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Broadband Dielectric Spectroscopy (BDS) in soft matter research

Broadband Dielectric Spectroscopy (BDS) in soft matter research. F.Kremer. The spectrum of electro-magnetic waves. UV/VIS IR Broadband Dielectric Spectroscopy (BDS). Questions to be addressed:.

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Broadband Dielectric Spectroscopy (BDS) in soft matter research

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  1. Broadband Dielectric Spectroscopy (BDS) in soft matter research F.Kremer

  2. The spectrum of electro-magnetic waves UV/VIS IR Broadband Dielectric Spectroscopy (BDS)

  3. Questions to be addressed: • What molecular processes take place in the spectral range from THz to mHz and below? • What is the principle of Broadband Dielectric Spectroscopy? • Excursion: What is the dynamics in a glass? • Example: Glassy dynamics in low molecular weight and polymeric amorphous materials. • Example: Glassy dynamics in nanoporous confinement, or „how many molecules form a liquid?“ • The counterbalance between surface and confinement effects

  4. What molecular processes take place in the spectral range from THz to mHz and below?

  5. Basic relations between the complex dielectric function e* and the complex conductivity s* The linear interaction of electromagnetic fields with matter is described by one of Maxwell‘s equations (Ohm‘s law) (Current-density and the time derivative of D are equivalent)

  6. + + - Electric Field - - Effect of an electric field on a unpolar atom or molecule: In an atom or molecule the electron cloud is deformed with respect to the nucleus, which causes an induced polarisation; this response is fast (psec), because the electrons are light-weight

  7. Effects of an electric field on an electric dipole m : An electric field tries to orient a dipole m; but the thermal fluct-uationsof the surrounding heat bath counteract this effect; as result orientational polarisation takes place, its time constant is characteristic for the molecular moiety under study and may vary between 10-12s– 1000s and longer.

  8. - - - - - - - - - - - - - - - - Effects of an electric field on (ionic) charges: Charges (electronic and ionic) are displaced in the direction of the applied field. The latter gives rise to a resultant polarisation of the sample as a whole. + + + + + + + + + + + + + + + + Electric field

  9. What molecular processes take place in the spectral range from THz to mHz and below? • Induced polarisation • Orientational polarisation • Charge tansport • Polarisation at interfaces

  10. What is the principle of Broadband Dielectric Spectroscopy?

  11. A closer look at orientational polarization: Capacitor with N permanent dipoles, dipole Moment  Debye relaxation complex dielectric function

  12. P. Debye, Director (1927-1935) of the Physical Institute at the university of Leipzig (Nobelprize in Chemistry 1936)

  13. Capacitor with N permanent Dipoles, Dipole Moment  Polarization : Mean Dipole Moment Mean Dipole Moment: Counterbalance Thermal Energy Electrical Energy Boltzmann Statistics: The factor exp(E/kT) d gives the probability that the dipole moment vector has an orientation between  and  + d. The counterbalance between thermal and electric ennergy Dipole moment

  14. Spherical Coordinates: The Langevin-function Only the dipole moment component which is parallel to the direction of the electric field contributes to the polarization x = ( E cos ) / (kT) a = ( E) / (kT) Langevin function (a)a/3 Debye-Formula 0 - dielectric permittivity of vacuum = 8.854 10-12 As V-1 m-1

  15. Analysis of the dielectric data

  16. Brief summary concerning the principle of Broadband Dielectric Spectroscopy (BDS): • BDS covers a huge spectral range from THz to mHz and below. • The dielectric funcion and the conductivity are comlex because the exitation due to the external field and the response of the system under study are not in phase with each other. • The real part of the complex dielectric function has the character of a memory function because different dielectric relaxation proccesses add up with decreasing frequency • The sample amount required for a measurement can be reduced to that of isolated molecules. (With these features BDS has unique advantages compared to other spectroscopies (NMR, PCS, dynamic mechanic spectroscopy).

  17. Excursion: What is the dynamics in a glass?

  18. Single molecule relaxation Liquid-like relaxation (dynamic glass transition) The temperature dependence of the relaxation rate enables one to distinguish between a single molecule and a liquid-like relaxation.

  19. Ellipsometry (capacitive scanning) dilatometry 10 Broadband Dielectric Spectroscopy Frequency-dependent calorimetry (20 Hz) 8 Differential scanning calorimetry Calorimetric Tg 6 Tg 4 (1/t)[1/s] 2 log 0 heat capacity C -2 -4 -6 5.0 2.0 3.0 4.0 180 200 220 240 280 1000/T [1/K] Temperature /K Heat capacity Molecular motion Heat capacity Optical constants n and d Thermal expansion The (dynamic) glass transition Dynamic glass transition: a gradual decrease over many orders of magnitude of the structural relaxation time upon cooling.

  20. Summary concerning glassy dynamics • Single-molecule relaxations are Arrhenius-like. Glassy dynamics is characterized by the empirical Vogel-Fulcher-Tammann (VFT) dependence. • The dynamic glass transition is assigned to relaxations between structural substates. It corresponds to a continuous slowing down of the molecular dynamics uponcooling which is usually described by the empirical Vogel-Fulcher-Tammann (VFT) dependence. • The dynamic glass transition scales with thecalorimetricglass transition. At Tg typically a relaxation rate of .01 Hz is reached. • There are manifold ways to measure the dynamic glass transition (Ac- and Dc-calorimetry, dilatometry, viscosimetry, scattering techniques, ellipsometry, Broadband Dielectric Spectroscopy etc). The latter has the advantage that it measures also the relaxation-time distribution.

