Predicting Nanoscale Dynamics of a Glass-Forming Liquid from Its

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Predicting Nanoscale Dynamics of a Glass-Forming Liquid from Its Macroscopic Bulk Behavior and Vice Versa Karolina Adrjanowicz, Kamil Kaminski, Magdalena Tarnacka, Grzegorz Szklarz, and Marian Paluch J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.6b02974 • Publication Date (Web): 17 Jan 2017 Downloaded from http://pubs.acs.org on January 18, 2017

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The Journal of Physical Chemistry Letters

Predicting Nanoscale Dynamics of a Glass-Forming Liquid from its Macroscopic Bulk Behavior and Vice Versa Karolina Adrjanowicz†§*, Kamil Kaminski†§, Magdalena Tarnacka†§, Grzegorz Szklarz†§ and Marian Paluch†§ †

Institute of Physics, University of Silesia, ulica Uniwersytecka 4, 40-007 Katowice, Poland

§

SMCEBI, ulica 75 Pulku Piechoty 1a, 41-500 Chorzow, Poland

AUTHOR INFORMATION Corresponding Author [email protected]

1 ACS Paragon Plus Environment


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ABSTRACT The properties of a molecular liquid confined at the nanometer length scale can be very much distinct from the bulk. For that reason, the macro- and the nanoscopic behaviors of glass-forming liquids are regarded as two non-connected realms, governed by their own rules. Here, we show that the glassy dynamics in molecular liquids confined to nanometer pores might obey the density scaling relation, ργ/T, just like in bulk fluids. Even more surprisingly, the same value of the scaling exponent γ superposes the α-relaxation time measured at different state points in nanoscale confinement and on increased pressure. We report this remarkable finding for van der Waals liquids tetramethyl-tetraphenyl-trisiloxane (DC704) and polyphenyl ether (5PPE) considered as simple, single-parameter liquids. Demonstrating that the density scaling idea can be fulfilled in both environments opens an exciting possibility to predict the dynamic features of the nanoconfined system close to its glass transition temperature from the high-pressure studies of the bulk liquid. Likewise, we can describe the viscous liquid dynamics at any given combination of temperature and pressure based on the analysis of its behavior in nanopores.

TOC GRAPHIC


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“When we get to the very, very small world we have a lot of new things that would happen (…). Atoms on a small scale behave like nothing on a large scale (....). We have new kinds of forces, and new kinds of possibilities, new kinds of effects (…) All things do not simply scale down in proportion. (…)” said Feynman in 1959 when introducing the concept of manipulating with atoms/molecules at the nanoscale.1 Nowadays, these famous quotes are still very relevant in many areas of nanoscience and nanotechnology, particularly when describing the peculiar behavior of various materials on the atomistic or molecular level. This also includes the dynamics of glass-forming liquids confined at the nanometer scale which is far from that reported for the bulk liquid phase. The most prominent changes in the properties of the molecular liquids confined at the nanoscale involve the shift of the melting and the glass transition temperatures.2,3,4 When confinement effect is achieved by impregnation of the molecular liquid within nanopores, the cooperative dynamics of molecules close to the pore walls is clearly slower than the molecules in the core. In consequence, two glass transition temperatures – two glassy dynamics can be observed.5,6,7 Additionally, when lowering the temperature of the nanoconfined liquid, the αrelaxation process associated with the glassy dynamics of the core molecules becomes suddenly faster than in bulk. As a result, a characteristic crossover from the VFT to the Arrhenius-like dependence of α-relaxation times, τα, is observed. By manipulating with the size of the spatial constraints it is also possible to affect the length scale of cooperative movements associated with the glassy dynamics.8 However, for some of the systems, the glassy behavior was found to be very weakly or even completely unaffected by confinement effects at the nanoscale. Understanding some of these experimental observations, and the behavior of the nanoconfined liquid close to the glass transition temperature Tg is a matter of hot debate.9,10,11,12 But even in the



