CA2348282A1 - Systems and methods for modifying ice adhesion strength - Google Patents

Abstract

The invention includes system for modifying ice adhesion strength of ice adhered to an object. The system includes an electrode that is electrically insulated from the object and a DC source, e.g., a battery, coupled to the object and the electrode. The source generates a DC bias to an interface between the ice and the object when the ice completes the circuit. The object is conductive or is doped as a semiconductor so that the DC bias applies a voltage to the interface which modifies the ice adhesion strength selectively as compared to the ice adhesion strength with substantially zero bias voltage at the interface. The strength can be increased or decreased relative to its static state (i.e., the state without applied voltage). In this manner, ice such as ice on an aircraft wing can be removed with less work. The system preferably includes an electrically insulating material disposed between the object and the electrode; the insulating material is substantially conformal to the object and the electrode. In most applications, the electrode includes a grid electrode shaped to conform to a surface of the object and each point of the grid electrode is in electrical contact with the source. Accordingly, a grid insulator is generally disposed between the object and the grid electrode. The invention of one embodiment incorporates porous materials to selectively dope the ice on a surface; and the invention of another embodiment incorporates self assembling monolayers to reduce the strength of hydrogen bonding between ice and metals. In one embodiment, the invention provides for coating a power line that changes properties with temperature such that the coating melts snow in freezing conditions.

Description

t Systems and Methods for Modifying lce Adhesion Strength 3 Field of the Invention The invention relates to methods and apparatus for modifying ice adhesion strength s between ice and selected materials. More particularly, the invention relates to systems and methods which apply electrical energy to the interface between ice and such materials so 7 as to either increase or decrease the ice adhesion strength to facilitate desired results.
s Background Ice adhesion to certain surfaces causes many problems. For example, excessive ice to accumulation on aircraft wings endangers the plane and its passengers. Ice on ship hulls t 1 creates navigational difficulties, the expenditure of additional power to navigate through 12 water and ice, and certain unsafe conditions. The need to scrape ice that forms on 13 automobile windshields is regarded by most adults as a bothersome and recurnng chore;
14 and any residual ice risks driver visibility and safety.
15 Icing and ice adhesion also causes problems with helicopter blades, and with public roads. Billions of dollars are spent on ice and snow removal and control. Ice also 1'7 adheres to metals, plastics, glasses and ceramics, creating other day-to-day difficulties.
18 Icing on power lines is also problematic. Icing adds weight to the power lines which causes power outages, costing billions of dollars in direct and indirect costs.
2o In the prior art, methods for dealing with ice adhesion vary, though most 21 techniques involve some form of scraping, melting or breaking. For example, the aircraft 1 industry utilizes a de-icing solution such as Ethyl Glycol to douse aircraft wings so as to 2 melt the ice thereon. This process is both costly and environmentally hazardous; however, 3 the risk to passenger safety warrants its use. Other aircraft utilize a rubber tube aligned along the front of the aircraft wing, whereby the tube is periodically inflated to break any ice disposed thereon. Still other aircraft redirect jet engine heat onto the wing so as to 6 melt the ice.
7 These prior art methods have limitations and difficulties. First, prop-propelled 8 aircraft do not have jet engines. Secondly, rubber tubing on the front of aircraft wings is 9 not aerodynamically efficient. Third, de-icing costs are extrerneiy high, at $2500-$3500 1o per application; and it can be applied up to about ten times per day on some aircraft!
11 The above-referenced problems generally derive from the propensity of ice to stick 12 and form onto surfaces. However, ice also creates difficulties in that it has an extremely 13 low coefficient of friction. Each year, for example, ice on the roadway causes numerous 14 automobile accidents, costing both human life and extensive property damage. If automobile tires gripped ice more efficiently, there would likely be fewer accidents.
16 It is, accordingly, an object of the invention to provide systems and methods which 17 modify ice adhesion strength beneficially.
18 A further object of the invention is to provide systems for reducing ice adhesion on 19 vehicle surfaces such as aircraft wings, ship hulls and windshields to facilitate ice removal.
2o Still another object of the invention is to provide systems for increasing the 2~ coefficient of friction between ice-clad roads and automobile tires, and between ice and 22 other objects such as shoe soles and cross-country skis.

These and other objects will become apparent in the description which follows.
2 Summary of the Invention 3 Certain of above-referenced problems would be lessened if the ice adhesion strength were decreased between the ice and the surface upon which the ice forms. For example, if the adhesion strength between the ice and an aircraft wing were decreased 6 sufficiently, wind pressure, buffeting or light manual brushing would remove the ice from 7 the wing. Similarly, scraping an automobile windshield so as to be free of ice would be 8 much less difficult if the ice adhesion strength between the ice and the windshield were 9 lessened.
to Other above-referenced problems would be lessened if the ice adhesion strength 11 between ice and surfaces in contact with the ice were increased. For example, if the ice 12 adhesion strength were increased between automobile tires and icy roadways, then there 13 would be less slippage and fewer accidents.
i4 Ice has certain physical properties which allow the present invention to selectively modify the adhesion of ice to conductive (and semi-conductive) surfaces.
First, ice is a 16 protonic semiconductor, a small class of semiconductors whose charge earners are protons 17 rather than electrons. This phenomenon results from hydrogen bonding within the ice.
18 Hydrogen bonding occurs because the hydrogen atoms of water molecules in ice share 19 their electrons with an oxygen atom. Thus, the nucleus of the water molecule - uniquely a single proton - remains available to bond with adjacent water molecules.
21 Similar to typical electron-based semiconductors, ice is electrically conductive.
22 While this electrical conductivity is generally weak, the conductivity can be altered by 1 adding chemical agents that donate or accept extra charge-carrying particles, i.e., protons 2 in the case of ice.
3 Another physical property of ice is its evaporability. Evaporability of a substance is a function of vapor pressure at the substance surface. In most materials, vapor pressure drops rapidly at the liquid-to-solid interface. In ice, however, there is virtually no change 6 in vapor pressure at the liquid-to-solid interface. The reason for this is that the surface of '7 ice is covered with a liquid-like layer ("LLL").
8 The LLL has important physical characteristics. First, the LLL is only nanometers 9 thick. Second, it ranges in viscosity from almost water-like, at temperatures at or near to 1o freezing, to very viscous at lower temperatures. Further, the LLL exists at temperatures as 11 low as -100 C, and thus practically exists for most temperatures around the planet.
12 The T .1.1. is also a major factor of ice adhesion strength. For example, if one brings 13 the smooth surface of ice in contact with the smooth surface of an airplane wing, the 14 actual area of contact between the two surfaces is on the order of one-thousandth of the total interface area between the two surfaces. The LLL functions as a wetting substance 16 between the surfaces - the principal behind almost all adhesives - and substantially 1'7 increases the effective contact area between the surfaces. This increase in contact area 18 strongly affects ice adhesion.
19 The combination of the semiconductive properties of ice and the LLL allows one 2o to selectively manipulate ice adhesion strength between ice and other surfaces. Generally, 2~ water molecules within a piece of ice are randomly oriented. On the surface, however, the 22 molecules are substantially oriented in the same direction, either outward or inward. As a 23 result, all their protons, and hence the positive charges, either face outward or inward.

While the exact mechanism is unknown, it is likely that the randomness of water 2 molecules transitions to an ordered orientation within the LLL. However, the practical 3 result of the ordering is that a high density of electrical charges, either positive or negative, occurs at the surface. Accordingly, if a charge is generated on the surface coming on contact with ice, it is possible to selectively modify the adhesion between the two surfaces.
6 As like charges repel and opposites attract, an externally applied electrical bias at the interface of the ice and the other surface either reduces or enhances the adhesion between 8 the ice and the surface.
9 In one aspect, the invention provides a power source connected to apply a DC
voltage across the interface between ice and the surface upon which the ice forms. By 11 way of example, the conductive surface can be an aircraft wing or a ship's hull (or evens the t2 paint applied to the structure). A first electrode connects with the surface; a 13 nonconductive or electrically insulating material is applied as a grid over the surface; and 14 a second electrode is formed by applying a conductive material, for example conductive ~5 paint, over the insulating material, but without contacting the surface.
The surface area of 16 the second electrode should be small as compared to the overall surface area protected by 1'7 the system. By way of example, the surface area under protection (i.e., that area sought to 1s be "ice-free") should be at least about ten times larger than the surface area of the second 19 electrode.
2o One or more wires connect the second electrode to the power source; while one or 21 more wires connect the first electrode to the power source. Ice forming over the surface 22 and the conductive grid second electrode completes the circuit. A voltage is then applied 23 to the circuit, selectively, which controllably modifies the ice adhesion strength of the ice 24 with the surface.

