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L16 CRE II Heterogeneous Catalysis
Prof. K.K.Pant
Department of Chemical EngineeringIIT
[email protected]
mailto:[email protected]:[email protected]
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Pore size distribution
An important property of catalysts is the distribution
of pores across the inner and outer surfaces. The
most widely used method for determining the poredistribution in
solids is mercury porosimetry and
Nitrogen adsorption/desorption method.
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3
Experimental Methods of Estimating
Pore Volume and DiameterTwo methods are used : one is based on
gasadsorption is suitable for the estimation of pore
sizes in the range 15-200A0
. (N2adsorption/desorption method)
Other is based on the volume of mercury which
can be forced under pressure into the pores of asolid and is
suitable in the pore size range 100-105
A0. (Mercury penetration method)
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N2Physisorption versus Hg
Porosimetry Hg cannot penetrate small (micro)pores, N2
can
Uncertainty of contact angle and surfacetension values
Cracking or deforming of samples
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Mercury Porosimetry
Pressure force. (p() r = -surface tension force, (2 r)
Surface tension (Hg)= 450-475 dyne/cmPore Size Distribution r
(nm)= 6300/p( atm abs.)
or r (A0) = 8.75X 105 / P (psia)
Hg does not wet surfaces; pressure is needed to force
intrusion
From a force balance:
(d in nm,pin bar)
Convenient method for determining pore volume versus pore
size
pd
14860p
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Mercury Porosimetry:
The pore size distribution is determined bymeasuring the volume
of mercury thatenters the pores under pressure.
Pressures of 0.1 to 200 MPa allow pore
sizes in the range 207500 nm to bedetermined.
sp rp
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Gas Adsorption Method:
The gas adsorption method of estimating pore
volume and diameter is based upon the fact
that gas condenses to liquid in narrow pores
at pressure less than the saturated vapour
pressure of the adsorbate .
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P 2Vcosln( )= -
P rRT0
By relating the relative pressure and the poreradius the pore
size distribution of the catalystis determined for pore size below
20nm.
The vapor pressure decreases as the capillary size
decreases as the capillary size decreases, such
condensation will occur in smaller pore. At saturation all
pores will get filled with adsorbed nitrogen.
If pressure is reduced by small increment , small amount
ofnitrogen will evaporate from the meniscus of largest pore.
(inwhich V.P of nitrogen is greater than chosen pressure.
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N2Desorption Method (Kelvin equation) :
The BET method can be used to determine the pore size
distribution of
porous materials with diameters less than 200, except that high
relativepressures are used for condensing N2in the catalyst pores.
Capillary
condensation occurs in the pores in accordance with the
Kelvin
equation:( variation of V.P WITH CURVATURE effect)
P= V.P of liquid over a curved surface, P0= V.P of liquid over a
plane
surface, = surface tension of liquid adsorbate ( 8.85 dyne/cm
for
nitrogen), V = molar volume of liquid adsorbate (35 cm3/mol for
N2)
By relating the relative pressure and the pore radius the pore
size
distribution of the catalyst is determined for pore size below
20nm.
0
2 cosln( )P VP rRT
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Pore Size Distribution
Kelvin Equation
Cylindrical pore
Ink-bottle pore
Pore with shape of intersticebetween close-packed particles
Adsorbed layertdpdm
r (pore radius) =t + 2 VCos/(RT (ln p/p0))
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Kelvin Equationt-Method
BET
only valid in small pressure interval
interpretation not very easy
thickness (t) of adsorbed layer can be calculated
plot of tversus pfor non-porous materials is the same (has
been
checked experimentally)
t-plot helps in interpretation
0.354 nm
0
2 cosln( )
P V
P rRT
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Kelvin EquationPore filling Model
Cylindrical Pore Channel
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Pore Size Distribution
Kelvin Equation
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Total pore volume and PSD
k
Po 2 VIn =P r RT
k2 V
r = +r
P PoRTln P
13
5t=4.3
Poln
P
Adsorbed layer thickness
= 8.85 dyne/cm, nitrogen , V=35 cm3/mol, t (A0)= 9.52 (log
p0/p)-1/3
rp-t (A0) = 9.52 (log p
0/p)-1
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Kelvin EquationPore Size Distribution
g-alumina
0.0
0.1
0.2
0.3
0.4
0.5
1 10 100 1000
dp(nm)
dV/dd(ml/g/nm
)
r = t + 2VCos/(RT (ln p/p0))
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N2Adsorption Isotherms & Pore Volume Distributions
0
5
10
15
20
25
0 0.2 0.4 0.6 0.8 1p/p
0
nad(mmol/g)1
wide-pore silica g-alumina
0
5
10
15
20
25
0 0.2 0.4 0.6 0.8 1p/p
0
nad(mmol/g)1
0.00
0.02
0.04
0.06
0.08
0.10
1 10 100 1000dpore(nm)
dV/dd(ml/g
/nm
0.0
0.1
0.2
0.3
0.4
0.5
1 10 100 1000dpore (nm)
dV/dd(ml/g
/nm)
N2Adsorption Isotherms & Pore Volume Distributions
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Pore Size Distributiont PlotMethod (for microporous
materials,)
nm354.0
m
ad
n
nt
nad
t
Slope is Proportional to surfacearea St
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Experiment:
The amount of N2adsorbed at equilibriumat the normal boiling
point temp (-195.80C) is measured over a wide range of N2
partial pressures below 1 atm.
Identify the amount required to cover theentire surface by a
mono-layer
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p/p0< 0.1Mono layer
0.1 < p/p0< 0.4Multi layer0.4 < p/p0< 1.0Capillary
condensation
VSTP
pNitrogen
Linear region
Mono Layer ads
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Total pore volume and PSD
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Hg Intrusion Curves & Pore
Volume Distributions
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0.00
0.02
0.04
0.06
0.08
0.10
1 10 100 1000dpore (nm)
dV/dd
(ml/g/nm
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Thank You
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