Evaluation of Growth Front Velocity in Ultrastable Glasses of

Article pubs.acs.org/JPCB

Evaluation of Growth Front Velocity in Ultrastable Glasses of Indomethacin over a Wide Temperature Interval Cristian Rodríguez-Tinoco,† Marta Gonzalez-Silveira,*,† Joan Ràfols-Ribé,† Aitor F. Lopeandía,† Maria Teresa Clavaguera-Mora,† and Javier Rodríguez-Viejo*,†,‡ †

Grup de Nanomaterials i Microsistemes, Departament de Física, Universitat Autònoma de Barcelona, 08193 Bellaterra, Spain MATGAS Research Centre, Campus UAB, 08193 Bellaterra, Spain

‡

ABSTRACT: Ultrastable thin film glasses transform into supercooled liquid via propagating fronts starting from the surface and/or interfaces. In this paper, we analyze the consequences of this mechanism in the interpretation of specific heat curves of ultrastable glasses of indomethacin for samples with varying thickness from 20 nm up to several microns. We demonstrate that ultrastable films above 20 nm have identical fictive temperatures and that the apparent change of onset temperature in the specific heat curves originates from the mechanism of transformation and the normalization procedure. An ad hoc surface normalization of the heat capacity yields curves which collapse into a single one irrespective of their thickness. Furthermore, we fit the surface-normalized specific heat curves with a heterogeneous transformation model to evaluate the velocity of the growth front over a much wider temperature interval than previously reported. Our data expands previous values up to Tg + 75 K, covering 12 orders of magnitude in relaxation times. The results are consistent with preceding experimental and theoretical studies. Interestingly, the mobility of the supercooled liquid in the region behind the transformation front remains constant throughout the thickness of the layers.

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INTRODUCTION Highly stable glasses produced by physical vapor deposition are receiving increased attention since their discovery in 2007.1−4 The enhanced surface mobility of molecules at free surfaces during deposition is thought to be at the core of the increased thermodynamic stability of these materials. In fact, the existence of highly mobile regions in the vicinity of free surfaces with diffusivity values as high as 106 times the bulk diffusivity has been demonstrated in organic glasses at temperatures near the glass transition temperature (Tg).5 Highly stable glasses are located much lower in the potential energy landscape than any glass obtained by cooling the liquid in human time scales.2 Their exceptional stability impacts many of the striking properties of these glasses, among them the differentiated mechanism by which these glasses transform into the liquid. In general, glasses transform into a supercooled liquid by a process that occurs throughout the volume of the sample. However, vapor-deposited highly stable glasses show different features. Their higher density, compared to conventional (cooled at 0.16 K/s) glasses,6,7 has remarkable implications in the transformation of the glass into a supercooled liquid when temperature is raised. Molecular packing is so tight in the bulk of the material that the transformation starts at regions where molecular mobility is higher, i.e., surfaces or interfaces. A propagation front has been directly identified by secondary ion mass spectrometry8,9 and indirectly by dielectric relaxation10 and ac nanocalorimetry.11 These previous experiments in highly stable glasses of indomethacin (IMC) and α,α,β-tris-naph© 2014 American Chemical Society

thylbenzene (TNB) demonstrated the existence of growth fronts parallel to the surface and were able to determine the temperature dependence of the growth front velocity in a reduced temperature range.9−11 In highly stable glasses of IMC, bulk transformation dominates the conversion into the liquid for thicknesses above 1 μm, whereas the heterogeneous, surface-initiated, mechanism dominates at smaller thicknesses.11 Propagation front velocities are 0.1 to 0.01 molecular diameters per τα.9 These data are consistent with several models and theories that have been developed to explain this striking behavior. In the framework of the random first order transition (RFOT) theory, the transformation of a glass into a liquid can be governed by homogeneous and heterogeneous mechanisms in agreement with experimental observations. The speed of the propagating front is directly related to the mobility of the supercooled liquid behind the front. The strong temperature dependence of the growth front velocity and a small influence of stability have been predicted using RFOT.12,13 Furthermore, Leonard and Harrowell used a facilitated kinetic Ising model to show, in agreement with experimental observations, that, for stable films with low fictive temperatures, the temperature dependence of the front propagation is mainly determined by the relaxation time of Received: July 8, 2014 Revised: August 1, 2014 Published: August 8, 2014 10795

dx.doi.org/10.1021/jp506782d | J. Phys. Chem. B 2014, 118, 10795−10801

The Journal of Physical Chemistry B

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Figure 1. SEM (top) and AFM (bottom) images of films with a nominal thickness of 5 nm (left) and 20 nm (right).