1 A voltage regulator subsystem also preferably connects with the circuit so as to 2 adjustably control the voltage applied across the interface and so as to achieve control over 3 the ice adhesion strength. By way of example, ice made from different concentrations of ions can modify the optimum voltage for which the ice adhesion strength is at a minimum;
and the voltage regulator subsystem thereby provides a mechanism by which the minimum can be changed selectively.
7 Other subsystems preferably connect with the circuit to provide other features, for 8 example to detect whether water or ice completes the circuit. In one aspect, the power 9 source is a DC supply (e.g., a battery) which provides voltage to the circuit and which 1o connects to the deicing electrodes. In another aspect, a DC ammeter connects with the 11 circuit to measure the DC conductivity of the ice (i..e., the semi-conductive layer which 12 "shorts" the two electrodes when formed over the surface and any part of the grid second 13 electrode). In another aspect, an AC supply connects with the circuit to generate AC
14 voltages between about lOkHz and 100kHz, selectively. According to another aspect, an AC ammeter also connects with the circuit to measure the AC conductivity of the ice at 16 frequencies within the 10-100kHz range. In still another aspect, a current comparator 17 compares the AC and DC conductivities.
18 These aspects thus provide circuitry which can, for example, distinguish whether 19 the semi-conductive layer formed over the surface is ice, which might be dangerous, or surface water. The AC conductivity (in the above-mentioned range) and DC
conductivity 21 of water are substantially the same. With respect to ice, however, the AC
conductivity and 22 DC conductivity differ by two to three orders of magnitude. This difference in 23 conductivity is measured by the respective ammeters and is compared in the current 24 comparator. When the difference in conductivity is greater than a predetermined set point, 1 the current comparator signals an icing alarm. At this point, for example, the voltage 2 regulator subsystem can operate to apply a DC bias to the circuit - and thus to the 3 interface - at a desired field strength which sufficiently reduces the ice adhesion strength.
4 According to one aspect of the invention, when ice is detected on an aircraft wing, the icing alarm initiates a feedback loop within the system which (a) measures ice 6 conductivities, (b) determines appropriate bias voltages to reach minimum (or near '7 minimum) ice adhesion conditions, and (c) applies a bias voltage to the ice-wing interface 8 to facilitate ice removal.
9 Those skilled in the art should appreciate that the above-described system can be applied to many surfaces where it is desired to reduce ice adhesion strength, such as on 11 car windshields, ship hulls and power lines. In such cases, if the surface material is 12 weakly conductive, it is desirable to "dope" the surface material such that it is sufficiently 13 conductive. Doping techniques are known to those in the art. Automobile tires, for 14 example, can be doped with iodine to make the rubber conductive. Automobile glass, likewise, can be doped with either ITO or fluoride doped Sn02 to make the windshield an 16 acceptable semiconductor.
1~ However, in another aspect, the above described system and circuit are also 18 applicable to situations where it is desirable to increase the ice adhesion strength. In this 19 aspect, for example, when the icing alarm detects ice, the system activates the feedback loop to regulate applied DC voltages to the interface so as to increase ice adhesion.
21 Situations and surfaces which can benefit from this system include, for example, the 22 bottom soles of a person's shoe (or shoes) and car tires on icy roads.

1 In still another aspect, the invention can include a variable ice adhesion/voltage 2 control subsystem which increases and then decreases ice adhesion strength between ice 3 and a surface, selectively. By way of example, cross country skis (or telemarking skis) ideally have higher friction when climbing an incline (or when descending an incline, in certain situations) and have lower friction when "skiing" down an incline.
According to 6 one aspect of the invention, the ice adhesion system and circuit described herein is 7 attached in circuit with the skis and the operator can adjustably control ski friction 8 selectively.
Other useful background to the invention may be found with reference to the to following papers, each of which is incorporated herein by reference:
Petrenko, The Effect 11 of Static Fields on Ice Friction, J. Appl. Phys. 76(2), 1216-1219 ( 1994);
Petrenko, 12 Generation of Electric Fields by Ice and Snow Friction, J. Appl. Phys.
77(9), 4518-4521 13 (1995); Khusnatdinov et al., Electrical Properties of the IcelSolid Interface, J. Phys.
14 Chem. B, 101, 6212-6214 (1997); Petrenko, Study of the Surface of Ice, IcelSolid and IcelLiquid Interfaces with Scanning Force Microscopy, J. Phys. Chem. B, 101, 16 (1997); Petrenko et al., Surface States of Charge Carriers and Electrical Properties of the 1~ Surface Layer of Ice, J. Phys. Chem. B, 101, 6285-6289 (1997); and Ryzhkin et al., 18 Physical Mechanisms Responsible for Ice Adhesion, J. Phys. Chem. B, 101, 19 (1997).
2o The invention is next described further in connection with preferred embodiments, 21 and it will become apparent that various additions, subtractions, and modifications can be 22 made by those skilled in the art without departing from the scope of the invention.

1 Brief Description of the Drawings 2 A more complete understanding of the invention may be obtained by reference to 3 the drawings, in which:
FIGs. lA-1C illustrate effects of DC bias on ice adhesion to a liquid metal (Mercury), smaller contact angles O indicating stronger adhesion;
6 FIG. 2 schematically illustrates an ice manometer used in measurements of ice-'7 mercury interfacial energy such as illustrated in FIG. lA-IC;
8 FIG. 3 graphically illustrates experimental results of DC bias versus ice-Hg 9 interfacial energy for ice doped with 0.5% NaCI, T = -10°C;
l0 FIG. 4 illustrates how production of gas bubbles at an ice/metal interface functions 11 as an interfacial crack to reduce interfacial strength;
12 FIG. 5 illustrates one system constructed according to the invention for modifying 13 ice adhesion to a generic conductive (or semiconductor) material;
14 FIG. 6 shows a cross-sectional view (not to scale) of the system of FIG. S;
FIG. 7 illustrates one system of the invention for decreasing the ice adhesion 1b strength of ice that forms on an aircraft wing;
1'7 FIG. 8 illustrates one system of the invention for removing ice and snow from 18 power lines through application of a coating on the power line;
19 FIG. 9 illustrates application of a ferroelectric coating onto a non-active surface, in 2o accord with the invention, to remove ice therefrom;

1 FIG. 10 shows a porous layer constructed according to the invention so as to 2 release ions into ice to facilitate reduction in ice adhesion;
3 FIG. 11 shows additional detail of a power line constructed according to the 4 invention; and FIG. 12 shows a self assembling monolayer constructed according to the invention to facilitate reduction of ice adhesion to surfaces.
Detailed Description of the Drawings 8 The invention includes systems and methods which modify ice adhesion strength 9 to materials such as metals and semiconductors by application of a DC bias to the interface between the ice and the materials. The invention can thus be used to reduce and in some i i cases eliminate the adhesion of ice onto such materials.
12 In certain embodiments, the invention modifies the electrostatic interactions 13 which form the bonding between ice and metals. These interactions are effectively 14 changed (either reduced or enhanced) by application of a small DC (direct current) bias is between the ice and the metals.
i6 Experimentation and theoretical calculations have shown that ice surfaces have i'7 high density electrical charges of 10-2 C/mz to 3~ 102 C/m2. See, Petrenko et al., Generation is of Electric Fields in Ice and Snow Friction, J. Appl. Phys., 77(9):4518-21 (1995);
19 Petrenko, A Study of the Surface of Ice. Ice/Solid and IcelLiquid Interfaces with Scanning 2o Force Microscony, J. Phys. Chem. B, 101,6276 (1997); and Dosch et al., Surface Science 21 366, 43 (1996), each of which is hereby incorporated by reference. This charge density 22 originates from the strong polarization of water molecules in the ice subsurface layer.

