Surface Area and Porosity Part IV - Centro Federal de ... · (Recommendations 1984) Pure & Appl....

Name of Institute, Faculty, Department1 10/15/17KIT – The Research University in the Helmholtz Association

Dr. Peter G. Weidler Institute for Functional Interfaces IFG KIT

www.kit.edu

Surface Area and PorosityPart IV

IFG, KIT Campus North - 2 -November 2017Dr. Peter G. Weidler Surface Area & Porosity

Overview I

Introduction:

What are surfaces ?

● Importance of surfaces ? Are they ?

● Basic concept of surface area measurement

BET equation

● derivation, concept

● criticism (physical reality)

Basics of gas sorption

● physisorption <--> chemisorption

● specific <--> unspecific


Overview II

Why nitrogen ?

● What if argon, krypton, H2O,.... ?

● --> what is the "real" surface area ?

Other adsorptives

● H2O

● organic gases


Overview III

Self-similarity --> fractal surfaces

● basic concept of fractal surfaces

● How to determine fractal dimensions

● Does it really matter ?

How precise is a specific surface area ?

● linear regressions and the R²....

Talking about errors..... sample preparation

First measurements in lab


Overview IV

Porosity

● What are pores ?

● Definition of pore size

Hysteresis

● IUPAC definitions and pore shape

● Which pore range detectable ?

Determination of porosity

● old method BJH

● advanced method DFT/MC

● some words about Hg-porosimetry

Imaging of porous samples


Overview V

Evaluation of data

● reporting gas sorption data:

● total pore volume, what is it ?

counter-check the SSA-value

● by TEM or REM

● by XRD

● PCS (light scattering)

● ...

Concluding remarks


Porosity I

What is porosity ?

What are pores ?

--> one definition:

anything deeper than wide is a pore.

Why are pores/porosity of interest ?

sorption kinetics (process kinetics)

surface area (inner and outer surface area)

density of material

distribution of surface are in a volume

--> fractality


Porosity II

Definition of pore sizes (IUPAC) :

micro pores : < 2 nm

meso pores : > 2 nm to < 50 nm

macro pores : > 50 nm

Now what about nanopores ?

no definition of "nanopores"

if you depend on nano, then maybe you are

1.78 *109 nm high and 75 *1012 ng heavy....

nano-pores or for the hard-cores femto-, atto- , chico-, harpo-, zeppo-,groucho-, gummo-pores.......


Porosity III

Geo-Water-Soil-Construction-people:

also (macro- und micro-) pores, but on a different scale--> 0.2 µm to cm

Detection of porosity

indication by sorption isotherm

(1) at certain p/po steep rise in adsorption branch

(2) divergence of desorption- and adsorption branch

-> hysteresis


Porosity IV

Classification after IUPAC

I Langmuir

II typical multi-layer

IV hysteresis

III, V, VI rare species


Porosity V

Classification after IUPAC

H1 narrow pore size distribution

H2 broader psd, smallest size

not clear from desorption

H3 aggregates of plate-like

particles

H4 plate-like system with

micro-porosity


Basic concept XIV

--> adsorption at low partial pressure p/po....


Basic concept XVI

... increasing number of molecules, i.e. partial pressure p/po....


Basic concept XVI

... finally reaching the filling of "all" pores...


Porosity VI

Obtaining pores sizes and distributions

Kelvin-equation:

γ surface tension

ρl density of liquid

t: statistical film thickness

de-Boer plot


Porosity VII

Kelvin-equation : instability during desorption

emptying of pores depends on pore width and

corresponding pressure p

p1/po << p2/po


Porosity VIII

Kelvin-equation


Porosity IX

Kelvin-equation -->

for larger pores >> 100 nm

gas sorption --> resolution low

small step in p/po results in high step in pore size !!

--> Mercury Hg-porosimetry

Washburn-equation Dp = 1470 kPa µm/ PHg

smaller pores demand higher pressure

1µm --> 1470 kPa (14.7 bar) 1nm --> 1.47 MPa (14.7 kbar)

(mbar = hPa)


Porosity X

Kelvin-equation -->

... problem with large pores..

... what about the small pores ?


Porosity XI

Comparison of different models and measurements


Porosity XII

Deviation for micro-pores and the smaller meso-pores !!!


