Constitutional repeating unit, defined

Constitutional repeating unit in a regular macromolecule, a regular oligomer molecule, a regular block, or a regular chain, the configuration of which is defined at least at one site of stereoisomerism in the main chain. 

For the polymer -[-CH(COOR)CH(CH3)-hp, if only the ester-bearing main-chain site in each constitutional repeating unit has defined stereochemistry, the configurational repeating unit is (7) and the corresponding isotactic polymer is (8). 

A unit cell is defined with a molar volume Vref. This reference volume may be selected as the molar volume of the thermoset precursor(s), VTS, or as the molar volume of the constitutive repeating unit of the modifier, VM- R is the gas constant and < )TS and < )M i are the volume fractions of the thermoset precursor(s) and of the modifier i-mer, respectively < )M = 4>M i. 

The CRU (constitutive repeating unit) can be considered as the monomer unit of the network. It has been defined in Chapter 2. 

Polymer is a substance composed of macromolecules, built by covalently joining at least 50 molecular mers, or the Constitutional Repeating Units or CRU. The longest sequence of CRU defines the main chain of a macromolecule. The main chain may be composed of a series of subchains, identified by some chemical of physical characteristic e.g., tactic placement). The main chain may also contain long or short side chains or branches, attached to it at the branch points. A small region in a macromolecule from which at least four chains emanate consti-mtes a crosslinking point. A macromolecule that has only one crosslink is the star macromolecule. 

Macromolecular chains defined in this way may be classified according to the nature of the atoms joined in the main chain, the constitutional repeating units and monomeric units, as well as by the molecular architecture. 

Stereochemical Definitions and Notations. Structure-based nomenclature of regular pol5mers (10) can denote stereochemical featiu-es if the repeating unit used is the configurational base unit, ie, a constitutional repeating unit having one or more sites of defined stereoisomerism in the main chain of a polymer molecule (22). Structure-based names are then derived in the usual fashion. The various stereochemical features that are possible in a polsmer must be defined. 

The term configuration refers to the permanent stereostructure of a polymer. The configuration is defined by the polymerization method, and a polymer preserves its configuration until it reacts chemically. A change in configuration requires the rupture of chemical bonds. Different configurations exist in polymers with stereocentres (tacticity) and double bonds cis and trans forms). A polymer with the constitutional repeating unit -CH2-CHX- exhibits... 

Dendrimers are monodisperse, highly branched and well-defined three-dimensional macrostructures. The pseudospherical shape of a dendrimer arises from its structure, which consists of an internal region (the core) which is connected to repeating units constituting a radial branching pattern (Fig. 1). 

The final stage in the creation of a crystal is to sequentially translate the unit cell and its contents along a, b, c, by distances a, b, c, respectively, many times, to generate a contiguous three-dimensional array of periodically repeated unit cells. The continuous solid so formed constitutes a crystal and exhibits all of its properties. In a sense, this final step of translation of the unit cell contents along a, b, and c is conceptually redundant with the previous definition of the unit cell parameters, which defines the directions and magnitudes of the translations. It is nonetheless necessary to actually carry out the operations in order to generate the physical crystal. 

The Fourier transform assumes that its input constitutes one complete repeat unit of an infinitely repetitive signal. For non-periodic signals, many problems (of which some are detailed in section 7.4) can be avoided by making sure that f(f) starts and ends at the same value, and with the same derivatives. Same ness here is not necessarily a mathematical identity, but is best defined in terms of the required precision. 

This term refers to the number of repeating units that constitute a polymer molecule. We shall use the abbreviation DP for the degree of polymerization defined in this way. The subscript n used on the parentheses in the foregoing structural formulas for polymers represents this DP. The relation between degree of polymerization and molecular weight M of the same macromolecule is given by... 

For mesomorphic structures F(s) is the. Fourier transform of the structure of an individual domain (or several domains if they constitute the repeat unit). In the case of X-rays, scattering structure is defined in terms of electron density, whilst for neutrons it is differences in scattering cross-sections, a nuclear characteristic, which is important. For the basic domain types (solid sphere, cylinder and lamella) the structure factors are rapidly oscillating functions " e.g, for spheres F(s) is a Bessel function of order 3/2 with the first two minima in reciprocal space occurring at s = 4.43 and 7.73). 

Considerations of the intra- and inter-molecular arrangements lead to a spectrum of order/ disorder. At one extreme of this spectrum we have a perfect crystalline structure where both the conformation of individual chain molecules and their mutual packing are exactly defined. The corresponding atoms of the repeating units form a perfect three-dimensional lattice. Needless to say, only polymer chains with a regular chemical structure (with respect to both constitution and configuration) can form a true three-dimensional lattice such polymers are crystallizable. 

A crystal is a given atomic pattern repeated in three dimensions. The unit cell is defined as constituting a basis for the crystal lattice. This basis, which generally is not orthonormal, is defined by the triplet (a,b,c) and the angles between these different vectors are a = (b, c) P = (a, c) y = (a,b). Inside this cell, the position of each atom in the crystal pattern is specified by the vector r. The position of each cell is specified by the vector R = ua -t vb -I- wc. The crystal is completely described by the translations along the cell s three vectors (a,b, c). 

A polymer is defined as a substance consisting of molecules that are characterized by multiple repetitions of one or more species of atoms or groups of atoms. These repeating species of atoms or groups of atoms are designated constitutional units. A regular polymer can be described by a certain sequence of... 

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