Physical Background

In the visible range dye lasers in their various modifications are by far the most widely used types of tunable lasers. Their active media are organic dye molecules solved in liquids, which display strong broad-band fluorescence spectra under excitation by visible or uv light. With different dyes the overall spectral range, where cw or pulsed laser operation has been achieved, extends from 300 nm to 1.2 ym. In this section we briefly summarize the basic physical background and the most important experimental realizations of dye lasers, used in high-resolution spectroscopy. For a more extensive treatment the reader is referred to the laser literature (e.g., [7.31,32b]). 

When dye molecules in a liquid solvent are irradiated with visible or ultraviolet light, higher vibrational levels of the first excited singlet state are populated by optical pumping from thermally populated rovibronic levels in the Sq ground state (Fig.7.13a). Induced by collisions with solvent molecules, the excited dye molecules undergo very fast radiationless transitions into the lowest vibrational level v. of S. with relaxation times of 

10 - 10 s. This level is depopulated either by spontaneous emission 

Because of the strong interaction of dye molecules with the solvent, the closely spaced rovibronic levels are collision broadened to such an extent that the different fluorescence lines completely overlap. The absorption and fluorescence spectra therefore consist of a broad continuum, which is homogeneously broadened (see Sect.3.3). 

At sufficiently high pump intensity, population inversion may be achieved between the level Vq in S and higher rovibronic levels V in Sq which have 

If matter is exposed to an electric field E, an electric displacement D results which formally is given by 

On the basis of Maxwell s theory, the reflected and the refracted waves are explicitely stated by Fresnel s equations. The coefficient r correlates the amplitude E of the reflected wave with the amplitude Eq of the incident one (Bom, 1933 Bom and Wolf, 1980 Bennett and Bennett, 1978)  

The polarization is specified by the plane in which the electric vector oscillates the index s stands for perpendicular to the plane of reflection, and the index p stands for parallel to it (note the traditional definition of the plane of polarization is perpendicular to the plane of the vector oscillations ). The condensed expressions on the very right side of these equations result from applying Snell s law. For optically active media and incident circularly polarized radiation see Sec. 6.3 compare also Secs. 3.2, 4.6.4 and 4.6.5. The square of an electric field strength E is measured as intensity the quotient of the reflected intensity and the incident one is the reflectance R 

The refracted intensity is r = (1 - R), however, this is not just fl. Since this radiation component is now travelling in a different medium, the energy density has to be taken into account. From considering the Poynting vector it follows 

It gives the intensity just behind the interface. It is further reduced by absorption when travelling through the medium. This attenuation is usually specified by the term ( inner ) transmittance T. 

Nuclei provide a large number of spectroscopic probes for the investigation of solid state reaction kinetics. At the same time these probes allow us to look into the atomic dynamics under in-situ conditions. However, the experimental and theoretical methods needed to obtain relevant results in chemical kinetics, and particularly in atomic dynamics, are rather laborious. Due to characteristic hyperfine interactions, nuclear spectroscopies can, in principle, identify atomic particles and furthermore distinguish between different SE s of the same chemical component on different lattice sites. In addition to the analytical aspect of these techniques, nuclear spectroscopy informs about the microscopic motion of the nuclear probes. In Table 16-2 the time windows for the different methods are outlined. 

PAD (perturbed angular distribution) is a variation of PAC with nuclear excitation by a particle beam from an accelerator. QMS is quasielastic MdBbauer-spectroscopy, QNS is quasielastic neutron spectroscopy. For MOBbauer spectroscopy (MS), perturbed angular correlation (PAC), and /J-nuclear magnetic resonance (/3-NMR), the accessible SE jump frequencies are determined by the life time (rN) of the nuclear states involved in the spectroscopic process. Since NMR is a resonance method, the resonance frequency of the experiment sets the time window. With neutron scattering, the time window is determined by the possible energy resolution of the spectrometer as explained later. 

