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Effects of Geometrical Corrugation and Energetical Heterogeneity of Graphene Pore Walls on Adsorption in Nanoporous Carbons . PSD Characterization Jacek Jagiello Micromeritics Corporation, Norcross GA, USA. Relationship between assumed carbon pore model and calculated PSD

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Effects of Geometrical Corrugation and Energetical Heterogeneity of Graphene Pore Walls on Adsorption in Nanoporous Carbons.PSD CharacterizationJacek Jagiello Micromeritics Corporation, Norcross GA, USA


Presentation outline

Relationship between assumed carbon pore model and calculated PSD

Standard slit pore model based on Steele potential

Artifacts resulting from this model

Modifications of the model

finite pores

energetically heterogeneous pore walls

geometrically corrugated (rough) walls

incorporation of both effects

Improvements in PSD analysis

Presentation outline


Fluid density calculated by dft for ar on graphite
Fluid Density calculated PSDCalculated by DFT for Ar on Graphite


How the psd is calculated
How the PSD is calculated calculated PSD

Theoretical Isotherms (Kernel)

Experimental Isotherm

Linear Fredholm integral equation of the first kind


Outline of 2d nldft calculations

Model NLDFT isotherms and density profiles are calculated using Tarazona approach [1, 2].

Attractive fluid-fluid interactions are modeled by Weeks-Chandler-Andersen potential [3].

Pore walls are constructed by structureless graphene sheets.

External solid-fluid interaction potential is determined by numerical integration of the 12-6 Lennard-Jones potential over the graphene geometries.

Outline of 2D-NLDFT calculations

  • ______________________________

  • Tarazona, P.; Marini Bettolo Marconi, U.; Evans R. Mol Phys 1987; 60, 573.

  • Lastoskie, C.; Gubbins, K.E.; Quirke N. J Phys Chem 1993; 97, 4786-96.

  • Weeks, J. D.; Chandler, D.; Andersen, H. C. J. Chem. Phys. 1971; 54,5237.


Carbon slit pore model history
Carbon Slit Pore Model using Tarazona approach [1, 2]. (History)

Rosalind E. Franklin

Proceedings of The Royal Society of London Series A.

Mathematical and Physical Sciences

1951, 209, 196-218

Steele WA. The Interactions of Gases with Solid Surfaces, Pergamon, Oxford, 1974

N. A. Seaton, J. P. R. B. Walton and N. Quirke

Carbon ,1989, 27, 853-861

C. Lastoskie, K.E. Gubbins, N. Quirke, Langmuir, 1993, 9, 2693.

J.P. Olivier, W.B. Conklin, M.V. Szombathely, in Characterization of Porous Solids (COPS-III) Proceedings,

ed. by F. Rodriguez-Reinoso, J. Rouquerol, K.S.W. Sing, K.K. Unger (Amsterdam, 1994)


Artifacts of carbon slit pore model nldft and molecular simulations
Artifacts of Carbon Slit Pore Model using Tarazona approach [1, 2].(NLDFT and Molecular Simulations)

Ustinov, E.A., Do, D.D., Fenelonov, V.B. Carbon2006, 44, 653-663.

Neimark, A.V., Lin, Y., Ravikovitch, P.I., Thommes, M. Carbon2009, 47, 1617-1628.

Lueking, A.D.; Kim, H.-Y.; Jagiello,J., Bancroft, K., Johnson, J.K., Cole, M.W.

J. Low Temp. Phys.2009,157, 410–428.

NLDFT adsorption N2 isotherms for uniform flat slit pores (kernel)

Kernels by GCMC and NLDFT

Are qualitatively similar.

4 Å

7 Å

10 Å

15 Å

30 Å

Source of

Numerical

Problem


Hrtem images of activated carbons
HRTEM Images of Activated Carbons using Tarazona approach [1, 2].

Skeletonized

images ->

Atul Sharma, Takashi Kyotani, Akira Tomita, Carbon 38 (2000) 1977–1984


Bright field stem image of umc westvaco carbon
Bright Field STEM using Tarazona approach [1, 2].Image of UMC (Westvaco) Carbon

(Oak Ridge National Lab)

Jagiello, J., Kenvin J., Olivier J.P., Lupini A.R., Contescu C.I., Ads. Sci & Tech. 29,2011, 769-780.


