Ice Adhesion. Группа авторов

2 Water and Ice Nucleation on Solid Surfaces

       Youmin Hou*, Hans-Jürgen Butt and Michael Kappl†

       Department of Physics at Interfaces, Max Planck Institute for Polymer Research, Ackermannweg 10, Mainz, Germany

       Abstract

      Nucleation, in which a new phase is spontaneously formed in an original phase, is normally regarded as the initial step for the phase transitions, for example, water condensation and icing. The ability to control nucleation is of significant importance for scientific research and many industrial applications, particularly for water and ice. Despite different properties in bulk configuration, the formation processes of nanoscopic water and ice nuclei have a lot in common. The study of nucleation can be traced back to the pioneering work of Fahrenheit in the 1700s, while the understanding of nucleation remains inadequate due to the difficulty in characterizing nucleation dynamics with conventional measurement tools. In this chapter, we present an overview of the most commonly used nucleation theory for analyzing the initial water condensation and ice crystallization, and the recent progress in the field of controlling heterogeneous nucleation on solid surfaces.

      Keywords: Nucleation theory, condensation, icing, hybrid wettability

2.1 Introduction

      Phase transitions of water play a prominent role in many natural processes like fog and cloud formation, precipitation as rain, snow or hail. In technical applications such as heat exchangers, fog harvesting or water desalination, high nucleation and condensation rates are favored; while in the case of anti-icing coatings, one targets for suppression of nucleation. These phase transitions occur when the original phase is supersaturated with respect to a more stable one. The formation of a new phase within a metastable original phase (i.e., mother phase), however, does not begin in a continuous manner. It rather arises spontaneously as a result of fluctuations of temperature and density in the original phase when a critical supersaturation of vapor or a critical supercooling of liquid water is exceeded. This spontaneous process is called nucleation.

As an established research area, the development of nucleation theory has been a long, gradual process, taking almost 100 years. Based on Gibbs’ thermodynamic works from the end of 19^th century, Volmer and Weber formulated the first kinetic model of nucleation for the vapor-to-liquid phase transition in 1926 [1, 2], which was further developed by Farkas [3], Becker [4], and Zeldovich [5]. Later, Turnbull and Fisher extended this theory to the crystal nucleation from liquid by redefining the kinetic model in the liquid phase [6]. These works constitute the “classical nucleation theory”, which provides a ready explanation for various nucleation processes [7-12]. It was originally developed for the ideal case of homogeneous nucleation, which involves the two phases of one material only. In practical situations, however, one has typically to deal with heterogeneous nucleation, where the presence of a third phase of another material (e.g., aerosol particles and solid surfaces) acts as nucleation site. This opens the way to control the nucleation in phase transitions by designing corresponding surfaces of the third phase. Recently, water condensation [13-24] and icing [25-32] involving heterogeneous nucleation on functional surfaces, has attracted much attention due to its significance in energy and environmental applications. To improve the condensation and anti-icing performance, durable super-hydrophobic [33-45] and super-icephobic surfaces [46-56] are urgently required in multiple industries, such as power generation, water harvesting, aviation, etc. Guided by the classical nucleation theory, considerable progress has been achieved in manipulating heterogeneous nucleation via surface topography [57-61] and chemistries [62-71]. Studies of interfacial effects on water molecules, e.g., surface charge [72-77] and recrystallization inhibitors [78-81], also enrich the understanding of water properties and nucleus formation at interfaces. To date experimental exploration of nucleation embryos remains inadequate, although considerable research effort using numerical investigations has been made [82-87].

      In this chapter, classical nucleation theory is introduced and applied to derive nucleation rates for the two cases of homogeneous and heterogeneous nucleations. The results are used for analyzing the initial steps of both water condensation and ice crystallization. On that basis, we subsequently discuss the recent progress in the field of controlling heterogeneous nucleation on solid surfaces for achieving enhanced condensation or ice inhibition.

2.2 Classical Nucleation Theory

      Up to now, classical nucleation theory (CNT) is still the theory most widely used to quantitatively describe the kinetics of nucleation. This theory was established based on two major assumptions: (1) the nuclei (i.e., embryos) can be regarded as spherical clusters, which possess the macroscopic densities and surface tensions, and (2) their distribution follows a Boltzmann statistics.

      In water vapor there are always clusters of a few molecules which exist due to random agglomeration of molecules. These agglomerates constantly form and decay. When the system is in a metastable, supersaturated state, such clusters should, in principle, be energetically favored because the chemical potential of a molecule within the cluster is lower than in the vapor phase. However, cluster formation also leads to the existence of a liquid-vapor interface, which inevitably leads to an energy penalty – the interfacial energy – for forming this interface. Therefore, whether such a cluster can develop into a nucleation embryo depends on the relative magnitudes of these two energy contributions. The change of Gibbs free energy ∆G for forming a cluster containing n molecules can be expressed as,

      (2.1)

      in which, Δµ is the change in chemical potential for a molecule on moving from the vapor phase (denoted by subscript 1) to the liquid phase (denoted by subscript 2). A and σ_1,2 denote the area of interface and the surface tension between liquid and vapor phases, respectively.