Layering Transitions and Dynamics in Confined Liquid Films

1. Layering Transitions and Dynamics in Confined Liquid Films Rashmi Patil and Jordan Vincent

2. A central property of fluid confined between solid boundaries that are smooth on the molecular scale is their tendency to organize into layered structures. Here the mean local density oscillates with distance normal to the boundaries. Liquids confined in ultrathin gaps may exhibit different mechanical responses. Using MD, this study attempts to gain insights into the nature of the transition by studying the variations of the static properties as a function of the distance between the slits. Introduction

3. The simulation cell contains both liquid molecules and solid blocks. The usual periodic boundary conditions are employed in the directions parallel to the solid surfaces in order to minimize surface effects in these directions. The distance between the two surfaces in the z direction defines the width of the gap (H) confining the fluid. The rest of the space in this three-dimensional cell is filled with fluid molecules. Simulation Technique

4. The size of the cell in the x and y directions was taken to be sufficiently large so that the atoms in the regions outside the confinement can exhibit bulk behavior. The size of the computational cell in the z direction is varied to give the desired film thickness in the gap. The pair potential used for the fluid is LJ(r) = 4((r/) -12 (r/) -6) where  is the interatomic LJ potential well depth. Simulation Technique(contd)

5. All distances and energies have been scaled with respect to zero and the minimum of LJ, respectively. The potential energy of a molecule in the field of the of an LJ solid is taken to be (z) = 2 [0.4 (r/) -10 (r/) -4] xThe temperature of the system is controlled via scaling of the atomic velocities. In the simulations of LJ films kBT = 1.2. The 10-4 parameters that were used are /kB = 119.8 K and  = 0.3405 nm. Simulation Technique(contd)

6. Simulation Technique(contd) • A potential cut-off radius of 3 was used to reduce the computation time and improve the efficiency of the algorithm. • The neighbor lists were updated every 10 MD steps. • The fluctuations in the energy were within 0.001kT. • The average temperature during the simulation period was computed and the number of MD steps was varied to give a temperature within about 5% of the desired temperature. • Each of the systems has been equilibrated for 5*106 — 10*106 MD steps (depending on the distance between the plates) with a time step of 0.001ps, followed by a simulation period of 10*106 —22*106 MD steps, during which the computed properties were averaged.

7. The density profiles (z) for the confined film, recorded versus distance in the direction normal to the surfaces, for a sequence of separations (gaps) H between the confining surface These profiles show clear oscillatory patterns. For wide gaps a uniform bulk density distribution develops in the middle of the confined film, with layering near the two surfaces. Results

8. Solvation forces f (D) recorded during the approach of the two surfaces It is the total force exerted by the confined liquid on the confining surfaces It is also the force which would be required in order to hold the two surfaces at the corresponding separation. The local positive force maxima corresponding to configurations with well-formed layers. Results(contd)

9. This fig shows a plot of solvation force vs. the distance between the plates with error bars. Though error bars were calculated for all cases they are not plotted to facilate easy observation of trends. Irrespective of the distance between the plates, the error bars were nearly constant at about 1.4kT/. It is suspected that it is largely due to systematic error but needs to be confirmed by running the code for longer times. Results(contd)

10. This figure which records of the number of atoms in the confined region N vs. the distance between the confining surfaces (D). It provides further insight into the layering transition processes. N varies in a step-like manner, with sharp drops in the number of confined atoms occurring for the transition from n-layer film to an (n-1)-layer one, with the steps becoming sharper as n decreases. This is because narrowing the gap width results in expulsion of atoms from the confined region (“squeezing” out of the film) and transition to a film with a smaller number of layers. Results(contd)

11. This is a plot of N/H versus H.(Here N/H is proportional to the number density of molecules in the gap ). The films exhibit certain features characteristic of the solid-like response. Starting from one of the well formed layered configurations of the film with nL layers (corresponding to the maxima in the solvation force shown in Fig. 2), the film “yields” through the expulsion of approximately a layers’s worth of molecules into the surrounding liquid, causing a sharp decrease in the confined film density. Results(contd)

12. This fig. shows ln(z1,max/z 1,min), ln(z2,max/z 2,min) and ln(z3,max/z3,min) as a function of pore length for *=0.65. ln(zmax, zmin) gives a measure of the barrier a particle has to overcome in order from one layer to the adjacent one. These profiles show clear oscillatory patterns. The local maxima correspond to configurations with well-formed layers. Results(contd)

13. This fig. shows the plot of the pair-distribution (PDF). Concentrating on the first two peaks of the PDF, we note that two smooth peaks exist at high pore widths. As the degree of confinement is increased, the first peak becomes more pronounced in magnitude and narrower in width and the first minimum decreases in magnitude. Results(contd)

14. Results(contd) • These results suggest that the confined spherical LJ liquid exhibits certain features of characteristic of solid-like response. • When the confining gap width is slightly reduced, starting from one of the well-formed layered configurations of the film with n layers, the film “yields” through expulsion of approximately a layer worth of atoms into the surrounding liquid. • This causes a sharp decrease in the confined film density. • Further reduction of the gap width, the number of confined atoms remains almost constant that is accompanied by the enhancement of the order in the layered structure of the film. • This process continues until a gap width corresponding to a maximally ordered layered film (with n –1 layers) is reached, for which the confined film density maximizes.

15. Summary • This study provides insight into the nature of equilibrium in confined LJ fluid. • Layered density oscillations in the confined films were found, with the number of layers depending on the width of the confinement. • The solvation force oscillations as a function of the gap width exhibits attractive and repulsive regions. • Furthermore, the nature of the transitions, and equilibrium intermediate states, between well formed layers exhibits solid-like response characteristics portrayed by step-like variations in the number of confined segments occurring in response to a small decrease in the gap width, starting from well-layered states of the film. 

16. Summary (contd) • These characteristics suggest that liquids with atomic structures that are more conducive to formation of ordered configurations (such as globular molecules) would develop solid-like characteristics under confinement. • This result may assist the molecular design of future thin-film lubricants.

17. Future Improvements • The error in an integrated quantity like solvation force was more than 20% and the errors in the estimation of errors in the density profiles was much higher. It is suspected that this is due to the fluctuations in the temperature. A thermostat can be incorporated to hold the temperature at its desired value. The reduced temperature T* in the present simulations varied within the limits 1.15 and 1.24 while the desired temperature was 1.2. • The bin size for calculating the density profile was chosen to be 0.025σ. The optimum size of the bin for minimization of the total error should be estimated and the code rerun to minimize the errors. • The walls were assumed to be smooth at the atomic scale. More realistic results may be obtained if the walls are approximated to have crystal structure.

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