1 The interaction between ice surface charges and the charge induced in a solid 2 affects the strength of an ice-solid interface. By estimation, the electrostatic attraction 3 (negative pressure Peg) of two plane surface charges is given by:
8 ~E~
4 Peg- °2 (j) where ~o is the dielectric permittivity of the vacuum, and E is the electric field strength in 6 the space between the charges. Since the charge distribution determines the contact 7 potential V of the two materials, we can estimate E as V /L, where L is the distance 8 between the plane charges located in the ice and in the solid. V~ for ice-metal interfaces 9 varies from a few tenths of a volt to about 1 V. See, Buser et al., Charge Separation by 1o Collision of Ice Particles on Metals: Electronic Surface States, Journal of Glaciology, 11 21(85): 547-57 (1978), which is incorporated herein by reference.
12 Taking L = lnm (the main screening length in the doped ice illustrations above), 13 s = 3.2 (the high-frequency dielectric constant of ice) and V~ = 0.5 V (the typical 14 magnitude of a contact potential), equation (1) provides that Peg ~ 3.3 Mpa, a magnitude comparable with, but exceeding, the macroscopic tensile strength of ice at 1.5 MPa. See, 16 Schulson et al., A Brittle to Ductile Transition in Ice Under Tension, Phil. Mag., 49, 353-1'7 63 (1984), which is hereby incorporated by reference.
18 More sophisticated calculations of the electrostatic interaction energy between ice 19 surface charges and metals are shown below, utilizing real space-charge distributions and 2o charge relaxation calculations. Specifically, it is shown below that this interaction energy 21 is 0.01 to 0.5 J/m at -10° C. The lower limit 0.01 J/m corresponds to pure ice; while the upper value 0.5 J/m corresponds to heavy doping. These values are comparable with 2 other experimental results, described below, which utilized scanning force microscopy 3 ("SFM"). The SFM results determined an electrostatic interaction energy of 0.08 ~ 0.012 J/m ; and experiments on ice/mercury interfaces return 0.150 +/- 0.015 J/m for that electrostatic part of ice/metal adhesion.
6 Since electrostatic interactions contribute to ice adhesions, the adhesion strength 7 between ice and a conductive material (e.g., a metal or semiconductor) is changed by an 8 external DC bias applied across the ice-material interface.
9 To determine the effect of DC bias on ice adhesion, the interface was modeled as a liquid-solid interface instead of a solid-solid interface. Indeed, the interfacial energy which 11 determines the adhesion is reliably measured in a contact-angle experiment when one 12 material is a liquid and the other a solid, as in the water-metal situation. A similar 13 technique is thus employed for an ice-metal interface if the metal is in the liquid phase.
14 Mercury, for example, with its melting point at -38.83°C, low chemical activity, and ease in preparing a clean surface, is well suited to prove the model; and the effects of small DC
16 biases on the adhesion of ice to Mercury is illustrated in FIGS. lA-1C.
1~ FIG. lA shows an initial adhesion of Mercury 18 to ice 20, the adhesion strength is being represented by ~o. Accordingly, Oo represents adhesion strength without applied 19 voltage (i.e., V = 0). FIG. 1B, on the other hand, illustrates the resultant adhesion strength 2o O~ which occurs with the application of -1.75V supplied by a DC voltage source 22. The 2 ~ source 22 can be, for example, a battery or other voltage source known in the art. Wiring 22 24 connects the source 22 to the Mercury 18 and to the ice 20 to complete the circuit. FIG.
23 1C illustrates another adhesion strength Oz which results from an applied voltage of -SV

1 provided by the source 22. It is noteworthy that OZ < Oo < (Oi even though the applied 2 voltage varies from OV (FIG. lA) to -1.75V (FIG. 1B) to -SV (FIG. 1C), indicating a 3 significant change of adhesion strength through a small range of negative voltage differentials. Adhesion strength O, shows a relatively "weak" adhesion as compared to Oz or even Oo. Adhesion strength O2, on the other hand, is relatively "strong" as compared to 6 O~ and Oo.
7 To measure the surface tension of the ice-mercury interface 16 of FIG. 1, an ice 8 manometer 26 (schematically shown in FIG. 2) was used. The DC power supply 22' was 9 used for the source 22 of FIG. 1. A DC ammeter 28 was placed in the manometer circuit l0 26 to measure current flow. The source 22' connects in circuit to the Mercury 18' and to a m mesh electrode 30 connected with the ice 20'. Accordingly, the circuit 26 is completed by 12 the current flow through the Mercury 18' and the ice 20'. The Mercury 18' is in fluid 13 communication with the ice 20' through a small capillary 32 of selected diameter. As the ~4 DC bias changes, the ice adhesion between the Mercury 18' and the ice 20' changes and forces due to gravity adjusts the height "h" of the Mercury 18' within the ice 20' (i.e., 16 within the capillary 32 extending upwards into the ice 20').
17 Specifically, the equilibrium position h of the Mercury 18' in the capillary 32 is:
18 h - 2'( Waa - Wi~~~$~'p (2) 19 where g is gravity acceleration, r is the capillary radius, p is the density of mercury, W;,a is 2o the surface energy of the ice-air interface, and W;,Hg is the surface energy of the ice-Hg 21 interface. When h is measured, equation (2) is used to calculate W;,Hg, and, thereby, the 22 adhesion strength of ice to the liquid metal (Mercury). In FIG. 2, the capillary's radius r 23 was 0.25 or 0.5 mm during testing.

WO 00/24b34 PCTNS99/25124 1 Additional experimentation such as within the configurations of FIGs. 1 and 2 include 99.9998% pure electronic grade Mercury and polycrystalline ices grown from:
3 very pure deionized water; distilled water; untreated tap water; and deionized water doped with small concentrations of NaCI or KOH or HF. The experiments were performed inside a cold room in the temperature range -20°C to -5°C, ~2°C
(most testing was conducted at 6 -10°C and with a relative humidity of 89-91%). For doped ices, it was noted that DC bias 7 had a strong effect on the ice-Mercury interfacial energy. The magnitude and sign of the 8 energy change ~(W;,~ - W;".,g) depends upon the bias polarity and magnitude and on the 9 type and concentration of the dopant. FIG. 3, for example, shows 0(W;,a -W~Hg) versus 1o bias V measured at T = -10°C for ice doped with 0.5% NaCI. As illustrated, the bias can 11 reduce or enhance adhesion of ice to Mercury: at approximately -1.75V, a minimum 12 adhesion strength was reached; while the adhesion strength increased from -2V to -6V.
13 The effect of interfacial energy is more pronounced for NaCl concentrations above 0.05%.
14 With lower concentrations of NaCI, or with ice grown from tap water, the adhesion strength varied little and was weakly reproducible when a low DC bias was applied. With 16 ice doped with 0.5% NaCI, on the other hand, the mercury moved immediately after the 17 voltage bias is applied; and the effect was completely reversible, i.e., W;"ig, was restored, 18 after the bias was shut off. These results are reproducible and easy to observe. The 19 maximum change in h was l2mm for a capillary radius r = 0.25 mm.
2o Measurements of current-voltage characteristics also show that it is the voltage, not 21 the current, that causes the changes in adhesion strength discussed above.
Typical 22 experimentation, for example, produced current strengths in tens of ~,A;
and the estimated 23 rate of the temperature change was less than 10 °C/s. In ice doped with KOH or HF, the 1 application of a DC bias caused a near-symmetrical decrease in W;iHg, which was 2 comparable in magnitude with that found on NaCI-doped ice. Application of an AC
3 voltage up to 40V in amplitude and in the frequency range IOHz to lOkHz did not produce any noticeable changes in W;,Hg. In pure deionized or distilled water, the application of a DC bias up to 40V also did not produce noticeable changes in W;,Hg. It thus takes 1 kV to 6 3 kV to change the adhesion of very pure ice to a metal. Different reactions of pure and '7 doped ice to a DC bias are attributed to their differences in screening length and electric 8 relaxation time.
9 The above experimentation confirms the important role played by electrical double layers on ice-metal interfaces in ice adhesion. Although the absolute magnitude of W;,Hg 11 can slightly differ in the case of solid Mercury, the electrostatic interactions are essentially 12 the same in both cases (for liquid Hg and solid Hg). It was also shown by experimentation 13 that ice adhesion to a metal is efficiently modified by application of a small potential 14 difference between the ice and metal. Variations of adhesion strength also occur for a DC
bias applied to ice containing different impurities, to different solid metals, and at different 16 temperatures.
1'7 The inventor has also studied an electrostatic model of ice adhesion based on the 18 existence of the surface states of protonic charge carriers on the surface of ice. At 19 distances greater than one intermolecular distance the model gives an order of magnitude 2o for the adhesive energy which is significantly greater than both chemical bonding energy 21 and van der Waals forces. It also provides an understanding of the time-and temperature-22 dependent phenomena that explain the difference between adhesive properties of ice and 23 water, the physical mechanisms of bonding between ice and other solids, and the nature 24 and strength of molecular bonding between ice and various solids.

