Structural and Surface Studies of Heterogeneous Catalysts using Small-Angle X-ray Scattering

(1)

Structural and Surface Studies of Heterogeneous Catalysts using Small-Angle X-ray Scattering

Greg Beaucage

Prof. Chemical/Materials Engineering University of Cincinnati

beaucag @uc.edu Outline:

-SAXS Instrument -SAXS Analysis

Construction of Scattering for Disordered Materials Particle Scattering

Aggregate Scattering -Supported Catalysts

Lab Source SAXS ASAXS/in situ SAXS -Particle Size Distributions -CODE (Ilavsky)

-Zeolites

-Summary/Advice

(2)

Small-Angle X-ray Scattering, (SAXS)

-Collimated Beam

-Monochromatic Beam -Coherent Beam

(-Focusing Optics Perhaps)

-Longer Distance for Lower Angle -Large Dynamic Range Detector -Evacuated Flight Path

-Extend Angle Range with Multiple SDD’s

Crystalline Reflections Can Also Be Used

We Get Intensity as A Function of Angle

(or radial position)

(3)

Small-Angle X-ray Scattering at the APS

We Get Intensity as A Function of Angle

(or radial position)

Pinhole Cameras at: 12 ID BESSRC 5 ID DND

18 ID BIOCAT 15 ID CARS 8 ID XOR

9 ID CMC-CAT

33 ID UNICAT

}

Variants on Build/Tear Down Motif

(Inside Traders)

Semi-Permanent (Easily Used)

(4)

The Scattering Event

I() is related to amount Nn²

 is related to size/distances

 

q d 2

sin 2 4



 





 q

We can “Build” a Scattering Pattern from Structural

Components using Some Simple Scattering Laws

(5)

Construction of A Scattering Curve

(6)

q  2d ^I⁽^q⁾ ^ ^N⁽^d⁾ⁿ_e²

 

^d N = Number Density at Size “d”

n_e = Number of Electrons in “d” Particles Complex Scattering Pattern (Unified Calculation)

(7)

Particle with No Interface

 

^d

n d N q

I( )  ( ) _e²











  

exp 3 )

(

2 1 , 2

1

Rg

G q q

I

6 2

2 V ~ R

N G  _e

6 8 2

R

~ R Rg

Guinier’s Law

(8)

Spherical Particle With Interface (Porod)

Guinier and Porod Scattering

) 4

(q  B q^

I _P

S N

B_P  2 _e²

~ R2

S

3 2

2I(q)dq N R

q

Q 



 _e

2 3

2 R

R B

d Q

P

p  



Structure of Flame Made Silica Nanoparticles By Ultra-Small-Angle X-ray Scattering

Kammler/Beaucage Langmuir 2004 20 1915-1921

(9)

Polydisperse Particles

Polydispersity Index, PDI

G R PDI B^P ^g

62 . 1

4



 

^ ^ ¹²

12 ln ln







 PDI

g



2 1 14

2

3

2

5  





 



 

_

e m R

^g

Particle size distributions from small-angle scattering using global scattering functions, Beaucage, Kammler, Pratsinis J. Appl. Cryst. 37 523-535 (2004).

(10)

Linear Aggregates

Beaucage G, Small-angle Scattering from Polymeric Mass Fractals of Arbitrary Mass-Fractal Dimension, J. Appl. Cryst. 29 134-146 (1996).











  

exp 3 )

(

2 2 , 2

2

Rg

G q q

I

df

R R G

z G 



 



 



1 2 1

2

df

f q B q

I( )  ^



²



2 , 2

d f g

f

f d

R d B G

f 



(11)



²



2 ,

min 2

d f g

f d

R d B G

f 

 Branched Aggregates

Beaucage G, Determination of branch fraction and minimum dimension of fractal aggregates Phys. Rev.

