Polymerization of monomeric lipids in an assembly proceeds in a linear or cross-linking manner depending on the number of polymerizable groups per monomeric lipid. Lipids that contain a single reactive moiety in either of the hydrophobic tails or associated with the hydrophillic head group yield linear polymers. Polymerization of lipids with reactive groups in each hydrophobic tail generally yield cross-linked polymeric networks. This report describes three approaches to the characterization of the gel point for polymerizations constrained by the two-dimensional nature of lipid bilayers. The gel point for two-dimensional lipid assemblies was determined by correlation of the onset of significant changes in the physical properties of the polymerized bilayers with the bilayer composition. The properties examined in this study were the lateral diffusion of a small molecule probe of the bilayer, the stability of polymerized bilayer vesicles in the presence of surfactants, and the solubility of lipid polymers isolated from the bilayers after removal of water. Each of the three methods used indicated that a substantial mole fraction (0.25−0.35) of the bis-substituted lipid was necessary to cause cross-linking of the bilayer. The general agreement between the methods provides confidence that these results accurately indicate the relative inefficiency of the cross-linking process in bilayers composed of lipids having a reactive group at the hydrophobic terminus of the lipid tail(s). The possible explanations for the inefficient nature of the lipid bilayer cross-linking are discussed with regard to the preferred conformation of monomeric lipids in the bilayer, the motions of the lipid tails, and competing side reactions. These studies provide a new insight into the behavior of polymerizations in organized assemblies, which will aid in the design of new materials based on bilayers or other types of assemblies, e.g. inverted hexagonal or bicontinuous cubic phases.

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The concept of gelation of step or chain polymerizations has been fruitfully employed for more than a half century.1•2 In three-dimensional polymerizations the gel point occurs when the polymer molecules have been cross-linked to one another to form an infinite network or macroscopic molecule. The physical properties of the polymer are dramatically altered at this point. The application of this concept to two-dimensional polymerizations is addressed here. By two-dimensional polymerizations we refer to the polymerization of supramolecular arrays of hydrated amphiphiles, e.g., monolayers, LB films, vesicles (liposomes), extended bilayers, cast multilayers, and tubules. The last decade has seen the introduction of several methods to polymerize these supramolecular assemblies (see ref 3-5 for reviews). Other approaches to twodimensional polymeric networks have been described for

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Static and dynamic light scattering measurements with nitrobenzene/isooctane mixtures of critical composition in combination with measurements of temperature dependence of specific heat and density are used to obtain values of parameters appearing in the Ferrell‐Bhattacharjee theory of ultrasound absorption of binary critical mixtures (σ0: characteristic temperature independent relaxation rate, ω0 = (43.8 ± 0.7) GHz; g: coupling constant, g = – (0.56 ± 0.01). Recent ultrasound absorption data of that system are reanalysed on the basis of Ferrell‐Bhattacharjee theory. The analysis of data measured at seven frequencies of ultrasound in the range 9 MHz to 45 MHz gives values of the parameters ω0 and g which are in satisfactory agreement with those obtained from light scattering and thermodynamic measurements (ω0 = (37 σ 3) GHz; lgl = 0.5).