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absence of geometrical constraints the glass transition phenomenon remains a major unsolved problem in condensed matter physics.13,14,15 The motivation behind the present work is focused on the fundamental problems: Is there any bridge between the dynamics of glass-forming liquids in small - nanoscale and large - bulk scales? What can tie up the most important dynamic features of the glass-forming liquids reported in macro- and nano- worlds to get a consistent picture of their glassy behavior? Another intriguing question is whether the dynamics of nanoconfined liquid in the vicinity of the glass transition temperature can be predicted from the macroscopic behavior of viscous liquid, and vice versa? Here, to address these questions we wish to exploit the idea of the density scaling which is one of the most important and general findings reported for many (bulk) glass-forming materials. So far, it has not been tested for liquids confined at the nanoscale. The density scaling emerges from the high-pressure studies of dynamics in supercooled liquids which can be described through a single scaling relation, ργ/T.16,17 However, behind the experimental observation that a single scaling parameter γ is able to superimpose the dynamics of glass-forming liquids at different thermodynamics conditions, there is also important scientific content. The scaling parameter γ is a material constant related to many dynamic and thermodynamic properties of the system, providing a set of the most relevant information about the intermolecular forces and the key factors responsible for the dynamic behavior of liquid close to Tg.18,19 What is more, for a supercooled liquid which satisfies ργ/T scaling relation, it is possible to describe or even predict with a high accuracy evolution of τα in T-p (T-ρ) space over the entire dynamic range. As a result of that, knowing that a given liquid obeys the density scaling law enable us to map out viscous liquid dynamics at any given condition.20 Testing if, at the nanoscale level, we can superpose the relaxation times from different thermodynamic state


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points could be a strong argument that the dynamics of liquid confined in nanopores follows exactly the same, universal rules as the macroscopic fluid. This might also prove that both environments are not two separate research domains. Confinement at the nanoscale level can be realized in the three different dimensions: (i) one-dimensional confinement refers to thin films, (ii) two-dimensional confinement is provided by rigid walls of the pores or tubes having a nanometric diameter, whereas (iii) threedimensional confinement to microemulsion systems. In this study, we have tested the density scaling concept only in 2D confinement which was achieved by infiltrating investigated samples insides straight cylindrical nanopores of well-defined geometry. For that, we have used anodized aluminum oxide (AAO) membranes which are known to form uniform arrays of unidirectional and non-crosslinking channels. The degree of confinement was modified by varying with the size of the pore (from 150 nm down to 18 nm). Investigated samples are two van der Waals glassforming liquids, DC704 (tetramethyl-tetraphenyl-trisiloxane) and 5PPE (polyphenylether) commercially used as oils for vacuum pumps. The choice of the tested substances was not accidental. Both materials were proven to possess the most important features characteristic for strongly correlating (single-parameter) liquids, developed within the isomorph theory.21,22,23 24,25 This includes the ability to scale the viscous liquid dynamics with a single value of the scaling exponent (γ=6.2±0.2 for DC704 and γ=5.5±0.2 for 5PPE).21,22 From this point of view, both systems seem to be the best candidates to examine if the density scaling relation also holds for liquid confined in nanopores. As a matter of fact, results of MD simulations indicate that the isomorph theory should also work in nanoscale confinement.26 To study the relaxation dynamics in confined geometry, we have employed dielectric spectroscopy. Calorimetry was used to detect



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the glass transition event. More details about investigated materials and experimental protocols that we have used can be found in the Methods Section. We start our investigation by showing typical changes in the relaxation dynamics of van der Waals liquid caused by confining to nanoporous media. Figure 1a presents the temperature dependence of the dielectric α-relaxation time for DC704 confined within AAO nanopores, as well as data taken at atmospheric pressure for a bulk liquid phase. As can be seen, upon lowering the temperature the dynamics of the confined liquid becomes suddenly faster than in bulk. This effect is manifested as a departure of the τα(T) dependence from the Vogel-Fulcher-Tammann (VFT) law. With decreasing the pore size, a characteristic ‘kink’ in the relaxation times occurs for much shorter time scales (i.e. at higher temperatures). Therefore, the most pronounced deviation from the bulk liquid dynamics is observed for DC704 confined in 18-nm pores. Recently, we have demonstrated that the point at which a characteristic departure from the bulklike behavior of α-relaxation time occurs, corresponds to the glass-transition temperature of the interfacial layer (molecules interacting directly with the pore wall).27 On the other hand, the liquid in the core vitrifies at a much lower temperature which can be estimated by extrapolating the resulting τα(T) dependence to longer times. The temperature at which τα=100 s is a typical way of calculating the glass transition temperature Tg from the dielectric data. In the present study, we wish to avoid extrapolation of any data. Therefore, the glass-transition temperature of the ‘core’ liquid, Tg_core, was defined for much shorter times, namely the temperature at which τα=1s. The signatures of the two glassy dynamics under nanoscale confinement (Tg_core and Tg_interface) are also clearly evident in the calorimetric data, as demonstrated for DC704 in Figure 1b. For nanoconfined samples of the same thermal history, we have observed a quite good


