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Macromolecules, Structure 875

FIGURE 18 Infrared spectra of (a) linear and (b) branched polyethylenes.

3
expressed in gm/cm , will be approximately unity. We carbon-13 NMR spectroscopy (see Section III.B). Such
then have short branches are of particular importance in polyethy-
lene since, as we have seen (Section I.E), their presence

2.303 log (I 0 /I) = a bc. (45)
10
reduces the melting point and extent of crystallinity.
The quantity log (I 0 /I) is the absorbance or optical den-
10 Vibrational spectroscopy is useful in many other deter-
sity and is the quantity on the vertical axis of typical in- minations, including geometrical isomerism in polydienes
frared spectra. (see Section III.D) and in the observation of conforma-
In Fig. 18 the infrared spectra of (a) linear and (b) tional isomers, which may be too short-lived or otherwise
branched polyethylenes are shown. The principal bands unobservable by NMR. It is often quicker and simpler,
are labeled in accordance with the vibrational assign- especially in the solid state.
mentsalreadydiscussed.TheintenseC Hstretchregionis
twofold owing to the splitting into asymmetric and sym-
B. Nuclear Magnetic Resonance
metric bands, as shown in the inset dashed spectrum in Spectroscopy (NMR)
−1
Fig. 18a. Bands for carbonyl groups (1725 cm ), result-
ing from slight oxidation, and terminal vinyl groups are This is a powerful and versatile technique, useful in both
observable in the spectrum of the linear polyethylene. If the solution and solid states for the qualitative and quanti-

accurate values of a (from model compounds) and b are tative observation of polymer structure. The phenomenon
established, the content of these groups can be measured of NMR depends on the fact that some nuclei possess
quantitatively. spin or angular momentum. Such nuclei are described by
Short branches in high-pressure polyethylene may be spin quantum numbers I (the “spin”) having integral or
determined by counting their terminal methyl groups: half-integral values. When placed in a magnetic field of
strength B 0 , such nuclei occupy 2I + 1 energy levels with
CH 2 CH 2 CHCH 2 CH 2
relative populations normally given by a Boltzmann dis-
1
19
CH 2 tribution. We shall deal here with the proton ( H), F, and
2
the 13 C nucleus only, although 29 Si, 15 N, 31 P, and H are
also useful for polymers and biopolymers.
The spacing of magnetic energy levels is given by
CH 3
In Fig. 18b the CH 3 distortion band at 1375 cm −1 (ar-
E = hν 0 = 2µB 0 , (46)
row) provides a measure of the methyl content if linear
material is employed as a blank. However, the determi- where µ is the magnetic moment of the nucleus. Transi-
nation of branch length, type, and distribution requires tions between these energy levels can be made to occur