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Gelation can occur either by physical linking or by chemical crosslinking. While the physical gels involve physical bonds, chemical gelation involves covalent bonds. The first quantitative theories of chemical gelation were formulated in the 1940s by Flory and Stockmayer. Critical percolation theory was successfully applied to gelation in 1970s.
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]
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 ...
Symbolab is an answer engine [1] that provides step-by-step solutions to mathematical problems in a range of subjects. [2] It was originally developed by Israeli start-up company EqsQuest Ltd., under whom it was released for public use in 2011. In 2020, the company was acquired by American educational technology website Course Hero. [3] [4]
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 ...
The step size is =. The same illustration for = The midpoint method converges faster than the Euler method, as .. Numerical methods for ordinary differential equations are methods used to find numerical approximations to the solutions of ordinary differential equations (ODEs).
Functions that maximize or minimize functionals may be found using the Euler–Lagrange equation of the calculus of variations. A simple example of such a problem is to find the curve of shortest length connecting two points. If there are no constraints, the solution is a straight line between the points. However, if the curve is constrained to ...
Genius (also known as the Genius Math Tool) is a free open-source numerical computing environment and programming language, [2] similar in some aspects to MATLAB, GNU Octave, Mathematica and Maple. Genius is aimed at mathematical experimentation rather than computationally intensive tasks. It is also very useful as just a calculator.
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