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agreement between Tg_core and Tg_interface determined from the dielectric and calorimetric techniques (±2-4 K). Values of Tg_core determined based on the analysis of the dielectric relaxation times are typically slightly higher than Tg_core from DSC calorimetry. The difference is due to the definition of (dielectric) Tg for much shorter times. Here, we wish to note that Tg_interface shows the key features characteristic for the glass transition event, namely (i) it depends on the cooling rate and (ii) we observe a physical aging phenomenon at T< Tg_interface. This we have demonstrated in Figures S1 and S2 (see Supporting Information). The change in the temperature dependence of the α-relaxation time was also observed for 5PPE filled in AAO nanopores (see Supporting Information, Fig. S3). Such effect detected in a more or less pronounced manner is often discussed in terms of crossover from the cooperative (liquid-like) dynamics to Arrhenius-like behavior characteristic for single molecules.

10,28

On the other hand,

it has been recently demonstrated that below Tg_interface the relaxation dynamics of the core molecules enters the isochoric dependence (V=const.) which obviously cannot be portrayed by a single Arrhenius equation.29 Starting from that point, the density of the confined liquid is invariable. To confirm this very important finding, we need to take advantage of studying the bulk liquid dynamics on increased pressure. In agreement with numerous experimental observations, the isochoric τα(T) dependences should always collapse when plotted versus Tg/T.30 In Fig. 2 and Figure S4a, we have prepared the corresponding isochoric scaling plots that include bulk and confined data. The upper inset in Fig. 2 indicates the range of α-relaxation times measured in confined geometry that was used to construct such scaling plot. Experimentally measured τα(T, p) dependencies for both materials as well as volumetric data used to calculate the specific volume of the liquid phase at varying thermodynamic conditions can be found in the



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literature.21,22 Bulk liquid isochores were generated by parametrizing τα(T,V) dependencies with the use of the modified temperature-volume version of the Avramov model.31 Representative evolution of τα in a T-V plane together with the fitting parameters can be found in the Supporting Information (please see Fig. S5). To avoid extrapolation of the τα(T) dependencies, we have determined Tg for the bulk liquid also as a temperature at which τα=1s. As can be seen in Figure 2, all data measured in confined geometry within Tg_core and Tg_interface collapse onto a master curve when plotted versus the reduced temperature, Tg_core/T. This is clear evidence that the molecular liquids inside AAO nanopores form a glass under isochoric conditions. In Fig. S6 we demonstrate that the relaxation dynamics of the core molecules follows below Tg_interface the isochoric dependences irrespectively of the cooling rate. Slower cooling rate (and hence lower Tg_interface) changes only the value of the volume which is fixed below that temperature. In other words, to describe τα(T) dependence below Tg_interface we need to use a slightly different isochore. However, this has no effect on the foregoing analysis (see Supporting Information). As a next step, we have estimated the value of the specific volume that becomes fixed below Tg_interface. For that, we have used parametrized τα(T, V) dependences obtained for the bulk liquid. Isochores describing the evolution of α-relaxation time in nanopores of different sizes were labeled by taking the values of the bulk liquid volume at respective T and τα at which the interfacial mobility was recognized to freeze. This gives the following set of isochores: 0.8882 cm3/g in 150 nm, 0.8907 cm3/g in 55 nm, 0.8917 cm3/g in 35 nm, 0.8932 cm3/g in 18 nm AAO. Dashed lines in Fig. 1a and Fig. S3a demonstrate obtained isochoric dependencies. Now, it is evident that the temperature evolution of the α-relaxation time in confined geometry can be described very well by extrapolating the corresponding isochoric curves from the high (positive)


