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Effects of surface mediation on the adsorption isotherm and heat of adsorption of argon on graphitized thermal carbon black
Journal of Colloid and Interface Science 342 (2010) 485–492
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Effects of surface mediation on the adsorption isotherm and heat of adsorption of argon on graphitized thermal carbon black Chunyan Fan a,b, G. Birkett b, D.D. Do b,* a b
Department of Storage and Transportation Engineering, China University of Petroleum, Qingdao 266555, China School of Chemical Engineering, University of Queensland, St. Lucia, Queensland 4072, Australia
a r t i c l e
i n f o
Article history: Received 5 September 2009 Accepted 11 October 2009 Available online 14 November 2009 Keywords: Gas phase adsorption Graphitized thermal carbon black Surface mediation Heat of adsorption Argon
a b s t r a c t In this paper, the effects of surface mediation on the adsorption isotherm and isosteric heat of adsorption on a graphite surface were investigated, as the surface mediation is known to affect the intermolecular interaction of adsorbed molecules close to the surface. Kim and Steele (Phys. Rev. B 45 (11) (1992) 6226–6233) and others have assumed that the surface mediation is confined only to the first layer. This will be tested in this paper with a combined experimental and Grand Canonical Monte Carlo (GCMC) simulation of adsorption of argon on graphitized thermal carbon black (GTCB) over a range of temperatures (77–95.25 K). By matching the simulation results against the experimental data, we have found that the surface mediation is extended up to the fourth layer, rather than only the first as suggested by Kim and Steele, and the extent of this mediation is reduced with distance from the surface. This reinforces the important role of surface on the intermolecular interaction. With regard to the heat of adsorption, we found that the isosteric heats obtained directly from the simulation agree fairly well with the heats calculated from the application of the Clausius–Clapeyron equation on experimental isotherms of 77 and 87.3 K. The temperature dependence of the isosteric heat was investigated with the GCMC simulation results. One interesting observation is the existence of a heat spike at 77 K and its absence at higher temperatures, a phenomenon which is common to both simulation results and experimental data. This lends good support to the molecular model with surface mediation as a proper one to describe adsorption of noble gases on GTCB. Ó 2009 Elsevier Inc. All rights reserved.
1. Introduction With molecular simulation techniques and the availability of computational power, the study of adsorption behavior at the molecular level is possible. Both simple and complex adsorption phenomena can be described by the correct molecular models. Comparing simulation results against experimental data will increase our understanding about the mechanisms of adsorption. Among various molecular simulation methods, Grand Canonical Monte Carlo (GCMC) is the most commonly used for the study of adsorption. It mimics the same conditions that are generally used in an adsorption experiment, where the temperature, volume, and chemical potential (pressure of the bulk phase) are specified [1]. In this work, the behavior of argon adsorption on a graphitized surface will be investigated with a combined study of experimental work and GCMC simulation. The adsorption of argon on GTCB is one of the simplest systems to study and it has received considerable experimental and theoretical attention [2–9]. Despite numerous simulation studies in * Corresponding author. Fax: +61 7 3365 2789. E-mail address: [email protected] (D.D. Do). 0021-9797/$ - see front matter Ó 2009 Elsevier Inc. All rights reserved. doi:10.1016/j.jcis.2009.10.018
the literature, the commonly used models do not account for the nonadditivity between the fluid–fluid interaction and the solid– fluid interaction and therefore fail to reproduce accurately the experimental data. Particularly they fail to describe correctly the regions where the first and higher layers are about to be completely formed. To be more specific they overpredict the experimental data in those regions, suggesting the overprediction of the interaction among adsorbed molecules. It has been argued [10–12] that in the presence of a surface the intermolecular interaction energy is reduced. Various reasons for this reduction include surface polarization and multibody effects. Both of these give rise to nonadditivity [10–12]. The concept of surface mediation is well known with its effects on the intermolecular interaction of adsorbed molecules close to the surface. The details of surface mediation will be discussed in Section 2.3. Kim and Steele [13] applied surface mediation in their study of adsorption of methane on graphite and they confine this effect only to molecules in the first layer. In this work, the same methodology will be applied to argon adsorption on GTCB over a range of temperatures (77–95.25 K), but with the range of surface mediation extended beyond the first layer. The effects of the surface mediation are investigated not only on the adsorption
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isotherm but also the isosteric heat of adsorption. The isosteric heats at different temperatures are obtained either by the application of the Clausius–Clapeyron equation to experimental isotherms at two different temperatures or by applying the fluctuation theory in the molecular simulation. 2. Theory
where F ia is the surface-mediation damping factor contributed by the particle i which resides in the layer a and F jb is that contributed by the particle j which resides in layer b. The variable uij is the intermolecular energy when two particles are in the bulk phase and are under no influence from the surface (i.e., calculated from Eq. (1)). The variable ueff ij is called the effective intermolecular potential energy. The values of the damping factors F ia and F jb are determined by matching the simulation results against the experimental data.
2.1. Fluid model and the interaction energy 2.4. Isosteric heat The potential model used for argon is a 1-center Lennard-Jones model. The interaction energy between two isolated argon atoms is calculated with the classical 12-6 Lennard-Jones potential equation
uij ¼ 4eff
"
rff
12
r ij
rff r ij
6 # ;
ð1Þ
where rij is the separation distance between two particles i and j, and the molecular parameters eff and rff are the well depth of interaction energy and the collision diameter of argon, respectively. The values of these parameters are rff = 0.3405 nm and eff/kB = 119.8 K. 2.2. Solid model and solid–fluid interaction energy A simple homogeneous (structureless) graphitized surface model is used in this study. The interaction energy between a fluid particle and the structureless surface is calculated with the Steele 10-4-3 potential [14],
" usf ðzÞ ¼ 2pqs r
2 sf sf
e
# r4sf 2 rsf 10 rsf 4 ; 5 z z 3Dðz þ 0:61DÞ3
ð2Þ
where qs is the surface density of the carbon center (38.2 nm2), D is the interlayer spacing between two adjacent graphene layers (0.3354 nm), z is the normal distance from the surface to the argon particle, rsf and esf are the cross solid–fluid molecular parameters and calculated from the Lorentz-Berthelot rule. The solid–fluid collision diameter is
rsf ¼ ðrss þ rff Þ=2:
ð3aÞ
The solid–fluid interaction energy is adjusted by the introduction of the solid–fluid binary interaction parameter, ksf, such that the Henry constant is reproduced by the GCMC simulation, that is,
esf ¼ ð1 ksf Þðess eff Þ1=2 :
ð3bÞ
The LJ parameters used for carbon atom in a graphene layer are rss = 0.340 nm and ess/kB = 28 K. 2.3. Surface mediation As noted in the Introduction, the interaction between fluid molecules close to the surface is affected by the presence of a solid surface. This is because the electric field of the surface will induce a dipole on the fluid molecules close to it, and these parallel induced dipoles point in the same direction, resulting in a slight repulsion between these molecules. Therefore the fluid–fluid interaction energy as calculated in Eq. (1) will overestimate the interaction of particles close to the surface. Surface mediation is the term used to consider the reduction of the intermolecular interaction due to the presence of a surface. In this paper, a simple approach suggested by Kim and Steele [13] will be applied to describe the surface mediation of argon adsorption on a graphitized surface. The effective intermolecular interaction energy is calculated from i j ueff ij ¼ F a F b uij ;
ð4Þ
The isosteric heat of adsorption is calculated by using two different approaches. The first is the classical method by applying the following Clausius–Clapeyron equation [15] on two experimental isotherms obtained at two sufficiently close temperatures.
