Polymer vibrations

At this stage it may be helpful to note some aspects of polymer vibrational spectroscopy that differ from those of small molecules. Two comprehensive works provide an excellent and thorough review of the subject [11, 12]. 

---

W. W. Urban and T. Provder, eds.. Multidimensional Spectroscopy of Polymers Vibrational, NMR, and Tluorescence Techniques, American Chemical Society, Washington, D.C., 1995. 

Figure II. Third-order mixing (CARS) in a solution of4 BCMU in2 / 3 hexane and 1 / 3 chloroform for the frequency region of the polymer vibration. Key —, experimental data and —, theoretical fit. (Reproduced with permission from Ref 23. Copyright 1978, American Institute of Physics.)...

Information concerning conformation, tacticity and crystallinity may also be obtained (1). Vibrational transitions accesssible to IR spectroscopy are governed by the selection rule that there must be a change in dipole moment during excitation of the polymer vibrations. Thus symmetric vibrations which are detected by Raman spectroscopy are inaccessible to IR absorption measurements. 

In addition to providing information about the chemical structure of a polymer, vibrational spectroscopy can also give very useful information about the physical structure, because any two regions of the polymer that differ in the way the repeat units are arranged may exhibit detectable differences in their spectra. Furthermore, measurements of the strength of IR absorption or of Raman scattering can give quantitative information about the composition of any mixture. 

Fig. 2. Calculated frequencies as a function of Fj 2 and F >2 force constants. The vertical dashed lines indicate the values used in our calculations for undoped polymer vibrational modes.

In an unbounded isotropic solid, two types of sound waves can be propagated. In the first type, called a longitudinal wave, the polymer vibrates in the direction of wave propagation. In the second type, called a shear wave, the polymer motion is perpendicular to the direction of propagation. Longitudinal waves are sometimes called dilatational, compressional, or irrotational waves. Shear waves are sometimes called distortional, isovoluminous, or transverse waves. These two types of waves propagate independently of one another and are the only two types possible in an unbounded soUd. 

The fact that, in going from the solid to the liquid state, many bands disappear has been taken by authors as an indication that these bands must be associated with the material in the crystalline state. In spite of the existence of clear and easy dynamical theories on polymer vibrations, a whole body of literature has accepted the direct correlation between k = 0 modes of the single chain and content of material in the crystalline (3D) state. 

Electron Models of Conjugated Polymers Vibrational and Nonlinear Optical Spectra... 

Progress in understanding the vibrational spectra of conjugated polymers has been slow in comparison with those of other polymers [42]. A traditional molecular spectroscopic approach to polymer vibrations would in fact be based on the GF formalism [43] and the solution of the secular equation... 

Diphenyllead(IV) dichloride was reported to form one-dimensional chains, as shown in 15, with the chloride atoms symmetrically bridging adjacent lead atoms. The lead atoms are octahedrally coordinated, with the phenyl groups mutually trans and the octahedra connected via opposite edges to give the chain coordination polymer. Vibrational studies were consistent with the iodine product being pentacoordinated and the chloride and bromide products being hexacoordi-nated. ... 

In all applications discussed in the following chapters the many-dimensional energy surfaces have been Scanned pointwise as a function of some appropriately chosen set of internal coordinates. Energy values thus obtained have been subjected to polynomial fits in order to find the equilibrium geometry and internal, harmonic force constants. In a few cases (polyyne, hydrogen fluoride, hydrogen cyanide) these force constants have been used for an evaluation of vibrational frequencies and phonon dispersion curves within the framework of the harmonic approximation using standard methods of polymer vibrational spectroscopy (see e.g. refs. l8,19 ). 

---