Michael T.
Ruggiero
a,
Marcin
Krynski
b,
Eric Ofosu
Kissi
c,
Juraj
Sibik‡
a,
Daniel
Markl
a,
Nicholas Y.
Tan
a,
Denis
Arslanov§
d,
Wim
van der Zande¶
d,
Britta
Redlich
d,
Timothy M.
Korter
e,
Holger
Grohganz
c,
Korbinian
Löbmann
c,
Thomas
Rades
c,
Stephen R.
Elliott
b and
J. Axel
Zeitler
*a
aDepartment of Chemical Engineering and Biotechnology, University of Cambridge, Philippa Fawcett Drive, Cambridge, CB3 0AS, UK. E-mail: jaz22@cam.ac.uk; Tel: +44 1223 334783
bDepartment of Chemistry, University of Cambridge, Lensfield Road, Cambridge, CB2 1EW, UK
cDepartment of Pharmacy, University of Copenhagen, Universitetsparken 2, 2100 Copenhagen, Denmark
dRadboud University, Institute for Molecules and Materials, FELIX Laboratory, Toernooiveld 7c, 6252 ED Nijmegen, The Netherlands
eDepartment of Chemistry, Syracuse University, Syracuse, New York 13244, USA
First published on 19th October 2017
The fundamental origins surrounding the dynamics of disordered solids near their characteristic glass transitions continue to be fiercely debated, even though a vast number of materials can form amorphous solids, including small-molecule organic, inorganic, covalent, metallic, and even large biological systems. The glass-transition temperature, Tg, can be readily detected by a diverse set of techniques, but given that these measurement modalities probe vastly different processes, there has been significant debate regarding the question of why Tg can be detected across all of them. Here we show clear experimental and computational evidence in support of a theory that proposes that the shape and structure of the potential-energy surface (PES) is the fundamental factor underlying the glass-transition processes, regardless of the frequency that experimental methods probe. Whilst this has been proposed previously, we demonstrate, using ab initio molecular-dynamics (AIMD) simulations, that it is of critical importance to carefully consider the complete PES – both the intra-molecular and inter-molecular features – in order to fully understand the entire range of atomic-dynamical processes in disordered solids. Finally, we show that it is possible to utilise this dependence to directly manipulate and harness amorphous dynamics in order to control the behaviour of such solids by using high-powered terahertz pulses to induce crystallisation and preferential crystal-polymorph growth in glasses. Combined, these findings provide compelling evidence that the PES landscape, and the corresponding energy barriers, are the ultimate controlling feature behind the atomic and molecular dynamics of disordered solids, regardless of the frequency at which they occur.
There have been attempts to link the experimental observations at frequencies exceeding the dielectric relaxations (such as mid-infrared, Raman or terahertz spectroscopies) to the fundamental process of collective translational and (hindered) rotational motions by means of a coupling process.21 However, given that most of these measurements probe processes that occur on drastically shorter timescales (femtoseconds to picoseconds probed in the infrared/terahertz vs. milliseconds to seconds for the relaxation processes associated with α- and β-relaxation) a more fundamental origin must exist that links the slow relaxation process with all the other experimental data. Given the importance of the PES on the properties of glasses, it is possible to explain the frequency-independence of the relaxation processes as a manifestation of the PES structure. Importantly, we believe that it is critical to explicitly consider the molecular nature of the solids, their complete intra- and inter-molecular interactions, and the corresponding anharmonicity in their PES, particularly the inter-molecular anharmonicity (responsible for thermal expansion). While there exists a large body of work related to this topic, with a wide variety of theories having been proposed over the years,22–25 it is not surprising that this level of detail has not yet been achieved since such considerations are far from trivial to implement into theoretical models.26–29 However, this work will demonstrate how important both of these factors are for understanding the origins of glassy dynamics, and that previous oversimplifications might be the cause of certain discrepancies in the quantitative agreement between theory and experiment. This interpretation is aligned with the coupling model, which is based on the corresponding anharmonicity in inter-molecular interactions, and helps to explain the origins of the inter-molecular dynamics (inclusive of any cage-rattling motions) within the context of a PES picture.
