Introduction to Data Analysis
Q-Sense Basic Training, April 4-5, 2006
Outline • Different types of data evaluation • Functions in QTools • Introduction to viscoelastic modeling
Analysis Methods 1) Qualitative analysis (raw data plot, D-f plot) 2) Quantitative analysis (low D=Sauerbrey) 3) Quantitative analysis (high D=viscoelastic modeling) 4) Curve fit functions
Qualitative Analysis 1) Raw data plot, relative comparison of responses Viscous/floppy/elongated
F_1:3
more mass
D_1:3
F_1:3
Less mass
Time (seconds) F_1:3
F_2:3
F_3:3
F_4:3
D_1:3
D_2:3
D_3:3
Time (seconds)
D_4:3
F_1:3
F_2:3
F_3:3
F_4:3
D_1:3
D_2:3
D_3:3
D_4:3
Rigid,/compressed/flat
Qualitative Analysis, cont. 1) D-f plot 0.5 Low affinity
0.3
-6
∆D (10 )
0.4
0.2
High affinity
0.1 0 0
-5
-10 ∆f (Hz)
-15
-20
Reveals reaction ”fingerprints”, multiple phases, time independant
D-f plot - Monoclonal antibodies 0.5 0.4
High affinity
-15
0.3 0.2
High affinity
0.1 0
-20 0
-25
-5
High affinity
Low affinity
Antigen covered sensor
∆D
∆f (Hz)
-10
Low affinity
-6
Low affinity
-5
∆D (10 )
0
0.2x10-6
0
500
1000 1500 2000 2500 Time (s)
Binding of antibodies
-10 ∆f (Hz)
-15
-20
Quantitative analysis the Sauerbrey equation D>>0, Sauerbrey will underestimate the mass
The Sauerbrey relation: m[ng*cm-2]=-17,7[cm2*ng-1*Hz-1]* f [Hz]
Sauerbrey mass
F_1:3
D_1:3
Time (seconds) F_2:3
F_3:3
F_4:3
D_1:3
D_2:3
D_3:3
D_4:3
D~0, Sauerbrey will give a correct mass estimate
Time (seconds) F_1:3
F_2:3
F_3:3
F_4:3
D_1:3
D_2:3
D_3:3
D_4:3
D_1:3
F_1:3
F_1:3
Time (seconds) Sauerbrey mass
The Sauerbrey relation Linear relationship between frequency and mass/surface area:
1 ∆m = −C ∆f n
C = 17,7ngcm −2 s −1 n − overtone
Film thickness
ρ
F3/3 (Hz)
D3 (1E-6)
δ=
∆m
F3/3 (Hz) F5/5 (Hz) D3 (1E-6) D5 (1E-6)
Time (min)
Overtones scaled by overtone number (n) The same constant can be used for all overtones
Qualitative analysis the viscoelastic model D>>0, Sauerbrey will underestimate the mass
F_1:3
D_1:3
Time (seconds) F_1:3
F_2:3
F_3:3
F_4:3
D_1:3
D_2:3
D_3:3
Input:
f1 f3 D1 D3
Viscoelastic voight model
D_4:3
Output: : density, (kg/m3) : viscosity (G’’/ ), (kg/ms) : elasticity (G’), (Pa) : thickness, (m)
Viscosity
Force
Deformation
1. Viscosity is a measure of a fluid's resistance to flow
Newton’s definition
, coefficient of viscosity, viscosity or dynamic viscosity τ = η
Time
∂u ∂y
Unit Pa·s, (which is identical to 1 N·s/m2 or 1 kg/m·s).
Shear modulus (Elasticity) Elasticity (Physics) The ratio of shearing stress proportional limit of a material.
to shearing strain
within the
Force
Deformation
1. 2.
G =
Time
Unit (Pa, or N/m2)
σ γ
Viscoelasticity • A viscoelastic material is, as the name suggests, one which shows a combination of viscous and elastic effects. Voight element Viscous (dashpot)
Elastic (spring)
Viscoelastic model f=f1(n, f, f, f, f) D=f2(n, f, f, f, f)
Fluid
( l, ηl)
: density, (kg/m3) : viscosity (G’’/ ), (kg/ms) : elasticity (G’), (Pa)
n=... n=1 n=3
Adlayer
( f, ηf, µf)
: thickness, (m)
Crystal
G* = G'+ jG' ' = + j2 fη Voinova et al., Physica Scripta 59 (1999) 391
df
Introduction to fitting Initial estimate of parameters
Calculation of Function value
Compare meas. & fun.
Model converged, results given
User input
QTools
Generate new parameters
User output
Fitting routine SIMPLEX Nelder, J. A., & Mead, R. 1965,Comp. J., 7, 308
Operating range Lab viscometers
QCM-D
Hz 100
101 102 103 104 105 106 107
108
Modeled output based on a narrow frequency window Data from lower frequency range cannot necessarily be compared with QCMD modeled data.
