Molecular dynamic simulation of water vapor interaction with blind pore of dead-end and saccate type

One of the varieties of pores, often found in natural or artificial building materials, are the so-called blind pores of dead-end or saccate type. Three-dimensional model of such kind of pore has been developed in this work. This model has been used for simulation of water vapor interaction with individual pore by molecular dynamics in combination with the diffusion equation method. Special investigations have been done to find dependencies between thermostats implementations and conservation of thermodynamic and statistical values of water vapor pore system. The two types of evolution of water – pore system have been investigated: drying and wetting of the pore. Full research of diffusion coefficient, diffusion velocity and other diffusion parameters has been made. 1 Molecular dynamics model In classical molecular dynamics, the behavior of an individual particle is described by the Newton equations of motion [1]. For a simulation of particle interaction we use the Lennard-Jones potential [2] with σ = 3.17Å and ε = 6.74 · 10−3eV . It is the most used to describe the evolution of water in liquid and saturated vapor form. Equations of motion were integrated by Velocity Verlet method [3]. Berendsen thermostat [4] is used for temperature equilibrating and control. Coefficient of the velocity recalculation λ(t) at every time step t depends on the so called ‘rise time’ of the thermostat τB which belongs to the interval [0.5, 2] ps. The Berendsen algorithm is simple to implement and it is very efficient for reaching the desired temperature from far-from-equilibrium configurations. 2 Computer simulation of microscopic model We made simulation for a pore of dimensions lx = 500 nm, ly = 50 nm, lz = 50 nm with integration time step ∆t = 0.016 ps and evolution time 65.3 ns. Otherwise, we have considered the following input data for the drying process: • 1000 H2O molecules in the pore volume 500 × 50 × 50 nm3 form a saturated water vapor at temperature T0 = 25 oC and pressure p0 = 3.17 kPa; ?e-mail: [email protected] ??e-mail: [email protected] ???e-mail: [email protected] ar X iv :1 70 8. 06 21 6v 1 [ ph ys ic s. fl udy n] 2 8 Ju l 2 01 7 • 1800 molecules in the outer area that form 20 % of the saturated water vapor and input data for the wetting process: • 200 H2O molecules in the pore volume 500 × 50 × 50 nm3 are 20 % of saturated water vapor; • 9000 molecules in the outer area form a saturated water vapor at temperature T0 = 25 oC and pressure p0 = 3.17 kPa. The diffusion coefficients for drying process (left) and for wetting process (right) are shown in Fig. 1. The left figure depicts diffusion coefficients for pore (upper curve), for outer area (down curve), for mean value of previous (middle curve) and for constant value D = 1779.1 [nm2/ps] (middle dashed line). The right figure shows diffusion coefficients for pore (upper curve), for outer area (down curve), for mean value of previous (middle curve) and for constant value D = 536.33 [nm2/ps] (middle dashed line). Figure 1. Diffusion coefficients for drying (left) and for wetting (right) processes (upper curves in pore, down curves in outer space, middle curves the mean of pore and outer space, and dashed lines constant values) 3 Macroscopic diffusion model Let us denote the water vapor concentration as wv(x, y, z, t) [ng/(nm)3] where x, y, z are space independent variables and t is time independent variable. Then, we consider the following macroscopic diffusion model ∂wv ∂t = D (∂2wv ∂x2 + ∂wv ∂y2 + ∂wv ∂z2 ) (1) 0 < x < lx, 0 < y < ly, 0 < z < lz, t > 0 wv(x, y, z, 0) = wv,0, 0 ≤ x ≤ lx, 0 ≤ y ≤ ly, 0 ≤ z ≤ lz (2) ∂wv ∂n (t) ∣∣∣∣∣ (x,y,z)∈Γ2∪Γ3∪Γ4∪Γ5∪Γ6 = 0, t > 0 (3) −Dv ∂x (t) ∣∣∣∣∣ (lx,y,z)∈Γ1 = β[wv(lx, y, z, t) − wv,out(t)] (4) 0 ≤ y ≤ ly, 0 ≤ z ≤ lz, t > 0 where D is the diffusion coefficient [(nm)2/ps]; lx, ly, lz are 3D pore dimensions [nm]; Γ1,Γ2,Γ3,Γ4,Γ5,Γ6 are boundaries of 3D pore (Γ1 is free boundary while the rest boundaries are isolated; wv,0 is the initial concentration of water vapor, wv,0 = 2.304 · 10−17 for the drying process, and wv,0 = 0.461 · 10−17 for the wetting process [ng/(nm)3]; wv,out(t) is the water vapor concentration in outer area [ng/(nm)3]; β is the coefficient of water vapor transfer from pore space to outer space, β = 50000 [nm/ps]. We suppose that the outer area water vapor concentration is expressed as wv,out(t) = φ0 · wsv(T0), where φ0 is the relative humidity of outer space (0 ≤ φ0 ≤ 1) and wsv(T0) is saturated water vapor concentration at outer temperature T0. The linear problem (1)–(4) can be solved exactly using the variables separation method [5] and the result of the solution is wv(x, y, z, t) = wsv(T0) · φ0 + [ wv,0 − wsv(T0) · φ0 ] · (5)