Stem image atomic resolution
STEM using Tarazona approach [1, 2].Image - Atomic Resolution

Annular dark-fi eld (ADF) STEM images of UMC (a,b) and PFAC (c,d) processed to remove high-frequency noise and probe tail effects. The in-plane carbon atoms are clearly resolved, and large areas of hexagonal lattice (marked in blue) with a few five- and seven-atom ring defects (marked in red) can be seen.

(Oak Ridge National Lab)

Guo J, Morris JR, Ihm Y, Contescu CI, Gallego NC, Duscher G, Pennycook SJ, Chisholm MF.

Small 2012;8:3283-3288.


Finite slit shape pores

Strip pore using Tarazona approach [1, 2].

x L, length

Width, H

y

Partially closed strip pore (channel)

L

H

Finite slit shape pores

Effective pore width, w=H-3.4 Ǻ

-∞

Disc pore

Marini Bettolo Marconi, U.; van Swol, F. Phys. ReV. A 1989, 39, 4109–4116.

Monson, P. A. J. Chem. Phys. 2008, 128, 084701.

Kozak, E., Chmiel, G., Patrykiejew, A., Sokolowski, S. Phys. Lett. A1994, 189, 94-98.

Wongkoblap, A, Do, D.D. J. Phys. Chem. B2007, 111, 13949-13956

Jagiello, J., Olivier, J. P. J. Phys. Chem. C 2009, 113, 19382-19385.

Jagiello, J., Kenvin J., Olivier J.P., Lupini A.R., Contescu C.I., Ads. Sci & Tech. 29,2011, 769-780


Density profiles across the pores h 27 6 w 24 l 30 p p 0 0 001
Density profiles across the pores using Tarazona approach [1, 2].H=27.6 Ǻ (w=24 Ǻ), L=30 Ǻ, p/p0=0.001

Disc pore

Strip pore

Channel


Density profiles across the pores h 27 6 w 24 l 30 p p 0 0 01
Density profiles across the pores using Tarazona approach [1, 2].H=27.6 Ǻ (w=24 Ǻ), L=30 Ǻ, p/p0=0.01

Disc pore

Strip pore

Channel


Density profiles across the pores h 27 6 w 24 l 30 p p 0 0 05
Density profiles across the pores using Tarazona approach [1, 2].H=27.6 Ǻ (w=24 Ǻ), L=30 Ǻ, p/p0=0.05

Disc pore

Strip pore

Channel


Density profiles across the pores h 27 6 w 24 l 30 p p 0 0 1
Density profiles across the pores using Tarazona approach [1, 2].H=27.6 Ǻ (w=24 Ǻ), L=30 Ǻ, p/p0=0.1

Disc pore

Strip pore

Channel


Density profiles across the pores h 27 6 w 24 l 30 p p 0 0 2
Density profiles across the pores using Tarazona approach [1, 2].H=27.6 Ǻ (w=24 Ǻ), L=30 Ǻ, p/p0=0.2

Disc pore

Strip pore

Channel


Density profiles across the pores h 27 6 w 24 l 30 p p 0 0 3
Density profiles across the pores using Tarazona approach [1, 2].H=27.6 Ǻ (w=24 Ǻ), L=30 Ǻ, p/p0=0.3

Disc pore

Strip pore

Channel


Density profiles across the pores h 27 6 w 24 l 30 p p 0 0 5
Density profiles across the pores using Tarazona approach [1, 2].H=27.6 Ǻ (w=24 Ǻ), L=30 Ǻ, p/p0=0.5

Disc pore

Strip pore

Channel


Density profiles across the pores h 27 6 w 24 l 30 p p 0 0 7
Density profiles across the pores using Tarazona approach [1, 2].H=27.6 Ǻ (w=24 Ǻ), L=30 Ǻ, p/p0=0.7

Disc pore

Strip pore

Channel


Nldft adsorption n 2 isotherms for slit pores
NLDFT Adsorption N using Tarazona approach [1, 2].2 Isotherms for Slit Pores

Finite Pores, L=30 Ǻ

Infinite Slit Pores

Strip

Channel


Psd analysis for umc westvaco carbon using infinite and finite pore models mix
PSD Analysis for UMC (Westvaco) Carbon using Infinite and Finite Pore Models (Mix)

Calculated PSDs

Fits of N2 Adsorption Isotherm

Fitting error=16.8

10-5<p/p0<10-2

Fitting error = 4.2

UMC sample kindly provided by Dr. Frederic Baker


Simple energetically and geometrically heterogeneous carbon infinite slit pore model
Simple energetically and geometrically heterogeneous carbon infinite slit pore model

  • The model is derived from the Steele potential where the geometrical

  • heterogeneity is introduced only to the surface layer.

