Thermal fluctuations and stiffening of symmetric heterogeneous fluid membranes

We study the effects of thermal fluctuations on symmetric tensionless heterogeneous (two-component) fluid membranes in a simple minimal model. Close to the critical point $T_c$ of the associated miscibility phase transition of the composition and for sufficiently strong curvature-composition interactions, mediated through a composition-dependent bending modulus, thermal fluctuations lead to enhancement of the effective bending modulus. Thus, the membrane conformation fluctuations will be suppressed near $T_c$, in comparison with a pure fluid membrane, for which thermal fluctuations are known to reduce the effective bending modulus at all nonzero temperatures.

Figure 1

One-loop Feynman diagram contributing to the fluctuation correction to $\kappa$. This originates from the geometric nonlinearity; see Eq. (8).

Figure 2

One-loop Feynman diagram contributing to the fluctuation correction to $\kappa$. This is due to the composition fluctuations and exists only for inhomogeneous membranes; see Eq. (9).

Figure 3

Schematic variation of order parameter $\overline{O}$ as a function of $\lambda$; $\overline{O}\propto (\lambda -{\lambda }_c)$ for $\lambda \le {\lambda }_c$, $\overline{O}=0$ for $\lambda {\lambda }_c$ as shown by the blue broken line; see the text.

Figure 4

Schematic phase diagram in the $\lambda -T_c$ plane for $\epsilon >0$. The continuous line represents Eq. (12).

Figure 5

Schematic plot of renormalized $\kappa$ for a system of size $L$ as a function of $r=T-T_c$; a rise in $\kappa$ as $T\to T_c$ due to a nonzero $\lambda$ is shown.