## 4 Validation of Model; Discussing and Comparing the Model With Experimental Data  
The very interesting experimental results related to gas transport through GO membrane are given in [12]. These results can be used in the study and optimization of processes such as the separation of gas mixtures and purification of gas phase on the impurity component by means of GO membranes. The authors of the aforementioned paper note that for gas permeation, different transport models were proposed, and these models negate each other and cannot be used to explain the results of the aforementioned paper. The explanation of these experimental results is necessary for understanding the mechanism of mass transfer in GO membranes. Let us consider some results presented in the above-mentioned paper. Figure 1 in this paper shows that the permeance for the three larger molecules CH\({}_{4}\), N\({}_{2}\) and CO\({}_{2}\) corresponds to the data that follow from the classic theory of the Knudsen diffusion. The permeance for the two smaller molecules He and H\({}_{2}\) are relatively far above these data. To explain these results authors of the above-mentioned paper, propose a two-pathway transport model for GO membranes: the inter-sheet pathway A and the inner-sheet pathway B. The inter-graphene sheet pathway (pathway A) is composed primarily of inter-galleries between stacked GO sheets which can be modeled by slit-like pores. The inner-sheet pathway (pathway B) represents the structural defects of the GO sheets and it is modeled in this paper by a straight channel. It is also assumed that the tortuosity factor for the pathway A is much greater than for the pathway B (the tortuosity factor for  
Figure 1: Dependence of \(J_{\rm i0}\) on \(f_{\rm i}\) for different values of parameter \(\gamma_{\rm i}=1\): \(\gamma_{\rm i}=5\), \(2\): \(\gamma_{\rm i}=3\), \(3\): \(\gamma_{\rm i}=1\); (a) A diffusion-specular scheme of gas molecule scattering; (b) A backscattering scheme for gas molecules. pathway B is assumed to be unity). The obtained experimental results are explained by a difference in the permeance for the larger molecules (CH4, N2 and CO2) and for the smaller molecules (H2 and He) for the pathways A and B. The greater permeance for smaller molecules in GO membrane is explained by their greater permeance by the pathway B. The transport of gas molecules through GO membranes is considered on the basis of the solution-diffusion model. The total permeance for the GO membrane in relation to gas molecules is written in the above-mentioned paper as a sum of the permeances by the pathway A and the pathway B. It should be noted that in a great quantity of graphene sheets of GO membranes, defects of individual sheets can be overlapped by adjacent graphene sheets [24; 25] that leads to an increase in the tortuosity factor in diffusion of gas molecules through the membrane by the pathway B and accordingly to a significant decrease in the permeance by the pathway B. As indicated in [25], the average area percentage of holes within a GO sheet is only approximately 2%, which is too small to make a significant impact on the permeability of GO membranes and only the interlayer galleries are assumed to be the major mass-transport pathways. It is worth to note that the model proposed in [12] does not include the parameters characterizing the features of the gas molecule scattering by the walls of pores in GO membranes and surface diffusion of molecules adsorbed on the walls of slit-like pores. The model involving the parameters describing features of scattering of gas molecules by the walls of the slit-like pores in GO membranes allows explaining some experimental results which are given in [12] without using the concept of two pathways for the transport of gas molecules in GO membranes.