Pressure coefficient of the glass transition temperature in the thermodynamic scaling regime

Koperwas, Kajetan; Grzybowski, Adam; Grzybowska, K.; Wojnarowska, Ż.; Pionteck, Jürgen; Sokolov, Alexei P.; Paluch, Marian

doi:10.1103/physreve.86.041502

Cited by 24 publications

(12 citation statements)

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“…For the latter, the state point dependence of the scaling exponent is an essential ingredient.As a special case, Alba-Simionesco, Kivelson and Tarjus (AKT) have investigated the validity of a scaling law for activated dynamics where the scaling exponent only depends on density [18][19][20], but not on temperature. Regarding γ a material constant is an even more constraining assumption, which is only valid if the potential part of the Hamiltonian can be approximated by a sum of inverse power-laws (IPL) r −n pair interactions plus an arbitrary constant (the IPL hypothesis) [3,[21][22][23][24][25]. Then the scaling exponent is independent of state-point (γ IPL = n/3) and the relaxation time falls on a master curve when plottet along ρ γ /T .…”

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confidence: 99%

Experimental Evidence for a State-Point-Dependent Density-Scaling Exponent of Liquid Dynamics

et al. 2019

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A large class of liquids have hidden scale invariance characterized by a scaling exponent. In this letter we present experimental evidence that the scaling exponent of liquid dynamics is statepoint dependent for the glass-forming silicone oil tetramethyl-tetraphenyl-trisiloxane (DC704) and 5-polyphenyl ether (5PPE). From dynamic and thermodynamic properties at equilibrium, we use a method to estimate the value of γ at any state point of the pressure-temperature plane, both in the supercooled and normal liquid regimes. We find agreement between the average exponents and the value obtained by superposition of relaxation times over a large range of state-points. We confirm the state-point dependence of γ by reanalyzing data of 20 metallic liquids and two model liquids.Decreasing the temperature (T ) or increasing the density (ρ) by applying pressure of liquids lead to slowing down of the molecular dynamics and eventually a glass transition if crystallization is avoided [1,2]. It has been demonstrated that for numerous low molecular weight liquids and polymers, the relaxation time or other dynamic quantities can be superimposed onto a master curve within the experimental uncertainty when plotted as a function of ρ γ /T . The scaling exponent γ is thus sometimes referred to as a material constant [3][4][5]. In this letter, we show that γ is in fact state-point dependent and can be measured at a single state point. In the following we will use subscripts to distinguish definitions of γ's.Let τ be the structural relaxation time measured from the loss-peak frequency of the electric permittivity. We will express τ in reduced units of m/k B T ρ 2/3 where m is a atomic/molecular/polymer-segment mass and define the scaling exponent of τ as [6]In this general definition the exponent depends on the state point and the fixed quantity (τ in the above case). A physical interpretation of γ τ is that it quantifies the relative contribution of volume and thermal energy to the temperature evolution of the molecular mobility [7]. Similar to the structural relaxation time, configurational adiabats can also be associated with a scaling exponent:In general, two scaling exponents of different observables (structural, dynamical or thermodynamic) will have different values. However, if the system has so-called "hidden scale-invariance" [6, 8] then all scaling exponents of different properties will have the same value. In Ref.[9] * asanz@ruc.dk † urp@ruc.dk it was experimentally shown that γ τ = γ Sex at one state point of the silicone oil DC704. This result is spectacular since hidden scale-invariance can only be present in a class of systems [10,11]. This class is believed to include systems where van der Waals (vdW) interactions dominate, but exclude systems where hydrogen-bondes (HB) dominates the Hamiltonian [12]. The isomorph theory [6,8,10,12] is a framework for describing systems where the potential energy function U (R) possesses hidden scale invariance (here, R is the collective coordinate of the system). Formally hidden scale inva...

