Lifshitz interaction can promote ice growth at water-silica interfaces

Abstract

At air-water interfaces, the Lifshitz interaction by itself does not promote ice growth. On the contrary, we find that the Lifshitz force promotes the growth of an ice film, up to 1-8 nm thickness, near silica-water interfaces at the triple point of water. This is achieved in a system where the combined effect of the retardation and the zero frequency mode influences the short-range interactions at low temperatures, contrary to common understanding. Cancellation between the positive and negative contributions in the Lifshitz spectral function is reversed in silica with high porosity. Our results provide a model for how water freezes on glass and other surfaces. DOI: 10.1103/PhysRevB.95.155422 Although water in its different forms has been studied for a very long time, several properties of water and ice remain uncertain and are currently under intense investigation [1][2][3][4]. The question we want to address in the present paper is to what extent the fluctuation-induced Lifshitz interaction can promote the growth of ice films at water-solid interfaces, at the triple point of water. Particles and surfaces, e.g., quartz, soot, or bacteria, in supercooled water are known experimentally to nucleate ice formation [5][6][7]. Here, we focus on interfaces between water and silica-based materials and examine the roles of several intervening factors in the sum over frequency modes (Matsubara terms) contributing to the Lifshitz free energy.Quantum fluctuations in the electromagnetic field result in van der Waals interactions, which in their unretarded form were explained by London in terms of frequency-dependent responses to the fluctuations in the polarizable atoms constituting the material medium [8]. The understanding of these interactions was revolutionized when Casimir introduced retardation effects [9]. The theory was later generalized by Lifshitz to include dielectric materials [10,11]. The Lifshitz formula in Eq. (1), derived for three-layer planar geometries [11], gives the interaction energy between two semi-infinite dielectric media described by their frequency-dependent dielectric permittivities as well as the dielectric permittivity of the medium separating them (see Fig. 1).The purpose of the present work is twofold. First, we want to show that a finite size ice film, nucleated by a solid-water interface, can be energetically favorable even when only the Lifshitz interaction is accounted for. Second, we want to highlight a relevant contribution from the zero frequency term in the expression for the Lifshitz energy in a region where it is not expected to be important. The temperature dependence * Mathias.A.Bostrom@ntnu.no † prachi.parashar@ntnu.no ‡ iver.h.brevik@ntnu.no of the Casimir force between metal surfaces [11][12][13][14] relies strongly on the exact behavior of the low-frequency dielectric function of metals. These and many other investigations have provided support for the notion that the zero frequency term would only be relevant at high temperatures or large surface separations at a moderate ...

Dispersion Forces Stabilize Ice Coatings at Certain Gas Hydrate Interfaces That Prevent Water Wetting

“…In contrast to their results, we have found that buoyancy combined with dispersion and double layer forces establish an equilibrium where large ice particles float on the surface while small (micron-sized) ice particles are trapped at a distance below a water surface [45]. Further, it was shown that ice formation can be induced by dispersion forces near silica-water interfaces (where silica can be used as a model for rock material) [34]. For CO 2 gas hydrates and the N 2 gas hydrate, energy minimum exist corresponding in each case to an equilibrium ice film thickness: d CO2 =44, 43 and 37 Å for CO 2 volume fractions p = 5.75, 6 and 7.67, respectively, and d N2 =32 Å.…”

“…These dielectric functions are for a system at the triple point of water, close to zero degrees Celsius at low pressure. The final results for ice melting [19,20,21,22,23,31,32] and water freezing [33,34] are sensitive to the dielectric functions of ice and water since these are extremely similar when the water is in equilibrium with the ice. We show in Fig.…”

“…In the remainder of this letter, we use ice JD , the Daniels [29] model for ice, since both models give very similar results. The thicknesses correlate with the frequency where the dielectric functions of ice and water have a crossing [34]. Figure 5 shows the free energy as a function of ice film thickness for different gas hydrates in ice cold water.…”

Role of zero point energy in promoting ice formation in a spherical drop of water

“…As an application of the results found here, that ice grows inside water at the triple point of water, we would like to investigate the relevance of this effect to the predictions for liquid water on distant planets and their moons. In presence of a silica surface we have predicted that ice can form in water based on Lifshitz theory [17]. Boström et al further proposed that Lifshitz forces could lead to ice formation on some specific gas hydrate surfaces in water [39].…”

“…This expression leads to d 1 ≈ 0.41 µm and d 2 ≈ 7.83nm, which are in the right ballpark of 0.37 µm and 3.56nm, respectively. We have been unable to find a more accurate analytical estimate, because we are dealing with a discrete function of the Matsubara mode numbers n, in addition to the fact that the zero mode behaves significantly differently from other modes [17].…”