We report the identification of a new equilibrium microdomain morphology in an intermediate to weakly segregated diblock copolymer melt. A polystyrene-polyisoprene (SI) diblock copolymer consisting of 37 wt % styrene and of total Afw = 27 400 was observed to transform from the lamellar morphology (in equilibrium at low annealing temperatures) to a new morphology at annealing temperatures approximately 50 °C below the order-disorder transition (ODT). The transformation was observed to be thermoreversible. Investigation of the new morphology via small-angle X-ray scattering (SAXS) and transmission electron microscopy (TEM) revealed the new structure to have remarkable three-dimensional long-range order, to belong to the cubic space group Ia3d, and to possess a bicontinuous cubic microstructure. From computer simulations of model structures and comparison with microscopy results, we propose models for the new morphology based on the triply periodic G minimal surface (gyroid) discovered by Schoen;1 similar morphologies have been observed in a variety of microphase-separated surfactant-water systems. Blends of this diblock with various short-chain homopolymers were used to investigate the compositional extent of the region of IaZd stability on the phase diagram; the results indicate that the Ia3d phase is stable over a wide range of minority component volume fractions.ogy, the ordered bicontinuous double diamond (OBDD), in a strongly segregated melt;3 the new structure has since been observed in a variety of block copolymer systems.4-6Recently, Olmsted and Milner7 have developed methods for calculating the free energy of bicontinuous morphologies in the strong segregation limit. A variety of new structures not predicted by the early theories have been observed in the weak segregation regime, including the lamellar-catenoid,8'9 hexagonally modulated lamellae, and hexagonally packed lamellae.10 As part of a study on block copolymer thermal behavior, Gobran11 observed an unusual microphase-separated morphology in a polystyrene-polyisoprene (SI) diblock copolymer. After casting from toluene, the sample formed a lamellar phase; upon heating to temperatures above 120

Recently, a new equilibrium microstructure, a second bicontinuous cubic morphology similar in many respects to the ordered bicontinuous double diamond (OBDD) structure, has been identified in a weakly segregated polystyrene-polyisoprene (SI) diblock copolymer melt.1'2 X-ray diffraction indicated that the new cubic phase was more consistent with a microstructure based on the Schoen G or "gyroid" minimal surface3 than with an analogous model of the OBDD morphology based on the Schwarz D minimal surface.4 This new cubic phase was therefore entitled the "gyroid*", with the "*" symbol serving to distinguish the block copolymer morphology from the G minimal surface.Model microstructures of the OBDD and gyroid* morphologies were developed to determine the characteristics of the new cubic phase.1'2,7 In these models, the majority component material (e.g., polyisoprene) is confined to lie within a constant distance from the underlying minimal surfaces (Schwarz D for OBDD, Schoen G for gyroid*). The resulting majority component phase has constant thickness (CT), and so the * To whom correspondence should be addressed.

X-ray diffraction is used to solve the low-resolution structures of fully hydrated aqueous dispersions of seven different diacyl phosphatidylethanolamines (PEs) whose hydrocarbon chains have the same effective chain length but whose structures vary widely. Both the lower-temperature, liquid-crystalline lamellar (L(alpha)) and the higher-temperature, inverted hexagonal (H(II)) phase structures are solved, and the resultant internal dimensions (d-spacing, water layer thickness, average lipid length, and headgroup area at the lipid-water interface) of each phase are determined as a function of temperature. The magnitude of the L(alpha) and H(II) phase d-spacings on either side of the L(alpha)/H(II) phase transition temperature (T(h)) depends significantly on the structure of the PE hydrocarbon chains. The L(alpha) phase d-spacings range from 51.2 to 56.4 A, whereas those of the H(II) phase range from 74.9 to 82.7 A. These new results differ from our earlier measurements of these PEs (Lewis et al., Biochemistry, 28:541-548, 1989), which found near constant d-spacings of 52.5 and 77.0-78.0 A for the L(alpha) and H(II) phases, respectively. In both phases, the d-spacings decrease with increasing temperature independent of chain structure, but, in both phases, the rate of decrease in the L(alpha) phase is smaller than that in the H(II) phase. A detailed molecular description of the L(alpha)/H(II) phase transition in these PEs is also presented.

This is the first of two papers dealing with the structural solution of physical systems based on infinite periodic minimal surfaces (IPMS), such as surfactant, lipid-water, and block copolymer systems. In the first paper, the mathematics of minimal surfaces is briefly reviewed and details of the construction of the associate D, P, and G IPMS are described. Electron density models of lipid-water systems based on these IPMS are then constructed. The resulting models are then Fourier transformed to calculate the amplitudes of the first few Fourier terms. These amplitudes are then used to reconstruct the electron density which is examined and discussed. The subsequent paper will utilize the modeling results to aid in solving the structure of several real physical systems based on the D surface.PACS. 61.30.Cz Theory and models of liquid crystal structure -87.15.By Structure and bonding -83.70.Jr

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This is the second of two papers dealing with the structure of lipid-water phases based on Infinite Periodic Minimal Surfaces (IPMS). The first paper describes mathematical modeling of such phases. In this paper, a new reconstruction method, called the methyl trough search, is described and used to solve the structures based on powder pattern X-ray diffraction data. Structures are derived for both a single chain lipid-water system (mono-olein) and a diacyl phospholipid-water system (2-2 methyl butyl 16:0 phosphatidylcholine). The methyl trough search uses the low electron density of the lipid methyl tails to determine the correct phasing for the electron density reconstruction. The data are consistent with a structure based on the IPMS D surface. The results are compared to other methods used to solve the mono-olein structure; the structure of the diacyl lipid has never before been solved. We discuss the subtleties involved in reconstruction of D surface based phases and the substantial artifacts that arise in low-resolution reconstructions of hydrocarbon lipids lacking heavy-atom sites.PACS. 61.30.Cz Theory and models of liquid crystal structure -87.15.By Structure and bonding -83.70.Jr

In addition to obtaining the highly precise volumes of lipids in lipid bilayers, it has been desirable to obtain the volumes of parts of each lipid, such as the methylenes and terminal methyls on the hydrocarbon chains and the headgroup. Obtaining such component volumes from experiment and from simulations is re-examined, first by distinguishing methods based on apparent versus partial molar volumes. While somewhat different, both these methods give results that are counterintuitive and that differ from results obtained by a more local method that can only be applied to simulations. These comparisons reveal differences in the average methylene component volume that result in larger differences in the headgroup component volumes. Literature experimental volume data for unsaturated phosphocholines and for alkanes have been used and new data have been acquired for saturated phosphocholines. Data and simulations cover extended ranges of temperature to assess both the temperature and chain length dependence of the component volumes. A new method to refine the determination of component volumes is proposed that uses experimental data for different chain lengths at temperatures guided by the temperature dependence determined in simulations. These refinements enable more precise comparisons of the component volumes of different lipids and alkanes in different phases. Finally, the notion of free volume is extended to components using the Lennard-Jones radii to estimate the excluded volume of each component. This analysis reveals that head group free volumes are relatively independent of thermodynamic phase, while both the methylene and methyl free volumes increase dramatically when bilayers transition from gel to fluid.

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