Characterization of porous solids and powders: Density ... · Characterization of porous solids and...

Dept. Inorganic Chemistry, Fritz Haber Institute

Characterization of porous solids and powders:Density, surface area and pore size

Christian Hess

0. Motivation

1. Introduction

2. Gas adsorption

3. Density measurements

4. Adsorption isotherms

5. Surface area determination

6. Mesopore analysis

Literature: Characterization of porous solids and powders, Lowell, Shields, Thomas, Thommes, Kluwer, Dordrecht, 2004.

0. Motivation

1. Introduction

2. Gas adsorption






Catalysis: Nanostructured materials as support

• High(er) specific surface area of nanostructured materials � increased activity� formation of isolated, catalytic sites

…an estimate based on a material with spherical particles

using (1) S = 4 Π r2 / m

(2) m = 4/3 ρ Π r3

with ρ ~ 3 g/cm3 (typ. oxide value)

shows that for r = 1 cm _ S = 10-2 m2/gr = 1 µm _ S = 1 m2/gr = 1 nm _ S = 1000 m2/g

_ S = 3/ρr

_ Creation of high surface requires nanoscale structuring

Novel mesoporous silica molecular sieve: SBA-15

TEM characterization

100 nm

in a section of hexagonal poresalong a longitudinal section

_ Silica SBA-15 is a very ordered large-pore (7 nm) material

Model catalysts based on mesoporous SBA-15

• Support properties are well defined (structural homogeneity)and tunable (pore diameter)

� control over support properties� well-structured silica platform for vanadia catalysts

_ 3-D model catalyst for partial oxidation reactions

50 nm

20 nm VO x/SBA-15

silica

OH OH

OO

VOO

OH2O

silica

O

OV

OO

0. Motivation

1. Introduction

2. Gas adsorption






Real surfaces - Factors affecting surface area

• Idealization: cube → S = 6 l2

sphere → S = 4 π r2

Reality: Surface roughness due to voids, pores, steps, other imperfectionsand surface atomic and molecular orbitals

� real surface area > corresponding theoretical area

• Particle size: e.g. cube l = 1 m → S = 6 m2

l = 1 μm → S = 6 10-12 m2

N = 1018 → S = 6 106 m2

• Particle shape: e.g. two particles with same composition and mass Mcube = Msphere

(Vδ)cube = (Vδ)sphere

l3cube = 4/3 π r3

sphere

(Scube lcube)/6 = Ssphere rsphere/3

Scube/Ssphere = 2 rsphere / lcube

Factors affecting surface area

• Porosity: can overwhelm size and shape factors e.g. powder consisting of spherical particles

St = 4 π (r12 N1 + r2

2 N2 + … + ri2 Ni) = 4 π Σ ri

2 Ni

V = 4/3 π (r13 N1 + r2

3 N2 + … + ri3 Ni) = 4/3 π Σ ri

3 Ni

S = St/M = 3 Σ ri2 Ni/δ Σ ri

3 Ni

S = 3/δ rfor spheres of uniform radius:

with r ~ 3 g/cm3 (typ. oxide value):r = 1 cm → S = 10-2 m2/gr = 1 mm → S = 1 m2/gr = 1 nm → S = 1000 m2/g

0. Motivation

1. Introduction

2. Gas adsorption






Introduction

• most popular method for surface and pore size characterization (0.35-100nm)

other methods include: - small angle X-ray scattering (SAXS) - neutron scattering (SANS) - electron microscopy (scanning and transmission) - NMR methods- mercury porosimetry

• adsorption: enrichment of components in interfacial layergas adsorption → gas/solid interface

W = f (P,T,E)W: weight of gas adsorbed (per unit weigth adsorbent)E: interaction potential between adsorbate and adsorbent

T = const. → W = f (P,E)plot of W vs. P referred to as sorption isotherm

Physical adsorption forces

• Physical adsorption forces

van der Waals’ forces: dispersion forces, ion-dipole, ion-induced dipole dipole-dipole, quadrupole

• physisorption on a planar surface:London-van der Waals’ interaction energy:

C1, C2: constantsUs(z) = C1z-9 – C2z-3

Thermodynamics: ΔG = ΔH - TΔS→ ΔH always negative for adsorption

→ at low T: δg << δads � nσ ~ nads

(e.g. N2 adsorption at 77K)

→ surface excess: nσ = ng - δgVg

ng = nads + nbulk

Vg = Vads + Vbulk

nσ = nads - δgVads = (δads- δg)Vads

Experimental

• Experimentalmeasure nads vs P under static or quasi-equilibrium conditions using- volumetric (manometric) methods - gravimetric methods

Gravimetric method: based on sensitive microbalance and pressure gauge→ adsorbed amount measured directly (sensitivity ~ 10-8 g)→ adsorbent not in direct contact with thermostat (→ T control difficult!)

