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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
how the psd is calculated
How the PSD is calculated

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 (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(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

Skeletonized

images ->

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

bright field stem image of umc westvaco carbon
Bright Field STEM 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 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

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 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 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 H=27.6 Ǻ (w=24 Ǻ), L=30 Ǻ, p/p0=0.05

Disc pore

Strip pore

Channel

nldft adsorption n 2 isotherms for slit pores
NLDFT Adsorption N2 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

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 distributionUnit 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
nldft adsorption n 2 isotherms for uniform and heterogeneous slit pores
NLDFT Adsorption N2 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

Uniform flat wall

Uniform cylindrical wall

Curved (corrugated) wall

pore geometry roughness unit cell periodic boundary conditions
Pore geometry (roughness)Unit 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

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

slide41

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
nldft adsorption n 2 isotherms for flat slit and curved pores
NLDFT Adsorption N2 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

slide57
Selected 2D-NLDFT isotherms for N2 adsorption calculated for carbon slit pores and open surface compared with BP 280 data
conclusions
Conclusions

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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