Frustration of crystallisation by a liquid–crystal phase

Frustration of crystallisation by locally favoured structures is critically important in linking the phenomena of supercooling, glass formation, and liquid-liquid transitions. Here we show that the putative liquid-liquid transition in n-butanol is in fact caused by geometric frustration associated with an isotropic to rippled lamellar liquid-crystal transition. Liquid-crystal phases are generally regarded as being “in between” the liquid and the crystalline state. In contrast, the liquid-crystal phase in supercooled n-butanol is found to inhibit transformation to the crystal. The observed frustrated phase is a template for similar ordering in other liquids and likely to play an important role in supercooling and liquid-liquid transitions in many other molecular liquids.

Raman spectra in the OH-stretch region used to determine the degree to which isotropic liquid is present in the LC droplets. The Raman spectra of n-butanol taken before transformation (isotropic liquid), after the phase transition (LC), and after cold crystallisation (crystal) at 140 K. The grey bar shows the range 3080-3110 cm -1 used to estimate how much isotropic liquid is left in the LC droplet.

S2 -Determination of the anisotropy in the Raman scattering intensity
In this study, Raman maps were made of the LC droplets and their immediate surrounding before and after cold crystallisation (see Figure S2) by using a vertically polarised excitation laser and un-polarised detection of the Raman scattered light. As the LC director is pointing away from the droplet centre, the projection of the laser polarisation vector onto the molecular axis varies throughout the droplet. This gives rise to anisotropic Raman maps as can be seen in Figure S3. Depending on the molecular Raman polarisability tensor of a particular vibrational mode, these maps are more or less intense in directions parallel or perpendicular to the excitation laser polarisation.
To quantify the degree of anisotropy, the Raman intensity is measured at two points displaced along the x-and yaxis. In Figure S3, we have indicated two typical sample positions with crosses where the measured Raman intensities are Ix and Iy respectively. The anisotropy is defined here as Iy/Ix.

S3 -Raman polarisability tensor and anisotropy
The derivative of the Raman polarisability tensor ( dα / dq ) of the OH-stretch vibrational mode was calculated for ethanol (which is faster to calculate than n-butanol but should give the same result for the OH-stretch) using the Gaussian 09 software package 1 using B3LYP/6-31+G(d,p) level of theory. The polarisability tensor is dominated by the polarisability in the direction of the O-H bond with a small rotation in the direction of the C-O bond. The eigenvalues of the polarisability tensor are -2.90, -0.28, and -0.12 Å 2 . Using these eigenvalues, it is straightforward to calculate the strength of the OH-stretch Raman band as a function of the direction of the electric field vector.
The unit cell of the crystalline form of n-butanol contains two molecules. Using the known coordinates of the OH groups, 2 one can calculate the Raman scattering strength as function of the direction of the electric field vector within the crystal lattice. The maximum ratio of the strongest vs. the weakest Raman scattering strength calculated this way is 7.6. When n-butanol (liquid 1) is cold crystallised, it forms a polycrystalline sample with randomly oriented but easily discernible crystals. Raman microscopy measurements on the OH-stretch mode of such a polycrystalline sample reveals a maximum intensity ratio of 5-10, consistent with the theoretical value.

S4 -Experimental determination of contamination of the LC with (nano) crystals
In order to estimate the crystalline component in the LC droplets prior to cold crystallisation, spectra were taken from LC droplets both before and after cold crystallisation and the peak intensities were compared in the phonon region, specifically at 58 cm -1 where a prominent peak appears upon cold crystallisation and at ~71-72 cm -1 . The shape of the Raman spectrum of the droplets after cold crystallisation is identical (within the signal to noise ratio) to that of polycrystalline n-butanol obtained by cold crystallising the isotropic liquid. It was necessary to subtract a background caused by librations and hydrogen-bond modes 3,4 from all data. The Raman bands corresponding to these underdamped molecular motions are not expected to change very much between liquid, LC, and crystal. Therefore, the contribution from librations and hydrogen-bond modes was estimated by using the isotropic liquid spectrum measured in the same setup. Figure S4 (a) and (b) show the Raman spectra of a droplet before and after cold crystallisation with the librations and hydrogen-bond mode background for both traces shown in grey. The resulting background subtracted spectra are shown in Figure S4 (c). The intensity of the background-subtracted data below 80 cm -1 is interpreted as being due to phonon modes of crystalline butanol. From these traces, we estimate that the amount of crystal contamination in the LC droplet prior to cold crystallisation is less than 2% based on the intensity of the 58-cm -1 phonon band and below 18% based on the intensity of the 72-cm -1 phonon band. This implies that the 72-cm -1 phonon band is sensitive to a degree of order that remains on melting the crystal to form the LC.

Figure S4 Low-frequency Raman spectra to determine the degree to which crystals are present in the LC droplets before cold crystallisation. The low-frequency Raman spectra of n-butanol taken after the liquid-LC transformation and in the same location after cold crystallisation. (a) The Raman spectrum of LC with the Raman spectrum of the isotropic liquid shown in grey. (b) Idem after a cold-crystallisation cycle. (c) The same spectra as shown in (a) and (b) with the isotropic-liquid spectrum subtracted.
Another way to estimate the crystalline component in the LC droplets prior to cold crystallisation involves using wide-angle x-ray scattering (WAXS). Figure S5 shows the microfocus WAXS data collected on a LC droplet before cold-crystallisation and a polycrystalline sample. The polycrystalline WAXS data shows numerous prominent sharp peaks. Some of these, such as the (001) and (012) peaks, re-appear in the LC WAXS data although much broadened as expected. Other peaks, such as the (101) peak, are essentially absent in the LC and can be used to estimate the degree of contamination with crystals. Based on the reduction of the intensity of peaks such as the (101) peak, it can be estimated that the contamination of the LC phase with crystals is less than 1.8%.
Thus, two independent techniques come to identical conclusions (within the signal to noise ratio) that the LC phase contains no more than 2% crystalline material.

S5 -Supplementary video
This video shows the formation of LC droplets in n-butanol at 140 K, followed by cold crystallisation at 173 K, and melting at 185 K. The crystals that grow at 173 K do not penetrate the LC droplet.