A Molecular polarisability

In Section 4.2.1 we present theoretical results concerning the electric modulus. Those results have been widely obtained in the field of ionic conductors [128]. In Section 4.2.2, we show how a molecular polarisation phenomenon would appear in the curv es AT = f u>). In Section 4.2.3, we present experimental results of relaxation phenomena in conducting polymer based materials. We will give here an example of a calculation using the electric modulus description and a comparison with experimental results will be made. We will show that a correlation between relaxation frequency and static conductivity level, already found for other materials, also holds in conducting polymers. 

The effect of a molecular polarisation on the evolution of M with frequency is investigated. The ideal material is characterised by electric field relaxation time under constant electrical induction D. If a molecular polarisation phenomenon, different from the long-range conducting process does exist, it is characterised by (relaxation time of the molecular process under the constraint of constant electrical induction). In this case Ambrus [135] has given an expression for the electric modulus ... 

McDowell, S. A. C., Amos, R. D., Handy, N. C., 1995, Molecular Polarisabilities - A Comparison of Density Functional Theory with Standard Ab Initio Methods , Chem. Phys. Lett., 235,1. 

Raman Bond vibrations (change in molecular polarisability) As IR, but complementary in application Fluorescence can be a problem As IR, but truly non-invasive... 

The origin of the n2 measured using the 10 ns pulses could be electronic or molecular rotation. These can be distinguished by measuring the ratio of the critical power for self-focusing for linear and circular polarised light. The observed ratio of 2.1 is consistent with a molecular rotation (11-13.161 and relates to the anisotropic polarisability of the molecule. The rotational relaxation time, calculated from the Debye formula (H), is about 0.5-2 ns, consistent with these results. 

McDowell SAC, Amos RD, Handy NC (1995) Molecular polarisabilities - a comparison of density functional theory with standard ab initio methods, Chem Phys Lett, 235 1-4... 

For non-polar materials the relationship between the molar polarisation Pll/ the dielectric constant e and the molecular polarisability a is known as the molar Clausius-Mosotti relation and reads... 

Molecular polarisability is the result of two mechanisms (a) distortional polarisation and (b) orientation polarisation. Distortional polarisation is the result of the change of electric charge distribution in a molecule due to an applied electric field, thereby inducing an electric dipole. This distortional polarisation is coined ad. Permanent dipoles are also present in the absence of an electric field. At the application of an electric field they will orient more or less in the direction of the electric field, resulting in orientation polarisation. However, the permanent dipoles will not completely align with the electric field due to thermal agitation. It appears that the contribution of molecular polarisability from rotation is approximately equal to p2/(3kT). Accordingly, the total molecular polarisability is... 

The polarisation itself is, just as the molecular polarisability is, the result of deformation polarisation Pd and the orientation polarisation Ps. Accordingly, the total polarisation is equal to P = Pd + Pa. Because of the resistance to motion of the atom groups in the dielectric, there is a delay between changes in the electric field and changes in the polarisation. The deformation polarisation takes place instantaneously (more precisely in a time of the order of 10-14 s) on the application of an electric field. There are two limiting values of e Erxi at short times or high frequencies and es at long times or low frequencies. This means that we have for the deformation polarisation... 

Figure 2.4 depicts the characteristic stepwise fall in polarisation of a material as the measurement frequency is raised, rendering it impossible for preceding components of molecular polarisation to make their contribution. The relative permittivity follows a similar pattern. 

Equation (2.35), known as the Lorenz-Lorentz relation, provides a method of calculating the molecular polarisability from a macroscopic, observable quantity, the refractive index. We must make the proviso that we stay away from any resonant absorption frequency, where the refractive index is anomalously high. If the refractive index refers to optical frequencies, the polarisability a will be purely electronic in origin. In practice, electronic polarisabilities derived in this way are remarkably insensitive to temperature and pressure, even for highly condensed phases in which intermolecular forces must be large. This is illustrated for the particular case of xenon in Table 2.1. 

In contrast to molar polarisation calculated from optical refractivities, that calculated from relative permittivities observed at lower frequencies is by no means always independent of temperature. Actually, materials tend to fall into one of two classes. Those in one class show a relatively constant molar polarisation in accord with the simple Clausius-Mosotti relation, whilst the members of the other class, which contains materials with high relative permittivities, show a molar polarisation that decreases with increase in temperature. Debye recognised that permanent molecular dipole moments were responsible for the anomalous behaviour. From theories of chemical bonding we know that certain molecules which combine atoms of different electronegativity are partially ionic and consequently have a permanent dipole moment. Thus chlorine is highly electronegative and the carbon-chlorine... 

MM methods provide a simpler representation of molecules, in which the fine detail of the electrons represented implicitly via partial charges and, is some cases, molecular polarisabilities. MM models represent molecules as a collection of atoms interacting through classical potentials. There are several MM models (or forcefields), and they dilfer in the functional forms of the interaction potential used between atoms, and in the means by which these interaction potentials are parameterized. Several good recent reviews of MM forcefields have been produced. Several MM forcefields have been developed for application to biomolecular systems. The most popular of these are the CHARMM, AMBER, ... 

Fig. 9. Schematic diagrams of the three types of polarisable potentials. The left-hand diagram shows a point polarisability model (e.g. SK [35] and DC potentials [36]). The centre diagram shows die polarisation on the two 0-H bonds (e.g. NCC potential [37]). The right-hand diagram shows the all-atomic (or three-) polarisation models (e.g. Bernardo et al [44] and Burnham [26]). The lower diagram schematically illustrates the relative orientations of molecular dipole moments of the four nearest neighbour molecules would in possible to cancel out due to the ice rule and give rise a strong local field.

The same ideas extend straightforwardly to deal with property surfaces describing the dependence of a molecular property on geometry, for example, the dipole moment and polarisability derivatives that control the activity of a vibrational mode in IR and Raman spectroscopy. Extension to the case of redundant internal coordinates, the typical situation for polyatomic molecules, is also straightforward. 

---