Wetting Behaviour of Carbon Dioxide on Graphite

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C: Surfaces, Interfaces, Porous Materials, and Catalysis

On the Non-Wetting/Wetting Behaviour of Carbon Dioxide on Graphite Hui Xu, Yonghong Zeng, Duong Dang Do, and David Nicholson J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.9b00635 • Publication Date (Web): 13 Mar 2019 Downloaded from http://pubs.acs.org on March 21, 2019

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The Journal of Physical Chemistry

On the Non-Wetting/Wetting Behaviour of Carbon Dioxide on Graphite Hui Xu, Yonghong Zeng, D. D. Do* and D. Nicholson School of Chemical Engineering University of Queensland St Lucia, QLD, 4072 Australia

Abstract Extensive simulations of CO2 adsorption on graphite were carried out over a range of temperature to investigate the effects of temperature on the non-wetting/wetting transition. CO2 adsorbed on graphite is non-wetting below the bulk triple point temperature (Ttr = 215K) but wetting above this temperature, and differs from noble gases, which form an adsorbed film at all temperatures. Our simulation results confirm that the CO2/graphite system is nonwetting at temperatures below 90K, as reported experimentally by Terlain and Larher1 and by Morishige2. For temperatures between the wetting temperature of 90K and the bulk triple point, incomplete wetting occurs and the adsorbed film has a finite thickness at the bulk coexistence pressure. This is a consequence of the fact that the isosteric heat of adsorption at zero loading, qst(0) is lower than the heat of sublimation of bulk CO2. On the other hand, at temperatures greater than Ttr, the adsorption isotherm exhibits continuous wetting as the pressure approaches the bulk coexistence pressure, because qst(0) is greater than the bulk heat of condensation. We support these findings with detailed analysis of the molecular configurations along the canonical isotherms, the isosteric heat as a function of loading, and the local orientation-density distributions. The 2D-critical temperature of the first adsorbate layer was determined as 130K, in excellent agreement with 127.5K estimated experimentally by Terlain and Larher1. In a final section, we present a parametric map showing regions of non-wetting, wetting and incomplete wetting for CO2 adsorption on the surface of adsorbents of different strengths.

* Author to whom all correspondence should be addressed, Email: [email protected]

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1 Introduction The phenomenon of wetting/non-wetting on non-porous substrates has attracted great interest because of its relevance to the growth mode of an adsorbed film and to condensation in porous solids. As a result, many theories on wetting transitions have been developed 3-7. On a macroscopic scale wetting and non-wetting behaviour is defined in terms of the amount adsorbed at the bulk coexistence vapour pressure P0 . Wetting is manifested as an adsorbed density that tends to infinity as the pressure approaches P0 , while non-wetting or incomplete wetting is characterised by a finite amount adsorbed at P0 , and is typically observed at low temperatures, usually below the bulk triple point. Whether wetting or non-wetting occurs is determined by the interplay between the adsorbate intermolecular interactions, the adsorbateadsorbent interactions and the temperature

6, 8.

At the wetting temperature, a first-order

transition from non-wetting to wetting occurs at the bulk coexistence pressure driven by entropy, which favours a more random distribution of molecules over the surface, rather than clustering. The wetting of simple molecules, such as Ar

9-10,

Kr

11-12,

Xe

13,

N2 14, and C2H4 15, and of

molecules such as water or ammonia, with strong leading dipoles, have been extensively studied experimentally and theoretically. However, there has been no systematic study on the wetting/non-wetting behaviour of molecules that have strong leading quadrupole moments such as carbon dioxide. Adsorption of CO2 on graphite is not only important from a practical perspective in tailoring adsorbents for carbon capture 16, but also from a fundamental point of view because its adsorption is intermediate between noble gases and those with leading dipoles, such as ammonia and water. Terlain and Larher 1 measured CO2 adsorption isotherms on graphite at temperatures ranging from 114K to 135K, well below the temperature at the bulk triple point, and reported that CO2 does not wet graphite at temperatures below 100K, and that over this temperature range only a monolayer is formed on the surface when the pressure approaches the bulk coexistence pressure P0 . They attributed the non-wetting observed at temperatures below 100K to the high quadrupole moment of CO2 and low thermal fluctuations that favour the growth of bulk crystals. This interpretation was later confirmed by a number of investigations

2, 12, 17-19.

