Stick-slip phase transitions in confined solidlike films from an equilibrium perspective

We investigate the transition from stick to slip conditions in sheared monolayer films confined between two plane parallel solid substrates. Each substrate consists of $N_s$ atoms rigidly fixed in the (100) configuration of the face-centered cubic lattice. Shearing of the film is effected in a quasistatic (reversible) process in view of the low shear rates (on a molecular scale) in corresponding laboratory experiments employing the surface forces apparatus (SFA). To mimic operating conditions of the SFA as closely as possible we employ the grand isostress ensemble in which the temperature $T$, the chemical potential $\mu$ of the film, the stress $T_{\mathrm{zz}}$ exerted normally on the substrates, and the shear stress $T_{\mathrm{zx}}$ acting on the film in the $x$ direction are among the thermodynamic state parameters. We analyze the average transverse alignment of the substrates (i.e., the registry) $〈{\alpha }_x\mathcal{l}〉$ (where $\mathcal{l}$ is the lattice constant of the substrate) and its fluctuations ${\xi }^2:=\mathbf{〈}({\alpha }_x\mathcal{l}-〈{\alpha }_x\mathcal{l}〉{)}^2\mathbf{〉}$ in corresponding Monte Carlo simulations. Up to the so-called yield point $〈{\alpha }_x^{\mathrm{yield}}\mathcal{l}〉$, $〈{\alpha }_x\mathcal{l}〉$ increases with $T_{\mathrm{zx}};$ in the thermodynamic limit $T_{\mathrm{zx}}$ reaches its maximum at $〈{\alpha }_x^{\mathrm{yield}}\mathcal{l}〉$ and ${\xi }^2\to \infty$. For $〈{\alpha }_x\mathcal{l}〉<~〈{\alpha }_x^{\mathrm{yield}}\mathcal{l}〉$ the substrate “sticks” to the film; for $〈{\alpha }_x\mathcal{l}〉>〈{\alpha }_x^{\mathrm{yield}}\mathcal{l}〉$ the substrate “slips” across the film’s surface. States characterized by $〈{\alpha }_x\mathcal{l}〉>〈{\alpha }_x^{\mathrm{yield}}\mathcal{l}〉$ are inaccessible in the grand isostress ensemble because they are thermodynamically unstable. Thus, the stick-slip phase transition occurs at $〈{\alpha }_x^{\mathrm{yield}}\mathcal{l}〉$ in the thermodynamic limit. An analysis of the grand isostress potential indicates that stick-slip transitions can be viewed as continuous phase transitions where the yield point is an analog of the (liquid-gas) critical point. In a finite system the stick-slip phase transition occurs at rupture points $〈{\alpha }_x^{\mathrm{rupture}}\mathcal{l}〉<〈{\alpha }_x^{\mathrm{yield}}\mathcal{l}〉$ because ${\xi }^2$ may exceed a system-size-dependent free-energy barrier.