Progress in the measurement and modeling of physisorbed layers

This review describes progress in the field of physisorption. Significant advances in the knowledge of microscopic structures and interactions of weakly bound adsorbates are reviewed, including the first studies for the adsorption sites of rare gases on flat metal surfaces and at surface steps, the structures of higher-order commensurate solids, collective excitations in rare-gas monolayers, molecular orientations and growth processes in alkane films, and adsorbate diffusion. The development and improvement of experimental techniques are reviewed, including high-resolution thermal desorption spectroscopy and ellipsometry for studying thermodynamics; low-temperature scanning tunneling microscopy, very low current electron diffraction, and surface x-ray diffraction for studying structures; inelastic atom scattering for studying collective excitations; quasielastic helium atom and neutron scattering and laser techniques for studying diffusion; and the quartz crystal microbalance for studying interfacial friction. The present state of knowledge of the physical adsorption potentials and the role of the van der Waals interaction are discussed in the context of the widespread use of density-functional theory. Experimental and theoretical results for many adsorption systems are described and tabulated; a few case studies are presented in which a unified picture has (nearly) been achieved by the synthesis of many contributions. Some new applications of physisorption are also presented.

Figure 1

Krypton multilayer adsorption isotherms. Adsorption of Kr multilayer films on exfoliated graphite at $77.3\mathrm{K}$, from 484. Coverage (in layers) as a function of the relative pressure ($p_0$ is the saturated vapor pressure). The expanded scales in the insets present the submonolayer and multilayer transitions at $p∕p_0$ less than 0.001 and greater than 0.8 more clearly. The points $B_1$ and $A_1^{″}$ are signatures of monolayer phase transitions. From 77.

Figure 2

$\mathrm{I}\text{−}\mathrm{C}$ and monolayer-bilayer phase transitions for Xe/graphite as they appear in lattice constants measured by THEED at 3D pressure $p=7.2\times {10}^{-8}\mathrm{Torr}$. The misfit $m=(L-L_c)∕L_c$ is the difference in lattice parameter of the adsorbed layer relative to the commensurate $\sqrt{3}$ structure. As the temperature is lowered at constant pressure, the monolayer misfit decreases continuously from 6% at $74\mathrm{K}$ to zero at $T=58\mathrm{K}$. About $2\mathrm{K}$ lower, the bilayer condenses with a misfit around 2%. Adapted from 227.

Figure 3

Monolayer adsorption of ${\mathrm{N}}_2$ on graphite at $T$ close to $78\mathrm{K}$. The small “substep” near the monolayer completion indicates a liquid-solid transition. The compressibility of the film, shown with a solid line as a guide to the eye, was calculated from the data. From 374.

Figure 4

A series of ellipsometric adsorption isotherms in the fluid regime of pentane on graphite. The optical thickness $t$ (proportional to a phase delay, in degrees) is shown as a function of the relative vapor pressure ($p_0$ is the saturated vapor pressure at the stated $T$). Each isotherm terminates in a very thick film and these films completely wet the substrate. From 310.

Figure 5

Experimental TPD spectra for rare gases on $\mathrm{Pt}\left(111\right)$ at several coverages. The desorption rates are given on a logarithmic (Arrhenius) scale. (a) Xe in the range up to 1.8 monolayer and $50<T<160\mathrm{K}$, with a heating rate of $2\mathrm{K}{\mathrm{s}}^{-1}$. From 527. (b) Ar in the multilayer range and $25<T<52\mathrm{K}$, rate $0.25\mathrm{K}{\mathrm{s}}^{-1}$. From 301.

Figure 6

Experimental and calculated TPD spectra for $\mathrm{Ar}∕\mathrm{Pt}\left(111\right)$. Note the nearly temperature-independent desorption rate for the compressed first monolayer from 34 to $41\mathrm{K}$ in both the experimental and calculated spectra. From 301.

Figure 7

Contributions to the quasielastic peak shape. (a) The generalized dependence of the quasielastic peak width upon momentum transfer $\left[E\right(K\left)\right]$ for a surface lattice constant of $2.55\mathrm{\AA }$. There are contributions due to both intracell and intercell diffusion, which may only be distinguished using high-resolution measurements. (b), (c), and (d) The $E\left(K\right)$ characteristics expected for continuous diffusion, ballistic diffusion, and jump diffusion, respectively, which together give rise to the overall form in (a). In general, continuous diffusion is expected over long length scales (small $K$) and ballistic motion over very short length scales (large $K$). In between, the surface potential affects the diffusion mode, often leading to jump behavior. From 280.