qiso ¼ R
ln P2 ln P 1 ; 1=T 2 1=T 1 C
ð5Þ
where R is the gas constant, T1 and T2 are temperatures, P1 and P2 are the pressures at which the surface excesses of the two isotherms are the same. The second method is based on the fluctuation theory applied to the simulation results. The following equation was obtained as a result in [16].
qiso ¼
hUihNi hUNi hN 2 i hNihNi
þ kB T;
ð6Þ
where h i is the ensemble average, N is the number of particles, and U is the configuration energy of the system. 2.5. Monte Carlo simulation method Among many Monte Carlo (MC) simulation methods, the Grand Canonical Monte Carlo is the one which mimics the same conditions that are generally used in an adsorption experiment, as the temperature, volume, and chemical potential (pressure of the bulk phase) are fixed. In this study, GCMC will be used to obtain the isotherm and the isosteric heat of argon adsorption on GTCB with the models described above. For a specific condition, 10,000 cycles are set for the equilibrium stage and another 10,000 cycles are used to obtain ensemble averages. Each cycle consists of one thousand displacement moves, insertion and deletion of equal probability. The final configuration of the previous condition is then used as the starting configuration for the next condition. The cutoff radius is taken to be either five times the collision diameter of argon or half of the box length, whichever is smaller. The initial displacement step length is half of the box length and it is adjusted during the equilibration step such that the acceptance ratio of movement is between 20% and 25%. The simulation box used in this work has a linear dimension of 5 nm in the x and y directions. A structureless carbon surface is at the bottom of the box (in the z direction) and the top boundary is treated as a hard wall. Any attempt of displacing a particle out of the hard wall will be rejected. The height of the simulation box is set as 6 nm. Periodic boundary conditions are applied in x and y directions to simulate the infinite extent of the surface in these directions. The surface excess per unit area is calculated by the equation
C¼
hNi qV acc ; Lx Ly
ð7Þ
where hNi is the ensemble total number of particles in the simulation box, and q is the density of bulk phase, which is calculated with the Johnson et al.’s equation of state [17]. The variables Lx and Ly are the dimensions of the surface in x and y directions, respectively. The
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volume Vacc is the accessible volume, which is defined as one in which the fluid–solid potential energy is nonpositive. The local density distribution of fluids is calculated from
qz ¼
hDNzþDz i : Lx Ly Dz
ð8Þ
In this equation, qz is the local density, hDNz+Dzi is the ensemble number of particles in the region from z to z + Dz. In this work Dz is set equal to 0.01 nm. 2.6. Experimental method The sample used in this work is a graphitized thermal carbon black, Carbopack F Lot No. 1665-84A, which is kindly supplied by Dr. Betz of Supelco. In our laboratories, the measurements of argon adsorption on this sample were carried out at 77 and 87.3 K using an ASAP 2020 static volumetric adsorption analyzer from Micromeritics (Altanta, GA, USA). The mass of Carbopack F used for measurement was 4.28 g, before the measurements, the sample was degassed under vacuum for at least 15 h at 473 K. The BET specific surface area was evaluated on the basis of argon data in the relative pressure range from 0.1 to 0.2 using the cross-sectional area of 0.14 nm2 [8], and was found to be 5.22 m2/g. 3. Results and discussion 3.1. Experimental data of 77 and 87.3 K The adsorption isotherms of argon on a Carbopack F (different lot from the one that we used in this work) using ASAP 2010 at 77 and 87.3 K have been reported by Gardner et al. [6]. This is shown in Fig. 1. Also plotted in this figure are the isotherms obtained in our laboratories, and it is interesting (but not surprising) that our data agree very well with Gardner’s data even their Carbopack F and ours come from different batches. This is an indication of a homogeneous surface because we do not expect such an agreement if these samples are heterogeneous. A further support of the homogeneity is the clear existence of the Henry law region as seen in the log–log plot in Fig. 1b and d for 77 and 87.3 K, respectively. Since the experiment results are in perfect agreement with Gardner’s data, they can be used to develop a molecular model which is used in the Monte Carlo simulation to describe adsorption isotherm and isosteric heat of argon adsorption on GTCB. Specifically the two parameters that we need to derive are the binary interaction parameter ksf and the damping factor F. The former is to ensure that the model can describe correctly the Henry constant, and the later is for the good description of the complete isotherm. 3.2. Simulation isotherms Two adjusting parameters used in the simulation are the binary solid–fluid interaction parameter ksf and the surface-mediation damping factor F. Since ksf affects the isotherm in the low pressure region and F only plays a role when the surface is reasonably covered with adsorbed molecules, we can determine them separately. By using the experimental Henry constant we obtain the binary interaction parameter ksf. Once this is done, the surface-mediation damping factor F (for four layers) can be determined by matching the simulation results of adsorption isotherm against the experiment data. We perform this task for up to four layers for a number of reasons. For layers above the fourth layer we have found that F is very close to unity, meaning that the surface mediation starts losing its influence at distances far away from the surface.
487
Furthermore, matching the simulation results and the data in the region where there are more than four layers is not credible because there is a strong possibility of the interference of the capillary condensation in the interstices between primary particles. To determine the specific surface-mediation damping factors for different layers, we have to define the boundary of each layer. This is realized by considering the local density distribution obtained from the GCMC simulation results. Take the case at 77 K as an example, the local density distribution of argon adsorption on GTCB at a pressure equal to 30,000 Pa is shown in Fig. 2. Each peak in this figure constitutes a layer. The first layer is the sharpest one, which is expected because of the strong adsorption forces experienced by this layer. The boundary of the first layer is marked with an arrow A, where the local density is a minimum. Likewise, the boundary of the second layer is marked by an arrow B, and so on for higher layers. The same procedure is applied to other temperatures studied in this work. 3.2.1. Adsorption at 77 K First we consider the adsorption of argon on the graphitized thermal carbon black at 77 K, which is below the triple point of argon (83.8 K). In Fig. 3 the simulated adsorption isotherm of argon on an infinite plane surface with no surface mediation is plotted both in log–log (Fig. 3a) and linear (Fig. 3b) scale, respectively. To correctly describe the experimental Henry constant, the binary interaction parameter ksf was found to be 0.035. In the region of the completion of the first layer (pressures between 10 and 40 Pa), the simulation results exhibits a shoulder, slightly overpredicting the experimental data. The overprediction is even more pronounced in the regions where the second and higher layers are about to be completely formed. This overprediction, as noted earlier, is due to the failure to account for the surface mediation. To eliminate these overpredictions by the molecular model, the surface mediation was induced in the model through the damping factor F. First, we apply the surface-mediation damping factor only for the first layer; the simulation isotherm is shown in Fig. 3a as the solid line. Compared with the case of no surface mediation, the fitting between the simulation results and the experimental data at the formation of monolayer is improved, but the overpredictions remain for the regions of second and higher layers formation. This suggests that the surface mediation must be extended beyond the confinement of the first layer. By accounting for the surface-mediation damping factor up to the third layer, we see a significant, although not perfect, improvement in the description of the experimental data. The surface-mediation damping factors of the first three layers are 0.97, 0.98, and 0.99, indicating that the surface mediation is losing its influence as we move away from the surface. A possible reason why the molecular model with surface mediation could not describe perfectly the experimental data (even though it is better than the model without surface mediation) is that the molecular parameters for argon are derived from the bulk vapor–liquid equilibrate. The temperature 77 K is below the tripe point, and the possible presence of solid argon in the adsorbed phase might not be accounted for correctly by the simple 12-6 LJ equation with r = 0.3405 nm and e/kB = 119.8 K. 3.2.2. Adsorption at 87.3 K The same procedures used in the analysis of the experimental data at 77 K can now be used to investigate the behavior of argon adsorption on GTCB at 87.3 K. The GCMC simulated isotherms and the experimental data are shown in Fig. 4. From these plots, a number of features that we observed earlier for 77 K data are repeated here at 87.3 K: (i) by using binary interaction parameter ksf, the experimental Henry constant is reproduced by the GCMC simulation; (ii) the isotherm obtained by simulation without surface
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Fig. 1. Experimental adsorption isotherms of argon at 77 K (a, b) and 87.3 K (c, d).
