Glassy dynamics in geometrical confinement as studied by Broadband Dielectric Spectroscopy F. Kremer Universität Leipzig

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1 Glassy dynamics in geometrical confinement as studied by Broadband Dielectric Spectroscopy F. Kremer Universität Leipzig Co-authors: M. Treß, E.U. Mapesa, W. Kipnusu, C. Iacob (Leipzig), Reiche (Halle), M. Erber, K.-J. Eichhorn, B. Voit (Dresden), A. Serghei (Lyon), C. Schick (Rostock)

2 Outline 1. Experimental realization of sub-nanometric and nanometric (onedimensional (1D) and two-dimensional (2D)) confinement 2. The calorimetric glass transition temperature, the dynamic glass transition and methods to measure it 3. The principle of Broadband Dielectric Spectroscopy (BDS) 4. Glassy dynamics in sub-nanometric geometrical confinement of zeolites 5. Polymethylphenylsiloxane (PMPS) in 1-D and 2-D geometrical constraints 6. Glassy dynamics of condensed isolated polymer chains.

3 1. Experimental realization of sub-nanometric and nanometric (one- dimensional (1D) and two-dimensional (2D)) confinement

4 sub-nanometric confinement as realized with zeolites

5 1D and 2D nanometric confinement 1D confinement Spin-coated film spacers 50nm 2D confinement Ultra-flat highly conducting Si wafers 50 nm 6 µ m 45 µm 6 m The air-gap geometry enables one to carry out BDS experiments on layers less than 5nm without the possibility of electrical shorts. No evaporated metal electrodes! Uni-directional silica nanopores; (Electro-chemical etching of highly conductive silicon and subsequent oxidation)

6 Summary 1. Sub-nanometric, two-dimensional confinement can be easily realized with zeolitic host systems. 2. Nanometric layers of thin polymer films can be easily prepared by spin-coating. 3. Unidirectional nanometric pores can be prepared down to diameters >= 4 nm. 4. With silanization the inner surfaces of the pores can be changed from hydrophilic to hydrophobic.

7 2. The calorimetric glass transition temperature, the dynamic glass transition and methods to measure it.

8 Volume The (calorimetric) glass transition liquid crystal no long-range order glass liquid long-range order scale invariant transition temperature glass 1 glass 2 crystal T g,2 T g,1 T c Temperature no long-range order transition temperature depends on cooling rate The glass transition is no phase transition!

9 log (1/t)[1/s] The calorimetric glass transition temperature as measured by (DC-) Differential Scanning Calorimetry (DSC) heat capacity C DC-calorimetric Tg T g /T [1/K] Temperature /K At the calorimetric glass transition temperature the dynamic glass transition has a typical relaxation rate of ~ 0.01 Hz

10 log (1/t)[1/s] C'( ) [a.u.] C''( ) [a.u.] The dynamic glass transition as measured by frequencydependent (AC) calorimetry Frequency dependent T g AC-calorimetric Tg /T [1/K] f = 100 Hz T [K] AC-calorimetry traces the dynamic glass transition over many orders of magnitude

11 n', n'' [a.u.] log (1/t)[1/s] n ( 540nm) Ellipsometric determination of the glass transition temperature Ellipsometrically determined Tg Tg /T [1/K] ( n) 2 T Temperature /K () n T With ellipsometry a kink in the temperature dependence of n and d is found indicating Tg

12 log (1/t)[1/s] '' The dynamic glass transition as measured by Broadband Dielectric Spectroscopy (BDS) Dynamic glass transition determined by BDS T g /T [1/K] f [Hz] 240 K 235 K 230 K 225 K 220 K 215 K BDS measures the dynamic glass transition in a wide frequency and temperature range, including the relaxation time distribution

13 Glassy dynamics is characterized by a temperature dependence of the relaxation rate following the empirical Vogel-Fulcher-Tammann (VFT)-equation log 10 (1/t max [Hz]) experimental data: propylene glycol bulk VFT-fit: 1/t=A exp(dt 0 /(T-T 0 )) (D is a constant and T0 the Vogel temperature) /T [K -1 ] At the calorimetric glass transition temperature Tg the relaxation rate has a typical value of.01 Hz.

14 Summary 1. The calorimetric and the dynamic glass transition are interlinked by the (empirical) Vogel-Fulcher-Tammann (VFT) relationship. 2. 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 to cover an extraordinarily broad spectral range. 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 described by the empirical Vogel-Fulcher-Tammann (VFT) dependence.

15 3. The principle of Broadband Dielectric Spectroscopy (BDS)?

