One of the most universal theories in physics and chemistry, the Gibbs phase rule, has succeeded in finding inaccuracies by means of computational research. The inaccuracy applies to liquid crystals, but an explanation has also been devised.

The Dutchman tells about the achievement Eindhoven University of Technology bulletin.

The phase rule states that no more than three states, i.e. phases at a time, can exist in a thermodynamic equilibrium of a pure substance. The rule was developed by an American chemist Josiah Willard Gibbs between 1875 and 78, or more than 140 years ago.

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If there are more substances, there may be more phases: for example, in the case of two chemical components, four. The whole equation is discussed in more detail below.

The theory has been considered flawless from the beginning and no inaccuracies have been found so far. Professor leading the research Remco Tuinier also points out in the press release about historical curiosity: reportedly itself Albert Einstein at one time called Gibbs’ thermodynamics “the only theory he really trusted.”

According to Tuinier’s group, very long and rigid molecules can ideally form as many as five equilibrium phases: two different solid crystals, a nematic and smectic phase, i.e. two different liquid crystals, and a fifth phase of a gas or solution.

In the mathematical phase, the direction of the elongated molecules is approximately constant, but there is no order in their place. In the smectic phase, molecules are not only parallel, but also organized into planes – but in each plane they can move with each other.

The explanation for the problem lies precisely in the strange structure of liquid crystals, which is partly like a liquid and partly like a solid. Namely, Gibbs’ theory assumes that matter is isotropic, that is, on a larger scale than the molecular level, similar in all directions.

Because liquid crystals violate this assumption, the rule may also be broken in certain cases.

Researchers scientific article has been published in Physical Review Letters and is free to read.

Phase rule formula and technical complications

The Gibbs phase rule belongs in its entirety

P = C + 2 – F

where P is the phases of and C the number of chemical components, and F degree of freedom of environmental variables, ie pressure and temperature (0, 1 or 2). The maximum number of equilibrium phases can be reached if the pressure and temperature are set constant (degrees of freedom zero).

As mentioned above, there may be 3 phases in a one-substance system, 4 in a two-substance system, and so on.

In the Tuinier group studies, the maximum number of phases would be three, as described above. Quite precisely, however, this does not follow directly from the equation, as there were two technical complications associated with the study design, the effects of which negated each other.

First, in addition to long and rigid bodies, the simulated system included smaller polymer molecules, which increased the number of possible phases by one. On the other hand, the researchers formulated their equations in such a way that the effect of temperature was completely ignored, leaving only the effect of entropy to be considered.

“This means there is one less variable and the maximum number of phases is reduced by one,” Tuinier explains to Technology & Economics in an email.

Unlike temperature, pressure was taken into account in the studies. Thus, the second of the previous formula changed to number one in the researchers’ equation, which is also evident from the scientific article.

“On the other hand, this also means that similar [tosielämän] in systems where temperature plays a role, even more simultaneous phases can be expected to exist, ”Tuinier adds.

The story was originally published In Tekniikka & Talous magazine.