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The regularity in the con gurations of successive stereocenters determines the overall order (tacticity) of the polymer chain. If the R groups on successive stereocenters are randomly distributed on the two sides of the planar zigzag polymer chain, the polymer does not have order and is termed atactic. Two types of ordered or tactic structures or placements can occur: isotactic and syndiotactic. An isotactic structure occurs when the stereocenter in each repeating unit in the polymer chain has the same con guration. All the R groups will be located on one side of the plane of the carbon carbon polymer chain either all above or all below the plane of the chain. A syndiotactic polymer structure occurs when the con gurations of the stereocenters alternate from one repeating unit to the next with the R groups located alternately on the opposite sides of the plane of the polymer chain. These different polymer structures are shown in Fig. 8-1. The various polymer structures are described by three different pictorial representations. The ones on the far left side of Fig. 8-1 show the polymer chain in the plane of this page with the H and R groups above (triangular bonds) and below (dotted bonds) that plane. The representations in the middle are the corresponding Fischer projections. Verticle lines in the Fischer projections correspond to bonds projecting behind the plane of this page; horizontal lines represent bonds projecting in front of the plane. This is the usual convention for Fischer projections [Bovey, 1982]. The con guration at each carbon atom in the polymer chain is drawn in the Fischer projection by imagining the rotation of each carbon carbon bond in the polymer chain into an eclipsed conformations as opposed to the staggered conformation that actually exists. The

which is unbounded as 2; * 0. However, the cross-entropy penalty function is usually paired with the the softmax activation function

representations on the far right side of Fig. 8-1, recommended by IUPAC [1981], are obtained by rotating the previous Fischer projections 90 counterclockwise. The resulting Fischer projections do have the advantage of showing the polymer chain going in the same direction as the far-left representations. Their disadvantage is that one must always keep in mind that the usual Fischer convention for horizontal (forward) and vetical (back) bonds is reversed. These rotated Fischer projections will be used in the remainder of this chapter. The Fischer projections show that isotactic placement corresponds to meso or m-placement for a pair of consecutive stereocenters. Syndiotactic placement corresponds to racemo (for racemic) or r-placement for a pair of consecutive stereocenters. The con gurational

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repeating unit is de ned as the smallest set of con gurational base units that describe the con gurational repetition in the polymer For the isotactic polymer from a monosubstituted ethylene, the con gurational repeating unit and con gurational base unit are the same For the syndiotactic polymer, the con gurational repeating unit is a sequence of two con gurational base units, an R unit followed by an S unit or vice versa Polymerizations that yield tactic structures (either isotactic or syndiotactic) are termed stereoselective polymerizations The reader is cautioned that most of the literature uses the term stereospeci c polymerization, not stereoselective polymerization However, the correct term is stereoselective polymerization since a reaction is termed stereoselective if it results in the preferential formation of one stereoisomer over another [IUPAC, 1996] This is what occurs in the polymerization.

A reaction is stereospeci c if starting materials differing only in their con guration are converted into stereoisomeric products This is not what occurs in the polymerization since the starting material does not exist in different con gurations (A stereospeci c process is necessarily stereoselective but not all stereoselective processes are stereospeci c) Stereoselective polymerizations yielding isotactic and syndiotactic polymers are termed isoselective and syndioselective polymerizations, respectively The polymer structures are termed stereoregular polymers The terms isotactic and syndiotactic are placed before the name of a polymer to indicate the respective tactic structures, such as isotactic polypropene and syndiotactic polypropene The absence of these terms denotes the atactic structure; polypropene means atactic polypropene The pre xes it- and st- together with the formula of the polymer, have been suggested for the same purpose: it-[CH2 CH(CH3 )]n and st-[CH2 CH(CH3 )]n [IUPAC, 1966].

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Figure 8.6 The five curves for an MLP of size 2.1.1. T h e weight vector is = = 1,wo = 0 , w l = 1,wz = -1) * 2. The factor of 2 is t o make the shapes of the curves more pronounced. Note that the function lc,u, redescends to a constant (not 0) in one direction. Note also the unboundedness of Q W , and along paths parallel t o the decision boundary while $J,.,~ is constant along these paths.

Both isotactic and syndiotactic polypropenes are achiral as a result of a series of mirror planes (ie, planes of symmetry) perpendicular to the polymer chain axis Neither exhibits optical activity 8-1b 8-1b-1 Disubstituted Ethylenes 1,1-Disubstituted Ethylenes.

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