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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 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 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 ...
In a chain reaction, positive feedback leads to a self-amplifying chain of events. Chain reactions are one way that systems which are not in thermodynamic equilibrium can release energy or increase entropy in order to reach a state of higher entropy. For example, a system may not be able to reach a lower energy state by releasing energy into ...
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".
In stereochemistry, mutarotation is the change in optical rotation of a chiral material in a solution due to a change in proportion of the two constituent anomers (i.e. the interconversion of their respective stereocenters) until equilibrium is reached. Cyclic sugars show mutarotation as α and β anomeric forms interconvert. [1]
Examples include high impact applications of the Beckmann rearrangement (for introduction of nitrogen into codeine) [14] and the Baeyer-Villiger oxidation (introduction of oxygen to cage-annulated ethers) [15] in synthesis. Both occur with the expulsion of a leaving group as the alkyl group migrates onto the exocyclic heteroatom, which is ...