Supercooled liquids with enhanced orientational order

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1 SUPPLEMENTARY INFORMATION for Supercooled liquids with enhanced orientational order Simona Capponi 1,, Simone Napolitano 2, Michael Wübbenhorst 1 1 Laboratory of Acoustics and Thermal Physics, Department of Physics and Astronomy, Katholieke Universiteit Leuven, Celestijnenlaan 200D, Leuven, 3001, Belgium 2 Laboratory of Polymer and Soft Matter Dynamics, Faculté des Sciences, Université Libre de Bruxelles, Boulevard du Triomphe, Bâtiment NO, Bruxelles 1050, Belgium current address School of Physics, University College Dublin, Belfield, Dublin, Ireland 1

2 Supplementary Figures Supplementary Figure S1: Simulated dielectric spectra during the conversion from MROL to OL. The impact of the separation in the timescale of the relaxation processes in the two liquids was studied by varying the ratio Γ = τ MROL / τ OL ; Γ=5000 (left panel) and Γ= 5 (right panel, reproducing max the experimental value). In both cases the maximum enhancement of the dielectric strength, Δε N was fixed at

3 Supplementary Figure S2: Values of the normalized dielectric strength (blue squares) and of the structural relaxation time (black squares), as a function of conversion. Simulation of the dielectric function was obtained assuming a linear convolution of the contributions of the two liquid phases, averaged over their volume fraction, ε TOT = x OL ε OL +x MROL ε MROL. 3

4 α HN /α OL HN α HN /α OL HN a) b) conversion Simulation Experimental ε N = ε TOT / ε OL β HN /β OL HN β HN /β OL HN c) conversion Simulation d) Experimental ε N = ε TOT / ε OL Supplementary Figure S3: Shape parameters α HN and β HN, as obtained from Havriliak Negami fit of the dielectric spectra, normalized to the values measured in the ordinary liquid. In panel b) experimental values found for a temperature scan of an 11 nm thick film of glycerol, which undertook the annealing protocol described in the experimental session of the manuscript. Analogous trends are reported for the values β HN / β OL HN, panels c) and d). 4

5 T fict (toluene) increasing stability increasing stability ε max N (glycerol) Toluene T fict max Glycerol ε N L (nm) Supplementary Figure S4.The centred black circles indicate the fictive temperature of thin films of toluene, measured by differential scanning calorimetry, 43 as a function of the film thickness (left ordinate). The red solid triangles indicate ε max N (right ordinate) for our films of glycerol (see data Figure 3 a) in the text). 5

6 T Toluene (K) on T glycerol on (K) 128 Toluene Glycerol L (nm) Supplementary Figure S5. The centred black circles indicate the onset temperature for the devitrification process of toluene (left ordinate axis); the black dashed line is a guide for the eye. Data and are taken from ref 43. The red triangles indicate the onset temperature for films of glycerol (right ordinate axis). These values have been evaluated from a series of isothermal experiments at progressively increasing temperatures: T on (glycerol) has been estimated as the first temperature at which a decrease of ε N could be detected during annealing. 6

7 log(t c /τ α ) Increasing T sub Increasing molecular size IMC at 320K IMC at 316K Glycerol at 233 K, T sub =166 K Glycerol at 231K, T sub from 130 K to 210K Xylitol Threitol L (nm) Supplementary Figure S6. The ratio between the conversion time and the structural relaxation time found for our films is compared to the results reported for Indomethacin (centred circles). 44 The red triangles refer to glycerol: the solid triangles to films of different thickness deposited at 166K and annealed at 233 K, while the empty triangles to 30 nm thick films deposited at different substrate temperatures. The conversion time t c has been evaluated at the first stages of the transformation, where x OL < Semiopen and center-pointed green hexagons refer respectively to threitol and xylitol, deposited at T sub = 0.88 T g. The values of T g are 227 K and K for threitol and xylitol respectively. All the dashed lines are fits of the data to models assuming a constant conversion rate. 7

8 Supplementary Figure S7: Temperature evolution upon annealing at 228 K of the conductivity of a 30 nm thick film and of the dielectric strength normalized to its value the time t=0. 8

