14206 | Phys. Chem. Chem. Phys., 2014, 16, 14206--14211 This journal is© the Owner Societies 2014

Cite this:Phys.Chem.Chem.Phys.,

2014, 16, 14206

Acoustic dynamics of supercooled indomethacinprobed by Brillouin light scattering

S. De Panfilis,a E. A. A. Pogna,b A. Virgab and T. Scopigno*ab

Acoustics dynamics of the molecular glass-former indomethacin (IMC) have been investigated by Brillouin

light scattering (BLS) at GHz frequencies. Elastic response of the system has been tracked from the melting

temperature down to the glass transition through the supercooled liquid. Both the structural arrest and the

vibrational dynamics are described by modeling the experimentally determined dynamic structure factor

within the framework of the Langevin equation, through a simplified choice of memory function which

allows one to determine sound velocity and the acoustic attenuation coefficient as a function of

temperature. The density fluctuation spectra in the glassy phase, as probed by BLS, are compared with

time-domain results from photoacoustics experiments. The arising scenario is discussed in the context of

current literature reporting inelastic X-ray scattering and BLS in platelet geometry. The link between the

probed elastic properties and the non-ergodicity factor of the glass phase is finally scrutinized.

1 Introduction

Pharmaceutical products must be stable over storage periods ofmany months, typically several years, and many biomolecules donot possess this long-term stability in the aqueous state atambient temperature. To attain extended stability at ambienttemperature during storage, molecular movement needs to bearrested by vitrification, a method that stops degradation bytransforming a liquid into a highly immobile, non-crystalline,amorphous solid state.1 The glass-former system below its glasstransition temperature (Tg) is stable due to the immobilization ofthe reactive entity. Moreover, the efficiency of most of thecommon active pharmaceutical ingredients in commercial drugsis limited in the crystalline state due to low water solubility andthe dissolution rate (bio-availability), which, instead, areenhanced in the amorphous glassy state.2,3 However, since theadvantages of the amorphous formulation are lost upon crystal-lization, achieving long term stability towards crystallization inthe glassy state becomes a key factor for the shelf life of drugsand their controlled delivery into the human body.

According to textbook definitions, glasses are often seen asout-of-equilibrium arrested states, obtained upon cooling a meltunder appropriate conditions below the glass transition tempera-ture avoiding the crystallization. Much effort, therefore, has beendevoted to the search for coupling between crystallization kineticsand diffusion processes in supercooled liquids. Conversely, it

seems that the crystallization kinetics responsible for degradationof pharmaceuticals, biomaterials and food is not directly coupledto diffusive motion, which is strongly inhibited below the glasstransition temperature. One possibility, therefore, is that thesekinetics are related to other mobility processes active in thearrested state, which ultimately correlate with slow dynamicsabove Tg.4 Within this context, fast vibrational dynamics survivingthe dynamical arrest occurring in glassy systems can be respon-sible for long term stability or degradation of pharmaceuticals,and more generally biological material and food, which oftenoccurs in the amorphous state. Investigations of the mechanicalproperties of a glass-former across its glass transition are criticalto detect any possible fast predictors of the structural arrest whichmight be embedded in the fast, vibrational dynamics.

Indomethacin (IMC) is an organic glass former with rela-tively high glass transition temperature Tg = 315 K, interestingfor its pharmaceutical application as a non-steroidal anti-pyretic. It has attracted a lot of interest as a model system forunderstanding the stability of amorphous drug formulations.As many pharmaceutical glass-formers, it is characterised byhigh values of kinetic fragility5–7 and a large tendency towardscrystallization even below Tg.8 Recently, IMC has been used forpreparing glasses of exceptional stability towards crystal-lization, endowed with low enthalpy, high density and highkinetic stability, by physical vapour deposition9 with relativelyslow deposition rates and controlled substrate temperature.

We report here a study of the mechanical properties, namelythe longitudinal modulus and the acoustic loss, of indomethacin,as performed by means of Brillouin light scattering (BLS) atdifferent temperatures, discussing the relationship between themechanical properties of the supercooled liquid and glass phase.

a Centre for Life Nano Science – IIT@Sapienza, Istituto Italiano di Tecnologia,

I-00161 Roma, Italyb Dipartimento di Fisica, Universita di Roma ‘‘Sapienza’’, I-00185 Roma, Italy.

