Project 8
Measuring Zeolitic Diffusion by the
Frequency Response Technique
Andreas Jentys
Johannes A. Lercher
Lehrstuhl II für Technische Chemie
Technische Universität München
Goals
■ Explore the diffusivity in molecular sieves as function of
− Pore size and connectivity
• AFI (uni-dimensional channels)
• Silicalite-1, Ferrierite (two intersecting channels)
• LTA, NaX (three-dimensional network)
− Pressure
− Temperature
■ Explore the diffusivity in the presence of more than one sorbing component
as function of
− Pore size and connectivity
− Pressure
− Temperature
Means
Means
• Frequency Response technique accessed via pressure variations
• Determination of averaged coverages by IR spectroscopy and TGA
Frequency response technique
■ Response of a closed system to a periodic perturbation
Volume modulation
Pressure response
− Empty system: the pressure modulation varies at the same
frequency as the volume perturbation (180° out of phase)
− Porous sample: change in the phase and the amplitude of the
pressure response to volume modulation is observed
■ Measuring the pressure response as function of the frequency of the
pressure perturbation
Æ Determination of diffusion coefficients
Experimental setup
Square-wave volume modulation
TurboPump
P
−
−
−
−
−
−
Sample in powder form (~ 50 mg)
UHV Vacuum system (base pressure < 10-7 mbar)
Thermal activation up to 600 °C
Magnetically driven separator plate, UHV bellows
Frequency range 0.001 – 5 Hz
High precision differential pressure gauge (MKS-Baratron)
Frequency response Method
1.06
5.5
1.05
4.5
1.04
3.5
1.03
2.5
1.02
1.5
1.01
0.5
1
0
50
100
Time (seconds)
150
-0.5
200
Magnet Signal (Volts)
Pressure (mbar)
Square-wave volume modulation
Frequency response method
Experimental data
Theoretical model
pB/pZ = amplitude ratio
δc, δs = f(f,r,D)
φZ - φB = phase lag
K = (RT0/Ve)(dBe/dPe)
(pB/pZ)cos(φZ- φB) – 1 = Kδc
(pB/pZ)sin(φZ- φB) = Kδs
■ Planar sheet model
δ1c = (1/η)(sinh η + sin η)/(cosh η + cos η) η = (ωL2/D)1/2
δ1s = (1/η)(sinh η - sin η)/(cosh η + cos η) ω = 2πf
■ More complex models
−
−
−
−
Spherical particles
Two (or more) independent diffusion processes
Non-isothermal behavior
Diffusion rearrangement
Frequency response method
Function
0,3
0,25
Out of phase function
0,2
(pB/pZ)cos(φZ- φB)–1 =∑Kδc
(p0,15
B/pZ)sin(φZ- φB) = ∑Kδs
0,1
In phase function
Fast diffusion
0,05
0.0
0,001
Slow diffusion
0,01
0,1
Frequency (Hz)
1
10
K = (RT0/Ve)(dBe/dPe)
δ1c = (1/η)(sinh η + sin η)/(cosh η + cos η) η = (ωL2/D)1/2
δ1s = (1/η)(sinh η - sin η)/(cosh η + cos η) ω = 2πf
Relationship between frequency range,
particle size and diffusion coefficient
Diffusion coefficient (m2/s)
10-6
10-8
10 Hz
1 Hz
10-10
0.1 Hz
0.01 Hz
10-12
0.001 Hz
10-14
10-16
10-18
10-8
10-7
10-6
10-5
Particle radius (m)
10-4
10-3
Advantages of the frequency response method
■ Small perturbation to the sorption equilibrium
− Concentration of the sorbed phase remains almost constant
− Determination of diffusion coefficients as function of coverage
■ Compression and expansion cycles
− Adsorption and desorption pressure response
− Differences in the diffusion mechanisms for the two processes
■ Investigation of multiple diffusion processes
− Separation of processes differing by half order of magnitude of D
■ Using higher harmonics to study faster processes
− Larger diffusion coefficients can be measured
Diffusion of toluene in H/ZSM-5
H/ZSM-5 (3 µm) 403 K
0,3
Function
0,25
0,2
0,15
0,1
2.6×10-13 m2/s
2×10-14 m2/s
0,05
0.0
0,001
ZSM-5
0,01
0,1
Frequency (Hz)
1
10
Application of the frequency response method
Diffusion coefficients as function of coverage
1000
m /s)
403 K
Diffusivity (10
-15
2
373 K
100
10
1
0
0.5
1
1.5
Toluene coverage (molecule/u.c)
2
2.5
Work programme
■ Diffusion in non uni-dimensional pore systems
− Study sorption of benzene and alkanes in
• AFI (uni-dimensional channels)
• Silicalite-1, Ferrierite (two intersecting channels)
• LTA, NaX (three-dimensional network)
− effects of pore diameter, channel intersections and transport barriers
− Link with other techniques within the project
■ Multi-component diffusion in zeolites
− Develop multi component detection of two (or more) molecules in the gas phase
using IR spectroscopy
− Study sorption of
• Alkyl substituted aromatic molecules
• n- and iso-alkanes (deuterated molecules)
− Describe multi-component diffusion pathways and molecular passages
− Differentiate between single-file and normal diffusion (passages possible)
Square-wave volume modulation
Multi component detection by IR spectroscopy
TurboPump
P
Analysis of gas composition by IR spectroscopy
− Multiple reflection IR gas cell (1 m path length)
− Rapid scan mode
− Vacuum IR spectrometer (high S/N)
IR Beam
Work programme
■ Diffusion in non uni-dimensional pore systems
− Study sorption of benzene and alkanes in
• AFI (uni-dimensional channels)
• Silicalite-1, Ferrierite (two intersecting channels)
• LTA, NaX (three-dimensional network)
− effects of pore diameter, channel intersections and transport barriers
− Link with other techniques within the project
■ Multi-component diffusion in zeolites
− Develop multi component detection of two (or more) molecules in the gas phase
using IR spectroscopy
− Study sorption of
• Alkyl substituted aromatic molecules
• n- and iso-alkanes (deuterated molecules)
− Describe multi-component diffusion pathways and molecular passages
− Differentiate between single-file and normal diffusion (passages possible)