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In polymer chemistry, branching is the regular or irregular attachment of side chains to a polymer's backbone chain. It occurs by the replacement of a substituent (e.g. a hydrogen atom ) on a monomer subunit by another covalently-bonded chain of that polymer; or, in the case of a graft copolymer , by a chain of another type.
Polymers prior (no gel) and after crosslinking (gel). In polymer chemistry, gelation (gel transition) is the formation of a gel from a system with polymers. [1] [2] Branched polymers can form links between the chains, which lead to progressively larger polymers.
In a diagnostic key, the branching structure of the key should not be mistaken for a phylogenetic or cladistic branching pattern. All single-access keys form a decision tree (or graph if reticulation exists), and thus all such keys have a branching structure. "Branching key" may therefore occasionally be used as a synonym for single-access key.
Diagram showing the Strahler stream order In mathematics , the Strahler number or Horton–Strahler number of a mathematical tree is a numerical measure of its branching complexity. These numbers were first developed in hydrology , as a way of measuring the complexity of rivers and streams, by Robert E. Horton ( 1945 ) and Arthur Newell ...
A simple branched pathway has one key property related to the conservation of mass. In general, the rate of change of the branch species based on the above figure is given by: = (+) At steady-state the rate of change of is zero. This gives rise to a steady-state constraint among the branch reaction rates:
Edward Hitchcock's fold-out paleontological chart in his 1840 Elementary Geology. Although tree-like diagrams have long been used to organise knowledge, and although branching diagrams known as claves ("keys") were omnipresent in eighteenth-century natural history, it appears that the earliest tree diagram of natural order was the 1801 "Arbre botanique" (Botanical Tree) of the French ...
This Halloween 2024, use these printable pumpkin stencils and free, easy carving patterns for the scariest, silliest, most unique, and cutest jack-o’-lanterns. These 55 Printable Pumpkin ...
The idea of a tree of life arose from ancient notions of a ladder-like progression from lower into higher forms of life (such as in the Great Chain of Being).Early representations of "branching" phylogenetic trees include a "paleontological chart" showing the geological relationships among plants and animals in the book Elementary Geology, by Edward Hitchcock (first edition: 1840).