title: Fractional hereditariness of lipid membranes: Instabilities and linearized evolution.
abstract: In this work lipid ordering phase changes arising in planar membrane bilayers is investigated both accounting for elasticity alone and for effective viscoelastic response of such assemblies. The mechanical response of such membranes is studied by minimizing the Gibbs free energy which penalizes perturbations of the changes of areal stretch and their gradients only (Deseri and Zurlo, 2013). As material instabilities arise whenever areal stretches characterizing homogeneous configurations lie inside the spinoidal zone of the free energy density, bifurcations from such configurations are shown to occur as oscillatory perturbations of the in-plane displacement. Experimental observations (Espinosa et al., 2011) show a power-law in-plane viscous behavior of lipid structures allowing for an effective viscoelastic behavior of lipid membranes, which falls in the framework of Fractional Hereditariness. A suitable generalization of the variational principle invoked for the elasticity is applied in this case, and the corresponding Euler-Lagrange equation is found together with a set of boundary and initial conditions. Separation of variables allows for showing how Fractional Hereditariness owes bifurcated modes with a larger number of spatial oscillations than the corresponding elastic analog. Indeed, the available range of areal stresses for material instabilities is found to increase with respect to the purely elastic case. Nevertheless, the time evolution of the perturbations solving the Euler-Lagrange equation above exhibits time-decay and the large number of spatial oscillation slowly relaxes, thereby keeping the features of a long-tail type time-response.
authors.affiliation: Dept. of Mechanical Engineering and Materials Science-MEMS-Swanson School of Engineering, University of Pittsburgh, 3700 O'Hara Street, Pittsburgh, PA 15261, USA; Dept. of Civil Environmental and Mechanical Engineering-DICAM, University of Trento, via Mesiano, 77 38123 Trento, Italy; Dept. of Mechanical Engineering, 5000 Forbes Av., Pittsburgh PA 15213-3890, USA; Dept. of Civil and Environmental Engineering, Carnegie Mellon University, 5000 Forbes Av., Pittsburgh PA 15213-3890, USA; The Methodist Hospital Research Institute-TMHRI-Department of Nanomedicine, 6565 Fannin St., MS B-490, Houston, TX 77030, USA. Electronic address: deseri@andrew.cmu.edu.
authors.forename: L
authors.initials: L
authors.lastname: Deseri
authors.affiliation: Dept. of Civil Environmental and Mechanical Engineering-DICAM, University of Trento, via Mesiano, 77 38123 Trento, Italy. Electronic address: pietro.pollaci@unitn.it.
authors.forename: P
authors.initials: P
authors.lastname: Pollaci
authors.affiliation: Civil, Environmental, Aerospace Engineering and Material Science, University of Palermo, Viale delle Science, Edificio 8, 90100 Palermo, Italy; Lab, Mediterranean Center of Human Health and Advanced Biotechnologies, University of Palermo, Viale delle Science, Edificio 8, 90100 Palermo, Italy. Electronic address: massimiliano.zingales@unipa.it.
authors.forename: M
authors.initials: M
authors.lastname: Zingales
authors.affiliation: Dept. of Civil and Environmental Engineering, Carnegie Mellon University, 5000 Forbes Av., Pittsburgh PA 15213-3890, USA. Electronic address: kaushik@cmu.edu.
authors.forename: K
authors.initials: K
authors.lastname: Dayal
mesh_terms: D004548:Elasticity; D008051:Lipid Bilayers / Q000737:chemistry*; D008560:Membrane Fluidity; D008566:Membranes / Q000737:chemistry*; D008956:Models, Chemical
chemical_list: D008051:Lipid Bilayers
keywords: Fractional hereditary lipid membranes; Material instabilities; Phase transitions; Viscoelastic lipid membranes