Fig. 2. Local density distribution of argon at 77 K.
mediation shows significant humps at the formation of monolayer and higher layers; (iii) applying the surface mediation for the first layer, the simulated isotherm describes the experimental data quite well in the monolayer region, but for higher layers the isotherm is the same as that for the case of no surface mediation; (iv) by extending the application of the surface mediation to the third layer, the description of the second and third layers is improved significantly, which can be seen in Fig. 4b as dash-dot line. Finally we extend this surface mediation up to the fourth layer, and
the result is plotted in Fig. 4b as a solid line, and as expected the agreement is very good up to four layers above the surface. The surface-mediation damping factors are 0.970, 0.980, 0.995, and 0.997, once again suggesting the decay of the damping as distance is increased from the surface. We have studied the effects of surface mediation on the description of adsorption isotherm of argon on GTCB at 77 and 87.3 K. One obvious difference is particularly noted. At 77 K, the surface mediation applied to three layers, it does improve the agreement between the simulation results and the experimental data but it fails to capture the correct behavior of the experimental data. However, for 87.3 K data, by accounting for the surface mediation, the simulated isotherm describes the experiment data very well up to four layers. The distinction between the behaviors of 77 and 87.3 K may be due to the formation of solid argon at 77 K, which is below the triple point of argon (83.8 K). Indeed, at this temperature, Grillet et al. [18] have suggested a phase change from a two-dimensional (2D) hypercritical fluid state to a 2D solid state. They supported this assertion with a detailed calorimetric study. This will be supported with the GCMC simulation on isosteric heat in Section 3.3 where the heat curve versus loading shows a sharp spike in the region where the phase change occurs. This only occurs with 77 K, not with higher temperature simulation results, which lends further support of the phase change at 77 K. 3.2.3. Adsorption at 90.05, 93.05, and 95.25 K To further support the inclusion of the surface mediation in the molecular model, we further test our model with experimental
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Fig. 3. Simulation results for the adsorption of argon at 77 K on GTCB: (a) logarithmic scale; (b) linear scale.
Fig. 4. Simulation results for the adsorption of argon on GTCB at 87.3 K: (a) logarithmic scale; (b) linear scale.
data at 90.05, 93.05, and 95.25 K in the literature [2,4,19] to supplement our own experimental data presented and analyzed in the last sections. These experimental data are shown in Fig. 5, and with the exception of 90.05 K data which span over two layers the other two data contain points only for the second layer. First we consider the experimental data at 90.05 K. This set of data covers the first and second layers and therefore we can derive the binary interaction parameter ksf (to fit the experimental Henry constant) and the surface-mediation damping factors for the first and second layers. The agreement between the simulation results (with ksf and F correctly accounted for) and the experimental data is excellent as shown in both log–log and linear scales in Fig. 5a and b. Since the 93.05 and 95.25 K data do not cover the first layer, it is not possible to determine ksf, but it is possible to derive the surface-mediation damping factors for these two sets of data. Once again we see in Fig. 5c and d that the inclusion of the surface mediation in the molecular model is very important in the description of the experimental data. Having analyzed experimental data of argon adsorption on GTCB at five different temperatures, we can draw a number of conclusions from these analyses.
ric shape of polyhedron. The finite size of the exposed basal faces of the polyhedron might be the cause of the small, but positive, solid–fluid binary interaction parameter. (ii) The surface-mediation damping factors for various layers are a weak function of temperature. These are summarized in Table 1. Where we see this weak dependence on temperature and the surface mediation becomes less significant with the distance from the surface (F = 1 means that the surface mediation is absent). It approaches unity in the fourth layer, and we may draw a tentative conclusion that the surface mediation is absent from the fifth layer onward. (iii) The agreement between the simulation results and the experimental data at four temperatures above the triple point is much better than that at 77 K (below the triple point) which might suggest the inadequacy of the potential model of argon in the correct description of solid argon in the adsorbed phase at 77 K. Nevertheless the present model with surface mediation describes the 77 K data better than the model that dose not account for it.
3.3. Isosteric heat (i) The solid–fluid binary interaction parameter ksf is very small but positive. This means that the adsorption force of GTCB is slightly weaker than that calculated from the ideal graphite (infinite in extent) surface. This is likely to be due to the geometrical aspects of GTCB, which is known to have a geomet-
The isosteric heat of adsorption can be obtained by two methods. In the first method, we apply the Clausius–Clapeyron equation to the experimental isotherms obtained at two different temperatures. In this work, only the 77 and 87.3 K isotherm data are
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Fig. 5. Adsorption isotherms of argon on GTCB: (a) 90.05 K, logarithmic scale; (b) 90.05 K, linear scale; (c) 93.05 K; (d) 95.25 K.
Table 1 The surface-mediation damping factors.
1st layer 2nd layer 3rd layer 4th layer
(Carbopack F)
(Sterling 2700)
77 K
87.3 K
90.05 K
93.05 K
95.25 K
0.970 0.980 0.990
0.970 0.980 0.995 0.997
0.970 0.978 0.997 0.998
0.960 0.970 0.995 0.997
0.960 0.970 0.980 0.995
available over the wide pressure range, and therefore they are used in the calculation of the isosteric heat. The other method is the application of the fluctuation theory in the GCMC simulation to derive the isosteric heat. In Fig. 6, we show the isosteric heat calculated with the Clausius–Clapeyron equation using our experimental data. The isosteric heat obtained with the Gardner et al. data is also shown in the same figure for comparison. They agree well with each other and also agree with the GCMC simulation results (shown as dotted line in Fig. 6). The perfect agreement between the two different sets of experimental data and the GCMC results is a clear indication of the high homogeneity of the GTCB used in this work as well as that used in Gardner et al.’s work. One interesting observation that is seen with the ‘‘experiment” calculated isosteric heat and the GCMC simulation heat is the appearance of a heat spike in the region where the first layer has reached its completion and the second layer is beginning to form. We postpone the discussion of the heat spike, and discuss the behavior of the isosteric heat with temperature first.