9 Supplementary Methods Dielectric response during MROL to OL conversion We simulated the dielectric response of the system upon transformation from the medium range crystalline ordered liquid (MROL) phase into the ordinary liquid (OL), by modelling the whole film as a bilayer where the two phases are separated by a flat interface parallel to the substrate (see the last paragraphs of this section for an alternative mechanism). The use of such a configuration is justified by the assumption of an interfacial growth-front-like transformation process, as suggested by the constant conversion rate measured during isothermal annealing (see text and Supplementary Figure S6) For the experiments, we used interdigitated comb electrode (IDE) sensors, where the electric field is applied parallel to the surface, which allows a linear deconvolution of the signal arising from the different layers composing the film. Consequently, the total dielectric response of the system can be written as: ε TOT = x OL Rε OL + x MROL ε OL = Rε OL (L-Δl)/L + ε OL Δl/L (S1), where x is the volume fraction and R=Δε max N /Δε OL. On the basis of Eq. (S1), it was possible to evaluate the dielectric permittivity as a function of the fraction of MROL phase. The value of the structural relaxation time of the related peak in the imaginary component of the dielectric permittivity was determined as τ=1/(2πf max ), where f max is the frequency of the maximum. We present results of calculations, performed in the two different cases, τ MROL /τ OL =5000 (A) and τ MROL /τ OL =4.5 (B), see Supplementary Figure S1. Case B corresponds to the value determined experimentally for glycerol. To reproduce the experimental conditions, we fixed, in both cases the max maximum enhancement of the dielectric strength, Δε N at 3.7. In the case of relatively large separation in the time scales of the relaxation processes of the two phases, the complex component of the dielectric permittivity would show two distinct peaks, associated to the two relaxation processes of the OL and MROL phases. 9

10 On the contrary, at smaller values of the ratio τ MROL /τ OL (B), the transformation into the OL phase proceeds as a continuous evolution of one single peak. This behaviour well reproduces the experimental trend shown in Figure 1. The broadening of the peak at intermediate conversion times instead reveals the coexistence of the two phases. It is possible to observe the shape evolution of the peak upon transformation by fitting the simulated spectra with the empirical Havriliak-Negami function ( ) ε ω σ ε ε = + a b εω 0 1+ ( iωτ HN ) (S1) where Δε, τ HN, α, β are the dielectric strength, the relaxation time and the shape parameters, respectively, accounting for the width and the asymmetry of the loss curves. The term σ/(ε 0 ω) is due to ionic ohmic conduction 45. Supplementary Figure S3 show the α and β parameters, as max obtained for ε N = 5 and τ MROL /τ OL =4.5, compared to the experimental values observed for an 11 nm thick film of glycerol. The presence of the MROL phase affects the dielectric strength to a much higher extent that the relaxation time of the overall dielectric signal (see Supplementary Figure S2), because the difference in ε between the two phases is large, while the small separation in τ is rather small. Indeed, while the overall dielectric strength, ε TOT, is given by the sum of the contributions coming from the two phases. This simple linear convolution relation does not hold for the relaxation time, which instead depends also on the shape, position and relative intensity of the peaks related to relaxation processes of the two phases. 46,47 As a consequence, τ and ε evolve independently during the conversion. Supplementary Figure S2 confirms that ε TOT starts to decrease at conversion degrees smaller than those necessary to observe a shift in τ, while the values of the ordinary liquid can be virtually recovered for τ at smaller conversion degrees compared to those necessary to see a total conversion for ε. In 10

11 particular, while Δε N shows the expected linear dependence on the OL volume fraction (i.e. on the conversion), a non-correlated decay is found for τ, which remains almost constant up to x OL ~ 0.3. The yellow area marks the conversion range within which τ appears constant (within the errors), while Δε N decreases. In the calculations, we considered errors on the same order of magnitude as the uncertainty usually observed on the quantities. The green area marks instead the conversion range where the relaxation time might, within the errors, already reach τ OL (i.e. an apparent conversion of 100 %), while Δε N can still be as large as ~ 1.7. We also considered a transformation based on nucleation of defects in the ordered structure and consecutive growth of the ordinary liquid phase in a spherulitic fashion, 48 and we assumed that the reduction of conversion rate v we observed below 20 nm (Figure 4) could be related to finite size effects, like for example to the truncation of spherulites at the interfaces. Schultz solved analytically this problem, considering the effects of the dimension of the sample on the effective transformation rate. Deviations from bulk-like kinetics are expected to occur when the ratio between the thickness of the sample, L, and the transformation rate is not infinite, i.e. L/v >>1. In our case v is on the order of nm/s, thus L/v > 10 3 for all the thicknesses investigated, and the same rate should have been observed for all films. Consequently, we had to discard this alternative mechanism. Finally, it is noteworthy noticing that the experiment described in the experimental method, see Supplementary Figure S7, where we monitored the evolution of the conductivity and of the dielectric strength upon annealing is in line with previous experiments (water/glycerol, 49 ionic salts/glycerol 50 ) which showed that upon controlled addition of ionic impurities, the dielectric strength remains constant or decreases, while the conductivity increases by several orders of magnitude. In our case instead, in films deposited below T g the dielectric strength is higher than in the ordinary liquid while the conductivity is not affected. We thus conclude that we have a genuine effect arising by the enhancement in orientational order, given by the presence of the MROL phase. 11