16 Purely insulating samples: orientational polarisation: E (t) (t)=(p(t) - P ) / E ' '' Capacitor with N permanent dipoles, dipole Moment Debye relaxation * s (1 i t ) 2 3,6 3,2 '= s 1 0 E 2,8 2,4 2,0 0,8 '=? = s -? ,6 '' max 0,4 = S - 00 S orientational polarization 00 induced polarization 0,2 max 0, [rad s -1 ] Time complex dielectric function ( ) 1 ( t) s ( ) t 1 ( t) 2 s 2

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

18 log '' log '' ' ' information content of dielectric spectra Debye-Relaxation Generalized Relaxation: Havriliak-Negami function 4.0 c =1/t c S 4.0 c =1/t c S * D * ( ) ( ) 1 i t c log ( / c ) log ( / c ) 3.0 HN ( 1 ( i t HN ) ) 0 c =1/t c c =1/t c log ( / c ) log ( / c ) Mean relaxation time τ c : Relaxation strength Δε: 1 1 tc thn sin sin NV kt 3 0 B Relaxation time distribution L(τ): D ( ) ( ) L ( t ) f( t,, ) L t t c HN HN Temperature dependence of τ c : Arrhenius or Vogel-Fulcher Tammann (VFT)

20 In real samples charge transport and orientational polarisation take place in parallel The linear interaction of electromagnetic fields with matter is described by one of Maxwell s equations D 0 curl H j E j E D t (Ohm s law) (Current-density and the time derivative of D are equivalent) ( ) i ( ) i i 0

21 Dielectric spectra as characterized by charge transport and electrode polarisation in parallel propylene glycol K 220 K K frequency [Hz] K frequency [Hz] Charge transport and orientational polarisation have quite different frequency dependencies

22 Summary concerning the principle of Broadband Dielectric Spectroscopy (BDS) and the information-content of dielectric spectra. 1. BDS covers a huge spectral range of about 15 decades from THz to below mhz. 2. Due to Maxwell s equations the complex dielectric function ( ) and the complex conductivity ( ) are directly interelated. 3. From dielectric spectra the relaxation rate of fluctuations of a permanent molecular dipole and it s relaxation time distribution function can be deduced. 4. The capacitance of a sample capacitor and hence the sensitivity of the measurement increases with decreasing separation between the electrodes. The sample amount required for a measurement can be reduced to that of isolated molecules.

24 4. Glassy dynamics in sub-nanometric geometrical confinement of zeolites.

25 Ethylene glycole as guest molecule in zeolites

26 Dielectric spectra of ethylene glycole in different zeolitic host systems

27 ethylene glycole in the bulk and in different zeolitic host systems

28 Summary for low molecular weight systems (e.g. ethylene glycole) in 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) temperature dependence. 2. For ethylenglycol in zeolites a sharp transition from a single molecule to a liquid-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)

29 5. Polymethylphenylsiloxane (PMPS) in 1-D and 2-D geometrical confinement

30 1D and 2D confinement a comparison 1D confinement Spin-coated film spacers 100nm 2D confinement Ultra-flat highly conducting Si wafers 260n m 6 µ m 45 µm 6 m The air-gap geometry enables one to carry out BDS experiments on layers less than 5nm without the possibility of electrical shorts. No evaporated metal electrodes! Uni-directional silica nanopores; (Electro-chemical etching of highly conductive silicon and subsequent oxidation)

31 PMPS in 1D confinement and in bulk bulk 31 nm film 14 nm film 5 nm film segmental mode f= 120 Hz '' / '' max surface induced modes T (K) Segmental mode: not broadened, peak position not shifted compared to bulk. Surface induced mode: intensity increases with decreasing thickness

32 Activation plot: bulk and 1D confinement of PMPS -log t (s) 8 6 Segmental mode Surface induced mode bulk 31 nm film 14 nm film 5 nm film -2 T DSC g /T (K) Segmental mode: not shifted compared to bulk Surface induced mode: spectral position seems to be not only dependent on the thickness.