E 70 031401 (2004).

c d

R z

p R ¹

1 2

min

 



 



 

df

d

Br R

R ^



 







min

1

1 2



d

min

c  d

^f

(12)

Large Scale (low-q) Agglomerates

) 4

(q  B q^

I _P

(13)

Small-scale Crystallographic Structure

(14)

5mm LAT 16mm HAB Typical Branched Aggregate

d_p = 5.7 nm z = 350

c = 1.5, d_min = 1.4, d_f = 2.1

_br = 0.8

Branched Aggregates

Beaucage G, Determination of branch fraction and minimum dimension of fractal aggregates Phys. Rev. E 70 031401 (2004).

APS UNICAT

Silica Premixed Flames J. Appl. Phys 97 054309 Feb 2005

(15)

5 mm LAT

-Behavior is Similar to Simulation d_f drops due to branching

-Aggregate Collapse

-Entrainment High in the Flame

(16)

Structure of flame made silica nanoparticles by ultra-snall- angle x-ray scattering. Kammmler HK, Beaucage G,

Mueller R, Pratsinis SE Langmuir 20 1915-1921 (2004).

Particle Size, d_p

(17)

Supported Catalysts

(18)

Nobel Metals (Gold) Become

Reactive Catalysts When of 1-6 nm Size

Onset of catalytic activity of gold

clusters on titania with the appearance of non-metallic properties.

Valden M, Lai X, Goodman DW Science 281, 1647-1650 (1998).

(19)

Solution Method For Au/Support Oxide

(Using HAuCl₄)

Gold Catalysts Prepared by coprecipitation for low-temperature oxidation of hydrogen and of Carbon Monoxide.

Haruta M, Yamada N, Kobayashi T, Iijima S, J. Of Catalysis 115, 301-309 (1989).

20 nm

Size- and support-dependency in the catalysis of gold. Haruta M, Catalysis Today 36, 153-166 (1997).

592 Citations

480 Citations

(20)

Consider Support Particle with Deposited Domains

We can obtain: Mean Size, Polydispersity,

State of Aggregation

For Both Particle Types.

This can be done in situ in almost

any environment that can be brought to the synchrotron.

Option 1: Brute Force/Lab Source

d_p, nm _g

3.97 1.35

14.9 1.08

Measurements with ETHZ (Eveline Bus, Jereon Van Bokhoven) ESRF (T. Narayanan)

(21)

How do the particles vary with concentration gold?

Option 1: Brute Force

Measurements with ETHZ (Eveline Bus, Jereon Van Bokhoven) ESRF (T. Narayanan)

(22)

In situ versus ex situ measurements.

Option 1: Brute Force

Measurements with ETHZ (Eveline Bus, Jereon Van Bokhoven) ESRF (T. Narayanan)

Desirable: In Situ Study/Contrast variation for Gold

(23)

Option 2: Anomalous Scattering/Synchrotron

In situ anomalous small-angle x-ray scattering from metal particles in supported- metal catalysts. I Theory and II Results. Brumberger H, Hagrman D, Goodisman J, Finkelstein KD, J. Appl. Cryst. 38 147-151 and 324-332 (2005).

G.Goerigk and D.L.Williamson

http://www.desy.de/~jusifa/solarzellentechnik.htm

Haubold et al. 1999

Goerigk et al. 2003 (Ge)

(24)

Scattered Intensity Depends on Contrast, G (For Each Phase)











   exp 3 )

(

2 1 , 2

Rg

G q q I

2

2 V

N G  _e

) 4

(q  B q^

I _P











 1.62 ₄

g

P R

G PDI B

 

   



₁ ₁ ₂ ₂



²

2

n f E n f E

e E







=

+

{ }

+

(25)

“f” Depends on Wavelength

Sintering of Ni/Al₂O₃ catalysts studied by anomalous small angle x-ray scattering.

Rasmussen RB, Sehested J, Teunissen HT, Molenbroek AM, Clausen BS

Applied Catalysis A. 267, 165-173 (2004). - =

(26)

Particle Size Distributions From SAXS

(27)

Particle Size Distribution Curves From SAXS

Assumption Method

i) Assume a distribution function.

ii) Assume a scattering function (sphere) iii) Minimize calculation

(28)

Assumption Method.

i) Assume a distribution function.

ii) Assume a scattering function (sphere) iii) Minimize calculation

Not unique &

Based on assumptions

But widely used & easy to understand

Sintering of Ni/Al₂O₃ catalysts studied by anomalous small angle x-ray scattering.

