Dissipative energy relaxation

It has often been pointed out for a long time that the hysteresis energy given from the hysteresis loop under large extension is too big compared with the viscoelastic dissipation energy. For example, the hysteresis loop given from the stress relaxation is only 20%-30% of that from the stress-strain curve, when both measurements are performed at the same relaxation time and the... 

Over the course of fluorescence, which accompanies energy relaxation, the molecule can keep part of the energy it received in the form of vibrational energy of the ground state. This excess vibrational energy is dissipated by collisions or other non-radiative processes called vibrational relaxation. The emission of lower energy photons is also possible and gives rise to fluorescence in the mid infrared. 

D. J. Tannor To understand the role of dissipation in quantum mechanics, it is useful to consider the density operator in the Wigner phase-space representation. Energy relaxation in a harmonic oscillator looks as shown in Fig. 1, whereas phase relaxation looks as shown in Fig. 2 that is, in pure dephasing the density spreads out over the energy shell (i.e., spreads in angle) while not changing its radial distribution... 

Independently of the strain rate and the test temperature, the toughness of the material depends on its ability to absorb or dissipate energy, and this requires chain mobility. In the glassy state the energy-absorbing mechanism is related to the p relaxation. Therefore, impact resistance... 

A many-atom system excited by light or by collisions, such as occurs in the photo-excitation of a molecule adsorbed on a surface or in photosynthesis and vision, leads to energy dissipation on different time scales. A fast dissipation typically occurs due to electronic energy relaxation in the medium, while a slow (delayed) dissipation arises from vibrational energy relaxation. Here we concentrate on localized phenomena where a relatively small number... 

Hygroscopic Hysteresis hydroxyl content of 1.0 g of polyol. A material that absorbs moisture readily. The ability of polyurethane to absorb and dissipate energy due to successive deformation and relaxation. A measurement of the area between the deformation and relaxation stress-strain curves. 

This chapter is concerned with how energy deposited into a specific vibrational mode of a solute is dissipated into other modes of the solute-solvent system, and particularly with how to calculate the rates of such processes. For a polyatomic solute in a polyatomic solvent, there are many pathways for vibrational energy relaxation (VER), including intramolecular vibrational redistribution (IVR), where the energy flows solely into other vibrational modes of the solute, and those involving solvent-assisted processes, where the energy flows into vibrational, rotational, and/or translational modes of both the solute and the solvent. 

Many materials, particularly polymers, exhibit both the capacity to store energy (typical of an elastic material) and the capacity to dissipate energy (typical of a viscous material). When a sudden stress is applied, the response of these materials is an instantaneous elastic deformation followed by a delayed deformation. The delayed deformation is due to various molecular relaxation processes (particularly structural relaxation), which take a finite time to come to equilibrium. Very general stress-strain relations for viscoelastic response were proposed by Boltzmann, who assumed that at low strain amplitudes the effects of prior strains can be superposed linearly. Therefore, the stress at time t at a given point in the material depends both on the strain at time t, and on the previous strain history at that point. The stress-strain relations proposed by Boltzmann are [4,39] ... 

This equation indicates that the dissipated energy is proportional to both the square of the amplitude of the deformation and the loss relaxation modulus. 

For the Hertzian contact, no force is needed to pull away the contacting sphere from the flat plane in excess of the weight of the sphere. However, for the JKR contact, due to adhesion forces, this does not hold. The value of the nonzero pull-off force represents the adhesion of the contacting sphere with the flat plane. Strictly speaking, this force corresponds to adherence of the surfaces as energy dissipation, surface relaxation, etc. also influence its value. It should be stressed that the value of the JKR pull-off force only depends on the sphere (lens) radius and the work of adhesion in the medium in which the JKR experiment is conducted. Thus, the contact area and mechanical properties for true JKR contacts do not play a role for its value. All the above considerations for contact mechanics were based on pairwise additivity of molecular forces. 

We have seen that vibrational relaxation rates can be evaluated analytically for the simple model of a hannonic oscillator coupled linearly to a harmonic bath. Such model may represent a reasonable approximation to physical reality if the frequency of the oscillator under study, that is the mode that can be excited and monitored, is well embedded within the spectrum of bath modes. However, many processes ofinterest involve molecular vibrations whose frequencies are higherthan the solvent Debye frequency. In this case the linear coupling rate (13.35) vanishes, reflecting the fact that in a linear coupling model relaxation cannot take place in the absence of modes that can absorb the dissipated energy. The harmonic Hamiltonian... 

The theory of energy transfer considered in this subsection was used to interpret the experiments with PbSe quantum dots (58) on the size-dependent energy relaxation in a quantum dot. In this paper it was shown that smaller dots have faster relaxation. In the theoretical paper by Hong et al. (59) it was assumed that the above energy transfer from a quantum dot exciton to surface states of the dot is a dominant channel of the electronic energy relaxation. Hong et al. considered in their calculations a spherical quantum dot of radius R and the transfer rate was obtained from the calculation of the power dissipation W on the surface of the quantum dot by the relation... 

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