Surface order in cold liquids: X-ray reflectivity studies of dielectric liquids and comparison to liquid metals

Oscillatory surface-density profiles (layers) have previously been reported in several metallic liquids, one dielectric liquid, and in computer simulations of dielectric liquids. We have now seen surface layers in two other dielectric liquids, pentaphenyl trimethyl trisiloxane, and pentavinyl pentamethyl cyclopentasiloxane. These layers appear below $T\sim 285\text{K}$ and $T\sim 130\text{K}$, respectively; both thresholds correspond to $T/T_{\text{c}}\sim 0.2$ where $T_{\text{c}}$ is the liquid-gas critical temperature. All metallic and dielectric liquid surfaces previously studied are also consistent with the existence of this $T/T_{\text{c}}$ threshold, first indicated by the simulations of Chacón et al. [Phys. Rev. Lett. 87, 166101 (2001)]. The layer width parameters, determined using a distorted-crystal fitting model, follow common trends as functions of $T_{\text{c}}$ for both metallic and dielectric liquids.

Figure 1

(Color online) Molecular structure using CHEM3D software: (a) PPTMTS; (b) PVPMCPS.

Figure 2

(Color online) The upper panel shows the temperature dependence of the surface tension $\left(\gamma \right)$ for PPTMTS and PVPMCPS: circles indicate data obtained using a Wilhelmy-plate method in the range 265–298 K, and solid lines show the fitted and then extrapolated $\gamma$ using $\text{ln}\left(\gamma \right)=A+n\text{ln}\left(T_{\text{c}}\text{−}T\right)$, where $A$ and $n$ are constants, and $T_{\text{c}}$ is the critical temperature of the liquid. The lower panel shows the calculated ${\sigma }_{\text{cw}}^2$ vs $T$ for PPTMTS and PVPMCPS.

Figure 3

(Color online) Specular reflectivity data (circles) before background subtraction, divided by the Fresnel reflectivity $R_F$, for PPTMTS at 235 K. $R_F$ is the theoretical reflectivity from an ideal surface. The two solid lines show slightly off-specular data (sample misaligned by $\pm 0.1°$).

Figure 4

(Color online) Specular reflectivity data (divided by $R_F$) for PPTMTS films on rough silicon substrates, at different temperatures. Lines are the best fits from which the electron-density profiles are determined.

Figure 5

(Color online) Electron-density profiles of PPTMTS films on rough silicon substrates, at selected typical temperatures. Solid lines (red) show best fit normalized electron densities $\left[\rho \left(\text{z}\right)/{\rho }_{\text{bulk}}\right]$. The dashed lines (blue) show the density profiles with capillary broadening removed (i.e., plotted with ${\sigma }_{\text{cw}}=0$). The profiles have been shifted vertically for clarity.

Figure 6

(Color online) Top: Patterson function and bottom: electron-density profile obtained using the distorted crystal model at 220 K for PPTMTS. A section of the profile is also shown enlarged. The vertical dashed lines in the bottom panel indicate the internal interfaces in the liquid, the distances between which correspond to minima and maxima in the Patterson function.

Figure 7

(Color online) Temperature dependence of the fitting parameters for PPTMTS. Symbols indicate the temperature history of the sample (○: temperature was lowered to the value shown; ☆: temperature was increased to the value shown). Top left: surface-density enhancement parameter $r$. Bottom left: $d_0$ (open symbols) and $d_1$ (filled symbols), the spacings between the first three layers and between subsequent layers, respectively. Top-right: ${\sigma }_0$, the top surface roughness, bottom-right: $\overline{\sigma }$, which measures how rapidly the layers broaden as one goes into the bulk. The dotted vertical lines show $T_{\text{g}}$ as measured in Ref. 29. The horizontal dashed lines are guides to the eye.

Figure 8

(Color online) (a) Specular reflectivity data (divided by $R_F$) of PVPMCPS films on rough silicon substrates. Lines are best fits. (b) The corresponding electron-density profiles. Solid lines (red) show best fit normalized electron densities $\left[\rho \left(\text{z}\right)/{\rho }_{\text{bulk}}\right]$. The dashed lines (blue) show the density profiles with capillary broadening removed (i.e., plotted with ${\sigma }_{\text{cw}}=0$). The profiles have been shifted vertically for clarity.

Figure 9

(Color online) Temperature dependence of the fitting parameters for PVPMCPS. Symbols indicate the temperature history of the sample (○: temperature was lowered to the value shown; ☆: temperature was increased to the value shown). Top left: surface-density enhancement parameter $r$. Bottom left: $d_0$ (open symbols) and $d_1$ (filled symbols), the spacing between the first three layers and between subsequent layers, respectively. Top right: ${\sigma }_0$, the top surface roughness. Bottom right: $\overline{\sigma }$, which measures how rapidly the layers broaden as one goes into the bulk.

Figure 10

(Color online) $T_{\text{c}}$ dependence of some surface-layering parameters for different isotropic liquids. The width parameters have been divided by the layer spacing in the same material to obtain scale-independent parameters so that atomic and molecular liquids can be compared. The lines are guides to the eye.