  • Objective:

  • Introduce minimal modifications to Steele potential that are necessary to improve the model.

  • Carbon pore heterogeneity may be considered a combined effect of:

  • Chemical composition (surface chemical groups)

  • Variation of local density

  • Variations of pore wall thickness

  • Geometry (curvature, roughness)


External potential in heterogeneous pore
External potential in heterogeneous pore infinite slit pore model

The solid-fluid interaction potential of a gas molecule interacting with the graphitic surface:

For a uniform infinite graphitic surface:

esf, ssf –solid-fluid interaction parameters

rs –solid surface density

D – distance between graphitic layers

For a pore wall consisting of 3 graphitic surfaces:

The total external interaction potential in the pore Vext:


Surface energy distribution unit cell in periodic boundary conditions
Surface energy distribution infinite slit pore modelUnit cell in periodic boundary conditions

Solid-fluid interaction parameter, esf

External potential at 1st adsorbed layer, Vext


Experimental and calculated adsorption isotherms on nongraphitized carbon black surface cabot bp280
Experimental and calculated adsorption isotherms on nongraphitized carbon black surfaceCabot BP280


N 2 local densities in heterogeneous and uniform slit pores with w 24
N nongraphitized carbon black surface2 local densitiesin heterogeneous and uniform slit pores with w=24 Ǻ

p/p0=0.00001


N 2 local densities in heterogeneous and uniform slit pores with w 241
N nongraphitized carbon black surface2 local densitiesin heterogeneous and uniform slit pores with w=24 Ǻ

p/p0=0.0001


N 2 local densities in heterogeneous and uniform slit pores with w 242
N nongraphitized carbon black surface2 local densitiesin heterogeneous and uniform slit pores with w=24 Ǻ

p/p0=0.0005


N 2 local densities in heterogeneous and uniform slit pores with w 243
N nongraphitized carbon black surface2 local densitiesin heterogeneous and uniform slit pores with w=24 Ǻ

p/p0=0.001


N 2 local densities in heterogeneous and uniform slit pores with w 244
N nongraphitized carbon black surface2 local densitiesin heterogeneous and uniform slit pores with w=24 Ǻ

p/p0=0.01


N 2 local densities in heterogeneous and uniform slit pores with w 245
N nongraphitized carbon black surface2 local densitiesin heterogeneous and uniform slit pores with w=24 Ǻ

p/p0=0.05


N 2 local densities in heterogeneous and uniform slit pores with w 246
N nongraphitized carbon black surface2 local densitiesin heterogeneous and uniform slit pores with w=24 Ǻ

p/p0=0.1


N 2 local densities in heterogeneous and uniform slit pores with w 247
N nongraphitized carbon black surface2 local densitiesin heterogeneous and uniform slit pores with w=24 Ǻ

p/p0=0.2


N 2 local densities in heterogeneous and uniform slit pores with w 248
N nongraphitized carbon black surface2 local densitiesin heterogeneous and uniform slit pores with w=24 Ǻ

p/p0=0.3


N 2 local densities in heterogeneous and uniform slit pores with w 249
N nongraphitized carbon black surface2 local densitiesin heterogeneous and uniform slit pores with w=24 Ǻ

p/p0=0.4


N 2 local densities in heterogeneous and uniform slit pores with w 2410
N nongraphitized carbon black surface2 local densitiesin heterogeneous and uniform slit pores with w=24 Ǻ

p/p0=0.5


Nldft adsorption n 2 isotherms for uniform and heterogeneous slit pores
NLDFT Adsorption N nongraphitized carbon black surface2 Isotherms forUniform and Heterogeneous Slit Pores

Uniform pores

Heterogeneous pores

4 Å

7 Å

4 Å

10 Å

7 Å

10 Å

15 Å

15 Å

30 Å

30 Å


Effect of pore geometry on external wall potential
Effect of pore geometry on external wall potential nongraphitized carbon black surface

Uniform flat wall

Uniform cylindrical wall

Curved (corrugated) wall


Pore geometry roughness unit cell periodic boundary conditions
Pore geometry (roughness) nongraphitized carbon black surfaceUnit cell - periodic boundary conditions

Pore wall: 3 graphene layers

Surface layer: z=0.3*sin(x)

H


External potential in flat slit and curved rough pores
External potential in flat slit and curved (rough) pores nongraphitized carbon black surface

The solid-fluid interaction potential of a gas molecule interacting with a graphene surface:

For a flat infinite graphene:

For a curved surface is obtained by numerical integration.

