Five different phases of a colloid-polymer mixture can co-exist at the same time, in defiance of the 150-year-old Gibbs phase rule, which states that only three simultaneous phases are possible. The result, which researchers in France and the Netherlands obtained using an algebraic model for the thermodynamics of binary rod-polymer mixtures, could help advance our understanding of phase transitions in complex systems, with possible industrial applications in areas such as food processing and paint manufacture.
The American physicist Josiah Willard Gibbs is an acknowledged founder of modern thermodynamics and physical chemistry. His phase rule, which he derived in the 1870s, sets out the maximum number of different phases that can simultaneously exist in a substance or mixture of substances. For pure substances, Gibbs’ phase rule predicts a maximum of three phases. One well-known example is water, which can co-exist as a liquid, solid and gas at its so-called triple point.
Clustering effect
In the new work, a team led by Remco Tuinier of the Eindhoven University of Technology simulated the behaviour of a colloidal mixture of two particle types – rods and polymers – dispersed in a background solvent. In their computations, they represented rods as hard spherocylinders and the polymers as spheres that freely overlap with each other.
“The system can increase the space available for the polymer chains by clustering the rods together,” Tuinier explains. “This results in a phase separation in the mixture into two (or more) phases containing a phase where the rods are enriched and another area that mainly contains polymers.”
Once this clustering occurs, the heavier rods sink to the bottom of the mixture, leading to segregation. Eventually, the lower part of the mixture becomes so crowded that the rods take up preferential positions so that they are “less in each other’s way”, Tuinier tells Physics World. The rods thus end up neatly arranged next to each other.
A quintuple point emerges
Building on previous models for dispersions of pure rods and disk-polymer mixtures, the researchers developed a quantitative theory to map out a complete phase diagram for their two-component rod-polymer mixtures. According to the calculations of team member Vincent Peters, up to five different phases appear in the system under a specific condition (see image). At this “quintuple point”, the possibilities are an isotropic gas phase with unaligned rods at the top; a nematic liquid crystal phase with rods pointing in roughly the same direction; a smectic liquid crystal phase with rods lying in different layers; and two solid phases with “ordinary” crystals at the bottom.
This five-phase system represents “the first time that the famous Gibbs rule has been broken,” team member Mark Vis says. The profusion of phases is possible, Tuinier adds, because of the shape of the particles (particularly their length and diameter), which Gibbs did not consider. “In addition to the known variables of temperature and pressure, you get two additional variables: the length of the particle in relation to its diameter, and the diameter of the particle in relation to the diameter of other particles in the solution,” he explains.
Serendipitous result
As sometimes happens in science, the result was in part a stroke of luck, since the researchers weren’t initially looking for more than three phases in their simulations. While studying plate-shaped particles and polymers, however, team member Álvaro González García and Vincent Peters observed a four-phase equilibrium. “Álvaro came to me one day and asked me what had gone wrong, because four phases just couldn’t be right,” Tuinier says.
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While the team obtained its results using simulations, members say that a real version of their system could easily be produced in the laboratory, and the results tested in experiments. According to Vis, the team’s findings could help advance our understanding of phase transitions in such systems and predict more precisely when phase transitions occur – knowledge that could come in useful for applications such as manufacturing complex colloidal mixtures like mayonnaise or paint.
Liquid crystals in displays could benefit too, Vis adds. “Most industries choose to work with a single-phase system, where there is no segregation,” he says. “But if the exact transitions are clearly described, then the industry can actually use those different phases instead of avoiding them.”
The research is detailed in Physical Review Letters.