In Table 16-2, the time scale for elementary activated motion is given in the first place. It is converted into an energy scale by virtue of the E = (2n-h/t) relation, If we assume that the atomic jump length a is 2 A, the time scale may be converted into a diffusion coefficient scale by D = az/(2-t). One notes that (with the exception of /J-NMR) nuclear spectroscopies monitor the atomic jump behavior of relatively fast diffusing species. 

The higher the photon energy, the smaller are in general absorption coefficients and the less severe are absorption problems, which simplifies the design of experiments. If radioactive (probe) nuclei can be embedded into the sample crystal (as is the case with PAC), no external radiation is needed for the investigation of solid state 

By assuming an Arrhenius type temperature relation for both the diffusional jumps and r, we can use the asymptotic behavior of /(to) and T, as a function of temperature to determine the activation energy of motion (an example is given in the next section). We furthermore note that the interpretation of an NMR experiment in terms of diffusional motion requires the assumption of a defined microscopic model of atomic motion (migration) in order to obtain the correct relationships between the ensemble average of the molecular motion of the nuclear magnetic dipoles and both the spectral density and the spin-lattice relaxation time Tt. There are other relaxation times, such as the spin-spin relaxation time T2, which describes the 

The dielectric polarization P of a medium with nonlinear susceptibility x. subject to an electric field E, can be written as an expansion in powers of the applied field 

Taking into account that the field amplitudes E, E2 are vectors and that the second-order susceptibility is a tensor of rank 3 with components Xijk depending on the symmetry properties of the nonlinear crystal [5.217], we can write the second-order term in the explicit form 

Note The direction of the polarization vector P may be different from those of E and 2- The components Xijk arc generally complex and the phase of the polarization differs from that of the driving fields. 

Equation (5.114) demonstrates that the components of the induced polarization P are determined by the tensor components Xijk and the components of the incident fields. Since the sequence EjE produces the same polarization as EkEj, we obtain 

This reduces the 27 components of the susceptibility tensor x to 18 independent components. 

The components Pi (/ = x, y, z) of the induced polarization are determined by the polarization characteristics of the incident wave (i.e., which of the components Ex, Ey, Ez are nonzero), and by the components of the susceptibility tensor, which in turn depend on the symmetries of the nonlinear medium. 

Let us first discuss the linear part of (5.114), which can be written as 

Taking into account that the field amplitudes E, E2 are vectors and that the second-order susceptibility x is a tensor with components Xijk 

Note that the direction of the polarization vector p may be different from those of El and Eg. 

In order to reduce the number of indices in the formulas, the components Xijk often written in the reduced Voigt notation. For the first index the convention x=l,y = 2, z = 3is used, whereas the second and third index are combined as follows xx = 1, yy = 2, zz = 3, yz = zy = 4, xz = zx = 5, xy = yx = 6, where the symmetry condition Xyk = Xikj of the susceptibility tensor has been used. 

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Physical background. MAS will narrow the inliomogeneously broadened satellite transitions to give a series of sharp sidebands whose intensity envelopes closely follow the static powder pattern so that the quadnipole interaction can be deduced. The work of Samoson [25] gave real impetus to satellite transition spectroscopy by showing that both the second-order quadnipolar linewidths and isotropic shifts are fiinctions of / and Some combinations of / and produce smaller second-order quadnipolar effects on the satellite lines than... 

In his classical paper, Renner [7] first explained the physical background of the vibronic coupling in triatomic molecules. He concluded that the splitting of the bending potential curves at small distortions of linearity has to depend on p, being thus mostly pronounced in H electronic state. Renner developed the system of two coupled Schrbdinger equations and solved it for H states in the harmonic approximation by means of the perturbation theory. 

Coercivity of Thin-Film Media. The coercivity ia a magnetic material is an important parameter for appHcations but it is difficult to understand its physical background. It can be varied from nearly zero to more than 2000 kA/m ia a variety of materials. For thin-film recording media, values of more than 250 kA / m have been reported. First of all the coercivity is an extrinsic parameter and is strongly iafluenced by the microstmctural properties of the layer such as crystal size and shape, composition, and texture. These properties are directly related to the preparation conditions. Material choice and chemical inborn ogeneties are responsible for the Af of a material and this is also an influencing parameter of the final In crystalline material, the crystalline anisotropy field plays an important role. It is difficult to discriminate between all these parameters and to understand the coercivity origin ia the different thin-film materials ia detail. 

