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This analogy is exploited to calculate the gel point and gel fraction for monomer precursors with arbitrary types of functional groups. Random graphs can be used to derive analytical expressions for simple polymerisation mechanisms, such as step-growth polymerisation, or alternatively, they can be combined with a system of rate equations that ...
Flory–Stockmayer theory is a theory governing the cross-linking and gelation of step-growth polymers. [1] The Flory–Stockmayer theory represents an advancement from the Carothers equation, allowing for the identification of the gel point for polymer synthesis not at stoichiometric balance. [1]
At the gel point, a solution undergoes gelation, as reflected in a loss in fluidity. After the monomer/polymer solution has passed the gel point, internal stress builds up in the gel phase, which can lead to volume shrinkage. Gelation is characteristic of polymerizations that include crosslinkers that can
Random graph theory of gelation is a mathematical theory for sol–gel processes.The theory is a collection of results that generalise the Flory–Stockmayer theory, and allow identification of the gel point, gel fraction, size distribution of polymers, molar mass distribution and other characteristics for a set of many polymerising monomers carrying arbitrary numbers and types of reactive ...
[3], [4] Theorists also have difficulties predicting characteristic gelation parameters, such as gel point and gelation time, with a single and simple equation. Gel point, the transition point from a polymer solution to gel, is a function of the extent of reaction or the fraction of functional groups reacted.
These Calculators Make Quick Work of Standard Math, Accounting Problems, and Complex Equations Stephen Slaybaugh, Danny Perez, Alex Rennie May 21, 2024 at 2:44 PM
Mechanics of gelation describes processes relevant to sol-gel process. In a static sense, the fundamental difference between a liquid and a solid is that the solid has elastic resistance against a shearing stress while a liquid does not. Thus, a simple liquid will not typically support a transverse acoustic phonon, or shear wave. Gels have been ...
Schematic representation of the different stages and routes of the sol–gel technology. In this chemical procedure, a "sol" (a colloidal solution) is formed that then gradually evolves towards the formation of a gel-like diphasic system containing both a liquid phase and solid phase whose morphologies range from discrete particles to continuous polymer networks.