## 3 Developing of the Model for Mass Transfer Through GO Membranes
As indicated in [17], this effect can be related to specular reflections of gas molecules from the pore walls. The Maxwell diffuse-specular model of gas molecule scattering leads to the factor \(\psi_{\text{i}}=(2-f_{\text{i}})/f_{\text{i}}\) in the value of the diffusion coefficient in the classic Knudsen diffusion [18]. Here \(f_{\text{i}}\) is the coefficient characterizing the probability of diffuse scattering of gas molecules of component i. The value \(1-f_{\text{i}}=f_{\text{i,sp}}\) describes the probability of specular reflection of gas molecules of component i. The probability of specular reflections of molecules from the pore walls depends in particular on the surface roughness, the relationship between the masses and sizes of molecule (atom) of the gas phase and the dense phase (pore walls) and on the adsorption energy of gas molecules. Let us consider the dependence of the value of \(f_{\text{i,sp}}\) on the mass of molecules of a gas phase in the simplest case of a smooth and clean (without adsorbed molecules) surface. The probability of elastic (which is assumed to be specular) reflection \(f_{\rm i,sp}\) of the gas molecule of component i according to [19] can be presented as  
\[f_{\rm i,sp}=\exp\biggl{(}-\frac{E_{\rm ic}}{kT}\biggr{)}. \tag{12}\]  
where \(E_{\rm ic}\) is the specific energy of the interaction of the gas molecules of component i with the pore walls, which depends on the adsorption energy \(E_{\rm ia}\) and can be estimated for light gas particles as  
\[E_{\rm ic}\approx 4\frac{m_{\rm i}}{m_{\rm w}}E_{\rm ia}, \tag{13}\]  
where \(m_{\rm w}\) is the mass of molecules (atoms) of the dense phase (material of the pore walls). It is seen from Equations (12) and (13) that the smaller the values of \(m_{\rm i}\) and \(E_{\rm ia}\) at the constant value of \(m_{\rm w}\), the greater the probability of elastic reflections of gas molecules. In particular, this fact can lead to a sufficiently large probability of specular reflections of light gas particles such as H\({}_{2}\) and He from the walls of the carbon nanotubes. The similar regularities may apparently take place in the transport of gases through the slit-like pores of GO membranes. In the backscattering scheme, it is supposed that a fraction \(f_{\rm i}\) of molecules of component i is scattered according to the cosine law (diffuse scattering) and a fraction \(1-f_{\rm i}\) is scattered in the direction opposite to the velocity of incident molecules and the value of \(\psi_{\rm i}=f_{\rm i}/(2-f_{\rm i})\)[20]. The backscattering may occur in the case of the roughness of the pore walls and adsorption of molecules of a foreign gas on the pore walls. It was shown in [21] that adsorption of one component of a gas mixture on the pore walls can influence the scattering of the second component of a gas mixture that affects the flux of the gas molecules of the second component passing through the channel (pore). The problems related to the effect of adsorption, surface diffusion, specular reflection, and backscattering of the gas molecules on the gas flux passing through a long cylindrical channel (pore) in the free molecular regime of gas flow are considered in [20; 21; 22; 23]. It is worth noting that surface diffusion of molecules adsorbed on the walls of the slit-like pores of the GO membrane can also increase the flux of molecules passing through the pores. Let us estimate the influence of surface diffusion of molecules adsorbed on the walls of the slit-like pore of the GO membrane on the total flux of molecules passing through the pore. For the sake of simplicity, we assume that the total flux of molecules of component i passing through the slit-like pore can be presented as a sum of the flux of the gas molecules and the surface flux of adsorbed gas molecule on both walls of the pore (the additive approximation).