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range of pressure to a negative pressure domain. The atmospheric pressure isobar separates these two regimes. Knowing the change of the α-relaxation times in nanopores as a function of temperature and volume, we are ready to find the density scaling exponent for confined materials. To do that, we wish to employ a very simple and well-established relation between the glass transition temperature Tg and volume Vg, log10Tg=A-γlog10Vg.32 From this expression, the scaling exponent γ can be determined from the slope of the linear logarithmic dependence Tg(Vg). For isochoric conditions, we use Vg=V. Fig. 2 (the lower inset) and Fig. S4b show the dependence of the glass transition temperature as a function of volume in a log-log plot for confined DC704 and 5PEE. The value of the glass transition temperature associated with the core dynamics along various isochores was defined as a temperature at which τα = 1 s. From the linear regression, we found that the scaling exponent γ is equal to 6.1 for DC70 and 5.5 for 5PPE. The R2 values are 0.99998 and 0.99991, respectively. In the inset of Fig. 2 we also show Vg(Tg) point that refers to the bulk liquid isochore V=0.8833 cm3/g for DC704. As can be seen, it is consistent with the confinement data. The same value of the scaling parameter γ we also obtained from the analysis of the different isochoric dependences for confined DC704 (Tg_interface approached by slow cooling, with the rate 0.5 K/min). Obtained in this way scaling parameters will be used to test the density scaling law for nanoconfined systems. In Figure 3 we have plotted isochoric α-relaxation times measured in AAO nanopores as a function of ργ/T (where ρ=1/V). For comparison with the results obtained in a standard way, we have also included dielectric relaxation time experimentally measured along different isotherms and along the atmospheric pressure isobar. Interestingly, the high-pressure and confinement data fall nicely on a single curve when described in terms of the same scaling 9 ACS Paragon Plus Environment


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variable ργ/T with γ=6.1 for DC704 and 5.5 for 5PPE. Qualitatively, the effect of rate dependence does not affect the principal idea of the present study. Confined DC704 of the different thermal protocol still obey the density scaling relation, and we get a consistent picture of its relaxation dynamics. To make it clearer, in the Supporting Information we have prepared a set of similar figures as that found in the main paper. However, instead of cooling with 10-12 K/min, we have approached Tg_interface at a much slower rate - 0.5 K/min (see Fig. S6c). In this work, we have provided for the first experimental evidence that the density scaling concept can be valid also under conditions of 2D geometrical nano-confinement. However, by taking into account the universal character of the density scaling idea, the result presented in this work has even more important scientific meaning. The same value of the scaling exponent for bulk and confined liquid phases results from the same character of the intermolecular interactions. So, by confining a liquid inside pores of nanometer scale, we are not able to invoke changes in the intermolecular forces related to the glassy dynamics. It is also remarkable that at the nanoscale level, where we expect an entirely different physics, we observe that the viscous liquid dynamics obeys the same rules as the macroscopic fluid. This finding gives us a unique opportunity to access to the fundamental information about thermodynamic and dynamic properties of materials near the glass transition that commonly require the results from the high-pressure experiments. For example, γ relates to Ev/Ep ratio which is a measure of the relative contribution of thermal activation and free volume to molecular dynamics of glassforming liquids.19,33

EV 1 = E p 1 + α PTg γ


(1)

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where EV = R(∂ lnτ α / ∂T −1 )V is the activation energy at constant volume, E p = R(∂ ln τ α / ∂T −1 ) p is the activation energy at constant pressure, and α p = V −1 (∂V / ∂T ) p is isobaric thermal expansion coefficient determined from the volumetric measurements. Ev/Ep ratio is calculated by comparing activation energies of the isochoric and isobaric dependencies of α-relaxation time at the glass transition temperature. For Ev/Ep=1 the glassy dynamics is controlled purely by the thermal effects, while for Ev/Ep=0 by the density effects. The scaling parameter γ can be also related to dTg / dp coefficient which provides information on the pressure sensitivity of the glassy

dynamics34 dT g dp

=

Tg κ T

γ

−1

+ α PTg

(2)