Non-wetting by CO2 was also observed on the outer surface of single walled carbon nanotubes (SWNT) at 124K

20,

which is greater than the wetting temperature on planar

2


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graphite, and which may be attributed to the convexity of the surface that weakens the interaction with CO2 and therefore raises the wetting temperature. Here we report extensive computer simulations of CO2 adsorption on graphite including adsorption isotherms, isosteric heats, local density and orientation distributions, and detailed examination of molecular configurations along the canonical isotherms. From the results, we have determined the wetting temperature and the 2D-critical temperature of the first adsorbate layer, and shown that the difference between the isosteric heat and the heat of a bulk phase change (gas-solid or gas-liquid) and the temperature are key factors governing wetting/non-wetting behaviour. Additionally, we have explored non-wetting/wetting of CO2 on substrates of different strength and established a parametric map for wetting, which should be useful in designing improved adsorbents for capture of carbon dioxide.

2 Theory 2.1 Monte Carlo Simulation Monte Carlo (MC) molecular simulations were performed in both the grand canonical (GC) 21and

canonical (C) ensembles22, and one billion configurations were used in the equilibration

and sampling stages for each simulation run. For each trial move, we select displacement, insertion and deletion with equal probability.

In the equilibration stage, the maximum

displacement length was initially set as half of the smallest dimension of the box and was adjusted to achieve the acceptance ratio of 20%. In the calculation of interaction energies, the cut-off radius was chosen as 5 times the collision diameter of the carbon atom of CO2 and long-range corrections were not applied. The thermodynamic properties collected here: surface excess, isosteric heat, local density distribution and orientation distribution, are defined in Appendix A.

2.2 Solid-Fluid ( U SF ) and Fluid-Fluid Interaction Energies ( U FF ) The intermolecular energy of CO2 was calculated as the sum of the LJ interaction energy with cross molecular parameters computed with the Lorentz-Berthelot mixing rules and the electrostatic energy was modelled by point charges. A number of potential models have been proposed for carbon dioxide 23-31. Here we selected the TraPPE model because of its good representation of vapour-liquid equilibria

3


31

and


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adsorption on graphitized carbon black 32. The molecular parameters for this model are listed in Table 1. Table 1 Molecular Parameters of TraPPE CO2 31 Model TraPPE

Atom

σ(nm)

 / kB ( K )

q(e)

C

0.28

27.0

0.7

O

0.305

79.0

-0.35

The solid-fluid potential energy between an LJ site and graphite, modelled as a continuum solid, was calculated with the 10-4-3 potential equation 33. The graphite was positioned at the bottom of the simulation box with its surface plane at the z-origin, and periodic boundary conditions were applied in the x- and y-directions. The box lengths were 4nm in the x- and ydirections, and the box height was 10nm, which is large enough for the local density in the zdirection to closely approach the bulk gas density. The molecular parameters for a carbon atom in a graphene layer are  ss  0.34nm ,  ss / k B  28 K , and the carbon density in a graphene layer is  s  38.2nm 2 . To characterise the strength of an adsorbent with respect to a given adsorbate, the ratio of the minimum of the solid-fluid ( U SF ) potential energy profile to the minimum of the fluid-fluid ( U FF ) potential energy profile can be used:

D* 

U SF ,min U FF ,min

Eq.1

For the carbon dioxide/graphite system, we obtained D*  3.3 , compared to D*  9 for an argon/graphite system 34, showing that carbon dioxide is a weaker adsorbate than argon with respect to graphite. However, to understand the wetting/non-wetting behaviour of an adsorbate on a given adsorbent, the two key parameters are the heat of condensation (sublimation) and the isosteric heat at zero loading for the adsorbate/adsorbent pair. The heat of condensation (sublimation), , is a measure of the cohesion in the bulk, and the isosteric heat at zero loading, qst(0) , is the heat released when one molecule adsorbs on the bare surface of the adsorbent, and is a measure of the adhesion to the surface. A ratio,  , proposed earlier by Prasetyo35, of the isosteric heat at zero loading to the heat of condensation (sublimation) is a better measure

4


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than D* because it accounts for the temperature, which also plays a critical role in determining a system whether a system is wetting or non-wetting.

