Characterization of porous solids and powders: Density ... · Characterization of porous solids and...
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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.
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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.
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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
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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
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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
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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.
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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
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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
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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.
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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
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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
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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
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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)
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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.
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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)
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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 −−
+=
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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.
![Page 18: Characterization of porous solids and powders: Density ... · Characterization of porous solids and powders: Density, surface area and pore size ... Characterization of porous solids](https://reader031.fdocuments.us/reader031/viewer/2022022512/5ae60c727f8b9aee078c68f0/html5/thumbnails/18.jpg)
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
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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
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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.
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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:
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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
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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−
=−
→
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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
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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
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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
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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)
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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.
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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
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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
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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
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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
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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!
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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.