Introduction to data analysis - Boston University

Analysis Methods 1) Qualitative analysis (raw data plot, D-f plot) 2) Quantitative analysis (low D=Sauerbrey) 3) Quantitative analysis (high D=viscoel...

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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!