On the Henry Constant of Water Adsorption on Functionalized

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C: Surfaces, Interfaces, Porous Materials, and Catalysis

On the Henry Constant of Water Adsorption on Functionalized Graphite - The Importance of the Potential Models of Water and Functional Group Yonghong Zeng, Hui Xu, Toshihide Horikawa, Duong Dang Do, and David Nicholson J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b08036 • Publication Date (Web): 27 Sep 2018 Downloaded from http://pubs.acs.org on October 5, 2018

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The Journal of Physical Chemistry

On the Henry Constant of Water Adsorption on Functionalized Graphite The Importance of the Potential Models of Water and Functional Group

Yonghong Zeng1, Hui Xu1, Toshihide Horikawa2, D. D. Do*1 and D. Nicholson1

1

School of Chemical Engineering, University of Queensland, St. Lucia, QLD 4072, Australia

2

Department of Advanced Materials, University of Tokushima, 2-1 Minamijosanjima, Tokushima 7708506, Japan

Abstract We present a theoretical study of the Henry constant for water adsorbed on graphite decorated with functional groups at the edges of the graphene layers. A general expression for the Henry constant is developed to describe the initial adsorption on the basal plane, functional groups and the confinement in micropores. To shed further light on the role of functional groups we have investigated the effects of partial charge, acidity and basicity, orientation and the separation between functional groups. Our main conclusions are: (1) The strength of adsorption is sensitive to the accessibility of water to the functional groups, (2) A basic functional group can be as strong as an acidic functional group, (3) The affinity varies significantly with orientation and the separation between the functional groups, and (4) Adsorption in microporous crevices may compete with functional group adsorption at very low loadings. While thermodynamics suggests that a Henry law region should always exist at low loading, this is not always observed in water/carbon systems because of the broad energy distribution of the possible adsorption sites (functional group, basal plane and confinement), or because the Henry law region, corresponding to the strongest adsorbing sites, falls well below the measurable pressure range.

*Corresponding author. E-mail: [email protected] (D.D. Do).

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Introduction Understanding the physics of water adsorption in carbonaceous materials is of broad scientific interest because of its practical implications for natural gas storage, air pollution control and catalyst supports

1-3

. Compared to simple gases, like argon and nitrogen, water

exhibits distinctive adsorption behaviour which is characterised by the large adsorptiondesorption hysteresis loop observed for both porous and non-porous carbons. The unique behaviour of water stems from the facts that: (1) water has very strong electrostatic intermolecular interactions between the positively charged hydrogen atoms and the lone pair of electrons on the oxygen atoms, which gives rise to strongly directional hydrogen bonded clusters. (2) At ambient temperatures, even graphite (which has a high atomic density) has a very weak affinity for water molecules through dispersion force interactions. For this reason, pure graphite is regarded as a hydrophobic substrate. (3) Water adsorption is sensitive to the strength and distribution of partial charges in functional groups, and to the distribution of functional groups on the graphene surface. The interplay between the above factors results in the complex macroscopic behaviour of water adsorption

2, 4

, and therefore understanding the

mechanism of water adsorption at the microscopic level is crucial in the correct interpretation of experimental data. The correlation between water adsorption isotherms and a variety of carbon materials has been extensively investigated experimentally, and found to be a complex function of pore size 5-7, temperature 8-9, and surface chemistry 10. The importance of functional groups on the initial stage of water adsorption has been highlighted in a number of experimental publications 10-13. The uptake of water on activated carbon at low relative pressures increases significantly with the degree of oxidation. Depending on the type of the oxidant and the method of activation, activated carbon can possess either acidic groups such as carboxyls or phenols; or basic groups such as amines or amides. Theoretical studies 2 ACS Paragon Plus Environment

14-16

suggest that,

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unlike simple adsorbates at low temperatures, where adsorption proceeds by molecule layering, the adsorption of water at around ambient temperatures is a clustering process: water molecules first adsorb on the functional groups due to the strong electrostatic interactions, which then form an anchor on which further water molecules adsorb to form nano-clusters. These clusters then grow with increasing pressure and because of the strong electrostatic interactions between water molecules compared to the weaker dispersive interaction between water and the graphite basal plane, water nano-clusters grow to maximize the hydrogen bonding between water molecules with minimal adsorption onto the basal planes. If the clusters are sufficiently close to each other, they coalesce to form larger clusters, which can fill micropores and small mesopores. Although functional groups are considered as primary adsorption sites for water adsorption, the basal plane occupies a much larger proportion of the surface area, compared to the small area occupied by the functional groups. This is an example of the interplay between the affinity and the concentration of sites, because at loadings low enough to be in the Henry law region, the Henry constant depends on the product of the affinity and the site concentration. The concentration of functional groups in graphitized carbon blacks is typically less than 1% of the monolayer density of the basal plane, which means that if the affinity of water for the basal plane is not much less than 1% of that of the affinity for a functional group, the contribution of the basal plane to the Henry constant is significant. Functional groups are not the only possible strong sites for water adsorption, ultra-micropores can also act as strong sites. The aim of this work is to determine theoretically the relative affinities of the basal plane, the ultra-micropores and various functional groups: acidic, basic and sulphur and nitrogen containing groups, in order to shed further light on the adsorption behaviour of different carbons. The Henry constant is calculated from a volume integration of the Boltzmann factor 3 ACS Paragon Plus Environment


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of the potential energy between a water molecule and the entity that water interacts with 17. From the knowledge of the affinities and concentration of the various entities we can calculate the contributions of these to the theoretical Henry constant, and compare the calculated values with the experiment. We have examined theoretical Henry constants and isosteric heats at zero loading for polar and non-polar molecules, on model carbons with functional groups having different partial charge, acidity or basicity, orientation and separation to reveal how water interacts with them microscopically. We find that when the adsorption energy is broadly distributed, a Henry law region is never observed because adsorption occurs progressively on sites of decreasing energy.

