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: 1.What molecular processes take place in the spectral range from THz to mHz and below? 2.What is the principle of Broadband Dielectric Spectroscopy? 3.Excursion: What is the dynamics in a glass? 4.Example: Glassy dynamics in low molecular weight and polymeric amorphous materials. 5.Example: Glassy dynamics in nanoporous confinement, or „how many molecules form a liquid?“ 6.The counterbalance between surface and confinement effects

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

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

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 Electric Field

Effects of an electric field on an electric dipole  : An electric field tries to orient a dipole  but the thermal fluct- uations  of 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.

Effects of an electric field on (ionic) charges: Charges (electronic and ionic) are 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

What molecular processes take place in the spectral range from THz to mHz and below? 1.Induced polarisation 2.Orientational polarisation 3.Charge tansport 4.Polarisation at interfaces

What is the principle of Broadband Dielectric Spectroscopy?

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

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

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

Spherical Coordinates : 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 = As V -1 m -1 The Langevin-function

Analysis of the dielectric data

Brief summary concerning the principle of Broadband Dielectric Spectroscopy (BDS): 1.BDS covers a huge spectral range from THz to mHz and below. 2.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. 3.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 4.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).

Excursion: What is the dynamics in a glass?

Single molecule relaxationLiquid-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.

Dynamic glass transition: a gradual decrease over many orders of magnitude of the structural relaxation time upon cooling. The (dynamic) glass transition 1000/T [1/K] Calorimetric T g log  /s] Frequency-dependent calorimetry (20 Hz) Heat capacity (capacitive scanning) dilatometry Thermal expansion Ellipsometry Optical constants n and d Broadband Dielectric Spectroscopy Molecular motion

Summary concerning glassy dynamics 1.Single-molecule relaxations are Arrhenius-like. Glassy dynamics is characterized by the empirical Vogel-Fulcher-Tammann (VFT) dependence. 2.The dynamic glass transition is assigned to relaxations between structural substates. It corresponds to a continuous slowing down of the molecular dynamics upon cooling which is usually described by the empirical Vogel-Fulcher-Tammann (VFT) dependence. 3.The dynamic glass transition scales with the calorimetric glass transition. At Tg typically a relaxation rate of.01 Hz is reached. 4.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.

Glassy dynamics in low molecular weight and polymeric amorphous materials

Vogel-Fulcher-Tammann (VFT)-equation: Arrhenius-type temperature dependence: Types of thermal activation: (E A is the activation energy, k B the Boltzmann constant and  the relaxation rate in the high temperature limit) (D is a constant and T 0 denotes the Vogel temperature)

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

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

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

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

Does time-temperature superposition holds in general? No!

Does time-temperature superposition holds in general? No!

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

Summary concerning glassy dynamics in low molecular weight and polymeric amorphous materials 1.The dynamic glass transition is not at all a „transition“. 2.The dynamic glass transition scales usually with the calorimetric glass transion T g. 3.At about 1 GHz a change in the temperature dependence of glassy dynamics takes place. 4.Time-temperature superposition does not hold in general. 5.The scaling of the dynamic glass transition shows in derivative- plots a signature which is characteristic for the material under study.

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

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

Simulation Experiment

Summary for ethylenglycol being in the confinement of zeolitic host systems 1.A single molecule dynamics is characterized by an Arrhenius temperature dependence - a liquid-like dynamics by a Vogel – Fulcher –Tammann (VFT)-like temperature dependence 2.For ethylenglycol in zeolites a sharp transition from a single molecule to a liquide-like dynamics is observed 3.An ensemble as small as 6 ethylenglycol molecules 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)

The counterbalance between surface and confinement effects

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.

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)

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.

Molecular dynamics in confinement – a result of the counterbalance between surface and confinement effects. surface effect (Increase of Tg) confinement effect (decrease of Tg) surface effect (Increase of Tg) confinement effect (decrease 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

Summary for low molecular weight systems 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) The molecular dynamics in confinement is determined by the counterbalance between surface- and confinement effects

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