On the other hand, it is noteworthy that the bounce probability for ε = 0.008 eV has a relatively long tail at the low-energy side.Fig. 12 (a) and (b) show the energy changes of the silica particle during the collision for two different particle initial velocities.As can be seen in these plots, the rotational excitation upon impact is significant in both the cases.In the case shown in Fig. 12 (a), the particle rotates on the surface and has multiple collisions with the surface.The rotational energy gained by the first collision is transferred to the surface by the multiple collisions in a stepwise manner.Therefore, it can be said that the energy losses to the surface are mediated by particle rotations.This phenomenon is similar to the "rotation mediated adsorption" of a diatomic molecule to a surface (Kuipers et al., 1989a(Kuipers et al., , 1989b)).The large energy loss of NO molecules colliding on a Pt(111) surface (see Fig. 7 (b)) could be explained by this phenomenon (Kleyn, 1997).Therefore, particle rotation is actually a key in understanding the large energy loss of the silica particle.transferred back to the center-of-mass energy.However, this phenomenon is rare, as also implied by Kuipers et al. (1989b) for diatomic molecules.Incidentally, Fig. 11 shows that, although the probability is low, the silica particles can bounce at a relatively low KE cm,i / E ad .It was found that this is caused by large variations of the adhesion energy due to their non-spherical shape.Namely, the adhesion energy can be very low, depending on the particle orientation, thus causing occasional particle bounce.

Temperature dependence
The results so far indicate that thermal rebound is unlikely under the simulated conditions (see Fig. 7(a)).However, thermal rebound can happen at higher temperatures if the bounce probability is not affected by the temperature increases.Simulations at a temperature of 500 K were performed to investigate the possible temperature effects.According to Lifshitz (1956), the van der Waals interaction is not affected by temperature if the separation distance is small compared to hc/(2πkT) (h: plank constant; c: speed of light; k: Boltzmann constant; T: absolute temperature).Thus, the interaction potential between the particle and surface atoms was assumed to be unchanged.Fig. 13 shows the bounce probabilities of the Ag55 particles at 500 K, along with the results at 298 K.The probability curve is less sharp at 500 K.This trend is the same as that for the collision of Ar atoms with a Pt(111) surface (Rettner et al., 1990), which is caused by a broadening of the relative velocity between the particle and the surface due to greater thermal motion of particle and surface atoms.More importantly, the results indicate that the critical energy for particle bounce remains unchanged.This implies that thermal rebound may be possible at a higher temperature.However, this issue is not so straightforward, since the material properties can be different at higher temperatures.

CONCLUSION AND FUTURE WORK
Collision dynamics of nanoparticles with a surface was studied by classical molecular dynamics simulations.Silver was mainly used as particle and surface materials.As for particle materials, nickel and silica were also employed.Approximate particle sizes ranged from 0.5 to 2 nm.The results show that the particles with thermal energy at room temperature do not bounce off a surface, even when a very weak particle-surface interaction potential is assumed.It therefore seems unlikely that thermal rebound can be a serious problem in nanoparticle filtration at room temperature.It should be mentioned that a small fraction of particles with high energy always exist due to the Maxwellian energy distribution, and can therefore bounce off filter surfaces.However, such a fraction is typically less than 0.01% at room temperature under our simulation conditions.
The mechanisms of the center-of-mass energy losses of nanoparticles were also investigated.It was found that energy losses to the surface and the rotational degree of freedom are of great importance.These losses have typically not been considered in studies on micron particle collision with a surface.The loss to the surface is significant when a harder particle hits a softer surface.This is because the center-of-mass energy is mainly transferred to the softer surface as elastic energy, and the energy is not effectively transferred back due to differences in mechanical behavior between the particle and surface.A very small particle, such as the Ag13, also behaves like a harder particle due to small degrees of freedom, and loses more energy to the surface than larger particles.Non-spherical silica particles were found to lose more energy than the other types of particles, due to an effective energy transfer to the rotational degree of freedom.The rotational energy is usually not transferred back to the center-of-mass energy, and is mainly lost to the surface via multiple collisions.By the way, only particles incident perpendicularly to the surface were considered in the simulations.The current results could be applied to particles with different incident angles by considering the normal component of the center-of-mass energy of such particles.
The simulations at a high temperature (500 K) show that the critical energy for particle bounce is unaffected by the temperature increase.This result suggests that thermal rebound might be possible at high temperatures.Moreover, there is the possibility that particles weakly bound to a surface leave it due to thermal fluctuations, like molecules do (Frenkel, 1947;Kuipers et al., 1988).This phenomenon could present a serious problem in nanoparticle filtration, and should be addressed in the future.

Fig. 1 .
Fig. 1.Illustration of thermal rebound.The thermal velocity increases more rapidly than the critical velocity as the particle diameter decreases.The critical velocities using both the B-H model and the JKR model are shown (from Wang and Kasper, 1991).

