Linear step polymerization

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

Step polymerizations of linear chains can involve either two different bifunctional monomers in which each monomer possesses only one type of functional group (commonly represented by X-X or Y-Y), or a single monomer containing both types of functional groups (common representation X-Y). However, whatever the monomer type, a linear polymer molecule contains, on average, one functional group of each species per chain (molecule). 

Chemical Crosslinking. Only linear polymers are produced from bifunctional monomers. The reaction system must include a polyfunctional monomer, i.e., a monomer containing 3 or more functional groups per molecule, in order to produce a crosslinked polymer. However, the polyfunctional reactant and/or reaction conditions must be chosen such that crosslinking does not occur during polymerization but is delayed until the fabrication step. This objective is met differently depending on whether the synthesis involves a chain or step polymerization. In the typical... 

A comparison of the covalent connectivity associated with each of these architecture classes (Figure 1.7) reveals that the number of covalent bonds formed per step for linear and branched topology is a multiple (n = degree of polymerization) related to the monomer/initiator ratios. In contrast, ideal dendritic (Class IV) propagation involves the formation of an exponential number of covalent bonds per reaction step (also termed G = generation), as well as amplification of both mass (i.e. number of branch cells/G) and terminal groups, (Z) per generation (G). 

The production of linear polymers by the step polymerization of polyfunctional monomers is sometimes complicated by the competitive occurrence of cyclization reactions. Ring formation is a possibility in the polymerizations of both the A—B and A—A plus B—B types. 

Reactants of the A—A (or B—B) type are not likely to undergo direct cyclization instead of linear polymerization. A groups do not react with each other and B groups do not react with each other under the conditions of step polymerization. Thus there is usually no possibility of anhydride formation from reaction of the carboxyl groups of a diacid reactant under the reaction conditions of a polyesterification. Similarly, cyclization does not occur between hydroxyl groups of a diol, amine groups of a diamine, isocyanate groups of a diisocyanate, and so on. 

Kricheldorf and coworkers [2001a,b,c] have stressed that step polymerizations can proceed either with kinetic control or thermodynamic control. Polymerizations under thermodynamic control proceed with an equilibrium between cyclic and linear products. Polymerizations under kinetic control proceed without an equilibrium between cyclic and linear products. 

Consider the situation where one polymer molecule is produced from each kinetic chain. This is the case for termination by disproportionation or chain transfer or a combination of the two, but without combination. The molecular weight distributions are derived in this case in exactly the same manner as for linear step polymerization (Sec. 2-7). Equations 2-86, 2-88, 2-89, 2-27, 2-96, and 2-97 describe the number-fraction, number, and weight-fraction... 

Recall the discussion in Sec. 2-3 concerning the competition between linear polymerization and cyclization in step polymerizations. Cyclization is not competitive with linear polymerization for ring sizes greater than 7 atoms. Further, even for most of the reactants, which would yield rings of 5, 6, or 7 atoms if they cyclized, linear polymerization can be made to predominate because of the interconvertibility of the cyclic and linear structures. The difference in behavior between chain and step polymerizations arises because the cyclic structures in chain polymerization do not depropagate under the reaction conditions that is, the cyclic structure does not interconvert with the linear structure. 

Many reactions familiar to organic chemists may be utilized to carry out step polymerizations. Some examples are given in Table 2.2 for polycondensation and in Table 2.3 for polyaddition reactions. These reactions can proceed reversibly or irreversibly. Those involving carbonyls are the most commonly employed for the synthesis of a large number of commercial linear polymers. Chemistries used for polymer network synthesis will be presented in a different way, based on the type of polymer formed (Tables 2.2 and 2.3). Several different conditions may be chosen for the polymerization in solution, in a dispersed phase, or in bulk. For thermosetting polymers the last is generally preferred. 

Fig. 13.42 Simulation results of the RIM process involving a linear step polymerization T0 = Tw = 60°C, kf— 0.5L/moles, t(lii = 2.4 s. (a) Conversion contours at the time of fill, (h) Temperature contours at the time of fill. [Reprinted hy permission from J. D. Domine and C. G. Gogos, Computer Simulations of Injection Molding of a Reactive Linear Condensation Polymer, paper presented at the Society of Plastics Engineers, 34th Armu. Tech. Conf, Atlantic City, NJ, 1976. (Also published in the Polym. Eng. Sci., 20, 847-858 (1980) volume honoring Prof. B. Maxwell).]...

J. D. Domine, Computer Simulation of the Injection Molding of a Liquid Undergoing a Linear Step Polymerization, Ph.D. Thesis, Department of Chemical Engineering, Stevens Institute of Technology, Hoboken, NJ, 1976. 

Because of the one-step polymerization procedure, hyperbranched polymers often contain not only D and T but also L repeating units. This can be expressed by DB, which is an important structural parameter of hyperbranched polymers. DB is estimated as the sum of the D and T units divided by the sum of all the three structural units, that is, D, T and L [41]. By definition, a linear polymer has no dendritic units and its DB is zero, while a perfect dendrimer has no linear units and its DB is thus unity. Frey has pointed out that DB statistically approaches 0.5 in the case of polymerization of AB2 monomers, provided that all the functional groups possess the same reactivity [42]. The structures of the hb-PYs could be analyzed by spectroscopic methods such as NMR and FTIR. The DB value of the phosphorous-containing polymer hb-F21, for example, was estimated to be 53% from its 31P NMR chemical shifts (Chart 1). 

Acrylates. Acrylamines are widely used to create polymeric coatings on fused silica capillaries in a two- to three-step process. Linear polyacrylamide is then grafted to the appropriately prepared surface. The problem of acrylamide stability can be solved by using a monomer that is inherently more hydrolytically stable. 

Polyethylene modeling using ADMET step-polymerization began with the production of strictly linear polyethylene by polymerization of 1,9-decadiene followed by exhaustive hydrogenation (Scheme 3) [68,69]. 

Why would this lead to a narrower molecular weight distribution Look at it this way let s imagine that the reaction proceeds in two separate steps first linear chains are polymerized almost to complete conversion, so that the polydispersity is close to 2 (Figure 5-27). 

In Section 1.2 it was noted that the linear homopolymer was only one possible chain conformation and it is appropriate to examine the types of different molecular architecmre that have been demonstrated to be formed through simple step-polymerization reactions. 

Equations (5.70) and (5.73) give the differential number and weight distribution functions, respectively, for linear step polymerizations at the extent of reaction p. These distributions are usually referred to as the most probable or Flory distributions. 

Molecular weight distribution in the above type of multichain step polymerization would be expected to be much narrower than for a linear polymerization. Consider, for example, polymerization of bifunctional monomer A—B with a small proportion of an /-functional substance Ay leading to... 

The simplest step-growth linear polymer is of the AB type. Typical examples of AB polymerization are the step polymerization of HORCOOH and H2NRCOOH. For example, the polymer from HORCOOH is... 

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