A practical modeling example Lipoprime (lipase) Lipase solution
Lipase (E.C. 3.1.1.3) Molecular Weight ~30kDa Concentration 1 g/ml
Lipid film
Triolein (triacylglycerol)
~100 nm
Quartz crystal
Formula: C H O Molecular Weight: 885.43 Da CAS Registry Number: 122-32-7
Snabe and Petersen, Aalborg University Chemistry and Physics of Lipids 125(2003), 69-82
Frequency, (Hz)
Dissipation (1e-6)
Enzymatic degradation of lipid films
Time (min)
Time (min) F1 (Hz) - 5MHz
F3/3 (Hz) -15MHz
F5/5 (Hz) - 25MHz
D1 (1E-6)
D3 (1E-6)
D5 (1E-6)
•Raw data indicates multiphase process •Viscoelastic modeling gives additional information
Snabe and Petersen, Aalborg University Chemistry and Physics of Lipids 125(2003), 69-82
Enzymatic degradation of lipids
5 4
C
D
6
120
5
100
4
80
3
60
2
40
D
1
100 80
20
0
3
120
0 0
Time (min) 1
60
2
2
40
1
20
A) Adsorption of lipase B) Cluster formation 0 C) Mass ejection
0
D) Lipid layer removal
Film Thickness (nm )
Visc (kg m-1 s-1) or Elasticity (105 Pa)
6 Visc (kg m-1 s-1 ) or Elasticity (105 Pa)
A B
Film Thickness (nm)
C B A
0 5
Lipid10 film
A C B D
15
20
Time (min) Quartz crystal Crystal Snabe and Petersen, Aalborg University Chemistry and Physics of Lipids 125(2003), 69-82
Thought process Comments If
∆D > 0
Sauerbrey will under estimate the thickness
Raw data, Qsoft data file
Are there high∆D values in my data?
Evaluation methods No
Sauerbrey D/f plot Raw data plot
No
D/f plot Raw data plot
Yes
Homogenous adlayer Newtonian fluid
Are the results within the model assumptions
Yes
Viscoelastic model D/f plot Raw data plot
Curve fitting functions Fitting of of f and D data to 1) Predefined adsorption models 2) User defined equations
Method: Determination of kinetic constants with QCM-D 1)
2)
Response parameter; - frequency - Dissipation - Modeled thickness
4)
Determine k
from dissociation phase
R(t ) = Req e
− k off t
Perform adsorption at different C F3/3 (Hz) D3 (1E-6)
F3/3 (Hz)
)
Ka =
[BS ] = kon [B][S ] koff
D3 (1E-6)
R (t ) = Req (1 − e
− ( k on C + k off ) t
B+S
R (t ) = Req (1 − e 3)
− ( k1C ) t
)
Time (min) Testdata kinetic2wfit: 2003-09-30 15:33:00
5)
Calculate k from k
6)
Calculate K
Equation system for k with C and R
k
kon koff
BS
Swelling of cellulose Cellulose coated crystal, (100nm) 500 200
•High charge, more swelling
0 -200 -400
F (15) Hz
0
-600
20 ueq/g 409 ueq/g
-800 -1000
•Swelling kinetics
-1200 -1400
-500
-1600
F(15) Hz
0
10
20
30
40
Time (min)
20 ueq/g 409 ueq/g
-1000
-1500
-2000 -5
0
5
10
15
20
25
30
35
40
45
50
Time (hrs)
EtOH
Swelling
H2O
Susanna Fält, Mitthögskolan, Sundsvall, Sweden
Swelling of Cellulose Determination of the decay constant C Fit C
F (t ) = A(1 − e −t*k ) ) + Offset F(t)= frequency
F2 (Hz) [3 * Hz]
F (t ) = y0 + Ae − t / b
t= time Y0=A+Offset= F at t=very large Offset= F at t=0 b=1/k, decay constant (swelling parameter)
Time (s)
b ~2000
Summary D3 (1E-6)
F3/3 (Hz)
D3 (1E-6)
1) Qualitative, Raw data, D-f
D3 (1E-6)
F3/3 (Hz) D3 (1E-6)
F3/3 (Hz)
2) Quantitative Sauerbrey
Sauerbrey mass
Time (min)
Time (seconds) Sauerbrey mas s
F3/3 (Hz)
D3 (1E-6)
3) Quantitative Viscoelastic
F3/3 (Hz) F5/5 (Hz) fir f3 fit f5 D3 (1E-6) D5 (1E-6) fit d3 fit d5
Time (min)
4) Curve fit
F2 (Hz) [3 * Hz]
C Fit C
Time (s)
Thank you for your attention!