Volumetric method: based on calibrated volumes and pressure measurements → known amounts of gas are

admitted stepwise into cell→ Vads difference between gas

admitted and gas filling void volume→ requires manifold (Vm) and void

volume (Vv) to be accurately known

Experimental

→ Vm determination via expansion of He intocalibrated reference volume VR

→ Vv determination via expansion of He intosample cell volume occupied by adsorbent

m

Rm2

m

m1 )(T

VVPTVP +

=

m

vm4

m

m3 )(T

VVPTVP +

=

→ total volume of adsorptive dosed:PT

TPV

TVPV ×

−=

me

m

m

mmd

vdS VVV −=→ adsorbed volume:

)( vvdS αpVVVV +−=→ correction for non-ideality of real gases:α: non-ideality factore.g. N2: α = 6.6×10-5 torr-1(77K)

0. Motivation

1. Introduction

2. Gas adsorption






Introduction

→ contribution by pores/internal voids must be subtracted

• Density measurementse.g. for permeametry

volume specific surface area

true density =mass

volume occupied by mass

No porosity: true density measured by displacement of fluid→ accuracy: fluid volume determination

Porosity: fluid displaced by powder does not penetrate (all) pores→ apparent density < true density → true density via gas displacement (pycnometer)

using e.g. He (inert, small size)

Experimental

• sample cell:

aapca RTnVVP =− )(

apc RTnVVP 11 )( =−

• open valve 2:

aRaRpc RTnRTnVVVP +=+− 12 )(

RaVP

(2) in (3): RapcRpc VPVVPVVVP +−=+− )()( 12 (4)

(1)

(2)

(3)

)/(1)/(1

21

2

PPPPVVV a

Rcp −−

+=

0. Motivation

1. Introduction

2. Gas adsorption






Pore size and adsorption potential

nearly flat surface

• classification: macropore mesopore micropored > 50nm 2nm < d < 50nm d < 2nm

fluid-wall andfluid-fluid i.a.(→ capillary condensation)

fluid-wall i.a.,overlapping ads. potential

internal pore width

Classification of adsorption isotherms

• classification → IUPAC 1985

• type I: ads. limited to a few layers (chemisorption, micropores)

• type II: unrestricted mono/multilayer ads. → at point B monolayer (non-porous, macropores)

• type III: unrestricted multilayer ads.• type IV: monolayer/multilayer ads.,

limited uptake, hysterisis due to pore condens. (mesopores)

• type V: multilayer ads. (→ type III),pore condensation (hysterisis)

• type VI: stepwise multilayer ads. on auniform, non-porous surface

0. Motivation

1. Introduction

2. Gas adsorption






Langmuir isotherm

• Langmuir isotherm: → applicable to chemisorption and type I physisorption- identical adsorption sites- no interactions between adsorbed molecules

ΔHads ≠ f (θ)

)1(aa θ−= Pkvθaa −− = kv

adsorption of A:

desorption of A:

equilibrium: θθ aa )1( −=− kPk

KPKP+

=1

θa

a

−=

kkK

mVV

=θ

substitute/rearrange:KPVVV mm

111+= plot 1/V vs 1/P → straight line:

intercept 1/Vm → nads

xA adst ANnS = Ax: cross-sectional areasurface area:

Brunauer, Emmett and Teller (BET) theory

• BET isotherm: - first layer serves as substrate for further adsorption (physisorption)- almost universally used → accommodates isotherm types I-V

)/(11]1)/[(

10

mm0PP

CVC

CVPPV−

+=−

→ derivation BET

→

Vm → nads

xA adst ANnS =surface area:

BET isotherm:

WMn = ads

C: BET constant

Single point BET method

plot 1/W[(P0/P)-1] vs P/P0

→ usually straight line within 0.05 < P/P0 < 0.35

)/(11]1)/[(

10

mm0PP

CWC

CWPPW−

+=−

intercept:

slope:

CWb

m

1=

CWCm

m

1−=

,1m

mbW

+= 1+=

bmC

• Single point BET method: → simplicity and speed with little loss of accuracy

1−= Cbm for large values of C → m >> b

→ b ≈ 0

)/(1]1)/[(

10

m0PP

CWC

PPW−

=−

→

Comparison of single point and multipoint methods

0

0

mpm

spmmpm

/)1(1/1

)()()(

PPCPP

WWW

−+−

=− mp: multipoint

sp: single point

→

BET isotherm: W = Wm

11

m0 −−

=

CC

PP

→m0mpm

spmmpm

11

)()()(

=

−−

=−

PP

CC

WWW

Applicabilitiy of the BET theory

- accommodates isotherm types I-V- good agreement between theory and exp.

within 0.05 < P/P0 < 0.30

why?