where κT = −V −1(∂V / ∂p)T is isothermal compressibility. From above equations, it is straightforward that knowing the value of Tg at atmospheric pressure, V(T,p) dependence in the bulk liquid, and the scaling exponent determined from the analysis of Tg_core_vs Vg_core dependence, we can predict the high-pressure dynamics of a given glass-forming liquid. In this way, we obtain for DC704 dTg / dp = 222 K/MPa and Ev/Ep=0.49. Meanwhile, values calculated in a traditional way (i.e. from the high-pressure studies) are as follows, dTg / dp = 226 K/MPa and Ev/Ep=0.50. It should be stressed that to be consistent with high-pressure data we have to redefined Tg for bulk DC704 as a temperature at which the α-relaxation time is equal to 100 sec. Taking a full advantage of the density scaling concept, we can also use confinement data to describe the evolution of α-relaxation times at varying thermodynamic conditions. In Fig. 4 we have illustrated that for DC704. Predicted dependence of the α−relaxation times along four different isotherms 228 K, 243 K, 260 K and 297 K was obtained by exploiting the idea of ργ/T



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scaling for relaxation times measured in 18 nm pores within a temperature range between Tg_core and Tg_interface. For comparison, we have also included isothermal data reported in the literature. 21, 22

As can be seen, predicted dependencies match very well the experimental ones. Along the

same line, having access to volumetric and dielectric relaxation studies on increased pressure, and knowing the value of Tg_interface in AAO nanopores of different pore diameters (e.g. from DSC calorimetry) we can estimate the temperature evolution of the α-relaxation times for liquid confined. This we have already demonstrated in Fig. 1a when describing τα(T) dependence in nanopores by using isochoric relaxation times from the high-pressure studies. Predicting glassy dynamics in 2D nanoconfinement from the macroscopic behavior of the liquid (and vice versa) is a consequence of fulfilling by the studied liquids the density scaling relation. For that reason, it could possibly help to find a missing link between the dynamics of glass-forming liquid at the macro- and nanoscales. CONCLUSIONS Summarizing, we show for the first time that the density scaling exponent, related to various physical properties of the materials, can be determined from the analysis of the αrelaxation times in AAO nanopores. The same value of the γ exponent for bulk and confined material results from the fact that the character of the intermolecular interactions remains essentially the same in both environments. This serves as a strong argument that γ, indeed, is related to the intermolecular forces responsible for the glassy behavior. Moreover, this study highlights the important role of the density scaling relation as a key to link and understand the dynamics of glass-forming liquids in the bulk and nanoscale. The γ exponent can tie up the properties of soft matter in the macro- and nanoscales. This study also shows how to access to the most important information about the relaxation dynamics of glass-forming liquids at varying 12 ACS Paragon Plus Environment

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thermodynamic conditions. From a broader perspective, this gives us a useful tool for describing the bulk liquid dynamics on increased pressure from the analysis of its nanoscale behavior, and vice versa. As we suppose, this should apply to all systems which obey the density scaling law. Dimensionality of the spatial constraints and surface interactions have an important impact on the dynamics of the systems subjected to 1D and 2D confinement. Interestingly, in both cases the density equilibration at the interface between substrate and molecules play an important role and has a strong impact on the molecular dynamics. However, it is not established yet if the density scaling idea, described herein to work very well for liquids incorporated in native porous materials, applies also to thin films (1D confinement) with planar substrate interface and free surface. Referring to the introductory paragraph, we expect an entirely different physics to happen under nanometer scale confinement. But when it comes to the dynamics of viscous liquid in nanopores, we see that paradoxically it follows the same rules as the macroscopic fluid. METHODS Materials. Tested samples, DC704 (tetramethyl-tetraphenyl-trisiloxane) and 5PPE (polyphenyl ether), are vacuum pump oils. DC704 (Chemical Formula: C28H32O2Si3, MW: 484,81 g/mol) was purchased from Santa Cruz Biotechnology, while 5PPE (Chemical Formula: C30H22O4, MW: 446,50 g/mol) from Inland Vacuum Industries. Both materials were used as received without further purification. From the dielectric relaxation studies, we have obtained the following values of the glass transition temperature, Tg=210.5 K for DC704 and Tg=244 K for 5PPE (for Tg defined as the temperature at which the α-relaxation time is 100 s). This agrees perfectly well with the literature values, Tg=210 K for DC704 and Tg=245 K for 5PPE.35 Preparation of samples. As confining templates, we have used commercially available anodized aluminum oxide (AAO) membranes (Synkera Technologies, Inc.) composed of uniform arrays of



