High-Frequency Dynamics in High-Frequency Dynamics in PEG+HPEG+H22O SystemO System

Mikołaj Pochylski

Adam Mickiewicz University (UAM)Department of Physics,

Poznań, Poland

PoznańPoznań

PoznańPoznań

Adam Mickiewicz UniversityAdam Mickiewicz University

Adam Mickiewicz University in numbers:

400 years of tradition

14 departments

5000 employees (2700 academic teachers)

55 000 students

University Campus - Department of PhysicsUniversity Campus - Department of Physics

OutlineOutline

• PolyEthylene Glycol – PEGPolyEthylene Glycol – PEG

• Brillouin Light ScatteringBrillouin Light Scattering

• Relaxation processRelaxation process– Visco–elasticity– Relaxation functions

• Results for PEG+HResults for PEG+H22O system:O system:

– Temperature analysis– Frequency analysis– Comparison with dielectric results

PolyEthylene Glycol - PEGPolyEthylene Glycol - PEG

OH-(CH2-CH2-O)n-H

PEG600(n=13)

PolyEthylene Glycol - PEGPolyEthylene Glycol - PEG

General properties:Non-toxic, flexible, hydrophilic (amphiphilic)

Application examples:• Separation, purification and fusion of biomolecules and cells,• Hydrophilic moiety in nonionic surfactants,• Matrix for ion conducting polymer electrolytes, • Coating of implants and ship hulls• ...

Industry fields:Biomedical, Pharmaceutical, Cosmetics, Textile, Paints, Food ...

PolyEthylene Glycol - PEGPolyEthylene Glycol - PEG

hydroxyl group

ether group

Light scatteringLight scattering

dtetqqqS ti

),()0,(2

1),(

( , ) ( , )I q S q

Dynamic structure factorDynamic structure factor

(shape of the spectrum)(shape of the spectrum)),(),( 0 trtr

– Dielectric constant fluctuations

),(),( trtrT

– density fluctuations

( , ) ?q t

0

2 22 2 2

0

2

0

0

0

( 1)0

S P SL

TP

t

v vT

t

T D Tt t

Linearized hydrodynamic equations for viscous fluid

)0,(),( qtq ),( qS

FT

Light scatteringLight scattering

Spectrum of scattered lightSpectrum of scattered light

2 2 2 2 2 2 2 2

2 2 2 2

2

2 2 2

2 2 2 2 2 2

0

2 2 2

2

2

1

( , )

1

1

(

( )

) ( )

( )

11

( )

B B B

B B

B B B

T

T

BB

B B B B B B B B

B T

B B B

S q

VD q

qk T

D

Frequency

Inten

sity

B

2 B

Brillouin Light ScatteringBrillouin Light Scattering

B Bv q Brillouin Frequency Shift

0

1.5

532

2000 /

90

B

n

nm

v m s

/ 2 8B GHz

Brillouin Light ScatteringBrillouin Light Scattering

B Bv q

21

2B L q

4sin( / 2)

nq q

Scattering Wave Vector:Brillouin Shift:(velocity of soundwave)

Brillouin Linewidth (HWHM):(attenuation of soundwave)

( 4 / 3 ) /L V S Kinematic longitudinal viscosity

Normalized attenuation

coefficient - /f2

Hypersound velocity - vB q

v BB

2 2

2 B

B Bf v

Acoustical parameters:

Brillouin Spectroscopy:

extension of Ultrasonic Spectroscopy for GHz

frequencies

Brillouin Light ScatteringBrillouin Light Scattering

Longitudinal Modulus, M:

Describes mechanical response of a medium (induced stress) subjected to longitudinal deformation

stress M deformation

Brillouin Light ScatteringBrillouin Light Scattering

Loss modulus – M”

Accumulation modulus – M’

Complex longitudinal modulus components:

2

BMq

2 B

B

M M

Normalized attenuation

coefficient - /f2

Hypersound velocity - vB

Acoustical parameters:

B

Mv

2

2

2

B B

M

f v M

Fabry-Perot SpectrometerFabry-Perot Spectrometer

3

7 1

100 0.1[ ]

1200[ / ]

3.5 10 [ ]

S cP Pa s

kg m

q m

2

2

1

24

433

2

3

B L

V SS

L

SB

q

q

2 140 !!!B GHz

Brillouin Light ScatteringBrillouin Light Scattering

2 3B GHz

/ 2 10B GHz

exp( / )t – Relaxation time

Visco-elasticityVisco-elasticity

( ); ( )L L M M

B

1B

[ ]B GHz

[ ]B ps

Peak conditionPeak condition

RelaxationRelaxation

0( )1

M MM i M

i

Debye relaxation functionDebye relaxation function

B

( )BM

( )BM

Results – PEG600Results – PEG600

vB , /f2

M’ , M”

Brillouin spectra for pure PEG600 at different temperatures

B , B

No

rmal

ized

in

ten

sity

Frequency shift [GHz]

PEG600

v [m

s-1

]

1200

1400

1600

1800

T [K]280 300 320 340 360 380 400

/f 2 x 10

14 [s

2 m-1]

