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Cascading time evolution of dissipative structures leading to unique crystalline textures.

Hashimoto T, Murase H - IUCrJ (2015)

Bottom Line: 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.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.

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Affiliation: Department of Polymer Chemistry, Graduate School of Engineering, Kyoto University , Katsura, Nishikyo-ku, Kyoto, 615-8510, Japan ; Quantum Beam Science Directorate, Japan Atomic Energy Agency , Tokai-mura, Ibaraki, 1319-1195, Japan ; Professor Emeritus, Kyoto University , Kyoto, 606-8501, Japan.

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 small-length-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.

No MeSH data available.


Related in: MedlinePlus

Concept of the flow-induced cascading reduction of a free energy barrier from A to B via cascading evolutions of a series of dissipative structures 1 to 4 for ordering from an initially homogeneous structure I into an ordered structure F. External fields assist to suppress an excessively large barrier A in the absence of the fields into a free energy landscape B, which enables the ordering from I to F that can be hardly attained in the absence of the fields.
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fig1: Concept of the flow-induced cascading reduction of a free energy barrier from A to B via cascading evolutions of a series of dissipative structures 1 to 4 for ordering from an initially homogeneous structure I into an ordered structure F. External fields assist to suppress an excessively large barrier A in the absence of the fields into a free energy landscape B, which enables the ordering from I to F that can be hardly attained in the absence of the fields.

Mentions: The self-organization of molecular assemblies in open nonequilibrium binary solutions depends on a competition of two characteristic rates: the rate intrinsic to the solutions, Γ, and the rate externally imposed on the system. The intrinsic rate Γ = Γ(q) can be the relaxation rate of the local concentration fluctuations (CF) which generally depends on q, the wavenumber of the Fourier modes of the fluctuations (Landau & Lifschitz, 1964 ▶; Cahn & Hilliard, 1958 ▶; Doi & Onuki, 1992 ▶; Toyoda et al., 2001 ▶). Frequently used abbreviations used in this work are listed in Table 1 ▶. The external rate can be the shear rate in the case of the simple shear flow being applied. If < Γ, the flow cannot affect the fluctuations, because the fluctuations are quickly decayed during the application of the flow. Thus, the shear flow would not essentially change the solution state: if it is homogeneous without the fields, it stays homogeneous even under the flow. However, if the fluctuations exist and hence are deformed during the application of the flow; thereby the flow changes the system state into a higher energy level. The flow-induced deformation may further enhance the building up of CF against osmotic pressure in some systems, as will be clarified later in §4.1. This building up of the CF is an effective energy dissipation mechanism for the solution under the flow into a lower energy level and creates the first flow-induced dissipative structure. If > Γd, the relaxation rate of the first dissipative structure, the flow may further create the second dissipative structure starting from the first one, and so forth, leading to the cascading evolution of a series of dissipative structures under the flow, as schematically illustrated in Fig. 1 ▶.


Cascading time evolution of dissipative structures leading to unique crystalline textures.

Hashimoto T, Murase H - IUCrJ (2015)

Concept of the flow-induced cascading reduction of a free energy barrier from A to B via cascading evolutions of a series of dissipative structures 1 to 4 for ordering from an initially homogeneous structure I into an ordered structure F. External fields assist to suppress an excessively large barrier A in the absence of the fields into a free energy landscape B, which enables the ordering from I to F that can be hardly attained in the absence of the fields.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4285881&req=5

fig1: Concept of the flow-induced cascading reduction of a free energy barrier from A to B via cascading evolutions of a series of dissipative structures 1 to 4 for ordering from an initially homogeneous structure I into an ordered structure F. External fields assist to suppress an excessively large barrier A in the absence of the fields into a free energy landscape B, which enables the ordering from I to F that can be hardly attained in the absence of the fields.
Mentions: The self-organization of molecular assemblies in open nonequilibrium binary solutions depends on a competition of two characteristic rates: the rate intrinsic to the solutions, Γ, and the rate externally imposed on the system. The intrinsic rate Γ = Γ(q) can be the relaxation rate of the local concentration fluctuations (CF) which generally depends on q, the wavenumber of the Fourier modes of the fluctuations (Landau & Lifschitz, 1964 ▶; Cahn & Hilliard, 1958 ▶; Doi & Onuki, 1992 ▶; Toyoda et al., 2001 ▶). Frequently used abbreviations used in this work are listed in Table 1 ▶. The external rate can be the shear rate in the case of the simple shear flow being applied. If < Γ, the flow cannot affect the fluctuations, because the fluctuations are quickly decayed during the application of the flow. Thus, the shear flow would not essentially change the solution state: if it is homogeneous without the fields, it stays homogeneous even under the flow. However, if the fluctuations exist and hence are deformed during the application of the flow; thereby the flow changes the system state into a higher energy level. The flow-induced deformation may further enhance the building up of CF against osmotic pressure in some systems, as will be clarified later in §4.1. This building up of the CF is an effective energy dissipation mechanism for the solution under the flow into a lower energy level and creates the first flow-induced dissipative structure. If > Γd, the relaxation rate of the first dissipative structure, the flow may further create the second dissipative structure starting from the first one, and so forth, leading to the cascading evolution of a series of dissipative structures under the flow, as schematically illustrated in Fig. 1 ▶.

Bottom Line: 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.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.

View Article: PubMed Central - HTML - PubMed

Affiliation: Department of Polymer Chemistry, Graduate School of Engineering, Kyoto University , Katsura, Nishikyo-ku, Kyoto, 615-8510, Japan ; Quantum Beam Science Directorate, Japan Atomic Energy Agency , Tokai-mura, Ibaraki, 1319-1195, Japan ; Professor Emeritus, Kyoto University , Kyoto, 606-8501, Japan.

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 small-length-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.

No MeSH data available.


Related in: MedlinePlus