Fig. 6. Isosteric heat of argon adsorption on GTCB using the Clausius–Clapeyron equation.
First we consider the 77 K data. Experimental isosteric heats of argon on GTCB at 77 K are available in the literature, for example, Beebe et al. [20,21], Grillet et al. [18]. Bobka et al. [22], Pace and Siebert [23], and Avgul and Kiselev [19]. Among these data, only the data of Grillet et al. has high enough resolution to reveal the heat spike in the isosteric heat curve versus loading. This is shown in Fig. 7, and also shown in this figure is the GCMC simulation result. The agreement is very good, at least quantitative, and the GCMC results also show the heat spike which is in accordance with the experimental result. Beside the presence of a heat spike for
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491
Fig. 7. Isosteric heat of argon adsorption on GTCB at 77 K.
Fig. 9. Isosteric heat of argon adsorption on GTCB at different temperatures.
77 K data, we also observe the three distinct linear portions of the heat curve in the submonolayer region. This is shown as 1, 2, and 3 in Fig. 7. Detailed explanation of these linear regions has been provided by Do and co-workers [8,24]. Readers are referred to these papers for more details. Another feature which is worthwhile to note in Fig. 7 is that the GCMC results with mediation agree better with the experimental data of Grillet et al. than those without accounting for surface mediation. The isosteric heats at 87.3 K obtained from the GCMC simulation with and without surface mediation are shown in Fig. 8. The same effects of surface mediation on the heat of adsorption at 77 K are observed again at 87.3 K. In the presence of surface mediation, the isosteric heat is slightly lower than that obtained from the model without surface mediation. This is expected because of the weaker intermolecular interaction, induced by the presence of the surface. Also shown in Fig. 8 is the GCMC simulation results for 77 K. Comparing the heat curves for 77 and 87.3 K, we see that they are of the same order. The only difference is the presence of a heat spike on the 77 K curve and the 77 K data is sharper in the transition region of the completion of the first layer and the beginning of the second layer. The heat spike that we observed earlier in Fig. 6 from the application of the Clausius–Clapeyron equation to the experimental isotherms of 77 and 87.3 K is a result of the contribution of the 77 K data. Having shown the effects of surface mediation on the isosteric heat at 77 and 87.3 K, the isosteric heat obtained from the GCMC simulation with surface mediation at different temperatures can be studied. In Fig. 9 the GCMC isosteric heats for all five tempera-
tures are presented. We see that the heat spike is only present with the 77 K results and it is completely absent at higher temperatures. Another feature that we observe in this figure is that the linear portions in the submonolayer region are less pronounced as temperature is increased. This is physically expected because of the greater mobility of adsorbed molecules at high temperatures [24], which results in adsorption in multiple layers at the same time rather than layerwise adsorption (i.e., layer by layer). Our GCMC simulation results at 77 K indeed confirm this layer by layer adsorption. The isosteric heat of adsorption at zero loading is practically the same, which is in agreement with the analysis given by Do et al. [25]. Let us now finally turn our attention to the heat spike observed with the 77 K data. According to Do and Do [26], this heat spike is due to the compression of the first layer, which occurs when the formation of monolayer is nearly completed and the second layer begins to form. During this process, some molecules will squeeze into the first layer instead of staying in the second layer. The particles that are squeezed into the first layer will interact with more neighboring particles resulting in the higher amount of heat released. The higher heat results from the: (i) greater interaction between these particles and the surface because they are closer to the surface, (ii) greater number of neighboring particles, and (iii) the better rearrangement of all molecules in the first layer. The compression of the first layer is also evidenced by the hump in the adsorption isotherm of 77 K (shown in the inset of Fig. 1b). To further explain the presence of the heat spike, the local density distributions at 80 and 1000 Pa, which are labeled as points A and B in Fig. 7, are presented in Fig. 10. At 80 Pa, the isosteric heat
Fig. 8. Isosteric heat of argon adsorption on GTCB at 87.3 K.
Fig. 10. The local density distribution at 77 K for points A and B.
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reaches a local maximum, which is due to the completion of the first layer, and at 1000 Pa the heat spike occurs. From the observation of the local density distribution in Fig. 10, the solid surface is reasonably covered with adsorbed molecules at 80 Pa, and there is no sign of the formation of the second layer. When the pressure is increased to 1000 Pa when the heat spike is observed, we observe a further jump in the density of the first layer, indicating the compression of the first layer while the second layer is still taking in more molecules. 4. Conclusions The surface mediation is important for describing properly the adsorption behavior of argon on GTCB. It was found to extend up to four layers and with such account in the computer simulation, the results agree well with the experimental data over a range of temperatures. The extent of mediation becomes weaker with distance from the surface. The isosteric heats of argon adsorption on GTCB at different temperatures were obtained either by the application of the Clausius–Clapeyron equation on the experimental isotherms or by the fluctuation theory applied on simulation results. The agreement of the adsorption isotherm and the isosteric heat between the simulation results and the experimental data confirms the correct molecular model to describe adsorption of noble gases on GTCB. One particular feature that we observed both in the simulation and in the experimental data is the existence of a heat spike at 77 K in the region where the first layer is practically filled and its absence at higher temperatures. This heat spike is absent at higher temperature, and this is once again confirmed by both simulation and experimental data. Acknowledgments The authors acknowledge the supply of Carbopack F, kindly provided by Dr. Betz of Supelco. Financial support provided by the
Australian Research Council is gratefully acknowledged. We also acknowledge the CSC for its financial support in the form of scholarship to C. Fan.