thicknesses of 20−120 nm were evaluated in situ inside the growth chamber with nanocalorimetry. The error in temperature for these two techniques is around ±0.05 K for the DSC and ±1.5 K for the nanocalorimetry measurements. Films thicker than 200 nm were deposited on aluminum foil, which was folded and introduced in the aluminum pan of the DSC. In this way, it was possible to measure samples with a total mass above 0.5 mg, enough to produce reliable calorimetric traces due to the large enthalpy excess characteristic of ultrastable glasses. The aluminum foil presents no transformations in the temperature range under study. Two consecutive heating ramps from 283 up to 356 K were always performed. Both heating and cooling were mainly carried out at 0.16 K/s. Thus, the first heating curve corresponds to the asdeposited glass (AD), while the second is representative of a conventional glass. A simplified procedure was used to convert the raw, power, calorimetric data to heat capacity values: for each specific mass and after baseline subtraction, the well documented specific heats of the glass and the liquid17 are imposed to the measured calorimetric signal, converting it to specific heat. The approach yields curves in excellent agreement with those obtained using more cumbersome procedures, which become necessary when the specific heats are not wellknown. Neglecting the small variation of heat capacity of the highly stable glass compared to a conventional glass (3−4% decrease in Cp for the glass deposited at 0.85 Tg11) does not affect the analysis of the transformation growth front and introduces an error at most of 2 K in the evaluation of the fictive temperature, which is lower than the error due to mass indetermination. The heat capacity of very thin films (20−120 nm) was measured by quasi-adiabatic nanocalorimetry in differential mode.16,18 This technique relies on the use of membrane-based microcalorimeters to attain high heating rates ((0.1−1) × 105 K/s), achieving very high sensitivities.16 Samples are deposited on an aluminum plate of 200 nm previously grown on the sensing area of the device (1 mm2). The aluminum layer

the liquid. The front travels at constant velocity with no induction time.14 Previous experiments have been mostly performed at constant temperature and in a limited temperature range a few degrees above the glass transition temperature of the conventional glass (up to Tg + 15 K). In this paper, we analyze the transformation kinetics using scanning calorimetry under continuous heating experiments. The heating rate spans 8 × 10−3 to 5 × 104 K/s, covering a temperature range of Tg + 10 K to Tg + 75 K.

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EXPERIMENTAL METHOD IMC films with thicknesses ranging from 20 nm to 4 μm were deposited by physical vapor deposition at a growth rate of 0.1 nm/s in an UHV chamber with a base pressure of 3 × 10−8 mbar. Sublimation of crystalline IMC was controlled with an effusion cell from CREATEC, and the deposition rate was monitored with a quartz microbalance located nearby the sample holder. A liquid nitrogen cold trap was installed to quench water molecules, improving the vacuum quality. The substrate temperature was controlled by means of a temperature controlled homemade socket. Highly stable films were grown at 266 ± 0.5 K, 0.85 Tg. IMC crystalline powder (99.9% purity) was acquired from Sigma-Aldrich and used without further purification. It is experimentally challenging to modify the glass transition temperature along a very wide temperature range. Here, we circumvent this difficulty by using a combination of calorimetric techniques, from standard differential scanning calorimetry (heating rate: β ≥ 8 × 10−3 K/s) to fast-scanning nanocalorimetry (β ∼ 5 × 104 K/s).15,16 In this way, we evaluate the kinetic parameters that control the transformation of the highly stable IMC glass into a supercooled liquid in a temperature range spanning more than 60 K up to Tg + 75 K, well above those previously measured. Films with thicknesses ranging from 200 nm to 4 μm were measured ex situ in a differential scanning calorimetry system, PerkinElmer DSC7, whereas those with 10796