33 Origin of surface induce relaxation mode Weakly adsorbed chains Strongly adsorbed chains Adsorption and desorption process

34 Summary: PMPS in 1D confinement 1. Segmental dynamics: not shifted compared to bulk down 5 nm; not broadened with respect to bulk. 2. Surface induced mode: increases in intensity with decreasing thickness; VFT-like temperature dependence; spectral position seems to depend not only on the thickness; it is presumably assigned to adsorption and desorption processes. 34

35 Dynamics of PMPS in 2D confinement 35

36 Due to silanization the SiO2 surfaces become hydrophobic 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.

37 PMPS in 2D confinement and in bulk f= 120 Hz bulk 8 nm pores 6 nm pores 4 nm pores 6 nm pores sil 4 nm pores sil '' / '' max T(K) Segmental mode: broadening in pores, which is removed by silanization, peak position shifted compared to bulk. Surface induced mode: intensity increases with decreasing pore diameter; removed by silanization

38 Activation plot: PMPS in 2D confinement and in bulk -log t (s -1 ) / T(K -1 ) bulk (BDS) 8nm pores 6 nm pores 4 nm pores 6 nm pores sil 4 nm pores sil T g (DSC) Segmental mode: faster for smaller pore sizes; slower in silanized pores Surface induced mode: no thickness dependence; much slower than segmental mode

39 Activation plot: PMPS in 2D confinement and in bulk -log t (s -1 ) / T(K -1 ) bulk (BDS) 8nm pores 6 nm pores 4 nm pores 6 nm pores sil 4 nm pores sil T g (DSC) Segmental mode: faster for smaller pore sizes; slower in silanized pores Surface induced mode: no thickness dependence; much slower than segmental mode

40 Summary: PMPS in 2D confinement 1. Segmental dynamics: increases with decreasing pore sizes; slower in silanized pores. 2. Surface induced mode: removed by silanization, no simple thickness dependence.

41 Normalized dielectric loss:1d&2d confinement 1,6 1,2 bulk 31 nm film 14 nm film 5 nm film 8nmpores 6nmpores 4nmpores 6 nm pores sil 4 nm pores sil '' / '' max 0,8 0,4 0, T (K) 1D: Segmental mode: not broadened, peak position not shifted surface induced mode: weak thickness dependence, if any 2D: Segmental mode: shifted from bulk, strongly broadened Surface induced mode: stronger than in 1D, removed by silanisation

42 Activation plot: PMPS in 1D&2D confinement -log t (s) bulk (BDS) 8nm pores 6 nm pores 4 nm pores 6 nm pores sil 4 nm pores sil 2 0 bulk 31 nm film 14 nm film 5 nm film -2 T DSC g /T (K) 2-D: Segmental: the faster, the smaller the pores; silanization causes removal of the surface effect

43 Consistent interpretation for PMPS in 1-&2-D confinement 1D Segmental mode: not broadened, peak position not shifted, but confinement induced process. Conclusion: The density is not changed, hence the dynamics is not altered. Due to surface effect surface induced modes.

Consistent interpretation for PMPS in 1D&2D conf.

shifted, but confinement induced process.

In unsilanized pores, strong interaction with inner

reduced density and more free volume resulting in a

44 Consistent interpretation for PMPS in 1D&2D conf. 1D 2D Segmental mode: not broadened, peak position not shifted, but confinement induced process. Conclusion: The density is not changed, hence the dynamics is not altered. Due to surface effect surface induced modes. In unsilanized pores, strong interaction with inner surfaces, thus a less efficient packing and hence a reduced density and more free volume resulting in a faster dynamics confinement effect. In silanized pores the surface interaction is suppressed, but the confinement effect is still visible for small pores.

45 Conclusions Conclusions 1. Dimensionality of confinement impacts the inter-molecular dynamics differently 2. Segmental dynamics in 2D becomes faster in smaller pores due to a confinement effect but remains bulk-like in 1D confinement. 3. Dynamics of the surface induced mode in both, 1D and 2D confinement show no systematic thickness dependence. Kipnusu, W.K. et al., ACS Appl. Mater. Interfaces, 7, (2015); Kipnusu, W.K. et al., J. Phys. Chem. Lett. 6, (2015); Kipnusu W.K. et al., J. Chem. Phys. 146, (2017)

46 6. Glassy dynamics of condensed isolated polymer chains (polyvinylpyridin (P2VP))

Nanostructured electrodes enable one to measure both in parallel,

wafer Si counter electrode with insulating nano-structures condensed

ultra-flat highly conductive Si wafers 35 nm insulating spacers

nano-structured electrodes enable one to avoid evaporation of a

47 Nanostructured electrodes enable one to measure both in parallel, structure (by AFM) and dynamics (by BDS) spin-coat solution on Si wafer Si counter electrode with insulating nano-structures condensed polymer coils Randomly distributed condensed polymer coils ultra-flat highly conductive Si wafers 35 nm insulating spacers (silica nanostructures) AFM optical microscope 45 m 5 m TEM 35 nm nano-structured electrodes enable one to avoid evaporation of a counterelectrode. For the identical sample dynamics by BDS and structure by AFM can be measured.