It is reasonable to classify bonding mechanisms into one of three groups: a 2 covalent or chemical bonding mechanism, a dispersion of or fluctuation in electromagnetic 3 interaction (van der Waals forces), or a direct electrostatic interaction.
See, e.g., 4 Israelachvili, Intermolecular and Surface Forces, 2nd ed., Academic Press:
London, Ch. 2 i (1991), which is herein incorporated by reference. The first mechanism corresponds to 6 chemical reactions and the formation of interfacial compounds. In covalent or chemical 7 bonding, the adhesive energy results from lowering of the quantum-mechanical energy of 8 the system due to overlap of the wave functions of the interacting solids.
Such an 9 interaction is essential only at a distance on the order of 0.1-0.2nm. In addition, this type l0 of adhesion is very sensitive to the chemical nature of adhesive solids. In a perfect contact, 11 the chemical bonding mechanism can provide adhesive energy of <_ 0.5 J/m2, a value 12 considered the lowest value of adhesion energy for the chemical bonding mechanism.
13 In contrast to chemical bonding, van der Waals forces are long-range and act i4 between all substances. These forces are defined only by the macroscopic characteristics of a solid (dielectric function at different frequencies), and for this reason they are rather 16 insensitive to experimental conditions. See, e.g., Mahanty et al., Dis,~ersion Forces, 17 Academic Press, London, Chapter 9 (1976); Barash et al., The Dielectric Function of i8 Condensed Systems, Eds. Keldysh, et al., Elsiever Science, Amsterdam, Chapter 9 (1989), 19 each of which is incorporated by reference.
2o In addition to chemical bonding and dispersion forces, two solids that contain 21 noncompensated or spatially separated charges also generate electrostatic forces. Its 22 importance and importance to adhesion have recently been rediscovered. See, Stoneham et 23 al., J. Phys. C: Solid State Physics, 18, L543 (1985); and Hays, Fundamentals of 1 Adhesion. Ed. Lee, Lee, Plenum Press, New York, Chapter 8 ( 1991 ), each of which is 2 incorporated by reference.
3 Model o~'Adhesion Properties~lce 4 A model is next developed to describe the electrical properties of the surface of ice.
The model reveals a connection between ice adhesion and other properties of ice. The 6 model is compared with van der Waals forces, the chemical bonding mechanism, and with 7 experimental results.
8 The main conclusion of the model discussed below is that electrostatic interaction 9 plays a significant, if not the major, role in ice adhesion. One important parameter in the model is that of the ordering of water molecules adjacent to the ice-solid interface or, in 11 other words, that of the appearance of the surface states for protonic charge carriers. This 12 reduces the problem to one of simulating water molecule behavior at the solid surface.
13 However, the below description will assume that there exist surface states that can be 14 occupied by protonic point defects. The occupancy of these surface states is defined by the interplay between the coulomb energy of captured charge Garners and the energy depth of 16 the surface states. Then, either the occupancy coefficient of a surface state (in the 17 nonequilibrium case) or the energy depth of the surface state will be taken as a parameter.
18 Ice includes polar water molecules that strongly interact with any solid substrate 19 which has dielectric permittivity different from that of ice. In addition, there is theoretical 2o and experimental evidence for the existence of a surface charge in ice.
This surface charge 21 can also interact with the substrate. Here we assume that the surface charge originates 22 from the capture of protonic charge Garners by the ice surface. The captured defects are 23 presumably D defects, H30+ ions, or protons. Positive ions are smaller in size than 1 negative ones, because they have fewer electrons or do not have them at all.
and exist as 2 protons. Thus we can use the image charge theory for smaller distances, where the 3 potential energy of the charge and its image may be less than the charge energy within the 4 ice. For negative ions of larger size it is more difficult to reach this. At thermal equilibrium the occupancy of surface states is not perfect because the gain in energy due to 6 captured charge carriers is compensated for by the rise in electrostatic energy. However, 7 the electrostatic energy itself can be reduced significantly by charge redistribution inside the substrate (by induced charges). This could lead to perfect occupancy of the surface 9 states and rather high adhesion energy (close to the electrostatic energy).
to The spatial distribution of charge earners in the subsurface layer of ice is described 11 below. The first integral of Poisson's equation can be written in the following form:
Q
12 E = ~ f(V) (3) EEO
13 where E and V are the electric field strength and electrostatic potential, respectively (both 14 are functions of the space coordinate z); ao = eB ~ ~,~ N; eB is the effective charge of Bjeirum defects; N is the concentration of water molecules; ~, is the screening length given 16 by EEOkT~eBN ; 8 and Eo are, respectively, the dielectric permittivities of ice (= 3.2) and of 1~ a vacuum' and k and T are the Boltzmann's constant and temperature, respectively. The 18 function f(V) is defined by the following equations:
19 f (V) _ ~ln(a(V) ~a(-V)'62 (V) ~b2 (-V)) (4) 1 a(V) = exp(E~ /2kT)+(~/3)exp(e~V/kT) exp( E~ /2kT) +4/3 exp(EB~2k~+exp{e~V~kT~
b(V ) _ 2 exp(EB ~2kT~ + 1 3 Here we use Bjerrum defects as charge Garners being captured in the surface states.
4 Equation (3) holds at any point of the ice crystal. Applying it to the ice surface, we get the relationship between the surface charge density 6s and the surface potential V5: as = ao 6 f(VS).
7 Using equations (3) through (6), we can now calculate the electrostatic 8 contribution to the adhesion energy of ice. First, the electrostatic energy of the screening 9 layer of ice as a function of the surface potential is calculated, since it gives the upper limit to for the adhesion energy. Using the definition of electrostatic energy and equation (3) we 11 get:
v 12 W(Vs ) _ ~ ~~° EZdx = ~° y.f (V O d"'~ = a° yf (v)dV
(7) 0 2 2 o dx 2 0 13 Now let us consider a metallic plate at a distance d from an ice surface.
The non-14 uniform charge distribution in the ice will induce a surface charge on the metal and, therefore, an electric field between the ice and the metal plate. The total electrostatic 16 energy of the system per unit area can be written in the following form:
f 1?
17 We{d,V)_~°.o yf(V) o~ +~°'jf(V~)dV' 2es Q 2 °

