Hidden Minima of the Gibbs Free Energy Revealed in a Phase Separation in Polymer/ Surfactant/Water Mixture R. Holyst,* ,²,‡ K. Staniszewski, ² A. Patkowski, § and J. Gapin ´ ski § Institute of Physical Chemistry, Polish Academy of Sciences, Department III, Kasprzaka 44/52, 01224 Warsaw, Poland, Department of Mathematics and Natural Sciences, College of Science, Cardinal Stefan Wyszyn ´ ski UniVersity, Dewajtis 5, 01-815 Warsaw, Poland, and Department of Physics, A. Mickiewicz UniVersity, Umultowska 85 61-614 Poznan ´ , Poland ReceiVed: February 4, 2005; In Final Form: March 24, 2005 We observed a very unusual kinetic pathway in a separating C 12 E 6 /PEG/H 2 O ternary mixture. We let the mixture separate above the spinodal temperature (cloud point temperature) for some time and next cool it into a metastable region of a phase diagram, characterized by two minima of the Gibbs potential, one corresponding to the homogeneous mixture and one to the fully separated PEG-rich and C 12 E 6 -rich phases. Despite the fact that in the metastable region the thermodynamic equilibrium corresponds to the separated phases (global minimum of the Gibbs free energy), we observe perfect mixing of the initially separated phase. The homogeneous state, obtained in this way, does not separate, if left undisturbed. However, many cooling- heating cycles or full separation with visible meniscus above the cloud point temperature induce the phase separation in the metastable region. The metastable region can exist tens of degrees below the cloud point temperature. This effect is not observed in the binary mixture of C 12 E 6 /H 2 O. A phase diagram for a binary mixture can be divided into three regions: the one-phase region, where the only minimum of the Gibbs free energy corresponds to the uniform (homoge- neous) state, the metastable region, where the global (the deepest) minimum of the free energy corresponds to the separated phases, but the local minimum corresponds to the homogeneous mixture, and finally the unstable (spinodal region), where the only minimum of the free energy corresponds to the separated phases. In the latter case the homogeneous mixture is unstable with respect to any small changes of concentrations, whereas in the metastable region, there is an energy barrier for the phase separation. The kinetic pathway, which is usually studied in the phase separation process, is the transformation of the initially homo- geneous state to a nonuniform (phase separated) state and its further coarsening in time. 1,2 When a homogeneous A/B mixture (say surfactant/water mixture) below its upper critical point is suddenly heated above its critical temperature, it ceases to be in the thermodynamical equilibrium and starts to separate. The homogeneous state can now be either a metastable or an unstable state. In the former case, the process of demixing requires, in the first place, nucleation of droplets of a minority phase, say A-rich phase. Then the droplets start to grow. When the system is quenched into the thermodynamically unstable region, the demixing proceeds via the spinodal decomposition mechanism; that is, the system becomes unstable with respect to infinitesi- maly small fluctuations of concentrations. In the metastable region, we have to wait for the separation process for a time needed to overcome the nucleation energy barrier via large fluctuation, while in the unstable region the demixing is instanteneous. The reverse process to the one described above of a decay of the nonuniform configurations into the homogeneous one has recently received more attention. 3-6 In ref 3, the fully separated binary mixture, with upper consolute (critical) point, was heated to the one-phase region and the processes of mixing was observed. It revealed unusually large fluctuations in composition, orders of magnitude larger than at equilibrium. It was also shown 4-6 that when a partially separated mixture (many domains of one phase in the matrix of another phase) is quenched into the metastable region the domains partially dissolve and afterward start to grow again. The dissolution of the domains in the homogeneous phase is of course complete. It is the purpose of this paper to show that the phase behavior can be much more complicated than the commonly accepted scenario. One of the issues not well understood is the energy landscape of the Gibbs free energy, which is responsible for different kinetic pathways in phase separation processes. The following question can be posed: Can we completely mix a phase-separated system in the metastable region? The answer depends on the Gibbs energy landscape. In Figure 1, we show one possible scenario where after a separation in the unstable region we can obtain a perfect mixing in the metastable region. Figure 1 shows a cartoon representation of the energy landscape of the Gibbs free energy in the one-phase, metastable, and unstable regions with two minima in the metastable state, one corresponding to the homogeneous mixture and one to the separated phases. If the minimum corresponding to the homo- geneous mixture is very wide and shallow, the system may stay very long in this minimum before crossing the barrier and going * To whom correspondence should be addressed. ² Polish Academy of Sciences. ‡ Cardinal Stefan Wyszyn ´ski University. § A. Mickiewicz University. 8533 2005, 109, 8533-8537 Published on Web 04/12/2005 10.1021/jp050634y CCC: $30.25 © 2005 American Chemical Society