Anharmonic Magnetic Deformation of Self-Assembled Molecular Nanocapsules

High magnetic fields were used to deform spherical nanocapsules, self-assembled from bolaamphiphilic sexithiophene molecules. At low fields the deformation—measured through linear birefringence—scales quadratically with the capsule radius and with the magnetic field strength. These data confirm a long standing theoretical prediction [W. Helfrich, Phys. Lett. A 43, 409 (1973)], and permit the determination of the bending rigidity of the capsules as $(2.6\pm 0.8)\times {10}^{-21}\mathrm{J}$. At high fields, an enhanced rigidity is found which cannot be explained within the Helfrich model. We propose a complete form of the free energy functional that accounts for this behavior, and allows discussion of the formation and stability of nanocapsules in solution.

Figure 1

(a) Chemical structure of a sexithiophene molecule (6T). Schematic representation of a spherical capsule with radius $R$ (b) and magnetically deformed capsule with semiaxes $a$ and $c$ (c). (d) Temperature dependence of the magnetic field ($B$) induced birefringence of a $1\mathrm{g}/\mathrm{l}$ 6T solution in 2-propanol. Inset: normalized birefringence Eq. (3) divided by $R^2$ and plotted versus $B^2$. The dashed line corresponds to a fit with constant bending rigidity $k$.

Figure 2

Normalized birefringence of magnetically deformed 6T capsules. Solid lines: experimental data for different temperatures. Dashed lines: calculated birefringence in the Helfrich model, fitting the low-field behavior using a constant $k$ for all $T$. Inset: calculated relation between birefringence and deformation for superspheroids (solid lines) and spheroids (dashed lines) compared to $\Delta n/\Delta n_{\max }\simeq (a-c)/R$ (dash-dotted line).

Figure 3

(a) Fit (dashed lines) of the experimental birefringence (solid lines) at different temperatures, using superspheroidal capsules with deformation energy ${\mathcal{F}}_{\mathrm{el}}$ given by Eq. (8). (b) Equilibrium shapes of the deformed capsules at 20 T.