Kinetics of the homogeneous freezing of water B. J. Murray,* a S. L. Broadley, a T. W. Wilson, a S. J. Bull,w a R. H. Wills,z a H. K. Christenson b and E. J. Murray c Received 16th February 2010, Accepted 26th May 2010 DOI: 10.1039/c003297b Rates of homogeneous nucleation of ice in micrometre-sized water droplets are reported. Measurements were made using a new system in which droplets were supported on a hydrophobic substrate and their phase was monitored using optical microscopy as they were cooled at a controlled rate. Our nucleation rates are in agreement, given the quoted uncertainties, with the most recent literature data. However, the level of uncertainty in the rate of homogeneous freezing remains unacceptable given the importance of homogeneous nucleation to cloud formation in the Earth’s atmosphere. We go on to use the most recent thermodynamic data for cubic ice (the metastable phase thought to nucleate from supercooled water) to estimate the interfacial energy of the cubic ice–supercooled water interface. We estimate a value of 20.8  1.2 mJ m 2 in the temperature range 234.9–236.7 K. Introduction The freezing of water to ice is of fundamental interest to many areas of science and technology such as cryopreservation, food science and the atmospheric sciences. Water droplets in the Earth’s troposphere are known to supercool to B236 K at which temperature ice nucleates homogeneously on a short timescale. There have been numerous experimental and theoretical studies of homogeneous ice nucleation, but recent advances mean it is appropriate to re-examine our quantitative under- standing of this fundamental process. In many previous studies it was assumed (implicitly and sometimes explicitly) that hexagonal ice (ice I h ) nucleates when supercooled water droplets freeze. The thermodynamic parameters associated with ice I h were therefore used when interpreting the data. Huang and Bartell 1 were the first to present direct diffraction based evidence that ice I h did not nucleate. In their experiments, very small liquid droplets (4000–6000 water molecules) were formed at B200 K and they found that these droplets crystallised to the metastable cubic ice (ice I c ). They were also able to derive a nucleation rate from their measurements and using this together with classical nucleation theory they estimated the interfacial energy for the ice I c –supercooled water interface. Huang and Bartell 1 then went on to reanalyse literature data 2,3 for nucleation in micrometre-sized droplets (at 230–240 K) and revealed that freezing in these droplets was also consistent with the nucleation of ice I c . The formation of cubic ice from micrometre-sized pure water droplets at around 236 K has only recently been experimentally confirmed using X-ray diffraction. 4,5 In fact, Murray and Bertram 6 showed that water droplets (suspended in an oil emulsion) smaller than 2 mm diameter froze exclusively to ice I c with no bulk ice I h . When water droplets are sufficiently small (o2 mm diameter) and are suspended in oil they efficiently lose the heat evolved during crystallisation. Larger droplets heat up, which allows ice I c to re-crystallise to the stable hexagonal phase. Experiments with a range of droplet sizes led Murray and Bertram 4,7 to conclude that ice I c is always the phase to nucleate and initially crystallise in water when it freezes homogeneously, but unless the heat of crystallisation is removed efficiently the metastable ice I c relaxes to the stable ice I h . Experiments with solution droplets also strongly suggest ice I c nucleates. 7–9 Based on these previous studies we assume that the metastable cubic phase of ice nucleates when water freezes homogeneously and analyse our data accordingly. While Huang and Bartell 1 undoubtedly made substantial progress in our understanding of ice crystallisation, their analysis was limited by the paucity of available thermo- dynamic data for ice I c . They were forced to make a crude estimate of the difference in free energy between ice I c and ice I h . Since Huang and Bartell’s paper in 1995, advances have been made in this respect. The vapour pressure of ice I c has been measured to be 10.5  2.5% larger than that of ice I h at 180–190 K. This vapour pressure measurement can be related to the free energy change on transformation from cubic to hexagonal ice. 10 We present measurements of the rate of nucleation of ice in micrometre-sized water droplets between 234.9 and 236.7 K. We employed a new instrument in which droplets were suspended on a hydrophobic substrate and freezing events recorded with an optical microscope. Classical nucleation theory is then used to estimate the ice I c –supercooled water interfacial energy based on the most recent thermodynamic data for ice I c . In order to compare these values with previous measurements we have re-evaluated the available literature data on a similar basis. Finally, we explore how classical a School of Chemistry, Woodhouse Lane, University of Leeds, Leeds LS2 9JT, UK. E-mail: b.j.murray@leeds.ac.uk b School of Physics and Astronomy, Woodhouse Lane, University of Leeds, Leeds LS2 9JT, UK c Murray Rix Geotechnical, 13 Willow Park, Upton Lane, Stoke Golding, Warwickshire CV13 6EU, UK w Present address: AstraZeneca, Alderley Park, Macclesfield, Cheshire, SK10 4TF, UK. z Present address: Department of Chemistry, University of Warwick, Gibbet Hill Road, Coventry, CV4 7AL, UK. 10380 | Phys. Chem. Chem. Phys., 2010, 12, 10380–10387 This journal is  c the Owner Societies 2010 PAPER www.rsc.org/pccp | Physical Chemistry Chemical Physics