12 Isothermal MROL to OL transition: transformation rate. Isothermal dielectric experiments performed during annealing experiments allowed to calculate the MROL OL transformation rate v at a given temperature, from the time evolution of ε N, which resulted linear during the measurement time (7200 s). Consequently, we considered v = l(t-t 0 )/(t-t 0 ), where t 0 is the onset time, and l the thickness of the layer transformed into the OL phase at time t, calculated from eq.(s1). Thus : v = L/(t- t 0 ) [Δε N (t 0 )- Δε N (t- t 0 )]/ (Δε N max -1), (S2) The transformation rate decreases with the film thickness, i.e. the conversion into the ordinary liquid is slower for thinner films (see Figure 4). We point out here that, although this might seem to contradict the temperature evolution shown in Figure 2, such apparent discrepancy is due to the fact that the dielectric strength ε N represents the amount of polarization normalized to the film thickness. On the contrary, the impact of the conversion degree on ε N depends on the total thickness of the film. In particular, considering films of different thickness, e.g. 10, 50, and 100 nm, the conversion of 5 nm of the sample would yield a drop of ε on the order of 50%, 10% and 5% respectively. Extra enhancement in ε N below 20 nm: any impact of the substrate? Investigation of the thickness dependence of ε N showed a continuous decrease of its value, reaching a plateau value of 3.7 for films thicker than 20 nm (see Figure 2). Such behaviour was rationalized in terms of a higher degree of bond orientational order in proximity of the substrate of the IDE sensor on top of which the films were grown. To discern the impact of the interface induced ordering caused by steric effects from the possible impact of molecular interactions with the substrate, 51 we designed an experiment where a first layer of glycerol was grown well above T g (OL). Subsequently the sample was cooled down to 0.88 T g, 12

13 where we deposited a film of glycerol on top of it (MROL). The value of Δε N of the top film was calculated from the dielectric response of the whole sample, assuming the full transformation of the underlayer of OL into the MRO rich phase. To prove the validity of this assumption, we prepared two bilayers, by keeping constant the thickness of the upper layer (UL) and varying the thickness of the bottom layer (BL). In both cases, considering that the whole film was transformed in the MROL phase yielded Δε bilayer N 3.7. This result is consistent with the trend observed for the single MROL layers, shown in Figure 4 in the text. On the contrary, assuming that the composition of the whole sample did not change during measurements led to inconsistent results, namely Δε UL N 14 for the 36 nm thick bilayer, and Δε UL N 5 for the 6 nm thick sample. Lifetime and stability of the liquid with enhanced dielectric strength. We introduced the parameter ε max N to quantify the enhancement in orientational order achieved in the as-deposited films of glycerol. We showed that ε max N, and the transformation rate v of the conversion MROL OL (see Figure 4 ), are strongly correlated, i.e. ε max N can be used to evaluate the stability of the system against annealing. Here we compare our results on poliols with literature data related to the solid to liquid transition in ultrastable glasses of toluene 43 and indomethacin, IMC. 44 The thermodynamic and kinetic stability of these systems is quantifiable respectively by the fictive temperature T fict, or the onset temperature T on at which the devitrification process takes place. In Supplementary Figure S4, T fict is plotted vs. the thickness of the films, L, for toluene, together with the values of ε max N (L) that we measured for glycerol. The two quantities have similar thickness dependence: showing an increase of stability against heating upon increase of the thickness. The remarkable similarity of the two trends suggests that: i. The two processes, devitrification of toluene and extinguishing of the enhanced medium range order in the liquid glycerol, might have the same physical origin, i.e. the transition 13

14 from a thermodynamic state characterized by very low excess in free enthalpy to the state corresponding to the ordinary supercooled liquid. ii. The enhancement in the orientational order in the MRO liquid results from the specific thermodynamic conditions of the as deposited glassy films, achieved with this preparation method. Such a strong similarity can also be observed in the thickness dependence of the onset temperatures T on of the two systems, as illustrated in Supplementary Figure S5. Furthermore, we compared the kinetics of conversion of MROL OL to the kinetics of devitrification of ultrastable glasses of indomethacin (IMC). In Supplementary Figure S6 we plotted the ratio between the conversion time t c and the structural relaxation time τ α found for films of glycerol, threitol and xylitol together with the values reported for IMC. 44 The dependence of log (t c /τ α ) on the thickness of the film is linear for all systems, below 1000 nm, which is explainable with a growth front transformation process. 52 Nevertheless a remarkable difference can be observed between the values of glycerol and IMC, separated by several orders of magnitude. This comparison shows a strong material dependence on the lifetime of the metastable state achieved with this preparation method: polyols reveal to be a much more stable class of materials with respect to toluene, IMC or TNB. Such high thermal stability though, (stability against annealing) is affected by thermodynamic conditions in which the film is grown: indeed, increasing the temperature of the substrate during deposition up to T g + 25 K (see Figure 3), leads to faster conversion at analogous annealing temperature, as revealed by the continuous decrease of t c /τ α upon increasing T sub. For glycerol, the condition t c /τ α =1 is eventually reached at T sub =178 K. Furthermore, films of threitol and xylitol, annealed at lower temperatures, (between T g +11 K and T g +30 K) present shorter conversion times, consistent with the trend of ε max N upon variation of the molecular weight, shown in Figure 2. Although the understanding of the high stability shown by the MROL phase of polyols requires further investigation, such large separation between the timescale of transformation and the 14

