Polyamorphism Mirrors Polymorphism in the Liquid–Liquid Transition of a Molecular Liquid

Liquid–liquid transitions between two amorphous phases in a single-component liquid have courted controversy. All known examples of liquid–liquid transitions in molecular liquids have been observed in the supercooled state, suggesting an intimate connection with vitrification and locally favored structures inhibiting crystallization. However, there is precious little information about the local molecular packing in supercooled liquids, meaning that the order parameter of the transition is still unknown. Here, we investigate the liquid–liquid transition in triphenyl phosphite and show that it is caused by the competition between liquid structures that mirror two crystal polymorphs. The liquid–liquid transition is found to be between a geometrically frustrated liquid and a dynamically frustrated glass. These results indicate a general link between polymorphism and polyamorphism and will lead to a much greater understanding of the physical basis of liquid–liquid transitions and allow the systematic discovery of other examples.


Materials
Experiments were carried out on triphenyl phosphite (TPP), which was purchased from Sigma Aldrich and used as supplied.
Polarization and phase-contrast microscopy Microscopy was carried out using an Olympus BX53 microscope with phase-contrast and polarization capabilities, and 10, 20, and 50 large workingdistance objective lenses. Samples were placed in a liquid-nitrogen-cooled Linkam THMS600 stage with 0.1-K accuracy temperature control and sandwiched between borosilicate glass slides (VWR) with 11-µm glass spacer beads (Whitehouse Scientific). Samples were typically quenched at 150 K min -1 from room temperature to the desired quench temperature in the range 211-250 K and held at that temperature. Crossed polarizers were placed above and below the sample with a consistent offset of 5° to aid in the consistency in the determination of contrast. Droplet crystallinity was determined by taking the average intensity and using the background and crystal at 273 K intensities as reference points (with the 20 objective lens). The Kohler illumination procedure was carried out prior to each experiment. Image data were analyzed using ImageJ.
X-ray diffraction XRD data were collected using a Bruker D8 Venture diffractometer equipped with a Photon-II CPAD detector and dual (Copper and Molybdenum) IS 3.0 microfocus sources. Samples were cooled in a nitrogen gas flow using an Oxford Cryosystem n-Helix lowtemperature device. For powder patterns the samples were housed in an open 500-µm diameter capillary, temperature changes were made at rate of 6 K min -1 and diffraction images collected at 273 K. Powder diffraction was carried out as a function of quench temperature as follows: the capillary was cooled to 230 K, held for 15 min and then warmed to 273 K, and the measured diffraction image was found to be consistent with crystal 2. The capillary was then warmed to 303 K, held for 15 min and then cooled to 247 K, held at this temperature for 45 min and then warmed to 273 K where the diffraction pattern did not match either of that of crystal 2 or 3 and was subsequently shown to match the crystal 1 from the single crystal measurement, confirming that crystal 1 is predominant >239 K, while crystal 2 is predominant 226 K < T < 239 K.
Single crystals of crystal 1 were grown in the Linkam stage used for microscopy using 155-µm spacer beads. Single crystals were then large enough to be extracted manually, mounted on a Mitegen micromount in Fomblin polyperfluroether oil. Single crystals of crystal 2 and crystal 3 were obtained by crystallizing TPP in a large sealed flask in a domestic freezer at -19°C. Single crystal data were collected with the crystal held at 150 K using Bruker Apex3 software. The structures were solved using SHELXT and refined using SHELXL2018 within OLEX2. Additional figures and analysis used Mercury.

Infrared spectroscopy
Mid-infrared spectra were obtained using a Bruker Vertex 70 FTIR spectrometer equipped with a globar lamp, a DLaTGS detector, and KBr beamsplitter. Data were taken with either 2 cm -1 or 4 cm -1 resolution between 400 and 4,000 cm -1 in transmission mode. Samples were housed in and temperature controlled using a liquid-nitrogen cooled Oxford Instruments cryostat with a temperature precision of ±0.1°C. The sample, inner and outer windows were made of CaF 2 , ZnS, and KRS-5 respectively. No spacer was used between the CaF 2 sample windows due to detector saturation with thicker samples. Samples were quenched at the maximum cooling rate of 10 K min -1 . The 'final peak position' refers to the position in wavenumber of the most intense peak in liquid 1 (starting out at 1997 cm -1 ), once the liquid-liquid transition has finished.
Infrared imaging was carried out at beamline B22 (multimode infrared imaging and microspectroscopy, MIRIAM) at the Diamond Light Source synchrotron, Oxford. Mid-infrared imaging data were recorded using a Bruker Vertex 80 combined with a Hyperion 3000 microscope, which had an automated translating sample stage. Samples were housed the same Linkam stage used in optical microscopy and sandwiched between BaF 2 windows with no spacer. A region between the windows was left clear of the sample to be used as a background. Samples were quenched at 150 K min -1 and held at 200 K to arrest dynamics. A typical infrared image used a 100 µm 2 aperture, which raster scanned a pre-set area with 5-µm spacing between points. Data were collected S2 using Bruker OPUS software and analyzed using OPUS and Mathematica.

