1

“Equilibrium and Transport Properties of

Small Alkanes and Alkenes Confined in

Single-W

alled Carbon Nanotubes.”

Fernando J. A. L. Cruz, ErichA. Müller

Imperial College London

f.cruz@

imperial.ac.uk

2

1 –Introduction

1.1 -Motivation

●Separation of close boiling point mixtures (olefin/paraffin) bydistillation are energy

intensive operations.

●Adsorption can play a role in improving this scenario (molecular-level knowledge of

adsorption in confined nanospaces spaces is required).

●For small scale separations (pharmaceuticals, higher added value), nanotube-based

membranes could be good future candidates.

●Extendourexpertisefromflatsurfaces(carbonslitpores) to cilindricalgeommetries.

1.2 –Adsorbents & Methodology

●Carbonnanotubes firstidentifiedintheearly90’s [Iijima1991]: possibleapplications

range fromstoragenanomaterials (H2,CH4) andcompositesfor electronics, to separating

agentsoforganicvaporsandchemicalsensors.

●Studytheadsorptionanddiffusionbehaviouroffluids, whena bulkphaseisexposedto

direct

contact

with

single-walledcarbonnanotubes: ClassicalMolecular Dynamics

(Newton’s3rdlaw) andGrandCanonical Monte Carlosimulations.

3

2 –Single-walledcarbonnanotubes (SWCNT)

Zig-zag(8,0)

arm

chair(5,5)

chiral (8,4)

graphene sheet

hexagonal simmetry

sp2carbons, 1.41 Å

4

3 –Force FieldsandMolecular Models

3.1 –All-atompotential(AA-OPLS)

●nonbondedinteractions: All-atomLennard-Jones(12,6) withexplicitCoulombiccharges

●bondsandangles: harmonic

●dihedrals: triple cosine

●nanotubes : All-atomgraphiticcarbons[Steele1973]

(

)∑∑

−

+

=i

j

ij

ijij

ijij

ij

ijji

ijf

rr

r

eq

qr

U

612

2

4σ

σε

()

[]

[]

[] )

cos(

)cos(

)cos(

i

i

i

i

i

i

i

i

VV

VU

φφ

φφ

31

22

12

12

32

1+

+−

++

=∑

3.2 –United-atompotential(2CLJQ)

●nonbondedinteractions: Lennard-Jones(12,6) beads(CH2, CH3) with

a quadrupole momentatthecenterofmass

()

()

()

()

[]

22

22

2

5

026

12

52

15

51

443

4j

ij

ij

i

ab

ij

ijij

ijij

ijab

ijc

cc

cc

cc

r

Q

rr

rr

U−

+−

+−

+

−

=∑∑

πε

σσ

ε,

3 –Force Fields

δ δδδ+ +++

δ δδδ+ +++

δ δδδ− −−−δ δδδ− −−−

δ δδδ− −−−

δ δδδ− −−− δ δδδ− −−−

δ δδδ− −−−

Q

5

4 –MD Simulations

3.3 –Single-walledcarbonnanotubes

●frozengraphiticcarbonatoms

d (C-C ) = 1.42 Å

squeezingoutoftheπorbitals

●explicitcarbonatoms: corrugatednanotubes

●effectivediameter: fromsurfaceto surface(accessiblevolume)

CRT

eff

DD

σ−

=

6

4 –SimulationsDetails

4.1 –ClassicalMolecular Dynamics

●NVTensemble(Nosé-Hoover thermostat)

●T= 300 K

●timestep = 1 fs(Verletleapfrogalgorithm)

●timescale0.5 –3ns

●Potentialcutoff= 15 Å

●Ewaldsummation (fluids)

MD box : 30 ×

30 ×302Å(60 ×60 ×302Å) ; SWCNT box : 30×30 ×

52Å(60 ×60 ×

52Å)

NCRT≈800 atoms(L

z=52 Å), N

fluid= 150-1200 atoms(density)

4.2 –GrandCanonical Monte Carlo

●µVTensemble

●Tpure= 300 K, 260 K ≤Tmix≤450 K

●cycles total= 30 ×106, cycles production= 5 ×106

●Potentialcutoff= 20 Å

●GCMC box : 25 ×25 ×

53 Å

7

5 –Equilibriumandadsorptionresults

5.1 -Adsorptionofpure

fluids

Bulkfluidequilibration@300K (t> 0.1ns)

Bulk ethylene being adsorbed onto a zig-zagSWCNT (16,0)

●fluids: 4 ×10-4≤pbulk≤53.6 bar

8

5 –Results

●typeI isotherms(IUPAC)

●similar behaviourwithSipsandTothisotherms

●overestimationwiththe2CLJQ (inaccuraterigidbehaviourandstaticchargedistributionfor

flexiblemoleculeslikeC2H6); convergenceafterp ≈10 bar [Cruz 2008]

●C2H6ispreferentiably adsorbedatlowp(dispersiveenergy); cross-overaround3 −6 bar

(activatedcarbons, slitpores, higherDSWCNTs); atmedium-highpressureC2H4isthe

dominantspecies(entropicfactor / packingefficiency) ; isosteric heatsofadsorption(q

iso=

−∆H)

()

[]t

ts

bP

bP

CC

Toth

1

1+

=µ

µ:

()

()nn

s

bP

bP

CC

Sips

1

1

1+

=µ

µ:

0

50

100

150

200

250

300

350

400

AA-OPLS

2CLJQ

0.01

1E-3

0.1

110

C2H4

Surface Coverage (µµµµmol/m2)

p / bar

050100

150

200

250

300

350

400

AA-OPLS

2CLJQ

C2H

6

Surface Coverage (µµµµmol/m2)

p / bar

0.01

1E-3

0.1

110

9

5 –Results

11.7 bar

1.45 bar

0.28 bar

pbulk

25 bar

10

5 –Results

●armchair(9,9) andchiral (12,6) nanotubes presentsimilar lowpressure(p< 1 bar)

adsorptioncapacities(−3.4 % to 7 %)

