# From ice to water

• Why is ice so slippery
• What happens on the melt?

## Why is ice slippery?

A couple of the students in the class have asked me about it. We are now in the position to understand the reasons for ice being so slippery using solid physical arguments. Before going into it lets review the facts (see Rosenberg, Physics Today Dec 2005, pg 50):

• Optimum T for ice skating = -5.5$^o$C. (softer ice, slower).
• Optimum T for ice Hockey = -9.0$^o$C.(harder, faster ice).
• for T< -30 $^o$C, ice stops being slippery.

The question is: Is it Pressure melting, frictional melting or both?

## Pressure Melting

Until 1950 the idea that pressure melting was the main reason why ice is so slippery was commonly accepted. Surprisingly, in 1850 Michael Faraday had an intuition about what would be the physical reason behind the frictionless ice surface. It was not until 1949 that the theory put forward by Michael Faraday in 1850 was accepted as correct.

Here is the phase diagram of water (From Chaplin's web site, see links). We have already seen it before, but now we can look in detail to the ice Ih-liquid border.

Although it is not very noticeable here, if we zoom in the slope of the line separating liquid and ice-Ih is negative.

.

This means that ice under pressure melts at a lower temperature or that we can melt ice by applying pressure.

## Pressure Melting: ice skates

We can do a simple calculation to estimate the pressure exerted by the blades of a skate. Remember that we already learnt this on the first lecture: Pressure is force per unit area. P=F/A .

If the area is small the pressure is large. In the case of the blades, the surface in contact with the ice is tiny because the width of the blade is less than 0.5 mm.

For an 80 Kg person, assuming a blade of 30 cm length and 0.5 mm wide, the pressure on each feet will be ~ 27 atm. Not so large, specially if you realize that the slope P Vs T for melting ice has such a large slope. This means that this pressure will change the melting temperature by less than 1 $^o$C!

## Pressure Melting: History

The idea behind pressure melting is quite simple. If liquid water is denser than ice, then pressure must facilitate he melting of ice because pressure increases density.

In 1850 James Thomson put this simple idea into an ecuation, proposing a linear relationship between pressure and melting temperature. Thomsom's brother, Lord Kelvin confirmed his results experimentally. However they did not mention ice skating at all.

In 1866 Jhon Joly used Thimson's results to explain the increased slipperiness of ice when skating. He calculated a pressure of 466 atm and a melting T of -3.5 $^o$C. At this T a thin film of water is created and the skater slides over it.

Note that his calculated pressure is much larger than the one I obtained. He probably used a much thinner blade.

However all these observations do not explain why is it possible to skate or sky at much lower T's, as low as -30$^o$C.

## Frictional Melting

It was only in 1939 that Bowden and Hughes (Proc. Roc soc London A172,280, 1939) noted that pressure melting does not work to explain the easy sliding of skiers in the snow. This is easy to show, because the contact area of a ski is much larger than the contact area of the blade.

They carried their research in the Jungfraujoch station in Switzerland, at 3346 m elevation.

They measured both static and kinetic friction. They showed that metal skies have higher friction than wooden ones. So they concluded that it was frictional heating and not pressure heating what caused the melting of ice. So only near the melting point pressure melting is important.

In 1997 Samuel Colbeck showed indeed that the faster the speed the larger the contact T and therefore the more melting occurs, confirming the frictional heating argument.

Note that for pressure melting to take place the T should decrease because it is an endothermic process.

The story is not completed yet. Many of you might ask about the slipperiness of ice, that you can feel standing on ice without skates of skies. Pressure and friction do not explain it!

Here is where Michael Faraday's experiments shed light into this conundrum. Probably one the best experimentalist in the history of physics, he devoted most of his life to the study of the electromagnetic force and its consequences. He was also the father of electrochemistry, and the person who explained the physics behind's Volta's battery.

Here is Faraday in his Lab at the royal Institution. Who would say from this picture he was a physicist?

In 1850, Faraday suggested that there was a liquid layer of water on the surface of ice even below melting T, and that this layer will freeze when two blocks of ice are brought together. He called this process regelation.

Thomson refused this and argued that it was pressure and not the thin film at the surface what made the two blocks to regelate.

Faraday continued to demonstrate he was right. In 1860 he performed new experiments, that showed that pressure had very little to do with the liquid layer at the surface. But Thomson's views prevailed and Faraday's experiments were forgotten for almost a century.

Had they known about the structure of ice, they would have realized that Faraday's intuition was correct.

## The surface of Ice

The surface of ice has been a intensive area of research since 1963, when Telford and Turner (Philos. Mag. Ser. 8, 527, 1963) re-activated the question of regelation and repeated Faraday's original experiments with much more detail and control.

They showed that up to -0.5$^o$C pressure melting plays a role, but below this T there is a different phenomena involved, which is active down to temperatures as low as -35$^o$C. They showed that indeed there is always a layer of liquid water over the surface of ice and that it remains liquid up to those very low temperatures.

Here is what the layer looks like from theoretical simulations (Ikeda-Fukazawa, The Journal of Chemical Physics, Vol. 120, No. 3, pp. 1395â1401, 15 January 2004)

## The Hbond and the surface of Ice

There is plenty of interesting physics behind the reasons why the surface of ice is partially melted even at T below freezing.

From a very simple point of view one can understand it with a simplistic argument.

As the molecules at the surface have less Hbonds than those in the bulk, ther will be less tightly bound, and their vibrations will have larger amplitudes than those of molecules in the bulk, allowing them to scape from the hexagonal ice structure.

You can see it here, taken from the same journal. (same authors as before):

What you see is how the mobility of H (bottom) and O (top) is larger for the molecules at the surface.

In reality, there is much more complexity involved. Breaking an H bond results in two non symmetrical sides. One that has a free H atom and another that has a free lone pair.

It comes out that free H atoms are more stable than free lone pairs. Or, if a water is going to loose one or more H bonds, it will always start by freeing its H atoms, rather that freeing its lone pairs. So the surface of ice, at Tâ35$^o$C will have a majority of dangling H atoms.

But the destabilization of the surface layer will extend several layers bellow, because the strength of H bonds increases when the molecules are fully coordinated. This is what is known as cooperativity behavior in Hbonds.

Experiments have shown that the layer of water thickness depends strongly with T. It can be as large as 70 nm (at T=-0.7$^o$C) and at T=-20$^o$C is ~ 20 nm. The melting starts at T~ -35$^o$C.

## Conclusions: slippery when wet

1. Pressure decreases the melting temperature of ice.
2. However pressure is not the main reason why ice is so slippery.
3. Pressure melting is only important down to -0.5$^o$C .
4. Frictional melting also contributes to the slipperiness of ice. At very low T's in order to gain speed it is necessary to ski faster!
5. Independently of pressure or friction, there is always a liquid layer at the surface of ice. This layer is what makes ice slippery even without skies or skates.