Fig. 1 (a) Plots of the sublimation and condensation heats and the isosteric heat at zero loading versus temperature. The heat of condensation (green triangles), is obtained from simulations of vapour-liquid equilibria 36, while the heat of sublimation (red squares), is taken from the simulation of vapour-solid equilibria 37, and the isosteric heat at zero loading (open circles), is computed by the Monte Carlo integration of the Boltzmann factor 38; (b) Plot of Ω versus temperature.

Fig. 1 shows plots of qst(0) ,  and the ratio  as a function of temperature. We divided these plots into Zones I and II according to   1 or   1 for temperatures below and above the bulk triple point, respectively. This demarcation at the triple point makes carbon dioxide an ideal adsorbate for a study of wetting/non-wetting on graphite. On a bare graphite (i.e. in the absence of the adsorbate-adsorbate interactions), Zones I and II correspond to non-wetting and wetting, respectively, but it will be shown later that the contribution from the adsorbateadsorbate interactions can change a non-wetting system to either incomplete wetting or wetting as the loading is increased. The former occurs for CO2/graphite discussed in Section 3.2 of this paper, and the latter is observed for argon adsorption on moderately strong adsorbents 34. 5



Non-wetting or wetting of CO2 on graphite is determined by the adsorbed density versus the reduced pressure, P / P0 , where P0 is the bulk coexistence pressure. It is important to note that the coexistence pressure between a thick adsorbed film and the gas phase, P0* , is not necessarily the same as P0 for a bulk phase. At temperatures above the triple point, we expect that P0*  P0 ，but at temperatures below the triple point, we expect that P0*  P0 since the density of an adsorbed film, in the potential field from a solid adsorbent, is non-uniform and therefore different from that of a uniform bulk liquid or solid. Appendix B lists the values of the bulk coexistence pressure P0 that we have used in this paper.

3 Results and Discussion 3.1 Temperature Dependence of CO2 Adsorption The grand canonical isotherms of CO2 adsorption on graphite are shown in Fig. 2 for temperatures up to the triple point, and we note the following features: 1. The Henry constant increases with temperature, indicating the dominance of entropy over the energy, as seen in the inset of Fig. 2a. This is a signature of non-wetting because qst(0) is less than . 2. The wetting temperature of the first adsorbate layer, Tw,1, is 90K, at which there is a first order transition at the bulk coexistence pressure. This is in good agreement with the experimental measurements of Terlain and Larher 1. 3. As the temperature is increased, the reduced pressure for the onset of the first adsorbate layer shifts to a lower value, and the magnitude of density jump across the transition is smaller. The 2D critical temperature of the first layer is around 130K, which agrees with the experimental value 1. It is interesting to note, though not widely recognized, that the closure point of the van der Waals (vdW) loop is to the left when the isotherms are plotted against the reduced pressure (Fig. 2a), but to the right when they are plotted against the absolute pressure (Fig. 2b). This is also observed in argon adsorption on weak surfaces35, and this is an evidence of the lesser isosteric heat than the heat of sublimation even with the contribution from the adsorbateadsorbate interactions. This is opposite to wetting systems, such as argon/graphite where the closure point of the vdW loop is always to the right for isotherms plotted against reduced pressure or against absolute pressure, as shown in Appendix C (Fig. 6


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10 ).

