Fig. 4: Structural relaxation of different classes of liquid crystalline tactoids.
a–c Evaluation of \({{{{{\mathcal{S}}}}}}\) (defined as \(\tfrac{S\left(t\right)\,-\,{S}_{{{{{{\rm{equil}}}}}}.}}{{S}_{{{{{{\rm{init}}}}}}.}\,-\,{S}_{{{{{{\rm{equil}}}}}}.}}\) for homogeneous and bipolar tactoids and \({{{{{\mathcal{S}}}}}}=\frac{S\left(t\right)\,-\,{S}_{{{{{{\rm{minimum}}}}}}}}{{S}_{{{{{{\rm{init}}}}}}.}\,-\,{S}_{{{{{{\rm{minimum}}}}}}}}\) for cholesteric tactoids, where Sequil., Sinit., and S(t) are order parameter values at equilibrium, at the initial time, and at a given time t, respectively) with respect to scaled time, \(\frac{t}{{\tau }_{{{{{{\rm{c}}}}}}}}\) with τc the characteristic configurational relaxation time, for tactoids that relax to homogenous (a), bipolar (b) and cholesteric (c) configurations at equilibrium. The experimental insets showing the retardance images taken with LC-PolScope along with numerical simulation results present the critical state of the relaxation for each class of the tactoids. Color bar denotes the order parameter values in numerical simulation insets. Note that the brightness of the experimental images is increased for better visualization. The symbols denote the experimental data, black solid lines are numerical simulation results. Colored and dashed black lines show the fitting that is used to obtain τc from experimental and numerical simulation results, respectively. d–f The changes in \(\frac{{{{{{\rm{d}}}}}}{{{{{\mathcal{S}}}}}}}{{dt}}\), obtained from the fitted lines in a–c, during relaxation for different classes of tactoids: homogenous (d), bipolar (e), and cholesteric (f) configurations. While homogenous and bipolar tactoids follow monotonic single exponential decay during relaxation \({{{{{\mathcal{S}}}}}}={{{{{\rm{exp }}}}}}\left(-\frac{t}{{\tau }_{{{{{{\rm{c}}}}}}}}\right)\), the cholesteric tactoids are characterized by a non-monotonic behavior of \({{{{{\mathcal{S}}}}}}\) during relaxation (see (c)), described by a second-order exponential decay, \({{{{{\mathcal{S}}}}}}\,=\,{c}_{1}{{{{{\rm{exp}}}}}}\left(-t/{\tau }_{{{{{{\rm{c}}}}}},1}\right)\,+\,(1\,-\,c_{1}){{{{{\rm{exp }}}}}}(-t/{\tau }_{{{{{{\rm{c}}}}}},2})\), where c1 is a constant.