For a pore wall consisting of 3 graphene surfaces:

The total external interaction potential in the pore Vext:

esf, ssf –solid-fluid interaction parameters

rs –solid surface density

D – distance between graphitic layers


N2 Isotherms measured for standard reference carbon blacks, graphitized carbon black Carbopak F and the standard NLDFT model


Experimental and calculated adsorption isotherms on nongraphitized carbon black surface cabot bp2801
Experimental and calculated adsorption isotherms on nongraphitized carbon black surfaceCabot BP280


N 2 local densities in curved and flat slit pores with w 24
N nongraphitized carbon black surface2 local densitiesin curved and flat slit pores with w=24 Ǻ

p/p0=0.00001


N 2 local densities in curved and flat slit pores with w 241
N nongraphitized carbon black surface2 local densitiesin curved and flat slit pores with w=24 Ǻ

p/p0=0.0001


N 2 local densities in curved and flat slit pores with w 242
N nongraphitized carbon black surface2 local densitiesin curved and flat slit pores with w=24 Ǻ

p/p0=0.0005


N 2 local densities in curved and flat slit pores with w 243
N nongraphitized carbon black surface2 local densitiesin curved and flat slit pores with w=24 Ǻ

p/p0=0.01


N 2 local densities in curved and flat slit pores with w 244
N nongraphitized carbon black surface2 local densitiesin curved and flat slit pores with w=24 Ǻ

p/p0=0.05


N 2 local densities in curved and flat slit pores with w 245
N nongraphitized carbon black surface2 local densitiesin curved and flat slit pores with w=24 Ǻ

p/p0=0.1


N 2 local densities in curved and flat slit pores with w 246
N nongraphitized carbon black surface2 local densitiesin curved and flat slit pores with w=24 Ǻ

p/p0=0.2


N 2 local densities in curved and flat slit pores with w 247
N nongraphitized carbon black surface2 local densitiesin curved and flat slit pores with w=24 Ǻ

p/p0=0.3


N 2 local densities in curved and flat slit pores with w 248
N nongraphitized carbon black surface2 local densitiesin curved and flat slit pores with w=24 Ǻ

p/p0=0.4


N 2 local densities in curved and flat slit pores with w 249
N nongraphitized carbon black surface2 local densitiesin curved and flat slit pores with w=24 Ǻ

p/p0=0.5


Nldft adsorption n 2 isotherms for flat slit and curved pores
NLDFT Adsorption N nongraphitized carbon black surface2 Isotherms forFlat Slit and Curved Pores

Flat slit pores

Curved pores

4 Å

4 Å

7 Å

7 Å

10 Å

10 Å

15 Å

15 Å

30 Å

30 Å

Source of

Numerical

Problem


Psd analysis of pc76 carbon using flat slit and curved pore models
PSD Analysis of PC76 Carbon using Flat Slit and Curved Pore Models

Calculated PSDs

Fits of N2 Adsorption Isotherms

PC76 – PET derived carbon,

J. Jagiello, C.O. Ania, J.B. Parra, J.J. Pis, Carbon 45 (2007) 1066–1071.


New model 2d nldft incorporating energetical heterogeneity and geometrical corrugation
New Model 2D- NLDFT Incorporating Energetical Heterogeneity and Geometrical Corrugation

Variation of the solid-fluid interaction parameter given by trigonometric series.

Vext/kT



Selected 2D-NLDFT isotherms for N2 adsorption calculated for carbon slit pores and open surface compared with BP 280 data


N 2 local densities in curved and energetically heterogeneous pores with w 24
N carbon slit pores and open surface compared with BP 280 data2 local densitiesin curved and energetically heterogeneous pores with w=24 Ǻ



Conclusions
Conclusions for EH-GC Surface

We modify the standard carbon slit pore model by changing surfaces of pore walls from flat and homogeneous to:

Flat energetically heterogeneous

geometrically corrugated (rough)

geometrically corrugated and energetically heterogeneous

These assumptions lead to the heterogeneity of the adsorption potential.

As a result, filling of pores is gradual and the layering transition steps are significantly reduced or eliminated.

The carbon PSD analysis from such models are free of known artifacts:

Fits are improved

Calculated PSDs do not show the typical gap at 10 Å.


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