Minimal Energy Requirements. The relative effect of the cost of the energy on the cost of the freshwater produced depends on local conditions, and is up to one-half of the total. In attempting to reduce this cost, it is of interest to determine the minimal energy amount thermodynamically needed for separating the water from the saline solution. The physical background to this will be introduced in a simple example. Because of the negligible... 

The occurrence of fine structures has already been noted in the sections on spectral information and ionization losses (Sects. 2.5.3 and 2.5.3.2). In the following text some principal considerations are made about the physical background and possible applications of both types of feature, i. e. near-edge and extended energy-loss fine structures (ELNES/EXELFS). A wealth of more detailed information on their usage is available, especially in textbooks [2.171, 2.173] and monographs [2.210-2.212]. 

This chapter introduces the important topics of fluid flow, properties of gases, heat and mass transfer, and physical/chemical characteristics of contaminants. The aim is to assist all engaged in industrial air technology in understanding the physical background of the issues involved. 

To understand the physical background behind these results we have tried to find and analyze the three invariants predicted by the Lie group analysis. Clearly there is a local Lie group symmetry when > 0 and... 

In all probability, further attempts at elucidating the physical background of the phenomenon of multiple desorption spectra will appear in the near future. 

Practically all classical methods of atomic spectroscopy are strongly influenced by interferences and matrix effects. Actually, very few analytical techniques are completely free of interferences. However, with atomic spectroscopy techniques, most of the common interferences have been studied and documented. Interferences are classified conveniently into four categories chemical, physical, background (scattering, absorption) and spectral. There are virtually no spectral interferences in FAAS some form of background correction is required. Matrix effects are more serious. Also GFAAS shows virtually no spectral interferences, but... 

Hoffmann s review.2) The number of specific examples mentioned in the text is severely limited in order to save space they can be easily found elsewhere.2) Instead, space is devoted to detailed discussion of topics likely to be less familiar to the organic chemist, such as some of the properties of potential energy hypersurfaces in multidimensional nuclear configuration space, etc. When in doubt, the author erred on the side of sounding too explicit and trivial at the risk of offending the reader with good physical background. 

A generalized model of an oscillator, subjected to the influence of external waves is considered. It is shown that the systems of diverse physical background which this model encompasses by their nature should belong to the broader class of kick-excited self-adaptive dynamical systems . 

The book has been written as an introductory text, not as an exhaustive review. It is meant for students at the start of their Ph.D. projects and for anyone else who needs a concise introduction to catalyst characterization. Each chapter describes the physical background and principles of a technique, a few recent applications to illustrate the type of information that can be obtained, and an evaluation of possibilities and limitations. A chapter on case studies highlights a few important catalyst systems and illustrates how powerful combinations of techniques are. The appendix on the surface theory of metals and on chemical bonding at surfaces is included to provide better insight in the results of photoemission, vibrational spectroscopy and thermal desorption. 

The theoretical design of donor oligomers that gives parallel spins upon electron transfer is reported (Mizonchi et al. 1995). TTF and TSeF were nsed as the donor units in the corresponding ion-radical salts. Reviews by Enoki and Miyazaki (2004) as well as Turner and Day (2005) consider and explained magnetic properties of these systems from physical background. 

In this review, we have discussed the properties of gels by stressing the physical background of the volume phase transition and their related phenomena. Polymer gels and their volume phase transition are well described in terms of... 

I have tried to present material as clearly and logically as possible, giving sufficient detail in the derivations to make them easy to follow. The text takes into account the limited mathematics and physics background of the average chemistry student. However, in no sense is the treatment superficial or watered down. ... 

Although the parabolic rate law has the same form as the mean square displacement (see Section 4.3.1), its physical background is quite different. Parabolic growth is always observed in a one dimensional experiment when due to a gradient-driven flux and where the boundaries are kept at constant potentials. 

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