In these systems, the isosteric heat is always greater than the heat of

condensation and the heat of sublimation. 4. Between 150K and Ttr, the isotherms cross the bulk coexistence pressure and no more than two layers are formed on the surface. We refer to this as ‘incomplete wetting’ because the contribution from the adsorbate-adsorbate interactions to the isosteric heat is not sufficient to make up for the difference between the heat of sublimation and the isosteric heat at zero loading. This is further substantiated in Section 3.2. 5. For temperatures greater than Ttr, there is continuous wetting, as evidenced by the approach of the isotherm to infinity when the pressure approaches P0 .

Fig. 2 Adsorption of CO2 on graphite at various temperatures as a function of (a) reduced pressure, and (b) absolute pressure

7



3.2 Microscopic Mechanism To examine wetting/non-wetting in this system in more detail, three temperatures were chosen: (1) 90K which is the wetting temperature of the first adsorbate layer; to represent non-wetting in Zone I, (2) 195K to represent incomplete wetting and (3) 215K at which temperature there is continuous wetting in the Zone II. 90K(Wetting of the first layer) We show in Fig. 3 the canonical (C) and grand canonical (GC) isotherms and snapshots at various points on the C-isotherms. The C-isotherm has a vdW loop enclosing the bulk coexistence pressure, indicating that there is a first-order transition in the GC-isotherm. The mechanism of adsorption is described as follows: At extremely low loadings (Point A), the surface is sparsely covered with clusters, which then grow with increased loading up to Point B, where the surface is only 10% covered. The pressures required to equilibrate the clusters at Points B and C are lower than that at Point A because of the larger convex radii of curvature of the clusters. At Point D, the interface separating a 2D-cluster and the 2Drarefied phase is flat, and therefore the pressure at this point is the coexistence pressure, P2D , between these phases. As the loading is increased beyond Point D, the 2D-adsorbed phase increases in size at the expense of the rarefied phase, at the constant pressure P2D because of the invariant flat interface. At Point E, the 2D-rarefied phase becomes circular with an interface which is concave to the rarefied phase, and the pressure therefore decreases to below the coexistence pressure P2D . At Point F, the spinodal point of the 2D-dense phase, the rarefied phase disappears. Beyond this pressure the monolayer becomes densified.

8


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Fig. 3 (a) GC- and C-isotherms of CO2 adsorbed on graphite at 90K, (b) Snapshots at various points marked on the C-isotherm.

The local density distribution (LDD) at the bulk coexistence pressure (just after the condensation) in Fig. 4 a shows only a single layer of molecules on the surface with molecules vibrating around a most probable distance of 0.33nm which is close to the collision diameter, of 0.323 nm, between the O-atom in CO2 and a C-atom in a graphene layer. This distribution confirms that the CO2 molecules are constrained to lie flat on the surface such that the interaction between the adsorbent and the C atom and O atoms in CO2 is maximised. At this low temperature there is insufficient entropy for molecules to rotate into other configurations. This is supported by the 3D-orientation density distribution in Fig. 4 b, where the 900 angle between the CO2 molecular axis and the normal vector from the graphite surface is dominant.

Fig. 4 c shows that at this temperature CO2 molecules form a

herringbone structure, as discussed by Terlain and Larher

1

and Hammond et al.

39.

This

arrangement corresponds to the minimum energy configuration between molecules at very low temperatures.

9



Fig. 4 (a) Local density distribution of the centre of mass of CO2 at the bulk coexistence pressure, (b) the 3Dorientation density distribution, (c) snapshot of CO2 molecules on the graphite surface at 90K.

195K (Incomplete Wetting)

Fig. 5 shows the isotherm at 195K and its decomposition into contributions from the first and second adsorbate layers, as demarcated by the minimum in the local density distribution. Wetting is incomplete since the isotherm intersects the bulk coexistence pressure P0 at a position where the adsorbed density is less than twice the statistical monolayer density. When the pressure is increased further, beyond the bulk coexistence pressure, the isotherm becomes Type II and the density approaches infinity asymptotically as the pressure approaches P0* , since the adsorbed phase is less ordered than the bulk crystal (see Fig. 11, Appendix D). This figure shows that the onset of the second adsorbate layer occurs at 0.2

P / P0 (Point B at which the loading is 7.5mol/m2). At Point D, the total loading is 14mol/m2, of which the second layer contributes 5mol/m2, indicating that the first adsorbate layer becomes densified as the second layer is built up.

