Layering Transitions and Dynamics in Confined Liquid Films

Rashmi Patil and Jordan Vincent



 

Results and Discussion

The density profiles r(z) for the confined film, recorded versus distance in the direction normal to the surfaces, for a sequence of separations (gaps) D between the confining surfaces is shown in Fig. 1. Here the reduced bulk density r* of the LJ fluid is 0.65 and efw=2eff. 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.

 

Fig. 1 Equilibrium density profiles for the commensurate film along the z direction (normal to the confining solid surfaces). The gap widths (H) for which the profiles were calculated are indicated. Note that the liquid density outside the confinement is uniform and remains constant for all values of H.

 

Solvation forces f (H) recorded during the approach of the two surfaces are shown in Fig. 2. It is the total force exerted by the confined liquid on the confining surfaces and this is the same as the force, which would be required in order to hold the two surfaces at the corresponding separation. The layering transitions in the confined films are portrayed in the solvation force oscillations (Fig. 2), with local positive force maxima corresponding to configurations with well-formed layers.

Fig. 2 Equilibrium solvation forces f in nN plotted versus the width of the confining gap in A for r*=0.65 and r*=0.78. Dashed line: efw= eff; Solid line: efw=2eff; Dotted and dashed line: efw=4eff.

 

Fig. 3 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 facilitate easy observation of trends. Irrespective of the distance between the plates, the error bars were nearly constant at about 1.4kT/e. It is suspected that it is largely due to systematic error but needs to be confirmed by running the code for longer times.

Fig. 3 Equilibrium solvation forces f with error bars in units of kT/e plotted versus the width of the confining gap in units of sigma for r*=0.65 and efw =eff. 

 

Further insight into the layering transition processes is obtained from Fig. 4 which records of the number of atoms in the confined region N vs. the distance between the confining surfaces (H). 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.

 

Fig. 4 Number of molecules in the confining gap n plotted versus the reduced pore length for r*=0.65 and r*=0.78.

 

 

Plots of N/H versus H (see Fig. 5 where N/H is proportional to the number density of molecules in the gap) suggest that below a certain thickness (~6 layers) the films exhibit certain features characteristic of the solid-like response; that is, when the confining gap is slightly reduced, 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 worth of molecules into the surrounding liquid, causing a sharp decrease in the confined film density. During further reduction of the gap width, the number of confined molecules remains almost constant (plateaus of N, Fig. 4), with an associated increase of the confined film density (Fig. 5), which is accompanied by enhancement of the order in the film. This process continues till a gap corresponding to a maximally ordered layered film (with nL 1 layers) is reached, for which the confined film density maximizes. This sequence of events is repeated with a period of ~0.35 nm.

 

 

Fig. 5 Number of molecules in the confining gap Nper unit gap width H plotted versus the gap width H in A for r*=0.65. The meaning of the lines remains the same as in fig. 2.

                                                                                                                               

Fig. 6 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 r*=0.65. The various z's have been defined in Fig. 1. ln(z1,max/z 1,min) 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.

 

 

Fig. 6 Plot of ln(z 1,max/z 1,min),  ln(z 2,max/z 2,min) and ln(z 3,max/z 3,min)  as a function of pore length for r*=0.65. The meaning of the lines remains the same as in fig. 2.

 

 

Fig. 7 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.

 

Fig. 7 plot of the pair-distribution (PDF) for reduced pore lengths 2.75s and 2.35s.

 

These results suggest that the confined spherical LJ liquid exhibits certain features of characteristic of solid-like response; that is, 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, causing 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.

The density profiles r(z) for the confined film, recorded versus distance in the direction normal to the surfaces, for a sequence of separations (gaps) D between the confining surfaces is shown in Fig. 1. Here the reduced bulk density of the LJ fluid is 0.65. 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.