Rasmussen RB, Sehested J, Teunissen HT, Molenbroek AM, Clausen BS

Applied Catalysis A. 267, 165-173 (2004).

(29)

Particle Size Distribution Curves From SAXS Unified Method

i) Global fit for B_P and G.

ii) Calculate PDI (no assumptions &

unique “solution”)

iii) Assume log-normal distribution for _g and distribution curve (or other models)

iv) Data to unique solution Solution to distribution

Advantages

Generic PDI (asymmetry also) Global fit (mass fractal etc.) Direct link (data => dispersion) Use only available terms

Simple to implement

G R PDI B^P ^g

62 . 1

4



 

^ ^ ¹²

12

ln ln 





 PDI

g



2 1 14

2

3 2

5











  _ e m R^g

(30)

Particle size distributions from small-angle scattering using global scattering functions, Beaucage, Kammler, Pratsinis J. Appl. Cryst.

37 523-535 (2004).

Particle Size Distribution Curves from SAXS

PDI/Maximum Entropy/TEM Counting

(31)

Maximum Entropy Method

i) Assume sphere or other scattering function

ii) Assume most random solution iii) Use algorithm to

guess/compare/calculate

iv) Iterate till maximum “entropy”

Advantages

No assumption concerning distribution function

No assumption for number of modes Matches detail PSD’s well

Related Alternatives Regularization

(32)

Software for My Collaborators/Students (And Me)

(33)

All Methods are available in Jan Ilavsky’s Igor Code http://www.uni.aps.anl.gov/usaxs/

Anomalous Scattering

(34)

Unified Fit (Not all implemented)

(35)

Sphere (or any thing you could imagine) Distributions

(36)

Maximum Entropy/Regularization Code (Jemian)

(37)

Zeolites/Spherical Colloids

Many Other Parts to Scattering Are Not Covered

For Instance:

(38)

Zeolites:

Ethyl acrylate Benzyl Peroxide Zeolite 13X

Polyethylacrylate in

Zeolite Pores

Pu Z, Mark JE, Beaucage G, Maaref S, Frisch HL, SAXS Investigation of PEA Composites J. Polym. Sci., Polym. Phys. 34 2657 (1996).

1 nm

2 nm

-4 -4

-Pore Structure -Nano-Structure -Micron Structure

(39)

Keep in Mind:

-SAXS Measurement is Generally Easy -SAXS Analysis is Generally Difficult -A Reasonable Model is Mostly Needed -You will Generally Have to Understand

What is going on.

(-This is not a good Technique for Those Interested only in Verifying)

(40)

Small-Angle X-ray Scattering at the APS Realistic Advice for Beam Time Application from a User

Pinhole Cameras at: 12 ID BESSRC 5 ID DND

18 ID BIOCAT 15 ID CARS 8 ID XOR

9 ID CMC-CAT

33 ID UNICAT

}

Variants on Build/Tear Down Motif

(Inside Traders)

Semi-Permanent (Easily Used)

Put

in situ/anomalous in proposal

(41)

(42)

Option 2: Anomalous Scattering

Following the formation of nanometer-sized clusters by time-resolved SAXS and EXAFS techniques. Meneau F, sankar G, Morgante N, Winter R, Richard C, Catlow A, Greaves CN,

Thomas JM, Faraday Discuss. 122, 203-210 (2002).

(43)

In situ anomalous small-angle x-ray scattering from metal particles in supported-metal catalysts. I Theory and II Results. Brumberger H, Hagrman D,

Goodisman J, Finkelstein KD, J. Appl. Cryst. 38 147-151 and 324-332 (2005).

(44)

Following the formation of nanometer-sized clusters by time-resolved SAXS and EXAFS techniques. Meneau F, sankar G, Morgante N, Winter R, Richard C, Catlow A, Greaves CN,

Thomas JM, Faraday Discuss. 122, 203-210 (2002).