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Playing the Long Game Wins the Cohesion–Adhesion Rivalry

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Playing the Long Game Wins the Cohesion–Adhesion Rivalry COMMENTARY Playing the long game wins the cohesion– adhesion rivalry COMMENTARY Richard C. Remsinga,1 When a liquid meets a solid wall, the competition that both were short-ranged (SR), often an approxima- between cohesive fluid–fluid (ff) and adhesive fluid– tion made to facilitate efficient numerical simulations. wall (fw) interactions determines whether the liquid Evans et al. consider all 4 combinations of SR and beads up into a droplet or spreads out over the sur- long-ranged (LR) ff and fw interactions, and demon- face. For typical liquids and moderate fw interactions, strate—through analytic theory and subsequent valida- the surface is partially wet or partially dry. If the fw tion via classical density functional theory and interactions decrease, the system will eventually un- molecular simulation—that each combination leads dergo a surface phase transition to a state where the to a different class of surface phase diagram (5): a) surface is dry—the liquid completely beads up into a SR ff + LR fw,b)LRff + LR fw,c)SRff + SR fw, and spherical droplet, as is the case for ideal superhy- d) LR ff + SR fw. The previously known class, in which drophobic water-repellant and self-cleaning sur- wetting and drying are equivalent at TC, is case c, faces. This is termed a drying transition. In contrast, where all interactions are SR. When LR interactions if the fw interactions increase in strength, the system are present, wetting and drying are not equal at the undergoes a surface phase transition to complete bulk critical point, and a gap appears at TC as a func- wetting—a wetting transition—in which the liquid tion of the fw interaction strength, «w; complete wet- completely spreads over the surface (1, 2). Our under- ting and drying become fundamentally different. standing of wetting and drying transitions stems from Each surface phase diagram ultimately originates the seminal work of Nakanishi and Fisher (3, 4): a sin- from the nature of the adhesive and cohesive interac- gle class of surface phase transitions with wetting and tions. The former are readily described by the fw in- drying becoming equivalent at the bulk critical point teraction potential, W(z). Cohesive forces arising with temperature TC. In PNAS, Evans et al. (5) predict from ff attractive interactions are more complex, but 3 additional classes of surface phase diagrams, with their average effects can be understood from a per- the differences in the 4 total classes arising from the spective dating back to van der Waals (2, 6, 7). In a ranges of the ff and fw interactions (5). uniform, bulk fluid, the vector sum of ff attractions is A fundamental observable characterizing wetting/ effectively zero in each configuration; fluid particles drying is the contact angle, θ, the angle of intersection are pulled equally forcefully by their neighbors on ev- between the solid wall (w) and the liquid–vapor (l–v) ery side. Thus, in bulk, attractive interactions do not interface at the 3-phase contact line [see figure 1 of alter the structure of the fluid and simply provide a Evans et al. (5)]. The contact angle quantifies the bal- uniform background potential in which the fluid parti- ance of surface tensions, γ, where the 3 phases meet cles move around. through Young’s equation, γlvcosθ = γwv − γwl. Typical Near a wall, the situation is vastly different. Fluid hydrophobic surfaces are characterized by θ > 90° and particles are still pulled by their neighbors’ attractive hydrophilic surfaces by θ < 90°, with complete drying forces, but because the symmetry of the system is and wetting occurring at θ → 180° and θ → 0°, broken, there is no cancelation in the direction of respectively. the surface normal, as schematically shown in Fig. Physically, θ is a manifestation of the competition 1A. Instead, a net cohesive force arises, opposing ad- between fw and ff interactions, that is, adhesion versus hesion and pulling the fluid particles away from the cohesion. Evans et al. (5) answer the important ques- surface. The net effects of ff cohesion can therefore tion, “How do the ranges of these competing interac- be captured by an effective potential, φ(z), which can tions affect wetting and drying transitions?” Most be determined from a well-justified statistical mechan- earlier work focused on cases where both ff and fw ical theory (8, 9). This potential, φ(z), encompasses interactions were truncated at some length scale, such the averaged effects of ff attractive interactions, such aDepartment of Chemistry and Chemical Biology, Rutgers University, Piscataway, NJ 08854 Author contributions: R.C.R. designed research, performed research, analyzed data, and wrote the paper. The author declares no competing interest. Published under the PNAS license. See companion article 10.1073/pnas.1913587116. 