Figure 8

Top down schematic of the complete ${}^3\mathrm{He}$ spin-echo spectrometer. The overall design follows a 45° fixed scattering geometry for sufficient momentum transfer on scattering. The recycling beam source (bottom left) produces the ${}^3\mathrm{He}$ beam and passes it through two differential pumping stages, prior to polarization. The polarizer focuses the beam to parallel, improving the intensity and reducing the aberrations within the solenoid. The scattered beam is passed through an identical solenoid and an analyzer magnet, which focuses the selected polarization from the crystal to the detector. From 3.

Figure 9

(Color online) Detected polarization signal vs solenoid current (left) and its Fourier transform (right) for ${}^3\mathrm{He}$ scattering from a 0.02 coverage of Na on $\mathrm{Cu}\left(001\right)$ at $155\mathrm{K}$. The decay constant of the exponential is proportional to the inverse lifetime of the diffusion process and the FT is analogous to a time-of-flight spectrum, where the peak width is the quasielastic broadening.

Figure 10

Potential wells for ${\mathrm{He}}_2$ to ${\mathrm{Xe}}_2$ presented in scaled, corresponding states, form. The pair potentials of 473 are plotted in the form $U=V\left(r\right)∕ϵ$ vs $x=r∕R_{\min }$, where $ϵ$ and $R_{\min }$ are the depth and position of the potential minimum, respectively. The curves for $\mathrm{Ar}\text{−}\mathrm{Ar}$, $\mathrm{Kr}\text{−}\mathrm{Kr}$, and $\mathrm{Xe}\text{−}\mathrm{Xe}$ are indistinguishable on this scale.

Figure 11

Monolayer phonon energies for $\mathrm{Xe}∕\mathrm{Cu}\left(001\right)$ at $50\mathrm{K}$. The filled circles are the inelastic HAS data of 220 at a beam energy of $8.1\mathrm{meV}$. The labels RW (Rayleigh wave), $S$ (perpendicular monolayer vibration), and $L$ (longitudinal mode) are those assigned in the original experiment. The solid lines are the results of model calculations using the Barker X2 $\mathrm{Xe}\text{−}\mathrm{Xe}$ potential augmented by the McLachlan substrate mediated dispersion energy (see 80). The lower solid line, which runs through the dispersive branch, has shear horizontal polarization; the upper solid line has longitudinal acoustic polarization. The mixing of the $S$ branch with the copper Rayleigh wave at $Q\approx 0.2{\mathrm{\AA }}^{-1}$ is an example of the damping by a Fano resonance treated by 226.

Figure 12

Phonon-dispersion curves for a monolayer of xenon on $\mathrm{Pt}\left(111\right)$ for the $\left[1\overline{1}0\right]$ and $\left[11\overline{2}\right]$ azimuths of the Pt substrate, at an angle of $2.6°$ to the $\Gamma K$ and $\Gamma M$ azimuths of the triangular incommensurate xenon monolayer with nearest-neighbor spacing $4.33\pm 0.01\mathrm{\AA }$. The experimental points, denoted by circles, were obtained with inelastic helium-atom scattering at energies from 6 to $17\mathrm{meV}$ and a surface temperature of $50\mathrm{K}$. The solid lines are the result of calculations with realistic Xe pair potentials and the McLachlan dispersion energy. The xenon branches are designated SH (shear horizontal), LA (longitudinal acoustic), and $S$ (perpendicular to the monolayer plane) and two branches of the $\mathrm{Pt}\left(111\right)$ are also indicated ($R$, Rayleigh and $L$, longitudinal resonance). From 80.

Figure 13

Phonon energies for the commensurate $(\sqrt{3}\times \sqrt{3})R30°$ monolayer solid of $\mathrm{Xe}∕\mathrm{Cu}\left(111\right)$ at $T\approx 60\mathrm{K}$. The filled circles are the inelastic HAS data of 60 at a beam energy of about $10\mathrm{meV}$. The two solid lines are the SH (lower curve) and LA (upper) branches calculated with the HFD-B2 $\mathrm{Xe}\text{−}\mathrm{Xe}$ potential augmented by the McLachlan energy and fitted to a zone-center gap of $0.4\mathrm{meV}$.

Figure 14

Schematic of the $\mathrm{Xe}∕\mathrm{Pt}\left(997\right)$ structure. (a) The vicinal $\mathrm{Pt}\left(997\right)$ surface. (b) The $(\sqrt{3}\times \sqrt{3})R30°$ structure with eight rows per terrace. (c) $R0°$ aligned incommensurate phase with five rows per terrace. Adapted from 327.