E-mail: tullio.scopigno@phys.uniroma1.it

Received 2nd April 2014,Accepted 29th May 2014

DOI: 10.1039/c4cp01427h

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Thanks to its non-destructive capability, this technique providesa unique opportunity to investigate the elastic properties ofamorphous pharmaceuticals in general, and to evaluate theirkinetic fragility, providing information on the stability of theglass phase.

2 Experimental

High purity indomethacin (IMC) was provided by Sigma-Aldrich.The sample was contained in a 10 mm side square quartz opticalcuvette. The cell was flame-sealed under vacuum to avoid anycontamination of the IMC powder by oxygen or humidity. Thequartz cuvette was placed inside a high temperature thermo-resistive furnace, able to thermostate the sample within �1 K,from 450 K to room temperature. The required power to set thesample temperature was delivered by a programmable highcurrent power supply, voltage controlled. The BLS measurementswere collected approximately every 20 K. Due to the strongabsorption of the molten IMC (a brown-yellow liquid), thescattering volume was limited to only 4 to 5 mm of the incominglaser beam, and the scattered intensity was collected through aminimal thickness of the sample by shifting the laser beam tothe side of the cuvette.

Brillouin light scattering is a frequency domain spectroscopyprobing thermally excited density fluctuations through the spec-trum of scattered light by collective acoustic excitations. For thepurposes of the present study, BLS measurements of IMC werecollected in the temperature range 298–438 K, comprising theequilibrium liquid, the supercooled liquid and glassy phase(glass transition Tg = 315 K, melting point Tm = 438 K) at a fixedvalue of exchanged momentum Q = 4pn sin(y)/l, where n is therefractive index of IMC, l the probe wavelength and y half theangle formed by the incident and the scattered light wavevector.

The scattering geometry was the standard 901 setup with theincident beam (514.5 nm line of an Ar+ laser, operating at anaverage power of 500 mW) vertically polarized with respect tothe scattering plane. The scattered light was collected in a VVpolarization configuration, through a linear film polarizer(extinction coefficient of B104). The squared cell geometryallowed scattering to be collected with a minimal stray light.

The spectral analysis of the scattered light was performedusing a SOPRA spectrometer,10 especially designed for highresolution and high contrast spectroscopy with visible radiationtaking advantages of a single pass, double monochromator(model DMDP 2000), based on a fully computerized gratingscanning. All the spectra were measured over a frequency shiftrange extending from �16 GHz to 16 GHz around the excitationfrequency. An average integration time of 5 s per point andfrequency steps of about 0.13 GHz were used over the entirespectral range for a total acquisition time of about 20 minutesper spectrum, which ensures a very good stability of the overalloptical alignments. Each spectral scan was repeated threetimes. The FWHM resolution obtained using 40–60–60–40 mmslit widths was 1.6 GHz. The collection solid angle aperture inthe scattering plane was kept constant and small enough to

reduce the lineshape broadening, due to scattering wavevectorspreading, well below the instrumental resolution.

The refraction index n, necessary to determine the exchangedmomentum modulus Q, was taken equal to n = 1.58 as reportedin the literature at T = 298 K11 since the temperature dependencewas considered negligible over the probed temperature rangeaccounting for a shift of 4%. Therefore, for the present study, weassumed a constant exchanged momentum Q E 0.0273 nm�1.

Raw BLS spectra are shown in the left panel of Fig. 1. Theyare characterized by a central peak with a linewidth ruled by theinverse relaxation time which varies with temperatures byseveral decades ranging from a few ps in the liquid up tohundreds of seconds at the glass transition, signaling thestructural arrest. Besides the elastic peak, the Brillouin doubletis observed as two symmetrically shifted inelastic components,located at frequency �n0, defining the phase velocity of theacoustic excitation as cs = 2pn0/Q = o0/Q. The Brillouin doubletlinewidth provides direct access to the life time of vibrationalexcitations, i.e. to the acoustic attenuation coefficient G(Q).

