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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 ...
A cycloaddition is a reaction that simultaneously forms at least two new bonds, and in doing so, converts two or more open-chain molecules into rings. [3] The transition states for these reactions typically involve the electrons of the molecules moving in continuous rings, making it a pericyclic reaction .
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".
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 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.
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.
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 ...
Example of a pericycle reaction: the norcaradiene–cyclohexatriene rearrangement. In organic chemistry, a pericyclic reaction is the type of organic reaction wherein the transition state of the molecule has a cyclic geometry, the reaction progresses in a concerted fashion, and the bond orbitals involved in the reaction overlap in a continuous cycle at the transition state.