Gyroid Lattice Research Articles

The stiffness and strength of the gyroid lattice

Recently, a nanoscale lattice material, based upon the gyroid topology has been self-assembled by phase separation techniques (Scherer et al., 2012) and prototyped in thin film applications. The mechanical properties of the gyroid are reported here. It is a cubic lattice, with a connectivity of three struts per joint, and is bending-dominated in its elasto-plastic response to all loading states except for hydrostatic: under a hydrostatic stress it exhibits stretching-dominated behaviour. The three independent elastic constants of the lattice are determined through a unit cell analysis using the finite element method; it is found that the elastic and shear modulus scale quadratically with the relative density of the lattice, whereas the bulk modulus scales linearly. The plastic collapse response of a rigid, ideally plastic gyroid lattice is explored using the upper bound method, and is validated by finite element calculations for an elastic-ideally plastic lattice. The effect of geometrical imperfections, in the form of random perturbations to the joint positions, is investigated for both stiffness and strength. It is demonstrated that the hydrostatic modulus and strength are imperfection sensitive, in contrast to the deviatoric response. The macroscopic yield surface of the imperfect lattice is adequately described by a modified version of Hill’s anisotropic yield criterion. The article ends with a case study on the stress induced within a gyroid thin film, when the film and its substrate are subjected to a thermal expansion mismatch.

Simulation of the gyroid phase in off-lattice models of pure diblock copolymer melts

Particle-based molecular simulations of pure diblock copolymer (DBC) systems were performed in continuum space via dissipative particle dynamics and Monte Carlo methods for a bead-spring chain model. This model consisted of chains of soft repulsive particles often used with dissipative particle dynamics. The gyroid phase was successfully simulated in DBC melts at selected conditions provided that the simulation box size was commensurate with the gyroid lattice spacing. Simulations were concentrated at conditions where the gyroid phase is expected to be stable which allowed us to outline approximate phase boundaries. When more than one phase was observed by varying simulation box size, thermodynamic stability was discerned by comparing the Helmholtz free energy of the competing phases. For this purpose, chemical potentials were efficiently simulated via an expanded ensemble that gradually inserts/deletes a target chain to/from the system. These simulations employed a novel combination of Bennett's [J. Comput. Phys. 22, 245 (1976)] acceptance-ratio method to estimate free-energy differences and a recently proposed method to get biasing weights that maximize the number of times that the target chain is regrown. The analysis of the gyroid nodes revealed clear evidence of packing frustration in the form of an (entropically) unfavorably overstretching of chains, a phenomenon that has been suggested to provide the structural basis for the limited region of stability of the gyroid phase in the DBC phase diagram. Finally, the G phase and nodal chain stretching were also found in simulations with a completely different DBC particle-based model.

Encapsulation of hemoglobin in a bicontinuous cubic phase lipid

The effects of encapsulating bovine hemoglobin (BHb) in the bicontinuous cubic phase formed by monooleoylglycerol and water was investigated with Fourier transform infrared (FTIR) spectroscopy and X-ray diffraction. Cubic phase was formed in the presence of 1–10 wt% BHb. Studies using X-ray diffraction reveal that at 0.5–2.5 wt% BHb, the cubic phase structure is characterized by the double diamond lattice ( Pn3m). At 2.5–5 wt% BHb, coexistence of two cubic phase structures, Pn3m and the gyroid lattice ( la3d), was observed while at BHb concentrations higher than 5 wt% the gyroid structure persists. FTIR shows there is an increase in intensity of the free νC = O (1745 cm −1) and a corresponding decrease in the intensity of the hydrogen bonded νC = O (1720 cm −1) cs the BHb concentration is increased. The νC-O-CO peak shifts from 1183 cm −1 to 1181 cm −1 as the concentration of BHb is raised from 2.5 to 10 wt% indicating BHb may induce subtle changes in the interfacial region of cubic phase monoolein. The bandwidth of the ν asCH 2 stretch (2926 cm −1) increased in the presence of 5 wt% BHb compared to samples with 2.5 or 10 wt% BHb. The increase in frequency of the ν sCH 2 stretch (2854 cm −1) induced by increasing temperature 20 to 60°C was dampened when BHb was present compared to samples heated in isotonic buffer. Analysis of the amide I band at 1650 cm −1 showed that the secondary structure of BHb is not affected by encapsulation in monoolein. In vitro release studies showed that 45% of the entrapped BHb was released after 144 h at 37°C. The porous nature of bulk cubic phase was further demonstrated by diffusion of K 2Fe(CN) 6 and conversion of 73% of the oxyhemoglobin to methemoglobin after 1 h. These results suggest that the cubic phase may be useful for encapsulation of Hb as a red cell substitute and for the encapsulation and delivery of other bioactive agents.