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School of Chemical Engineering and Analytical Science, The University of Manchester, Manchester M13 9PL, UK. Email: [email protected]; Tel: +44-1613064342† Electronic Supplementary Information (ESI) available: density and orientation profiles from adsorption simulations, and calculations results at the minimum energy configuration and from direct numerical integration. See DOI: 10.1039/x0xx00000x


Journal Name

ARTICLE

Received 00th January 20xx,Accepted 00th January 20xx

DOI: 10.1039/x0xx00000x

www.rsc.org/

Design of 2D materials for selective adsorption: a comparison between Monte Carlo simulations and direct numerical integrationHuan Xiang, Xiaolei Fan and Flor R. Siperstein *

Understanding the behaviour of fluids in confinement is essential to predict adsorption selectivity and develop adsorbents that can address challenging separations, such as ethane/ethylene mixtures. In this work we show that adsorption selectivity for an ethane/ethylene mixture can be predicted from direct numerical integration of the solid-fluid interaction potential because fluid-fluid interactions are negligible when compared to solid-fluid interactions, and adsorption sites are indistinguishable in pure component and mixture simulations. We present a comprehensive analysis of the density and orientation distributions in the pores as a function of pore size and pressure, providing tools that can be used for the design of 2D materials for the selective adsorption of gases.

1. Introduction Hydrocarbon purification is essential to their use as energy resources and building blocks in petrochemical industries. Separation of alkenes from alkanes is considered as one of the seven chemical separations to change the world.1 Among them, ethane/ethylene separation is of extremely prime industrial and societal importance.2,3 For example, high purity ethylene can be used in the manufacture of polyethylene, the most widely used plastic in our daily life, such as packing films and carrier bags.

The industrial separation of ethylene from ethane relies on cryogenic distillation, which is typically performed at 248 K and 23 bar in a column consisting of over 100 trays.4 This operation at low temperature and also high pressure is quite energy intensive. During ethane cracking, the separation of their binary mixture consumes about 7 GJ/t, which constitutes approximately 20–30% of the total energy consumption.5-7 Therefore, highly efficient and non-energy intensive alternatives for ethane/ethylene mixture separation are demanded.

It was demonstrated that separations involving no phase change could significantly reduce energy consumption compared to phase-change-based separations.1,8 Adsorption is considered as a promising option for ethane/ethylene separation due to its low energy requirement and high efficiency. Adsorption selectivity is one of the most important parameters to evaluate the separation performance, which is directly determined by the properties of adsorbents. To date, various adsorbents including activated carbons,9,10 zeolites4,11,12 and metal-organic frameworks13,14 have been proposed for ethane/ethylene separation. Microporous carbons are the most widely used adsorbents for gas systems.15 Besides experimental works on ethane/ethylene separation using carbon materials,10,16-19 Monte Carlo (MC) simulation has been proved to be a useful tool to study microscopic behaviour of adsorption, such as characterise adsorbed gas molecules within different carbon pores, and then to obtain high selectivity.

Klochko20 and Calleja et al.15 investigated the density and orientation distributions of ethane molecules in slit-shaped micropores, and found both of them depended strongly on the pore width. Ethane adsorbed parallel to the surface in most pore sizes, but tilted and perpendicular orientations were observed in the contact layer when the pores were between 0.49 nm and 0.65 nm. Zhang and co-workers21 simulated ethane adsorption in single walled carbon nanotube arrays, and they found that at room temperature molecules formed a distinct monolayer close to the surface without much ordering

This journal is © The Royal Society of Chemistry 20xx Molecular Systems Design & Engineering , 2018, 00, 1-3 | 1



ARTICLE Journal Name

in the rest of the tube. The adsorbed molecules were mostly parallel to the surface (perpendicular to the pore normal axis), but without much ordering relative to the axial direction of the pore. Monte Carlo simulations were also used to study ethylene adsorption in slit pores by Do et al.22 showing excellent agreement with experimental data of ethylene adsorption on graphitized thermal carbon black. Most of the simulations for adsorption of ethane and ethylene neglect electrostatic interactions.

