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Statistical thermodynamics of irreversible aggregation: the sol-gel transition.

ABSTRACT: Binary aggregation is known to lead, under certain kinetic rules, to the coexistence of two populations, one consisting of finite-size clusters (sol), and one that contains a single cluster that carries a finite fraction of the total mass (giant component or gel). The sol-gel transition is commonly discussed as a phase transition by qualitative analogy to vapor condensation. Here we show that the connection to thermodynamic phase transition is rigorous. We develop the statistical thermodynamics of irreversible binary aggregation in discrete finite systems, obtain the partition function for arbitrary kernel, and show that the emergence of the gel cluster has all the hallmarks of a phase transition, including an unstable van der Waals loop. We demonstrate the theory by presenting the complete pre- and post-gel solution for aggregation with the product kernel.

SUBMITTER: Matsoukas T

PROVIDER: S-EPMC4352918 | biostudies-literature | 2015 Mar

REPOSITORIES: biostudies-literature

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Statistical thermodynamics of irreversible aggregation: the sol-gel transition.

Matsoukas Themis T

Scientific reports 20150309

Binary aggregation is known to lead, under certain kinetic rules, to the coexistence of two populations, one consisting of finite-size clusters (sol), and one that contains a single cluster that carries a finite fraction of the total mass (giant component or gel). The sol-gel transition is commonly discussed as a phase transition by qualitative analogy to vapor condensation. Here we show that the connection to thermodynamic phase transition is rigorous. We develop the statistical thermodynamics ...[more]

PMID: 25748055

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Project description:Advances in supramolecular assembly have enabled the design and synthesis of functional materials with well-defined structures across multiple length scales. Biopolymer-synthetic hybrid materials can assemble into supramolecular structures with a broad range of structural and functional diversity through precisely controlled noncovalent interactions between subunits. Despite recent progress, there is a need to understand the mechanisms underlying the assembly of biohybrid/synthetic molecular building blocks, which ultimately control the emergent properties of hierarchical assemblies. In this work, we study the concentration-driven self-assembly and gelation of π-conjugated synthetic oligopeptides containing different π-conjugated cores (quaterthiophene and perylene diimide) using a combination of particle tracking microrheology, confocal fluorescence microscopy, optical spectroscopy, and electron microscopy. Our results show that π-conjugated oligopeptides self-assemble into β-sheet-rich fiber-like structures at neutral pH, even in the absence of electrostatic screening of charged residues. A critical fiber formation concentration cfiber and a critical gel concentration cgel are determined for fiber-forming π-conjugated oligopeptides, and the linear viscoelastic moduli (storage modulus G' and loss modulus G″) are determined across a wide range of peptide concentrations. These results suggest that the underlying chemical structure of the synthetic π-conjugated cores greatly influences the self-assembly process, such that oligopeptides appended to π-conjugated cores with greater torsional flexibility tend to form more robust fibers upon increasing peptide concentration compared to oligopeptides with sterically constrained cores. Overall, our work focuses on the molecular assembly of π-conjugated oligopeptides driven by concentration, which is controlled by a combination of enthalpic and entropic interactions between oligopeptide subunits.

Dataset Information

Statistical thermodynamics of irreversible aggregation: the sol-gel transition.

Publications

Statistical thermodynamics of irreversible aggregation: the sol-gel transition.

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