Theory 2.1

Experimental Henry constant

At very low adsorbate concentrations, the bulk phase density can be calculated from the ideal gas equation, ρG = P / (kBT ) , and the Henry law equation written in terms of pressure as:

C = K ρG =

K P RgT

(1)

where C is the concentration of adsorbed phase, ρG is the gas phase concentration (mol/m3), P is the pressure, Rg is the gas constant, T is the temperature of the system and K is the Henry constant whose units depend on the units chosen for the concentration of the adsorbed phase. When the adsorbed amount is expressed as the number of moles adsorbed per unit kg of adsorbent, the Henry constant K has units of m3/kg. This choice does not give a direct measure of the adsorption strength of the surface. For example, two adsorbents that have different masses but the same surface area and surface chemistry, the Henry constant based on unit mass will be smaller for the heavier adsorbent despite the fact that they have the same 4 ACS Paragon Plus Environment

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adsorbent strength. In such a case it is more logical that the adsorbed concentration is expressed as the number of moles adsorbed per unit surface area, mol/m2, and the corresponding Henry constants will have unit of length, m. In this example they would be the same for both adsorbents.

2.2

Theoretical Henry constant

We define the intrinsic Henry constant as the ratio of the excess number of molecules, N ex , to the bulk gas molecular density (molecule/m3) 17

K intrinisic =

K intrinisic =

N ex

ρG

 ϕ (r , ω )   d ω d r − Vacc k BT 

∫∫∫ exp  − Ω

 ϕ (r , ω )   d r dω − k BT 

∫∫∫ exp  − Ω

=

(2a)

∫∫∫ H [−ϕ ( r , ω )] d r d ω

(2b)

Ω

where the integration is carried over the volume Ω and over the orientation space of adsorbate molecule, φ is the potential energy of interaction between a molecule, having an orientation ω, at the position r, and a site in the adsorbent, and H is the Heaviside step function. The second term on the RHS of eq. (2b) is the accessible volume which we define as the region where the adsorbate-adsorbent potential energy is non-positive. In a recent paper we have given a new definition of the absolute accessible volume

18

, which ensures

physical consistency at high temperatures. However, in the temperature range of practical interest, the accessible volume, as defined here, is essentially the same as the absolute accessible volume. The intrinsic Henry constant has units of volume (expressed here in nm3). The volume Ω in the integrals could be either the volume of the system or any volume that encompasses the potential exerted by the adsorbent. Figure 1 illustrates this schematically.



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Figure 1. Schematic illustration of different choices for the integration volume in equation (2). Ω1 and Ω2 give the same intrinsic Henry constant, but Ω3 does not encompass the whole of the adsorbent potential.

The surface excess molecular density is defined as the excess number of molecules per unit area of the interfacial surface area, the surface Henry constant is

HA =

 ϕ (r , ω )  1   K intrinisic  ∫∫∫ exp  −  d r d ω − Vacc  = A  Ω k BT  A  

(3)

The surface Henry constant has units of length. The volumetric excess density, in the confined space of a pore, is defined as the excess number of molecules per unit pore volume, and the corresponding volumetric Henry constant, which is dimensionless, is given by:

HV =

 ϕ (r , ω )  1   K intrinisic  ∫∫∫ exp  −  d r d ω − Vacc  = V  Ω k BT  V  

The isosteric heat at zero loading is given by 17


(4)

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qst(0),ex = kBT

−

∫∫∫ Ω

 ϕ (r , ω )  exp  −  d r dω kBT  kBT  Kintrinisic

ϕ (r , ω )

(5)

and does not depend on the choice of the interfacial area or volume.

2.3

Simulations

The theoretical Henry constant was calculated by Monte Carlo integration (MCI) of the Boltzmann factor of the potential energy (eq. 2a and b).

For a given configuration

(temperature, orientation and position) of functional groups, 108 trial insertions of a water molecule were carried out for the integration. The simulated adsorption isotherm was obtained by canonical (NVT) and grand canonical (GCMC) ensembles. 2× 108 configurations were used in both the equilibration and sampling stages. Periodic boundary condition was applied in x- and y- direction. Cut-off radius was chosen as 10 times the collision diameter of the oxygen atom. No long range corrections were applied for either dispersion or electrostatic interactions.

