Introduction to Data Analysis. Q-Sense Basic Training, April 4-5, 2006

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Q-Sense Basic Training, April 4-5, 2006

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Outline

• Different types of data evaluation

• Functions in QTools

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Analysis Methods

1) Qualitative analysis (raw data plot, D-f plot)

2) Quantitative analysis (low D=Sauerbrey)

3) Quantitative analysis (high D=viscoelastic

modeling)

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Qualitative Analysis

1) Raw data plot, relative comparison of responses

F_1:3 F_2:3 F_3:3 F_4:3 D_1:3 D_2:3 D_3:3 D_4:3 Time (seconds) F_ 1: 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 Time (seconds) F _1 :3 D_{_1} :3 Less mass more mass Viscous/floppy/elongated Rigid,/compressed/flat

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Qualitative Analysis, cont.

0 0.1 0.2 0.3 0.4 0.5 -20 -15 -10 -5 0 ∆D (1 0 -6 ) ∆f (Hz) Low affinity High affinity

1) D-f plot

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Antigen covered sensor Binding of antibodies -25 -20 -15 -10 -5 0 ∆f (H z) Low affinity High affinity 0 500 1000 1500 2000 2500 ∆D Time (s) 0.2x10-6 Low affinity High affinity 0 0.1 0.2 0.3 0.4 0.5 -20 -15 -10 -5 0 ∆D (1 0 -6 ) ∆f (Hz) Low affinity High affinity

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Quantitative analysis the

Sauerbrey equation

F_1:3 F_2:3 F_3:3 F_4:3 D_1:3 D_2:3 D_3:3 D_4:3 Time (seconds) F _1 :3 D_{_1} :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 Time (seconds) F_ 1: 3 D_{_1} :3

D>>0, Sauerbrey will underestimate the mass

D~0, Sauerbrey will give a correct mass estimate

The Sauerbrey relation:

m

[ng*cm-2_]

=-17,7

_[cm2_*ng-1_*Hz-1_]

* f

_[Hz] Sauerbrey mass Time (seconds) S au er br ey m as s

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The Sauerbrey relation

Overtones scaled by overtone number (n)

The same constant can be used for all overtones

f

n

C

m

=

−

∆

1

n overtone s ngcm C − =₁₇_,₇ −2 −1

Linear relationship between frequency and mass/surface area:

ρ

δ

=

∆

m

F3/3 (Hz) F5/5 (Hz) D3 (1E-6) D5 (1E-6) Time (min) F 3/ 3 (H z) D_{3 (} 1E -6 )

Film thickness

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Qualitative analysis the

viscoelastic model

F_1:3 F_2:3 F_3:3 F_4:3 D_1:3 D_2:3 D_3:3 D_4:3 Time (seconds) F _1 :3 D_{_1} :3

D>>0, Sauerbrey will underestimate the mass

Viscoelastic voight model

Output:

: density, (kg/m3)

: viscosity (G’’/ ), (kg/ms)

: elasticity (G’), (Pa)

: thickness, (m)

Input:

f1

f3

D1

D3

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Viscosity

1. Viscosity is a measure of a fluid's

resistance to flow

Newton’s definition , coefficient of viscosity, viscosity

or dynamic viscosity

Unit

Pa·s, (which is identical

to 1 N·s/m2_{or 1 kg/m·s).} y u ∂ ∂ = η τ Time D ef or m at io n Fo rc e

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Shear modulus (Elasticity)

1. Elasticity

2. (Physics) The ratio of shearing stress to shearing strain within the

proportional limit of a material.

Unit (Pa, or N/m

2

₎

γ σ = G Time D ef or m at io n Fo rc e

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Viscoelasticity

• A viscoelastic material is, as the name

suggests, one which shows a

combination of viscous and elastic

effects.

Elastic (spring)

Viscous (dashpot)

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Viscoelastic model

f=f

₁

(n,

_f

,

_f

,

_f

,

_f

)

D=f

₂

(n,

_f

,

_f

,

_f

,

_f

)

Crystal

Adlayer

(

_f

, η

_f

, µ

_f

)

d

f

Fluid

(

_l

, η

_l

)

n=1 n=3 n=...

Voinova et al., Physica Scripta 59 (1999) 391

G* = G' + jG''

= + j2

f

η

: density, (kg/m3)

: viscosity (G’’/ ), (kg/ms)

: elasticity (G’), (Pa)

: thickness, (m)

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Introduction to fitting

Model

converged,

results given

User output

QTools

Fitting routine SIMPLEX

Nelder, J. A., & Mead, R. 1965,Comp. J., 7, 308

Compare meas. & fun.

Calculation of

Function value

Generate new

parameters

Initial estimate of

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Operating range

10

0

₁₀

1

₁₀

2

₁₀

3

₁₀

4

₁₀

5

₁₀

6

₁₀

7

₁₀

8

Lab viscometers

QCM-D

Modeled output based on a narrow frequency window

Data from lower frequency range cannot necessarily be compared with

QCM-D modeled data.

