end of the First Industrial Revolution also saw the introduction of another artificial refrigeration concept: thermoelectrics. French watch dealer-turned physicist Jean Charles Athanase Peltier described in his 1834 paper “Nouvelles Expérences sur la Caloricité des Courans Électriques” [New Experiments on the Heat Effects of Electric Currents] that passing a current through bimetallic circuits caused the absorption of heat at one of the metal junctions and rejection of heat at the other. When Peltier welded bismuth with antimony, the semiconductor yielded a temperature of -45°C [50]. In 1838 physicist Emil Lenz used the same bismuth-antimony junction in his experimental apparatus to freeze water when current was applied in one direction, and melt the ice when current was reversed [51]. Almost simultaneously to the work of Peltier and Lenz, German medical doctor and physicist Thomas Johann Seebeck described how bimetallic circuits would deflect the needle of a compass when the circuit’s junctions were held at different temperatures [52]. Danish physicist Hans Christian Ørsted connected Seebeck’s work with his own on the relationship between current and magnetism and realized that the temperature difference between the junctions produces a voltage, driving an electric current [53]. We now call these two thermoelectric effects the “Peltier-Seebeck effect”, connoting that they are converse manifestations of the same physical process. The Seebeck portion of the effect forms the basis of the working principle for thermocouples, the temperature measurement devices which have become indispensable in rigorous surface icing research, and indeed in scientific research as a whole [54]. The Peltier effect gained considerable attention in the 1950’s after Abram Ioffe demonstrated the increased thermoelectric effect possessed by doped semiconductors [55]. It was theorized that thermoelectric cooling could surpass vapour-compression technology for domestic refrigeration. This time of frenzied semiconductor research culminated in H. Julian Goldsmid’s discovery of Bi2Te3-Sb2Te3 as the material with the highest thermoelectric effect [56]. Even so, bismuth-telluride alloys only produce moderate amounts of cooling compared to vapour-compression refrigerators. Nonetheless, the Peltier plate has become widely used in surface icing experimentation as it offers researchers high reliability and control over temperatures [57].
The turn of the 20th century ushered in the Second Industrial Revolution, a period of transition from the steam power which was typical of the earlier industrial revolution, to the more modern energy sources of electricity and petroleum [58]. Although attempts at designing an internal combustion engine date back to the early 1800’s, the German locomotive engineer Karl Benz is credited with developing the first gasoline engine for which he was granted a patent in 1879. Benz’s subsequent patents all centred around the practical use of his engine for mobility, culminating in the Benz Patent Motorwagen, the world’s first automobile introduced in 1886 [59]. By 1901 Benz & Cie was producing nearly 600 automobiles per year and Ransom E. Olds had implemented a stationary assembly line at his car factory in Lansing, Michigan increasing production to 2500 cars that year [60]. When Henry Ford introduced the moving assembly line at his Highland Park, Michigan factory in 1913, productivity was increased 8-fold with a completed car exiting the factory every 15 minutes [61]. The sheer number of automobiles on the road, their increased reliability (and therefore range), and their increased speed necessitated a solution be devised for slippery surface ice conditions - in much the same vein that horse-powered transportation had required increased traction in past centuries. Beginning in 1940, Detroit, Michigan fittingly became the first city in the world to spread salt on its streets to combat surface icing. The city relied on its vast underground reserves of rock salt to melt surface ice using the principles of frigorific mixtures discovered in the 1790’s [62]. The use of road salt has dramatically increased in the past 80 years. In 2010, between 10 and 20 million tons of salt was used in the United States alone [63].
The increased power-to-weight ratio of the internal combustion engine had a second dramatic impact on human transportation in the 20th century. For the first time, heavier-than-air powered flight was made possible by the new propulsion technology. American bicycle sales and repairmen - turned aviators Orville and Wilbur Wright made the first controlled and sustained airplane flights in 1903. Their plane was powered by a 8.9 kW engine weighing 82 kg and made a flight of 37 m at a velocity of 10.9 km/h [64]. Airplane technology advanced quickly after the Wright brothers’ flight. Airplanes would play a significant role in World War I both in terms of reconnaissance and combat. And the first trans-Atlantic airplane flight would take place between Newfoundland and Ireland by John Alcock and Arthur Brown in 1919 [65]. By the start of World War II, it was apparent that the accretion of ice on the surface of airplanes greatly affected the airflow over their wings and tails, with typical tests showing that less than 0.5 mm of ice along the leading edge can decrease lift by up to 25% [66]. Manual removal of surface ice which formed on the wings while the plane was grounded proved to be an impossible task, leading to the development of the first glycol-based deicing fluid which, much like road salt, forms a frigorific mixture with the surface ice allowing it to flow from the airplane [67]. A typical modern commercial jet requires between 550 and 3800 litres of deicing fluid to completely remove surface ice during wet-weather conditions [66].
As can be seen from the previous discussion of man’s attempts at researching and combatting surface ice formation, the implemented solutions have been rather active solutions, necessitating reapplication for continued effect. Contrarily, research since the turn of the 21st century has aspired toward anti-icing/icephobic materials which offer a passive method of keeping a surface free of ice. In the next section we outline an important 20th century concept which was omitted from the previous historical discussion, the Classical Nucleation Theory (CNT). CNT has re-emerged with the introduction of new nano-scale manufacturing techniques as a way to rationally design surfaces which thermodynamically inhibit the formation of ice.
1.2 A Thermodynamically Designed Anti-Icing Surface
The Classical Nucleation Theory (CNT) arose from the work of German chemists Volmer and Weber in 1926 in which they estimated the rate of the condensation of over-saturated vapours to liquid, as a function of the degree of over-saturation [68]. Becker and Döring furthered this research in 1935 when they noted that the condensation process has a certain activation energy that must be overcome for the new phase to form [69]. Finally, the homogeneous CNT was completed in 1939 when Frenkel made the important conclusion that the Volmer-Weber/Becker-Döring condensation model also applies to systems which are not over-saturated. Frenkel correctly hypothesized that even under-saturated solutions have a steady-state distribution of small-sized clusters due to continuous nucleation and decay of unstable clusters [70].
It is now known that the Classical Nucleation Theory, even though it is an approximation, gives a reasonable prediction of nucleation rates of any new thermodynamic phase [71]. This includes the nucleation of solid ice from liquid water. In the following sections we outline the derivation of the homogeneous CNT with regards to liquid water homogeneously nucleating into solid ice. Next, we show the extension of the homogeneous case to the more pertinent heterogeneous nucleation scenario of ice forming on a solid surface. In doing so, a method of rational thermodynamic design for anti-icing surfaces is presented.
1.2.1 Homogeneous Classical Nucleation Theory
The Classical Nucleation Theory models a growing ice embryo of clustered H20 molecules as a sphere of radius re, as shown in Figure 1.3(a). The change in free energy of a liquid water system due to spherical ice embryo growth is a result of the competing energy effects of: (i) creating a new lower energy (solid) phase, and (ii) creating a new higher energy (solid-liquid) interface. The balance of these energy terms is given in Equation 1.1.
where ∆GIW(T) and γIW(T) denote the free energy difference between ice and water (per unit volume) and the interfacial energy