Figure 15

STM image of the low-coverage adsorption of $\mathrm{Xe}∕\mathrm{Cu}\left(111\right)$, $T=10\mathrm{K}$. (a) All Xe adsorbed at the lower step edge, panel $200\mathrm{\AA }\times 200\mathrm{\AA }$. (b) Almost all Xe adsorbed at Cu steps, with some Xe at the upper step edges as marked by arrows, panel $300\mathrm{\AA }\times 300\mathrm{\AA }$. (c) Another perspective on (b), with arrows marking the same Xe atoms. From 393.

Figure 16

$\mathrm{Cu}\left(110\right)$ surface. (a) Schematic model showing steps along the $\left[1\overline{1}0\right]$ and [001] directions. (b) Potential energy map for a single adsorbed Xe atom on this configuration. From 158.

Figure 17

(Color online) $\log \left(p\right)\text{−}{T}^{-1}$ phase diagram of Xe/graphite. The solid lines indicate the phase boundaries between 2D gas and $I$-solid, 2D gas and 2D liquid, 2D liquid and $I$-solid, monolayer and bilayer, and the 3D sublimation curve. The 2D triple point is also indicated. The squares are experimental points locating the $I-C$ transition (434; 227). The diamonds are experimental points locating the coverage $=0.92$ isostere (where coverage $=1$ for the $C$ structure). The dashed lines are isosteres from coverage $=0.90$ to 1.0 in increments of 0.02, calculated from a multiparameter potential model using Einstein vibrations for the vertical motion and the cell model for lateral motion (434). Point $H$ on the bilayer line is from 255 as described in the text.

Figure 18

$\theta \text{−}T$ phase diagram of Xe/graphite in the 0–2 layer regime from 511, adapted from 254. Note that this plot emphasizes coexistence regions, e.g., $\mathrm{CS}+\mathrm{IS}$, where IS denotes incommensurate solid, CS denotes commensurate solid, $G$ denotes 2D gas, $L$ denotes 2D liquid, and $F$ denotes fluid phases. The adsorption and desorption paths studied by 511 are shown as dot-dashed lines.

Figure 19

(Color online) Composite $\mu \text{−}T$ phase diagram for Xe/graphite at temperatures that span the 2D monolayer, bilayer, and 3D bulk phases and the monolayer melting transitions. (a) Phase diagram containing the phases and phase boundaries discussed in the text. The 2D gas is at the lower left. A monolayer condensation line, which contains the 2D triple and critical points, separates the 2D gas from the 2D liquid and incommensurate monolayer solid phases. The 2D melting line extends from the 2D triple point toward higher $T$. A bilayer adsorption line ends in a bilayer critical point, and the 3D bulk sublimation line (with the 3D triple point) separates the 2D film from the 3D bulk. The phase boundary between 3D solid and liquid extends up from the 3D triple point. Within the monolayer domain, there are additional phase boundaries between the incommensurate aligned (IA) and rotated (IR) monolayers (dashed lines) and between the IA and commensurate ($C$) solid phase (solid line). (b) The same phase diagram with some of the supporting experimental data. The filled symbols on the 2D gas-liquid line and the monolayer melting line are from volumetric isotherms by 484 (squares), 479 (diamonds), and 198 (triangles). The open pentagons at the high-$T$ end denote second-order melting (479). The gas-solid transition line is supported by electron diffraction observations (467; 434) (open squares). Electron diffraction was also used to locate $C$-IA-IR transition (227) (open diamonds) and the reentrant IA-IR phase boundary (555) (closed and open stars for the IR-IA states, respectively). IA-hexatic transitions were observed with electron diffraction (556) (filled inverted triangles) and x-ray diffraction (387) (open circles). Hexatic-liquid transitions were also observed by Zerrouk et al. (open inverted triangles). The IA-IR transitions observed by 255 are denoted by $H1$ and $H2$. Two bilayer points of 558 (filled squares) are also shown.

Figure 20

STM image of Xe on graphite, showing atomically resolved hexagonal domains arranged in a honeycomblike structure. The image size is $16\times 16{\mathrm{nm}}^2$. The distance between two opposite domain walls is about $5\mathrm{nm}$. From 223.

Figure 21

Close-up STM images of Xe on graphite, showing atomically resolved hexagonal domains that change between frames. In (b), a dislocation has been formed, resulting in a changed domain structure. The image size is $14\times 14{\mathrm{nm}}^2$. Time to scan each image was $10\min$. From 222.

