CRE L 16

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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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    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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