Weitz and Potoff found that the correct description of the bulk phase behaviour of ethylene containing mixtures, such as xenon/ethylene, required partial charges on ethylene to reproduce its quadrupole moment, but that the properties of the CO2/ethylene mixture were better described without taking into account ethylene’s quadrupole moment, and for n-butane/ethylene are insensitive to the charges used in the model.23 However, Jorge et al. confirmed that the electrostatic interactions could be neglected in ethane and ethylene mixture adsorption on CuBTC.24

Do et al.25-27 also assessed the performance of different force fields for simulating the ethane/ethylene mixture on graphitized carbon black and in slit pores, and found that TraPPE-UA model performed slightly better than AUA4 model. Extensive molecular simulations of ethane/ethylene mixtures on carbon slit pores28 and carbon nanotubes29 showed similar features: the selectivity decreased with the increase in temperature and pressure, and an oscillating selectivity that converged for large pore sizes, and reached its highest values for small pore sizes.

A rapid estimation of the zero coverage selectivity can also be obtained from the ratio of pure component adsorption Henry’s constants. These can be calculated by integration of the Boltzmann factor over the pore volume.30,31 Monte Carlo integration is often used in complex adsorbent geometries (such as zeolites), but direct numerical integration can be used in simple geometries when the potential energy of a molecule inside the pore is given by a simple expression. Although direct numerical integration has been extensively used for calculating single site molecule’s Henry’s constant, it has not been reported for linear molecules to the best of our knowledge, and more importantly, the errors associated with the prediction of zero coverage selectivity and finite pressure selectivity have not been carefully analysed. This may lead to incorrect estimations of the adsorbent’s selectivity when carrying out in silico design of 2D materials. In this paper we show that important physical insight on the location and orientation of adsorbed molecules can be obtained using direct numerical integration to calculate the selectivity of an adsorbed mixture.

Monte Carlo simulations were also used to study the adsorption of pure ethane, ethylene and an equimolar mixture in carbon slit pores to assess the importance of lateral interactions as well as the location and orientation of adsorbed molecules. We showed good agreement in the selectivity obtained from Monte Carlo simulations of adsorption and those obtained using direct numerical integration calculations at low pressure, and increasing deviations at higher pressures

as lateral interactions became more important. We show that differences of up to 125% in the adsorption selectivity can be obtained depending on the assumptions used in the calculation. The methodology presented in this work can be used as a rapid and accurate estimation of the adsorption selectivity for realistic design of 2D materials.

2. Method2.1. Fluid-fluid interactions

Ethane and ethylene molecules were described using a United Atom (UA) model, which considers each CHx (x = 3 or 2) group and the centre of mass (M) as a single interaction site. The fluid-fluid intermolecular interactions were modelled using Lennard-Jones (12-6) potential plus Coulomb potential, then the interaction energy of a site i and a site j is given by:

(1)where ij and ij

are the well depth and collision diameter of

interaction energy, respectively. qi and qj are the partial atomic

charges of the interaction sites, and 0 is the dielectric constant (8.854×10-12 C2 J-1 m-1).

The interactions were cut at 1.875 nm (five times the collision diameter of ethane ethane). Lennard-Jones parameters (listed in Table 1) of ethylene and ethane including their centre of mass used in the simulation were taken from the TraPPE-UA force field,32 and Coulomb charges of gas adsorbates were assigned according to Jorge et al.24 The fixed carbon-carbon bond length lbond of ethane and ethylene are 0.154 nm and 0.133 nm, respectively. Parameters for interactions between two different types of sites (cross-terms) were calculated using the Lorentz-Berthelot mixing rules:32

(2)

(3)

Table 1 Potential parameters for ethane and ethylene.

kB is the

Boltzmann constant (1.381×10–23 J K-1).

2.2. Solid-fluid interactions

The solid phase is modelled as a single slit pore, where the surface is assumed to be flat and homogeneous. The slit pore has two infinite parallel walls in the x and y directions separated by a distance H in the z direction. The interaction potential energy between the fluid and the solid surface was calculated by the well-known Steele Wall (10-4-3) potential:33

2 | Molecular Systems Design & Engineering , 2018, 00, 1-3 This journal is © The Royal Society of Chemistry 20xx

Atom /kB (K) (nm) q(e)

CH3_C2H6 98 0.3750 -0.118

M_C2H6 0 0 0.236

CH2_C2H4 85 0.3675 0.393

M_C2H4 0 0 -0.786



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(4)where ss is the volumetric carbon atom density (1.14×10–4 nm–