The interaction energy between an adsorbate molecule i and a functional group j attached to the pore surface, ϕij, is given by the sum of the Lennard-Jones (LJ) and Coulomb interaction energies:

 σ cd ϕi, j = ∑∑ 4ε  cdij  rij c =1 d =1  C

D

cd ij

12

  σ ijcd  −  cd   rij

6

  

 A B q a qb  + ∑∑ i j ab  a=1 b=1 4πε 0 rij 

(6)

where A and B are the number of partial charges and C and D are the numbers of LJ sites on ab

the molecule i and the functional group j respectively, ε0 is the permittivity of the vacuum, r ij

is the separation distance between the charge a on the molecule i and the charge b on the 7 ACS Paragon Plus Environment


a

b

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cd

functional group j having charges q i and q j , respectively. r ij is the separation between the LJ cd

cd

site c on the molecule i and the LJ site d on the functional group j. The parameters σ ij and ε ij

are the cross collision diameter and the cross well depth for the two sites, which are calculated from the Lorentz-Berthelot rule. The potential models for the adsorbates were taken from the literature: nitrogen dioxide 19, ammonia 20, methanol 21, SPCE water

22

19

, carbon

and TIP5P water 23, and their molecular

parameters are listed in Table 1.


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Table 1. Molecular parameters of adsorbates. ϕ min/ kB and zmin are the minimum potential well depth and minimum position for the adsorbate molecule on a graphitic surface. Adsorbate

ϕ min / k B (K)

zmin (nm)

Site

σ (nm)

ε/kB (K)

q (e)

geometry

N

0.331

36

-0.482

lN-N=0.11nm

1168.14

0.3343

centre

--

--

0.964

C

0.28

27

0.7

∠OCO=180o

1998.6

0.3192

O

0.305

79

-0.35

lC-O=0.12088nm

N

0.3385

170

-1.035

∠HNH=106.68o

1301.6

0.3368

H

--

--

0.345

lN-H=0.10124nm

CH3

0.375

98

0.265

∠COH=108.5o

1874.70

0.3450

O

0.302

93

-0.7

lC-O=0.143nm

H

--

--

0.435

lO-H=0.0945nm

H2O

O

0.3166

78.2

-0.8476

∠HOH=109.47o

820.05

0.3261

(SPCE)

H

--

-

0.4238

lO-H=0.1nm

H2O

O

0.312

80.51

--

∠HOH=104.52o

818.90

0.3245

(TIP5P)

H

--

--

0.241

∠qOq=109.47o

q

--

--

-0.241

lO-H=0.9572nm

N2

CO2

NH3

CH3OH

lO-q=0.7nm

We considered functional groups containing oxygen (OFGs), nitrogen (NFGs) and sulphur (SFGs). For OFGs, the potential models were chosen from Jorge et al. 24, which is used as the reference for subsequent discussion of other potential models. For NFGs, the models for nitrile, amide, nitro and amine were taken from Wick et al.

25

. Thiol was chosen as a

representative SFG, and its molecular parameters were taken from Lubna et al. lists the molecular parameters for the functional groups. 9 ACS Paragon Plus Environment

26

. Table 2


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Table 2. Molecular parameters of acidic and basic functional groups Functional

Site

σ (nm)

ε/kB (K)

q (e)

geometry

Ca

--

--

0.5

lCa-O=0.1233nm

O

0.296

105.8

-0.5

Ca

--

--

0.2

lCa-O=0.1364nm

O

0.307

78.2

-0.64

lO-H=0.096nm

H

--

--

0.44

∠CaOH=110.5o

Ca

--

--

0.08

lCa-O=0.152nm

C(COOH)

0.375

52

0.55

lC=O=0.1214nm

O(=O)

0.296

105.7

-0.5

lC-O=0.1364nm

O(-H)

0.3

85.6

-0.58

lO-H=0.097nm

H

0.0

0.0

0.45

∠CaCO=111o

group Carbonyl

Hydroxyl

Carboxyl

∠OCO=123o ∠COH=107o nitrile

amine

Ca

--

--

0.269

lCa-C=0.1535nm

C

0.348

67.5

0.129

lC≡N=0.1157nm

N

0.295

60.0

-0.398

Ca

--

--

0.18

lCa-N=0.1448nm

N

0.334

111

-0.892

lN-H=0.101nm

0.356

∠CNH=112.9o

H

∠HNH=106.4o nitro

Ca

--

--

0.14

lCa-N=0.149nm

N

0.331

40

0.82

lN-O=0.1225nm


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O

0.29

80

-0.48

∠CaNO=111.5o ∠ONO=125o

amide

Ca

--

--

--

lCa-C=0.152nm

C

0.372

34

0.424

lC=O=0.1229nm

O

0.305

79

-0.424

lC-N=0.1448nm

N

0.334

111

-0.8

lN-H=0.101nm

H

--

--

0.4

∠CaCN=115.7o ∠CaCO=121.4o ∠HNH=106.4o

thiol

Ca

--

--

0.171

lS-H=0.134nm

S

0.362

232.0

-0.377

∠CaSH=96o

H

--

--

0.206

The potential energy between a water molecule and a functional group is dominated by electrostatic interactions. Several different sets of partial charges for a given functional group are available in the literature, which may give rise to different values of the Henry constants. In this study, we have compared the partial charges on OFGs obtained from: (1) the parameters from the OPLS model 24, (2) those from Tenney et al., derived from the Gaussian 03 software package 27. Table 3 lists the partial charges of OFGs derived by these methods.



