Liquid crystal models of biological materials and silk spinning

Abstract

A review of thermodynamic, materials science, and rheological liquid crystal models is presented and applied to a wide range of biological liquid crystals, including helicoidal plywoods, biopolymer solutions, and in vivo liquid crystals. The distinguishing characteristics of liquid crystals (self-assembly, packing, defects, functionalities, processability) are discussed in relation to biological materials and the strong correspondence between different synthetic and biological materials is established. Biological polymer processing based on liquid crystalline precursors includes viscoelastic flow to form and shape fibers. Viscoelastic models for nematic and chiral nematics are reviewed and discussed in terms of key parameters that facilitate understanding and quantitative information from optical textures and rheometers. It is shown that viscoelastic modeling the silk spinning process using liquid crystal theories sheds light on textural transitions in the duct of spiders and silk worms as well as on tactoidal drops and interfacial structures. The range and consistency of the predictions demonstrates that the use of mesoscopic liquid crystal models is another tool to develop the science and biomimetic applications of mesogenic biological soft matter.

Actuation of flexoelectric membranes in viscoelastic fluids with applications to outer hair cells

“…The main objective is to identify material conditions that lead to a biologically relevant power spectrum with a well-defined resonant peak and Q-factor less than one (Q(ω) < 1), using the transfer function methodology of § §4 and 5. Table 2 figure 5; the other modes {II, IV, VI} corresponding to stiff (large k) membranes are not biologically relevant [18] either because they do not form power peaks or because Q(ω) > 1 (store more membrane elastic energy than inject momentum into the fluids). In the case when the inertial mechanisms are neglected, De 1, the real Re[F D (ω)] and imaginary Im[F D (ω)] parts of the transfer function behave as would be expected for a simple viscoelastic system displaying a single peak and two asymptotic plateaus separated by a power-law region (PLR).…”

“…which coincides with E H , and gives 4k c = (K 1 + 8K 24 ),k c = −2K 24 ; the surface gradient is given by the tangential projection of the total gradient: ∇ s (·) ≡ I s · ∇(·), I s = I − kk, since thin layers and membranes behave like LCs, membranes should also exhibit flexoelectricity or couplings between polarization and bending [1][2][3][4]7,11,[17][18][19]. Figure 2 shows a schematic of flexoelectric polarization in rod-like and banana-like molecules and the corresponding membrane flexoelectric polarization; as noted above the physics and modelling are affected by identifying the director field n with the membrane normal k. Using the same approach as above, equation (1.4) gives the membrane polarization P due to membrane bending (∇ s · k): 10) where c f is the membrane flexoelectric coefficient, as indeed found experimentally [4].…”

“…A distinguishing and novel property of nematics is flexoelectricity [1][2][3][4]11], which describes the coupling between orientational gradients and electric polarization, such that an applied electric field creates orientational distortions and distortions create macroscopic polarization [1][2][3][4]11,[17][18][19]. The polar nature of splay S = n∇ · n and bend B = −n × ∇ × n orientational deformations can polarize the nematic LC medium [11][12][13] (b) Flexoelectricity in biological membranes due to bending curvature described by surface gradients of the unit normal k. The correspondence between nematic flexoelectricity and membrane flexoelectricity is obtained when the director n is identified with the membrane unit normal k (adapted from [11]).…”

“…where H is the average curvature and K the Gaussian curvature, which follows from the nematic Frank elastic energy [11][12][13][14][15]: 8) where K 1 is the splay and K 24 is the saddle-splay constant; the geometrical quantities and definitions used in this paper are reported elsewhere [11,[17][18][19]. Nemato-membranology is applied by identifying the director n with the outer unit normal n = k in equation (1.8), and considering surface gradient ∇ s , we obtain…”

“…Both the direct and converse membrane flexoelectric effects are sensor-actuator properties when membrane curvature and polarization are coupled as in nematic LCs. Membrane flexoelectricity due to its inherent sensoractuator capabilities is an area of current interest in soft matter materials [1,7,8,[14][15][16][17][18][19][20][21][22][23][24]. Over the years, much literature has dealt with the problem of measuring flexoelectric coefficients in various LCs [11,13].…”