1 However, V in equation (8) is the surface potential of ice, which has to be found from 2 minimization of the energy for each value of distance d. Surface charge density can be 3 considered a constant, which arguably corresponds to a non-equilibrium occupancy of the surface states. Performing a minimization procedure for We (d,V),we arrive at the adhesion energy per unit area as a function of d:
6 Wa (d) = Wmin (d) - Wmin (°°) (9) 7 Under equilibrium conditions, the surface charge density of ice increases with a 8 decrease in the distance d because of screening of the ice surface charge by an induced 9 charge on the metal plate. Indeed, in this case the coulomb energy of captured charge to Garners decreases, so higher occupancy becomes possible. In considering this case one 11 first has to sum up the electrostatic energy, the energy gain due to occupancy of the 12 surface states, and the entropy contribution of the surface defects:

da2 r Q ~ Q V Q kT r cr a 13 F= o ~~f(V) o ~ + o vf(V')dV'--~Eo+-~~Q~ln(-)+(Qm-Q)~In(1--)~ (10) Zee a 2 o a a 14 Here Eo is the energy of surface states (assuming Eo = -0.5 eV), Qm = e/S, and S is the surface area of one water molecule. The free energy F is then minimized over V
and a.
16 This procedure also assumes that the chemical potential of the ice bulk is kept constant 17 and equals zero. Doing so for every value of d, we arnve at the equilibrium free energy as 18 a function of the distance or equilibrium adhesion energy.
19 A similar procedure enables us to find the equilibrium occupancy of the surface 2o state or the surface potential of ice as a function of the energy of surface states Eo or 1 temperature. Let us assume that the metallic plate is infinitely far from the ice surface.
2 Then, to minimize the first positive element in equation (8), it is assumed that a = ao f(V).
3 F then becomes a function of only one parameter, either V or a. It is somewhat easier to 4 perform the final minimization over V, but the results can also be recalculated as a function of 6.
6 Typical values of the adhesion energy are located between 1.3 J/m2 and 0.08 J/m2, 7 depending on the type of charge carriers and the energy of their surface states. This 8 magnitude is comparable to, or even higher than, the experimentally measured adhesion 9 energy of ice-metal interfaces at -20°C. In fact, the adhesion energy is as high as the 1o chemical bonding mechanism; however, in contrast to the latter, the electrostatic 1 t mechanism remains significant up to a larger distance (about 10 ~ rte; r~
= 0.276 nm).
12 Thus, at distances larger than roo, the electrostatic mechanism is significantly more 13 important than the chemical bonding mechanism. Accordingly, at distances greater than 14 roo, the electrostatic energy exceeds that of the van der Waals forces if the Hamaker constant equals 3 ~ 10 Z~ J. Note that the last estimation concerns an ice-ice (or water-16 water) interface, but not an ice-metal interface. The van der Waals interaction between ice m and metal, which is also long-ranged, can also be considered.

18 The adhesive energy thus equals 0.01 J/m even at z ~ 90 ~ roo for the maximum density of a surface charge, indicating long range character. The adhesive energy for a 2o non-equilibrium detaching experiment should be higher than that for an attaching one. The 21 latter can be explained by efficient screening of electrostatic energy by a metallic plate 22 when ice and metal are in contact. The behavior of adhesion energy with distance in 23 equilibrium experiments is thus readily understood. At small distances a metallic plate 1 screens the electrostatic energy and there is high adhesive energy because the occupancy 2 of surface states is high. However, when the distance increases, the electrostatic energy 3 also increases, leading to lower occupancy coefficients and a lower surface charge density.
These curves are equivalent to the more rapid decay of free energy with distance than in the case of constant occupancy.
6 The behavior of the occupancy coefficient (for the model of the surface states for 7 D defects) as a function of the surface state energy, Es, is also considered The occupancy 8 coefficient is close to zero when Es = 0.1 eV. One reason that the charge Garners are captured into the surface states with positive energy has to do with the entropy gain in the free energy. For the same reason, defects exist in the ice bulk. Note that for the bulk 11 D defects, the "creation energy" equals 0.34 eV per defect, and this energy is significantly 12 greater than 0.1 eV. Eventually this leads to an "occupancy coefficient"
for the bulk states 13 on the order of 3 ~ 10 .
14 Time-dependent phenomena can also be associated with ice adhesion, and are inherent in the above-described model. In order to enter or leave the surface state, defects 16 have to overcome some electrostatic barner, and this leads to non-equilibrium situations 17 and time-dependent phenomena.
18 One important element of this model is the electrostatic attraction between the ice 19 surface charges and the charges induced in metals, a mechanism also applicable to an ice-insulator interface except for the difference in magnitude of the induced charges. A charge 21 q on the ice surface induces the "image charge" -q in a metal; while the same charge q will 22 induce a smaller "image" charge q' in the insulator according to the following 23 relationship:

1 ~l~ 9~ E+1 (11) 2 where ~ is a dielectric permittivity of the insulator. In most solid dielectrics, ~ is much 3 larger than one and the induced charges are comparable with charges induced in metals. A
smaller ~ results in smaller electrostatic related adhesion. By way of example, Teflon, has a permittivity a = 2.04; and is well known for its low adhesion to ice.
6 It is useful to consider why ice is more adhesive than water. Due to higher 7 concentrations of charge Garners in water, the screening of the surface charge in water (if it is present) is more effective than in ice (the corresponding initial electrostatic energy is 9 much less than in ice). Thus the screening of the electric field due to the substrate cannot to lower the energy significantly. Note that at temperatures close to the melting point of ice, a 11 thin liquid layer may appear on an ice-solid interface. See Dash et al., Rep. Prog. Phys. 58, 12 115 (1995), which is hereby incorporated by reference. The model can thus be updated to 13 include the effect of surface premelting on ice adhesion.
14 The above-described electrostatic model of ice adhesion shows a relationship between the electrical properties of the surface of ice and ice adhesion. The model gives a 16 correct order of magnitude for the adhesive energy. The electrostatic interaction between 1~ ice and metals supplies energy which is significantly higher than chemical bonding energy 18 and the van der Waals forces at distances greater than intermolecular ones.
The model also 19 provides an intuitive way to understand the time- and temperature-dependent phenomena that help explain the difference in adhesive properties of ice and water.

1 As illustrated in FIG. 4, bubbles 67 play a role in development of interfacial cracks 2 which appear when the interface (between the ice 69 and metal 71 ) is loaded, reducing the maximum interfacial strength.
FIG. 5 (and cross-sectional view 6) illustrate a system 100 constructed according to the invention. System 100 operates to reduce the adhesion of ice 102 formed onto the 6 surface 104a of a material 104. The system 100 forms a circuit that includes the material 7 104, a conductive grid 106 (including illustrative points "A" - "F" on the grid), and a 8 power supply 109. The grid 106 is suspended above the surface 104a so that it remains 9 electrically insulated from the material 104.
1o In a preferred embodiment of the invention, the suspension of the grid 106 over the 11 surface 104a is obtained through use of an insulating grid 108 disposed between the grid 12 106 and the surface 104a. FIG. 6 illustrates the grid 108 in greater detail. The cross-13 sectional view of FIG. 6 is not to scale so as to illustrate the relationship of the insulating 14 grid 108 and the conducting grid 106. In reality, the thickness (in the dimension of FIG. 6) of the grids 106, 108 can be much smaller than an inch (even as low as 0.010 to 0.020 16 inch); and can be considered as "coatings". By way of example, the grid 108 can be made 17 from a thin coating of electrically insulating paint; while the grid 106 can be made from a 18 thin coating of electrically conductive paint. The grid 106 is connected so as to function as 19 a single electrode. The material 104 thus becomes a first electrode of the system 100; and 2o the grid 106 becomes the second electrode in the circuit.
21 Grids 106, 108 can also be pliant and formable over the surface 104a, which can 22 represent any shape even though a flat surface 104a is shown. By way of example, the WO 00!24634 PCTNS99/25124 1 material 104 can represent an aircraft wing or a car windshield; and the grids 106, 108 are 2 conformal to the structure material 104.
3 When ice 102 forms onto the surface 104a, the circuit of system 100 is completed 4 as the ice 102 operates as a semiconductor (as discussed above). When the circuit is completed, the power supply 109 provides a DC bias to the interface between the ice 102 6 and the material 104. The bias is typically less than a few volts; and thus a battery can '7 function as the supply 109.
8 The magnitude of the bias depends upon the desired application. In the case of a 9 car windshield or an airplane wing, the bias is selected so that a minimum (or near-1o minimum) ice adhesion results, thereby facilitating the removal of the ice 102 from the 11 materia1104.
12 A voltage regulator subsystem 112 is also preferably connected in circuit with the 13 system 100. As described in more detail below, the voltage regulator subsystem 112 14 operates in feedback with the circuit and the supply 109 so as to decrease or increase the DC bias in an optimum fashion. By way of example, the subsystem can include circuitry 16 and a microprocessor 112a to measure data from the circuit and to determine the 1'7 conductivity (and/or temperature) of the ice 102. Such measurements are used in turn by 18 the subsystem 112 to generate a signal which effectively changes the amount of the DC
19 bias applied to the circuit. Specifically, in one embodiment, the power supply 109 is 2o responsive to the signal to generate the right voltage at the ice-material interface. The 21 value of the DC bias can be stored in memory 112b within the subsystem 112 such as 22 through a look-up table and based upon experimental data. For example, ice with a 23 conductivity of "X" (as measured by the subsystem, in real time preferably) in contact t with a material 104 of conductivity "Y" (known a priori, as the system 100 is installed 2 with the material 104 for a given application) will be used through the look-up table in 3 memory 112b to determine which voltage to apply to the ice-material interface.
4 The grid electrode 106 is preferably spaced so as to ensure (as best as possible) that ice 102 formed onto the surface 104a will contact at least some portion of the grid 106.
6 With reference to FIG. 5, for example, the ice 102 comes in contact with several areas of '7 the grid 106, including at points "C" - "E". Accordingly, the circuit of system 100 will be s completed as the ice 102 "shorts" at least one part of the grid to material electrodes 106, 9 104, respectively.
The actual size of the spacing between conductive areas of the grid 106 - for t t example, the area 114 of FIG. 5 -should be sized for the specific application. By way of 12 example, if the surface 104a is the surface of an aircraft wing, then the spacing can be 13 relatively small to provide sufficient current density through a low conductive atmospheric t4 ice. However, for a more conductive river or sea ice area, area 114 can be larger, if desired.
16 FIG. 7 illustrates a system 130 constructed according to the invention. One t'7 electrode of the subsystem 130 is the aircraft wing 132. The aircraft wing 132 is 18 electrically coupled to ground 134. A DC power supply 136 is electrically coupled to a 19 DC ammeter 138. The DC ammeter 138 is electrically coupled to an inductor 140. The inductor 140 is electrically coupled through wiring 141 to a conductive paint 142 (or other 2t wing-conformal, conductive equivalent) which is applied to the insulating layer 144 fixed 22 on the aircraft wing 132.

