The parameter b, the dimensionless entropic coefficient, is calculated from the equilibrium equation of lateral pressure and surface tension of the water–lipid tail interface:

$$\frac_}}}} = - \gamma ,$$

(A1)

where Ft is the free energy of the hydrophobic chain (“tail”) of a lipid,

$$b = \frac}^}}} + \frac^} \right. \kern-0em} 3}}}}}^} \right. \kern-0em} 3}}}}}},$$

(A2)

where \(\nu = \frac_}_}}}^}}}\) is a dimensionless coefficient,

$$\nu = \frac_}_}}}^}}}.$$

(A3)

Here Kf is the bending stiffness of the lipid chain; A0 = 0.2 nm2 is the incompressible area of the lipid chain; a = A/A0 is a dimensionless area, which is calculated from the self-consistency equation:

$$_}}}} = L\left\langle ^}}}\left( z \right)} \right\rangle }.$$

(A4)

Or in dimensionless form:

$$}}}b}} + \frac}}}\sqrt } ^} \mathord} }}} \right. \kern-0em} }}}}}}} = \nu })}}^}}}}.$$

(A5)

Differentiating Eq. (A5) and taking into account (A3) gives the first derivative of b by l:

$$\frac}} = \frac^}\nu }^}}} ^} \right. \kern-0em} 4}}}}}},$$

(A6)

\(\frac^}b}}^}}}\) is calculated in a similar way.