References [1] D. Frenkel, B. Smit, Understanding Molecular Simulation, Academic Press, San Diego, 1996. p. 443. [2] S. Ross, W. Winkler, J. Colloid Sci. 10 (4) (1955) 319–329. [3] S. Ross, W.W. Pultz, J. Colloid Sci. 13 (4) (1958) 397–406. [4] J.R. Sams Jr., G. Constabaris, G.D. Halsey Jr., J. Phys. Chem. 66 (11) (1962) 2154– 2158. [5] L.D. Belyakova, A.V. Kiselev, N.V. Kovaleva, J. Phys. Chem. 42 (9) (1968) 1204– 1208. [6] L. Gardner, M. Kruk, M. Jaroniec, J. Phys. Chem. B 105 (50) (2001) 12516– 12523. [7] D.D. Do, H.D. Do, J. Colloid Interface Sci. 287 (2) (2005) 452–460. [8] D.D. Do, H.D. Do, D. Nicholson, Adsorpt. Sci. Technol. 25 (6) (2007) 347–363. [9] P. Luangkiattikhun, A. Wongkoblap, D.D. Do, Adsorpt. Sci. Technol. 24 (3) (2006) 193–204. [10] O. Sinanoglu, K.S. Pitzer, J. Chem. Phys. 32 (5) (1960) 1279–1288. [11] J.R. Sams Jr., G. Constabaris, G.D. Halsey Jr., J. Chem. Phys. 36 (5) (1962) 1334– 1339. [12] D.H. Everett, Discuss. Faraday Soc. 40 (1965) 177–187. [13] H.Y. Kim, W.A. Steele, Phys. Rev. B 45 (11) (1992) 6226–6233. [14] D.D. Do, H.D. Do, Adsorpt. Sci. Technol. 21 (5) (2003) 389–423. [15] D.D. Do, Adsorption Analysis: Equilibria and Kinetics, Series on Chemical Engineering, Imperial College Press, London, 1998, p. 892. [16] D. Nicholson, N.G. Parsonage, Computer Simulation and the Statistical Mechanics of Adsorption, Academic Press, London, 1982. [17] J.K. Johnson, J.A. Zollweg, K.E. Gubbins, Mol. Phys. 78 (3) (1992) 591–618. [18] Grillet Yves, Rouquerol Francoise, Rouquerol Jean, J. Colloid Interface Sci. 70 (2) (1978) 239–244. [19] N.N. Avgul, A.V. Kiselev, Chem. Phys. Carbon 6 (1970) 1–124. [20] R.A. Beebe, B. Millard, J. Cynarski, J. Am. Chem. Soc. 75 (1953) 839–845. [21] R.A. Beebe, D.M. Young, J. Phys. Chem. 58 (1954) 93–96. [22] R.J. Bobka, R.E. Dininny, A.R. Siebert, E.L. Pace, J. Phys. Chem. 61 (1957) 1646– 1648. [23] E.L. Pace, A.R. Siebert, J. Phys. Chem. 64 (1960) 961–963. [24] D.D. Do, D. Nicholson, H.D. Do, J. Colloid Interface Sci. 325 (1) (2008) 7–22. [25] D.D. Do, D. Nicholson, H.D. Do, J. Colloid Interface Sci. 324 (1–2) (2008) 15– 24. [26] D.D. Do, H.D. Do, Mol. Simul. 31 (9) (2005) 651–659.
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Journal of Colloid and Interface Science www.elsevier.com/locate/jcis
Effects of surface mediation on the adsorption isotherm and heat of adsorption of argon on graphitized thermal carbon black Chunyan Fan a,b, G. Birkett b, D.D. Do b,* a b
Department of Storage and Transportation Engineering, China University of Petroleum, Qingdao 266555, China School of Chemical Engineering, University of Queensland, St. Lucia, Queensland 4072, Australia
a r t i c l e
i n f o
Article history: Received 5 September 2009 Accepted 11 October 2009 Available online 14 November 2009 Keywords: Gas phase adsorption Graphitized thermal carbon black Surface mediation Heat of adsorption Argon
a b s t r a c t In this paper, the effects of surface mediation on the adsorption isotherm and isosteric heat of adsorption on a graphite surface were investigated, as the surface mediation is known to affect the intermolecular interaction of adsorbed molecules close to the surface. Kim and Steele (Phys. Rev. B 45 (11) (1992) 6226–6233) and others have assumed that the surface mediation is confined only to the first layer. This will be tested in this paper with a combined experimental and Grand Canonical Monte Carlo (GCMC) simulation of adsorption of argon on graphitized thermal carbon black (GTCB) over a range of temperatures (77–95.25 K). By matching the simulation results against the experimental data, we have found that the surface mediation is extended up to the fourth layer, rather than only the first as suggested by Kim and Steele, and the extent of this mediation is reduced with distance from the surface. This reinforces the important role of surface on the intermolecular interaction. With regard to the heat of adsorption, we found that the isosteric heats obtained directly from the simulation agree fairly well with the heats calculated from the application of the Clausius–Clapeyron equation on experimental isotherms of 77 and 87.3 K. The temperature dependence of the isosteric heat was investigated with the GCMC simulation results. One interesting observation is the existence of a heat spike at 77 K and its absence at higher temperatures, a phenomenon which is common to both simulation results and experimental data. This lends good support to the molecular model with surface mediation as a proper one to describe adsorption of noble gases on GTCB. Ó 2009 Elsevier Inc. All rights reserved.
1. Introduction With molecular simulation techniques and the availability of computational power, the study of adsorption behavior at the molecular level is possible. Both simple and complex adsorption phenomena can be described by the correct molecular models. Comparing simulation results against experimental data will increase our understanding about the mechanisms of adsorption. Among various molecular simulation methods, Grand Canonical Monte Carlo (GCMC) is the most commonly used for the study of adsorption. It mimics the same conditions that are generally used in an adsorption experiment, where the temperature, volume, and chemical potential (pressure of the bulk phase) are specified [1]. In this work, the behavior of argon adsorption on a graphitized surface will be investigated with a combined study of experimental work and GCMC simulation. The adsorption of argon on GTCB is one of the simplest systems to study and it has received considerable experimental and theoretical attention [2–9]. Despite numerous simulation studies in * Corresponding author. Fax: +61 7 3365 2789. E-mail address: [email protected] (D.D. Do). 0021-9797/$ - see front matter Ó 2009 Elsevier Inc. All rights reserved. doi:10.1016/j.jcis.2009.10.018
the literature, the commonly used models do not account for the nonadditivity between the fluid–fluid interaction and the solid– fluid interaction and therefore fail to reproduce accurately the experimental data. Particularly they fail to describe correctly the regions where the first and higher layers are about to be completely formed. To be more specific they overpredict the experimental data in those regions, suggesting the overprediction of the interaction among adsorbed molecules. It has been argued [10–12] that in the presence of a surface the intermolecular interaction energy is reduced. Various reasons for this reduction include surface polarization and multibody effects. Both of these give rise to nonadditivity [10–12]. The concept of surface mediation is well known with its effects on the intermolecular interaction of adsorbed molecules close to the surface. The details of surface mediation will be discussed in Section 2.3. Kim and Steele [13] applied surface mediation in their study of adsorption of methane on graphite and they confine this effect only to molecules in the first layer. In this work, the same methodology will be applied to argon adsorption on GTCB over a range of temperatures (77–95.25 K), but with the range of surface mediation extended beyond the first layer. The effects of the surface mediation are investigated not only on the adsorption
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isotherm but also the isosteric heat of adsorption. The isosteric heats at different temperatures are obtained either by the application of the Clausius–Clapeyron equation to experimental isotherms at two different temperatures or by applying the fluctuation theory in the molecular simulation. 2. Theory
where F ia is the surface-mediation damping factor contributed by the particle i which resides in the layer a and F jb is that contributed by the particle j which resides in layer b. The variable uij is the intermolecular energy when two particles are in the bulk phase and are under no influence from the surface (i.e., calculated from Eq. (1)). The variable ueff ij is called the effective intermolecular potential energy. The values of the damping factors F ia and F jb are determined by matching the simulation results against the experimental data.