The insulating layer 144 and paint 142 are preferably arranged as a grid pattern, 2 such as described in connection with FIG. 5. The voltage applied between the wing 132 3 FIG. 7 is generally adjusted to between five and fifty volts, with a corresponding current 4 below lA to 100A per m2 of the grid area, depending on how soon de-icing should occur.
Those skilled in the art should appreciate that a wide variety of commercially 6 available insulating lacquers 144' and conductive paints 142 exist; and that a particular brand should be chosen after testing of icing simulations. Furthermore, the optimal 8 spacing of the grid 145 (i.e., to size the area 114 of FIG. 5) should also be determined 9 experimentally or through analysis for a particular design.
1o With further reference to FIG. 7, the DC ammeter 138 can additionally couple to a 11 feedback subsystem 150. The feedback subsystem 150 in turn electrically couples to the 12 DC power supply 136 to "control" the DC bias applied to the wing-ice interface, ~3 depending upon characteristics such as ice conductivity and temperature. A
temperature sensor 152 thus also preferably connects with the circuit 130 to measure the temperature of the ice 154.
16 Further features of the system 130 can include an AC power supply 156 (operating 1'7 between about lOkHz and 100kHz) electrically coupled to an AC ammeter 158, which in ~ 8 turn electrically couples to the conductive paint 142. A current comparator 160 is 19 electrically coupled to both the AC ammeter 158 and the DC ammeter 138.
2o An icing alarm subsystem 162 can also be included with the system 130. The 2~ current comparator 160 can for example couple to the icing alarm subsystem 144 and to 22 the feedback subsystem 150 so as to initiate certain events, such as discussed below.

WO 00/24634 PC'f/US99/25~24 1 The DC ammeter can be used to measure the DC conductivity of the circuit 130.
2 The DC conductivity signal measurement is provided to the feedback subsystem 150, 3 which in turn regulates the current supplied by the DC power supply 136, and to the current comparator 160.
The AC ammeter can be used to measure the AC conductivity of the circuit 130 within the applied frequency range of 10-100kHz, for example. The AC
conductivity '7 signal measurement is provided to the current comparator 160 (and optionally to the s feedback 150 for A/D and data processing). A comparison between the AC and DC
9 conductivities is used by the system 130 to distinguish between water and ice, both of 1o which "short" and complete the circuit. Specifically, the ratio of the AC
to DC
ii conductivity is 2-3 orders of magnitude greater in the case of ice as compared to water, 12 providing a signal measurement which readily distinguishes ice over water.
13 As ice forms on the wing 132, therefore, the current comparator 160 signals the 14 feedback subsystem 150 which in turn commands the DC power supply 136 to increase or decrease the DC bias at the ice-wing interface. The DC bias is selected at a magnitude i6 (generally between one and six volts) so as to minimize ice adhesion strength of the ice 1'7 154 on the wing 132.
18 Upon deicing of the wing 132, the signal differential received by the current 19 comparator 160 drops below a preset value; and the current comparator 160 deactivates the icing alarm 162. Simultaneously, the current comparator 160 signals the feedback 21 subsystem 150 which in turn commands the DC power supply 136 to decrease the bias to 22 the initial level.

1 In summary, the ammeters 138 and 158 are used to determine conductivity of the 2 material which shorts between the grid electrode 142 and the wing 132. As shown, that 3 material is ice 154. The system 130 thus distinguishes between ice and water in an automatic manner. The inductor I40 prevents AC voltage from entering the "DC"
parts of the circuit, which should be accurately controlled to modify the ice adhesion strength. The feedback subsystem 150 can and preferably does include a microprocessor and memory to command and control the power supply 136 at a near-optimum DC bias based upon 8 feedback data such as ice temperature and ice conductivity (and/or ice purity). The 9 feedback circuitry preferably increases or decreases DC bias voltages at a level that provides a density of about O.ImA/cmz (or about 1mA/inz current density at the ice-wing 11 interface) after receiving an ice alarm signal from the subsystem 162.
Accordingly, for a 12 current of about 10-30A, a total energy consumption of about 100-500 watts is required ~3 for a typical large airplane.
14 The "DC" parts of the circuit of FIG. 7 thus primarily operate to provide DC bias to the ice-wing interface, and, secondarily (if desired) to measure the DC
conductivity of 16 the ice 154. The "AC" parts of the circuit of FIG. 7 thus primarily operate to measure the 17 AC conductivity. The remaining portions of the circuit of FIG. 7 thus provide: (a) an 18 inductor to prevent signal coupling between the DC and AC parts; (b) feedback and 19 measurement and control circuitry to control the applied DC bias based upon detection of 2o ice (as compared to water) and/or measured feedback parameters such as ice temperature 21 and conductivity.
22 FIG. 8 shows one preferred embodiment of the invention suitable to reduce or 23 remove ice from power lines 700. The inset to FIG. 9 shows a cross-sectional view of the 24 power line 700 constructed according to the invention. As known in the art, the normal 1 power line 702 generates power at 60Hz but with very high E-fields such as 10,000 volts 2 per inch. In accord with the invention, a coating 704 is applied over the line 702 at a 3 thickness of "t".
4 In one embodiment, the coating ?04 is a ferroelectric material, as known in the art.
Ferroelectric materials are essentially ceramics that exhibit a very high dielectric constant 6 (e.g., 10,000) and very high dielectric loss (e.g., tan8 = 10) at certain conditions, and a '7 relatively low dielectric constant (3-5) and small dielectric loss at other conditions. One 8 condition that can change the constant is temperature. In a preferred aspect, the material is selected so that above freezing, the dielectric constant is low, and below freezing to temperatures, the constant is high. When ambient temperature drops below the freezing 1 ~ point, the coating is intensively heated by the AC electric field due to the high dielectric 12 constant and dielectric loss.
13 Those skilled in the art should appreciate that the above-described embodiment can 14 be self-regulating in keeping the coating temperature close to (or slightly above) the melting point. If the coating is overheated by the power line's electric field, it t6 automatically undergoes a phase transformation from the ferroelectric to the normal state, 17 at which point the coating stops absorbing the electric field energy. By choosing a phase 18 transition temperature, therefore, the coating temperature can be adjusted per user needs 19 and per the environmental conditions of the local area.
2o The coating 704 generates heat in the presence of an AC field such as generated by 21 the line 702. Specifically, it exhibits hysteresis that generates heat over the AC cycle; and 22 the coating thus generates heat due to the oscillating E-field of the line 702.

