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Suppose a function f(x, y, z) = 0, where x, y, and z are functions of each other. Write the total differentials of the variables = + = + Substitute dy into dx = [() + ()] + By using the chain rule one can show the coefficient of dx on the right hand side is equal to one, thus the coefficient of dz must be zero () + = Subtracting the second term and multiplying by its inverse gives the triple ...
In polymer chemistry, ring-opening polymerization (ROP) is a form of chain-growth polymerization in which the terminus of a polymer chain attacks cyclic monomers to form a longer polymer (see figure). The reactive center can be radical, anionic or cationic. Ring-opening of cyclic monomers is often driven by the relief of bond-angle strain.
Cyclic compounds may or may not exhibit aromaticity; benzene is an example of an aromatic cyclic compound, while cyclohexane is non-aromatic. In organic chemistry, the term aromaticity is used to describe a cyclic (ring-shaped), planar (flat) molecule that exhibits unusual stability as compared to other geometric or connective arrangements of ...
Cyclic rearrangements include cycloadditions and, more generally, pericyclic reactions, wherein two or more double bond-containing molecules form a cyclic molecule. An important example of cycloaddition reaction is the Diels–Alder reaction (the so-called [4+2] cycloaddition) between a conjugated diene and a substituted alkene to form a ...
Cyclic tetrapyrroles having four one-carbon bridges include: [1] Porphin, the simplest tetrapyrrole; Porphyrins, including heme, the core of hemoglobin; Chlorins, including those at the core of chlorophyll. Cyclic tetrapyrroles having three one-carbon bridges and one direct bond between the pyrroles include:
In macromolecular chemistry, a catenane (from Latin catena 'chain') is a mechanically interlocked molecular architecture consisting of two or more interlocked macrocycles, i.e. a molecule containing two or more intertwined rings. The interlocked rings cannot be separated without breaking the covalent bonds of the macrocycles.
In chemistry, catenation is the bonding of atoms of the same element into a series, called a chain. [1] A chain or a ring may be open if its ends are not bonded to each other (an open-chain compound), or closed if they are bonded in a ring (a cyclic compound). The words to catenate and catenation reflect the Latin root catena, "chain".
The use of metal hydrides (tin, silicon and mercury hydrides) is common in radical cyclization reactions; the primary limitation of this method is the possibility of reduction of the initially formed radical by H-M. Fragmentation methods avoid this problem by incorporating the chain-transfer reagent into the substrate itself—the active chain ...