F. Rodriguez
School of Chemical Engineering Cornell University Ithaca, New York 14850
I
Simple Models for Polymer Stereochemistry
Despite the advances made in formal notation for stercoisomers and conformational variants, the student encountering these in organic or polymer chemistry for the first time has quite an energy harrier of a sort to overcome. Once he has accepted the principles and the formalisms for expressing them, he can start to absorb the quantitative differences that arise from arrangements of atoms in space by studying the two-dimensional representations. Some text puhlishers have experimented with adding colors in illustrations or with printing "three dimensional" pairs of drawings with special means of viewing as in a stereoscope. Many schools have recommended the purchase by the student of atomic-model kits. The drawbacks to this last method are the expense involved and the limited number of structures that the individual can accumulate. Models made by drawing on the folding transparent plastic sheets are proposed here as being an alternative which is especially attractive for illustrating polymer structures. Configurations and Conformations
The structure of a covalently-bound chemical compound is a description of the way in which each atom is linked to the other atoms. If the compound contains an asymmetric carbon, one with four different substituent groups, there will exist two configurationshaving the same structure but differing in the order of connection to the suhstituent groups. The two configurations cannot be superimposed by rotations of the asymmetric carbon about any axis. I n polymer chemistry configurations have always been important in naturally occur-
ring materials. I t is only in the last decade that stereoisomeric polymers made by coordination-complex catalyst systems have assumed theoretical as well as commercial importance. The tacticity of a carbonchain polymer can be defined in terms of the orientation of a substituent occurring a t regular intervals on a planar, zig-zag, extended chain. Polypropylene (-CHpC(CH,)H-) can be pictured as an extended chain of carbons bearing a methyl group on every other chain atom (Fig. la). Because of the tetrahedral hond structure of carbon, the methyl group must choose one side or the other of the main chain. The isotactic configuration bears all the methyl groups on one side. The syndiotactic configuration has groups that alternate regularly from one side of the chain to the other. The atactic configuration has groups on both sides in random sequence. The student can look a t such a diagram and regurgitate the definitions; homever, until he has carried out all allowable rotations about single bonds he may remain skeptical about the non-interchangeability of such isomers. A second source of stereoisomerism stems from the lack of rotation about double bonds. In polymers the cis and trans isomers are differentiated by the manner of bonding to the main chain (Fig. 2 ) . 1,4-Poly butadiene
lsotactic Polypropylene
trans
Figure 2. Stereoiromerirm in ore shown.
Figure 1. a, lratoctis polypropylene. The lorge spheres represent the pendont methyl groups. b, The H.31 helix with hydrogens omined. c, The pendant methyl gmupr or o helix.
1 ,A-polybutadiene.
Only the chain bonds
While a two-dimensional representation is adequate for the douhle-bonded carbons and their four substituents, there remains the problem of illustrating the permanence of this arrangement when it occurs in a polymer along with many single bonds. Since conformations involve only rotations about single bonds, an infinite number arc possible for any compound with at least one such hond. The only restrictions are that bond distance and bond angle remain constant. In organic chemistry, the subject often is introduced by considering the boat and chair forms of cyclohexane. I n polymer chemistry, the arrangement of a polymer in a crystal lattice is of profound imporVolume 45, Number 8, August 1968
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tance. The plnuar, zig-zag form (Fig. 1) is assumed by some polymers in the crystal. Polyethylene, polyhutadieues, both cis and trans, poly(viny1 alcohol) and poly(ethy1ene terephthalate) are some common examples. Helices are typical of crystalline polymers bearing bulky foliage which does not pack readily when confined to the planar form. Helix-formers include polypropylene, other poly(a-olefins), polystyrene, and poly(methy1 methacrylate), a11 of the isotactic or syndiotactic variety.' A helix can be characterized by an integer with a subscript referring to the number of monomer units per number of complete turns, respectively. The H , ~ Ihelix assumed by isotactic polypropylene is illustrated in Figure l b . Its formation from the planar, zig-zag conformation can be imagined as involving wrapping the polymer about a triangular mandrel so that every other hond lies on an edge of the mandrel, and the bonds in between lie on faces. An end view shows that the methyl substituents, still in the isotactic configuration, now form a second triangle which contains the triangle formed by the chain carbons. An attempt to show this as a righthanded helix (Fig. lc) is not very satisfying. The H,21 helix of syndiotactic polypropylene (Fig. 3) involves wrapping Syndiotactic Polypropylene
