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Polymerization by trialkylamines is useful for synthesizing polypeptides of molecular weights of up to $0.5 million, and the polymerization has many characteristics similar to those of living polymerizations. Polymerizations by the most powerful bases, especially organometallic compounds, are not as useful for polymerizations to such high molecular weights because of side reactions [Imanishi, 1984; Kricheldorf, 1989]. NCA polymerization by secondary amines may involve the amine or activated monomer mechanisms or both mechanisms simultaneously. Unhindered secondary amines such as dimethylamine and piperidine react like primary amines, and polymerization occurs by the amine mechanism. Polymerization by slightly hindered amines such as diethylamine, Nmethylbenzylamine, and di-n-propylamine involves a combination of the amine and activated monomer mechanisms. More hindered secondary amines, such as di-n-isopropylamine and dicyclohexylamine, react almost exclusively via the activated monomer mechanism. NCA polymerizations in aprotic solvents such as 1,4-dioxane and THF proceed with acceleration in rate at about 20 30% conversion where the propagating species have grown

The standard MLP model with two layers of adjustable weights, inputs, hidden layer units and output units, and no skip- or intra-layer connections, was described in 2, p. 9. The MLP is an M-estimator as the weights are arrived a t by minimizing an objective function, p. In this section we consider the error function pi with logistic output units. In Section 8.6 (p. 136) we discuss influence curves of the cross-entropy penalty function with the softmax activation function. For a sample of size N and classes, we define pl by

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to the hexamer to dodecamer size [Kim et al., 1979]. Since this is approximately the size at which a-helical conformations become established for many poly(a-amino acids), the autoacceleration is generally attributed to a conformational enhancement of reactivity; the reacting species are bound to the a-helix in a steric arrangement that enhances reactivity. Molecular weight broadening occurs under these conditions. 7-4b Polymerization by Transition Metal Complexes

Various transition metal compounds have been studied to achieve better control of NCA polymerization [Deming, 2000; Deming and Curtin, 2000]. Covalent early transition metal alkoxides, amides, alkyls and other derivatives, such as CpTiCl2 OR (Cp cyclopentadienyl), do not initiate NCA polymerization, contrary to the high reactivity of the corresponding ionic derivatives such as lithium alkoxide (Sec. 7-4a). However, late transition metal complexes, including various nickel and cobalt derivatives, initiate NCA polymerization with the level of control of molecular weight dependent on the structure of the initiator, especially its ligands. Zero-valence Ni and Co initiators such as bpyNi(COD) and [P(CH3 3 4 Co (bpy 2; 20 -bipyridyl, COD 1; 5-cyclooctadiene) are effective initiators for NCA polymerization. The reactions proceed as living polymerizations with good control over molecular weight. Molecular weights as high as 500,000 have been achieved with PDI <1.2. A transition metal complex such as bpyNi(COD), generalized as L2 Ni, reacts with NCA in a complex reaction sequence that generates a propagating species XLV whose active center is a 5-membered amido amidate metallacyclic complex. Propagation involves a nucleophilic attack by the amido nitrogen of the amido amidate at the C-5 carbonyl of NCA. The

7-74

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where t,, is the qth element in the target vector, and mlp,(z,) is the output of the qth output unit for a data vector For an MLP with one output, we have

reaction forms the 10-membered intermediate XLVI. The metallic center of the amido amidate bonds (coordinates) with the carboxylate chain end, and this is largely responsible for molecular weight control and a lack of side reactions. The 10-membered intermediate contracts to the 5-membered amido amidate by proton migration and loss of carbon dioxide. Molecular weight control is also attributed to the stability of the amido amidate.

When polymerization is carried out in DMF the degree of polymerization is given by the monomer : initiator ratio as expected. However, polymerization in solvents less polar than DMF, such as THF, dioxane, toluene, and ethyl acetate, yields polymers with higher molecular weights than indicated by the monomer : initiator ratio [Deming and Curtin, 2000]. Higher molecular weights are also observed by altering the ligands bound to Ni or Co. The higher molecular weights are achieved while maintaining a narrow PDI. Solvent and ligand changes do not alter the propagation process, but do hinder the initiation process. This effectively increases the monomer : initiator ratio by decreasing the concentration of initiator species and results in the increased molecular weights.

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