●nanotubes loadingcapacityseemsto bea quadraticfunctionofthetubes’diameter

(4.46 Å, 6.80 Å, 9.15 Å, 11.49 Å, 13.83 Å)

05

1015

20

020406080100

120

140

C2H

4 (9.5 Å)

C2H

6 (10 Å)

Surface Coverage (µµµµmol/m

2)

D / Å

11

5 –Results

5.2 -Separationofbinary

mixtures(C

2H4/C

2H6)

i )refinery mixture (90 mol % C

2H4), p= 1 bar

●Sdecreaseswith

T(high temperatures reduce

the energetic differences between molecules);

Selectivity’s

values

are similar

to larger

nanotubes andotherporegeommetries

ii )equimolar mixture, 0.1 ≤

p≤30 bar

●Sdecreasesrapidlyupto p≈10bar, andfrom

thenonwardsgainsa monotonical behaviour.

●the higher selectivity values coincide with the

low pressure regions, where ethane is the

preferentially adsorbed species

bulk

ethylene

ethane

nanotube

ethylene

ethane

xx

xx

S)

/(

)/

(=

250

300

350

400

450

1234

1 bar

Selectivity

T / K

05

1015

2025

3001234

200K

300K

400K

Selectivity

p / bar

12

6.1 -Methodology

●Once the adsorption runs were finished, the upper volume of the simulation cell,

containing the nanotube and the adsorbed molecules, was separated from the bulk fluid

and replicated four times along the z-axis to produce a 30 ×

30 ×206Åsupercell

containing ca.3000 graphitic carbon atoms.

●Molecular displacementhasbeenmonitoredfor 0.5 ns: bulkandconfinedfluids.

●0.026 ≤ρ/mol�L–1≤15.751 (C2H4)

●0.011 ≤ρ/mol�L–1≤14.055 (C2H6)

6 –Dynamicalproperties

13

6.2 -Porecontact

●A previouslyreportedhelicaldiffusivepathfor pureC2’s inzig-zagSWCNT’s[Mao2000],

hasalsobeenobservedherefor denseconfinedfluidsandcorrespondingbinary

mixtures(wallsimmetryandC –C bonds) .

ethaneSWCNT

●Notsurprisingly, chiral tubesexhibita more pronouncedspirallingeffect!

●No coherentdisplacementfor armchairtubes.

14

5 –Results

Ddt

dr

Fickian

∝2

:

22

Bdt

dr

Ballistic

∝:

6.3 -Effectivediffusion

●Linear behaviour=> Fickian-typediffusion=> self-diffusion(effective), D(10-8m2/s,)

()()

[]2

061

rt

rdtd

D−

=

()()

[]2

20

rt

rr

MSD

−=

=

50100

150

200

250

300

1

2,5x10

3

5,0x10

3

7,5x10

3

1,0x10

4

C2H

4 @ (16,0)SWCNT

MSD / ÅÅÅÅ2

t / ps

Ballistic

Fickian

15

5 –Results

6.3 -Effectivediffusion

●increaseofD, withdecreaseofmoleculesinsidethetube, untilltransitionto outsidethe

Fickian regime: ρ< 5.5 mol�L–1(@SWCNT) [Cruz 2008]

●lowdensitysystems: ballisticandmixedtyperegimes (freespaceavailablefor molecular

jumps)

●no significative influenceoftheSWCNT’ssimmetryontheFickian diffusivities(Zig-zag,

armchairandchiral nanotubes)

110

100

1000

1

101

102

103

104

105

106

C2H4 @ bulk

MSD / ÅÅÅÅ2

t / ps

ρρρρρρ

110

100

1000

1

101

102

103

104

105

106

C2H6 @ bulk

MSD /

ÅÅÅÅ2

t / ps

ρρ

110

100

1000

1

101

102

103

104

105

106

C2H4 @ bulk

MSD / ÅÅÅÅ2

t / ps

ρ

16

5 –Results

6.3 -Scalinglaws

●confined phase diffusion data can be estimated by the knowledgeof the corresponding

bulk fluid structural properties, and this idea can become immediately appealing when

one keeps in mind practical and industrial applications (e.g.nanofluidics).

●Dbulk= A �ρ–B : empiricalcorrelationverifiedfor ethylene, againstexperimental data upto

ρ≈9.9 mol�L–1(discrepancieslessthan5 %).

00,01

0,1

110

100

10-8

10-7

10-6

10-5

10-4

SWCNT

bulk

C2H4

D / mmmm2s-1

ρ ρρρ / mol�L-1

00,01

0,1

110

100

10-8

10-7

10-6

10-5

10-4

SWCNT

bulk

C2H6

D / mmmm2s-1

ρ ρρρ / mol�L-1

17

7 –Conclusions& Futurework

7.1 -Conclusions

●Resultsseem to show that the adsorption and transport behaviourof the pure fluids is

relatively independent of host simmetry.

●Relatively small changes in the nanotube diameter can have a marked effect on the

transport and adsorption properties. Further work would be required to confirm the

present findings in a larger pore with/temperature range.

●Ethane is the preferred adsorbed species (low p), ethylene diffusivities are larger than

those of ethane, although the difference is relatively minor.

●Confinedfluids’diffusiondata canbeestimatedfromthecorrespondingbulkphases

(scalinglaw).

7.2 -Perspectives

●C3fluidsandtheirbinarymixtures(D-ρscalinglaw).

18

Acknowledgements

EPSRCGrantEP/D035171/1, UK