Nonequilibrium polarization

In recent years many attempts have been made to extend the implicit solvent models to the description of time-dependent phenomena. One of these phenomena is nonequilibrium solvation [3] and it can be described effectively in a very simplified way, despite the fact that it actually depends on the details of the full frequency spectrum of the dielectric constant. Typical examples of nonequilibrium solvation are the absorption of light by the solute which produces an excited state which is no longer in equilibrium with the surrounding polarization of the medium [11-13], Another example is intermolecular charge transfer within the solute, also leading to a nonequilibrium polarization [14],... 

Marcus (92) elaborated the continuum theory by separating the polarization of the dielectric into two superimposed polarizations the "nonequilibrium polarization, and the "equilibrium polarization. In the precursor complexp there is a characteristic charge distribution giving a field Ecp, and both polarizations are at equilibrium. When the photon is absorbed the charge distribution rapidly changes to a new value with an associated field Et. The nonequilibrium polarization remains at its old value, but the equilibrium polarization changes to a new value, jointly determined by the charges and the nonequilibrium polarization. 

R. A. Marcus, Electrostatic free energy and other properties of states having nonequilibrium polarization, J. Chem. Phys. 24 (1956) 979. 

An important step in the definition of combined solute and solvent coordinates is presented in some papers by van der Zwan and Hynes (1984) and particularly by Lee and Hynes (1988), who have shown how Marcus treatment of nonequilibrium polarization effects may be accomplished for model charge-transfer reactions (e.g. proton transfer, hydride transfer, and Sjv2 reactions) in a generalized continuum description of nondissipative... 

For such an experiment to work, we have to be able to distinguish the different domains during the evolution and the detection period of the two-dimensional experiment. Since proton spectral resolution in typical solids is very poor, we have to use homonuclear dipolar-decoupling methods to narrow the lines sufficiently to obtain spectral resolution. The 2D spin-diffusion CRAMPS spectrum was first recorded by Caravatti et al. [68] for blends of polystyrene (PS) and polyvinyl methyl-ether (PVME). There are other methods to generate an initial nonequilibrium polarization based on differences in linewidth or relaxation times. The reader is referred to the excellent book of Schmidt-Rohr and Spiess [67] for an overview. 

The total net magnetization of spins created by unequal spin populations. When nuclear spins are placed in a magnetic field their random motion becomes orientated with respect to the field direction. For I —1/2 nuclei, there are two spin states orientated with or against the field. At equilibrium the spin states are populated according to the Boltzmann distribution and so there are more spins in the lower energy state. This population imbalance creates an overall magnetization of the sample -the spins are polarized. Pulses generate nonequilibrium polarizations and polarization may be transferred between spins. 

The nonequilibrium polarization is not directly observable at the instant after SCRP formation if the radical pair is formed from a singlet precursor (formally diamagnetic pair with S = 0) or from a triplet precursor in which all the triplet sublevels T i, To, and T+i were equally populated. In these cases there are as many molecules with emissively polarized transitions in the ensemble as there are molecules with absorptively polarized transitions. 

R. A. Marcus,/. Chem. Phys., 24, 979-989 (1956). Electrostatic Free Energy and Other Properties of States Having Nonequilibrium Polarization. I. 

Two particles participate in a homogeneous redox reaction. Therefore, the total work for creating nonequilibrium polarization includes another similar term corresponding to the charging and discharging of the second particle, as well as a term describing their interaction. Indeed, particle A is in the field of the particle B, i.e. a potential Aeg/eR (here, R is the distance between the reagents) is applied to This potential is the difference... 

This work corresponds to the creation of such a nonequilibrium polarization of the inertial subsystem that would bgcome equilibrium polarization if the charge of the first ion were Ae, and that of the second were equal and opposite to it, i.e. -Ae, Ae being an arbitrary quantity. On the potential diagram, each value of Ae has its... 

The charge Ae is a sort of generalized coordinate, since each of its values corresponds to a certain dipole configuration. This charge was introduced because it can be used for a macroscopic model with the help of the Born charging-discharging process described above, to calculate the minimum work of creation of nonequilibrium polarization of the slow subsystem. 

The metal reacts to the external electric field practically without any inertia. Therefore, nonequilibrium polarization should be taken into consideration only in the vicinity of one ion. The additional term due to the interaction between ions is replaced by a similar term describing the interaction of the ion with the dielectric polarization caused by the image of the ion in the metal. The corresponding expression for Es is quite similar to Equation (3.14). 

---