10


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Fig. 5 Adsorption of CO2 at 195K on graphite surface as a function of the reduced pressure. The contributions from the first and second adsorbate layers are also shown.

The isosteric heat versus loading and the contributions from the first and second adsorbate layers are shown in Fig. 6a, b and c, respectively. The isosteric heat reaches a maximum of 23 kJ/mol at Point A, around 60% of the monolayer coverage. This value is still lower than the heat of sublimation, even with the contribution from the adsorbate-adsorbate interactions. This differs from isosteric heat curves for the adsorption of simple gases, like argon, where the maximum usually occurs at the monolayer density

34.

The contribution from the solid-

fluid (SF) interactions begins to decrease at this point because some adsorption is in the second layer where molecules are further away from the surface, and because of reorientation of CO2 molecules in the first adsorbate layer.

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Fig. 6 (a) Isosteric heat for CO2 adsorption on graphite at 195K and (b) contribution of the first adsorbate layer, (c) the contribution from the second layer. The contributions from the SF and FF interactions are shown as red and blue symbols, respectively. Points A to D are marked in

Fig. 5

Fig. 7 shows the local density distributions (LDD) at 195K for various loadings. As the loading increases, the second layer is formed and at the same time the first layer becomes denser, confirming that the second layer coverage begins before first layer is completed. It is interesting to note that the maximum in the first layer LDD at Point D is lower than at C although the total loading at Point C is lower. This does not mean that molecules migrate to a higher layer with an increase in the total loading, but rather that some of them change orientation to accommodate more molecules in the first and second layers, and this is signalled by the appearance of a shoulder in the LDD of the first layer.

This is also

confirmed in the 3D plot of the orientation density distribution shown in Fig. 7b, where a second peak occurs at angles of less than 900 at locations in the first adsorbate layer.

12


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Fig. 7 (a) Local density distribution of the centre of mass of CO2 on a graphite surface at 195K, (b) 3D orientation density distributions. Points A to D are marked in Fig. 5.

215K (Continuous Wetting) Fig. 8 shows the adsorption isotherm at 215K the separate contributions from the first three adsorbate layers. In contrast to lower temperatures, where the adsorption is either nonwetting or incomplete wetting, the 215K-isotherm is Type II and approaches infinity asymptotically as the pressure approaches the bulk coexistence pressure.

This is

characteristic of a continuous wetting. The onset of the second and third layers here occurs at lower pressures than at 195K, due to the higher molecular mobility.

13



Fig. 8 Adsorption isotherm for carbon dioxide at 215K plotted as a function of the absolute pressure and the separate contributions from the first three layers.

3.3 Effect of Surface Affinity To study the effects of the strength of the adsorbent field on CO2 adsorption (i.e. the affinity of surfaces stronger or weaker than graphite), we carried out simulations for substrates with different values of D*. The non-wetting/wetting behaviour for these systems is summarised

in Fig. 9 . The blue dashed line in Fig 9a is the wetting line, below which carbon dioxide does not wet the surface. The horizontal line marked with crosses is the roughening temperature for the adsorbed film of carbon dioxide (discussed below). The area between this line and the wetting line is the region of incomplete wetting, where only a finite number of layers are formed on the surface at the bulk coexistence vapour pressure P0 . At temperatures above the wetting line and the roughening line, there is continuous wetting.

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Fig. 9 (a) A parametric map for wetting as a function of the surface affinity, (b) GC-adsorption isotherms plotted as functions of the reduced pressure for a substrate with D*=2, (c) the same as (b) for a substrate with D*=9.