In order to account for the finite experimental resolution ofthe spectrometer, the BLS spectra have been fitted as theconvolution of a Gaussian profile describing the instrumentalresponse and the model function representing the elastic andinelastic components. Where the sound speed cs and theacoustic attenuation coefficient G(Q) have been evaluated fromthe analysis of the inelastic components.

As said, BLS probes acoustic modes by phase matching withspontaneous, thermally activated density fluctuations. Acoustic wave-packets, however, can alternatively be stimulated and detected bypump–probe spectroscopies. Among them, broadband picosecondphotoacoustic (BPA) is an experimental technique to coherentlygenerate propagating density fluctuations and subsequently detectthem in the time domain through an interferometric approach.12

Fig. 1 Left panel: Brillouin light scattering spectra of supercooled bulkindomethacin at fixed exchanged momentum Q = 0.0273 nm�1 (circles:experimental points; continuous red line: best fit). Data are verticallyshifted for different temperatures. The experimental error is within thesymbol. Right panel: deconvoluted DHO components as determined byfitting the experimental data.

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BPA measurements were collected by means of an experi-mental setup whose details are described elsewhere.13,14 In a fewwords, the output of an ultrashort 800 nm pulsed laser is splitinto two beams, the pump and the probe. The pump beam isloosely focused on metallic coating deposited onto the sample togenerate a longitudinal acoustic wavepacket by thermal expan-sion. The acoustic pulse, then, travels inside the sample and itsmotion is detected by interferometric probing of the transientreflectivity DR/R of a broadband femtosecond probe pulse.12,15

The oscillating behaviour of the reflectivity as a function of thedelay between pump and probe pulses provides relevant infor-mation on the acoustic wave travelling in the sample.

For the purpose of the present study, 1.5–2 mm thick glassesof IMC were deposited on a crystalline Si substrate, and ametallic coating on top of the deposition acts as the opto-mechanical transduction medium. The sample temperaturewas controlled using a liquid nitrogen reservoir cold fingercryostat, coupled with a resistive heater. BPA data were collectedin a quasi-backscattering geometry, over a probe continuousspectrum extending from 370 to 730 nm, corresponding to anexchange momentum interval of about 0.025–0.049 nm�1.

3 Results

In a BLS experiment, the spectral response can be modeled (redline in Fig. 1) by the combination of a Lorentzian function forthe central peak and the power spectrum of a damped harmo-nic oscillator (DHO) for the Brillouin doublet, both convolutedwith the experimental resolution. This model has been shownto be an appropriate description for glass and supercooledliquid in the hydrodynamic limit.16,17 A quantum correctionaccounting for the detailed balance condition is also required.The right panel in Fig. 1 shows the pure deconvoluted inelasticspectral component (DHO) as it is obtained by fitting theexperimental data at various temperatures. It can be observedthat the attenuation, related to the FWHM of the peak, decreasesupon lowering the temperature while the acoustic frequency n0,related to the peak position, shifts to higher frequencies. As aconsequence of the peak frequency shift, the sound speed cs alsoincreases. The temperature dependencies of the sound speed cs

and of the attenuation G normalised by the corresponding n02

are shown in Fig. 2 and in Fig. 3 respectively. The hypersonicsound velocity exhibits the characteristic sigmoid dispersioncurve, limited by the unrelaxed sound velocity cN and relaxedsound velocity c0, as expected in the presence of the structuralrelaxation process.18–20 The kink in cN observed at Tg parts thesolid-like velocity in cglass

N and cSCLN , reflecting the structural arrest

of the supercooled liquid at the glass transition.While the BLS signal is proportional to the dynamic struc-

ture factor S(Q,o), BPA provides direct access to its Fouriertransform, the intermediate scattering function F(Q,t). In Fig. 4(upper panel) we show a typical transient reflectivity DR/R timetrace, measured in a film of amorphous IMC at T = 263 K.In order to evaluate the acoustic frequency n0 and the dampingG(Q), we analyzed the differential optical reflectivity oscillations

