Thermodynamic Scaling of Molecular Dynamics in Supercooled

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Thermodynamic Scaling of Molecular Dynamics in Supercooled Ibuprofen K. Adrjanowicz,* Z. Wojnarowska, and M. Paluch Institute of Physics, University of Silesia, ul. Uniwersytecka 4, 40-007 Katowice, Poland

J. Pionteck Leibniz Institute of Polymer Research Dresden, Hohe Strasse 6, D-01069 Dresden, Germany ABSTRACT: It was shown recently that ibuprofen revealed a strong tendency to form hydrogen bonded aggregates such as dimers and trimers of either cyclic or linear geometry, which somehow seems to control molecular mobility of that drug [Br
as et al. J. Phys. Chem. B 2008, 112 (35), 11 087
11 099]. For such hydrogen-bonded liquids, superpositioning of dynamics under various temperature T, pressure P, and volume V conditions, when plotted versus the scaling function of T
1 V
γ (where γ is a material constant), may not always be satisfying. In the present work, we have tested the validity of this scaling for supercooled ibuprofen. In order to do that, pressure
volume
temperature (PVT) measurements combined with isobaric and isothermal dielectric relaxation studies (pressure up to 310 MPa) were carried out. The scaling properties of the examined drug were derived from the fitting of the τR(T,V) dependences to the modified Avramov equation and by analyzing in double logarithmic scale the Tg(Vg) dependences, where the glass transition temperature Tg and volume Vg were defined for various relaxation times. In view of the obtained results, we conjecture that for ibuprofen the thermodynamic scaling idea works but not perfectly. The slight departure from the scaling behavior is discussed in the context of the hydrogen bonding abilities of the examined system and compared with the results reported for other strongly associated liquids.

1. INTRODUCTION The history of glasses can be traced back to more than 3000 years ago. Nowadays, glassy materials are ubiquitous in all aspects of daily life. Glassy behavior can be found for a broad group of materials starting from ceramics, polymers, or metallic alloys to soft matter or biological systems. However, despite years of studies and great efforts made by several research groups, the nature of the glass transition itself is one of the most fundamental issues of the modern condensed matter physics (refs 1
5 and refs therein). In order to understand the mechanism of the dramatic slowdown of molecular dynamics on approaching the glass transition, various interpretations of that phenomenon have been proposed (e.g., refs 6
11). It is commonly accepted that an increase of structural relaxation times by many orders of magnitude while cooling reflects two events: (i) a decrease of thermal energy of molecules, which do not have enough energy to jump over the potential barrier, and (ii) an increase of molecular crowding. So, with the study of the relative importance of these two effects governing the dynamics of glass-formers, it is possible to get a complete description of the still puzzling glass transition phenomena. In the last several years, much interest have been paid to find some universal classification scheme of dynamic properties for the variety of glass-forming materials based on differences in their supercooled dynamics while reaching the r 2011 American Chemical Society

glassy state. In this context, it is worthy to mention an empirical fact known as thermodynamic or density scaling, which was successfully applied to many kinds of glass-forming systems and polymers (e.g., refs 12
17). In accordance with thermodynamic (or density) scaling idea, structural relaxation times τR (or any other dynamic property of supercooled system such as viscosity or diffusion coefficient) measured under different conditions of temperature T and pressure p are unique scaling functions F of the quantity Γ, namely, log10 τR ¼ FðΓÞ

ð1Þ

where γ is a scaling exponent, Γ = T
1 V
γ or alternatively Γ = Fγ/T. What is more, with the relaxation times plotted versus the scaling product T
1 V
γ, superposition of data onto one master curve is obtained, irrespective of thermodynamic conditions. The validity of this scaling, with γ = 4, was first observed for o-terphenyl (OTP),18,19 in which intermolecular interaction can be approximately described by the Lenard-Jones (LJ) 6
12 potential (strong, short-range repulsive and weaker, long-range Received: September 24, 2010 Revised: January 18, 2011 Published: April 01, 2011 4559