A
Visualization Techniques
Most of the less expensive atomic model kits available to the student are of the ball-and-stick variety. Foamed plastic or rubber halls can be connected by wooden rods or dowel screws (Edmund Scientific, Barrington, N. J.). Each bond angle must he decided individually and the number of rotations is limited because eventually a hole is worn which no longer fits the dowel tightly. In another kit (Central Scientific, Chicago, Ill.) the atoms have holes which specify the angles. However, the connectors are springs which do not allow free rotation. The "Framework Rlolecular Rlodels" (Prentice-Hall, Englewood Cliffs, N. J.) are superior in this respect. I n any case, when one wishes to compare the several configurations of a polymer, the total number of monomer units available a t a reasonable price is limited to a dozen or so depending on the complexity of the repeating unit. Paper-folding has been commercialized for the construction of the DNA double-helix (Burgess Publishing Co., Minneapolis, Rlinn.). Although the model shows the overall arrangement in three dimensions, it does not illustrate the role of free rotation in arriving a t the preferred conformation. Lightweight, transparent plastic sheeting has numerous advantages for modelmaking. Cellulose acetate and poly(ethy1ene terephthalate), "i\lylar" sheet about 0.005-in. thick have been found suitable. These are stiff enough to maintail1 planarity where desired and can be creased to give a rather constant angle when the bond lcngths are on the order of 1 in. or so. The structures can be put on these sheets with some felt-tipped pens, crayons, or acetatebased drawing inks. An even faster method is to reproduce a drawing in an office copying machine such as the Xerox using the film supplied for making transparencies for the overhead projector. If color is desired, this can be added to the transparencies also by the felt-tipped pens or crayons. The Decorated Mandrel
Figure
3.
The H.21 helix of ryndiotactis polypropylene.
the polymer around a square mandrel with all bonds on faces. For a non-integral helix such as poly(y-methylL-glutamate), H,1S6, the principle is the same but a simple mandrel cannot be used. In many polypeptides, rotation is assumed to be free about all honds except that between (CO) and (NH).
Polypeptide Repeat Strocture
Otherwise, the major criteria for selection of a conformation involves the possibility of attraction between two atoms (hydrogen-bonding, (-C=O. .H-N-), in polypeptides) or steric hindrance between adjacent, bulky groups. 'See, for example, MILLER,M. L.. "The Structure of Polymen," Reinhold, New Yark, 1966, pp. 503-,507.
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The simplest model for a helix that has an eveu number of monomer units per repeat period is a mandrel on which is drawn the skeleton of the polymer. By itself, such a model shows only the chain atoms and bonds. Subsequcntly, one can supply foliage to the mandrel in order to display all the atoms. Example 1. The H,3, helix. A triangular prism with edges A , B, and C (Fig. lb) is folded from acetate sheeting. Each side of the triangle is equal to the bond length times sin(7O032') or 0.9428 for a carbon chain. One proceeds to draw with a felt-tip pen a hond on edge A , the next bond on the face AB making an angle of 10Q02S'with the previous bond in the plaue of that face. The next honds are, successively, on the edge B, the face BC, the edge C , and the face C A as indicated. Example 2. The H,3, helix of isotactic polypropylene. We can add foliage to the last example. To preserve the tetrahedral structure a t each carbon, it is necessary to slit the mandrel about a fourth of the way down in a plane which bisects the chain angle and which is perpendicular to the face in which one of the bonds crosses (Fig. 4). Careful attention must be paid as one rotate3 the model and proceeds from bond to bond to he sure that the pendant methyl group always is on one side.
In the case of poly(r-methyl-L-glutamate) a righthanded spiral results. Poly (P-benzyl-L-aspartate)gives a left-handed spiral. However, if it is substituted by a r~itrogroup in the benzene ring, it gives a right-handed spiral. Example 4. The H,2, helix of syndiotactic polypropylene. The helix of Example 3 is wrapped around a metal or wooden dowel. Now each triangle is slit bisecting the angle a t the carbon atom, and a sheet with a pair of atoms drawn on it is inserted with its plane perpendicular to that of the triangle. For the syndiotactic polymer sight along the hond from the same end each time putting the first methyl group on your right, the next one on your right, and so on. The H , ~ helix I can he made from flat ribbon also by folding every other hond in the same direction. Folded Chain with Integral Substituents
Figure 4.
Insertion of pendmtgroupr into slots in mandrel.