5,0

5,5

6,0

6,5

7,0

7,5

8,0

0( )1

M MM i M

i

Debye relaxation functionDebye relaxation function

B

Mv

2

2

2

B B

M

f v M

2 22 2 2 2

0 0 2 2

22 2

02 3 2 2

1

2

1

B

B

v v v v

v v Cf v

Vogel-Fulcher-Tamman

RT

Eaexp0

Arrhenius

0

00 exp TT

DT

Temeprature dependence of relaxation time:Temeprature dependence of relaxation time:

Results – PEG600Results – PEG600

PEG600

v [m

s-1

]

1200

1400

1600

1800

ArrheniusVFT

T [K]280 300 320 340 360 380 400

/f 2 x 10

14 [s2 m

-1]

5,0

5,5

6,0

6,5

7,0

7,5

8,0

v0 (3MHz)

Maisano, G.Maisano, G., et al.,, et al., Mol. Phys. Mol. Phys. 1993, 1993, 7878, 421, 421

Relaxation in complex liquidsRelaxation in complex liquids

Vogel-Fulcher-Tamman

0 expaE

RT

Arrhenius

0

00 exp TT

DT

ResultsResultsTemperature experiment for PEG400 solutionsTemperature experiment for PEG400 solutions

* 0( )1 ( )

M MM M

i

Havriliak-Negami functionHavriliak-Negami function

0 1, 0 1 Havriliak-NegamiHavriliak-Negami

DebyeDebye

Cole-ColeCole-Cole

Cole-DavidsonCole-Davidson

1, 1

1, 0 1

0 1, 1

ResultsResultsTemperature experiment for PEG400 solutionsTemperature experiment for PEG400 solutions

0( )1 ( ) CC

M MM i M

i

Vogel-Fulcher-TammanVogel-Fulcher-Tamman

00

0

( ) expDT

TT T

Cole-Cole functionCole-Cole function

ResultsResultsTemperature experiment for PEG400 solutionsTemperature experiment for PEG400 solutions

Brillouin Light ScatteringBrillouin Light ScatteringFull Spectrum AnalysisFull Spectrum Analysis

0

2 22 2

( )( , )

/ ( ) ( )

I MS q

q M M

Havriliak-Negami functionHavriliak-Negami function

Dynamic structure factor

0( )

1

M MM i M

i

Full Spectrum Analysis – PEG600Full Spectrum Analysis – PEG600

Debye relaxationDebye relaxation

Poor quality of fit: presence of the distribution

of relaxation times

More complicated relaxation function is needed

0( )1

M MM i M

i

Cole-Davidson Cole-Davidson relaxation functionrelaxation function

0( )

1 CD

CD

M MM i M

i

Full Spectrum Analysis – PEG600Full Spectrum Analysis – PEG600

Full Spectrum Analysis – PEG400Full Spectrum Analysis – PEG400

Havriliak-NegamiHavriliak-Negami

and taken directly from

dielectric experiment

0( )

1 B

J JJ i J

i

( ) 1/ ( )J i M i

T. Sato, T. Sato, et al.,et al., J. Chem. Phys.J. Chem. Phys. 1998, 108, 4138 1998, 108, 4138

Debye relaxationDebye relaxation

Full Spectrum Analysis – PEG400Full Spectrum Analysis – PEG400

Modulus expressed in terms of

the Longitudinal Compliance, J

(Havriliak-Negami function)

Relaxation times vs PEG concentrationRelaxation times vs PEG concentrationcomparison with Dielectric Spectroscopy resultscomparison with Dielectric Spectroscopy results

[1] M. Pochylski et al., [1] M. Pochylski et al., J.Phys. Chem. BJ.Phys. Chem. B 20062006, 110, 20533, 110, 20533[2] T. Sato et al, [2] T. Sato et al, J.Chem.Phys.J.Chem.Phys. 19981998, 108, 4138, 108, 4138[3] N. Shinyashiki et al, [3] N. Shinyashiki et al, J.Chem.Phys.J.Chem.Phys. 19901990, 93, 760, 93, 760[4] C.H. Wang et al., [4] C.H. Wang et al., J. Non-Cryst. SolidsJ. Non-Cryst. Solids 19911991, 131, 970., 131, 970.[5] T. Noudou et al., [5] T. Noudou et al., Jpn. J. Appl. Phys.Jpn. J. Appl. Phys. 19961996, 35, 2944., 35, 2944.

PEG282, x’=0.42

DVFT = 7.6

PEG400, x’=0.50

DVFT = 7.2

[1] Murthy, S.S.N. et al., [1] Murthy, S.S.N. et al., J. Phys. Chem. BJ. Phys. Chem. B 2000, 104, 6955 2000, 104, 6955[2] Sudo, S. et al., [2] Sudo, S. et al., J. Chem. Phys. J. Chem. Phys. 2004, 121, 73322004, 121, 7332

Relaxation times vs TemperatureRelaxation times vs Temperaturecomparison with Dielectric Spectroscopy resultscomparison with Dielectric Spectroscopy results

Thanks for Your Thanks for Your Attention !Attention !