Fig. 9b and c show the isotherms for CO2 adsorption on substrates with D*=2 and 9, and illustrate the adsorption behaviour for adsorbents weaker or stronger than graphite. For the D*=2 substrate, the wetting temperature is 210K, compared with 90K for graphite. On the other hand, for the D*=9 substrate, the CO2 always forms the first layer and depending on the temperature, this system exhibits either incomplete wetting or continuous wetting. The adsorbent strength affects wetting, in that the weaker the adsorbent, the higher is the wetting temperature because larger thermal fluctuations are required before adsorption can occur on weak adsorbents. There is no report in the literature of the roughening temperature for adsorbed CO2. This is defined as the temperature when a given facet disappears from the equilibrium shape of a crystal

40.

However, in the context of adsorption, Larher and Angerand

41

defined the

roughening temperature as the limit of the wetting temperature for layering, as more layers are formed on the substrate, and they argued that this temperature is independent of the strength of the adsorbent. Using this criterion, we estimated the roughening temperature to be approximately 215K, below which layer by layer adsorption is observed, and above which an infinite number of layers are formed at the bulk coexistence pressure.

15



4 Conclusions We have presented a comprehensive simulation study of CO2 adsorption on graphite using grand canonical and canonical simulations to investigate the mechanism of wetting and nonwetting. A parameter  is defined as the ratio of the isosteric heat at zero loading to the heat of condensation or sublimation to evaluate the interplay between solid-fluid interactions, fluid-fluid interactions and temperature (entropy). Below the triple point,   1 , adsorption of CO2 exhibits non-wetting, or incomplete wetting, because the isosteric heat at zero loading is lower than the heat of sublimation. On the other hand, above the triple temperature,   1 , the adsorption isotherms show continuous-wetting, and CO2 molecules adopt many different orientations at higher loadings. A parametric map of wetting has been presented based on simulations of CO2 adsorbed on substrates of different strength, and shows that the substrate affinity affects wetting, and that the wetting temperature is higher on weaker substrates.

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5 Appendix A The isosteric heat, qst , is calculated from the following equation42 :

qst 

Nb f U , N  k BT f  Nb , Nb  f  N , N  - (Vacc / Vb ) f  N b , N b 

where N b is the number of molecules occupying the accessible volume of the system at the same density as the bulk phase, N is the number of molecules in the system, Vacc is the accessible volume within which the solid-fluid potential energy is non-positive, Vb is the volume that used to simulate the bulk gas phase, U is the configurational energy of the system, f  X , Y  is the fluctuation variable, defined as f  X , Y   X Y  X Y , and g denotes an ensemble average. The excess number of molecules in the system, N ex , is calculated from N ex  N  Vacc b , where b is the density of the bulk gas. The local density distribution (LDD) of the center of mass of CO2 as a function of the distance from the surface is:

  z 

N z , z z Lx Ly z

where N z , z z is the number of molecules whose centers of mass are located in the region bounded by [z, z+z], and Lx and Ly are the box lengths in the x- and y-directions parallel to the surface. The orientation of a CO2 molecule is defined as the angle,  between the CO2 molecular axis and the normal vector through the graphite surface. The orientational density distribution was calculated from the following equation:

  z,  

N z ,

Lx Ly z  sin   

where N z , is the number of molecules in the region bounded by [z, z+z], and angles are bounded by [,+].

17



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6 Appendix B Table 2 Summary of

P0 for different temperature used in our simulations. P0 ( Pa) 5.14E-04 1.90E-02 4.15E+00 3.24E+01 1.87E+02 1.04E+05 4.80E+05 8.87E+05

Temperature (K)

90 100 120 130 140 195 215 230

7 Appendix C

Fig. 10 Adsorption isotherms for argon plotted as a function of the absolute pressure for adsorbent amount obtained with GC simulations at different temperatures.

8 Appendix D

Fig. 11 Adsorption isotherms of CO2 on graphite plotted as a function of the absolute pressure at 195K. Here, P0 is the bulk coexistence vapour pressure and P0* is the coexistence pressure between the adsorbed film and the gas phase. The insert figure shows the contribution of the first layer in terms of absolute pressure.

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9 Acknowledgement: This project is supported by Australian Research Council (DP160103540)

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10 Reference (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16) (17) (18) (19) (20)

(21) (22)

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Wetting Behaviour of Carbon Dioxide on Graphite

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