1
Introduction

Polymers are ubiquitous in our daily lives. Natural polymers such as the DNA, RNA, and proteins have played a major role in the evolution of life itself. Cellulose, hemicelluloses, starch (amylose), and other naturally occurring polymers have been studied thoroughly, modified for useful applications and have been the key components of industrial advancement. Familiar to many is the chronological transition of the belief of these substances as colloids to the concept of "polymers." The "Rise of the Macromolecular Hypothesis" was discussed by Flory [1]. Supporting the Staudinger school of thought were, among others, the X-ray diffraction studies of cellulose by Meyer and Mark [2, 3]. Cellulose is perhaps the first polymer for which oriented X-ray fiber diffraction was recorded [2]. Synthetic polymers have also entered the scene around that time, with the synthesis of polystyrene [4] in 1839.

According to the International Union of Pure and Applied Chemistry (IUPAC) nomenclature [5], the terms polymer and macromolecule do not mean the same thing. A polymer is a substance composed of macromolecules. All macromolecules are not polymers.

1.1 Polymer Tacticity

As a polymer (Figure 1.1) is built up of many small molecular monomer units, the dimer (diad), trimer (triad), tetramer (tetrad), pentamer (pentad), and hexamer refer to two, three, four, five, and six monomers, respectively, linked together. Longer sequences of up to about 50-mers are called "oligomers." However, it is not uncommon in the studies on self-assembly to call such short chains polymers. Although natural or biopolymers such as poly(nucleic acids) (e.g., DNA), proteins and polysaccharides are also long chain molecules, the commonplace notion is that a polymer refers to the synthetic variety. Of these, vinyl polymers such as polyethylene (PE) and polystyrene are popularly known as plastics. The simplest of polymers is PE, with just a sequence of (CH2) units (Figure 1.2). Polymerization of ethylene, vinyl fluoride, vinylidene fluoride, and tetrafluoroethylene lead to PE, poly(vinyl fluoride) (PVF), poly(vinylidene fluoride) (PVF2), and poly(tetrafluoroethylene), respectively. The latter is the well-known Teflon®.

Figure 1.1 Schematics of a monomer, dimer, and a polymer.

Figure 1.2 Chemical structures of polyethylene and analogous fluorinated polymers. The dashed circles highlight the fluorine atoms.

With bulkier substituents, polymers such as polystyrene, poly(methyl methacrylate), and poly(propylene) are obtained (Figure 1.3). Note that in the case of PE, PVF2, and PTFE, the substitution is symmetric, whereas with PVF, polystyrene, PMMA, and polypropylene, it is asymmetric. In the schematics shown in Figures 1.2 and 1.3, the bulkier substituent (R) is shown above the plane of the page. A general rendition is shown in Figure 1.4. In the figure [6], with the skeletal bonds in the all-trans conformation, the configuration with R above the page at the asymmetric carbon is designated as d and as l if it is below. If the substituents on two successive asymmetric carbons are in the same dd configuration, it is known as a "meso" (m) diad.

Figure 1.3 Chemical structures of polystyrene, poly(methyl methacrylate), and polypropylene.

Figure 1.4 (a)-(c) Schematic of the definition of tacticity for asymmetric chains.

(Source: Sundararajan [6]. Reproduced with permission of Springer.)