DR/R as a function of the time with a damped sine function.Since the signal is probed in the time range 0 � tmax = 700 ps,its functional form can be expressed as

F(Q,t) =Ae�pGt[sin(2pn0t)]Y(tmax � t) (1)

where Y(x) is the Heaviside step function, and the Q depen-dence is hidden in the corresponding dependence of the G and

Fig. 2 Sound velocity, cs, of indomethacin as a function of temperature T.BLS data (black symbols) are extracted from the spectra of Fig. 1, while theBPA value (green triangle) is related to the time trace in Fig. 4. Previousliterature data are also reported (red solid symbol).21 An inelastic x-rayscattering determination25 is also reported (solid blue square). Liquid-likevalues of the sound velocity, c0, around Tg have also been determinedthrough the procedure explained in the text. The dashed lines indicate theliquid, supercooled liquid and glass sound velocity limits.

Fig. 3 Acoustic attenuation coefficient G of indomethacin, normalised tosquare frequency n = o0/(2p), as a function of temperature T. Blacksymbols are obtained from the fit of BLS spectra in Fig. 1. Green triangleis referred to BPA data, shown in Fig. 4. An inelastic x-ray scatteringdetermination, obtained in the THz range at different exchanged momen-tum Q,25 is also reported (blue square), with a grey region indicating theerror (no significant temperature dependence is expected at such highfrequencies18). Red symbol indicates a BLS datum available in the literaturefor acoustic attenuation (see Fig. 3a in ref. 21), but for an exchangedmomentum (Q E 0.0156 nm�1), i.e. lower than that reported here.

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n0 parameters, both depending on the wavelength of theprobe pulse.

For a valid comparison with the BLS experimental determi-nations, then, it is essential to match the isometric condition,i.e. to compare data from the two techniques at the same Q. Wethen selected a specific wavelength comprised in the broad-band white light continuum probe pulse lBPA in such a waythat the corresponding exchanged wavevector QBPA equals the Qused in the BLS scattering experiment, i.e.

QBPA ¼4plBPA

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffin lBPAð Þ2� sin2ðfÞ

q¼ QBLS ¼

2pffiffiffi2p

lBLSn lBLSð Þ

¼ 0:0273 nm�1 (2)

where f = 391, and n(l) is the refraction index of the sample atthe given wavelength.

The resulting probe wavelength turns out to be lBPA E666.8 nm. Fig. 4 (lower panel) shows the normalised timeFourier transform of the BPA signal at l = lBPA. This spectrumcan be fitted by the power spectrum of the function F(Q,t).Conveniently, the Fourier transform of a damped sine functionwave packet is related to the DHO model, which is its powerspectrum, to be convoluted with a cardinal sine functionsin(x)/x as a result of the limited time extension of the BPAmeasurement. The analytic expression of the convolution, usedto analyse the spectrum, therefore reads as:

where, as in eqn (1), the Q dependence is hidden in G and n0. Atvariance with the BLS response, the BPA spectrum does not

show any quasi-elastic peak associated with the structuralrelaxation: the probed timescale (t r 700 ps) is much shorterthan the structural relaxation time nearby the glass transition.The corresponding sound speed and acoustic attenuationcoefficients were evaluated to be 2480.8 � 2.6 ms�1 and0.245 � 0.019 GHz respectively. Green symbols in Fig. 2 and 3are related to these BPA determinations.

4 Discussion

Brillouin light scattering measurements of supercooled and glassyIMC exist in the literature at temperatures up to 340 K.21 Theresulting sound velocity is reported in Fig. 2 as red symbols,together with our measurements. The agreement shown in Fig. 2is rather convincing. It is important to remark that the acousticparameters reported in the literature21 were obtained at a differentexchanged momentum (Q E 0.0156 nm�1) with respect to our BLSexperimental conditions.

