Theory and Simulation of Cholesteric Film Formation Flows of Dilute Collagen Solutions

Abstract

Dilute isotropic collagen solutions are usually flow processed into monodomain chiral nematic thin films for obtaining highly ordered materials by a multistep process that starts with complex inhomogeneous flow kinematics. Here we present rigorous theory and simulation of the initial precursors during flow steps in cholesteric collagen film formation. We first extract the molecular shape parameter and rotational diffusivity from previously reported simple shear data of dilute collagen solutions, where the former leads the reactive parameter (tumbling function) which determines the net effect of vorticity and strain rate on the average orientation and where the latter establishes the intensity of strain required for flow-birefringence, both crucial quantities for controlled film formation flow. We find that the tumbling function is similar to those of rod-like lyotropic liquid crystalline polymers and hence it is predicted that they would tumble in the ordered high concentration state leading to flow-induced texturing. The previously reported experimental data is well fitted with rotational diffusivities whose order of magnitude is consistent to those of other biomacromolecules. We then investigate the response of the tensor order parameter to complex flow kinematics, ranging from pure vorticity, through simple shear, to extensional flow, as may arise in typical flow casting and film flows. The chosen control variable to produce precursor cholesteric films is the director or average orientation, since the nematic order is set close to typical values found in concentrated cholesteric type I collagen solutions. Using the efficient four-roll mill kinematics, we summarize the para-nematic structure-flow process diagram in terms of the director orientation and flow type. Using analysis and computation, we provide a parametric envelope that is necessary to eventually produce well-aligned cholesteric films. We conclude that extensional flow is an essential ingredient of well-ordered film precursors with required Deborah numbers on the order of unity.

Relaxation dynamics in bio-colloidal cholesteric liquid crystals confined to cylindrical geometry

“…Unwinding the helices of a chiral nematic liquid crystal drives the cholesteric phase (N*) to a para-nematic phase (PN) 1 , characterized by a higher energy state compared to the equilibrium chiral nematic phase. Thus, the para-nematic phase thermodynamically tends to relax by relieving the excess free energy 2 .…”

Theoretical Platform for Liquid-Crystalline Self-Assembly of Collagen-Based Biomaterials

“…The derived LdG coefficients satisfy two general theoretical expectations; (1) the first-order phase transition (i.e., B = 0), and (2) two minima correspond to isotropic and ordered phases (i.e., A<0 and C>0) [46]. Furthermore, in the cholesteric phase, W can be about 10, and under such conditions the proposed LdG coefficients becomes similar to the well-established lyotropic LCP Doi's model, were b ≈ c [14,15,61].…”

“…Furthermore, their structures are analogous with architecture of tropocollagen in liquid-crystalline states [12], hence these materials are called "solid analogs." This correspondence establishes the role and impact of liquidcrystalline morphogenesis [13][14][15] and singles out liquid-crystalbased biomimetic material process engineering as a promising route to enhance the quality of collagen-based biomaterials or even to explore new ones [3,[16][17][18][19].…”

“…The long-range orientational order in a liquid-crystalline phase is parameterized by a second-order symmetric traceless tensor called Q-tensor [14,15,46].…”

“…A heavy computational load is expected because the self-assembly process covers a wide range of length scale (i.e., ranging from nano-to macro-scale) and it may go through a variety of complex microscopic mechanisms [41,[55][56][57][58][59]. Thus, to improve tractability, we expand the functional part of Equation (15), Ŵ (γ), in terms of the second Legendre polynomial by use of Equation 8:…”