Elastic constants of biological filamentous colloids: estimation and implications on nematic and cholesteric tactoid morphologies

Abstract

Biological liquid crystals, such as cellulose and amyloid fibrils, show a physical behaviour difficult to predict and characterize. Here we present four different techniques to estimate the elastic constant K1, K2 and K3 for three different biological filamentous colloids.

Liquid–liquid crystalline phase separation in biological filamentous colloids: nucleation, growth and order–order transitions of cholesteric tactoids

“…For BLG 20 , where L = 550nm and ω = 1.3, we can compute the above mentioned quantities and obtain a minimal volume of V min = 19.6µm 3 , for a nucleating concentration of φ = 3.8. For C-CNC, 21 where L = 450nm and ω = 0.8, the minimal volume is V min = 8.9µm 3 , while for S-CNC, 21 where L = 330nm with ω = 0.5, we obtain V min = 3.0µm 3 . The resulting shape of the curve is represented in Figure 2(a).…”

“…49 In what follows, we show the prediction on the total free energy of the system during evolution of the volume of the three colloids considered, which is now obtained based on the theoretical approach described in the earlier sections, by taking into account liquid crystalline interactions within the growing droplets. The evaluation of the free energy follows the same approach used in the work of Bagnani et al, 20,21 where an extensive analysis has been performed to understand the change in shape and in the configuration of the nematic director field and how these different phases appear.…”

“…20 This functional correctly predicts the shape and nematic field configuration for all the classes of nematic and cholesteric tactoids found experimentally. 20 The values of the constants used can be found in Reference, 21 for the three systems under study and have been reported in Table 1.…”

“…19,20 To date, however, several thermodynamic, structural and kinetics aspects of this LLCPS process remain still unclear, such as the nature of the transitions between the different configurations, the dynamics of the growth process, and the change in cholesteric periodicity (pitch) observed with increasing volume of the droplets. This last effect has been observed experimentally in different chiral systems, 18,21 and requires a more refined treatment to be explained, since the confinement effects are not sufficient to elucidate this phenomenon.…”

“…The Onsager theory 10 predicts accurately the phase boundaries of nematic and isotropic phases for the three systems under analysis, even though they are composed of charged polydisperse rods. 21,26 The rods considered have a contour length well below persistence length and deflection length, therefore they can be considered effectively rigid rods. 26 Moreover, the theory enables to compute pressure and chemical potential at each concentration.…”