3), is the spacing between two adjacent carbon layers (0.335 nm), z is the distance between the interaction site and carbon wall, and the solid-fluid molecular parameters, the well depth sf and collision diameter sf, were also calculated from the Lorentz-Berthelot mixing rules:

(5)

(6)For the carbon solid surface, ss = 0.34 nm, ss/kB

= 28 K.27

The force field Usf in a slit pore of width H is the sum of the interactions with both solid surfaces and can be expressed mathematically as:

(7)The total potential energy of a molecule confined in the slit

pore, is the result of fluid-fluid and solid-fluid contributions. In all simulations, the temperature was held constant at 298 K.2.3. Simulation details

Monte Carlo simulations were carried out in the grand canonical ensemble using Towhee34 to study the adsorption of fluids in carbon slit pores. Typical simulations required 300,000,000 steps for equilibration and 200,000,000 steps were used to obtain equilibrium averaged properties. The chemical potential was calculated from independent simulations in the canonical ensemble using the Widom insertion method.34,35 The pore width was varied from 0.675–2.250 nm (1.8–6.0 ethane) and the solid-fluid interactions were specified as external fields. The width is large enough for slit pores to mimic two independent surfaces. The surface area, Lx×Ly, of each solid surface was 12 × 12 nm2. This area was selected to ensure that at least 10 molecules were present at the lowest pressure studied (10 kPa). This ensured that no significant size effects are observed. The average amount adsorbed (av) is defined as:

(8)where Npore is the ensemble average number of gas molecules in the slit pores, and Lx and Ly are the box length in the x and y directions, respectively.

Based on the simulations, the selectivity towards ethane over ethylene is calculated from:

(9)where xethane and xethylene are the mole fractions of ethane and ethylene inside the adsorbed phase (slit pores), whereas

yethane

and yethylene are their fractions in the bulk phase.Local density profiles were used to study how molecules

are layered and their distribution within the slit pores. These profiles were obtained from histograms with z = 0.06 nm, averaged over 50 configurations:

(10)where N(z) is the average number of interaction sites of gas molecules whose centres of mass are located in the segment having boundaries at z and z + z.

The local density does not contain information on the molecule’s orientation inside the pores. We define the orientation of a molecule relative to the surface as shown in Figure 1, where:

(11)where is the angle between the bond and solid surface. z1

and z2 are the distance between the two CHx (x = 3 or 2) sites

and the solid surface in the z direction, respectively. If = 0°, it means the molecule is parallel to the slit wall; if = 90°, the molecule is perpendicular to the slit wall.

Figure 1 Definition of angle for a linear molecule relative to the carbon solid surface.

2.4. Direct numerical integration

The Henry’s constant (KH)31 can be calculated as:

(12)where V is the volume of gas phase in the adsorption equipment and r is the position vector of a single adsorbate molecule. The exponential term is the Boltzmann factor, where u(r) is the total potential energy of a single adsorbate molecule in the pore. T is the adsorption temperature and R is the gas constant (8.314 J mol-1 K-1).

In general, for a linear molecule in the carbon slit pores, the potential energy of adsorbed molecule is a function of its position (z) and orientation () inside the pore, so Henry’s constant can be expressed as:

(13)At the limit of zero pressure, the selectivity of ethane over

ethylene is defined as the ratio of Henry’s constants of the pure components and can be calculated as:

This journal is © The Royal Society of Chemistry 20xx Molecular Systems Design & Engineering, 2018, 00, 1-3 | 3




(14)where uethane(z) and uethylene(z) are the potential energy of ethane and ethylene, respectively. At finite loadings, lateral interactions would need to be considered, but at sufficiently low loadings considering the selectivity as the ratio of Henry’s constants is reasonable. Moreover, if both of the Boltzmann factors of ethane and ethylene are much larger than one, the selectivity can be estimated by:

(15)Finally, if the lowest energy configuration occurs on an

extremely narrow range of distances to the wall and orientations, the selectivity equals to the ratio of their Boltzmann factors, and is given by:

(16)where uethane,min, uethylene,min and umin are the potential energy of a single ethane and ethylene molecule and their energy difference at the lowest energy configuration.

Based on the potential energy of the two kinds of molecules, the selectivity can be predicted directly from the numerical integration without any simulation input.