  21. Glassy dynamics in low molecular weight and polymeric amorphous materials

  22. Types of thermal activation: Vogel-Fulcher-Tammann (VFT)-equation: (D is a constantand T0 denotes the Vogel temperature) Arrhenius-type temperature dependence: (EA is the activation energy, kB the Boltzmann constant and  the relaxation rate in the high temperature limit)

  23. Activation- and derivative-plot for relaxation-processes having different types of thermal activation

  24. Activation- and derivative-plot for glycerol The dynamics can not be described by a single VFT-function

  25. Activation- and derivative-plot for propylene- glycol and poly(propylene glycol) The dynamics can not be described by a single VFT-function

  26. Activation- and derivative-plot for salol The dynamics can not be described by a single VFT-function

  27. Does time-temperature superposition holds in general? No!

  28. Does time-temperature superposition holds in general? No!

  29. Is there a characteristic change in glassy dynamics? Yes! Between about .1 GHz - 1 GHz the temperature dependence of glassy dynamics changes

  30. Summary concerning glassy dynamics in low molecular weight and polymeric amorphous materials • The dynamic glass transition isnot at alla „transition“. • The dynamic glass transition scales usually with thecalorimetric glass transion Tg. • At about 1 GHz achange in the temperature dependenceof glassy dynamics takes place. • Time-temperature superpositiondoes not hold in general. • The scaling of the dynamic glass transition shows in derivative-plots a signature which is characteristic for the material under study.

  31. Example: Glassy dynamics in nanoporous confinement, or „how many molecules form a liquid?“

  32. 5. Glassy dynamics of low molecular-weight systems in the geometrical confinement of zeolitic hosts systems - or how many molecules form a liquid?

  33. Simulation Experiment

  34. Summary for ethylenglycol being in the confinement of zeolitic host systems • A single molecule dynamics is characterized by an Arrhenius temperature dependence - a liquid-like dynamics by a Vogel – Fulcher –Tammann (VFT)-like temperature dependence • For ethylenglycol in zeolites a sharp transition from a single molecule to a liquide-like dynamics is observed • An ensemble as small as6ethylenglycolmolecules is sufficient to perform a liquid-like dynamics • R.Stannarius et al. PRL 75,4698,(1995); M.Arndt et al. PRL 79,2077,(1997); A.Huwe et al. PRL 82,2338,(1999); F.Kremer et al. J.Phys.Cond.Matter 11:A175 (1999); F.Kremer et al.; Chap.6 in: • „Broadband Dielectric Spectroscopy“ (Eds.:F.Kremer and A.Schönhals),Springer (2002)

  35. The counterbalance between surface and confinement effects

  36. Salol in coated and non-coated Sol-Gel glasses In uncoated nanopores two relaxation processes are observed due to the adsorbed and “free” salol molecules. In silanized nanopores the suface effect is fully removed.

  37. Salol in silanized nanopores Confinement effect:The molecular dynamics becomes faster with increasing con-finement.An inherent lengthscale exists for the dynamic glass transtion. M.Arndt et al.PRL 79,2077(1997), F.Kremer et al. J.Phys.Cond.Matter 11:A175 (1999)

  38. Attractive vs.repulsive interactions between guest and host (e.g. Propylenglycol in uncoated and silanised SiO2 surfaces of Sol-gel glasses) The attractive interaction between guest and host causes a slowing down of the molecular dynamics (Surface effect).Due to the silanization this effect is fully removed and a dynamics becomes comparable to that of a bulk liquid .

  39. Molecular dynamics in confinement – a result of the counterbalance between surface and confinement effects. confinement effect (decrease of Tg) confinement effect (decrease of Tg) surface effect (Increase of Tg) surface effect (Increase of Tg) Surface effect: Due to the attractive interaction between host and guestsystem the molecular dynamics is slowed down Confinement effect: The growth of the inherent lengthscale of the dynamic glass transition is limited by the external confinement. This causes a change from a VFT- to an Arrehnius temperature dependence

  40. Summary for low molecular weight systems The molecular dynamics in confinement is determined by the counterbalance between surface- and confinement effects The dynamic glass transition has an inherent lengthscale which increases with decreasing temperature. At the calorimetric glass transition temperature it has a value in the nanometer range which varies strongly from system to system. The growth of this inherent lengthscale is the physical origin for the Vogel-Fulcher-Tammann (VFT)-dependence. If due to an external confinement the inherent lengthscale can no longer grow the Vogel-Fulcher-Tammann-dependence turns into an Arrhenius-dependence. R.Stannarius et al. PRL 75,4698(1995); M.Arndt et al.PRL 79,2077(1997); A.Huwe et al. PRL 82,2338 (1999); F.Kremer et al. J.Phys.Cond.Matter 11:A175 (1999);F.Kremer et al. Chap.6 in: „Broadband Dielectric Spectroscopy“ (Eds.:F.Kremer and A.Schönhals),Springer (2002)

  41. Thanks to ...DFG for financial support and you for attention

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