Time-dependent polarization

The method is based on the ability of the excited state of suitable chromophores to both drive and respond to motions in their immediate environment. For example, coumarin excited states have a large dipole moment that causes nearby charged groups to move to stabilize the dipole. As these groups move and reduce the energy of the excited state, the fluorescence shifts toward the red. In simple solutions, this time-resolved Stokes shift (TRSS) experiment measures the time-dependent polarity of the solvent surrounding the coumarin [9]. 

Extending this experiment to DNA relies on a coumarin-102 deoxyriboside as a base-pair replacement [10]. Standard oligonucleotide synthesis techniques allow this probe to be placed into a DNA strand of any desired sequence. The TRSS experiment becomes sensitive to the time-dependent polarity experienced in the interior of the DNA. The polarity may have contributions from the movement of any of the charged groups intrinsic to the structure, such as the full charges on the backbone phosphates, the partial charges of the base pair heteroatoms, or the surrounding water and counterions. 

We start with the time dependent polarization function P(t). This quantity may be expressed in the form of an integral equation ... 

The dielectric loss factor arises from two sources energy loss associated with the time-dependent polarization, and bulk conduction. The loss factor is written e"eo, where e" is the relative loss factor. 

Photoinduced birefringence illustrates what is happening in bulk, but use of time-dependent polarization modulation infrared spectroscopy can offer a detailed insight at the molecular level. Different infrared bands can be monitored in time, and the change in their orientation function allows one almost to watch the different groups move in real time. In order to do this, the process must be slowed down considerably, which is achieved by using a fraction of the pump intensity. 

Here E° f) are the bare or vacuum electric fields of the reactant (R) and product (P) states. Peq r) denotes the equilibrium solvent polarization for the R state, while P(F) is the actual time dependent polarization. 

With a frequency decomposition that appears as in Fig. 3. According to Eq. (5) and including terms up to second-order in the field, the time-dependent polarization will be... 

When an alternating electric field (a.c.) is applied across an insulator, a time dependent polarization current flow is induced. This is because the electrical charges present in the atoms and molecules in the material respond to the changing directions of the field. This is also referred to as dielectric response of the material. When the frequency of the applied field is well below the phonon frequencies, the dielectric polarization of the bound charges is instantaneous. Therefore, the dielectric constant, e (oo), characterizing the bound charge response, is frequency independent. The frequency dependent part of dielectric constant is by definition related to the frequency dependent conductivity, CT (co) as... 

The ratio of the anisotropy of the acceptor to that of the donor for this worst case is only 2.5 times greater than for a randomly distributed solution. For the 2-VN/MMA copolymers used in this study the occurrence of 2-VN dlads is very small and the influence on the time dependent polarization is certainly negligible. The equivalence of the determinations for... 

The dielectric permittivity of a medium (relative to the permittivity of free space, 8q = 8.85 X 10 F/m) is given by e and measures the polarization of the medium per unit applied electric field. The dielectric loss factor arises from energy loss during time-dependent polarization and bulk conduction. The loss factor is written as a". The loss tangent or dissipation of the medium, tan<5 is defined by e"/e. The orientation of molecular dipoles has a characteristic time r. Typically is short early in the cure but grows large at the end of the cure. 

Physical origin of dielectric loss The foregoing conclusions correspond to a static description or cases for which the polarization can perfectly follow the oscillation of the electric field. Indeed, the electric field orientation depends on time with a frequency equal to 2.45 GHz (the electric field vector switches its orientation approximately every 10 s). The torque exercised by the electric field induces rotation of polar molecules, but they cannot always orient at this rate. The motion of the particles will not be sufficiently rapid to build up a time-dependent polarization P(t) that is in equilibrium with the electric field at any moment. This delay between electromagnetic stimulation and molecular response is the physical origin of the dielectric loss. 

The time-dependent polarization which determines all optical properties is finally given by... 

For small electric field strength, the dielectric relaxation can he described in the framework of the linear response theoiy (Landau and Lifschitz 1979). The relevant materials equation which links the time-dependent polarization P(t) with the time-dependent electric field E(t) is given by (Schonhals and... 

A time-dependent polarization P (0 due to the orientation of dipoles in the electric field. If the field remains in place for an infinitely long time, the resulting total polarization Pj defines the static dielectric constant e/. 

We report here an interesting new nonlinear optical phenomenon—self-induced time-dependent polarization rotation in a liquid-crystal medium. It occurs as a result of angular momentum transfer from the radiation field to the medium, causing the molecules to precess around the beam propagation direction. An elliptically polarized light beam of frequency o), intensity /, and ellipticity 5 3 (/+—/-)// carries an average angular momentum of per unit time and unit area, where I/hm... 

In tMs chapter we consider those aspects of the interaction of solvent and solute that are most clearly physical in nature, setting aside the more chemical aspects until the next chapter. The intermolecular potential characteristic of nonpolar substances, the London or dispersion interaction, arises from the mutual, time-dependent polarization of the molecules. For two molecules weU separated in vacuo it is approximated by the London formula ... 

V. TIME-DEPENDENT POLARIZATION A. General and Debye Equations... 

Then, the time-dependent polarization resistance with the micro-structure could be written in the form by combining Equations (7.1), (7.2) and (7.7) as ... 

In the presence of a generic time-dependent perturbation V (r), the time-dependent polarization charges Q( t) may be formally defined as ... 

The expansions (3.18a and 3.18b) imply an expansion in time-dependent polarization charges of (3.15) ... 

On the contrary, when the time-dependent electric field varies on a time scale faster than the relaxation time of one or more molecular degrees of freedom there is not time to reach at any moment a time-dependent polarization which is in equilibrium with the electric field. In this regime, which is called non-equilibrium polarization, the actual value of polarization will also depend values of the electric field at previous time, and the relation between the polarization of a dielectric medium and the time-dependent polarizing field is phenomenologically described in terms of the whole specuiim of the dielectric permittivity as a function of the frequency co of the oscillating electric field. 

In the non-equilibrium polarization regime, the time-dependent polarization charges of the PCM model may be written as... 

Time dependent polarization charges, 24, 29 Time dependent quasi fl ee-energy functional, 25... 

The TD approach is the natural candidate for the interpretation of data coming from pump-probe spectroscopies [13]. If both pump and probe fields are weak, the third-order time-dependent polarization can be computed propagating wave-packets with field-free Hamiltonians [14]. A nonperturbative approach can also be followed, numerically solving the TDSE with the external fields included in the Hamiltonian [15, 16]. Chapter 9 of this book presents the equation-of-motion phase-matching approach (EOM-PMA), which can be considered a mixed perturbative-nonperturbative method. 

If the experiment is carried out with a constant field Eq being switched on at zero time, one finds in general a time dependent polarization P(t), set up of an instantaneous part P and a retarded part Por... 

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