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Table 3. Partial charges of functional groups calculated by different methods. Functional group

Site

Carboxyl

Hydroxyl

Carbonyl

q(e) from

q(e) from

Jorge et al.24

Tenney et al.27

α-C

0.08

-0.06

C(COOH)

0.55

0.75

O(=O)

-0.5

-0.5

O(-H)

-0.58

-0.55

H

0.45

0.36

α-C

0.2

0.3

O

-0.64

-0.6

H

0.44

0.3

α-C

0.5

--

O

-0.5

--

The interaction between a site c on an adsorbate molecule, at a position z above the basal plane of graphite, and a graphite adsorbent, was calculated with the 10-4-3 potential:

ϕ cC ( z ) = ( 2π ρ s ε cC σ

2 cC

4  2  σ 10  σ  4   σ cC  )  5  zcC  −  zcC  −  3    3∆ ( z + 0.61∆ )  

(7)

where εcC and σcC are the molecular parameters for site c interacting with a C atom, ρs is the atomic density of C in a graphene plane (38/nm2) and ∆ is the inter-planar spacing. The potential well depth is given the symbol ϕ min .

Values of ϕ min and the position of the

minimum (zmin) are listed in Table 1. When the adsorbed molecule is trapped in a pore space of width H, the potential at z is ϕ cC ( z ) + ϕ cC ( H − z ) . The potential well at each wall is deeper and, as the pore is narrowed 12 ACS Paragon Plus Environment

Page 13 of 35

the two wells eventually merge to form a single minimum. The deepest possible well occurs when H=2zmin. In general, the maximum well depth for a molecule will depend on it orientation, but for the spherical water models, the maximum well depth is 2ϕ m in . For example, the dispersionrepulsion interaction (/kB) of a TIP5P water molecule in a wedge shaped micropore is 1634K in a pore of width 0.62nm; for SPCE water, the values are 1636K and 0.65nm. For linear molecules with C2v symmetry such as CO2 or N2, the maximum well depth is the same for both normal and axial orientations, and can easily be calculated from the figures in Table 1.

Result and discussion 3.1. The relative strength of adsorption sites Basal plane of graphene In Figure 2, we present the Henry constant and isosteric heat at zero loading as a function of temperature, for water adsorption on pure graphite.

105

H2O (SPCE) H2O (TIP5P) N2 CO2 CH3OH NH3

104

103

30


25

20

15

0

102

(b)

qst (kJ/mol)

(a) Henry constant (nm)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


101

100

10

5

10-1

0 0

100

200

300

400

500

600

0

100

T(K)

200

300

400

500

600

T(K)

Figure 2. The intrinsic Henry constant and isosteric heat at zero loading as a function of temperature for water on graphite. The filled circles are the SPCE model, and the unfilled circles are the TIP5P model.



Page 14 of 35

Methanol and carbon dioxide have the highest affinity for graphite (Figure 2a and b) due to their strong dispersive interactions. Ammonia, argon and nitrogen are intermediate, and water is only weakly adsorbed, with a Henry constant two orders of magnitude smaller than those of methanol and carbon dioxide at ambient temperatures.

The isosteric heat of

adsorption at zero loading of water on graphite is about 8kJ/mol, which is much lower than the heat of condensation (40kJ/mol). Graphite is therefore considered to be a hydrophobic adsorbent, since water molecules interact more strongly between themselves than with the graphite surface. However, this situation changes as the temperature approaches the critical temperature (647K) when the isosteric heat at zero loading increases slightly to 13kJ/mol, but the heat of condensation decreases rapidly to zero. This means that if adsorption on graphite is carried out at temperatures close to the critical temperature, adsorption will occur, but because of thermal fluctuations the adsorbate will form multiple layers with no clear boundary between them.

Slit Micropores In Figure 3, we present the Henry constant and isosteric heat at zero loading as a function of temperature, for water adsorption in graphitic slit micropores of different widths.

The

optimum pore size for water adsorption to occur in slit micropores (Figure 3a and b) is around 0.65nm, the size of which the solid fluid potential has the deepest potential well (Figure S1 in supporting information). In pore widths less than 0.65nm, the affinity for water is lower because repulsion from the opposite walls begins to override attraction, while for larger pore widths, the affinity decreases because the attraction by each pore wall is decreasing.


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(b) 25

5

(a) 10

SPCE SPCE SPCE

TIP5P 0.6nm TIP5P 0.65nm TIP5P 1nm

103

2

10

SPCE SPCE SPCE

W

20

q st0 (KJ/mol)

104

H enry constant(-)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


TIP5P 0.6nm TIP5P 0.65nm TIP5P 1nm

15

10 101

100

5 0

100

200

300

400

500

0

600

100

200

300

400

500

600

T(K)

T(K)

Figure 3. The intrinsic Henry constant and isosteric heat at zero loading as a function of temperature for water in slit micropores of different widths. The filled circles and lines represent the SPCE model, and the unfilled circles are the TIP5P model. The inset figure is the schematic of the slit pore and its structural parameter, the pore size, W.

Wedge Micropores In Figure 4, we compare the Henry constant and isosteric heat at zero loading as a function of temperature, for water adsorption in wedge pores as they better represent pores in activated carbon. The size of the smaller end, WN, of the wedge is 0.3354nm, and the axial length L is 10nm, and the angle α (as shown in the inset of Figure 4) is the half angle of the wedge. For α other than zero, there is a position at which the “local” width is 0.65nm, and since the potential energies of the regions on either side of the 0.65nm local width are higher the Henry constants for wedge pores are smaller than that of the 0.65nm slit pores. This is exemplified with α = 1 and 2 degrees in Figure 4. We also showed in the same figure the Henry constant for 0.8nm slit pore, and it is seen that at low temperatures the wedge pore with α=20 has almost the same affinity as the 0.8nm slit. But when the temperature is increased above 300K,



the Henry constant of the wedge is smaller because the greater contribution of the larger parts of the wedge due to the thermal fluctuations.

