Kapitza Resistance between Few-Layer Graphene and Water: Liquid Layering Effects

Abstract

In this section we present the details on simulations we performed. Initially N + 2 graphene layers of size L × L are placed along z axis with d = 3.35Å spacing between each other. Followed is the water block of size L × L × W and N + 2 more graphene layers of the same size. The resulting system is mirrored with respect to a XY plane and shifted along Z such that distance d between graphene layers of the original system and its symmetric image is maintained. The schematic of the setup is shown in Fig. 1 of the Main Text.Each simulation consists of three stages: equilibration to isothermal-isobaric (N, P, T ) ensemble; applying temperature gradient at canonical ensemble (N, V, T ); collecting the statistics at canonical ensemble while the temperature gradient is maintained. To achieve the temperature gradient, a high temperature Nosé-Hoover heat bath is applied to four central graphene layers and a low temperature Nosé-Hoover heat bath is applied to four outermost graphene layers (two leftmost and two rightmost). Periodic boundary conditions are applied in all directions. Equilibration always takes 400 ps. Applying temperature gradient takes from 1 ns to 3 ns depending on the number of used layers, and collecting the statistics takes from 2 ns to 3 ns.Water was modeled with flexible simple point charge (SPC) model [1]. We also perform a simulation using rigid SPC water model [2]. The result are almost identical to the corresponding simulation with flexible water model: see Table S1.Typical pressure evolution versus time is shown in the Fig. S3. High pressure oscillations are observed due to the high stiffness of both water and graphene. However, the average pressure remains constant. DATA EXTRACTIONKapitza resistance R K was calculated as R K = ∆T /J, where ∆T is the temperature jump at the solid-liquid interface, and J is the heat flux through the interface. The heat flux is defined as the conducted energy from the high temperature heat bath to the low temperature heat sink per unit time across unit area. Due to the symmetry of our simulation setup (Fig. 1), the heat flux can be computed as half of the slope of the energy change with respective to time in the heat bath: J = 0.5 d dt ∆E(t), where ∆E is induced energy in heat bath (Fig. S2). In our calculations, we average the local temperature in two symmetric copies. As shown in Fig. S1, ∆T is computed from the solid and liquid temperature at the interface. Solid temperature at the interface is determined by a linear fitting of the temperatures in different graphene layers. Water is divided into bins of 0.1Å in thickness along z, thus liquid temperature at the interface is determined by fitting the temperatures of water in different bins on a straight line. The error in Kapitza resistance is given by errors of two linear fits.Important to note that with the described procedure, we calculate two Kapitza resistances -one at a high temperature interface, and the other at a low temperature interface (Fig. S1). In all our simulation, the low temperature Kapitza resis...

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