Naked Folded Chain
I n the decorated mandrel, oue must draw in angles on the three-dimensional model. There is a pedagogic advantage in starting a conformation from a planar, zig-zag position. When we start with a ribbon containing the chain atoms and bonds, and restrict our operation to folding on bond lines, we know that we cannot distort any bond from the original angle. Example 5. The H,2, helix. On a ribbon with a width of (hond length times cos 54'44', 0.5774) are drawn a succession of bond joined a t a constant angle of 109"2S1. Now one creases (to an angle of GO0 between planes) along every hond starting a t one end and changing direction of fold each time (Fig. 5). An end view should give the square cross section of Figure 3. Passing a rod through the holes between bonds stiffens the model. Every fifth bond is in the same plane as, and parallel to, the first. I t is instructive to start with two identical flat ribbons and to start the folding operation on each one in an opposite direction. A right- and a left-handed spiral are generated which are not interconvertible by changiug end for end. 111 the case of syndiotactic polypropylene, there is no energetic advantage in a right-handed versus a left-handed conformation. Hence, the two are equally probable and are formed in equal amounts with no net optical rotation. I n the case of polypeptides, the polymer syuthesis preserved the D or L configuration of the repeat unit.
Figure 5. Formation of H.2, helix orcvnd o dowel b y folding a Rot ribbon. Holes opposite the carbon atoms flt on the dowel.
The previous methods allow one to observe the orientation of suhstituent groups only by slitting and adding the groups on a separate piece of film. Careful folding of a flat ribbon with the groups already drawn on yields a much better picture and is highly recommended. Configurations are nicely presented also. Zxample 5. Isotactic polypropylene. Trace the planar, zig-zag pattern of Figure G on a sheet of transparent plastic film. Now cut around each group as
Figure 6. Polypropylene ribbon with all bond ongles = 109'28'. along thin liner and fold on chain-bond liner.
Cut
indicated. For the substituent groups thc center cut should separate the two and penetrate to the point where the two bonds iutersect. The cuts on either side should go down to the bond itself so that folds can he made on the bond lines without moving substituents. Each pair of substituent groups now can be bent to make a tetrahedral set of bonds a t each carbon. The isotactic polymer has all the large methyl groups on one side of the chain. The syndiotactic and atactic configurations can he made easily also. Example 6. The H,3, helix of isotactic polypropylene. Make a triangular mandrel as in Example 1. Now instead of drawing on the bonds, merely fold the planar, zig-zag ribbon of Example 5 on every other hond and wrap it around the mandrel. Cellophane tape can be used to hold it down here and there. The H,4, helix of poly(viny1 cyclohexaue) could be made by wrapping a similar ribbon about a square mandrel. For the H,Z1helix of syndiotactic polypropylene repeat Example 4 with the pattern of Figure 6. Example 7. The a-helix of some poly-a-amiuo acids (H, I&). Start with the planar, zig-zag represenVolume 45, Number
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Figure 7. Poly-ar-omino m i d ribbon with oxygen I01 and nitrogen Fold only on choin-bond lines Wlot connect to the orymmetric carbon.
(A).
tation (Fig. 7). Use a t least S monomer units (amino acid residues). Fold to about 60' (the "dihedral" angle) on each of the bonds coming to the substituted carbon, first down, then up and so on. If you bold one end of the chain horizontally before you so that the sequeuce from left to right is N-CRH-CO-, the N-H points up, and the bond connecting N a n d CRH
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is folded away from you, you should have generated a right-handed helix in which all the carbon-oxygen bonds point down, and the nitrogen bonds point up. If the flaps are folded inward on the dotted lines, a dowel passed through the holes marked will position the residues so that the carboxyl group of one residue is about a bond length away from the fourth amide hydrogen downstream. Another way of making a rigid model is to cut along the dotted lines and to wrap the helix around a tube. The transparent tube can be made by rolling up a sheet of cellulose acetate about 0.003 in. thick. Cellophane tape holds the residues on the surface of the tube. Example 8. Cyclohexane. It is instructive for the student to make the boat and chair conformations of cyclohexane from a 7 carbon sequence of planar, zig-zag ribbon. Each structure is obtained by folding on bond lines thus preserving bond distances and angles. The seventh carbon is superimposed on the first to give the 6-membered ring in perspective. Geometric isomerism becomes apparent if the substituent groups are differentiated. The same kind of model can be used for the monosaccharides.