3. Results and discussion3.1. Importance of lateral interactions

Molecules in confined spaces have less neighbouring molecules than those in bulk systems, and as a result, the interactions with the solid adsorbent can be significantly more important than the interactions between adsorbed molecules. We consider lateral interactions as the interactions between adsorbed molecules within the pores. It is expected that lateral interactions will become more important as pore sizes increase and as pressure increases as the number of neighbouring molecules can be larger.

Figure 2 shows a snapshot of the ethane/ethylene mixture adsorption in three different pore sizes, i.e. H = 0.750, 1.125 and 1.500 nm. Only a monolayer adsorption is observed in pores of 0.750 nm regardless of the pressures because the pore size is too small to allow the formation of more adsorbed layers. When the pore size is increased to 1.125 nm, molecules adsorbed form two distinct layers next to the two solid walls,

which can be clearly seen at pressures of 100 kPa and 1000 kPa. These molecules are more disordered than those in smaller pores, consistently with what has been reported in the literature.21 There is no obvious difference in the snapshots for H = 1.500 nm and H = 1.125 nm at 10 kPa because only a few molecules are adsorbed. When pressure increased to 100 kPa, two distinct layers are formed in pores of 1.500 nm, separated by a large enough distance that can accommodate isolated molecules at a gas phase density. A third layer appears at 1000 kPa, but it is clearly more disordered than the layers in contact with the solid.

Figure 2 Snapshots of ethane/ethylene mixture adsorbed in the carbon slit pore at 298 K.

An estimate of the importance of the lateral interactions can be obtained from comparing the contributions to the total energy of the solid-fluid and fluid-fluid interactions, which are discussed in section 3.1.1. Considering that the fluid-fluid interactions can have a van der Waals and electrostatic contribution, the importance of the electrostatic interactions are discussed in section 3.1.2.3.1.1. Van der Waals interactions In this work, van der Waals interactions exist between the solid and the fluid (via the 10-4-3 potential), and between fluid molecules (via the 12-6 potential). The importance of the lateral interactions can be assessed by looking at the fraction of the van der Waals energy that corresponds to the fluid-fluid interactions compared to the fluid-solid interactions (shown in Figure 3). The fluid-fluid contribution to the total energy increases with increasing pressure, from about 0.5% to 36%. Nevertheless, this contribution does not grow monotonically with the pore size, and the shape of the curves describing the contribution of the lateral interactions closely follow the curves describing the amount adsorbed in different pore size materials at a given pressure (Figure 4): lateral interactions are more important at high densities.

In general, it is reasonable to consider that the interaction energy between the solid walls and gas molecules is more important than lateral interactions between adsorbed molecules in this system.

Figure 3 Fractions of van der Waals energy for pure ethane (black), pure ethylene





(red) and binary mixture (blue) adsorption in different slit pore sizes at (a) 10 kPa, (b) 100 kPa and (c) 1000 kPa and 298 K. Solid symbols are for solid-fluid interactions, whereas open symbols are for fluid-fluid interactions.

3.1.2. Electrostatic interactions Considering that the solid surfaces are not charged, the only electrostatic effects are those observed in the lateral interactions. Simulation results for models where electrostatic contributions were or not considered are shown in Figure 4. It is clear that for all cases the simulations yield essentially the same amount adsorbed of gas molecules regardless of whether the partial atomic charges on the gas molecules were included in the calculations.

The calculated selectivity towards ethane over ethylene obtained from binary mixture simulations is shown in Figure 5,

showing no significant difference between the results that considered electrostatic interactions and those that ignored them. This indicates that the electrostatic contributions can be neglected when simulating this system. The validity of neglecting electrostatic interactions needs to be assessed carefully as it will depend on the material used; nevertheless other works have also shown that electrostatic interactions are negligible in simulations of ethane and ethylene adsorption on CuBTC.24

Figure 4 Amount adsorbed of ethane and ethylene in different slit pore sizes at (a) 10 kPa, (b) 100 kPa and (c) 1000 kPa and 298 K. Solid symbols (black for ethane and blue for ethylene) represent models where electrostatic contributions are ignored and open symbols (red for ethane and pink for ethylene) represent models where electrostatic contributions are considered. Solid lines with circle symbols are for pure component simulations, whereas dashed lines with square symbols are for simulations of mixtures with a bulk equimolar composition.

Figure 5 Selectivity based on simulations of ethane/ethylene mixture with a bulk equimolar composition in different slit pore sizes at (a) 10 kPa, (b) 100 kPa and (c) 1000 kPa and 298 K. Red solid lines represent models where electrostatic contributions are considered and black solid lines represent models where electrostatic contributions are ignored.