48 y [ m] Isolated polymer chains: AFM characterization Height [nm] Height [nm] 1,0 0,8 0,6 0,4 0, Zoom Height profiles V ~ nm 2 0,0 0,0 0,2 0,4 0,6 0,8 1,0 x [ m] Lateral extension [nm] Calculated single chain volume (assuming bulk density) for M n = kg/mol: V chain = nm 3 Experimental (AFM) mean coil volume (55 droplets ): V coil = (±500) nm 3 Tress, M. et al. Science, 2013, 341, 1371

y [ m] Isolated polymer chains: AFM characterization Height [nm] Height [nm] 1,0 0,8 0,6 0,4 0,2 5 4 3 2 1 Zoom 4 3 2 1 Height profiles V ~ 2 500 nm 2 0,0 0,0 0,2 0,4 0,6 0,8 1,0 x [ m] 0 0 0 20 40

49 y [ m] Isolated polymer chains: AFM characterization Height [nm] Height [nm] 1,0 0,8 0,6 0,4 0, Zoom Height profiles V ~ nm 2 0,0 0,0 0,2 0,4 0,6 0,8 1,0 x [ m] Lateral extension [nm] Calculated single chain volume (assuming bulk density) for M n = kg/mol: V chain = nm 3 Experimental (AFM) mean coil volume (55 droplets ): V coil = (±500) nm 3 Tress, M. et al. Science, 2013, 341, 1371 V chain / V coil = 1.1 ±0.2 49

50 log '' The dynamics of condensed (semi)-isolated chains -1,0-1,5 bulk f = 1.2 khz f = 300 Hz f = 120 Hz log '' -3,0-3, Temperature [K] semi-isolated chains f = 1.2 khz f = 300 Hz f = 120 Hz isolated chains f = 1.2 khz f = 300 Hz f = 120 Hz (semi)-isolated P2VP chains perform a dynamic glass transition

51 The dynamics of condensed (semi)-isolated chains log( f (Hz)) -log(t (s)) M W = kg/mol T = 407 K 12% log(f (Hz)) bulk semi-isolated chains isolated chains Temperature (K) bulk semi-isolated chains isolated chains '' / ''max M W = kg/mol bulk semi-isolated chains /T (1/K) The mean relaxation rate of (semi)-isolated P2VP chains time is bulklike with a VFT-temperature dependence; The relaxation time distribution is broadened on the low frequency side.

AFM characterization P2VP on mica Roiter, Y.

, JACS 127 (2005), 15688 thickness of P2VPchain:

$broadening in BDS (~15% slowed fraction) only$

52 AFM characterization P2VP on mica Roiter, Y. & Minko, S., JACS 127 (2005), thickness of P2VPchain: 0.4 nm ~30% of segments contact the substrate directly (= 1 st layer) factor of ~2 more than broadening in BDS (~15% slowed fraction) only ~50% of segments in 1 st layer affected by the surface?

Glassy dynamics of isolated condensed P2VP chains mostly bulk-like glassy dynamics ~50% of segments in 1st layer are slowed ~50% of segments in 1st layer establish bonds ~0.

53 Glassy dynamics of isolated condensed P2VP chains mostly bulk-like glassy dynamics ~50% of segments in 1st layer are slowed ~50% of segments in 1st layer establish bonds ~0.5 1 nm) studies on polymer adsorption* suggest: bound segments are largely immobilized and segments in between are slowed range of interfacial effects on glassy dynamics ~0.5-1 nm (P2VP/ silica) Tress, M. et al. Science, 2013, 341, 1371

54 Final summary 1. Glassy dynamics is based on the fluctuation of ~ 2-3 polymer segments i.e. a length scale of about 5Å still below the typical dimensions of nanometric (1-D or 2-D) confinement. 2. For segmental fluctuations (dynamic glass transition) no thickness and no molecular weight dependence is found. Even a broadening of the relaxation time distribution function is not detected in nanometric layers. 3. Dimensionality of confinement impacts the inter-molecular dynamics differently 4. Segmental dynamics in 2D becomes faster in smaller pores due to a confinement effect but remains bulk-like in 1D confinement. Dynamics in Geometrical Confinement, F. Kremer (Ed.); Springer (2014) ISBN

55 Thanks to K.-J. Eichhorn, B. Voit, IPF (Dresden) C. Schick, (Rostock) M. Reiche (Halle) W. Paul. M. Solar (Halle)

Molecular Dynamics in geometrical confinement F. Kremer

Molecular Dynamics in geometrical confinement F. Kremer Coauthors: A. Huwe Universität Leipzig L. Hartmann Universität Leipzig A. Serghei Universität Leipzig A. Gräser Universität Chemnitz S. Spange Universität