In this work lipid ordering phase changes arising in planar membrane bilayers is investigated both accounting for elasticity alone and for eective 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 [1]. 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 [2] show a power-law in-plane viscous behavior of lipid structures allowing for an eective viscoelastic behavior of lipid membranes [3], 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.

Fractional Hereditariness of Lipid Membranes: Instabilities and Linearized Evolution / Deseri, Luca; Pollaci, Pietro; Zingales, M.; Dayal, K.. - In: JOURNAL OF THE MECHANICAL BEHAVIOR OF BIOMEDICAL MATERIALS. - ISSN 1751-6161. - 2016:58(2016), pp. 11-27. [10.1016/J.JMBBM.2015.09.021]

Fractional Hereditariness of Lipid Membranes: Instabilities and Linearized Evolution

Deseri, Luca;Pollaci, Pietro;
2016-01-01

Abstract

In this work lipid ordering phase changes arising in planar membrane bilayers is investigated both accounting for elasticity alone and for eective 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 [1]. 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 [2] show a power-law in-plane viscous behavior of lipid structures allowing for an eective viscoelastic behavior of lipid membranes [3], 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.
2016
58
Deseri, Luca; Pollaci, Pietro; Zingales, M.; Dayal, K.
Fractional Hereditariness of Lipid Membranes: Instabilities and Linearized Evolution / Deseri, Luca; Pollaci, Pietro; Zingales, M.; Dayal, K.. - In: JOURNAL OF THE MECHANICAL BEHAVIOR OF BIOMEDICAL MATERIALS. - ISSN 1751-6161. - 2016:58(2016), pp. 11-27. [10.1016/J.JMBBM.2015.09.021]
File in questo prodotto:
File Dimensione Formato  
Fractional hereditariness lipids 2016-arxive.pdf

accesso aperto

Tipologia: Pre-print non referato (Non-refereed preprint)
Licenza: Tutti i diritti riservati (All rights reserved)
Dimensione 3.8 MB
Formato Adobe PDF
3.8 MB Adobe PDF Visualizza/Apri
1-s2.0-S1751616115003586-main.pdf

Solo gestori archivio

Tipologia: Versione editoriale (Publisher’s layout)
Licenza: Tutti i diritti riservati (All rights reserved)
Dimensione 1.48 MB
Formato Adobe PDF
1.48 MB Adobe PDF   Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/115334
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 14
  • ???jsp.display-item.citation.isi??? 10
social impact