Such a dependence implies that the manipulation of the condensed phase molecular dynamics according to the PES structure should have a clear effect on the physical properties of disordered solids, which has effectively been shown on previous studies involving vapour deposition of molecular glass-formers.30,31 Terahertz radiation is an ideal tool to investigate this, since the low-frequencies excite large-amplitude motions of entire molecules, and has indeed been shown to guide disordered processes, such as governing protein–ligand binding and driving biomolecular DNA mechanisms.32,33 This work extends this by using high-powered terahertz pulses to drive solid-state crystallisation in amorphous pharmaceutical solids. Such experiments add to the strong evidence in support of the PES picture of disordered dynamics, and that related phenomena can be directed through this fundamental understanding.
Fig. 1 (a) Experimental variable-temperature data from THz-TDS, FTIR, BLS,34 DMA, and theoretical AIMD-simulated volume for amorphous sorbitol, showing changes in the temperature dependence at the α and β glass-transitions, (b) BLS linewidths,36 neutron MSD,37 and 2H-NMR spin–lattice relaxation38 data for ortho-terphenyl, and (c) neutron MSD,39 PS hole-fraction,40o-PS lifetime,41 QELS,39 and 10 GHz dielectric loss42 data for PMMA, all showing similar behaviour. The DSC-determined values for Tgα (black vertical lines) and the THz-TDS determined Tgβ for sorbitol,43 DSC-determined Tgβ for OTP,44 and the dielectric determined Tgβ for PMMA42 (blue vertical lines), are shown. It should be noted that the identification of Tgβ has been previously reported.18,19 The data are plotted with different vertical axes (not shown, see ESI† for individual plots). |
There is a clear agreement between the data obtained from all techniques in both the temperatures of the glass transitions and the relative change in the three regions that are typically attributed to the α- and β-relaxations. However, it is somewhat surprising that, while the fundamental α- and β-relaxations occur at relatively low frequencies (kHz to MHz) in dielectric spectroscopy, their associated dynamics can also be observed at much higher frequencies. For example, THz-TDS covers the spectral region of 0.1–3 THz i.e. frequencies some nine orders of magnitude greater than the fundamental α-relaxation process. There have been attempts to reconcile these observations within the context of the coupling model,45 which argues that spectral changes observed at terahertz frequencies are coupled to their fundamental relaxations via a so-called ‘fast process’, typically referred to as ‘cage-rattling’ motion.17–19,21 However, given that a wide range of methods all yield similar results, even though they are based on very different measurement principles and probe molecular properties over a wide range of energies, it is possible, and indeed likely, that a more fundamental feature, that is, the PES, that relates the experimental observations and atomic-level interactions. This is what is suggested in the coupling model, but rather than limit the application to ‘cage-rattling’ dynamics, we propose that the PES, both intramolecular and inter-molecular, is responsible for dictating the complete inter-molecular dynamics, inclusive of any cage-rattling motions.46 This is particularly important in the case of organic molecular-solids, as the low-frequency mode-types are often a mixture of intra- and inter-molecular motions that cannot be easily separated from one another.47
Fig. 2 shows the FTIR spectra of amorphous sorbitol from 113–313 K acquired in 5 K increments. The frequency of the OH-stretch peak in the IR-absorption spectra exhibits the same temperature-dependent variation as measured using the other techniques, as shown in Fig. 1, with clear changes in the slope being observed at both Tgα and Tgβ (Fig. 2 inset). The origins of the temperature-induced frequency shift must arise from a change in the OH-bond strength. Since the OH-bond potential energy surface is relatively hard (with the first excited vibrational level occurring at ≈5100 cm−1, equivalent to ≈7300 K), only the vibrational ground state is populated under ambient conditions, indicating that the change in the OH-bond strength must arise from temperature-altered inter-molecular interaction strengths rather than higher order vibrational transitions (which would be expected to exhibit an anharmonically-caused red-shift in frequency with increasing temperature, rather than the observed blue-shift). Further evidence for this is the lack of any significant changes with temperature in the CH-bond stretch that occurs at ≈2900 cm−1, since the CH-bond is not significantly influenced by inter-molecular interactions and there is little change in the CH-bond strength itself as a function of temperature.
