When ice melts into water, the molecules of water become more disordered and less organized as they absorb energy from their surroundings. At the microscopic level, this process is known as thermal motion. As the temperature of the ice increases, the molecules of water gain more energy and begin to vibrate more rapidly. This causes the bonds between the molecules to weaken, and the molecules become more mobile. Eventually, the bonds between the molecules break completely, and the ice turns into liquid water. At this point, the molecules of water are able to move around freely and take on a more disordered arrangement, as is characteristic of liquids.

How do you know ice is melting into water? The appearance of the ice changes as it melts, becoming slushy and wet as the molecules become more disordered and more mobile. But, that’s not science. We need to measure it. So, the question becomes to how do you know ice is melting into water a microscopic perspective?

To identify the water molecules from the ice: two methods are considered in Sun’s paper (Sun et al. 2021). I will introduce the concept here in this blog post.

Tetrahedral order parameter

Mochizuki et al. (Mochizuki, Matsumoto, and Ohmine 2013) proposed that the location changes in water molecules will determine the state of the water molecule. Specifically, the offset between the water molecule to the nearest lattice point of the ice structure is greater than than 0.1 nm.

In 2010, Moore et al. (Moore et al. 2010) introduced the CHILL algorithm, which was based on the local bond order parameter method developed by Rein et al. (Rein ten Wolde, Ruiz-Montero, and Frenkel 1996) in 1996. The CHILL algorithm used the coherence of the orientational order of molecules with that of their neighbours to distinguish between the crystal and liquid phases. Errington et al. (Errington and Debenedetti 2001) proposed the tetrahedral order parameter in 2001, which was widely used to define ice-like and liquid-like molecules. This parameter was calculated in Equation:.

\[ Q_i=1-\frac{3}{8} \sum_{j=1}^3 \sum_{k=j+1}^4\left(\cos \theta_{j \mathrm{i}, \mathrm{k}}+\frac{1}{3}\right)^2 \]

where \(i, j\) and \(k\) are indices for \(O\) atoms.

Conde et al. (Conde, Vega, and Patrykiejew 2008) suggested a molecule as classified as ice when \(0.91 \leqslant Q_i \leqslant 1\).

Averaged hydrogen bonds for ice or water molecules

The second way to differentiate between water and ice state is to calculate the averaged hydrogen bond. At a temperature of 25°C, the average number of hydrogen bonds per water molecule is estimated to be 3.59. For ice molecules, the average number of hydrogen bonds is estimated to be 4.0 (Jorgensen and Madura 1985). Carignano et al. (Carignano, Shepson, and Szleifer 2005) similarly applied this criterion to identify the ice or water molecules.

Among many definitions of hydrogen bond, such as calculating potential energy of each pair of ice/water molecules (Starr, Nielsen, and Stanley 1999), electronic structure-based method (Kumar, Schmidt, and Skinner 2007), the geometric distance-angle identification criterion (Sun et al. 2021) is a straightforward method to calculate it.

There are two parameters in geometric distance-angle identification criterion: the cutoff angle (\(\theta_{hb}\)) between the \(\mathrm{OH}\) hydrogen bond and the \(\mathrm{OH}\) covalent bond, and the cutoff distance (\(r_{hb}\)) between the \(O\) and \(H\) atoms in different molecules.

A hydrogen bond is considered to be present when the distance (\(r\)) between the \(H\) and \(O\) atoms on different molecules and the angle (\(\theta\)) between the water molecules meet the following conditions: \(r \leqslant r_{hb}\) and \(\theta \leqslant \theta_{hb}\).

As it was suggested in the work by Kim and Yethiraj (Kim and Yethiraj 2008) , \(r_{h b}\) and \(\theta_{h b}\) are chosen as \(3.5 \mathrm{~A}\) and \(40^{\circ}\), respectively.

Reference(s)

Carignano, MA, PB Shepson, and I Szleifer. 2005. “Molecular Dynamics Simulations of Ice Growth from Supercooled Water.” Molecular Physics 103 (21-23). Taylor & Francis: 2957–67.
Conde, MM, C Vega, and A Patrykiejew. 2008. “The Thickness of a Liquid Layer on the Free Surface of Ice as Obtained from Computer Simulation.” The Journal of Chemical Physics 129 (1). American Institute of Physics: 014702.
Errington, Jeffrey R, and Pablo G Debenedetti. 2001. “Relationship between Structural Order and the Anomalies of Liquid Water.” Nature 409 (6818). Nature Publishing Group: 318–21.
Jorgensen, William L, and Jeffry D Madura. 1985. “Temperature and Size Dependence for Monte Carlo Simulations of Tip4p Water.” Molecular Physics 56 (6). Taylor & Francis: 1381–92.
Kim, Jun Soo, and Arun Yethiraj. 2008. “The Effect of Salt on the Melting of Ice: A Molecular Dynamics Simulation Study.” The Journal of Chemical Physics 129 (12). American Institute of Physics: 124504.
Kumar, R, JR Schmidt, and JL Skinner. 2007. “Hydrogen Bonding Definitions and Dynamics in Liquid Water.” The Journal of Chemical Physics 126 (20). American Institute of Physics: 05B611.
Mochizuki, Kenji, Masakazu Matsumoto, and Iwao Ohmine. 2013. “Defect Pair Separation as the Controlling Step in Homogeneous Ice Melting.” Nature 498 (7454). Nature Publishing Group: 350–54.
Moore, Emily B., Ezequiel de la Llave, Kai Welke, Damian A. Scherlis, and Valeria Molinero. 2010. “Freezing, melting and structure of ice in a hydrophilic nanopore.” Phys. Chem. Chem. Phys. 12 (16). The Royal Society of Chemistry: 4124–34. doi:10.1039/B919724A.
Rein ten Wolde, Pieter, Maria J Ruiz-Montero, and Daan Frenkel. 1996. “Numerical Calculation of the Rate of Crystal Nucleation in a Lennard-Jones System at Moderate Undercooling.” The Journal of Chemical Physics 104 (24). American institute of physics: 9932–47.
Starr, Francis W, Johannes K Nielsen, and H Eugene Stanley. 1999. “Fast and Slow Dynamics of Hydrogen Bonds in Liquid Water.” Physical Review Letters 82 (11). APS: 2294.
Sun, Qiangqiang, Yong Zhao, Kwing-So Choi, and Xuerui Mao. 2021. “Molecular Dynamics Simulation of Thermal de-Icing on a Flat Surface.” Applied Thermal Engineering 189. Elsevier: 116701.