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unidirectional and non-crosslinking nanopores of different pore sizes (18 nm, 35 nm, 55 nm, 150 nm). Before filling, AAO membranes were dried at 453 K in a vacuum oven to remove any volatile impurities from the nanochannels. Then, they were used to confine investigated van der Waals liquids. For that, AAO membranes were placed in small containers filled with DC704 or either 5PPE. The infiltration procedure was carried out at 314 K under vacuum to let both compounds flow into the nanopores by the capillary forces. Dielectric measurements. Dielectric relaxation studies were carried out by using a Novocontrol alpha analyzer. Nanoporous AAO templates (of 50 µm thickness and 13 mm diameter) filled with investigated liquids were placed between two circular electrodes and measured as a function of temperature in the frequency range 10-2-107Hz. The temperature was controlled with stability better than 0.1 K by Quatro system. Our thermal protocol involved cooling (~10-12 K/min) of the confined material from the room temperature down to the glassy state. Then, dielectric measurements were performed on heating with the rate of 0.5 K/min. Temperature scans for bulk samples at atmospheric pressure were performed as well. Obtained temperature evolution of the characteristic α-relaxation times at 0.1 MPa agrees with the data reported in the literature.36 Calorimetric Measurements. Calorimetric measurements were carried out by using a MettlerToledo DSC apparatus equipped with a liquid nitrogen cooling accessory and an HSS8 ceramic sensor (heat flux sensor with 120 thermocouples). Temperature and enthalpy calibrations were performed by using indium and zinc standards. Crucibles with prepared samples (crushed membranes containing confined samples) were sealed cooled down to 175 K at the rate of 10 K/min. DSC thermograms were recorded on heating with the rate 10 K/min over a temperature range from 175 to 320 K. Tg values were determined as the point corresponding to the midpoint


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inflection of the extrapolated onset and end of the transition curve. The literature value of Tg determined from the calorimetric measurements is 215 K for DC70437 and 263 K for 5PPE38. ASSOCIATED CONTENT * Supporting Information Analysis of the dielectric and calorimetric data obtained for 5PPE confined to AAO nanopores, representative evolution of the τα(T, V) for 5PPE which was described in terms of the modified Avramov equation, the effect of rate dependence on Tg_interface and hence the volume fixed below that temperature, test of the density scaling relation for nanoconfined liquid of the different thermal protocol. The Supporting Information is available free of charge on the ACS Publications website at DOI: AUTHOR INFORMATION Corresponding Authors *E-mail address: [email protected] (KA) Notes The authors declare no competing financial interest. ACKNOWLEDGMENTS KA acknowledge financial support from Ministry of Science and Higher Education within 'Iuventus Plus ' project (0001/IP3/2016/74). KK is thankful for a financial support from the National Science Centre within the OPUS Project (DEC-2015/ 17/B/ST3/01195). REFERENCES