Normal-mode calculations
Density functional theory (DFT) calculations were performed in Gaussian using the method/basis set M06-2X/def2-TZVP. 1 Structure optimizations were performed starting both from a set of manually generated conformations and from the conformations that were resolved using single-crystal XRD. Data were processed using GaussView.
Corrections to normal-mode harmonic frequencies DFT-calculated normal-mode frequencies systematically overestimate "true" frequencies. The frequencies need to be corrected by applying a single scaling factor that is specific to the method/basis and the purpose for which the frequencies are used (zero-point energies, harmonic frequencies, fundamental frequencies). For M06-2X/def2-TZVP, the scaling factor is 0.971 for the calculation of the ZPE and 0.946 for the comparison to experimental fundamental frequencies. 23 Moreover, low-frequency vibrational modes are not adequately described by the harmonic-oscillator approximation; they may even correspond to hindered rotations, rather than vibrations proper. The frequencies of such modes are therefore not reliable. However, low frequencies contribute significantly to the vibrational entropy. In order to mitigate the undue influence of unreliable low frequencies, all frequencies below 100 cm -1 were raised to that threshold value for the purpose of calculating the vibrational entropy. 45

Nomenclature for conformations
The relevant conformational degrees of freedom in P(OPh 3 ) are rotations about the P-O bonds (torsions OPOC ipso ) and rotations about the C ipso -O bonds (torsions POC ipso C). The P-O rotamers are conveniently classified by indicating for each OPh group whether the ring is positioned "up" (u) or "down" (d) with respect to the P atom; that is, whether the ring's C ipso is on the same or the opposite side as the P atom of the plane that is spanned by the three oxygens. The u/d descriptor is equivalent to considering the torsion C ipso -O-P-lp (where lp designates the lone pair on P): with respect to that torsion, syn = "up" and anti = "down".

Generation and optimization of conformers
The set of starting structures included (i) manually generated conformations of each type (i.e., uuu, uud, udd, ddd), which were pre-optimized using MMFF94s in Avogadro; (ii) an ideally C 3 -symmetric uuu conformation; (iii) the conformers taken from the three crystal structures, which are all uud.
The structures were fully optimized at DFT level (M06-2X/def2TZVP) in Gaussian. The udd and ddd starting structures both optimized to uud conformers. All uud and uuu structures retained their configuration during optimization; in particular, the uud conformers from the crystal structures changed very little when optimised in the gas phase.

Optimized conformers
Optimization yielded eight conformers (see Supplementary Table 1 and Supplementary Figure 10). Structurally, they differ by distinct rotations about the PO or OC torsions. All low-energy conformers have the uud configuration and lie within 4 kJ mol -1 of each other. The most stable conformer is the one found in crystal 1, which is almost perfectly C s -symmetric. The uuu conformers are higher in energy than any of the uud conformers, with a gap of about 4 kJ mol -1 . Notably, the C 3 -symmetric conformer (No. 7), which has been considered in previous conformational studies of TPP, is about 8 kJ mol -1 above the minimum, which corresponds to a relative population of 0.04 at 298 K.

Raman spectroscopy and imaging
Confocal Raman microscopy experiments were carried out using a Horiba LabRAM HR confocal microscope using a vertically-polarized 532-nm 28-mW frequencydoubled DPSS laser as the excitation source. Raman spectra over 0-3200cm -1 were collected using a confocal aperture of 200 μm, a 1200 lpm diffraction grating, and averaging for circa 100 s. Sample temperature and quench rate were controlled using a Linkam THMS600 stage. Spectra were analyzed using LabSpec5 software.
Samples were quenched to the desired temperature at a rate of 100 K/min. To nucleate liquid 2 droplets, the sample was quenched to 220, 223, 226, or 230 K. At a quench temperature of 223 K, it took circa 170 minutes to obtain large enough droplets (circa 50 μm diameter). The sample was subsequently rapidly quenched to the glass-transition temperature 6 of liquid 1 T g,1 = 203 K to arrest further growth allowing leisurely collection of Raman data.
To nucleate crystal 2, after the formation of liquid 2 droplets as per above, the sample temperature was raised rapidly to 260 K to induce cold crystallization followed by rapid quenching to 203 K as before for data collection. To nucleate crystal 1, the liquid 1 sample was quenched to 250 K for 15 minutes and subsequently heated to 273 K before being re-quenched to 203 K to allow data collection.
The experimental parameters for Raman imaging were the same except a 600 lpm grating was used. Raman maps of 6060 pixels were acquired with a (1 μm) 2 pixel size and 0.5 s of averaging per pixel.
Optical Kerr-effect spectroscopy Ultrafast optical Kerr-effect (OKE) data were taken in purpose-built time-domain pump−probe set-up as described previously. [7][8] Very briefly, OKE data are taken in an ultrafast pump−probe spectroscopy set-up using a Micra laser (Coherent) yielding 800-nm 20-22 fs laser pulses at a repetition rate of 82 MHz. A maximum delay time of 1 ns resulted in spectral coverage down to 1 GHz in the frequency domain after numerical Fourier transformation. Samples were held in quartz cuvettes S3 inside a liquid-nitrogen cooled cryostat (Oxford Instruments) with a temperature precision of ±0.1 °C.
Supplementary Figure 8 shows the OKE spectra of liquid 1 (room temperature and in the glassy state at 180 K) and liquid 2 (LLT carried out at 220 K over 24 hours). In Supplementary Figure 9, the OKE data are converted to a spontaneous Raman spectrum by using [7][8][9] (1) and compared with the spontaneous Raman spectra used in this work. This shows that the OKE and spontaneous Raman spectra are identical above ~60 cm -1 . Below ~60 cm -1 , Raman edge filters distort the spontaneous Raman spectrum. The most common crystal polymorph, crystal 2 ( PUXLUP03 hexagonal) 10 -dark blue, a polymorph that crystallizes from ionic liquid (PUXLUP04 monoclinic) 11 -cyan, and the newly discovered polymorph crystal 1 (monoclinic) -orange. Crystals 1 and 2 differ mostly in their packing rather than conformation as well as a rotation of a phenyl ring (on right-hand side in this plot).