Geometric and elastic properties and mechanical phase separation phenomena in self-assembling mesoscopic helical springs

Abstract

Helical ribbons with pitch angles of either 11⁰ or 54⁰ self-assemble in a wide variety of quaternary surfactant-phospholipid/fatty acid-sterol-water systems. In all of the systems studied, the thermodynamically stable state for the sterol is plate like mono-hydrate crystals. However, the sterol is typically found to pass through a serious of metastable intermediates from filaments to helical ribbons to tubules before reaching the stable crystalline state. In the present work, we chose to focus on helical ribbons formed in the Chemically Defined Lipid Concentrate (CDLC) system. These helices typically have radii on the order of a few to a few tens of microns and lengths on the order of hundreds of microns. By tethering to these mesoscopic helical ribbons using Devcon 5-Minute Epoxy®, we have been able to elastically deform them, and thus examine their response to uniaxial tension. For small deformations, the low pitch helices behave like linear elastic springs with a spring constant for a typical example measured to be (4.80 +/- 0.77) x 10-6 N/m. From the observed spread in helix dimension, our theory predicts a corresponding range of spring constants for the structures of 10-7 to 10-4 N/m allowing, in principle, a great range of forces to be examined. Under larger tensions, both low and high pitch helices have been observed to reversibly separate into a straight domain with a pitch angle of 90Ê» and a helical domain with a pitch angle of (16.5 +/1 1.3)⁰ for the low pitch or (59.6 +/- 1.7)⁰ for the high pitch. Using a newly developed continuum elastic free energy model, we have shown that this phenomena can be understood as a mechanical phase transition of first order.

(cont.) From this analysis, we have also been able to determine all of the parameters within our model, and to show that it is capable of self-consistently and quantitatively explaining all of the observed properties of these self-assembled helices.