Fig. 3 .
Fig. 3.A trajectory of the Ag55 particle colliding with the silver surface.The left vertical axis shows the center-of-mass (CM) distance from the surface, and the right vertical axis shows the particle CM velocity perpendicular to the surface.The particle initial velocity (V cm,i ) and the energy parameter (ε) are 170 m/s, and 0.05 eV, respectively.

Fig. 4 .
Fig. 4. Bounce probabilities of the Ag55 particle on the silver surface as a function of the initial center-of-mass velocity for ε = 0.02, 0.05, and 0.125 eV.
Fig. 5 (b)  shows the kinetic and potential energies of the surface, KE s and PE s .Both energies show a slight increase upon collision.Overall, about 80% of the center-of-mass energy is transferred to other degrees of freedom.The energy loss, however, is not large enough to cause particle deposition onto the surface.

Fig. 5
Fig. 5(a).Particle kinetic and potential energies as a function of time during the collision of the Ag55 particle with the silver surface (V cm,i = 170 m/s, ε = 0.05 eV).The kinetic energy is divided into four parts: vertical center-of-mass energy, horizontal center-of-mass energy, rotational energy, and random-motion and vibrational energy.

Fig. 5
Fig. 5(b).Surface kinetic and potential energies during the collision of the Ag55 particle with the silver surface (V cm,i = 170 m/s, ε = 0.05 eV).

Fig. 6
Fig. 6(a).Particle kinetic and potential energies as a function of time during the collision of the Ag55 particle with the silver surface (V cm,i = 500 m/s, ε = 0.05 eV).

Fig. 6
Fig. 6(b).Surface kinetic and potential energies as a function of time during the collision of the Ag55 particle with the silver surface (V cm,i = 500 m/s, ε = 0.05 eV).

Fig. 7
Fig. 7(b).Bounce probabilities as a function of the initial center-of-mass energy divided by the adhesion energy (KE cm,i / E ad ) for the silver particles colliding with the silver surfaces (ε = 0.02, and 0.05 eV), along with the results for Ar atoms and NO molecules colliding with a Pt(111)

Fig. 8
Fig. 8(a).Energy changes during collision.The vertical center-of-mass energy, and the changes of horizontal center-of-mass energy, rotational energy, particle internal energy and surface total energy from the initial values are shown: (a) the Ag13 particle, V cm,i = 500 m/s, ε = 0.02 eV (KE cm,i / E ad = 7.27).

Fig. 8
Fig. 8(b).Energy changes during collision.The vertical center-of-mass energy, and the changes of horizontal center-of-mass energy, rotational energy, particle internal energy and surface total energy from the initial values are shown: (b) the Ag55 particle, V cm,i = 250 m/s, ε = 0.02 eV (KE cm,i / E ad = 4.23).

Fig. 9 .
Fig. 9. Bounce probabilities as a function of the initial center-of-mass energy divided by the adhesion energy (KE cm,i / E ad ) for the nickel particles colliding with the silver surfaces (ε =0.02, and 0.05 eV), along with the results for the Ag55 particle (ε =0.02 eV).

Fig. 10 (
Fig. 10(a).Energy changes during collision.The vertical center-of-mass energy, and the changes of horizontal center-of-mass energy, rotational energy, particle internal energy and surface total energy from the initial values are shown: (a) the Ni13 particle, V cm,i = 350 m/s, ε = 0.02 eV (KE cm,i / E ad = 2.06)

Fig. 11 .
Fig. 11.Bounce probabilities as a function of the initial center-of-mass energy divided by the adhesion energy (KE cm,i / E ad ) for the Silica54 particles colliding with the silver surface (ε =0.008, and 0.02 eV), along with the results for the Ag13 particles (ε =0.02 eV).

Fig. 12 (
Fig. 12(a).Energy changes during collision.The vertical center-of-mass energy, and the changes of horizontal center-of-mass energy, rotational energy, particle internal energy and surface total energy from the initial values are shown: (a) the Silica54 particle, V cm,i = 350 m/s, ε = 0.008 eV (KE cm,i / E ad = 1.98).

Fig. 12
Fig. 12(b).Energy changes during collision.The vertical center-of-mass energy, and the changes of horizontal center-of-mass energy, rotational energy, particle internal energy and surface total energy from the initial values are shown: (b) the Silica54 particle, V cm,i = 750 m/s, ε = 0.008 eV (KE cm,i / E ad = 2.64).

Fig. 13 .
Fig. 13.Bounce probabilities as a function of the initial center-of-mass energy divided by the adhesion energy (KE cm,i / E ad ) for the Ag55 particles colliding with the silver surface at T = 500 K (ε =0.02 eV), along with the results at T = 298 K.

Table 1 .
Parameters for the tight binding potential.

Table 2 .
Ranges of simulation parameters, and materials for a particle and a surface.

Table 4 .
Size of the surface domains used for the MD simulations.