Linear macromolecules, structural control

Perhaps the most viable short-term use for dendritic macromolecules lies in their use as novel catalytic systems since it offers the possibility to combine the activity of small molecule catalysts with the isolation benefits of crosslinked polymeric systems. These potential advantages are intimately connected with the ability to control the number and nature of the surface functional groups. Unlike linear or crosslinked polymers where catalytic sites may be buried within the random coil structure, all the catalytic sites can be precisely located at the chain ends, or periphery, of the dendrimer. This maximizes the activity of each individual catalytic site and leads to activities approaching small molecule systems. However the well defined and monodisperse size of dendrimers permits their easy separation by ultrafiltration and leads to the recovery of catalyst-free products. The first examples of such dendrimer catalysts have recently been reported... 

Amino acids link together linearly to form proteins, nucleotides link linearly to form RNA and DNA, and sugars link in a more complicated way to form complex carbohydrates. The specific sequence in which these units link together to form the final polymeric macromolecule is called its primary structure. In a way that is still very ill-understood, the primary structure ultimately controls the macromolecule s three-dimensional structure and thereby largely determines its function. There is therefore great interest in analyzing primary structural information in order to detect similarities and relationships between macromolecules. However, as we shall see later, although similar primary structures imply similar three-dimensional structures, it is possible for three-dimensional structures to resemble each other without any sequence similarity. 

It should be emphasized that for the Markovian copolymers, the knowledge of these structure parameters will suffice for finding the probabilities of any sequences LZ, i.e., for a comprehensive description of the structure of the chains of such copolymers at their given average composition. As for the CD of the Markovian copolymers, for any fraction of Z-mers it is described at Z 1 by the normal Gaussian distribution with covariance matrix, which is controlled along with Z only by the values of structure parameters (Lowry, 1970). The calculation of their dependence on time and on the kinetic parameters of a reaction system enables a complete statistical description of the chemical structure of a Markovian copolymer. It is obvious therewith to which extent a mathematical modeling of the processes of the synthesis of linear copolymers becomes simpler when the sequence of units in their macromolecules is known to obey Markov statistics. 

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