D–R curves of the NC 100 sample under different experimental conditions. 

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... expression for the second derivative is relatively com- plicated, so its values are computed numerically. The derived isotherms (experimental and simulated) obtained for both samples are presented in Figs. 1a and 1b. They show a resolved peak close to the limited experimental window ( ln P /P 0 ∼ − 3 ) . As a consequence, the mono- layer approach following the Dubinin–Astakhov isotherm has been adopted for the DIS modeling. This simulation has been realized using the minimum number of domains according to the best experimental curve fitting. Four domains were necessary to obtain the best description of the surface heterogeneities for both samples. The quantitative determination of the adsorbed volume is given in Fig. 1c. The positions of the peaks correspond to the maximum of the bell-shaped curve. It appears that the values of ln P /P 0 for each domain are always slightly shifted toward the low- est energies according to increasing burnoff. The volume of domain I that corresponds to the most energetic sites is quite similar for both samples. In contrast, noticeable changes occur for the volumes of domains II and III, which are the microporous network concerned by the activation process. The last domain is attributed to the less energetic micropores and, in a first approach, could be considered a transition between wider micropores and the beginning of mesoporosity. In this case, the adsorption is generally associated with cooperative effect [12], corresponding to multilayer adsorption, which was not taken into account in the present case. As a consequence, the adsorbed volumes determined for this last peak are overestimated. In the case of the adsorption study of a molecular probe, the size distribution of the pores is strongly connected to the adsorption equilibrium and kinetics. The pore connectivity is a parameter to take into consideration for the modelling of the isotherms [13–16]. Adsorption of argon in quasi-equilibrium conditions shows for the initial state of adsorption some oscillations on the experimental curves for ln P /P 0 between 14 and 10 (Fig. 2). A mag- nification of part of the derived curve is given in Fig. 2. It could be observed that the oscillations are of slight ampli- tude for NC60 and become most important for NC100 with some clear negative contributions on the derived curve. The origin of this phenomenon could be connected to a localized overheating. One possible way to check this assumption is to modify the experimental conditions of acquisition. It can be assumed that the burnoff opens closed pores connected to the others by geometric restrictions. A slow process of diffusion occurring across the constriction leads to a large mass transfer of gases for a given pressure corresponding to localized overheating. Indeed, the quasi-equilibrium technique presents a dynamic character and in the presence of a large amount of high-energy adsorption sites the thermal equilibrium of the sample can be broken due to insufficient heat transfer toward the liquid nitrogen thermostatic bath. As a consequence, two ways can be tested to limit oscillations: decreasing the number of high-energy adsorption sites in the adsorption system by using smaller sample mass or decreasing the adsorption rate by decreasing the introduction flow rate (i.e., the running pressure before the microleak). Both approaches were tested for an NC100 sample (Fig. 3), showing that such changes of the experimental conditions lead to a significant decrease of the oscillations, which is in agreement with the expected reduction of the overheating phenomenon. In addition, the shape of the mass uptake after the domain of pressure corresponding to these oscillations is similar to the initial part. This phenomenon is close to the activated diffusion described in Refs. [10,17,18]. The D–R equation has been applied on the corresponding isotherm and the obtained curves are reported in Fig. 4. Negative deviations from the DR relationship appear at very low relative pressure and could arise from the existence of activated diffusion or a molecular sieve effect. Furthermore, the inflection point at ln P /P 0 = − 12 . 5 corresponds to the beginning of the oscillations of the isotherm derived curve. The pore size concerns L by 0 these [nm] domains 10 , 800 of nm relative J mol pressure /(E 0 are 11 probably , 400 ) J compara- mol . ble E 0 and to the W 0 molecular are usually size obtained and therefore from the molecules adsorption may of never small molecules, completely such escape as the carbon potential dioxide field in of our the case. pore This walls. simple Gas approach transport could provides probably a rough occur estimate according equal to an to activated 0.53 nm dif- for NC60 fusion and mechanism. 0.57 nm It for has NC100. been shown As can [19] be seen, that in the the values case are where quite the similar DR equation although applies, the total the volume average of micropore micropore width has increased L is related more to E than by 45% (Table 1). The effect of burnoff on our sample is probably to open some closed pores, leading to an increase of the entire pore structure, including some deadend pores. Recently, it has been shown [20] that these pores are associated with significant mass transport resis- tance, since they could be selective regarding the molecular size of argon. L 0 [nm] 10 , 800 nm J mol /(E 0 11 , 400 ) J mol . E 0 and W 0 are usually obtained from the adsorption of small molecules, such as carbon dioxide in our case. This simple approach provides a rough estimate equal to 0.53 nm for NC60 and 0.57 nm for NC100. As can be seen, the values are quite similar although the total volume of micropore has increased more than 45% (Table 1). The effect of burnoff on our sample is probably to open some closed pores, leading to an increase of the entire pore structure, including some deadend pores. Recently, it has been shown [20] that these pores are associated with significant mass transport resis- tance, since they could be selective regarding the molecular size of argon. To sum up, the study of the micropore network of two commercial activated carbons differing in the burnoff level has been realized using low-pressure argon adsorption. The obtained isotherms were modeled using DIS method. Four energetic domains of micropores were defined and the effect of burnoff was attributed to a moderate enlargement of the pores corresponding to 10 − 9 < ln P /P 0 < 10 − 5 . Furthermore, some unusual oscillations were observed on the derived curve of NC100, which were attributed to a localized overheating due to a spontaneous mass transfer of argon through constrictions between former pores and the new opening pore or deadend pores, as suggested by the strong increases of micropore volume without significant variation of the average micropore size. This work takes advantage of the dynamic character of the experimental method and mainly the discrepancy of the quasi-equilibrium state to deduce key parameters related to the porosity topology. This research work is supported by the CNRS, in the frame of the Jumelage “Matériaux carbonés et catalytiques pour ...