5

(a) 10

(b) SPCE SPCE SPCE SPCE

TIP5P Slit-0.65nm TIP5P Wedge-1° TIP5P Wedge-2° TIP5P Slit-0.8nm

25

α

WN

L

20

q st (KJ/mol)

104

103

SPCE SPCE SPCE SPCE

TIP5P Slit-0.65nm TIP5P Wedge-1° TIP5P Wedge-2° TIP5P Slit-0.8nm

15

0

Henry constant(-)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 16 of 35

102

10

101

100 0

100

200

300

400

500

600

5 0

100

T(K)

200

300

400

500

600

T(K)

Figure 4. The intrinsic Henry constant and isosteric heat at zero loading as a function of temperature for water in wedge pore of different angles and slit pore of different widths. The filled circles and lines represent the SPCE model, and the unfilled circles are the TIP5P model. The inset figure is the schematic of the wedge pore and its structural parameters are: the pore size at the narrow end, WN=0.3354nm, the angle of the wedge pore is 1° and 2°, and the axial length L=10nm

The isosteric heat at zero loading in Figure 4b shows interesting behaviour with respect to temperature for the wedge pore with α= 2°. At very low temperature, below 50K, molecules dominantly reside at the position where the solid fluid interaction is highest (i.e. at the local pore width of 0.65nm).

However, at temperatures greater than 100K, the entropy is

becoming important and molecules span along the pore where the solid-fluid interaction is lower, resulting a decrease in the isosteric heat at zero loading. As the temperature is further increased the kinetic energy (kBT) plays the dominant role, resulting in an increase of the isostatic heat.


Page 17 of 35

Hydroxyl functional group: Hydroxyl groups adsorb water or methanol more strongly than nitrogen at ambient temperatures, by an order of magnitude, due to their stronger electrostatic interactions (Figure 5a and b). We modelled water with two potential models: TIP5P and SPCE and used partial charges for the hydroxyl group from Jorge et al.24 The TIP5P gives a much higher Henry constant than the SPCE model, in contrast to the plane graphite surface or the graphitic slit micropore, where only dispersive forces are operating and their LJ parameters are almost identical. Now electrostatic interactions dominate the interaction, and therefore the relative configuration of the partial charges on both water molecule and the functional group is a very important, especially in a non-uniform environment, as is the case here. It is not surprising that the TIP5P model has a higher affinity for the pairwise interaction between one water molecule and one functional group because this model has a tetrahedral arrangement of partial charges: two positive charges on the hydrogen atoms and two negative charges on the lone pair electrons.

106

10

(b)


3

5

104

60 H2O (SPCE) H2O (TIP5P) N2 CO2 CH3OH NH3

50

qst (kJ/mol)

(a) Henry constant (nm )

103

40

30

0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


102

101

20

10

100

0 0

100

200

300

400

500

600

0

100

T(K)

200

300

400

500

600

T(K)

Figure 5. The intrinsic Henry constant (Kintrinsic) and isosteric heat at zero loading as a function of temperature for water on hydroxyl functional groups attached to graphite calculated using the parameters from Jorge et al.24. The filled circles represent the SPCE model, and the unfilled circles are the TIP5P model.



Page 18 of 35

In Figures 2 to 5, the units of the Henry constant for different adsorbent entities are different: nm3 for a functional group, nm for a surface and dimensionless for slit pores. To compare these contributions to the overall (observed) Henry constant, one needs to know the concentrations of these entities (number of functional groups, surface area of the basal plane, and pore volume of a slit pore) referred to a unit mass of the total adsorbent. Let us consider a graphitized carbon black that is composed mostly the basal planes, wedge pores at the junctions joining the basal planes, and functional groups at the edge of the graphene layers. The amount adsorbed is now expressed as molecule/kg, and the overall Henry constant (m3/kg) is  m3  H total   = C FG K int rinsic + S H A + V H V  kg 

(8a)

where CFG is the number of functional groups per unit mass mol/kg, S is the specific area of the basal plane (m2/kg) and V is the specific volume of slit pores (m3/kg). The units of the total Henry constant are m3/kg. Similarly, when the adsorbed amount is expressed as the number of moles per unit of the area of the basal plane (mol/m2), the overall Henry constant in terms of area (m3/m2) can be obtained from eq. (8a) by dividing it by the specific surface area of the basal plane H total S

 m 3   C FG  V   K int rinsic + H A +   H V  2= m S S    

(8b)

where (CFG/S) is the number of functional group per unit area of the basal plane (mol/m2) and (V/S) is the volume of slit pores per area of the basal plane (m3/m2). The contributions of the functional groups, the basal plane and the micropores are shown in the three terms on the RHS of eq. (8b).