2.1. Fluid model and the interaction energy 2.4. Isosteric heat The potential model used for argon is a 1-center Lennard-Jones model. The interaction energy between two isolated argon atoms is calculated with the classical 12-6 Lennard-Jones potential equation
uij ¼ 4eff
"
rff
12
r ij
rff r ij
6 # ;
ð1Þ
where rij is the separation distance between two particles i and j, and the molecular parameters eff and rff are the well depth of interaction energy and the collision diameter of argon, respectively. The values of these parameters are rff = 0.3405 nm and eff/kB = 119.8 K. 2.2. Solid model and solid–fluid interaction energy A simple homogeneous (structureless) graphitized surface model is used in this study. The interaction energy between a fluid particle and the structureless surface is calculated with the Steele 10-4-3 potential [14],
" usf ðzÞ ¼ 2pqs r
2 sf sf
e
# r4sf 2 rsf 10 rsf 4 ; 5 z z 3Dðz þ 0:61DÞ3
ð2Þ
where qs is the surface density of the carbon center (38.2 nm2), D is the interlayer spacing between two adjacent graphene layers (0.3354 nm), z is the normal distance from the surface to the argon particle, rsf and esf are the cross solid–fluid molecular parameters and calculated from the Lorentz-Berthelot rule. The solid–fluid collision diameter is
rsf ¼ ðrss þ rff Þ=2:
ð3aÞ
The solid–fluid interaction energy is adjusted by the introduction of the solid–fluid binary interaction parameter, ksf, such that the Henry constant is reproduced by the GCMC simulation, that is,
esf ¼ ð1 ksf Þðess eff Þ1=2 :
ð3bÞ
The LJ parameters used for carbon atom in a graphene layer are rss = 0.340 nm and ess/kB = 28 K. 2.3. Surface mediation As noted in the Introduction, the interaction between fluid molecules close to the surface is affected by the presence of a solid surface. This is because the electric field of the surface will induce a dipole on the fluid molecules close to it, and these parallel induced dipoles point in the same direction, resulting in a slight repulsion between these molecules. Therefore the fluid–fluid interaction energy as calculated in Eq. (1) will overestimate the interaction of particles close to the surface. Surface mediation is the term used to consider the reduction of the intermolecular interaction due to the presence of a surface. In this paper, a simple approach suggested by Kim and Steele [13] will be applied to describe the surface mediation of argon adsorption on a graphitized surface. The effective intermolecular interaction energy is calculated from i j ueff ij ¼ F a F b uij ;
ð4Þ
The isosteric heat of adsorption is calculated by using two different approaches. The first is the classical method by applying the following Clausius–Clapeyron equation [15] on two experimental isotherms obtained at two sufficiently close temperatures.
qiso ¼ R
ln P2 ln P 1 ; 1=T 2 1=T 1 C
ð5Þ
where R is the gas constant, T1 and T2 are temperatures, P1 and P2 are the pressures at which the surface excesses of the two isotherms are the same. The second method is based on the fluctuation theory applied to the simulation results. The following equation was obtained as a result in [16].
qiso ¼
hUihNi hUNi hN 2 i hNihNi
þ kB T;
ð6Þ
where h i is the ensemble average, N is the number of particles, and U is the configuration energy of the system. 2.5. Monte Carlo simulation method Among many Monte Carlo (MC) simulation methods, the Grand Canonical Monte Carlo is the one which mimics the same conditions that are generally used in an adsorption experiment, as the temperature, volume, and chemical potential (pressure of the bulk phase) are fixed. In this study, GCMC will be used to obtain the isotherm and the isosteric heat of argon adsorption on GTCB with the models described above. For a specific condition, 10,000 cycles are set for the equilibrium stage and another 10,000 cycles are used to obtain ensemble averages. Each cycle consists of one thousand displacement moves, insertion and deletion of equal probability. The final configuration of the previous condition is then used as the starting configuration for the next condition. The cutoff radius is taken to be either five times the collision diameter of argon or half of the box length, whichever is smaller. The initial displacement step length is half of the box length and it is adjusted during the equilibration step such that the acceptance ratio of movement is between 20% and 25%. The simulation box used in this work has a linear dimension of 5 nm in the x and y directions. A structureless carbon surface is at the bottom of the box (in the z direction) and the top boundary is treated as a hard wall. Any attempt of displacing a particle out of the hard wall will be rejected. The height of the simulation box is set as 6 nm. Periodic boundary conditions are applied in x and y directions to simulate the infinite extent of the surface in these directions. The surface excess per unit area is calculated by the equation
C¼
hNi qV acc ; Lx Ly
ð7Þ
where hNi is the ensemble total number of particles in the simulation box, and q is the density of bulk phase, which is calculated with the Johnson et al.’s equation of state [17]. The variables Lx and Ly are the dimensions of the surface in x and y directions, respectively. The
C. Fan et al. / Journal of Colloid and Interface Science 342 (2010) 485–492
volume Vacc is the accessible volume, which is defined as one in which the fluid–solid potential energy is nonpositive. The local density distribution of fluids is calculated from
qz ¼
hDNzþDz i : Lx Ly Dz
ð8Þ
In this equation, qz is the local density, hDNz+Dzi is the ensemble number of particles in the region from z to z + Dz. In this work Dz is set equal to 0.01 nm. 2.6. Experimental method The sample used in this work is a graphitized thermal carbon black, Carbopack F Lot No. 1665-84A, which is kindly supplied by Dr. Betz of Supelco. In our laboratories, the measurements of argon adsorption on this sample were carried out at 77 and 87.3 K using an ASAP 2020 static volumetric adsorption analyzer from Micromeritics (Altanta, GA, USA). The mass of Carbopack F used for measurement was 4.28 g, before the measurements, the sample was degassed under vacuum for at least 15 h at 473 K. The BET specific surface area was evaluated on the basis of argon data in the relative pressure range from 0.1 to 0.2 using the cross-sectional area of 0.14 nm2 [8], and was found to be 5.22 m2/g. 3. Results and discussion 3.1. Experimental data of 77 and 87.3 K The adsorption isotherms of argon on a Carbopack F (different lot from the one that we used in this work) using ASAP 2010 at 77 and 87.3 K have been reported by Gardner et al. [6]. This is shown in Fig. 1. Also plotted in this figure are the isotherms obtained in our laboratories, and it is interesting (but not surprising) that our data agree very well with Gardner’s data even their Carbopack F and ours come from different batches. This is an indication of a homogeneous surface because we do not expect such an agreement if these samples are heterogeneous. A further support of the homogeneity is the clear existence of the Henry law region as seen in the log–log plot in Fig. 1b and d for 77 and 87.3 K, respectively. Since the experiment results are in perfect agreement with Gardner’s data, they can be used to develop a molecular model which is used in the Monte Carlo simulation to describe adsorption isotherm and isosteric heat of argon adsorption on GTCB. Specifically the two parameters that we need to derive are the binary interaction parameter ksf and the damping factor F. The former is to ensure that the model can describe correctly the Henry constant, and the later is for the good description of the complete isotherm. 3.2. Simulation isotherms Two adjusting parameters used in the simulation are the binary solid–fluid interaction parameter ksf and the surface-mediation damping factor F. Since ksf affects the isotherm in the low pressure region and F only plays a role when the surface is reasonably covered with adsorbed molecules, we can determine them separately. By using the experimental Henry constant we obtain the binary interaction parameter ksf. Once this is done, the surface-mediation damping factor F (for four layers) can be determined by matching the simulation results of adsorption isotherm against the experiment data. We perform this task for up to four layers for a number of reasons. For layers above the fourth layer we have found that F is very close to unity, meaning that the surface mediation starts losing its influence at distances far away from the surface.