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(3) Jackson, C. L.; McKenna, G. B. The Glass Transition of Organic Liquids Confined to Pores. J. Non-Cryst. Solids 1991, 131-133, 221-224. (4) Roth, C. B.; Dutcher, J. R. Glass Transition and Chain Mobility in Thin Polymer Films. Journal of Electroanalytical Chemistry 2005, 584, 13–22. (5) Park, J. Y.; McKenna, G. B. Size and Confinement Effects on the Glass Transition Behavior of Polystyrene/O-terphenyl Polymer Solutions. Phys. Rev. B 2000, 61, 6667–6676. (6) Le Quellec, C.; Dosseh, G.; Audonnet, F.; Brodie-Linder, N.; Alba-Simionesco, C.; Haüssler, W.; Frick, B. Influence of Surface Interactions on the Dynamics of the Glass Former Orthoterphenyl Confined in Nanoporous Silica. Eur. Phys. J. Special Topics 2007, 141, 11–18. (7) Li, L.; Zhou, D.; Huang, D.; Xue, G. Double Glass Transition Temperatures of Poly (methyl methacrylate) Confined in Alumina Nanotube Templates. Macromolecules 2014, 47, 297−303. (8) Richert, R. Dynamics of Nanoconfined Supercooled Liquids. Annu. Rev. Phys. Chem. 2011. 62, 65-84. (9) Arndt, M.; Stannarius, R.; Gorbatschow, W.; Kremer, F.; Dielectric Investigations of the Dynamic Glass Transition in Nanopores. Phys. Rev. E 1996, 54, 5377. (10) Kremer, F. (ed.) Dynamics in Geometrical Confinement; Springer: New York, USA, 2014. (11) Jackson, C. L., McKenna, G. B.: Vitrification and Crystallization of Organic Liquids Confined to Nanoscale Pores. Chem. Mater. 1996, 8, 2128–2137. (12) Simon, S. L.; Park, J.-Y.; McKenna, G. B. Enthalpy Recovery of a Glass-forming Liquid Constrained in a Nanoporous Matrix: Negative Pressure Effects. Eur. Phys. J. E 2002, 8, 209– 216. (13) Anderson P. W. Through the Glass Lightly. Science 1995, 267, 1610. (14) Seife C. So Much More to Know. . . Science 2005, 309, 78-102. 16 ACS Paragon Plus Environment

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(15) Chang K. Anything but Clear. The New York Times, 2008, July 29. (16) Alba-Simionesco, C.; Cailliaux, A.; Alegria, A.; Tarjus, G. Scaling out the Density Dependence of the α-relaxation in Glass-Forming Polymers. Europhys. Lett. 2004, 68, 58–64. (17) Roland, C. M.; Hensel-Bielowka, S.; Paluch, M.; Casalini, R. Supercooled Dynamics of Glass-forming Liquids and Polymers Under Hydrostatic Pressure. Rep. Prog. Phys. 2005, 68, 1405–1478. (18) Coslovich, D.; Roland. C. M. Thermodynamic Scaling of Diffusion in Supercooled Lennard-Jones Liquids. J. Phys. Chem. B 2008, 112, 1329. (19) Floudas, G.; Paluch, M.; Ngai, K. L. (eds.) Molecular Dynamics of Glass-Forming Systems: Effects of Pressure, Springer-Verlag, Berlin, 2011. (20) Xiao, W.; Tofteskov, J.; Christensen, T. V.; Dyre, J. C.; Niss, K. Isomorph Theory Prediction for the Dielectric Loss Variation Along an Isochrone. J. Non-Cryst. Solids, 2015, 407, 190-195. (21) Gundermann, D.; Pedersen, U. R.; Bailey, N. P.; Jakobsen, B.; Christensen, T.; Olsen, N. B.; Schrøder, T. B.; Fragiadakis, D.; Casalini, R.; Roland, C. M.; Dyre, J. C.; Niss, K. Predicting the Density Scaling Exponent from Prigogine-Defay Ratio Measurements. Nature Physics 2011, 7, 816. (22) Gundermann, D. Testing Predictions of the Isomorph Theory by Experiment, PhD Thesis Roskilde University, Danmark, 2013. (23) Jakobsen, B.; Hecksher, T.; Christensen, T.; Olsen, N. B.; Dyre,J. C.; Niss, K. Communication: Identical Temperature Dependence of the Time Scales of Several Linear Response Functions of Two Glass-Forming Liquids. J. Chem. Phys. 2012, 136, 081102.



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(b)

(a) 2

DC704 Tg=214 K

bulk

0

88 3 cm

3

/g

0. 0. 88

82

bulk (0.1 MPa) 150 nm 55 nm 35 nm 18 nm V=0.8833 cm3/g V=0.8882 cm3/g V=0.8907 cm3/g V=0.8917 cm3/g V=0.8932 cm3/g

V=

-4

Tg_interface -6

0.0044

0.0048

Tg_interface = 225 K

Heat Flow (a.u.)

cm

3

/g

Tg_core

3

-2 V=

log10(τα/s)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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150 nm

Tg_core= 207 K Tg_core = 202 K Tg_interface= 231 K

55 nm

Tg_core= 198 K Tg_interface= 233 K

35 nm Tg_core= 195 K Tg_interface= 237 K

0.0052

180

200

1/T (K-1)