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To gain an idea of the contributions of various adsorbing entities on water adsorption at low loadings, we consider our previous work on water adsorption on Carbopack F as an example, where the concentration of carboxylic functional groups was around 1 × 10-5 mmol/m2

28

The concentration of the crevices was around 0.1% of the monolayer coverage of argon

29

. ,

and the liquid molar volume of argon was 2.86×10-5m3/mol, therefore the estimated volume of crevices is 3.5×10-3nm3/m2. The theoretical Henry constant for this model for Carbopack F and the contributions from each adsorbing entity, calculated from eq. (8b) are shown in Table 4. For N2 and CO2, the contribution from the functional groups to the Henry constant is negligible, the contribution from the micropores is greater than that contributed by the basal plane by 3 orders of magnitude; therefore their adsorption will occur initially in micropores, and is characterised by a two-stage adsorption process identified in the adsorption isotherm 29. For NH3 and CH3OH, although the affinity of the functional groups (and micropores) is higher than the basal plane, it is compensated by the large surface area of the basal plane, and as a result, the contribution to the Henry constant from the functional groups is lower from the basal plane.

H2O, represents a distinct case from the other

adsorbates; although the concentration of the functional groups is very low, their contribution to the total Henry constant is 100 times greater than that from the basal plane; therefore there is no doubt that initial adsorption of water proceed by attachment to the functional groups. Once adsorption is initiated, a water cluster grows but does not spill onto the basal plane because the intermolecular energy in the water cluster is greater than the potential energy of the water-basal plane interaction.

Table 4. Comparison of theoretical Henry constants on carbopack F and its contributions from graphite surface, ultrafine pore and hydroxyl groups



Page 20 of 35

adsorbate

Htotal (nm)

HA (nm)

V HV (nm)

CFG Kintrinstic (nm)

N2 at 77K

4.37×107

6.8×104

4.40×107

0.082

CO2 at 210K

1.31×103

2.19×102

1.02×103

0.032

CH3OH at 298K

62.0

48.6

9.54

4.32

NH3 at 195K

27.8

25.6

0.622

1.41

H2O at 298K

157

1.60

0.012

156

3.2. Water on Functional Groups 3.2.1 Partial charges on functional group Figure 6 shows the Henry constant for water attached to a single hydroxyl group with parameters taken from two different sources: (1) Mooney et al.

30

, cited charges from the

OPLS model for a phenol molecule. This model gives a good agreement between thermodynamic properties, such as liquid density, and experimental data. (2) The partial charges calculated by Tenney and Lastoskie

27

using the Gaussian 03 software package.

Experimental observation of isosteric heat at zero loading is 27kJ/mol at 298K for Carbopack F

31

. The OPLS model gives a better agreement at this temperature, while the Gaussian

estimate is too low. However, it should be noted that experimental data at very low loadings are not available because the pressure is well below the measurable range of a pressure transducer.

Therefore, the reported experimental value of 27kJ/mol may be due to

interactions between a water molecule and other water molecules in a cluster.


Page 21 of 35

(a)

107 Tenney and Lastoskie Mooney et al.

106

(b)

60 Tenney and Lastoskie Mooney et al. 50

3

Henry constant (nm )

105

qst (kJ/mol)

104 103

40

30

0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


102

20

10

101 100

0 0

100

200

300

400

500

600

0

100

T(K)

200

300

400

500

600

T(K)

Figure 6. The intrinsic Henry constant and isosteric heat at zero loading for water TIP5P model on a single hydroxyl group of different models.

3.2.2 Acidic group vs basic group Figure 7 shows the Henry constants of TIP5P model at 300K for a range of functional groups with different acidity and basicity. Among the groups considered here, the carboxylic group has the highest affinity towards water and therefore gives the highest Henry constant and the isosteric heat at zero loading. This is due to the strong dipole of the carboxylic group and the better accessibility for a water molecule to the atoms of the carboxylic group. In particular the H-atom, has a strong interaction with the O-atom of the water molecule (hydrogen bond). The importance of accessibility is illustrated by the nitrile group. Despite the fact that its partial charges are lower than those on the hydroxyl group, the N-atom is further away from a carbon atom on the basal plane than the O-atom of a hydroxyl, giving a water molecule easier access to this atom (i.e. less frustration by repulsive forces); resulting in a higher Henry constant for nitrile than for hydroxyl. The Henry constants for hydroxyl and amide groups are comparable, which is consistent with the experimental observations by Tóth et al. who found no statistical difference between water adsorption on O- or N-containing multiwall carbon nanotubes 32. 21 ACS Paragon Plus Environment


8

carbonyl hydroxyl carboxylic nitrile amine nitro thiol amide

107 3

106 105 104 103 102 101 100 100

(b) Heat at zero loading (kJ/mol)

(a) 10 Henry constant (nm )

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 22 of 35

80 carbonyl hydroxyl carboxyl nitrile

60

amine nitro thiol amide

40

20

0 200

300

400

500

600

0

100

T(K)

200

300

400

500

600

T(K)

Figure 7 The intrinsic Henry constant of TIP5P water at 300K on different functional groups.

Figure 8 presents optimal configuration (separation and orientation) of TIP5P water on different functional groups that give the minimum potential energy. Apart from carbonyl, nitrile and nitro groups that contain no H-atom, the other functional groups, where the Hatom is covalently bonded, act as a hydrogen donor with a strongly electronegative atom such as N, O or S, and the water molecule acts as a hydrogen acceptor with a lone pair electron to forming a hydrogen bond with the functional group. The groups with no H, act as hydrogen acceptors through their strongly electronegative atom such as N, O, and water becomes a hydrogen donor. The ease with which water can form H-bonds means that functional groups can act as an initiator for water adsorption.