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Quartz crystal Lipid film Lipase solution

~100 nm

A practical modeling example

Lipase (E.C. 3.1.1.3) Molecular Weight ~30kDa Concentration 1 g/ml

Lipoprime (lipase)

Formula: C H O

Molecular Weight: 885.43 Da CAS Registry Number: 122-32-7

Triolein (triacylglycerol)

Snabe and Petersen, Aalborg University

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Enzymatic degradation of lipid films

•Raw data indicates multiphase process

•Viscoelastic modeling gives additional information

Chemistry and Physics of Lipids 125(2003), 69-82

F1 (Hz) - 5MHz F3/3 (Hz) -15MHz F5/5 (Hz) - 25MHz Time (min) Fr eq ue nc y, (H z)

D1 (1E-6) D3 (1E-6) D5 (1E-6) Time (min) D is si pa tio n (1 e-6)

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0 1 2 3 4 5 6 0 Time (min) 1 2 V is c (k g m -1 s -1) o r E la st ic ity (1 0 5 P a) 0 20 40 60 80 100 120 Fi lm T hi ck ne ss (n m ) Quartz Crystal Lipid film A A A) Adsorption of lipase Quartz crystal Lipid film B B B) Cluster formation Quartz Crystal Lipid film C C C) Mass ejection Quartz Crystal Lipid film D D

D) Lipid layer removal

Enzymatic degradation of lipids

0 1 2 3 4 5 6 0 5 10 15 20 Time (min) V is c (k g m -1 s -1 ) o r E la st ic ity (1 0 5 P a) 0 20 40 60 80 100 120 Fi lm T hi ck ne ss (n m ) A D BC 0 1 2 3 4 5 6 0 5 10 15 20 Time (min) V is c (k g m -1 s -1 ) o r E la st ic ity (1 0 5 P a) 0 20 40 60 80 100 120 Fi lm T hi ck ne ss (n m ) A D BC

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Thought process

Are there high values in my

data?

Sauerbrey D/f plot Raw data plot

D/f plot Raw data plot Are the results

within the model assumptions

Viscoelastic model D/f plot Raw data plot Homogenous adlayer Newtonian fluid 0 > ∆D ∆D If Sauerbrey

will under estimate the thickness

Raw data, Qsoft data file

Yes

No

Yes

No

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Curve fitting functions

Fitting of of f and D data to

1) Predefined adsorption models

2) User defined equations

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Method: Determination of kinetic

constants with QCM-D

1) Response parameter; - frequency - Dissipation - Modeled thickness

)

1 (

)

(

t

R

_eq

e

(konC koff )t

R

=

−

− +

)

1 (

)

(

(k₁C)t eq

e

R

t

R

=

−

2) Perform adsorption at different C

3) Equation system for k with C and R

t k eq

e

off

R

t

R

(

)

=

−

4) Determine k from dissociation phase

F3/3 (Hz) D3 (1E-6) Testdata kinetic2wfit: 2003-09-30 15:33:00 Time (min) F 3/ 3 (H z) D_{3 (} 1E -6)

B+S BS

kon koff

[ ]

[ ][ ]

off on a _k k S B BS K = = 5) Calculate k from k k 6) Calculate K

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Swelling of cellulose

Cellulose coated crystal, (100nm)

EtOH _Swelling H2O

Susanna Fält, Mitthögskolan, Sundsvall, Sweden

•High charge, more swelling

•Swelling kinetics

-2000 -1500 -1000 -500 0 500 -5 0 5 10 15 20 25 30 35 40 45 50 Time (hrs) F( 15 ) H z 20 ueq/g 409 ueq/g -1600 -1400 -1200 -1000 -800 -600 -400 -200 0 200 0 10 20 30 40 Time (min) F (1 5) H z 20 ueq/g 409 ueq/g

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Swelling of Cellulose

Offset

e

A

t

F

Ae

y

t

F

k t b t

+

−

=

+

=

− −

)

1 (

)

(

)

(

) * / 0

Determination of the decay constant

F(t)= frequency t= time

Y0=A+Offset= F at t=very large Offset= F at t=0

b=1/k, decay constant (swelling parameter)

C Fit C Time (s) F 2 (H z) [3 * H z] b ~2000

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Summary

1) Qualitative, Raw data, D-f

2) Quantitative Sauerbrey

3) Quantitative Viscoelastic

4) Curve fit

F3/3 (Hz) D3 (1E-6) Time (min) F 3/ 3 (H z) D3 (_1E -6 ) D3 (1E-6) F3/3 (Hz) D 3 (1 E -6 ) F3/3 (Hz) F5/5 (Hz) fir f3 fit f5 D3 (1E-6) D5 (1E-6) fit d3 fit d5 Time (min) F 3/ 3 (H z) D3 (1E -6 ) Sauerbrey mas s Time (seconds) S au er br ey m as s C Fit C Time (s) F2 (H z) [3 * H z]