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An exactly solvable model of hierarchical self-assembly
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10.1063/1.3148893
/content/aip/journal/jcp/130/22/10.1063/1.3148893
http://aip.metastore.ingenta.com/content/aip/journal/jcp/130/22/10.1063/1.3148893
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

Schematic models of hierarchical clusters for various and : , (a), , (b), and , (c).

Image of FIG. 2.
FIG. 2.

The order parameters for a few initial steps of the hierarchical self-assembly as a function of temperature . The initial monomer concentration is fixed , and the number of monomers in the cluster is taken as . The overall order parameter is indicated by a dashed line. The energy and entropy of the formation of a single associative link are chosen as and and are also employed in the calculations presented in Figs. 3–9.

Image of FIG. 3.
FIG. 3.

The order parameter (, ) for the first step of the hierarchical self-assembly [see Eq. (2)] as a function of temperature . Different curves correspond to the indicated (fixed) initial monomer concentrations .

Image of FIG. 4.
FIG. 4.

The maximum of the order parameter for the hierarchical self-assembly as a function of the generation of the self-assembly. Different curves correspond to the indicated numbers of monomers in the first generation clusters . The maxima of the corresponding order parameters for the model are included for comparison.

Image of FIG. 5.
FIG. 5.

The order parameters for hierarchical self-assembly as a function of the initial monomer concentration at . The number of monomers in the cluster is taken as . Different curves correspond to the indicated generation of the hierarchical self-assembly. The upper dotted curve presents the overall order parameter .

Image of FIG. 6.
FIG. 6.

The hierarchical assembly transition temperature as a function of the initial monomer concentration . The number of monomers in the cluster is taken as . The index labels the generation of the hierarchical self-assembly.

Image of FIG. 7.
FIG. 7.

The average cluster mass for the hierarchical self-assembly as a function of the initial monomer concentration . Different curves correspond to the indicated fixed temperatures and a common .

Image of FIG. 8.
FIG. 8.

The overall order parameter for hierarchical self-assembling systems as a function of temperature for fixed initial monomer concentration and for the indicated values of . The long-dashed curve illustrates the order parameter for the model [, ].

Image of FIG. 9.
FIG. 9.

The constant volume specific heat for hierarchical self-assembling systems as a function of temperature for fixed initial monomer concentration . Different curves correspond to the indicated values of .

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/content/aip/journal/jcp/130/22/10.1063/1.3148893
2009-06-11
2014-04-20
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: An exactly solvable model of hierarchical self-assembly
http://aip.metastore.ingenta.com/content/aip/journal/jcp/130/22/10.1063/1.3148893
10.1063/1.3148893
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