Computation of accommodation coefficients and the use of velocity correlation profiles in molecular dynamics simulations

For understanding the behavior of a gas close to a channel wall it is important to model the gas-wall interactions as detailed as possible. When using molecular dynamics simulations these interactions can be modeled explicitly, but the computations are time consuming. Replacing the explicit wall with a wall model reduces the computational time but the same characteristics should still remain. Elaborate wall models, such as the Maxwell-Yamamoto model or the Cercignani-Lampis model need a phenomenological parameter (the accommodation coefficient) for the description of the gas-wall interaction as an input. Therefore, computing these accommodation coefficients in a reliable way is very important. In this paper, two systems (platinum walls with either argon or xenon gas confined between them) are investigated and are used for comparison of the accommodation coefficients for the wall models and the explicit molecular dynamics simulations. Velocity correlations between incoming and outgoing particles colliding with the wall have been used to compare explicit simulations and wall models even further. Furthermore, based on these velocity correlations, a method to compute the accommodation coefficients is presented, and these newly computed accommodation coefficients are used to show improved correlation behavior for the wall models.

Figure 1

An orthographic representation of the system under consideration for the MD simulations. In this case the argon particles are trapped between two parallel platinum plates, which form an FCC lattice. The central wall is the warm wall (600 K) and the outside walls are the cold walls (300 K). The dimensions of the system are $50\times 10\times 10\text{nm}$, and the total number of atoms is approximately $28000$.

Figure 2

Two snapshots from the contact angle simulations for an argon droplet near a platinum wall. In this simulation the interaction parameter ${\epsilon }_{\text{Pt-Ar}}$ equals 0.6 kJ/mol. In (a) the system is shown as it is around 40 ps after the start of the simulation, and in (b) the same system but now around 300 ps. For clarity the vapor is omitted from the snapshots.

Figure 3

In (a) the radial density profile for an argon droplet on a platinum surface is shown, which is used to compute the contact angle belonging to the Lennard-Jones interaction parameter ${\epsilon }_{\text{Pt-Ar}}=0.6\text{kJ}/\text{mol}$. The horizontal line indicates the first layer of the platinum wall and the circle approximates the argon droplet. The contact angle is the angle between the horizontal and the tangent line of the circle at the contact point (dashed). In (b) the relation between the Lennard-Jones interaction parameter and the cosine of the contact angle is shown for both argon and xenon. The bars denote the standard deviation found for a specific contact angle (see text). The linear least square fits including their regression coefficients are also shown.

Figure 4

Velocity correlation distributions for the 150 K wall in the platinum-argon system. These distributions are for incoming and outgoing velocities for the velocity components indicated at the bottom of each column. On the $x$ axis always is the incoming velocity and on the $y$ axis the outgoing velocity, both in nm/ps. The dashed lines indicate the reflective (diagonal) and thermal (horizontal) cases. In the last column the corresponding velocity distributions (perpendicular black and parallel gray) for the reflecting particles (circles) are shown in comparison with the distribution obtained from the explicit wall simulations (dashed), with the outgoing velocity on the $x$ axis and the probability on the $y$ axis.

Figure 5

Velocity correlation distributions for the 600 K wall in the platinum-argon system. These distributions are for incoming and outgoing velocities for the velocity components indicated at the bottom of each column. On the $x$ axis always is the incoming velocity and on the $y$ axis the outgoing velocity, both in nm/ps. The dashed lines indicate the reflective (diagonal) and thermal (horizontal) cases. In the last column the corresponding velocity distributions (perpendicular black and parallel gray) for the reflecting particles (circles) are shown in comparison with the distribution obtained from the explicit wall simulations (dashed), with the outgoing velocity on the $x$ axis and the probability on the $y$ axis.

Figure 6

Velocity correlations for the platinum-xenon system with 150 K wall (a and c) and the 600 K wall (b and d), with the incoming velocity on the $x$-axis and the outgoing velocity on the $y$ axis, both in nm/ps. Both the parallel (a and b) and the perpendicular (c and d) correlation profiles are shown. In all figures the mean value for the incoming and outgoing velocities is depicted by the circle, whereas the solid line indicated the linear least square fit through all collision data.

Figure 7

In (a) the velocity correlations from the explicit wall simulation for platinum-argon at the 600 K wall is shown, and in (b) the correlations from the Cercignani-Lampis model (CL) using the accommodation coefficients computed using Eq. (2) are shown. In (c) the same correlations but now from the Cercignani-Lampis model using as input parameters the accommodation coefficients derived using the linear least-squares method, see Table , are shown. In all these three figures the incoming velocity is on the $x$ axis and the outgoing velocity on the $y$ axis, both in nm/ps. In (d) the velocity distributions (perpendicular black and parallel gray) of the Cercignani-Lampis model with the new accommodation coefficients is shown compared with the explicit wall simulations (dashed line), with the outgoing velocity on the $x$ axis and the probability on the $y$ axis.