220

240

260

18 nm 280 300

T (K)

Figure 1. (a) The α-relaxation time versus inverse temperature for DC704 in the bulk (open symbols) and confined to AAO templates of different sizes (pore diameter from 150 nm to 18 nm). Solid line denotes VFT fit of τα(T) dependence for the bulk liquid. Dashed lines are isochoric dependences of α-relaxation times determined based on the high-pressure dielectric relaxation and pVT data. Arrows indicate the glass transition temperature of the interfacial layer (Tg_interface) and the ‘core’ liquid (Tg_core). Panel (b) presents the corresponding DSC thermograms obtained for bulk and confined samples. 20 ACS Paragon Plus Environment

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0

DC704 3

0

log10(τα/s)

1

-1 -2

-2

V=

0 V=

8 0.

8 .8

3 83

cm 3

82

cm

/g

Tg_core bulk (0.1 MPa) 150 nm 55 nm 35 nm 18 nm V=0.8833 cm3/g V=0.8882 cm3/g V=0.8907 cm3/g V=0.8917 cm3/g V=0.8932 cm3/g

/g

-4

Tg_interface 0.0044

0.0046

0.0048

0.0050

-1

1/T (K )

-3

2.33

log10(Tg_core/K)

log10(τα/s)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


-4 -5

bulk (V=0.8830 cm3/g) 150 nm 55 nm 35 nm 18 nm

-6 0.85

Tg_core=T(τα=1s) bulk

2.32 150 nm 55 nm 35 nm

2.31 2.30 18 nm

2.29 0.048

0.050

0.052

slope γ=6.1 0.054

log10(Vg/cm3g-1)

0.90

0.95

1.00

Tg_core/T

Figure 2. Scaling of the isochoric α-relaxation times vs. Tg_core/T as obtained for DC704 confined to AAO templates of pore diameter from 150 nm to 18 nm. Isochore V=0.8833 cm3/g generated based on high-pressure data for the bulk liquid phase is shown as well. Lower inset: Dependence of the glass transition temperature Tg_core vs the glass-transition volume Vg_core (for isochores Vg_core =V) in double logarithmic scale obtained for DC704 confined to AAO nanopores. From the slope, we get the scaling exponent γ=6.1. Upper inset indicates τα(T) dependences measured in confined geometry (within Tg_core and Tg_interface) that were used to construct the scaling plot present in the main panel. 21 ACS Paragon Plus Environment


log10(τα/s)

(a)

DC704

high-pressure data 0.1 MPa 228 K 243 K 260 K 297 K data for confined system 150 nm 55 nm 35 nm 18 nm

2 0 -2 -4 -6

γ=6.1

-8 7

8

9

10

γ

1000∗ρ /T

(b) 2

5PPE

high-pressure data 0.1 MPa 268 K 284 K 297 K 314 K

0

log10 (τα/s)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 22 of 23

-2

γ=5.5

data for confined system 18 nm 35 nm 80 nm 150 nm

-4 -6 -8 9

10

11

12

13

γ

1000*ρ /T Figure 3. The dielectric relaxation time τα as a function of ργ/T with (a) γ=6.1 and (b) γ=5.5 for DC704 and 5PPE, respectively. Confinement data include τα(T) dependencies measured in the temperature range between Tg_core and Tg_interface. Isobaric and isothermal data from the highpressure studies are shown as well. These data were taken from the literature. 21,22


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Predicted based on density scaling relation and τα(T) dependance measured in 18 nm pores 228 K

243 K

260 K

297 K

2 1

Experimental data 228 K 243 K

DC704

260 K

297 K

0 -1

log10(τα/s)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


-2 -3 -4 -5 -6 -7 1.12

1.13

1.14

1.15

1.16

1.17

1.18

1.19

1.20

ρ(g/cm3)

Figure 4. Evolution of α-relaxation time as a function of density for DC704 (open symbols) predicted by using confinement data and the density scaling relation. Experimentally measured isothermal dielectric data were taken from the literature (filled symbols). 21, 22


Predicting Nanoscale Dynamics of a Glass-Forming Liquid from Its

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