Dynamic mechanical spectra, experimental

This chapter discusses the dynamic mechanical properties of polystyrene, styrene copolymers, rubber-modified polystyrene and rubber-modified styrene copolymers. In polystyrene, the experimental relaxation spectrum and its probable molecular origins are reviewed further the effects on the relaxations caused by polymer structure (e.g. tacticity, molecular weight, substituents and crosslinking) and additives (e.g. plasticizers, antioxidants, UV stabilizers, flame retardants and colorants) are assessed. The main relaxation behaviour of styrene copolymers is presented and some of the effects of random copolymerization on secondary mechanical relaxation processes are illustrated on styrene-co-acrylonitrile and styrene-co-methacrylic acid. Finally, in rubber-modified polystyrene and styrene copolymers, it is shown how dynamic mechanical spectroscopy can help in the characterization of rubber phase morphology through the analysis of its main relaxation loss peak. 

All of this information about vibrational frequencies and transition intensities is observable directly in the frequency domain absorption spectrum, A"= o(w) The autocorrelation function picture is an alternative way of deriving a ball-and-spring physical picture (or dynamical mechanism) from the raw experimental data. Although there is a simple Fourier transform relationship between Ivn (to) and ( f (f)l F(O)), profoundly different intuitive pictures are used to make sense of experimental results and to guide the design of new experiments. 

We have alluded to the comrection between the molecular PES and the spectroscopic Hamiltonian. These are two very different representations of the molecular Hamiltonian, yet both are supposed to describe the same molecular dynamics. Furthemrore, the PES often is obtained via ab initio quairtum mechanical calculations while the spectroscopic Hamiltonian is most often obtained by an empirical fit to an experimental spectrum. Is there a direct link between these two seemingly very different ways of apprehending the molecular Hamiltonian and dynamics And if so, how consistent are these two distinct ways of viewing the molecule ... 

In our approach [1, 2] termed the dynamic method the complex susceptibility x = x — ix" is determined by a law of undamped motion of a dipole in a given potential well and by dissipation mechanism often described as stosszahlansatz in the underlying kinetic or Boltzmann equation. In this review we shall refer to this (dynamic) method as the ACF method, since it is actually based on calculation of the spectrum of the dipolar autocorrelation function (ACF). Actually we use a one-particle approximation, in which the form of an employed potential well (being in many cases rectangular or close to it) is taken a priori. Correlation of the particles coordinates is characterized implicitly by the Kirkwood correlation factor g, its value being taken from the experimental data. The ACF method is simple and effective, because we do not employ the stochastic equations of motions. This feature distinguishes our method from other well-known approaches—for example, from those described in books [13, 14]. 

The scope of the series covers the entire spectrum of solid mechanics. Thus it includes the foundation of mechanics variational formulations computational mechanics statics, kinematics and dynamics of rigid and elastic bodies vibrations of solids and structures dynamical systems and chaos the theories of elasticity, plasticity and viscoelasticity composite materials rods, beams, shells and membranes structural control and stability soils, rocks and geomechanics fracture tribology experimental mechanics biomechanics and machine design. 

Concerning the slow dynamics below the crossover temperature Tc, the predictive power of the theory seems to be rather limited. In particular, the emergence of intrinsic slow secondary processes, which seems to be associated with the dynamic crossover in the experimental spectra, is not contained even in the extended versions of the theory consequently, the slow dynamics spectrum is not reproduced correctly. In this respect, the extended theory introducing the hopping mechanism for describing the susceptibility minimum below Tc is misleading. On the other hand, the most prominent prediction of MCT below Tc is the anomaly of the nonergodicity parameter, which, as discussed, is found by different model-independent approaches. However, within the framework of MCT, this anomaly is closely connected with the appearance of a so-called knee feature in the spectral shape of the fast dynamics spectrum below Tc. This feature, however, has not been identified experimentally in molecular liquids, and only indications for its existence are observed in colloidal systems [19]. In molecular systems, merely a more or less smooth crossover to a white noise spectrum has been reported in some cases [183,231,401]. Thus, it may be possible that the knee phenomenon is also smeared out. 

Figure 3.10 Predictions of the temporary network model [Eq. (3-24)] (lines) compared to experimental data (symbols) for start-up of uniaxial extension of Melt 1, a long-chain branched polyethylene, using a relaxation spectrum fit to linear viscoelastic data for this melt. (From Bird et al. Dynamics of Polymeric Liquids. Vol. 1 Fluid Mechanics, Copyright 1987. Reprinted by permission of John Wiley Sons, Inc.)...

In this article we mainly focus on the central issue of vibronic coupling in the benzenoid systems viz., the phenyl radical (Ph ) and phenylacetyleneradical cation (PA +) and the lowest members of the family of the PAH radical cations viz., naphthalene (N +) and anthracene (AN +) radical cations. Consequences of this coupling for the nuclear dynamics of these systems are studied at length. The difficulties faced in the quantum mechanical treatments of these large systems are also discussed. Dynamical observables like the rich vibronic spectrum are calculated and assigned. The ultrafast nonradiative dynamics of the excited states is also studied. These observables are compared with the available experimental data to validate the established theoretical model [19-22]. 

Figure 13 Comparison of the experimental and a quantum mechanically computed (by exact wave packet propagation using an ab initio computed potential energy) spectrum of a nonrotating Na, molecule pumped to its B electronic state. (Courtesy of Experiment by S. Rutz, E. Schreiber, and L. Woste Computations by B. Reischl, all of the Free University of Berlin) (a) The short time dynamics Shown is the population of the excited state vs. time as determined by a pump-probe experiment and by the computation (points connected by a straight-line segments). The periodicity (about 320 fs) is due to the symmetric stretch motion, (b) A frequency spectrum. The long time dynamics (as reflected in the well-resolved spectrum) show the contribution of a different set of vibrational modes. The dominant peaks can be identified as the radial pseudorotation motion of Na,(B) while the splittings are due to the angular pseudorotational motion. (Adapted from B. Reischl, Chem. Phys. Lett., 239 173 (1995) and V. Bonacic-Koutecky, J. Gaus, J. Manz, B. Reischl, and R. de Vivie-Riedle, to be published.)...

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