487
Furthermore, matching the simulation results and the data in the region where there are more than four layers is not credible because there is a strong possibility of the interference of the capillary condensation in the interstices between primary particles. To determine the specific surface-mediation damping factors for different layers, we have to define the boundary of each layer. This is realized by considering the local density distribution obtained from the GCMC simulation results. Take the case at 77 K as an example, the local density distribution of argon adsorption on GTCB at a pressure equal to 30,000 Pa is shown in Fig. 2. Each peak in this figure constitutes a layer. The first layer is the sharpest one, which is expected because of the strong adsorption forces experienced by this layer. The boundary of the first layer is marked with an arrow A, where the local density is a minimum. Likewise, the boundary of the second layer is marked by an arrow B, and so on for higher layers. The same procedure is applied to other temperatures studied in this work. 3.2.1. Adsorption at 77 K First we consider the adsorption of argon on the graphitized thermal carbon black at 77 K, which is below the triple point of argon (83.8 K). In Fig. 3 the simulated adsorption isotherm of argon on an infinite plane surface with no surface mediation is plotted both in log–log (Fig. 3a) and linear (Fig. 3b) scale, respectively. To correctly describe the experimental Henry constant, the binary interaction parameter ksf was found to be 0.035. In the region of the completion of the first layer (pressures between 10 and 40 Pa), the simulation results exhibits a shoulder, slightly overpredicting the experimental data. The overprediction is even more pronounced in the regions where the second and higher layers are about to be completely formed. This overprediction, as noted earlier, is due to the failure to account for the surface mediation. To eliminate these overpredictions by the molecular model, the surface mediation was induced in the model through the damping factor F. First, we apply the surface-mediation damping factor only for the first layer; the simulation isotherm is shown in Fig. 3a as the solid line. Compared with the case of no surface mediation, the fitting between the simulation results and the experimental data at the formation of monolayer is improved, but the overpredictions remain for the regions of second and higher layers formation. This suggests that the surface mediation must be extended beyond the confinement of the first layer. By accounting for the surface-mediation damping factor up to the third layer, we see a significant, although not perfect, improvement in the description of the experimental data. The surface-mediation damping factors of the first three layers are 0.97, 0.98, and 0.99, indicating that the surface mediation is losing its influence as we move away from the surface. A possible reason why the molecular model with surface mediation could not describe perfectly the experimental data (even though it is better than the model without surface mediation) is that the molecular parameters for argon are derived from the bulk vapor–liquid equilibrate. The temperature 77 K is below the tripe point, and the possible presence of solid argon in the adsorbed phase might not be accounted for correctly by the simple 12-6 LJ equation with r = 0.3405 nm and e/kB = 119.8 K. 3.2.2. Adsorption at 87.3 K The same procedures used in the analysis of the experimental data at 77 K can now be used to investigate the behavior of argon adsorption on GTCB at 87.3 K. The GCMC simulated isotherms and the experimental data are shown in Fig. 4. From these plots, a number of features that we observed earlier for 77 K data are repeated here at 87.3 K: (i) by using binary interaction parameter ksf, the experimental Henry constant is reproduced by the GCMC simulation; (ii) the isotherm obtained by simulation without surface
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Fig. 1. Experimental adsorption isotherms of argon at 77 K (a, b) and 87.3 K (c, d).
Fig. 2. Local density distribution of argon at 77 K.
mediation shows significant humps at the formation of monolayer and higher layers; (iii) applying the surface mediation for the first layer, the simulated isotherm describes the experimental data quite well in the monolayer region, but for higher layers the isotherm is the same as that for the case of no surface mediation; (iv) by extending the application of the surface mediation to the third layer, the description of the second and third layers is improved significantly, which can be seen in Fig. 4b as dash-dot line. Finally we extend this surface mediation up to the fourth layer, and
the result is plotted in Fig. 4b as a solid line, and as expected the agreement is very good up to four layers above the surface. The surface-mediation damping factors are 0.970, 0.980, 0.995, and 0.997, once again suggesting the decay of the damping as distance is increased from the surface. We have studied the effects of surface mediation on the description of adsorption isotherm of argon on GTCB at 77 and 87.3 K. One obvious difference is particularly noted. At 77 K, the surface mediation applied to three layers, it does improve the agreement between the simulation results and the experimental data but it fails to capture the correct behavior of the experimental data. However, for 87.3 K data, by accounting for the surface mediation, the simulated isotherm describes the experiment data very well up to four layers. The distinction between the behaviors of 77 and 87.3 K may be due to the formation of solid argon at 77 K, which is below the triple point of argon (83.8 K). Indeed, at this temperature, Grillet et al. [18] have suggested a phase change from a two-dimensional (2D) hypercritical fluid state to a 2D solid state. They supported this assertion with a detailed calorimetric study. This will be supported with the GCMC simulation on isosteric heat in Section 3.3 where the heat curve versus loading shows a sharp spike in the region where the phase change occurs. This only occurs with 77 K, not with higher temperature simulation results, which lends further support of the phase change at 77 K. 3.2.3. Adsorption at 90.05, 93.05, and 95.25 K To further support the inclusion of the surface mediation in the molecular model, we further test our model with experimental
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489
Fig. 3. Simulation results for the adsorption of argon at 77 K on GTCB: (a) logarithmic scale; (b) linear scale.
Fig. 4. Simulation results for the adsorption of argon on GTCB at 87.3 K: (a) logarithmic scale; (b) linear scale.
data at 90.05, 93.05, and 95.25 K in the literature [2,4,19] to supplement our own experimental data presented and analyzed in the last sections. These experimental data are shown in Fig. 5, and with the exception of 90.05 K data which span over two layers the other two data contain points only for the second layer. First we consider the experimental data at 90.05 K. This set of data covers the first and second layers and therefore we can derive the binary interaction parameter ksf (to fit the experimental Henry constant) and the surface-mediation damping factors for the first and second layers. The agreement between the simulation results (with ksf and F correctly accounted for) and the experimental data is excellent as shown in both log–log and linear scales in Fig. 5a and b. Since the 93.05 and 95.25 K data do not cover the first layer, it is not possible to determine ksf, but it is possible to derive the surface-mediation damping factors for these two sets of data. Once again we see in Fig. 5c and d that the inclusion of the surface mediation in the molecular model is very important in the description of the experimental data. Having analyzed experimental data of argon adsorption on GTCB at five different temperatures, we can draw a number of conclusions from these analyses.
ric shape of polyhedron. The finite size of the exposed basal faces of the polyhedron might be the cause of the small, but positive, solid–fluid binary interaction parameter. (ii) The surface-mediation damping factors for various layers are a weak function of temperature. These are summarized in Table 1. Where we see this weak dependence on temperature and the surface mediation becomes less significant with the distance from the surface (F = 1 means that the surface mediation is absent). It approaches unity in the fourth layer, and we may draw a tentative conclusion that the surface mediation is absent from the fifth layer onward. (iii) The agreement between the simulation results and the experimental data at four temperatures above the triple point is much better than that at 77 K (below the triple point) which might suggest the inadequacy of the potential model of argon in the correct description of solid argon in the adsorbed phase at 77 K. Nevertheless the present model with surface mediation describes the 77 K data better than the model that dose not account for it.