15 structural relaxation time is not unprecedented. It is worthwhile to mention the isothermal crystallization process in ultra thin films of poly(3-hydroxybutyrate) at 255 K, 46 where the ratio between crystallization time t cry, determined by the diffusion process, and the structural relaxation time τ α increases upon thickness reduction. Its value is in the order of 10 7 for 26 nm thick films. This behaviour is due to interfacial effects, as well as to the reduction of nucleation grains with decreasing thickness. Concerning our experimental findings, we suggest that our preparation method led to the presence of long living LPSs, assuring the long persistence of the enhanced BOO in our systems. On that respect we point out that Zondervan et al. have shown, via rheological measurements and single dye molecule spectroscopy, 53,54 the existence, in supercooled glycerol, of solid-like structures able to survive for a time t c ~ 10 6 τ at temperatures up to T g + 30 K. Such a stability of the solid-like structures has been achieved aging the system up to 2 weeks. The even higher values we found in films of glycerol can be explained by an enhanced aging achieved performing PVD below T g, which has been proven to be the most efficient way to age glasses. It s noteworthy though, that differently from these works, here we could sense the enhanced bond orientational order of the MRO domains rather than finding evidence of the mere solid-like structures. 15

16 Supplementary References 43 E. Leon-Gutierrez, G. Garcia, A. F. Lopeandia, M. T. Clavaguera-Mora, and J. Rodriguez- Viejo, "Size Effects and Extraordinary Stability of Ultrathin Vapor Deposited Glassy Films of Toluene," The Journal of Physical Chemistry Letters 1, (2009). 44 L. Kearns Kenneth, R. Whitaker Katherine, M. D. Ediger, Huth Heiko, and Schick Christoph, "Observation of low heat capacities for vapor-deposited glasses of indomethacin as determined by AC nanocalorimetry," The Journal of Chemical Physics, 133, (2010). 45 M. Wubbenhorst and J. van Turnhout, "Analysis of complex dielectric spectra. I. Onedimensional derivative techniques and three-dimensional modelling," Journal of Non- Crystalline Solids 305, (2002). 46 S. Napolitano and M. Wubbenhorst, "Slowing down of the crystallization kinetics in ultrathin polymer films: A size or an interface effect?," Macromolecules 39, (2006). 47 C. Rotella, M.Wubbenhorst, and S. Napolitano, "Probing interfacial mobility profiles via the impact of nanoscopic confinement on the strength of the dynamic glass transition," Soft Matter 7, (2011). 48 J. M. Schultz, "Effect of Specimen Thickness on Crystallization Rate," Macromolecules 29, (1996). 49 Y. Hayashi, A. Puzenko, I. Balin, Y. E. Ryabov, and Y. Feldman, "Relaxation dynamics in glycerol-water mixtures. 2. Mesoscopic feature in water rich mixtures," Journal of Physical Chemistry B 109, (2005). 16

17 50 M. Köhler, P. Lunkenheimer, and A. Loidl, "Dielectric and conductivity relaxation in mixtures of glycerol with LiCl," The European Physical Journal E: Soft Matter and Biological Physics 27, (2008). 51 S.Napolitano and M. Wubbenhorst, "The lifetime of the deviations from bulk behaviour in polymers confined at the nanoscale," Nat. Commun. 2, 260 (2011). 52 S. F. Swallen, K. Traynor, R. J. McMahon, M. D. Ediger, and T. E. Mates, "Stable Glass Transformation to Supercooled Liquid via Surface-Initiated Growth Front," Physical Review Letters 102, (2009). 53 R. Zondervan, F. Kulzer, G. C. G. Berkhout, and M. Orrit, "Local viscosity of supercooled glycerol near Tg probed by rotational diffusion of ensembles and single dye molecules," Proc. Natl Acad. Sci. 104, (2007). 54 R. Zondervan, T. Xia, H. van der Meer, C. Storm, F. Kulzer, W. van Saarloos, and M.Orrit, "Soft glassy rheology of supercooled molecular liquids," Proc. Natl Acad. Sci. 105, (2008). 17