Page 23 of 35

Figure 8. Optimum configuration for the TIP5P model interacting with different functional groups.

3.2.3 Effect of functional group orientation The O-H in a carboxylic group can rotate around the C-O bond, which changes the dihedral angle of the group; the interaction of a water molecule on a carboxylic group changes according to the distance between the charges on the water molecule and those on the carboxylic group. Figure 9 shows the Henry constant of SPCE and TIP5P water on a single carboxylic group as a function of the dihedral angle.

107 SPCE TIP5P 106 3


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


105 104 103 102 101 0

20

40

60

80

100

120

140

Dihedral angle of C-O-O-H (degree)


160

180


Figure 9. The intrisic Henry constant for SPCE and TIP5P water models on a carboxyl group at 263K as a function of the C-O-O-H dihedral angle. The dashed lines show the average Henry consant.

For the both models, the maximum Henry constant is observed when the angle is 90o, and is two orders of magnitude greater than its minimum value at 180o. As a result, the average Henry constant is governed by the optimum configuration. The same is true for the TIP5P model. 3.2.4 Effect of functional group separation Figure 10 shows the Henry constant for TIP5P water on two functional groups as a function of the separation distance between the two groups. For two hydroxyl groups, the maximum Henry constant occurs when the separation is 0.45nm and is 7 times higher than that on a single group. This is due to a synergetic effect, where a positive H-atom of the water molecule interacts with the negative O-atom of one hydroxyl group, and the negative lone pair electron interacts with the positive H-atom on the second group, to form two hydrogen bonds. At distances greater than 0.6nm, both hydroxyl groups act independently. For two carboxylic groups, the optimum distance is 0.7nm, and the Henry constant is three times higher than for a single group. The optimum distance for the carboxylic group is greater than for the hydroxyl group because of its larger molecular size.


Page 24 of 35

5

1200

3

1x10

hydroxyl carboxylic

4

8x10

3

1000


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


800 4

6x10 600

4

4x10 400

4

2x10

200 0 0.0


Page 25 of 35

0.2

0.4

0.6

0.8

0 1.0

Distance between two groups (nm)

Figure 10. The intrisic Henry constant for the TIP5P water model at 300K on two functional groups as a function of separation distance. The insets show the optimum configurations of TIP5P water on two hydroxyl groups seperated by 0.45nm and two carboxylic groups separated by 0.7nm.

3.3. The initial stage of water adsorption Figure 11 shows the adsorption isotherm for water on Hex carbon at 298K.

Hex is

graphitized at a temperature greater than 2400K and the O/C ratio by X-ray diffraction (XRD) analysis is lower than 0.05 indicating that Hex possesses a low concentration of functional groups 8. The adsorption isotherm in Figure 11 is Type III, which is typical for associating fluids on graphite. The adsorbed amount is less than 1µmol per m2 of the basal plane for P/P0 up to 0.8, which is much lower than the statistical monolayer concentration of water (18µmol/m2). This is due to the localized growth of water clusters around the functional groups, which occupy a very small area compared to the basal plane. In the inset in Figure 11 the isotherm is plotted on double logarithmic scales, showing that at low loadings: (1) the adsorbed amount of water is not linearly dependent on the pressure, and (2) the slope of the isotherm is smaller than unity and continues to decrease with pressure up to the inflection



point. These observations do not conform with Henry’s law where the adsorbed amount is proportional to the pressure and the double logarithmic plot has a slope of unity. The slope of less than unity in the log-log plot in Figure 11, suggests that the initial adsorption of water occurs predominantly around functional groups followed by the growth of a cluster by adsorption on sites of progressively weaker energy at an interface at an increasing distance from the functional group.

10

100 2

Adsorbed amount (µmol/m )

2 Adsorbed amount (µmol/m )

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 26 of 35

8

6

4

10-1

10-2

10-3

10-4

10-3

10-2

10-1

100

P/P0 2

Hex 0 0.0

0.2

0.4

0.6

0.8

1.0

P/P0 Figure 11. Experimental isotherm of water on Hex carbon at 298K 8. The inset shows the isotherms of water plotted on logarithmic scales.

To shed further light on this failure to conform with Henry’s law, we considered a graphite surface grafted with carboxylic groups separated by 6nm which is large enough for them to act independently, as shown in Figure 12a. Figure 13a shows the simulated isotherms for water at 298K on a log-log scale. The adsorbed amount is plotted as the excess number of water molecules divided by the total number of carboxylic groups (denoted as NF/NFG in the 26 ACS Paragon Plus Environment

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following discussion). Figure 12b shows the isosteric heat and the contributions from the fluid-fluid (FF) and fluid-functional group (F-FG) interactions.

Figure 12. Top view of the functional groups configurations. The simulation box is 30×30×3nm in xyzdirections. (a) The carboxylic groups (blue dots) are separated by 6nm which behave independently. (b) Two carboxylic groups are separated by a distance from 0.7 to 1nm. The pairs are widely separated by 6nm.

