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Domain-shape instabilites are investigated in a two-dimensional binary mixture of near-critical composition, a monomolecular film confined to an air-water interface and composed of a phospholipid and cholesterol. We apply the methodology of spectral analysis to the quantitative description of domainwall configurations. This permits us to identify an elliptic instability and a branching instability leading into a "melted" stripe phase in the vicinity of the consolute point. In between, a regime exists in which domain-wall fluctuations exhibit a capillary-wave spectrum. PACS numbers: 68.10.-m, 61.30.Cz, 64.60.-i, 77.80.DjCompeting interactions give rise to a variety of complex phases in condensed matter. x A realization of this principle is afforded by systems whose constituents simultaneously experience mutual magnetostatic or electrostatic repulsion and an attractive interaction of short range. This scenario has been invoked to account for the formation of domains in uniaxial ferromagnets, 2 " 5 in ferrofluids, 6 and in ferroelectrics 7 by predicting periodic modulations of the magnetization and polarization, respectively. The competition of demagnetizing and domain-wall contributions to the free energy also leads to instabilities of individual domain and droplet shapes and governs the dynamics of their fluctuations. 4,8 Recently, the formation of domains has been discovered during phase coexistence in monomolecular films of phospholipids confined to an air-water interface. 9 Theoretical analyses 10,11 assume the complete equivalence, at the level of mean-field theory, of this phenomenon in two-dimensional amphiphilic films to domain formation in the aforementioned magnetic systems. Specifically, they invoke the van der Waals attraction between aliphatic chains as the source of a domainwall energy which is balanced by a depolarizing term arising from repulsive electrostatic interactions between the polar moieties of these compounds. Consequently, the predicted phase diagram contains a coexistence region marked by the appearance of periodic intralayer density or composition modulations. 10 In contrast to the rich diversity of domain morphologies and patterns documented to date in amphiphilic monolayers, 912 one notes the relative scarcity of quantitative analysis. In this Letter we introduce the methodology of spectral analysis, based on digital imageprocessing techniques, to the quantitative description of domain-wall configurations and their excitations. Its application to the study of binary mixed monomolecular films containing cholesterol and dimyristoylphosphatidylcholine (DMPC) (Ref. 13) permits us to identify several distinct regimes of domain-shape stability which are encountered as a film of near-critical composition ap-proaches the upper consolute point terminating a fluidfluid coexistence region. 14 In particular, we document the existence of an elliptic and of a branching instability of the domain walls. The latter manifests itself in the immediate vicinity of the critical point and represents the pr...

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The cholesteric blue phases (BP I and BP II) can be modeled as cubic lattices of disclinations in a cholesteric matrix. In an earlier paper we presented results of free-energy calculations for three models with 0 (F4232), 0 (I432), and 0 (I4&32) space-group symmetry. In the present paper calculations for a fourth model, also of 0 symmetry, are presented (we differentiate these models as 0 '+' and 0 ' ', respectively). For a number of cholesterol derivatives we assign the 0 ' ' structure to the BP I, and the 0 structure to BP II, on the following evidence: For the case of equal elastic constants the calculations show a crossover of the free energy, the 0 structure being lowest at the higher temperatures, and 0 ' ' at lower temperatures. (However, the crossover may disappear for other values of the elastic constants. ) The assignment is consistent with the observed BP I and BP II lattice constants in terms of cholesteric pitch. There is excellent agreement between calculated and observed intensities of the Bragg reAections. Some details of the observed Braggdiffraction spectra are also discussed.

In modern GaAs/AlxGa1−xAs heterostructures with record high mobilities, a two-dimensional electron gas (2DEG) in a quantum well is provided by two remote donor δ-layers placed on both sides of the well. Each δ-layer is located within a narrow GaAs well, flanked by narrow AlAs layers which capture excess electrons from donors. We show that each excess electron is localized in a compact dipole atom with the nearest donor. Nevertheless, excess electrons screen both the remote donors and background impurities. When the fraction of remote donors filled by excess electrons f is small, the remote donor limited quantum mobility grows as f 3 and becomes larger than the background impurity limited one at a characteristic value fc. We also calculate both the mobility and the quantum mobility limited by the screened background impurities with concentrations N1 in AlxGa1−xAs and N2 in GaAs, which allows one to estimate N1 and N2 from the measured mobilities. Taken together, our findings should help to identify avenues for further improvement of modern heterostructures.