Super-Arrhenius behavior of the structural relaxation times Viscosity measurements under high pressure Thermodynamical scaling Marian Paluch Institute of Physics Silesian University Katowice, POLAND

Marian PaluchSilesian University 1:3:5-tri-  -naphthylbenzene; D. J. Plazek and Magill, J. Chem. Phys. The Arrhenius law: Activation energy: Is the super-Arrhenius behavior near Tg at ambient pressure governed primarily by the decreasing volume, the decreasing temperature, or both ?

Marian PaluchSilesian University “unambiguously that it is temperature, and not density, that is the overwhelmingly dominant control variable”; „This suggest that theories which focus on thermal effects and totally ignore density variations can be appropriate” (Ferrer, et al., 1999) “relaxation processes arise from molecular motions that are driven by temporal fluctuations in thermal energy … not a time-averaged quantity such as free volume” (Williams, 1997) Prevailing viewpoint:

Marian Paluch Temperature dominatedVolume dominated T=T 1 T=T 2 T=T 3 Log(  ) T 1 < T 2 < T 3 Volume isobar isotherm Volume Log(  ) isotherm isobar

Marian PaluchSilesian University F[Hz], C[pF], R[  ] Impedance Analyzer Thermal bath T[°C] P[bar] Pressure meter Hydraulic press High pressure chamber Tensometric sensor Valve Hz – 10 7 Hz Schematic illustration of the high pressure dielectric set-up

PDE T g =294 K Dielectric measurements M. Paluch, R. Casalini, C. M. Roland, Phys. Rev. B 2002 Marian PaluchSilesian University

Schematic illustration of the light scattering technique used in high pressure measurements Thermal bath T[°C] Membrane compressor Laser P [bar] Avalanch diode detector Valve Correlator Manometer sample High pressure chamber Marian PaluchSilesian University

Dynamic light scattering measurements A. Patkowski, M. Paluch, H. Kriegs, J. Chem Phys Marian PaluchSilesian University

Marian PaluchSilesian University Capillary Diamond-anvil cell Centrifuge Diamond-anvil cell Falling ball Rolling ball Falling body

Marian PaluchSilesian University metal sphere 0.05 mm diameter 0.25 mm 0.5 mm diamond stainless steel gasket ruby chip

Frequency counter Laser Mirror F=  2 R  Marian PaluchSilesian University The centrifugal force viscometer

Tait equation: M. Paluch, R. Casalini, A. Best, A. Patkowski, J. Chem Phys PVT measurements: Marian PaluchSilesian University

M. Paluch, R. Casalini, C. M. Roland, Phys. Rev. B 2002 Volume dependence of the  - relaxation times Marian PaluchSilesian University

isochronal expansivity :  P =  V  1 (  V/  T) P isobaric expansivity :   =  V  1 (  V/  T)  (Ferrer, Lawrence, Demirjian, Kivelson, Alba-Simonesco & Tarjus, 1998 ) First approach: Expansion coefficients using >>1 ~ 1 comparable 0 P T dominate V dominate            Marian PaluchSilesian University

PDEPPGE 1bar kbar M. Paluch, R. Casalini, C. M. Roland, Phys. Rev. B 2002 Marian PaluchSilesian University

Volume  Temperature (steric constraints) (thermal fluctuations) 0  E V /E P  1 M. Naoki and M. Matsushita, Chem. Soc. Jap. 56, 2396 (1983) Second approach: Activation energies activation energy at constant volume: activation energy at constant pressure: Marian PaluchSilesian University

M. Paluch, R. Casalini, C. M. Roland, Phys. Rev. B 2002 Marian PaluchSilesian University

Marian PaluchSilesian University Name TgTg E V /E P BMPC BMMPC Salol KDE PDE o-terphenyl PMPS PTMS polystyrene DGEBA polyvinylacetate PPGE polyvinylmethylether ,2-polybutadiene polypropyleneglycol (0.78)* propylene glycol trimer 0.77 sorbitol propylene glycol0.89 glycerol Small molecules Polymers H-bonded liquids Temperature dominant control variable for H-bonded materials density and thermal energy have nearly the same effect on molecular dynamics weaker effect of density due to intramolecular bonding

R. Casalini, and C. M. Roland J. Chem. Phys. 119, 4052 (2003) Marian PaluchSilesian University

Marian PaluchSilesian University TV  scaling Parameter  is material constant, and independent on P, T and V The scaling quantity TV -  can be followed from the generalized LJ potential with its modiefied repulsive and attractive parts proportional to r -3  and r -3  /2 - for OTP PMPS 2PG PDE

At T=T g  Marian PaluchSilesian University

Marian PaluchSilesian University For polymer Boyer-Spencer rule:  P T g =0.2

Marian PaluchSilesian University

Marian PaluchSilesian University BMMPC PTMPS PDE

Marian PaluchSilesian University