Cascading time evolution of dissipative structures leading to unique crystalline textures

Abstract

This article reports unique pattern formation processes and mechanisms via crystallization of materials under external flow fields as one of the general problems of open nonequilibrium phenomena in statistical physics. The external fields effectively reduce step-by-step the exceedingly large free energy barriers associated with the reduction of the enormously large entropy necessary for crystallization into unique crystalline textures in the absence of the fields. The cascading reduction of the free energy barrier was discovered to be achieved as a consequence of a cascading evolution of a series of dissipative structures. Moreover, this cascading pattern evolution obeys the Ginzburg-Landau law. It first evolves a series of large-length-scale amorphous precursors driven by liquid-liquid phase separation under a relatively low bulk stress and then smalllength-scale structures driven by a large local stress concentrated on the heterogeneous amorphous precursors, eventually leading to the formation of unique crystalline textures which cannot be developed free from the external fields. Here the multi-length-scale heterogeneous structures developed in the amorphous precursors play a dominant role in the triggering of the crystallization in the local regions subjected to a large stress concentration even under a relatively small applied bulk stress.

Formation of crystal-like structures and branched networks from nonionic spherical micelles

“…Summarizing our findings, we suggest that transition from spherical micelles to CLS at T ≤ 15 °C, 10 3 s −1 , and γ ~ 10 4 –10 6 is likely to undergo a similar energy cascading mechanism as those observed in non-equilibrium binary systems (i.e., flexible polymers) 46 47 , see cartoons in Figs 4(a) and 7 . The self-organization of molecular assemblies in non-equilibrium binary solutions depends on the competition between the intrinsic rate of the system (Γ), and the rate introduced by the external field 47 . In our case, the external rate corresponds to the shear rate when the nonionic precursor is sheared at 15 °C, while the intrinsic rate could be the relaxation rate of the local concentration fluctuations of nonionic micelles.…”

“…2(c) ). We speculate that due to the coupling between low temperature and high strain ( T < 15 °C and γ ~ 10 4 –10 6 ), the spherical micelles in the precursor are initially aligned in the flow direction, subsequently stacked in both neutral and velocity gradient directions over time, inducing micellar growth, creating possible nucleation sites for crystallization 29 30 33 34 35 36 37 38 39 40 41 42 43 44 46 47 . This observation is consistent with existing reports for both surfactants and colloidal solutions 29 30 33 34 35 36 37 38 39 40 41 42 43 44 46 47 , where isotropic phases could grow in the neutral direction of the flow velocity.…”

“…However, if , entropic fluctuations are influenced by the shear flow and temperature, triggering a flow-induced cascading reduction in the free energy barrier, promoting spherical micelles to follow the free energy landscape trajectory (blue curve shown in Fig. 7(a) ) and form dissipative structures 46 47 . Based on the measurements from rheo-SALS, birefringence imaging, and cryo-EM, we suggest that the nonionic spherical micelles would first form micellar strings under shear, which fuse and develop into elongated wormlike micelles 48 49 50 .…”

“…In the absence of external fields, homogenous structures require significantly higher amount of energy to form ordered structures (red curve). ( b ) Under external fields, spherical micelles can follow the free energy landscape trajectory (blue curve shown in ( a )) and form dissipative structures such as wormlike micelles, branched micelles, triggering the formation of unfolded/aligned/stacked branched micelle aggregates and nano-crystal nuclei, eventually transforming into crystal-like structures (CLS) 47 .…”

“…Shear flow is also known to induce ordering, crystallization, and phase transitions in surfactant solutions, polymer solutions, and colloidal systems 3 14 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 . The transition from nonionic surfactant micelles to higher order structures (e.g., lamellar, nematic, or onion phases) has been accomplished by coupling shear flow with temperature variations 29 30 33 34 35 36 37 38 39 40 41 42 .…”