Step polymerization branching

Keywords. Statistical chemistry of polymers, Chain and step polymerizations, Linear and branched polymers... 

Alternatively, the one-step polymerization of branched monomers results in what is called a hyperbranched polymer [53] possessing a higher degree of polydispersity and lower degree of branching compared to the analogous dendrimer. 

Finally, hyperbranched polymer layers by surface-initiated step polymerization was intensively studied mainly by Bergbreiter et al. and Crooks et al. Patterned surfaces were prepared on the micrometer scale and a variety of functional groups introduced interesting optical, electrochemical, biological, and mechanical properties into the films. For a recent review on surface-initiated step polymerization resulting in branched polymer layers see [352]. 

Hyper-branched polymers are prepared in a single-step polymerization from ABX monomers. Thus, a perfectly branched structure is present in dendrimers, whereas irregular branching is present in hyper-branched polymers. Aluminum alkoxide-based initiators or tin-based catalysts have been successfully used for the preparation of, hyper-branched [160-162, 166-168], dendrimer-like star polymers [160], and star-shaped polymers. The first and second generations of the benzyl ester of 2,2-bis(hydroxymethyl)propionic acid (bis-MPA) are effective initiators for the ROP of lactones (e-CL) in the presence of Sn(Oct)2. The... 

Figure 1.18. Branching during step polymerization, (a) Addition of a trifunctional agent (e.g. a triol, BBB) to a self-condensing difunctional system (e.g. a hydroxy acid, BA), (b) Hyperbranching from a system AB2. In both cases A may react only with B.

Thus a step-polymerization system synthesized from an AB2 monomer should be highly branched but never reach gelation even at full conversion of the available functional groups. This is the basis of the formation of hyperbranched polymers by step-growth polymerization (Jikei and Kakimoto, 2001) and a reaction scheme for AB2 hyperbranching is shown in Scheme 1.11. 

A special step polymerization involves an acyclic diene methathesis polymerization, ADMET [12]. A diene, CH2=CH(-CH2) -CH=CH2, sets up a condensation equilibrium, evolving ethylene in the presence of an ADMET catalyst and allows polymerization. Substituted dienes can produce precisely branched polymers [13]. 

Step polymerization reactions, where little molecules such as epoxies (oxiranes) react with amines, or isocyanates react with polyols with functionality greater than two to form short, branched chains, eventually condensing it into epoxies or polyurethanes, respectively. Schematically... 

The polymerization model used by Gerrens is very simple. A more complete description of the polymerization process would include steps like thermal initiation chain transfer to monomer, solvent and polymer diffusion control of propagation lass effect) and of termination (Trommsdorff effect). As second steps in a series of consecutive reactions the chain transfer, or branching, steps, are very sensitive to mixing effects. They are very important for the polymer properties. 

According to the transformation procedure, the population balance equations in terms of discrete variables (chain length, number of branch points) are transformed into a set of equations in z. The transformed set is solved and subsequently inverted to the original discrete variable domain. This process makes use of some interesting properties of certain mathematical expressions as transformed into the z-domain. Transformations and inversions are tabulated in textbooks [3). As an example we take linear AB step polymerization in a batch reactor with equal initial end group concentration Po ... 

We will illustrate this procedure on a simple linear step-polymerization (/ = 2) to obtain the CLD and on single metallocene ethylene polymerization to find the 2D distribution of chain lengths and numbers of branch points. 

Here the diol and diacid monomers each have two identical functional groups (i.e. they are dimers). The product has two different functional groups, but as it is still difunctional it can be involved in further steps of the polymerization. Step polymerizations involving species with functionality greater than two often lead to the formation of networks of highly branched chains. 

The product of their reaction is an ester which possesses one carboxylic acid end-group and one hydroxyl end-group (i.e. it also is difunctional). This dimer, therefore, can react with other molecules of terephthalic acid, ethlyene glycol or dimer leading to the formation of difunctional trimers or difunctional tetramer. Growth of linear polymer chains then proceeds via further condensation reactions in the manner indicated for step polymerization in Table 2.1. Hence linear step polymerizations involve reactions of difunctional monomers. If a trifunctional monomer were included, reaction at each of the three functional groups would lead initially to the formation of a branched polymer but ultimately to the formation of a network. For example, if terephthalic acid were reacted... 

In the early stages of such reactions the polymer has a branched structure and, consequently, increases in molar mass much more rapidly with the extent of reaction than for a linear step polymerization. As the reaction proceeds, further branching reactions lead ultimately to the formation of complex network structures which have properties that are quite different from those of the corresponding linear polymer. For example, reaction of a dicarboxylic acid R(COOH)2 with a triol R (OH)3 would lead to structures of the type... 

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