Perpetuation of such meso sequence would lead to an isotactic chain (Figure 1.4a). If the R groups are up and down the page, that is, dl, it is the racemic (r) diad (Figure 1.4b). The repetition of the racemic diad (dl sequence) would result in a syndiotactic polymer. Random occurrence of m and r results in an atactic polymer. The designation of d and l for the configuration at the asymmetric carbon is arbitrary. It follows the convention developed by Flory [7], which then led to the formulation of statistical weight matrices to calculate the statistical chain conformations. If the chain is rotated through 180° about a vertical axis such that the ends of the chain are reversed, all the d would become l and vice versa. But the chain configuration would remain the same as long as the chain ends are indistinguishable. The ll would define the meso diad. With the diad configurations m and r defined earlier, a triad could have sequences of mm, rr, and mr (or rm). A tetrad could have sequences mmm, mmr, rmr, mrm, rrm, and rrr, of which only two of them would lead to stereoregular isotactic or syndiotactic chains. A pentad could have 10 such sequences, 8 of which will be heterotactic. Determining the distribution of such sequences in vinyl polymer chains that were prepared by various synthetic procedures was an active field, concurrent with advances in the NMR techniques [8-11]. Although synthetic methods for stereoregular polymers have been developed, some of them such as isotactic polystyrene are of academic interest rather than of commercial use. Atactic polystyrene, in the form of, for example, Styrofoam, finds widespread applications. Likewise, PMMA in its atactic form, is used as a substitution for glass in the form of Plexiglass, as well as in microelectronic chips, etc. Studies on highly isotactic or syndiotactic polymers led to the understanding of aspects such as polymer crystallization and chain folding. In the studies of self-assembly of polymers, tacticity was seldom taken into consideration.

Some of the other polymers commonly used in studies of polymer self-assembly are polyesters, polyamides, polyurethanes, and polysiloxanes, the constituent units of which are shown in Figure 1.5. A summary of the synthetic procedures adopted for various types of polymers and their primary characterization properties was given by Sundararajan [6].

Figure 1.5 Schematics of the segments of polyester, polyamide, polyurethane, and polysiloxane.

1.2 Big versus Small

As the small molecule "mono" mer units are joined together to build a "poly" mer, the properties change as the polymer increases in length. For example, ethane has boiling temperature of -89° and melts at -183°C. After growing by a few units, hexadecane melts at 18.5°C. With a further increase in chain length, triacontane [CH3─(CH2)28─CH3] melts at 65°C, and does not boil. High-molecular-weight PE melts at 138°C. While the small molecules could melt and vaporize, polymer molecules melt and degrade rather than vaporizing. Most polymers show a glass-rubber transition (Tg), whereas not all small molecules show a glass transition. Both could crystallize, but polymers should have a regular sequence of monomers (e.g., isotactic or syndiotactic) to be able to crystallize. Those with random sequence remain amorphous. The Tg is an important property of a polymer since it dictates the processing conditions for industrial applications. Small molecules such as D-glucose have a finite number of conformations, for example, the C1 chair form. However, amylose, which is a high-molecular-weight polymer of D-glucose, could have a large number of conformational sequences between contiguous D-glucose units due to rotations about the interunit C1─O─C4 single bonds. The number of accessible conformations without steric overlap determines the "flexibility" of a polymer.

1.3 Entanglement

When a small molecule is dissolved in a solvent medium (lattice model) as shown pictorially in Figure 1.6a, both molecules can move and exchange lattice points just by diffusion and thermal motion. However, when a polymer is placed in a solvent (Figure 1.6b), coordinated movement of the monomer units is necessary for the chain to diffuse. This results in loss of entropy of mixing. This would increase the viscosity of the solution compared to the small molecule/solvent mixture. One of the most important properties of a polymer is the "entanglement" between its segments. A small molecule cannot entangle. As the polymer chain grows in length, due to coiling in solution or the melt, entanglement would set in. Most text books would mention a bowl of spaghetti as an example of entangled polymer chains. The polymer must be of a certain minimum length for entanglement to occur. For a bowl of cooked spaghetti to be an entangled stock, the length of the dry noodle should be about one foot. The average length of commercially sold dry spaghetti is 12-14 in., which assures the entanglement upon cooking. The critical molecular weight Mc for entanglement for polystyrene is about 37 000, while it is only about 5000 g/mol for polycarbonate [12]. Conformational analysis showed that polycarbonate chain can adopt flat helical as well as extended chain shapes with equal probability [13]. Thus, a low molecular weight is sufficient for entanglements to occur in the case of polycarbonate. Mc varies depending on the polymer structure and conformation. Another parameter is the entanglement molecular weight, Me, which corresponds to the average molecular weight...