Different from the sound velocity cs, the damping acousticcoefficient G heavily depends on the exchanged momentum Q.The acoustic attenuation in disorder systems results indeedfrom the interplay between different mechanisms, dependingon the observed frequency range.22–24 Therefore, it is interes-ting to extend our BLS determination of acoustic attenuation toa wider frequency range considering the reported study ofvibrational dynamics in the THz regime by inelastic x-rayscattering.25 The acoustic attenuation coefficient G shows analmost quadratic dependence on the frequency n0 in the THzregime. In this region wavelengths are comparable to inter-atomic distances, and the dynamics is dominated by the effectsof structural disorder.26 In contrast, in the GHz regime anhar-monicity effects become relevant and the power dependenceexponent of G(n0) becomes smaller. To emphasize the differentdependencies, in Fig. 3 we compare our n2-scaled BLS resultswith inelastic X-ray scattering data. The latter were obtainedconsidering all the measurements at different exchangedmomentum Q, i.e. different acoustic frequency n, and fittingthem as G = An2. The blue symbol corresponds to the parameterA = 0.679 � 10�3 GHz�1, while the shaded region to its error. Tofurther extend the comparison, we added additional BLS litera-ture data.21 As expected, it falls above the smooth decreasingtrend of the normalized sound attenuation18,27 due to the non-quadratic dependence of the attenuation in the GHz regionwhich, however, represents an upper estimate in the absence ofQ-dependent BLS data.

In the high-temperature region, the acoustic attenuation, asmeasured by BLS, is largely due to the presence of the structuralrelaxation. Below Tg, instead, the structural relaxation is notexpected to contribute to the dynamics in the GHz range, being

located at lower frequencies. By comparing the BLS acousticattenuation in the proximity of the glass transition to the IXS

Fig. 4 Upper panel: differential optical reflectivity of indomethacin as afunction of time delay at lprobe = 666.8 nm at T = 263 K, detected by BPA.A slow decaying thermal contribution has been subtracted by the originaltrace to account for electron driven heat diffusion. Furthermore, the tracehas been smoothed, using a moving average, binning over 13 adjacenttime values. Lower panel: Fourier transform of the original trace in thefrequency domain. Data have been fitted (red line), as described in the text.

SðQ;oÞ ¼ eð�io�GpÞtmax ð�io� GpÞ sin 2pn0tmaxð Þ � 2pn0 cos 2pn0tmaxð Þ½ � þ 2pn0ð�io� GpÞ2 þ 2pn0ð Þ2

�����

�����2

(3)

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unrelaxed data, however, we observe an excess damping. Onepossibility that has been advanced also in other glass formers(polybutadiene, o-terphenyl and m-toluidine)18,28–30 is to invokesecondary relaxations, which in IMC has been detected bydielectric relaxation and NMR spectroscopy.31 On the otherhand, it is also true that secondary relaxations in indomethacinare much slower than the timescale probed in this experiment.32

In view of that, it seems to be more reasonable to explain theexcess damping observed in the proximity of the glass transitionbased on the nearly constant loss phenomenon as related to thecage dynamics in the anharmonic potential. This mechanism isalso responsible for the transition observed at Tg for elasticneutron scattering amplitude measured at the ps timescale.33

The fast vibrational dynamics surviving the structural arrestoccurring at the glass transition has been proven to stronglycorrelate with the slow diffusive dynamics at the supercooledliquid state for a number of diverse systems ranging fromstrong (as SiO2) to fragile glasses (as oTP).34 The relationshipis encoded in the non-ergodicity factor, i.e. the long time limitof the intermediate scattering function F(Q,t) normalised to thestatic structure factor S(Q):

f ðQÞ ¼ limt!1

FðQ; tÞSðQÞ (4)

Specifically, to its low temperature dependence in the Q - 0limit, quantified by the steepness index a:

a ¼ limQ!0

df ðQ;TÞdT

(5)

Within the harmonic approximation for the vibrational dynamicsin the glass, the temperature dependence of the non-ergodicity factorin the low Q region follows the analytical dependence:

f ðQ! 0;TÞ ¼ 1

1þ aT

Tg

(6)

and a is determined by the eigenvalues and eigenvectors of thevibrational normal modes. On the other hand, the non-ergodicity factor is also related to the sound velocity jump atthe glass transition Tg as:

f Q;Tg

� �¼ 1�

c02 Tg

� �

c12 Tg

� � ¼ 1�cliquid

2 T ! Tgþ� �

cglass2 T ! Tg�

� � : (7)

Therefore, according to eqn (6) and (7) it follows that

a ¼ c02

c12 � c02

����T¼Tg

(8)

providing the way to extract a entirely from the sound velocitytemperature dependence measured by BLS across the glasstransition.

