Physical adsorption at the nanoscale: Towards controllable scaling of the substrate-adsorbate van der Waals interaction

Abstract

The Lifshitz-Zaremba-Kohn (LZK) theory is commonly considered as the correct large-distance limit for the van der Waals (vdW) interaction of adsorbates (atoms, molecules, or nanoparticles) with solid substrates. In the standard approximate form, implicitly based on local dielectric functions, the LZK approach predicts universal power laws for vdW interactions depending only on the dimensionality of the interacting objects. However, recent experimental findings are challenging the universality of this theoretical approach at finite distances of relevance for nanoscale assembly. Here, we present a combined analytical and numerical many-body study demonstrating that physical adsorption can be significantly enhanced at the nanoscale. Regardless of the band gap or the nature of the adsorbate specie, we find deviations from conventional LZK power laws that extend to separation distances of up to 10-20 nm. Comparison with recent experimental observations of ultra-long-ranged vdW interactions in the delamination of graphene from a silicon substrate reveals qualitative agreement with the present theory. The sensitivity of vdW interactions to the substrate response and to the adsorbate characteristic excitation frequency also suggests that adsorption strength can be effectively tuned in experiments, paving the way to an improved control of physical adsorption at the nanoscale. DOI: 10.1103/PhysRevB.95.235417 Noncovalent van der Waals (vdW) interactions constitute a universal cohesive force whose impact extends from the atomistic scale [1,2] to a wealth of macroscopic phenomena observed on a daily basis [3,4]. With an influence ranging from protein-drug binding to the double helix in DNA [5], the peculiar pedal adhesion in the gecko [6,7], and even cohesion in regolith and rubble-pile asteroids [8,9], these nonbonded forces are quantum mechanical in origin and arise from electrodynamic interactions between the constantly fluctuating electron clouds that characterize molecules and materials [10]. While our understanding of vdW interactions is rather complete at the smallest atomistic and the largest macroscopic scales, these pervasive forces exhibit a range of surprising and poorly understood effects at the nanoscale [10][11][12][13][14][15][16].This lack of understanding is best exemplified by recent puzzling experimental observations, which include (i) ultralong-range vdW interactions extending up to tens of nanometers into heterogeneous Si/SiO 2 dielectric interfaces [17,18], and influencing the delamination of extended graphene layers from silicon substrate [19]; (ii) complete screening of the vdW interaction between an atomic force microscope (AFM) tip and a SiO 2 surface by the presence of a single layer of graphene adsorbed on the surface [20]; (iii) superlinear sticking power laws for the physical adsorption of metallic clusters on carbon nanotubes with increasing surface area [21]; and (iv) nonlinear increases in the vdW attraction between homologous molecules and an Au(111) surface as a function of the molecula...

Hidden by graphene – Towards effective screening of interface van der Waals interactions via monolayer coating

“…We note that, due to strong χ 1 G non-locality, the power law decay of E L I substantially differs from standard ∼ D −4 pairwise predictions [24]. In fact, a ultraslow ∼ D −3 scaling characterizes the short D range (due to the linear q dependence of χ 1 G at high q) and gradually varies with D, asymptotically reaching ∼ D −4 in the large distance limit [27] (well beyond the 10 nm scale). Comparison with the dispersion interaction due to isolated G (E L Graf ), obtained from Eq.…”

Influence of Pore Size on the van der Waals Interaction in Two-Dimensional Molecules and Materials

“…In the short range, R/D → ∞ and this finite-sized disk mimics an infinite plate from the perspective of A; in this case, one analytically recovers P A−disk vdW = −4, as expected for an atom interacting with an extended (2D) surface [50,51]. This is followed by monotonic decay with D as R/D → 0 and P A−disk vdW → −6, which is consistent with the wellknown asymptotic expression for two finite-sized systems obtained from non-relativistic quantum mechanics (i.e., E vdW ∝ D −6 ).…”

“…Since the inclusion of many-body vdW interactions often leads to power laws with significant deviations from conventional pairwise predictions [37,43,[51][52][53][54][55], we now consider how an infinite-order many-body expansion of E A−ann vdW would influence the vdW scaling behavior in the presence of a pore. Under the same assumptions, we computed P A−ann vdW for the smallest (r = 1Å) and largest (r = R = 10Å) pore sizes considered above within the random phase approximation (RPA) of the ACFDT (see Supplemental Material) [56].…”

“…To investigate the vdW scaling behavior in porous 2D materials, we now consider a model system consisting of periodic layers tiled by hexagons with inner and outer radii, r and R (denoted by layer[r, R]). When interacting with a point particle, A, numerical evaluation of E vdW [56] shows that P A−layer vdW → 0 in the short range once pores are present in the periodic layer, and P A−layer vdW → −4 in the long range, as expected for A interacting with an infinite 2D surface [50,51]. This shortrange behavior is completely analogous to P A−ann vdW , which again highlights the difference between porous and nonporous molecules and materials.…”

Periodic and fragment models based on the local correlation approach

“…However, the solid state theory only since recently has started focusing on van der Waals dispersion interactions systematically (cf. e.g., Ambrosetti, Ferri, DiStasio, & Tkatchenko, ; Ambrosetti, Silvestrelli, & Tkatchenko, ; Bygrave et al, ; DiStasio, Gobre, & Tkatchenko, ; Gao & Tkatchenko, ; Gobre & Tkatchenko, ; Halo et al, ; Hammerschmidt, Müller, & Paulus, ; Hermann, DiStasio, & Tkatchenko, ; Hermann & Schwerdtfeger, , ; Karttunen et al, ; Li, Sode, Voth, & Hirata, ; Liu et al, ; Marom et al, ; Martinez‐Casado et al, ; Maschio, Usvyat, Schütz, & Civalleri, ; Müller & Spångberg, ; Müller & Usvyat, ; Podeszwa et al, ; Reilly & Tkatchenko, ; Rościszewski et al, ; Santra et al, ; Schütz et al, ; Schwerdtfeger et al, ; Shulenburger, Baczewski, Zhu, Guan, & Tománek, ; Sode et al, ; Steenbergen, Gaston, Müller, & Paulus, ; Tsatsoulis et al, ; Usvyat, ; Usvyat, Sadeghian, Maschio, & Schütz, ; Yang et al, ; Zhang, Tkatchenko, Paier, Appel, & Scheffler, ) and many aspects of this effect including the influence of the screening are currently under active research.…”