3.2. Adsorbed phase structure

In an ideal system, adsorbed molecules are well mixed. Any segregation in the adsorbed phase leads to non-ideal behaviour. Differences in the distribution of molecules in the pore for pure component adsorption can usually give insight on the sources of non-ideality.3.2.1. Density profiles Density profiles of the CHx (x = 3 or 2) groups and the centre of mass are obtained to identify the distribution of adsorbed molecules inside the slit pores. Considering the similarity of the profiles obtained at different pressures, only the density profiles at 100 kPa are shown in Figure 6, whereas others are presented in the Electronic Supplementary Information (ESI). As shown in Figure 6, for a very small pore size, there was only a well-defined adsorbed layer inside the pore for both pure component and mixture

adsorption, since only one peak occurred in the centre of the pore for both CHx (x = 3 or 2) groups and the centre of mass. A comparison of the density profiles of the centre of mass and the CHx (x = 3 or 2) groups provides some information on the orientation of the adsorbed molecules, suggesting that in general they are parallel to the solid wall, except at some specific pore sizes (H~1.0 nm) where the density profile of the CHx (x = 3 or 2) groups is wider than the one of the centre of mass. In small pores a single adsorbed layer is observed, and as the pore size increases, two clear adsorbed layers are formed close to the walls.

Although the densities for C2H6 and C2H4 in mixture adsorption simulations were lower than corresponding pure component (see Figure 4), the simulated density profiles are similar for pure components and mixtures, which indicates





that the presence of a second component does not affect the distribution of molecules in the pore.

Figure 6 Density profiles (kmol/m3) for CH3 groups and CH2 groups, and the centre of mass in the carbon slit pores at 100 kPa and 298 K: (a) M-pure C 2H6; (b) CH3-pure C2H6; (c) M-pure C2H4; (d) CH2-pure C2H4; (e) M-C2H6 in mixture; (f) CH3-C2H6 in mixture; (g) M-C2H4 in mixture; (h) CH2-C2H4 in mixture. The origin in the x-axis represents the pore centre.

3.2.2. Orientation profiles Angle distribution profiles are used to illustrate molecule orientation in the adsorbed phase. Figure7 shows the orientation profiles for pure component adsorption at different pressures. C2H6 always forms an angle with the solid surface smaller than 20° for the smallest pore size of 0.675 nm, while C2H4 forms an angle with the surface below 25°, meaning that the preferential orientation of both

molecules is parallel to the solid walls. Molecules can explore a wider range of orientations in larger pores, which leads to a broader angle distribution. While in most pore sizes the adsorbed layer is parallel to the wall, tilted and perpendicular orientations become more favourable in pores with H = 0.825–0.975 nm (2.2–2.6 ethane), shown as a finger in the orientation distribution. The transition from one to two adsorbed layers





also happens there, and in pores larger than H = 1 nm we recover the parallel orientation of the molecules in the adsorbed layer. The parallel orientation becomes unfavourable for C2H6 adsorption in pores with H = 1.275 nm at 100 kPa, where the formation of a second finger is observed. This is not as clear as in pores with H = 0.825–0.975 nm, and denotes the formation of a third layer. The orientation of the adsorbed molecules becomes insensitive to pore size for larger pores (H > 1.5 nm), in the range of pressures studied. A similar behaviour is observed for mixtures with the results reported in

the ESI. The main difference between the orientation of pure component adsorbed molecules and their mixtures is the clarity of the second finger (H = 1.275–1.350 nm) at 100 kPa.

The similarity in the density and orientation profiles of pure components and mixtures suggests that ethane (or ethylene) molecules always exhibited the same adsorption behaviour within the slit pores. Based on this, it is reasonable to predict ethane/ethylene binary mixture adsorption from pure component adsorption.

Figure 7 Orientation profiles for C2H6 and C2H4 in pure component simulations in the carbon slit pores at 298 K (a) C2H6 at 10 kPa; (b) C2H4 at 10 kPa; (c) C2H6 at 100 kPa; (d) C2H4 at 100 kPa; (e) C2H6 at 1000 kPa and (f) C2H4 at 1000 kPa.

