## Why is ice slippery?

It is only a thin layer of water that is responsible for making ice slippery. Not everyone actually understands this.

A frozen pond and a pane of glass have a few things in common. Both are solid bodies, more or less transparent and rather smooth. However ice is certainly slippery while dry glass offers detectable resistance to a finger rubbed over it. For ice, friction appears to have been removed and there is no 'grip' - to the enjoyment of winter sportsmen and the terror of car drivers.

Why however is ice slippy and glass not? Many people believe they know why, but most are wrong. The idea according to which the surface of the ice melts due to strong pressure from the likes of ice skates, producing a lubricating film of water, is definitely not true. In spite of this, water does appear to play some sort of a role. From everyday life, we do know that at temperatures way above freezing point, slippery effects similar to that of ice do occur - when a tiled floor is wet, for example. You only have to moisten a glass pane and it becomes extremely slippy. We postulate therefore the hypothesis that moisture is a reason for slipperiness. Yet would not fluid water on ice instantly freeze?

In an attempt to solve the problem, let's first look a bit closer at the ice skating argument. As a rule, materials react to an increase in pressure by decreasing their volume; increased pressure can thus harden substances. Ice represents the great exception in all this. During an increase in pressure it reacts likewise with a decrease in volume, yet by virtue of this it does not becomes harder, but instead melts - for water is one of the few substances which has a greater volume when solid than in its fluid state.

This state of affairs can be readily confirmed by a simple but rather misleading experiment (see images). For this you lay a thin wire over an ice block and load it down with heavy weights. Under the pressure the ice melts so that the wire gradually melts through the cube, while above the wire the ice freezes again.

The phase diagram of water tells us that at a temperature of $-1^\circ$ C a pressure of 14 million Pascals is required to warm the ice by one degree, and thereby to melt it. As the mechanical pressure p corresponds to the quotient of force F and area A, i.e. $p=\frac{F}{A}$; and since the lower surface of the blades on ice-skates is very small, ice skaters exert great pressure. Considering a person of mass 80 kg and taking the acceleration due to gravity to be $a = 10 m/s^2$, their weight will be given by $F=ma\approx 800 N$. In the case of very fine blades with a lower surface of $0.0001 m^2$ (that is, a square centimeter) the pressure exerted will be 8 million Pascals. That is far from being sufficient to melt the ice.

## The overlooked message of the ice-block experiment

Only for ice temperatures not too far from the zero point can a noticeable effect be yielded. There exists a further, but mostly overlooked, feature of the ice-block experiment. If the temperature difference to be overcome is low, then a second factor comes into play apart from the pressure - the heat conductivity of the material lying on the ice. The 'melting- through' only functions as well as it does because the metal wire conducts the heat away. If the metal wire is replaced by an equally thick nylon thread, the procedure runs considerably slower.

So this offers no solution, from the knowledge that pressure melting is only of any relevance near to the freezing point. An inversion of this could mean that ice at colder temperatures would be as dull as a dry glass pane. This is not so however : according to experiment the optimal temperature for figure skating is $-5.5^\circ$ and for ice hockey even $-9^\circ$. And even if the temperature sinks down as far as $-30^\circ$, you can still skate on frozen lakes.

In the search for a better explanation, you soon come across a further mechanism : could frictional warming play an important role? In the existing logs from Robert Scott's Terra Nova expedition, which ended tragically in 1913 with the death of all participants, the expedition members reported of snow which at a temperature of $-40 C$ felt "sand-like". At least when it is dry and very cold, snow consisting of fine ice crystals offers resistance in this manner.

With heating, this resistance is indeed reduced : the energy that you have to expend in overcoming friction, is transmitted to the icy ground and thereby contributes to raising its temperature. In 1997, researchers around American Samuel C. Colbeck also showed this experimentally. They equipped ice skates and skis with heat detectors and measured how the temperature climbed with speed.

But we have not yet solved our problem because the amount of heat arising in this way is very small. Quite apart from this, however ice at temperatures below zero still retains its slipperiness even when ice-skaters do not move at all, but simply stand still: so pressure and friction alone are not suitable in providing an explanation.

That had already occured to Michael Faraday. Around 1850 he showed that blocks of ice froze together at temperatures below zero when they were brought into contact, and concluded from this that they must be coated with a fluid film. Because Faraday was not able to convince his colleagues of this, his ideas were forgotten. It was only 100 years later that they were revived and various methods were able to show a sort of small-scale liquifying of the ice - i.e. a melting of the ice before the actual melting point is reached.

Astrid Döppelnschmidt and Hans Jürgen Butt of the University of Mainz succeeded in a precise measurement of this so-called "pre-melting effect" in 1998. As they found out using an atomic force microscope, the thickness of the water film on ice at $-0.7^\circ C$ amounts to around 70 nanometers (billionths of a meter), while at $-24^\circ C$ it is still at least 12 nanometers. The thickness of the water film - and therefore the slippyness of ice - thus decreases with temperature. The lower limit is reached at $-33^\circ C$; if it is any colder - like at the South Pole - no melt layer is present any more.

However, how is this compatible with the Second Law of Thermodynamics? According to this law, nature always strives to give up as much energy as possible to the surroundings. It would be expected that water molecules would freeze rather than melt, because in this manner they lose energy. Yet the boundary areas also play a role in the energy balance. Obviously more energy is required to form and maintain a bounding surface between a perfect ice crystal and the air, than it costs for both boundary areas between ice and melt-film and melt-film and the air. Thus altogether maximum energy indeed flows to the surroundings.

You can also spell out demonstratively why ice tends to form a water film : because the outer particles possess less binding energy, and are therefore not so bound as the molecules in the interior of the crystal, the surface of the ice melts earlier than the phase diagram predicts.

In the meantime, in many studies researchers have found out that surface melting occurs not only in ice but also in all materials. So when lead falls below its melting point by $40^\circ$ it is still covered with a fluid film.

Because everyday materials mostly have a very high melting temperature - that of lead is 327.5 degrees - hardly anyone is aware of this phenomenon. The slipperiness of ice during winter offers the best evidence of it.