We have designed a facile synthetic strategy for the selective deposition of Au metal on all-inorganic CsPbBr perovskite nanocrystals that includes the addition of PbBr salt along with AuBr salt. PbBr is necessary because the addition of Au to solutions of CsPbBr nanocrystals otherwise results in the exchange of Au ions from solution with Pb cations within the nanocrystal lattice to produce CsAuAuBr nanocrystals with a tetragonal crystal structure and a band gap of about 1.6 eV, in addition to Au metal deposition. Including excess Pb ions in solution prevents the exchange reaction. Au metal deposits on the surface of the nanocrystals to produce the Au-CsPbBr heterostructure nanoparticles with an Au particle diameter determined by the Au ion concentration. Fluorescence quenching caused by Au deposition monotonically increases with deposition size, but the fluorescence quantum yield (QY) is significantly greater than if any cation exchange has occurred. An optimized synthesis can produce Au-CsPbBr nanoparticles with 70% QY and no evidence of cation exchange.

The Bragg-Williams free energy is used to incorporate nearest-neighbor interactions into the lattice gas model of a solvent-free ionic liquid near a planar electrode. We calculate the differential capacitance from solutions of the mean-field consistency relation, arriving at an explicit expression in the limit of a weakly charged electrode.The two additional material parameters that appear in the theory -the degree of nonideality and the resistance to concentration changes of each ion type -give rise to different regimes that we identify and discuss. As the nonideality parameter, which becomes more positive for stronger nearest-neighbor attraction between like-charged ions, increases and the electrode is weakly charged, the differential capacitance is predicted to transition through a divergence and subsequently adopt negative values just before the ionic liquid becomes structurally unstable. This is associated with the spontaneous charging of an electrode at vanishing potential. The physical origin of the divergence and the negative sign of the differential capacitance is a nonmonotonic relationship between surface potential and surface charge density, which reflects the formation of layered domains alternatingly enriched in counterions and coions near the electrode. The decay length of this layered domain pattern, which can be many times larger than the ion size, is reminiscent of the recently introduced concept of "underscreening".

We employ the quasi-chemical approximation to incorporate ion–ion correlations into a lattice gas model for the electric double layer formed by a compact, size-symmetric ionic liquid. The resulting differential capacitance, which we calculate for planar and weakly curved electrodes up to first order in curvature, transitions from a bell-shape to a camel-shape profile for increasing correlation strength. No such transition is present if the quasi-chemical approximation is replaced by a random mixing approximation. The bell-to-camel shape transition is, up to first order, independent of curvature. If Coulomb interactions dominate on molecular length scales, the differential capacitance has a tendency to adopt a camel-shape profile. Hence, our model offers a physical interpretation for the observed camel shape (or even U-shape) of the differential capacitance in many ionic liquids. Correlations also cause “underscreening” where the characteristic decay length of the electric double layer grows with the correlation strength and can become much larger than the size of a single ion.

It is well known that the formation and spatial correlation of lipid domains in the two apposed leaflets of a bilayer are influenced by weak lipid–lipid interactions across the bilayer’s midplane. Transmembrane proteins span through both leaflets and thus offer an alternative domain coupling mechanism. Using a mean-field approximation of a simple bilayer-type lattice model, with two two-dimensional lattices stacked one on top of the other, we explore the role of this “structural” inter-leaflet coupling for the ability of a lipid membrane to phase separate and form spatially correlated domains. We present calculated phase diagrams for various effective lipid–lipid and lipid–protein interaction strengths in membranes that contain a binary lipid mixture in each leaflet plus a small amount of added transmembrane proteins. The influence of the transmembrane nature of the proteins is assessed by a comparison with “peripheral” proteins, which result from the separation of one single integral protein into two independent units that are no longer structurally connected across the bilayer. We demonstrate that the ability of membrane-spanning proteins to facilitate domain formation requires sufficiently strong lipid–protein interactions. Weak lipid–protein interactions generally tend to inhibit phase separation in a similar manner for transmembrane as for peripheral proteins.

Amphipathic peptides that partition into lipid bilayers affect the curvature elastic properties of their host.