The AIMD simulations enable the atomic-level mechanisms that occur in amorphous sorbitol to be uncovered. For example, the vibrational dynamics of the system can be determined via the Fourier transform of the dipole-moment autocorrelation function,50,51 and the results are in good agreement with the experimental data (Fig. 2(b)), providing validation in the utilised theoretical model. Furthermore, the calculations can provide information that is difficult to obtain experimentally, for example the average hydrogen bond distance as a function of temperature (Fig. 2), which also follows the trend described in Fig. 1(c).
To further explore the temperature-induced changes in the dynamics of the system, an analysis of the OCCO dihedral angles of sorbitol in the glassy state was performed at a number of temperatures. The results, shown in Fig. 3, show that there exist three distinct structural features corresponding to dihedral angles of approximately 60°, 180°, and 300°, with sub-maxima within the regions emerging as the temperature is decreased (Fig. 3(a)), in agreement with a previous report.52 It is significant that the onset of the localised sub-regions occurs near 260 K, corresponding to the Tgα of sorbitol, while significant localisation occurs near 180 K, corresponding to the Tgβ of sorbitol. An analysis of the time-evolution of dihedral angles in glassy sorbitol helps to uncover the changes in atomic dynamics that occur as a function of temperature in such disordered molecular solids. For instance, low-temperature simulations (T < Tgβ) show only small-magnitude oscillations of each dihedral angle about its respective average value, with little to no structural rearrangement occurring, implying that the molecules are confined to the sub-minima in the PES. However, as the temperature is increased above Tgβ and through Tgα, the magnitude of the oscillations increases and fluctuations in the sub-minima populations become increasingly prevalent, as shown in the average dihedral angle standard deviation shown in Fig. 3(b). Additionally, above Tgα, there are an increasing number of large-scale conformational changes, evidenced by jumps between the principal dihedral angle basins over the course of the simulation (Fig. 3(c)). This is direct evidence confirming previous theories related to dihedral-angle changes determined by FTIR and NMR studies, where large changes in absorption corresponding to dihedral angle vibrational motions were observed as a function of temperature.53,54
These effects can also shed light on the ‘intramolecular’ versus ‘intermolecular’ hypotheses regarding the origins of the JG-β relaxation.8,17,55 For example, the well-studied glass former, ortho-terphenyl (OTP), is regularly referred to as being ‘rigid’ in the literature, and has been used as a benchmark in the debate surrounding the origins of the JG-β relaxation. A simple simulation of the gas-phase vibrational properties (using DFT in CP2K) of a single-molecule of OTP puts this description in dispute, however, since there exist a number of lower-frequency features in the vibrational spectrum (<400 cm−1) that are torsional type motions of the OTP ring moieties. These motions will be thermally excited at ambient conditions (using the Boltzmann relation for a 400 cm−1 transition yields an excited state population of ≈13% at 298 K), and will contribute to the overall spectral response of OTP. We propose that, rather than restrict a description of the type of motions involved in the various relaxation processes to being either internal or external, it is better to simply refer to the nature of the PES and the energies of the various dynamical variables.
