Random graph theory of gelation

<p>Random graph theory of gelation is a mathematical theory for <a href="/facts/Sol%25E2%2580%2593gel_process/u4vtn2uj">sol–gel processes</a>. The theory is a collection of results that generalise the <a href="/facts/Flory%25E2%2580%2593Stockmayer_theory/Kphp3Ymr">Flory–Stockmayer theory</a>, and allow identification of the <a href="/facts/Gel_point/DTUA9wtI">gel point</a>, gel fraction, size distribution of polymers, <a href="/facts/Molar_mass_distribution/Bh3Fsd4r">molar mass distribution</a> and other characteristics for a set of many polymerising monomers carrying arbitrary numbers and types of reactive <a href="/facts/Functional_groups/GXkSPsjM">functional groups</a>. 
</p><p>The theory builds upon the notion of the <a href="/facts/Random_graph/gfQhq1Sz">random graph</a>, introduced by mathematicians <a href="/facts/Paul_Erd%25C5%2591s/63LoUTe1">Paul Erdős</a> and <a href="/facts/Alfr%25C3%25A9d_R%25C3%25A9nyi/q7Dx7fgB">Alfréd Rényi</a>, and independently by <a href="/facts/Edgar_Gilbert/r6g0Tlun">Edgar Gilbert</a> in the late 1950s, as well as on the generalisation of this concept known as the random graph with a fixed degree sequence. The theory has been originally developed to explain <a href="/facts/Step-growth_polymerisation/MHMGpt0g">step-growth polymerisation</a>, and adaptations to other types of polymerisation now exist. Along with providing theoretical results the theory is also constructive. It indicates that the graph-like structures resulting from polymerisation can be sampled with an algorithm using the <a href="/facts/Configuration_model/9MolJJeV">configuration model</a>, which makes these structures available for further examination with computer experiments. 
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Random graph theory of gelation open-in-new

Random graph theory of gelation