Extended Data Table 1 |. Range of required interfacial tension reduction needed for spontaneous shape transitions of NLCO drops with “physical” saddle-splay modulus.

This table summarizes parameter values that permit shape transitions (with reasonable saddle-splay elastic constants) based on our model free energy calculations. The calculations fix the interfacial tension (γ_{measured;mm-drop}) at 30 °C measured by the pendant drop technique. A fairly wide range of estimated elastic constants (K) and anchoring energy coefficients (W_a) are employed in the calculations too. Per criteria for a spontaneous shape transition, we demand that the required saddle-splay elastic constant (K₂₄) be of order ∼6 times the splay modulus (or less). The calculations show that a smaller “true” interfacial tension, γ_{true;micro-emulsion} (expressed as reduction factor of γ_{measured;mm-drop} in the Table), will significantly relax the saddle-splay requirement. This reduction of γ can be realized through oligomer polydispersity and resultant oligomer spatial segregation in the elastic stress field. Note, a reasonable range for K is 5×10⁻¹¹ N to 10⁻¹⁰ N; a value of K =10⁻¹¹ N is probably too small, since it is the same order of magnitude as small molecule LCs such as 5CB.

γmeasured; mm-drop (mN/m)	K (N)	Wa (J/m2)	Required K24 for shape transition	Reduction factor of γmeasured; mm-drop gives γtrue; micro-emulsion	Required K24 for shape transition with reduced γ
2.36	5 × 10−11	5 × 10−5 ∼5 × 10−4	60.2 × K11	20x	5.7 × K11
2.36	10−10	5 × 10−5 ∼5 × 10−4	31.6 × K11	10x	5.7 × K11
2.36	5 × 10−10	5 × 10−4	8.6 × K11	2x	5.7 × K11