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shift of the curves that reflects an apparent variation of the glass transition temperature with thickness is clearly appreciated. This effect seems counterintuitive, since the films have thicknesses above 200 nm, well above the thickness range where one could expect size effects in glasses of small molecules. We note that mass normalization equally weights the whole sample and it is mainly valid for bulk reactions that transform the whole sample volume. However, highly stable glasses convert to liquid through a heterogeneous mechanism with a growth front that originates at the surface of the film and/or at the interface with the substrate. In that case, the normalization of the experimental data should incorporate the area of the sample, since it controls the fraction of sample that transforms per unit time. To carry out the new normalization procedure to the DSC data, we first consider that the experimental heat capacity, Cexp p (T), can be decomposed into three terms: the contributions from the glass and from the liquid and the excess enthalpy, evaluated for each temperature. Thus, Cexp p (T) can be written as

homogenizes the temperature of the sensing area, improving the temperature resolution of the calorimetric signal. A first scan, performed at a heating rate around 5 × 104 K/s, provided the calorimetric trace of the AD glass. After passive-cooling at 500 K/s, the sample is scanned several times at the same rate in order to obtain the heat capacity of the fast-cooled (FC) sample with improved resolution. For the thinner samples, multiple depositions and data averaging were required in order to obtain a reliable signal for the AD glass. The raw voltage data of the calorimetric chips acquired in differential mode during the temperature up scans is converted to heat capacity. For each sample, the mass was determined by considering that the specific heat of the liquid was in all cases equal to the one reported by Shamblin et al.17 The morphology of the thinnest films was analyzed by fieldemission scanning electron microscopy (SEM) and atomic force microscopy (AFM) in tapping mode.

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RESULTS The continuity of the very thin IMC films depends strongly on the interaction with the underlying substrate. Growth on an Al surface yielded discontinuous films for nominal thicknesses below 20 nm, while those above 20 nm had almost complete coverage and are considered continuous in this work. Figure 1 displays SEM and AFM images of those films. The analysis that follows is based on films that are continuous on the substrate surface. Figure 2a shows the raw calorimetric traces measured by DSC for highly stable IMC films ranging in thickness from 200 nm to 4 μm. Specific heat is typically evaluated by normalization of the heat capacity by the total mass of the sample. The result of such a procedure is shown in Figure 2b. A

⎛ d x (T ) ⎞ C pexp(T ) = mo ⎜cpg(1 − xl(T )) + cpl xl(T ) + Δh l ⎟ ⎝ dT ⎠ (1)

cgp

clp

where and denote, respectively, the specific heat of the glass and the supercooled liquid, mo is the total mass of the sample, Δh is the excess specific enthalpy, and xl is the fraction of glass that has already transformed into supercooled liquid. Thus, xl is time/temperature dependent and ranges from 0 to 1. No change in density, ρ, between the glass and the liquid has been considered in this simplified approach. If we take into account that the transformation into the supercooled liquid occurs by a parallel growth front, we can rewrite eq 1 substituting: (a) the total mass by the product mo = doAρ, where A is the surface area and do is the total thickness of the film, and (b) the transformed fraction by xl = dl/do, where dl is the thickness of glass that has already transformed into the liquid. A comparison between all the curves is only possible when removing from the right-hand side of eq 1 the parameters that are not common to all samples, i.e., A and do. Equation 1 can be rewritten as cpnorm(T )

=

C pexp(T ) ρA

− cpgdo

= dl(T )(cpl − cpg) + Δh

d(dl(T )) dT

(2)

Figure 2c shows the calorimetric heat capacity curves after applying the parallel front normalization stated in eq 2. The inset in Figure 2c illustrates that the onsets of the calorimetric traces of the various samples overlap into a single curve for thicknesses below ∼900 nm. This coincidence confirms that, within the experimental uncertainty, the transformation rate scales with the surface of the film. The temperature variation at the end of the transformation clearly depends on the sample thickness and is compatible with a mechanism where the extent of the transformation is dominated by parallel growth fronts. Figure 2c also reveals that it is not straightforward to define an onset temperature for the glass transition when the transformation mechanism does not occur simultaneously in the whole sample. As stated above, surface normalization is more suited when the predominant transformation mechanism is via a heteroge-