dx.doi.org/10.1021/jp109135w | J. Phys. Chem. B 2011, 115, 4559–4567

The Journal of Physical Chemistry B attractive forces). The interpretation of the thermodynamic scaling concept is suggested to be linked with the repulsive part of the intermolecular potential, which dominates the local structure while approaching the glass transition, since the attractive forces are negligible in supercooled regime.20 This way of describing dynamic properties of supercooled liquid leads to the inverse power law U(r)
r
3γ.21,22 However, the scaling behavior with exponent γ = 4 predicted for simple LJ liquids is not valid anymore for materials in which the effective intermolecular potential cannot be described in terms the of LJ equation (repulsive term ∼r
12 and attractive term ∼r
6).14 Generally, most of those systems obeyed the scaling relation with γ varying from 0.13 to 8.5.12 In the last several years, it has been proven experimentally that eq 1 works very well for a broad group of materials like polymers, van der Waals liquids, some ionic liquids, and a few H-bonded systems.12
16,23,24 Moreover, in some cases superpositioning of relaxation times when plotted versus T
1 V
γ was found to be satisfying over a broad range of dynamics, from the glass transition regime up to and above the dynamic crossover.15 This type of scaling was supported by results from dielectric, light scattering, and viscosity measurements as well as molecular simulations.12,13,18,25 Until now, the only deviations from the scaling law (eq 1) were observed for some strongly associated systems with strong attractive interactions (like water, propylene glycols with different chain length23,26,27) and few ionic liquids (e.g., verapamil hydrochloride28). As shown recently,27 in strongly associated liquids, specific hydrogen bonded intermolecular interactions are responsible for a breakdown of the thermodynamic scaling law. What is more, removal of H-bonds restores superimposition of relaxation data according to eq 1, along with an increase of the value of the material constant γ. As proposed by Dyre’s group,16,29 viscous liquids which obeyed the scaling power-law (eq 1) can be classified as “strongly correlating liquids”, and those that do not scale are not strongly correlated. Strongly correlated liquids, van der Waals and metallic liquids, exhibit 100% correlation between virial and potential energy fluctuations. For nonstrongly correlated liquids, like hydrogen or covalently bonded as well as strongly ionic liquids, the scaling fails due to competing intermolecular interactions.29 Significant consequences of the thermodynamic scaling idea rely on the fact that the scaling exponent γ has a very important meaning and can be related to other parameters describing dynamic properties of glass-forming liquids. First, it should be noted that the scaling exponent γ is often correlated with the Ev/Ep ratio, being a commonly used measure of the relative contribution of temperature and volume effects on dynamics of supercooled liquids.30 However, the γ parameter itself can be considered as an alternative measure of the relative importance of thermal energy and molecular packing in governing molecular dynamics while approaching the glass transition.14,31,32 The parameter γ is a unique material constant, whose value varies from 0 to ¥. For the scaling exponent γ = 0, purely thermally activated dynamics are expected, while the opposite limited value (γ f ¥) implies dynamic behavior fully dominated by intermolecular free volume. As shown by Casalini and Roland,33 the γ parameter is also related to the isochoric fragility mV. For almost 30 compounds, they found a strong inverse correlation between these two quantities, i.e., the larger γ, the smaller fragility (mV), and vice versa. Finally, the scaling parameter γ can be also used as an indicator of the steepness of an intermolecular repulsive potential.33,34 In the present paper, we have tested the validity of the thermodynamic scaling concept for ibuprofen. To do that, we have performed PVT measurements along with isothermal and isobaric dielectric studies carried out in the pressure range not

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exceeding 310 MPa to avoid significant data extrapolation. The motivation for the current studies takes source from a few issues: (i) the examined drug is of the most essential painkillers widespread around the world, but surprisingly, so far thermodynamic scaling of pharmaceutical systems has not been widely studied, and furthermore (ii) to check the context of the strong tendency of ibuprofen to form hydrogen bonded aggregates, whether their existence is sufficient to cause the breakdown of the scaling law, especially since for some strong hydrogen bonding systems, deviations from eq 1 were observed. The ability of ibuprofen to form noncovalent aggregates, also in the supercooled state, has been studied very recently by Br
as et al.35 They confirmed experimentally by means of infrared spectroscopy and electrospray ionization mass spectrometry that ibuprofen revealed a strong tendency to form hydrogen bonded aggregates such as dimers and trimers of a cyclic or linear structure. From molecular dynamics simulations, it is also known that a significant number of cyclic dimers (43%) and cyclic trimers (31%) among the total number of all dimers and trimers was found, whereas at the same time an insignificant number of cyclic tetramers (