Why are the simple ideas the most powerful?

In our last post we defended the idea that a useful water model should be as simple as possible. Recent water models describe water as a heterogeneous mixture, thereby raising more questions than answers. In my search for simplicity, I found the model of Narten, Danford and Levy (developed in the sixties) that fundamentally changed my view on the water structure.

Fig. 1 The magnified structure of a snow flake 

Their main idea couldn’t be easier. Narten, Danford and Levy assumed that liquid water just has the structure of ice.  As a matter of fact, the structure of ice is really remarkable. The hydrogen bonds structure the water molecules in a hexagonal crystal structure whose symmetries are visible in the shapes of snowflakes (see Fig. 1). Also special is that the ice structure is very open. The water molecules are sitting rather far away from each other allowing extra water molecules to sit in between them. In theory, there is room for one extra water molecule per 2 water molecules of the crystal structure. These extra water molecules are called interstitial water molecules. They are water molecules sitting in the free space of the crystal structure. In Fig. 2 you find a two dimensional representation of them.

Fig. 2 The blue water molecules are interstitials.  

In real ice, the number of interstitial molecules is negligible (only 3 per million water molecules) but in water the interstitials are the reason for its high density. If there is around 1 interstitial per 10 water molecules in the structure this peculiar property is easily explained. These interstitial molecules cannot bond to the other water molecule of the ice structure because all the hydrogen bonds are used to form this specific structure. The fact that only a fraction of the hydrogen bonds is broken in water seems a logical consequence of the model. This looks too easy to be true.

Fig. 3 X ray spectrum compared to the model predictions. 

This simple model is so straightforward that you cannot link it to one scientist. But Narten, Danford and Levy were the first to test it. (That is the way science works, a simple idea is not sufficient. The idea must predict the scientific measurements very sharply.) Narten, Danford and Levy had access to a set of very accurate X ray diffraction spectra of pure water. The interaction of X rays with a substance is one of the best ways to get information about the microstructure of this substance. The researchers compared their data with the data derived from the different water models that were popular in the sixties and their results were remarkably clear. Only the model based on the presence of interstitials (later called the interstitial-ice model) could explain the data (see Fig. 3). If you read their communication (Communication to the editor, 1962) it is clear that they report about a major breakthrough. The paper with all the details was only published in 1967, so they wanted to make clear that they were the first ones. Narten, Danford and Levy solved the central water problem.

But the story runs out differently. Only a few groups succeed to find some applications for the model and no further breakthroughs have been seen since then. Other groups show that also mixture models can explain the X ray data and the interstitial-ice model becomes one of the many existing water models.

It took me some time to understand why the model crashed in the seventies. There were two hidden problems. To get a good quantitative match Narten & co had to deform the ice crystal a little bit, making the ice structure anisotropic (the means not equal in all directions). This was strange because it was difficult to find a reasonable physical reason for this. The other problem was even more fundamental and is related to liquidity. The crystal structure derived by Narten, Danford and Levy didn’t have any free places, what are called vacancies. Vacancies give the water molecules of the crystal structure the possibility to move. Without them their model resulted in a ‘solid’ water structure. Even moving interstitials couldn’t explain the liquidity water.

Fig. 4 In liquid water there are also a significant amount of vacant places in the ice crystal. 

I was lucky. I initially didn’t use the results of Narten, Danford and Levy. I just started from scratch using only the basic ideas of their model to explain an electric property of water, namely the dielectric constant of water (which is anomalously high). So, I designed my own version of the model and my results were fundamentally different. There was no trace of anisotropy in the ice structure and I systematically found the presence of significant concentration of vacancies in the structure (see Fig. 4).

Only by comparing all the details of both models, I had my AHA moment. Narten, Danford and Levy had assumed that the interstitials were situated in the centre of the cages in the ice structure. This was just an assumption to reduce the complexity of their calculations.  I found that this assumption was wrong. Van de Waals forces are sticking the interstitials to the ice structure, situating them in an off-centre position. If they leave this assumption, the anisotropy disappears and vacancies in the ice structure become possible.

If I look from a certain distance to my process, it becomes clear that only my belief in simple ideas was able to guide me through the labyrinth. My results transport us 50 years back in time. The interstitial-ice model deserves a second chance and the scientific community will be obliged to take a close look at it. In the meantime, this same community is now specialised in complex mixture models for water. We will need strong arguments to convince them to change the path of history and it is even not sure if I will succeed. However, I do have two strong weapons to my disposal: the first one is a powerful simple idea (water has an intact ice structure inside with a significant concentration of both interstitials and vacancies). The second one is no time pressure. Thanks to both I could also explain other electromagnetic properties of water, that are still problematic using classical approaches. The ball is rolling, there is no way back.