Figure 2. (a) Mass normalized DSC power output for samples of different thickness (in nm) as a function of temperature, measured at 0.16 K/s. The curves are shifted for clarity. (b) Specific heat (Cexp p /mo) vs temperature. (c) Surface-normalized heat capacity vs temperature highlighting the heterogeneous mechanism of transformation. The inset shows a close-up of the first stages of the transformation into the supercooled liquid, when the growth front dominates. 10797



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neous mechanism starting at surfaces/interfaces, which, in agreement with previous observations, occurs for thicknesses below 1 μm.11 Above this thickness, the bulk transformation is not negligible and the normalization procedure of eq 2 is no longer valid. Figure 2c illustrates that samples thicker than 1 μm have a steeper slope when the bulk starts to transform and the two mechanisms contribute to the growth of the supercooled liquid. This is due to the fact that, once a second transformation mechanism sets in, the sample transforms faster. On the other hand, when normalizing every sample by its mass, in the case of thick films where the bulk transformation dominates, mass normalization is more accurate. In this case, the curves begin to collapse to a single one, as can be observed in Figure 2b by the asymptotic behavior of the peak maxima as the thickness increases. We now focus our attention to calorimetric data obtained by quasi-adiabatic fast scanning nanocalorimetry on thinner films, between 20 and 120 nm. Figure 3 demonstrates the impact of the stability of the glass on the transformation mechanism. The mass-normalized specific heat of samples of different thicknesses grown at 0.85 Tg (as-deposited, AD) and obtained from the liquid (fast-cooled, FC) are plotted in parts a and c of Figure 3, respectively. The data of Figure 3a reproduce the behavior observed in the DSC scans; that is, the mass normalization introduces an apparent dependence of the onset temperature with sample thickness. On the contrary, normalizing by the surface area produces the collapse of all curves to a common onset of the transformation that can be described by a parallel growth front mechanism (Figure 3b). In this thickness range and at these heating rates, the propagation of the growth front dominates the transformation of the entire glass into the supercooled liquid. On the contrary, FC glasses (Figure 3c,d) exhibit the opposite behavior. Mass normalization produces the collapse of all curves into a single, master curve, irrespective of their thickness, while the surface normalization yields curves with different onsets. In FC glasses, the transformation takes place homogeneously in the volume of the sample and the transformed fraction per unit time is independent of the total mass/volume of the film, and therefore of its thickness/surface. In the past, the difference in the specific heat between AD and FC thin film glasses of toluene was attributed to the presence of size effects, since there was an apparent variation of the onset temperature with thickness.19 While we still do not rule out the presence of size effects for ultrathin films of highly stable glasses, the observed variation could be attributed to a change in the transformation mechanism. A remarkable characteristic of the data in Figure 3 is that the high heating rates used in the nanocalorimetry scans drive the glass transition temperature to much higher values compared to conventional DSC data. Another interesting feature when comparing parts a and b of Figure 3 with parts c and d of Figure 3 is the different temperature range of the onset of the glass transition between AD and FC glasses. In a 120 nm thick AD highly stable glass, the maximum of the calorimetric peak occurs at 391 K, while for the same thickness of a FC glass the maximum is located at 357 K. This behavior is similar to what is observed at slower heating rates with conventional calorimetry. A possible dependence of the thermodynamic stability of the glass on the thickness of the films can be analyzed by calculating the limiting fictive temperature, Tf. Figure 4 shows the values obtained for Tf as a function of thickness for ultrastable and fast-cooled IMC films. Tf values were obtained

Figure 3. Heat capacity curves of IMC glasses versus temperature obtained by nanocalorimetry: (a) Mass-normalized specific heat and (b) surface-normalized heat capacity of highly stable IMC thin film glasses. (c) Mass-normalized specific heat for fast-cooled glasses and the effect of surface normalization on these curves (d). The heating rate in all cases is 5 × 104 K/s. Legend: the thickness of the films in nm.