WO 00/24634 PC'f/US99/25124 The thickness "t" is typically on the order of one to ten millimeters, though other 2 thicknesses can be applied depending upon coating materials and desired heating. By 3 changing the thickness, for example, temperatures at the surface 704a can be increased by 1-10 degrees, or more. The thickness "t" is chosen so that a desired amount of heat is generated (i.e., heat sufficient to generally melt ice and snow on the surface 704a of the 6 line 700).
7 When the coating exhibits low dielectric constant and loss (i.e., when the coating is s above "freezing" or some other desired temperature), much less heat is generated by the 9 coating 704 and, thereby, much less energy is expended by the line 702.
to The coating 704 can also be constructed by ferromagnetic materials with the same 11 or similar effect. In this case, the coating absorbs the energy of the magnetic field 12 generated by a power line.

13 More particularly, when a ferroelectric material is placed in an oscillating electric 14 field (AC), the material is heated by the field due to a dielectric loss.
The heating power per cubic meter is:
16 W =~4 ~°tan8 2 (12) 17 where ~' is a relative dielectric permittivity (usually ~' is approximately 104 for typical 18 ferroelectrics), Eo is a dielectric permittivity of free space (~ = 8.85E-12 F/m), w is an 19 angular frequency of the AC field (w = 2~f, where f is a usual frequency for the power line, e.g., 60Hz in conservative power lines), tan8 is the tangent of dielectric loss, and 21 ( E Z ) is the average of electric field squared.

1 Fewoelectrics are characterized with very large values of ~' and tan8 below the so-2 called Curie Temperature, T~, and small E' and tan8 above T~. Thus, the dielectric loss (or 3 heating power of the AC electric field) is very high below and close to T~;
and it drops by a large factor (e.g., 106) above that temperature. This makes ferroelectrics with T~ close to or just above the melting temperature an optimum choice for a coating 704 such as 6 described above. Such coatings absorb the electric power when the outside temperatures 7 drop below the melting point, Tm, and are heated by the field to a temperature above Tm so 8 that they again transform into usual insulators (i.e., no longer absorbing the electric field in 9 significant quantity).
1o Accordingly, when such coatings are placed in an AC field, the ferroelectric 11 material maintains a constant temperature which is close to T~ and just above Tm, This 12 self-adjusting mechanism to prevent icing is very economic: the maximum heating power 13 per one meter of the power line, or per m2 at any surface to be protected, can be increased 14 or decreased by changing the coating thickness and/or by adding a neutral (not ferroelectric) insulating paint or plastic to the coating. Examples of suitable ferroelectric 16 materials according to the invention include:
1'7 Table 3: Ferroelectric materials Name Formula T~ (Kelvin) Rochelle salt NaKC~06 4Hz0 255-297 Deuterated Rochelle NaKC4H2 DZO6 4H20 251-308 salt TGSe (NH2CHZCOOH)3 H2Se~ 295 Potassium tantalate KT;~~,~ Nb"~ O; 271 niobate Antimonium nitrate NH4N03 255, 305 Pb3MgNb20g ~273K (0 degrees C) i 2 By way of example, consider the heating power calculations for Pb3MgNb20g.
In 3 this example, a middle range power line is considered with V z = IOkV and with a wire diameter of lcm = 2*radius. The electric field strength on the wire surface is:
E= L =3x1(~sv~m (I3) 1 - *r r 6 or 3kV/cm, where L is the distance between the wires (L=lm). Substitution as above, i.e., E Z = 3E5 V/m, cn = 2~t* 60Hz, ~' = 104 and tan8 = 10, computes to W (lmm, 60Hz) _ 8 4.SE5 watts/m3. A lmm thick film, for example, thus generates 450 watt/m2, which is more than sufficient for typical melting of ice.
When applied to power lines, the maximum power that can be dissipated in the i i coating is limited by a capacitance C2 between the wires:
12 Wm,x ~Z .V 2 (14) 13 For wires of 2cm thickness, with lm distance between wires, C2 - 1.21E-11 F/m. For a 14 power line at V=350kV, W~ - 300 Watt/m, which is sufficient energy to keep a lm long cable free office.

WO 00124634 PCTNS99i25124 In addition to ferroelectrics, almost any semiconductor coating will provide similar 2 effects. To reach the maximum performance of Equation (24), the coating dielectric 3 conductivity a should satisfy the condition:
6~e~cn (15) where E is the coating's dielectric constant, and Eo is that of free space.
For a 60Hz line 6 and ~ = 10, a = 3.4E-8 (ohm.m;) -1. Such conductivity is very typical for many undoped semiconductors and low-quality insulators. Thus, such a coating is not expensive (certain 8 paints qualify for these coatings). Moreover, the same temperature "tuning" -described 9 above - can be achieved due to a strong temperature dependence of conductivity of 1o semiconductor materials (e.g., an exponential dependence). Thus, the optimal conditions 11 according to Equation (22) are satisfied only in a narrow temperature interval, e.g., -10°C
t2 <_ T <_ 10°C, where the coating will melt ice, otherwise consuming little power.
13 Those skilled in the art should appreciate that other surfaces such as described 14 herein can also be treated with these coatings. For example, applying such a coating to an airplane wing will also provide melting capability by subjecting the coating to AC and, 16 particularly, by increasing that AC as in Equation (19) above. By way of example, for 17 Pb3MgNbZOg, a frequency of 100kHz will heat a lmm thick coating to W(lmm, 100kHz, 18 3ESV/m) = 750 kWattlm2.
19 The invention thus attains the objects set forth above, among those apparent from preceding description. Since certain changes may be made in the above apparatus and 21 methods without departing from the scope of the invention, it is intended that all matter 22 contained in the above description or shown in the accompanying drawing be interpreted 23 as illustrative and not in a limiting sense.

