Molecular dipoles, dielectric spectroscopy

When a chain has lost the memory of its initial state, rubbery flow sets in. The associated characteristic relaxation time is displayed in Fig. 1.3 in terms of the normal mode (polyisoprene displays an electric dipole moment in the direction of the chain) and thus dielectric spectroscopy is able to measure the relaxation of the end-to-end vector of a given chain. The rubbery flow passes over to liquid flow, which is characterized by the translational diffusion coefficient of the chain. Depending on the molecular weight, the characteristic length scales from the motion of a single bond to the overall chain diffusion may cover about three orders of magnitude, while the associated time scales easily may be stretched over ten or more orders. 

The molecular origin of ferroelectricity in FLCs is attributed to a pronounced anisotropy of the angular orientations of the lateral dipole moments, induced by the tilt of the molecular long axes with respect to the normal of the smectic layers. This is supported by the results of broadband dielectric spectroscopy performed on a low molecu-... 

For polymers, dielectric spectroscopy is sensitive to fluctuations of dipoles, which are related to the molecular mobility of groups, segments, or the polymer chain as well [38]. The molecular mobility is taken as a probe for structure. The basic quantity is the complex dielectric function e f) = t (f) - it"(f) as a function of the frequency/and the temperature T. s (/) is the real whereas e"(/) is the loss part i = >f ). A relaxation process is indicated by a step-like decrease of s (/) with increasing frequency and a peak in e"(/). From the maximum position of the peak a mean relaxation rate can be deduced, which corresponds to the relaxation time of the fluctuation of the dipole moment of a given structural imit. For details see reference [49]. All shown measurements were carried out isothermally in the frequency range from 10 to 10 Hz by an ALPHA analyzer (NovocontroF). The temperature of the sample is controlled by a Quatro Novocontrol system with stability better than 0.1 K. 

Dielectric spectroscopy is similar to rheology and in many ways complementary. It especially has the advantage that it covers an extraordinary spectral range. If an electric field is applied to the sample, the induced polarization will be equal to the srmi of all molecular dipoles. In so-called A-type chains, the dipoles are parallel to the chain backbone, and, therefore, the induced polarization of each chain is proportional to its end-to-end vector R ... 

Dielectric spectroscopy, in the context of this system, deals with the interaction of an applied alternating electric field with the orientable dipoles in matter that account for polarizability. Macroscopic polarization is microsopically related to the dipole density of N permanent molecular dipoles of moment in a volume F. In low molecular weight molecules, the net dipole moment can... 

Dielectric relaxation thus resembles self-diffusion. Both processes observe the motion of single macromolecules through a uniform albeit fluctuating background. In a two-component polymer-solvent system, dielectric spectroscopy reveals the effect of intermacromolecular interactions on single-molecule size and reorientation. Dielectric measurements on a three-component polymer-polymer-solvent mixture, in which a tracer polymer has a nonzero type-A dipole and a potentially nondilute matrix polymer has none, can be used for example to separate the effects of probe and matrix molecular weights on dielectric relaxation. This motif in the comparative study of binary and ternary solutions appears repeatedly below. Finally, dielectric measurements on block copolymers in which some copolymer subchains have been inverted end-to-end or have no dipole moment allow one to observe internal motions and dynamic cross-correlations of subchains. 

Reports on the rate of spontaneous fluctuations in confinement are relatively recent. With regards to thin polymer films, pioneering studies in this sense have been performed by broadband dielectric spectroscopy (BDS) on Al-capped thin PS films more than one decade ago by Fukao and Miyamoto [60]. This technique probes the reorientation of dipoles under the application of electric fields in the linear regime [88], and therefore is ideal to characterize the intrinsic molecular mobility in glass formers. Fukao and Miyamoto found that the typical relaxation time remains bulk-like down to thicknesses of 20 nm. For smaller thicknesses, acceleration of the rate of spontaneous fluctuations was observed. Similar results were later reported by others [73, 165]. 

Dielectric spectroscopy is a valuable tool for studying the conformational and dynamic properties of polar macromolecules. The conformational features can be determined by dielectric relaxation strength measurements, whereas the dielectric spectrum provides information on the dynamics of the macromolecules. Phenomenological and molecular theories of dielectric permittivity and dielectric relaxation of polymers have also been developed to elucidate the experimentally observed phenomena. As Adachi and Kotaka have stressed (see Further reading), experimental information depends on each monomer s dipole vector direction as related to the chain contour. A classification of polar polymers into three categories was introduced by Stockmayer type-A polymers, where the dipole is parallel to the chain contour (Fig. 12.4), type-B, where it is perpendicular to the chain contour, and type-C, where the dipoles are located on mobile side groups. For type-A chains, the global dipole moment of each chain is directly proportional to the chain s end-to-end vector R. 

Experimental dipole moments can be obtained in several different ways. The first and most widely used approach is based on the measurement of dielectric constants. The second group of methods utilizes microwave spectroscopy and molecular beams (the Stark effect method, the molecular beam method, the electric resonance method, Raman spectroscopy, etc.). 

This table gives selected values of the electric dipole moment for over 800 molecules. When available, values determined by microwave spectroscopy, molecular beam electric resonance, and other high-resolution spectroscopic techniques were selected. Otherwise, the values come from measurements of the dielectric constant in the gas phase or, if these do not exist, in the liquid phase. Entries are listed alphabetically compounds not containing carbon are listed first, followed by compounds containing carbon. 

In Chapter 7, Mano and Dionisio describe how electrical methods, and particularly dielectric relaxation spectroscopy (DRS) and thermally stimulated depolarisation current (TSDS) techniques, play a major role as tools for e2q)loring molecular mobility. DRS enables molecular relaxational processes (both slow and fast) to be studied. For example, the localized motions of glass formers in the glassy state give rise to local fluctuations of the dipole vector that are the origin of the secondary relaxation processes detected by dielectric relaxation spectroscopy, while above, but near, the glass transition, cooperative motions result in a distinguishably different relaxation process (the a-relaxation). 

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