Hypothesis: Control of the nanostructure of self-assembled systems may be achieved through manipulation of surfactant molecular packing and interfacial curvature. In order to phase engineer the inverse micellar cubosomes in some monoolein-fatty acid systems, lipids with wedge shaped molecular geometry were incorporated to promote the formation of this phase, that is of interest as potential sustained released nanocarriers. Experiments: Liquid crystalline nanoparticle dispersions of monoolein with some cis unsaturated fatty acids were prepared and their partial temperature-composition phase diagrams and structure were established using high throughput Small Angle X-ray Scattering (SAXS) and cryogenic transmission electron microscopy (cryo-TEM). The pH responsiveness of these systems was evaluated in the presence of phosphate buffered saline (PBS). Findings: The partial temperature-composition phase diagrams of five nanoparticle formulations containing monoolein and unsaturated fatty acids were established and identified the presence of micellar cubosomes in each of these systems. The results indicate that temperature, fatty acid concentration and structure, as well as pH all directly impact the formation and stability of this phase. Low energy inverse micellar cubic to emulsion phase transformations were identified in the monoolein with oleic acid and vaccenic acid systems at physiological temperatures that may be advantageous for staged therapeutic release strategies in nanomedicine. (C) 2020 Elsevier Inc. All rights reserved.