The decay time of the luminescence of a molecule S in front of a metal mirror depends markedly on its distance from the mirror. This phenomenon is quantitatively explained by considering the radiation field of this dipole, given by Hertz classical equation. This field arrives at the molecule, after being reflected at the mirror, with a retardation of the order of 10−15 sec. The decay time of the luminescence depends on the phase shift produced by this retardation, and thus on the ratio of the distance of the oscillator from the mirror, and the wavelength of the emitted light. By measuring the distance dependence of the decay time of the luminescence this retardation effect can be studied. In quantum-mechanical terms the phenomenon can be described as being due to a stimulation or inhibition of the emission of the light quantum. In contrast to the known cases of stimulated emission, the stimulating field is the radiation field of the emitter quantum itself. The energy transfer from an excited molecule S to an acceptor A can be treated in a similar manner by considering the phenomenon as a retardation effect. In classical terms the field of S induces A to oscillate, and the induced field of A arriving at S slows down this oscillator. Simple equations are given for the energy transfer from an excited dipole or quadrupole, and for a row of many dipoles, oscillating in phase, to a weakly absorbing acceptor layer. The latter case is considered as a model for a J-aggregating dye and by comparison with experimental data conclusions concerning the size of a J aggregate are drawn.

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Articles you may be interested inTemperature dependence of interfacial fluctuations of polymerized fatty acid salt multilayers Sandwiches of monolayers of Cd salts of fatty acids CH3(CH2)n_2COOH of different chain lengths between metal electrodes show the exponential decrease of conductivity VB thickness predicted by the tunnel theory. The electron work function from metal to dielectric is obtained. The current-on-voltage dependence is predicted and it is found to be in good agreement with experiment. The effects of changing the electrode material are quantitatively predicted from the differences between the vacuum work functions of the metals used (Hg, AI, Pb, and Au), The good agreement between theory and experiment can be taken as an extremely sensitive test for the uniformity of the monolayers obtained by the monolayer assembling technique used in this investigation.

The most important organic compounds which absorb visible light can be classified into three groups typified: (a) by symmetrical polymethines, (b) by porphyrines, (c) by polyenes. Recently it was shown that the position of the absorption maxima of symmetrical polymethines and related compounds (symmetrical cyanine and oxanole dyes; Michler's hydrol blue and derivatives; malachite green and other triphenyl methane dyes; etc.) can be calculated by adopting a model of the dye molecule which is analogous to the free-electron gas model used in particular by Sommerfeld to describe the condition of metals. The π-electrons of the polymethine chain are considered as a one-dimensional free-electron gas which extends itself along the length of the chain. In the normal state the stablest energy states of the electron gas each contain two electrons in accordance with Pauli's exclusion principle. The remaining states are empty. The existence of the first absorption band is a consequence of the jump of a π-electron from the highest energy level occupied in the normal state to the lowest empty level. For the wave-length of the maximum of the first absorption band of this group of dyes, the relationship obtains that λ1=(8mc/h)(L2/[N+1]),where L is the length of the polymethine zig-zag chain, N, the number of π-electrons, m, the mass of the electron, c, the velocity of light, h, Planck's universal constant. Good agreement with experimental results for λ1 is obtained by the use of this equation. The problem of porphyrine and phthalocyanine compounds can also be dealt with on the basis of a free-electron gas model. We treat the π-electrons of the porphyrine ring as electrons which are confined to move in a closed ring-shaped path in a field of constant potential energy. In the case of polyenes and related compounds (Carotenes, unsymmetrical cyanines and oxanoles, merocyanines, azo- and stilbene dyes, etc.) a description by means of a free-electron gas model is no longer permissible. The electron gas in this case suffers a disturbance from its condition in the case of the first and second groups of dyes, and, to allow for this, the π-electrons are considered placed in a one-dimensional potential having a sine curve periodicity. The wave-length λ1 is expressed by λ1=[V0hc(1−1N)+h8mcN+1L2]−1,where V0 is the amplitude of the sine-shaped potential along the chain. This relation is confirmed by the experimental data. It also gives an explanation for the markedly different manner (compared with the symmetrical polymethines) in which the position of the absorption bands of polyenes and related compounds depends on the chain length. The results of the classical color theory of Witt are capable of a simple explanation when considered in the light of the electron gas model.

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