A patch of membrane carries a sparse negative surface charge density, (about one…

PHYSICS · Subjective · Fermi University Physics · Condensed Matter, Materials & Soft Matter · Biophysics & Medical Physics · Macromolecules, membranes and cell architecture

Forces, Machines and Signals, Ch Charges in salt water and the assembly of amphiphiles

Problem

A patch of membrane carries a sparse negative surface charge density, σ=−0.010 C m−2\sigma = -0.010\,\mathrm{C\,m^{-2}} (about one elementary charge per 16 nm216\,\mathrm{nm^2}), and sits in 30 mM30\,\mathrm{mM} monovalent salt at 298 K298\,\mathrm{K}. At 150 mM150\,\mathrm{mM} the Grahame prefactor is 8c∞ε0εrkBT=0.0454 C m−2\sqrt{8c_\infty\varepsilon_0\varepsilon_rk_BT} = 0.0454\,\mathrm{C\,m^{-2}}. Find the prefactor at 30 mM30\,\mathrm{mM}, then use the Grahame equation, σ=8c∞ε0εrkBT sinh⁡ ⁣(eψ02kBT)\sigma = \sqrt{8c_\infty\varepsilon_0\varepsilon_rk_BT}\,\sinh\!\left(\dfrac{e\psi_0}{2k_BT}\right), to find the membrane's surface potential.

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