- porosity: micropores/mesopores ~2-4nm pore filling ↔ mono/multilayer

- variation from linearity at P/P0 > 0.30→ ΔHads varies throughout the layers

Cross-sectional area

xaadst ANnS =surface area: Ax: cross-sectional area (temperature, ads.-ads. i.a.,ads.-surface i.a., texture)

• approximation of Ax of adsorbate molecules→ spherical, exhibiting bulk liquid properties

3/2

Ax 091.1

×=

NVA

• surfaces of high polarity (such as silica) may show significant deviation…

→ N2 is standard BET adsorptive

e.g. N2 (77.35 K): Ax = 13.5 Å2

Permeametryknown amount of air is drawn through compacted bed of powder→ resistance to air flow is a function of the surface area

• ambient p and T (λ < d): gas collisions → viscous flow→ ignores blind pores→ `envelope` area of particle

• reduced p (λ ≈ d): → no flow retardation near wall

• small p (λ > d): gas-wall collisions (→ diffusion)→ senses blind pores and gives

good agreement with BET

−

∆

=vfp

plPS

ηδ 22

32 1

)1(

viscous flow through cylindrical pores → Poiseuille

p: porosity, v: velocityf = 2(l/lp)2

aspect ratio

→ aspect ratio highly dependent upon particle size and shape (typically f = 3-6)

0. Motivation

1. Introduction

2. Gas adsorption






Adsorption in mesopores - multilayer adsorption

depends on fluid-wall and attractive fluid-fluid interactions → multilayer adsorption and pore condensation

)/ln( 00 PPRTaa −=−=∆ µµµ

• Adsorption in mesopores:

• Multilayer adsorption:

- novel ordered mesoporous materials (e.g. MCM, SBA)- Microscopic methods (e.g. NLDFT)

Fluid in contact with planar surface → thickness l: l → ∞ for P/P0 → 1

m−×−= lα(m typ. 2.5-2.7)

α: fluid-wall interaction parameterμa: chem. potential of adsorbed liquid-like filmμ0: chem. potential of bulk fluid at gas-liquid coexistence

Pore condensation – modified Kelvin equation

• in pore l can not grow unlimitedca µµµ ∆+∆=∆

for small l: m−×−=∆≈∆ la αµµfor large l: ρθγµµ ∆−=∆≈∆ ac /cos2

a: core radius(a = rp – l; rp: pore radius) γ: surface tensionΔρ = ρl - ρg

• at critical thickness lc:pore condensation (i.e. gas-like state → liquid-like state at μ < μ0)

Kelvin equation:aRT

VPP γ2)/ln( 0−

=

for complete wetting, i.e. θ = 0

Methodes based on modified Kelvin equation

→

- from isotherm: Vads/g catalyst as function of P/P0

τ)/( ma WWl =

• Calculation of the pore size distribution:

- Kelvin equ.: calulate a for θ=0 as function of P/P0

- calculate statistical film thickness l: lar −=p

- calculate a and rp in each decrement from successive entries- calculate Δl, the change in film thickness in successive steps - calculate ΔVads, the change ads. volume in successive steps - calculate ΔVliq, corresponding to ΔVads

- calculate ΔlΣS, the volume change of film remaining adsorbed - calculate the pore volume Vp:

- calculate the surface area S:p

p2rVS =

p2

pp lrV ⋅⋅= π[ ])(liq

2p

p SlVar

V Σ∆−∆

=

SllaV Σ∆+⋅⋅=∆ pliq π

Testing the modified Kelvin equation

• direct exp. test of Kelvin eq. (MCM, SBA) and comparison with XRD, TEM results→ Kelvin eq. underestimates pore size

• accurate pore size analysis by applyingmicroscopic models based on stat. mech.→ local fluid structure near curved wall→ capture properties of confined fluid

Adsorption vs desorption branch of hysteretic isotherm

• ordered mesoporous materials → desorption branch of hysterisis loop reflects equilibrium phase transition

• disporered mesoporous materials→ desorption branch not necessarily correlated with the pore size

e.g. tensile strength effect → artifact!

0. Motivation

1. Introduction

2. Gas adsorption






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