As Goldstein originally hypothesised,2 the AIMD results for sorbitol show that below Tgα structural changes are localised, while temperatures above Tgα lead to large-scale conformational rearrangements of the molecules. While this phenomenon is clearly associated with overcoming potential-energy barriers, the origins are slightly more complex, as the barrier heights (and indeed the entire PES) are as dynamic as are the processes themselves. This arises because the PES, which dictates the atomic dynamics and structures, evolves in time as the interactions themselves change, with various factors influencing its structure at any time. For example, inter-molecular anharmonicity, which is responsible for thermal expansion, can lead to a larger accessible free volume of the particles with increasing temperature, which in turn can weaken the inter-molecular interaction strength and thereby lower potential energy barriers for conformational rearrangements.
These conclusions highlight the importance of accounting for a varying PES as a function of time in MD simulations, a factor that classical MD simulations are not capable of reproducing. This also has implications for the coupling model,45 where the changing of the PES as a function of time (and temperature) means that the relative coupling between molecules is dynamic and must be accounted for. However as previously mentioned, the PES is not only dependent on static atomic positions, as any change in these values will cause a corresponding change in the PES. For example, changing a single dihedral angle (as shown in Fig. 3(d)) results in the breaking of an intra-molecular hydrogen bond. A new hydrogen bond can easily form along this direction, provided that the OH group can readily rotate so as to take advantage of this, which can occur throughout the time-evolution of the system. Thus, forming a model of amorphous dynamics would require every combination of structures and interactions to be known. Given these conclusions, the glass transitions and temperature-dependent dynamics can be related to the number of accessible states that the system has, implying that a thermodynamic partition function might be an appropriate means of predicting such phenomena. However, because the PES is both temperature- and time-dependent (since the various conformations that the molecules can achieve will change the PES accordingly), the expression would become much more complex, depending on both the temperature and time-dependent barriers. Thus, while the problem might appear intuitively simplistic, it becomes highly complex to solve analytically. However, approaches to its solution are currently under investigation.
Samples of amorphous indomethacin (C19H16ClNO4), a popular active pharmaceutical ingredient (API), were prepared by melt quenching from a molten liquid and were exposed to the focused terahertz beam (1.5 mm diameter) with an average power of 200 mW (power density of 3 MW cm−2) operating at a frequency of 1.56 THz, chosen due to the presence of an absorption feature in the crystalline form near this frequency. After 1 minute of exposure to the terahertz beam, visual inspection showed that a clear transparent region had formed at the focal point of the beam, which did not extend beyond this region (Fig. 4b). Subsequently, after an additional 4 minutes of exposure (5 minutes total), a crystalline region had formed within the beam spot (Fig. 4c), with the transparent region extending slightly beyond the focal point of the beam. Continued exposure (10 minutes total) resulted in the entire focus region of the beam converting to a crystalline phase (Fig. 4d). It is important to note that other than the focal point of the beam and the extension region (which is in direct contact with the beam focus spot), there was no discernible change in the rest of the sample. Further characterisation with THz-TDS showed that the crystalline areas, both within the focus of the beam and the area that extended outwards, contained a mixture of α and γ polymorphs of indomethacin. However, the region within the focal point of the beam contained a larger proportion of the γ form, indicating that the intense terahertz pulses were preferentially promoting one form over the other. It is important to note that while temperature is known to have an effect on the polymorphic outcome of indomethacin,57 it is not believed to be the origin of the observed phenomena, as these effects were also observed when the sample was placed under active cooling, helping to highlight that the terahertz radiation, rather than thermal effects, was responsible.