by integration of the specific heat data to yield enthalpy plots. In a plot of H vs T, Tf is derived as the intersection between the extrapolation of the liquid line and the glass line (see inset in Figure 4). This method is very sensitive to experimental uncertainties. A small indetermination in the mass of the sample can introduce errors of several degrees. This uncertainty is usual when working with thin films, and therefore, the Tf values have a significant error. The difference in fictive temperature between AD and FC samples highlights the strong variation in thermodynamic stability. While a glass cooled from the liquid at 0.16 K/s has Tf = 315 K,20 the value for the highly stable glass deposited at 0.85 Tg at 0.1 nm/s decreases to Tf = 281 K, 34 K below. On the contrary, Tf(FC) = 330 K due to the fast cooling used for their preparation. As expected, the fictive temperature evaluated from heating scans is independent of the heating rate, and DSC and nanocalorimetry data yield similar values. Figure 4 also illustrates that the stability of the glass does not depend on the thickness of the sample in the 10798



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Figure 4. Fictive temperature, Tf, as a function of film thickness for highly stable (black) and FC (red) IMC glasses evaluated from nanocalorimetry (circles) and DSC (down triangles) data. As a reference, a black dotted line denotes the fictive temperature of a conventional glass, cooled at 0.16 K/s. Inset: Calculation of the fictive temperature from the intersection of the enthalpy of the supercooled liquid with the integral of the specific heat.

range 20−4000 nm. Continuous films of lower thickness should be produced to test this behavior for ultrathin layers. The transformation rate can be extracted from the heat capacity curves by introducing the experimental data in the left side of eq 1 and solving the differential equation. If the transformation is surface-initiated and propagates parallel to the surface, the transformation rate and the derivative term of eq 1 are related by vgr =

d(dl) dx = βd 0 l dt dT

Figure 5. (a) Transformation speed as a function of temperature for films with thicknesses from 20 nm to 4 μm evaluated from nanocalorimetry and DSC data using eq 3. (b) Velocity of transformation vs relaxation time. Continuous lines: this work. Symbols: blue circles, data from SIMS;9 violet circles, data from dielectric spectroscopy;10 red square, data from ac nanocalorimetry.11 The value in the graph indicates the initial thickness (from the surface) at which the velocity of the transformation is evaluated. In both graphs, the black dashed line corresponds to the function vgr = 0.1·τ−0.78, where τ = τo exp(DTo/(T − To)) is the VFT fit of the relaxation time using the bulk values for IMC.21

(3)

When solving eq 1, the excess enthalpy is obtained by imposing that xl must go from 0 (glass) to 1 (supercooled liquid). The results shown in Figure 5a correspond to a growth front velocity as a function of temperature. Since the glass transition is a kinetic event with a Tg that shifts to high temperatures as the heating rate is increased, we probe a much wider temperature interval than previously explored through isothermal scans. The transformation speed is derived for films ranging in thickness from 20 nm to 4 μm and heating rates from 8 × 10−3 to 5 × 104 K/s. In the case of the thicker films measured by DSC at low heating rates, we have only considered the temperature range where the transformation is dominated by a parallel growth front, i.e., the first stages of the calorimetric trace. Samples of different thickness collapse into a single curve in the region 325−340 K. In those measurements, we neglect the velocity values derived from the first few nm close to the surface of the films, since the DSC data is not very precise at this scale. Therefore, the represented data in the range 325− 340 K correspond to depths from 20 nm to approximately 400 nm. While most DSC data was evaluated at 0.16 K/s, several experiments at 8.3 × 10−3 K/s permitted transformation velocities to be obtained down to lower temperatures (red line in Figure 5b). Similarly, samples evaluated from fast-scanning data collapse into a single curve in the region 365−390 K. That is, our data spans from Tg + 10 K to Tg + 75 K or, equivalently, more than 8 orders of magnitude in relaxation times (Figure 5b), which permits a thorough analysis of the growth front velocity in terms of the relaxation dynamics of the liquid. To our knowledge, this is the first time that calorimetric data can

be used to follow the correlation between transformation rate and the alpha relaxation dynamics over such a broad temperature range. Our data complement previous values obtained isothermally up to Tg + 12 K by secondary ion mass spectrometry9 (SIMS) dielectric spectroscopy10 and nanocalorimetry.11 As shown by the dashed lines in Figure 5, the experimental data is well represented by vgr = Cτα, considering that τ follows the VFT relation of the alpha relaxation in bulk IMC, τ = τ0 exp(DTo/(T − To)). We use the parameters log τo = −19.36, To = 234 K, and D = 17, deduced by Paluch et al.21