1Email: [email protected]. www.pnas.org/cgi/doi/10.1073/pnas.1916911116 PNAS Latest Articles | 1of3 Downloaded by guest on September 26, 2021 A B C D LR+LR LR+SR SR+SR Adhesion Adhesion SR+LR LR ff SR ff LR fw SR fw Cohesion Potential Cohesion + Cohesion + Cohesion Adhesion Fig. 1. (A) Schematic illustration of how cohesion arises from unbalanced fluid–fluid (ff) interactions at a liquid interface, highlighting the directionality of ff forces (arrows) felt by a single tagged particle (outlined). The net cohesive interaction opposes attractive adhesive interactions from a solid wall. (B) The effective potential leading to cohesion is repulsive, and its range depends on whether the ff interactions are short- ranged (SR) or long-ranged (LR). (C and D) The total potentials controlling drying and wetting is a sum of ff cohesion and fluid–wall (fw) adhesion potentials. In C, this is shown for a state point where LR + LR leaves the interface dry (phase diagram class b). Note the minimum and attractive tail in the total potential for SR ff interactions, indicating a lack of complete drying until the adhesive interactions tend to zero (class a). In D, the total potentials are shown for a SR fw adhesion, at a state of partial wetting for phase diagrams of class d. Note the maximum and repulsive tail in the LR cohesion + SR adhesion curve after the cutoff distance for adhesions, indicating partial wetting unless the adhesive interactions become infinitely strong. that comparison of φ(z) and W(z) describes the quantitative bal- The discovery of these 3 classes of surface phase diagrams has ance between ff and fw interactions that underlie wetting and profound consequences for the use of computer simulations in drying in the 4 classes of phase diagrams. understanding physical systems. For efficiency, most molecular The effects of truncating the ff attractions are apparent in the simulations employ truncated interaction potentials, especially effective cohesion potentials shown in Fig. 1B for both LR and SR between fluid particles, working under the assumption that the interactions, with the latter truncated and shifted at 2.5σ, where σ essential physics does not change. For a bulk fluid, such an as- is the diameter of a Lennard–Jones particle and φ(z) was deter- sumption is valid. The bulk phase diagram remains qualitatively mined using a sharp-kink approximation for the density: ρ(z) = 0 the same, with the location of the critical point and liquid densities for z < 0, ρ(z) = ρB for z > 0. For LR ff interactions of the Lennard– shifting toward lower values, for example. At an interface, the 6 3 Jones form, φLR(z) ∼ +«ρBσ /6z at large distances, the same scal- neglect of long-ranged interactions changes even the qualitative 3 3 ing form as the LR fw potential WLR(z) ∼−«w«σ /z , where « is the behavior of the system. The work of Evans et al. highlights that energy scale for ff attractions. In this case, cohesion and adhesion most simulation studies of wetting and drying employing trun- can compete at all length scales, giving rise to class b phase cated interactions are not modeling the intended reality with diagrams. When adhesion dominates everywhere, e.g., large long-ranged ff and/or fw interactions. Modeling long-ranged, but finite «w, wetting occurs. When cohesion dominates every- power law interactions in interfacial geometries is a challenge, where, e.g., small but finite «w, drying occurs. The drying case is hence the oft-used truncation schemes, but advances in theoret- illustrated in Fig. 1C through the sum of cohesion and adhesion ical techniques for handling these potentials (8, 9) combined with interactions, φLR(z) + WLR(z), which is repulsive for all z. efficient computational methods for probing surface thermody- When the ff interactions are truncated at some finite distance, namics (10–12) should provide a path forward to modeling real the cohesive interactions encompassed by φSR(z) rapidly go to nonuniform systems. zero near the cutoff distance as shown in Fig. 1B. For phase dia- While the focus of Evans et al. (5) is largely on macroscopic grams of class a—SR ff and LR fw—when the fw interactions win systems, their results will be important in a variety of important out, partial and complete wetting can occur. However, because contexts at the nanoscale. Capillary evaporation and condensa- the ff potential is truncated, φSR(z) is of finite range, there will tion in nanoconfined spaces between complex surfaces are necessarily always be a range of z where the fluid only feels the thought to mediate biomolecular self-assembly processes (13), attractive potential WLR(z), and the width of the low-density vapor as well as the complex switching mechanisms of ion channels un- phase will always be finite for «w > 0. Thus, the drying transition derlying biological temperature sensing (14), for example.
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