Pattern Formation and Morphology Evolution in Langmuir Monolayers A. Flores, † E. Corvera-Poire ´ , ‡ C. Garza, † and R. Castillo* ,† Instituto de Fı ´sica, UNAM, P. O. Box 20-364, D. F. 01000, Me ´ xico, and Facultad de Quı ´mica, UNAM, Cd. UniVersitaria, D. F. 45010, Me ´ xico ReceiVed: July 7, 2005; In Final Form: January 18, 2006 We present a study of how patterns formed by Langmuir monolayer domains of a stable phase, usually solid or liquid condensed, propagate into a metastable one, usually liquid expanded. During this propagation, the interface between the two phases moves as the metastable phase is transformed into the more stable one. The interface becomes unstable and forms patterns as a result of the competition between a chemical potential gradient that destabilizes the interface on one hand and line tension that stabilizes the interface on the other. During domain growth, we found a morphology transition from tip splitting to side branching; doublons were also found. These morphological features were observed with Brewster angle microscopy in three different monolayers at the water/air interface: dioctadecylamine, ethyl palmitate, and ethyl stearate. In addition, we observed the onset of the instability in round domains when an abrupt lateral pressure jump is made on the monolayer. Frequency histograms of unstable wavelengths are consistent with the linear-instability dispersion relation of classical free-boundary models. For the case of dendritic morphologies, we measured the radius of the dendrite tip as a function of the dendrite length as well as the spacing of the side branches along a dendrite. Finally, a possible explanation of why Langmuir monolayers present this kind of nonequilibrium growth patterns is presented. In the steady state, the growth behavior is determined by Laplace’s equation in the particle density with specific boundary conditions. These equations are equivalent to those used in the theory of morphology diagrams for two-dimensional diffusional growth, where morphological transitions of the kind observed here have been predicted. 1. Introduction Amphiphilic molecules that are nearly insoluble in water can form Langmuir monolayers (LMs) at the air/water interface. The most common way to study LMs has been through measure- ments of the pressure-area isotherms, Π(A,T) ) γ 0 (T) - γ(A,T), where T is the temperature, A is the area per molecule, and γ and γ 0 are the surface tensions of the monolayer and of pure water, respectively. In the last 15 years, new experimental techniques have revealed that many of the singularities observed in surface pressure-area isotherms since the works of Sten- hagen 1 and Ludquist 2,3 are due to phase changes, where each phase can be described in terms of four order parameters. 4,5 Grazing incidence X-ray diffraction gives the most explicit information about monolayer order. 6 Nevertheless, it is not practical for studying the dynamics of phase transitions. Other powerful techniques have been developed to study monolayer organization, such as polarized fluorescence microscopy 7 and Brewster angle microscopy 8,9 (BAM). These techniques comple- ment the information given by X-ray experiments, because they survey larger scales (∼200 µm), providing information about homogeneity, texture, structure, and dynamics. In particular, BAM is a noninvasive optical technique quite sensible for observing very fine details during phase transformations, and it is probably the best suited to be used in direct observations during compression or expansion of monolayers. In this paper, we present a study of how patterns formed by monolayer domains of a stable phase, usually solid or liquid condensed, propagate into a metastable one, usually liquid expanded. During this propagation, the interface between the two phases moves as the metastable phase is transformed into the more stable one. The interface becomes unstable and forms patterns because of the competition between a chemical potential gradient that destabilizes the interface on one hand and line tension that stabilizes the interface on the other. The further the system is out of equilibrium, the faster the metastable phase will turn into the stabler phase and, consequently, the faster the interface will propagate. The competition between effects that stabilize and destabilize the system gives rise to charac- teristic length scales of growing domains and determines, together with the anisotropy, the overall shape and symmetry of domain patterns. The balance between competing effects varies as the growth conditions change. The observed patterns may be grouped into a small number of typical patterns or morphologies, each representing a different dominant effect. Here, we will focus on tip-splitting growth, which gives rise to dense branched morphologies called seaweeds, and on dendritic growth, which is characterized by side branching. For a given system, each morphology is observed over a range of growth conditions, bringing to mind the idea of a morphology diagram and the existence of a morphology selection principle. This one would select a particular morphology and, consequently, the corresponding transitions, as we vary the growth conditions. In equilibrium, the phase that minimizes the free energy is selected and observed. The existence of an equivalent principle for out- of-equilibrium systems is one of the longest pursued and yet unsolved questions in the study of pattern formation. In LMs made of a single component, the problem of nonequilibrium growth morphologies is subtler than that in * To whom correspondence should be addressed. † Instituto de Fı ´sica. ‡ Facultad de Quı ´mica. 4824 J. Phys. Chem. B 2006, 110, 4824-4835 10.1021/jp0537308 CCC: $33.50 © 2006 American Chemical Society Published on Web 02/23/2006