Porosity XIII

Solution:

better models -->

DFT / MC calculations

Calculation of the interaction of single gas-molecules with

surfaces (atoms) with different conditions:

oxygen-surfaces

carbon-surfaces

with defined pore geometry (more to that later)


DFT/MC I

Density Functional Theory / Monte Carlo Simulation


DFT/MC II

Density Functional Theory / Monte Carlo Simulation

Calculation ofmodel isothermsfor defined

- pore geometry

- pore surface chemistry

- adsorbate


DFT/MC III

Generalized Adsorption Isotherm (GAI) equation


DFT/MC IV

Generalized Adsorption Isotherm (GAI) equation


DFT/MC V

Criticism :

limited kernels available

N2, Ar, CO2

missing Kr, H2O

pore geometry: cylinder, spheres, slits

and combination with adsorbates

computational effort immense


pore geometry I

✔ pore volume determined

✔ pore size determined

--> pore shape ???

where is the information about pore shape ?


pore geometry II

type of hysteresis

correspondence of isotherm

with DFT/MC kernel

--> fit quality parameter

imaging ! (TEM, REM, ...)


pore geometry III

type of pore geometries:

these plus spheres


pore geometry IV

independent of pore geometry...

... but you still do not know the pore geometry 8o(


pore geometry V


Counter-checking I

SSA obtained by gas sorption

determine particle diameter by TEM

(if particles exhibit regular shape)

--> find specific density

--> find shape model

--> calculate SSA


Counter-checking II

SSA obtained by gas sorption

determine particle diameter by XRD

(if particles are single crystals)

--> find specific density

--> find shape model

--> calculate SSA


Counter-checking III

What if calculated SSA deviates from measured SSA ?

if calculated < measured :

-- porosity

-- smaller particles present

-- TEM particles statistics not complete

if calculated > measured :

-- TEM particles statistics not complete

-- XRD no single crystals


Counter-checking IV

example: magnetite ρ = 5.2 g/cm³ ©by Frederik


Counter-checking V

example: magnetite ρ = 5.2 g/cm³ ©by Frederik


Counter-checking VI

example: magnetite ρ = 5.2 g/cm³

crystallite size determined by XRD: 33 nm

assuming cubes : SSA = 35 m²/g

particle size determined by TEM : 35 nm

assuming cubes : SSA = 33 m²/g

BET: m²/g (practical)


Last word on sizes

simple model: cubes edge a or sphere diameter d

cube split, every step n edge an+1 = an / 2

what is number of particles and SSA ?

cube edge a1 = 10000nm (10µm)

specific density = 2.5 g/cm³


Last word on sizes

after 14 step:

edge = 1.22 nm

one particle split into 5.50 1011 particles

SSA one particle: 0.2 m²/g

after 14 steps : 1200 m²/g


Last word on sizes


Last word on sizes


Last word on sizes

Last remark:

sorption data based on mass, e.g., mg stuff /kg

or

based on surface e.g., mg stuff /m² ???

last can lead to that material, different on mass bases

adsorbed same amount on surface base !!!


Last word on sizes

sample: Mat A Mat B

sorption: 1 mg/kg 10 mg/kg

SSA: 10 m²/g 100 m²/g

--> 1 µg/m² for both

which material is better ??

If interested on surface phenomena: use per m²


Example: MOF


Example: MOF DAY 2 26.6 Å


Example: MOF DAY 2


Example: MOF


Summary

surfaces are tough business

somewhat imprecise

got to know the limitation resp.

parameters applied

same applies to porosity

pore shape limited

... even not possibly for most material

use specific surface area in relation to

surface processes


Thanks to following person for their support:

Prf. Virginia Ciminelli and Angela de Mello Ferreira

Paulo and Frederik

Pof. Wander Vasconcelos and Eduardo

Sebastian

Matthias Thommes (Quantachrome)


muito obrigado !!


Literature

Gregg and Sing, (1982), Adsorption, Surface Area, & Porosity, 2nd ed. Academic Press; pp.303

Thommes, Lowell, Shields, Thomas, Thommes, (2006), Characterization of PorousSolids And Powders: Surface Area, Pore Size and Density, Springer, The Netherlands

Thommes, (2004), Physical adsorption characterization of ordered and amorphousmesoporous materials,in: G.Q. Lu, X.S. Zhao (Eds.), Nanoporous Materials;Science and Engineering, Imperial College Press, London, UK, pp. 317– 364(Chapter 11)

Sing et. al, (1985), REPORTING PHYSISORPTION DATA FOR GAS/SOLID SYSTEMSwith Special Reference to the Determination of Surface Area and Porosity(Recommendations 1984)Pure & Appl. Chem, 57(4) pp 603-619

Rouquerol, Rouquerol, Sing, (1998) , Adsorption by Powders and Porous Solids: Principles, Methodology and Applications Publisher: Academic Press; 1 ed. , pp. 467


Literature

Peitgen, Jürgens, Saupe, (1992), Bausteine des Chaos. Fraktale Klett-Cotta, pp. 514

Benoit B. Mandelbrot, (1990),The Fractal Geometry of Nature Spektrum Akademischer Verlag, pp. 480

Kindle Edition; W. H. Freeman; file size: 10.1MB

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Surface Area and Porosity Part IV - Centro Federal de ... · (Recommendations 1984) Pure & Appl....

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