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confidence: 99%

Experimental Evidence for a State-Point-Dependent Density-Scaling Exponent of Liquid Dynamics

et al. 2019

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“…In the last decade, a lot of interest has been directed toward the analysis of molecular dynamics of supercooled liquids in terms of thermodynamic scaling 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 . This alternative approach is very appealing due to the possibility of universal description of relaxation phenomena for all supercooled liquids based on the generalized Lennard-Jones potential 18 .…”

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Adam-Gibbs model in the density scaling regime and its implications for the configurational entropy scaling

Masiewicz

Grzybowski

Grzybowska

et al. 2015

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To solve a long-standing problem of condensed matter physics with determining a proper description of the thermodynamic evolution of the time scale of molecular dynamics near the glass transition, we have extended the well-known Adam-Gibbs model to describe the temperature-volume dependence of structural relaxation times, τα(T, V). We also employ the thermodynamic scaling idea reflected in the density scaling power law, τα = f(T−1V−γ), recently acknowledged as a valid unifying concept in the glass transition physics, to differentiate between physically relevant and irrelevant attempts at formulating the temperature-volume representations of the Adam-Gibbs model. As a consequence, we determine a straightforward relation between the structural relaxation time τα and the configurational entropy SC, giving evidence that also SC(T, V) = g(T−1V−γ) with the exponent γ that enables to scale τα(T, V). This important findings have meaningful implications for the connection between thermodynamics and molecular dynamics near the glass transition, because it implies that τα can be scaled with SC.

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“…1 , which shows that the values of calculated from equations (5 ), ( 6 ), and ( 7 ) are very consistent with each other over a wide range of pressures and as well as to that received from the analysis of the experimental data. In this context, it has to be noted that equation (5) was earlier successfully verified at ambient pressure for many glass-forming liquids that belong to the different material groups 33 .…”

Section: Resultsmentioning

confidence: 91%

“…(9) in Ref. 53 ) for glibenclamide (GLB) 33 , verapamil hydrochlorine (VH) 54 , carvedilol base (CB), ibuprofen (IBP), indometacin (IND), N,N-dimethyl-3-methylbenzamide (DEET) (all in Ref. 55 )polystyrene (PS) 56 , and polyvinylacetate (PVAc) 53 .…”

Section: Methodsmentioning

confidence: 99%

“…Then, combining it with Bartenev relation, one obtains that the constant value depends on , which implies that values of do not have to be invariant for all isobaric conditions. However, established by experimental data of the structural relaxation times , obtained from dielectric spectroscopy of different glass formers, is a slowly varying function of the pressure, which usually results in the increase in in only a few seconds with increasing the pressure from 0 to 200 to 300 MPa 33 . Hence, the glass transition can be defined, with very good agreement, by a constant value of (which for simplicity in the later part will be denoted by ).…”

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Thermodynamic consequences of the kinetic nature of the glass transition

Koperwas

Grzybowski

Tripathy

et al. 2015

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In this paper, we consider the glass transition as a kinetic process and establish one universal equation for the pressure coefficient of the glass transition temperature, dTg/dp, which is a thermodynamic characteristic of this process. Our findings challenge the common previous expectations concerning key characteristics of the transformation from the liquid to the glassy state, because it suggests that without employing an additional condition, met in the glass transition, derivation of the two independent equations for dTg/dp is not possible. Hence, the relation among the thermodynamic coefficients, which could be equivalent to the well-known Prigogine-Defay ratio for the process under consideration, cannot be obtained. Besides, by comparing the predictions of our universal equation for dTg/dp and Ehrenfest equations, we find the aforementioned supplementary restriction, which must be met to use the Prigogine-Defay ratio for the glass transition.

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Pressure coefficient of the glass transition temperature in the thermodynamic scaling regime

Cited by 24 publications

References 50 publications

Experimental Evidence for a State-Point-Dependent Density-Scaling Exponent of Liquid Dynamics

Experimental Evidence for a State-Point-Dependent Density-Scaling Exponent of Liquid Dynamics

Adam-Gibbs model in the density scaling regime and its implications for the configurational entropy scaling

Thermodynamic consequences of the kinetic nature of the glass transition

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