As in Figure 13a, the isotherms simulated in both the GCMC and NVT ensembles are in good agreement with the theoretical Henry constant at loadings below 1 NF/NFG, confirming that water molecules first adsorb around the functional groups by electrostatic interaction until all pairs of functional groups are covered with one water molecule. This is the Langmuir model, where molecules are adsorbed in a localized monolayer. The isosteric is heat of 60kJ/mol is the isosteric heat at zero loading calculated by Monte Carlo integration, shown in Figure 7b) and F-F interactions are negligible. At loadings greater than 1 NF/NFG, the slope of the isotherm is less than the Henry law slope, because water adsorbs on the FG-water complex at distances away from the functional groups to form clusters, resulting in an increase in the FF interactions and the decrease in the F-FG interactions (Figure 13b). 27 ACS Paragon Plus Environment


1

Number of water per group

(a) 10

100

10-1 GCMC simulation NVT simulation Theoretical Henry constant 10-2 10-4

10-3

10-2

10-1

100

101

P/P0

(b) 80 Isosteric heat (kJ/mol)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 28 of 35

Total heat FF contribution F-FG contribtion

60

40

20

0 10-4

10-3

10-2

10-1

100

101

P/P0

Figure 13. (a) Simulated isotherms of TIP5P water at 300K on a graphite adsorbent grafted with widely separated carboxylic groups. (b) total isosteric heat and the contributions from FF and F-FG interaction energies calculated by GCMC simulation.

Next we consider a case where the carboxylic groups are closer to each other (0.7nm -1nm), as shown in Figure 12b. As discussed above, the affinity of two carboxylic groups is the strongest at a separation of 0.7nm due to the synergetic effect. The isotherms and the


Page 29 of 35 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


isosteric heat are shown in Figures. 14a and b, respectively. The slope of the isotherm deviates from the Henry constant at the loading of 0.1 NF/NFG, which is much lower than when functional groups were widely separated. Now the initial adsorption occurs on pairs of functional groups separated by the optimum distance of 0.7nm. These pairs contribute 25% of the total number of functional groups in this system. Once these pairs have been covered with water molecules, the slope of the isotherm is less than the Henry constant and continues to decrease with loading as adsorption proceeds not only on progressively weaker functional groups with separation greater than 0.7nm, but also on the preliminary FG-water clusters forming on the 0.7nm pairs of functional groups. This is reflected in the decrease of the FFG contribution and the increase in the FF contribution to the isosteric heat seen in Figure14b. Because of the simultaneous adsorption on the weakly adsorbing functional groups and on the FG-water clusters no plateau is observed in the isotherm at loadings close to 1 NF/NFG.



Number of water per pair groups

(a)

10

1

0.1

GCMC simulation NVT simulation Theoretical Henry constant 0.01 10-5

10-4

10-3

10-2

10-1

100

101

P/P0

(b) Isosteric heat (kJ/mol)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 30 of 35

80 Total heat FF contribution F-FG contribution 60

40

20

0 10-5

10-4

10-3

10-2

10-1

100

101

P/P0

Figure 14. (a) Simulated isotherms for TIP5P water at 300K on a graphite surface grafted with carboxylic groups separated by distances ranging from 0.7m to 1nm. (b) Total isosteric heat and its contributions from FF and F-FG interaction energies calculated by GCMC simulation.


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Conclusions We have presented a comprehensive study of the Henry constant and the isosteric heat at zero loading for water adsorption on functional groups. The intrinsic Henry constant is calculated by Monte Carlo integration of the Boltzmann factor of the potential energy between water and functional groups. We find that: (1) There is an interplay between different adsorption mechanisms: molecular layering and clustering, depending on the relative strength of the various adsorption sites. For non-associating fluids, like nitrogen and carbon dioxide, adsorption primarily occurs in micropores, followed by molecular layering on the graphite surface, while for strong associating fluids, like water, clustering around the functional groups is the dominant process. (2) The TIP5P model of water has a larger Henry constant than the SPCE model when functional groups are present on the adsorbent, because the TIP5P model has a tetrahedral shape with two positive charges on the hydrogen atoms and two negative charges on the lone pair electrons. (3) The affinity of a functional group toward water depends not only on its partial charges but also on its accessibility to water molecules. The carboxylic group is the most strongly adsorbing group of those examined here due to its large dipole and molecular size, which provides better accessibility to a water molecule. The nitrile group has smaller partial charges than carbonyl, but gives a higher Henry constant, because it is more accessible to water molecules. The Henry constants for hydroxyl and amide functional groups are comparable, indicating that there is no difference between acidic and basic groups.



Page 32 of 35

(4) For functional groups that have more than one sigma bond, the Henry constant depends on the orientation of the functional group.

For carboxylic groups, the

optimum C-C-O-H dihedral angle is 90o for both TIP5P and SPCE models. (5) For two nearby functional groups, the Henry constant of water is enhanced at an optimal separation due to the synergetic effects. The optimum separation distances for hydroxyl and carboxylic groups are 0.45nm and 0.7nm, respectively. (6) The simulated isotherm of water on a graphite surface grafted with functional groups follows Henry’s law only at extremely low pressures, which could be well outside the measurable range of practical pressure transducers.

The slope of the isotherm

decreases with loading due to the growth of water clusters, which is confirmed by experimental isotherms for water on highly graphitized carbon.

Acknowledgement: This project is supported by the Australian Research Council (DP160103540) Supporting information: Figure S1 Potential profile of water (SPCE) molecule in slit pores with different pore sizes


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Optimum configurations for the TIP5P model interacting with different acidic and basic functional groups.


On the Henry Constant of Water Adsorption on Functionalized

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