Remarkably, the parameter a describing the vibrationalmodes in the glass deeply correlates with the kinetic fragility

m ¼ limT!Tg

dZd Tg=T� �, where the latter describes how fast the

shear viscosity Z (or the relaxation time Z = GNt) changes

approaching the glass transition from the liquid side, as thediffusive motion slows down. The correlation observed forglass-former systems with m o 100 is linear as:

m = ga = (140 � 10)a (9)

such that the parameter a can be referred to as glass fragility.The kinetic fragility m of IMC has been investigated by

different methods5–7 and it is in the range 60 o m o 79.Accordingly, IMC is classified as fragile glass-former as themajority of amorphous pharmaceuticals. The correspondingglass fragility, a, of IMC has been recently evaluated by an IXSexperiment.25 Specifically, by isothermal measurement of thenon-ergodicity factor via the elastic to inelastic scattering ratio,we obtained 0.514, in excellent agreement with the expectationsfrom eqn (9). By plugging this glass fragility value into eqn (8),and using the cN(Tg) value from ref. 21, c0(Tg) can be deter-mined. A further determination of c0 can be directly obtainedby the already mentioned, room temperature IXS study, renor-malizing the measured sound velocity by the non ergodicityfactor. Both estimates are shown in Fig. 2. In the absence ofultrasonics data, which would probe the liquid like limit at anytemperature above Tg, we report in the same figure c0(T)assuming the same steepness as cglass

N (T). All together, Fig. 2shows that our data depart from cSCL

N approaching c0 at themelting temperature. This is at ease with the expectations fromot E 10�2 { 1, having in mind that t E 1 ps in molecularliquids nearby the melting point. Higher temperatures couldnot be reached due to sample degradation.

5 Conclusions

In conclusion, we have used time and frequency domain Brillouinlight scattering for characterisation of the elastic response ofglass-forming indomethacin as a function of temperature, fromthe melting down to the supercooled and glass state. Longitudinalsound velocity and acoustic attenuation have been extractedthrough the analysis of the Brillouin doublets in the context ofa hydrodynamic framework with a simple memory functionmodeling. We tracked the down shift of the mode frequency withtemperature, with a characteristic kink occurring near the glasstransition and a viscoelastic relaxation towards the liquid-likedynamical regime. The acoustic attenuation displays an increasewith temperature across the same range, testifying the dominanceof structural relaxation in the GHz range accessed by BLS.

Our determination of acoustic properties of the indomethacinsample extends those previously measured in thin films of IMC byBLS at larger acoustic wavelength21 around the glass transitiontemperature, and in bulk ordinary IMC by inelastic X-ray scattering25

at shorter wavelengths. The comparison required to consider iso-metric conditions which for the acoustic attenuation were deter-mined under the assumption of a quadratic dependence on thewave vector. Moreover, we discussed the equivalence of the timedomain and frequency domain light scattering techniques, and howthe former approach is not able to access structural relaxations inthe glass due to the involved time-scale.

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Finally, the measured values of the longitudinal soundvelocity and the indirect estimate of the liquid-like asymptoticregime provide support to the correlation of the kinetic fragi-lity, which is believed to represent a key parameter for thestability of amorphous pharmaceuticals,35 with the non-ergodicity factor as determined from the sound velocity jumpat the glass transition. This result suggests a non-destructivemethod to assess the kinetic fragility of amorphous pharma-ceuticals uniquely from the elastic properties at the glasstransition, accessible by inelastic light scattering.

Acknowledgements

T.S. and E.A.A.P. have received funding from the EuropeanResearch Council under the European Community SeventhFramework Program (FP7/2007–2013)/ERC grant AgreementFEMTOSCOPY No. 207916.

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