Figure 22

Phase diagram of $\mathrm{Xe}∕\mathrm{Pt}\left(111\right)$ monolayer with temperature $T$ and coverage $\vartheta$ as the axes. The $\sqrt{3}$-monolayer coverage has $\vartheta =1∕3$. The phases are 2D gas $\left(G\right)$, liquid $\left(L\right)$, commensurate solid $\left(C\right)$, uniaxial incommensurate solid (stripe, SI), hexagonal incommensurate aligned solid (HI), and hexagonal incommensurate rotated solid (HIR). A two-phase coexistence region of SI and HI is noted. Adapted from 290.

Figure 23

Diffusion of 2D Xe gas on $\mathrm{Xe}∕\mathrm{Pt}\left(111\right)$ at $T_s=105\mathrm{K}$ by QHAS. (a) The momentum transfer dependence of the QHAS peak intensity at $\mathrm{\Delta }E=0$, $E_i=10.15\mathrm{meV}$. (b) Measured momentum dependence (circles, $E_i=10.15\mathrm{meV}$; squares, $E_i=26.85\mathrm{meV}$) of the peak width (FWHM) compared to calculations for an ideal 2D gas and for a 2D gas on a flat surface with specified friction coefficients. From 168.

Figure 24

Surface diffusion coefficient of $\mathrm{Xe}∕\mathrm{Pt}\left(111\right)$ at $80\mathrm{K}$. Monolayer coverage is $5\times {10}^{14}{\mathrm{cm}}^{-2}$. The data points show the actual diffusion constants and the solid lines are the results of calculations with a simple model for a coverage-dependent activation barrier for diffusion. Adapted from 358.

Figure 25

Results of an MD simulation of monolayer tetracosane (C24) on graphite. The left panel shows a smectic phase at $230\mathrm{K}$ and the right panel shows the fluid phase at $350\mathrm{K}$. The transition temperature is $\sim 340\mathrm{K}$. From 230.

Figure 26

Multilayer adsorption isotherms for Ar/graphite measured by ellipsometry and illustrating the phenomenon of reentrant layering. Coverage as a function of reduced pressure ($p_0$ is the saturated vapor pressure at the stated temperature, at the left axis). The integer indices number the layering transition and the primed indices identify the offset resumption of discontinuous layering. From 545.

Figure 27

Derivative of the adsorbed amount as a function of pressure for Xe/graphite at $137\mathrm{K}$. The ordinate is $\partial N_{\mathrm{ads}}∕\partial \ln p{\mid }_T$, where $10{\mathrm{cm}}^3$ STP is $4.5\times {10}^{-4}\mathrm{mol}$. The film goes through a layering sequence with increasing pressure and sharp peaks correspond to nearly vertical steps in the adsorption isotherm. The peak at $40\mathrm{torr}$ reflects the condensation of a solid second layer. The succeeding peaks are as follows: at $66\mathrm{torr}$, condensation of liquid third layer; at $70\mathrm{torr}$, freezing of third layer under a liquid fourth layer; and a sharp (reentrant step) peak at $76\mathrm{torr}$ for the freezing of layer four under a liquid fifth layer. From 405.

Figure 28

The orientation of three planes in a cubic crystal and the surface lattice of the corresponding planes for an fcc crystal. The (100), (111), and (100) planes are shown in (a), (b), and (c), respectively. The labels for the primitive vectors of these surface lattices are also given.

Figure 29

(Color online) Schematic drawing of the $\mathrm{Cu}\left\{110\right\}\text{−}c(8\times 2)\text{−}10\mathrm{Kr}$ structure. The open circles are the top-layer Cu atoms, the shaded circles are Kr atoms. The oblique primitive cell, denoted by $\mathrm{Cu}\left\{110\right\}\text{−}\left(\genfrac{}{}{0ex}{}{41}{02}\right)\text{−}5\mathrm{Kr}$, is indicated.

Figure 30

Brillouin zone for the triangular lattice. The six equal length primitive reciprocal-lattice vectors are shown as arrows. The perpendicular bisectors are drawn as dotted lines and they form the boundary of the first Brillouin zone. The center is denoted by $\Gamma$, a corner of the boundary by $K$, and a midpoint of the boundary wall by $M$. The normal modes of the monolayer lattice have pure SH and LA polarizations along the $\Gamma M$ and $\Gamma K$ azimuths. From 77.