3.3. Isosteric heat (i) The solid–fluid binary interaction parameter ksf is very small but positive. This means that the adsorption force of GTCB is slightly weaker than that calculated from the ideal graphite (infinite in extent) surface. This is likely to be due to the geometrical aspects of GTCB, which is known to have a geomet-
The isosteric heat of adsorption can be obtained by two methods. In the first method, we apply the Clausius–Clapeyron equation to the experimental isotherms obtained at two different temperatures. In this work, only the 77 and 87.3 K isotherm data are
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Fig. 5. Adsorption isotherms of argon on GTCB: (a) 90.05 K, logarithmic scale; (b) 90.05 K, linear scale; (c) 93.05 K; (d) 95.25 K.
Table 1 The surface-mediation damping factors.
1st layer 2nd layer 3rd layer 4th layer
(Carbopack F)
(Sterling 2700)
77 K
87.3 K
90.05 K
93.05 K
95.25 K
0.970 0.980 0.990
0.970 0.980 0.995 0.997
0.970 0.978 0.997 0.998
0.960 0.970 0.995 0.997
0.960 0.970 0.980 0.995
available over the wide pressure range, and therefore they are used in the calculation of the isosteric heat. The other method is the application of the fluctuation theory in the GCMC simulation to derive the isosteric heat. In Fig. 6, we show the isosteric heat calculated with the Clausius–Clapeyron equation using our experimental data. The isosteric heat obtained with the Gardner et al. data is also shown in the same figure for comparison. They agree well with each other and also agree with the GCMC simulation results (shown as dotted line in Fig. 6). The perfect agreement between the two different sets of experimental data and the GCMC results is a clear indication of the high homogeneity of the GTCB used in this work as well as that used in Gardner et al.’s work. One interesting observation that is seen with the ‘‘experiment” calculated isosteric heat and the GCMC simulation heat is the appearance of a heat spike in the region where the first layer has reached its completion and the second layer is beginning to form. We postpone the discussion of the heat spike, and discuss the behavior of the isosteric heat with temperature first.
Fig. 6. Isosteric heat of argon adsorption on GTCB using the Clausius–Clapeyron equation.
First we consider the 77 K data. Experimental isosteric heats of argon on GTCB at 77 K are available in the literature, for example, Beebe et al. [20,21], Grillet et al. [18]. Bobka et al. [22], Pace and Siebert [23], and Avgul and Kiselev [19]. Among these data, only the data of Grillet et al. has high enough resolution to reveal the heat spike in the isosteric heat curve versus loading. This is shown in Fig. 7, and also shown in this figure is the GCMC simulation result. The agreement is very good, at least quantitative, and the GCMC results also show the heat spike which is in accordance with the experimental result. Beside the presence of a heat spike for
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491
Fig. 7. Isosteric heat of argon adsorption on GTCB at 77 K.
Fig. 9. Isosteric heat of argon adsorption on GTCB at different temperatures.
77 K data, we also observe the three distinct linear portions of the heat curve in the submonolayer region. This is shown as 1, 2, and 3 in Fig. 7. Detailed explanation of these linear regions has been provided by Do and co-workers [8,24]. Readers are referred to these papers for more details. Another feature which is worthwhile to note in Fig. 7 is that the GCMC results with mediation agree better with the experimental data of Grillet et al. than those without accounting for surface mediation. The isosteric heats at 87.3 K obtained from the GCMC simulation with and without surface mediation are shown in Fig. 8. The same effects of surface mediation on the heat of adsorption at 77 K are observed again at 87.3 K. In the presence of surface mediation, the isosteric heat is slightly lower than that obtained from the model without surface mediation. This is expected because of the weaker intermolecular interaction, induced by the presence of the surface. Also shown in Fig. 8 is the GCMC simulation results for 77 K. Comparing the heat curves for 77 and 87.3 K, we see that they are of the same order. The only difference is the presence of a heat spike on the 77 K curve and the 77 K data is sharper in the transition region of the completion of the first layer and the beginning of the second layer. The heat spike that we observed earlier in Fig. 6 from the application of the Clausius–Clapeyron equation to the experimental isotherms of 77 and 87.3 K is a result of the contribution of the 77 K data. Having shown the effects of surface mediation on the isosteric heat at 77 and 87.3 K, the isosteric heat obtained from the GCMC simulation with surface mediation at different temperatures can be studied. In Fig. 9 the GCMC isosteric heats for all five tempera-
tures are presented. We see that the heat spike is only present with the 77 K results and it is completely absent at higher temperatures. Another feature that we observe in this figure is that the linear portions in the submonolayer region are less pronounced as temperature is increased. This is physically expected because of the greater mobility of adsorbed molecules at high temperatures [24], which results in adsorption in multiple layers at the same time rather than layerwise adsorption (i.e., layer by layer). Our GCMC simulation results at 77 K indeed confirm this layer by layer adsorption. The isosteric heat of adsorption at zero loading is practically the same, which is in agreement with the analysis given by Do et al. [25]. Let us now finally turn our attention to the heat spike observed with the 77 K data. According to Do and Do [26], this heat spike is due to the compression of the first layer, which occurs when the formation of monolayer is nearly completed and the second layer begins to form. During this process, some molecules will squeeze into the first layer instead of staying in the second layer. The particles that are squeezed into the first layer will interact with more neighboring particles resulting in the higher amount of heat released. The higher heat results from the: (i) greater interaction between these particles and the surface because they are closer to the surface, (ii) greater number of neighboring particles, and (iii) the better rearrangement of all molecules in the first layer. The compression of the first layer is also evidenced by the hump in the adsorption isotherm of 77 K (shown in the inset of Fig. 1b). To further explain the presence of the heat spike, the local density distributions at 80 and 1000 Pa, which are labeled as points A and B in Fig. 7, are presented in Fig. 10. At 80 Pa, the isosteric heat
Fig. 8. Isosteric heat of argon adsorption on GTCB at 87.3 K.
Fig. 10. The local density distribution at 77 K for points A and B.
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reaches a local maximum, which is due to the completion of the first layer, and at 1000 Pa the heat spike occurs. From the observation of the local density distribution in Fig. 10, the solid surface is reasonably covered with adsorbed molecules at 80 Pa, and there is no sign of the formation of the second layer. When the pressure is increased to 1000 Pa when the heat spike is observed, we observe a further jump in the density of the first layer, indicating the compression of the first layer while the second layer is still taking in more molecules. 4. Conclusions The surface mediation is important for describing properly the adsorption behavior of argon on GTCB. It was found to extend up to four layers and with such account in the computer simulation, the results agree well with the experimental data over a range of temperatures. The extent of mediation becomes weaker with distance from the surface. The isosteric heats of argon adsorption on GTCB at different temperatures were obtained either by the application of the Clausius–Clapeyron equation on the experimental isotherms or by the fluctuation theory applied on simulation results. The agreement of the adsorption isotherm and the isosteric heat between the simulation results and the experimental data confirms the correct molecular model to describe adsorption of noble gases on GTCB. One particular feature that we observed both in the simulation and in the experimental data is the existence of a heat spike at 77 K in the region where the first layer is practically filled and its absence at higher temperatures. This heat spike is absent at higher temperature, and this is once again confirmed by both simulation and experimental data. Acknowledgments The authors acknowledge the supply of Carbopack F, kindly provided by Dr. Betz of Supelco. Financial support provided by the
Australian Research Council is gratefully acknowledged. We also acknowledge the CSC for its financial support in the form of scholarship to C. Fan.
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