Self-assembly thermodynamic model

The threshold concentration of monomer that must be exceeded for any observable polymer formation in a self-assembling system. In the context of Oosawa s condensation-equilibrium model for protein polymerization, the cooperativity of nucleation and the intrinsic thermodynamic instability of nuclei contribute to the sudden onset of polymer formation as the monomer concentration reaches and exceeds the critical concentration. Condensation-equilibrium processes that exhibit critical concentration behavior in vitro include F-actin formation from G-actin, microtubule self-assembly from tubulin, and fibril formation from amyloid P protein. Critical concentration behavior will also occur in indefinite isodesmic polymerization reactions that involve a stable template. One example is the elongation of microtubules from centrosomes, basal bodies, or axonemes. 

In principle, the expressions for pair potentials, osmotic pressure and second virial coefficients could be used as input parameters in computer simulations. The objective of performing such simulations is to clarify physical mechanisms and to provide a deeper insight into phenomena of interest, especially under those conditions where structural or thermodynamic parameters of the studied system cannot be accessed easily by experiment. The nature of the intermolecular forces responsible for protein self-assembly and phase behaviour under variation of solution conditions, including temperature, pH and ionic strength, has been explored using this kind of modelling approach (Dickinson and Krishna, 2001 Rosch and Errington, 2007 Blanch et al., 2002). 

A Thermodynamic Model Self-Assembly of Zinc Porphyrin Complexes... 

The thermodynamics of self-assembled systems are often characterized by positive co-operativity at the molecular level, however the thermodynamic analysis of co-operativity in self-assembly is complexes such as helicates is complicated by the occurrence of both inter- and intramolecular steps. It may be understood using the extended site binding model. 

Not mentioned in this review but certainly important to multiscale modeling related to solid mechanics are topics, such as self-assemblies, thin films, thermal barrier coatings, patterning, phase transformations, nanomaterials design, and semiconductors, all of which have an economic motivation for study. Studies related to these types of materials and structures require multiphysics formulations to understand the appropriate thermodynamics, kinetics, and kinematics. 

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