A similar behaviour was observed in samples of amorphous API carbamazepine (C15H12N2O), which were exposed to a 1.0 THz beam, again chosen due to the resonance found in the crystalline spectrum. In the absence of any external perturbation, carbamazepine regularly crystallises on heating in the Form III polymorph.58 However, upon exposure to the FLARE terahertz beam, the crystallised region within the focus only contained Form I, while the edges of the sample, which were in contact with the copper sample holder that was subsequently heated while exposed to FLARE to in an attempt to speed crystallisation, contained the expected Form III. These results strongly indicate that the intense terahertz radiation produced by FLARE is capable of inducing crystallisation, as well as preferentially promoting particular polymorphic forms. Detailed information can be found in the ESI.†
The results from the FLARE experiments, together with the interpretation of the large-scale conformational rearrangement of molecules associated with overcoming potential-energy barriers at Tgβ, fully explains our previous observation regarding the critical role of Tgβ for the crystallisation process from a disordered solid.59 Additionally, these results are in agreement with previous studies using gamma-rays, where in that particular work the authors observed that upon irradiation their sample underwent significant ageing thought to be caused by structural rearrangement due to pushing molecules over their energy barriers.60 In samples of a quench-cooled melt of naproxen (C14H14O3), which contained crystalline nucleation seeds due to an insufficient cooling rate, we found that upon heating the crystallisation rate increased dramatically at temperatures above Tgβ and full crystallisation was observed at temperatures well below Tgα. Whilst our simple method of quench-cooling molten APIs can reliably produce stable glasses in most cases, this is not the scenario for naproxen – even when quenching the melt to liquid nitrogen temperatures – given its extremely high propensity to crystallise and limited heat transfer in our experimental apparatus. The resulting solid is hence mostly disordered, but there exists significant near-range order between a large number of molecules. For a system like this, further nucleation and crystal growth requires only the subtle movement of neighbouring molecules and no significant translational or (hindered) rotational motions, and as the potential-energy barriers that govern the conformational rearrangement are exceeded (at Tgβ), the crystallisation process can commence much more readily. This idea also explains why we observe the formation of different polymorphs during the stimulated crystallisation process by FLARE compared to the crystallisation at high temperatures. The near-range order in the disordered solid will determine the crystal structure that can form during FLARE excitation, as only the weak potential-energy barriers that are linked to the large-scale conformational rearrangement of molecules are pumped by the terahertz beam, implying there is no significant enhancement of the translational or (hindered) rotational motions associated with the terahertz stimulation. It is therefore not surprising that the polymorph formed during such crystallisation is not necessarily that with the lowest energy crystal structure, but the only that which is structurally closest to the near-range structure in the disordered solid. There is empirical evidence that different polymorphs may result from crystallising from melt-quenced, spray-dried, lyophilised or cryo-milled amorphous solids.61 It is important to note that while the net-outcome of these experiments produces crystalline phases, there is no evidence for or against other possible outcomes due to the terahertz radiation, for example accelerated aging or rejuvenation of the amorphous solid itself. Future experiments will have to confirm whether this is predetermined by the existing near-range order, as suggested in the literature, and whether it is hence possible to selectively crystallise different polymorphic forms from such disordered solids, e.g. by terahertz stimulation.
For a fully disordered solid (i.e. no crystal nuclei present) we hypothesise that no crystallisation is possible at temperatures below Tgβ as the molecular interactions are confined by localised energy minima. It is only at temperatures above Tgβ that large-scale conformational changes can take place that provide sufficient molecular mobility for crystal nuclei to form. However, whilst crystallisation will be possible at such temperatures it will be a very slow process for most materials as there is not sufficient free volume available in the solid for translational or rotational motions to take place. As the temperature increases further the density of the solid decreases as the amount of free volume increases until at Tgα there is sufficient mobility and free volume available for the glass transition to take place. Whether or not a material will fully crystallise at temperatures Tgβ < T < Tgα, or indeed at all, will depend on the molecular size, flexibility and inter-molecular bond strength of the molecule.
Footnotes |
† Electronic supplementary information (ESI) available. See DOI: 10.1039/c7cp06664c |
‡ Present address: F. Hoffmann-La Roche AG, Konzern-Hauptsitz, Basel, Switzerland. |
§ Present address: ASM Laser Separation International, Beuningen, The Netherlands. |
¶ Present address: ASML, Veldhoven, The Netherlands. |
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