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DISCUSSION The strictly linear relationship between log(vgr) and log(τ) in Figure 5b in a very wide temperature (relaxation time) range emphasizes that the transformation speed is mostly driven by the mobility of the liquid. This observation agrees with theories based on kinetic facilitation models that are based on the idea that the mobility of a region depends on the mobility of the adjacent regions. That is, an immobile, glassy, region can become mobile, liquid, only if a very mobile region neighbors it.14,22 In this framework, the velocity of the transformation front will mainly depend on the mobility of the liquid behind the liquid/glass interface.12 If we assume that the transformation into the liquid is initiated at surfaces/interfaces and is planar, we can assimilate the transformation velocity with a growth front velocity on the 10799



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whole area A. The velocity of the transformation evaluated from calorimetric data scales as vgr = Cτα with α = −0.78 and C = 0.1 (black dashed line in Figure 5b, vgr in nm/s). In spite of the uncertainty in the front speed of every line in Figure 5b, the wide temperature range analyzed lowers the error on the slope compared to previous works. We estimate the error as ±0.01. Extrapolation to lower temperatures matches with previous front speed measurements on ultrastable IMC glasses by dielectric spectroscopy10 and ac nanocalorimetry.11 The slope agrees within the experimental uncertainty with previous data obtained by SIMS by Ediger and co-workers (α = −0.85 ± 0.06).9 Remarkably, the evaluated exponent, around 0.8, holds for a very wide temperature range spanning almost 80 K and 12 orders of magnitude in relaxation time and it is independent of the experimental technique or the heating rate. The failure of the Einstein−Stokes relationship has been previously reported in a number of molecular glasses, including indomethacin.9 Obviously, the calorimetric signal during the conversion of glass to supercooled liquid is proportional to the transformed fraction and does not directly probe the existence of one or two propagation fronts. The different value of the parameter C, which corresponds to a higher transformation speed, compared to SIMS data9 and the coincidence of our low temperature values with the dielectric spectroscopy data10 suggest that our transformation occurs through a double front that initiates both at the free surface and at the interface with the substrate. The two fronts hypothesis provides a growth front velocity that halves the one estimated in the case of just one front propagation. The sensitivity of the nanocalorimetric technique permits evaluation of the growth front velocity, and hence the liquid mobility, from the first stages of the transformation, i.e., from the near-surface/interface regions. Therefore, our higher temperature data can be used to compare mobility at different depths, from regions near free surfaces/interfaces to the interior of the film. The curves of Figure 5 in the region 360−390 K show that the growth front velocity strictly follows the VFT fit previously evaluated, which basically means that the mobility of the liquid region behind the liquid/glass interface remains constant irrespective of the position in the film. That is, the growth front velocity is independent of the thickness of the film. If we consider two transformation fronts, the constancy of the front speed from the very first few nm of the transformation requires both fronts to start almost simultaneously at the same temperature. Otherwise, we should observe a change in the growth front velocity, i.e., an acceleration of the transformation rate, when the second front starts the propagation. This observation is consistent with the lack of complete coverage during the first stages of the deposition (Figure 1a), which is the result of a weak interaction between the IMC molecules and the Al surface. In fact, a weak interaction with the substrate may accelerate the dynamics in the liquid region near the substrate, as has been recently reported from molecular dynamics simulations.23 On the basis of these premises, it is reasonable to think that both fronts could be initiated at approximately the same temperature. As outlined above, the high temperature data clearly shows the growth front velocity is thickness independent from the very first nm of the transformation (Figure 5b). This observation is compatible with two related scenarios: (i) the existence of a liquid-like layer with enhanced mobility with respect to the glass even in this temperature range or (ii) the crossing of surface diffusion and bulk diffusion in the

