The work by Staudinger prepared the ground for physics to intrude into the
“Polymer World” — it had become possible to explain physical properties of various polymers by taking into account the chain structure of their con-stituent molecules. But first, polymer scientists had to discern the specific shapes, or conformations, of molecular chains for di↵erent polymers.
For example, let’s consider a polymer molecule diluted in some ordinary solvent (say, in water). What kind of shape does the molecule’s chain have?
a b
Fig. 2.2 (a) Rectilinear conformation of a polymer chain; (b) conformation of an entan-gled coil.
Judging from the linear structure of the polymer chains (Figure 2.1), at first glance it seems reasonable to assume that the chain looks vaguely like a straight line (Figure 2.2 a). But this is not true; as a matter of fact, it gets tangled up into a random loose three-dimensional coil (Figure 2.2 b). This is simply a result of the chain’s flexibility. Let’s emphasize: it is not the result of any particular specific chemical structure, it is the general physical consequence of the linear chain structure of the molecules.
Generally speaking, the idea of flexible polymer chains may appear rather surprising. At school one is taught that the atoms in a molecule are joined together by covalent bonds in some specific order. Therefore their positions in space with respect to each other must be fixed too — just following from the chemical formula for the structure. And if one looks at a small strand of the chain only, this argument will be quite correct.
For example, Figure 2.3 shows the spatial structure of a little segment of a polyethylene macromolecule. One can see that the main chain is a sequence of carbon atoms connected with covalent bonds, and that each carbon atom is also joined to two hydrogen atoms. So in complete agree-ment with the naive chemical concept, the atoms of each monomer unit as well as the atoms of neighboring units are located in a well determined way with respect to each other2. And although the main chain bonds form a zigzag pattern, Figure 2.3 seems to suggest that overall chain shape should be more or less like a straight rod, as in Figure 2.2 a.
There is even a separate branch of research called conformational analy-sis of polymers. It deals with the geometry of atoms’ positions in reasonably short chain segments, for much more complex structures than polyethylene, of course. An example is depicted in Figure C2.4: a strand of a DNA double helix. (We shall talk about DNA structure in more detail in Sections 5.5
2For the moment, we ignore the fact that the conformation of a polyethylene segment shown in Figure 2.3 is not the only possible one. A few di↵erent conformations can be realized because there are several rotational isomers of the molecule (see later). By the way, this is the main reason for the flexibility of polyethylene chains.
What Does a Polymer Molecule Look Like? 9
Fig. 2.3 Spatial structure of a polyethylene chain segment in the most energetically fa-vorable configuration.
and 5.6.) The “portrait” of double helix is really one of the cultural icons of our time, it is found everywhere, from calendars and T-shirts to some ar-chitectural designs. The very fact that it is so easily recognizable indicates that each atom really does occupy a particular place.
At the same time, in reality, of course, the atoms of a molecule are not strictly fixed in their equilibrium positions. Indeed, if we think physically, the atoms may be pushed away from their equilibrium positions by a force or a kick, resulting, say, from thermal collisions between a given macro-molecule and macro-molecules of the solvent. Left alone after the kick, the atoms may also oscillate around these equilibrium positions. In a real system, changes in atoms’ positions occur, firstly, because the bond angles (i.e. the angles between adjacent chemical bonds) can be deformed. Secondly, parts of the molecule can rotate with respect to each other, around the axes of sin-gle covalent bonds (but not around double ones). This rotation is sometimes expressed in terms of a molecule having a few di↵erent “rotational-isomeric forms”. But the oscillations hardly ever alter the lengths of covalent bonds.
Thus, in many cases, you can regard a molecule as a construction of rigid rods, a bit like a miniature imitation of the Ei↵el tower. The rods, representing covalent bonds, swing slightly from side to side, about the atoms, with angles between bonds changing. The amplitude of such bond-angle oscillations, as well as the probability of various rotational-isomeric forms, depends on the temperature. For example, at room temperature (T ⇡ 300 K) the oscillation amplitude of the bond angles for typical molecules normally varies from one to ten degrees: ( )T = 300 K ⇠ 1 ÷ 10 . Obviously, for an ordinary small molecule such oscillations would not appear too significant. Indeed, Ei↵el tower also undulates a little bit, with
its top swinging by several meters in a windy weather, which does not seem like much when you either look at the tower from afar or sit in the famous restaurant on top. Similarly, in a short segment of a polymer chain only low-amplitude fluctuations occur. This is why the chain’s flexibility is hardly noticeable at such a small scale, and short chain segments can indeed be depicted in the way shown in Figures 2.3 and C2.4.
At larger scales, however, all the small angle deformations add up along the chain and eventually result in the chaotic coiling of the polymer (Fig-ure 2.2 b). Exactly how long the chain should be in order for the local fluctuations to result in global tangling up depends on the specifics of a particular chemical structure, but if the chain is long enough, then the coiling is inevitable.