A bilayer has hydrophobic thickness and area-stretch modulus

PHYSICS · Multi-part · Fermi University Physics · Biophysics & Medical Physics · Macromolecules, membranes and cell architecture · Macromolecules, membranes and cell architecture

Soft Matter at the Thermal Scale, Ch Membranes, fluctuations and soft matter in biology

Problem

A bilayer has hydrophobic thickness d=3.5 nmd = 3.5\,\mathrm{nm} and area-stretch modulus KA=0.24 N m−1K_A = 0.24\,\mathrm{N\,m^{-1}}. The bending modulus follows from the stretching modulus and thickness as κb=KAd2/β\kappa_{\rm b} = K_Ad^2/\beta, where β=12\beta = 12 if the two monolayers are rigidly coupled (a solid plate) and β=48\beta = 48 if they slide freely past each other, with β=24\beta = 24 as a middle estimate. ((a)) Estimate κb\kappa_{\rm b}, in units of kBTk_BT at 298 K298\,\mathrm{K}, for β=12\beta = 12, β=24\beta = 24 and β=48\beta = 48. ((b)) Real bilayers of this thickness are typically measured to have κb\kappa_{\rm b} in the range 2020-25kBT25k_BT. Which value of β\beta gives the closest estimate?

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