supercooled liquid at the very high temperatures of the nanocalorimetry experiments. With respect to the first possibility, in effect, if a liquid layer with enhanced mobility exists at the surface/interfaces, as suggested in recent experiments,5,24 the first stages of the transformation observed by nanocalorimetry would involve the molecules that are already buried in the interior of the film, i.e., beneath this liquid-like layer. Therefore, neighboring molecules will remain identical independently of their position within the film. Mobility would always reflect a bulk property, and the transformation velocity remains constant throughout the thickness of the layer. The second scenario relates to the comparison between surface and bulk dynamics at temperatures far above 315 K, the glass transition temperature of the conventional glass when heating at 0.16 K/s. As surface mobility has activation energies half the value of liquid mobility,5 it may well be that the nanocalorimetric measurements are actually probing the transformation of the molecules that are at the surface, but the similarity of surface and liquid diffusion at these very high temperatures leads to a thickness independent mobility. However, although we are not aware of surface mobility data in this temperature range, both RFOT25 and the coupling model (CM)26 predict a temperature crossing between surface and liquid bulk relaxation times at high temperatures. Calculated values yield τs = τb in the region around 460−470 K, much higher than the experimentally accessed temperatures by nanocalorimetry. That is, at 360−380 K, the surface relaxation times are still faster than the liquid by several orders of magnitude. Although not conclusive, the hypothesis of the existence of a liquid-like layer seems more feasible to account for the observed thickness independent growth front velocity. Since the calorimetric chips permit very fast stabilization times, isothermal measurements may prove useful to evaluate the impact of surface mobility. Further experiments are underway to explore this timely issue.

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CONCLUSIONS We have shown for the first time that heat capacity data obtained during temperature scans can be very valuable to extract information about the transformation kinetics in highly stable glasses that transform into the liquid through a heterogeneous surface/interface initiated mechanism. Our calorimetric data also revealed that standard mass normalization of the heat capacity yields specific heat curves that exhibit apparent dependencies of the glass transition temperature on film thickness. A new normalization procedure that incorporates the area and the thickness of the film correctly describes the surface initiated transformation. The new data extend by many orders of magnitude previous evaluations of the growth front velocity and permit the extraction of a clear dependency of the front velocity on the mobility of the supercooled liquid.

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. Notes

The authors declare no competing financial interest. 10800



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Stability of Ultrathin Vapor Deposited Glassy Films of Toluene. J. Phys. Chem. Lett. 2010, 1, 341−345. (20) Kearns, K. L.; Swallen, S. F.; Ediger, M. D.; Sun, Y.; Yu, L. Calorimetric Evidence for Two Distinct Molecular Packing Arrangements in Stable Glasses of Indomethacin. J. Phys. Chem. B 2009, 113, 1579−1586. (21) Wojnarowska, Z.; Adrjanowicz, K.; Wlodarczyk, P.; Kaminska, E.; Kaminski, K.; Grzybowska, K.; Wrzalik, R.; Paluch, M.; Ngai, K. L. Broadband Dielectric Relaxation Study at Ambient and Elevated Pressure of Molecular Dynamics of Pharmaceutical: Indomethacin. J. Phys. Chem. B 2009, 113, 12536−12545. (22) Wolynes, P. G. Spatiotemporal Structures in Aging and Rejuvenating Glasses. Proc. Natl. Acad. Sci. U. S. A. 2009, 106, 1353−1358. (23) Haji-Akbari, A.; Debenedetti, P. G. The Effect of Substrate on Thermodynamic and Kinetic Anisotropies in Atomic Thin Films. J. Chem. Phys. 2014, 141, 024506. (24) Brian, C. W.; Zhu, L.; Yu, L. Effect of Bulk Aging on Surface Diffusion of Glasses. J. Chem. Phys. 2014, 140, 054509. (25) Stevenson, J. D.; Wolynes, P. G. On the Surface of Glasses. J. Chem. Phys. 2008, 129, 234514. (26) Capaccioli, S.; Ngai, K. L.; Paluch, M.; Prevosto, D. Mechanism of Fast Surface Self-Diffusion of an Organic Glass. Phys. Rev. E 2012, 86, 051503. (27) Bhattacharya, D.; Sadtchenko, V. Enthalpy and high temperature relaxation kinetics of stable vapor-deposited glasses of toluene. arXiv 2014, http://arxiv.org/abs/1406.4562.

ACKNOWLEDGMENTS This work was financially supported by the Spanish MINECO MAT2013-40896-P and by 2009SGR-1225 from Generalitat de Catalunya.

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REFERENCES

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NOTE ADDED IN PROOF After finishing this manuscript, we have learned that Bhattacharya et al. 27 have recently used fast-scanning calorimetry to show that the transformation of stable glasses of toluene follows a zero-order kinetics.

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Evaluation of Growth Front Velocity in Ultrastable Glasses of

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