1 For example, those skilled in the art should appreciate that grid electrodes such as 2 described in connection with FIG. 5 can also be applied to surfaces including the roof of a 3 house, oil pipelines, driveways, and other areas prone to ice collection.
4 FIG. 10 depicts an illustration of one embodiment of the invention for utilizing a porous layer. A porous layer 2904 of material is attached to a surface 2902. A
first 6 insulating layer 2906 and a second insulating layer 2908 are attached to the porous layer '7 2904 of the material. A first electrode 2910 is attached to the first insulating layer 2906. A
8 second electrode 2912 is attached to the second insulating layer 2908. Ice 2914 covers the 9 porous layer 2904 of material, the first insulating layer 2906, the second insulating layer 2908, the first electrode 2910, and the second electrode 2912.
11 The porous layer 2904 of material could be any material that has pores that can be t2 doped to release ions into the ice 2914. The material of the porous layer 2904 could be any 13 porous ceramic, metal or alloy. In some embodiments, the porous layer 2904 could be a 14 very thin layer, which is nearly insolvable with respect to water, such a coat of paint covering the surface 2902. Some examples of the material of the porous layer 2904 are:
16 (1) percolated porous electrodes composed of sintered metal; see, Vilar et al., Percolated 1~ porous electrodes composed of sintered metal - Hydrodvnamics and mass transfer, 18 Canadian Journal Of Chemical Engineering, 76:(1): 41-SO (1998), which is 19 incorporated herein by reference;
(2) porous graphite-intercalation system for rechargeable batteries; see, Barsukov, Porous 21 Graphite-Intercalation System For Rechargeable Batteries, New Materials:
Conjugated 22 Double Bond Systems, 191: 265-268 (1995); which is incorporated herein by 23 reference; and 1 (3) porous iron electrodes containing metal additives; see, Jayalakshmi et al., 2 Electrochemical Characterization Of Porous Iron Electrodes, Proceedings Of The 3 Indian Academy Of Sciences-Chemical Sciences, 103:(6): 753-761 (1991), which is 4 incorporated herein by reference.
The porous layer 2904 of material is saturated with a water solution of dopants that 6 enhance electrical conductivity. These dopants could be alkali, acids or salts. Some '7 examples are electrolyte solutions of KOH, HF, NaCI, and KCI. When the porous layer s 2904 of material comes into contact with the ice 2914 or supercooled water droplets, the 9 porous layer 2904 releases a small amount of the dopants to the ice 2914.
The dopants 1o dopes the ice 2914 with ions. The ice's conductivity is then enhanced because of the 11 presence of the dopants. In very cold, high altitude conditions such as in aircraft travel, ice 12 is very pure and/or non-conductive. To enhance electrical conductivity of pure ice and of 13 ice at very low temperature, the operation of the porous layer 2904 provides the missing 14 conductivity. The porous layer 2904 may be refilled with dopants by reapplying the water solution of dopants to the porous layer 2904.
16 The first electrode 2910 and the second electrode 2912 could be any electrode that 1'7 voltage is applied to in order to carry electrical current. In one embodiment of the 18 invention, the first electrode and the second electrode are porous in nature and release 19 dopants to the ice 2914 as described with the porous layer 2904. In other embodiments of 2o the invention, the first electrode 2910 and the second electrode 2912 can be configured 21 into any shape such as a grid. These embodiments are not shown in FTG. 29 for the sake of 22 clarity. The first insulating layer 2906 and the second insulating layer could be any 23 material that keeps the first electrode 2910 and the second electrode 2912 from shorting 24 with the porous layer 2904.

In operation, a voltage is applied to the first electrode 2910 and the second 2 electrode 2912. The first insulating layer 2906 and the second insulating layer 2908 3 prevent the first electrode 2910 and the second electrode 2912 from shorting with the porous layer 2904. The ice 2914 begins to form on the porous layer 2904. The porous layer 2904 releases the dopants to the ice 2914, which improves the ice's 2914 6 conductivity. The voltage applied from the first electrode 2910 and the second electrode 7 2912 reduces the ice adhesion of the ice 2914 and melts the ice 2914.
s 9 FIG. 11 depicts an illustration of one embodiment of the invention for removing ice from a power line 3000. The power line 3000 is suspended above a ground 3002. The 11 power line 3000 is coated with a ferroelectric, ferromagnetic or semiconductive coating ~2 that has a suitable temperature dependence of the dielectric or magnetic loss. When the ~3 temperature reaches this activation temperature, the coating of the power line removes ice ~4 by reducing ice adhesion.
The power line 3000 passes electrical current, which creates an E-field or magnetic 16 field. The coating of the power line 3000 reacts to the E-field or the magnetic field when 17 the temperature reaches the power line 3000 coating's activation temperature. The coating 18 of the power line 3000 removes any ice that forms on the power line 3000 based on the 19 fields from the electrical current and the coating's properties.
2o FIG. 12 depicts an embodiment of the invention for ice on a Self Assembling 2~ Monolayer. A quartz substrate 3102 is attached to a chrome layer 3104. The chrome layer 22 3104 is attached to a gold layer 3106. The gold layer 3106 is attached to a Self 23 Assembling Monolayer (SAM) 3108. A drop 3110 of water or ice is on top of the SAM
24 3108. A DC power supply 3112 is attached to the drop 3110 and an electrometer 3114.
The electrometer 3114 is attached to the gold layer 3106.

1 The electrometer 3114 measures the interfacial charge density by operating in coulomb-meter mode while the DC bias of the DC power supply 3112 and the 3 hydrophobic properties of the SAM 3108 varies. Without an external DC
voltage applied, 4 the contact angle of the water with the hydrophobic SAM 3108 is between 98 degrees and 104 degrees. The contact angle of the water with the hydrophilic SAM 3108 is between 36 degrees to 38 degrees. With varying hydrophobic and hydrophilic properties, the work of '7 adhesion of the water to the SAM 3108 is from 130 mJ/m2 to 54 mJ/m2.

9 With a -4.5V applied, the contact angle of the water with the hydrophobic SAM
3108 is 40 degrees. The work of adhesion of the water to the SAM 3108 is from 59.5 11 mJ/m2 to 127 mJ/m2.
12 The preparation of the SAM 3108 uses gold-plated optical mirrors. For 13 hydrophobic samples, a 1mM stock solution of reagants is prepared from 1 dodecanethiol 14 [CH3(CH2)~,SH] by dissolving the 138.8 p,I. dodecanethiol in 1L of either methanol or ethanol. For hydrophilic samples, a 1mM stock solution of reagants is prepared from 11-16 mercapto-1-undecanol [HO(CH2)~ 1SH] by dissolving the .2044g N,L 11-mercapto-1-17 undecanol in 1L of methanol. To prepare the SAM 3108 with certain hydrophobic and ~8 hydrophilic properties, the two solutions are mixed in the ratio of interest.
19 To prepare the SAM 3108, the gold layer 3106 is rinsed with ethanol and then 2o dried with a stream of nitrogen. The gold layer 3106 is then immersed for 12-36 hours 21 within the appropriate solution described above for the specific hydrophobic and 22 hydrophilic properties. The gold layer 3106 is then removed from the solution and rinsed 23 5-10 times in ethanol. The gold layer 3106 is dried under a stream of nitrogen for 10-15 24 seconds.
In view of the foregoing, what is claimed is:

Claims (13)

1. A system for modifying ice adhesion strength of ice adhered to an object, comprising: an electrode electrically insulated from the object, a DC source coupled to the object and the electrode to generate a DC bias to an interface between the ice and the object, the electrode having a porous material for doping the ice to increase ice conductivity, the DC bias having a voltage which modifies the ice adhesion strength selectively as compared to the ice adhesion strength with substantially zero bias voltage at the interface.

2. A system according to claim 1, further comprising an electrically insulating material disposed between the object and the electrode, the material having substantially the same shape as the electrode.

3. A system according to claim 1, wherein the electrode comprises a grid electrode shaped to conform to a surface of the object, each point of the grid electrode being in electrical contact with the source.

4. A system according to claim 4, further comprising a grid insulator disposed between the object and the grid electrode.

5. A system according to claim 1, further comprising a DC ammeter connected in circuit with the electrode and source for determining a DC conductivity of the ice.

6. A system according to claim 5, further comprising a AC source and AC
ammeter connected in circuit with the electrode and source for determining an AC
conductivity of the ice.

7. A system according to claim 6, wherein the AC source generates one or more frequencies between about 10kHz to 100kHz.

8. A system according to claim 6, further comprising a current comparator, coupled to the DC and AC ammeters, for generating a signal representative of a ratio between the DC and AC conductivities.

9. A system according to claim 8, further comprising a feedback subsystem to assess the signal and to determine whether ice or water shorts the circuit between the electrode and the object.

10. A system according to claim 9, further comprising a temperature sensor constructed and arranged to measure ice temperature and for transmitting a signal representative of ice temperature to the feedback subsystem.

11. A system according to claim 9, further comprising an icing alarm which activates the system upon detecting ice corresponding to a pre-set value of AC to DC ice conductivities.

12. A system for modifying ice adhesion strength of ice adhered to an object, comprising: an electrode electrically insulated from the object, a DC source coupled to the object and the electrode to generate a DC bias to an interface between the ice and the object, a porous material disposed over at least part of the object to increase ice conductivity, the DC bias having a voltage which modifies the ice adhesion strength selectively as compared to the ice adhesion strength with substantially zero bias voltage at the interface.

13. A system according to claims 1 or 12, wherein the object comprises a self assembling monolayer, the monolayer having varying hydrophobic and hydrophilic properties to modify the adhesion of ice to the object.