3.3. Selectivity

Adsorption selectivity can be obtained directly from mixture simulations, but mapping the entire phase space may be time consuming and computationally intensive. Based on the results obtained from the simulations, the adsorption behaviour of ethane (or ethylene) molecules is similar for pure component adsorption and binary mixture adsorption. Therefore, selectivity towards ethane over ethylene can be estimated

from single component adsorption as the ratio of Henry’s constants. In this work, direct numerical integration is used to predict the selectivity in slit pores without using information from mixture simulations. Considering that the solid-fluid interactions are much more important than lateral interactions between fluids (as shown in section 3.1), only Steel Wall potential is considered in the integration.

Henry’s constant can be calculated using equation (12) and is dependent on the interaction of an isolated molecule with





the two solid surfaces. Thus, it is related to the position and orientation of adsorbed molecules since the properties of solid walls are fixed. At zero temperature, when the adsorption system is at the minimum energy, the maximum selectivity value can be obtained. The position and orientation for an ethane and ethylene molecules that result in the minimum energy configuration were calculated (and are available in the ESI), and the selectivity calculated using equation (16) is shown as a red line in Figure 8. Nevertheless, it is clear that the selectivity calculated based exclusively on the minimum energy configuration overestimates the selectivity calculated directly from mixture simulations. Adsorbed molecules explore different orientations and positions at finite temperatures for both ethane and ethylene adsorption. The black line in Figure 8 shows the selectivity calculated using equation (15), considering all possible positions and orientations of a molecule inside the pore. Details of the calculation are available in the ESI.

All selectivity profiles in Figure 8 follow the same tendency. The selectivity increases to the highest value at around H = 0.750 nm where only monolayer adsorption is observed, and then decrease slowly, and finally converges when the pore size is larger than 1.500 nm. The selectivity calculated from direct numerical integration is in good agreement with the one obtained from mixture adsorption simulations at 10 kPa and 100 kPa. The selectivity calculated from simulations at 1000 kPa is sensibly lower than the one obtained from direct numerical integration, suggesting that lateral interactions become important at this pressure.

Figure 8 Selectivity in the carbon slit pores from numerical integration and simulations at 298 K. Symbols are from mixture simulations, black line was calculated using equation (15) and red line using equation (16).

4. ConclusionsAdsorption of ethane, ethylene and their binary mixture in carbon slit pores of various pore sizes has been investigated by Monte Carlo simulations. The analysis of the density and orientation profiles in the pores suggests that there is no significant difference in the adsorption behaviour for molecules in pure component systems or in mixtures. Our simulation results showed that there is not a single, most preferable location and orientation of molecules inside the pores, but that a wide distribution is observed. We proposed a

rapid visualisation approach to identify the pore density as a function of pore width and position in the pore, that provides quick insight into the transition conditions and regions that could lead to changes in selectivity.

In general, molecules prefer to be parallel to the solid surfaces. As pore width and pressure increases, one, and then two and even three layers are formed in adsorbed phase. At the pore sizes where the transition occurs, it is likely to have adsorbed molecules perpendicular to the surface.

Our simulation results also showed that the energetics of the system is dominated by the solid-fluid interactions, with lateral van der Waals interactions representing no more than 36%, and electrostatic interactions being negligible. In all cases studied, regardless of pore size and pressure, the solid surface always prefers ethane adsorption.

We also showed that the low pressure selectivity can be accurately calculated from direct numerical integration of the potential energy of a single molecule inside the pore, but that it is necessary to consider all positions and orientations of the molecule inside the pore, and not just the minimum energy configuration. Despite the low selectivity for ethane over ethylene in carbons, the approach presented here can be valuable for studying functionalized carbon materials where higher selectivity can be achieved.

The comprehensive analysis carried out in this work, and the representation of the probability density and orientation inside the pores as a function of pore width, provide an easy tool for the design of 2D materials. The rapid estimation of the selectivity using direct numerical integration can easily be extended to rapidly scan a wide range of functionalised materials.

Conflicts of interestThere are no conflicts to declare.

AcknowledgementsWe acknowledge the assistance given by IT Services and the use of the Computational Shared Facility at The University of Manchester. Huan Xiang thanks The University of Manchester President’s Doctoral Scholar Award and the China Scholarship Council (file no. 201606150068) for supporting her PhD research.

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€¦ · Web viewThe industrial separation of ethylene from ethane relies on cryogenic distillation, which is typically performed at 248 K and 23 bar in a column consisting of over