Longest wavelength mode

On the basis of this argument, the equation of motion for the longest wavelength mode in the elastomer is... 

The depolarized scattering for the Rouse-Zimm dynamical model of flexible polymer chains (cf. Section 8.8) may also be calculated. Ono and Okano (1971) have performed this calculation for q = 0 (zero scattering angle) and find that the scattered light spectral density is a series of Lorentzians each with a relaxation time characteristic of one of the Rouse-Zimm model modes. However the contribution of each mode to the spectrum is equal. This behavior should be contrasted with that of the isotropic spectrum where the scattering spectrum is dominated by contributions from the longest wavelength modes. 

There is a correlation between reactivity of the pyrrolinones, 3-ethoxyisoindolenone and the oxazolinones and their UV spectra5 2 The pyrrolinones all have distinct n-7r bands as the longest wavelength transitions in their UV spectra (Table 1), they all react by a-cleavage, and they do not cycloadd to olefins. The molecules studied which cycloadd to olefins and do not a-cleave are 3-ethoxyisoindolenone (50) and the methoxyphenyloxazolinones (65 b and 65c). These show no resolved n-rr transitions (Table 4). Of the two molecules, 65a and 65d which undergo both modes of photochemical reactivity, 65d has a slightly resolved n-7r band as a shoulder on the intense tt-tt transition (Table 4). 

The internal modes are periodic functions of bead position along the chain the characteristic wavelength of internal mode i is N/i. Thus the lower modes govern the large scale motions and have the longest relaxation times. 

The motion actually observed by i.r. absorption is a small part of the whole pattern, since for effective absorption one must match both frequency and wavelength in the electromagnetic and crystal osdllations. Absorption occurs essentially at the frequency of the longest waves present in the crystal These waves are damped by anharmonic interaction with the numerous short-wave modes, except at very low temperatures where interaction with ctystal ddects and surfaces takes over. In spite of the complexity of the process one has to expect a simple lineshape and a fairly simple temperature dependence for a wave propagating in one crystal direction. 

The large number of simultaneous laser modes (40-50 for the longest-resonator lasers) lends itself to exploiting them for the generation of short pulses by inserting a mode locker into the resonator. Indeed, mode-locked Ar lasers, with their picosecond-duration output pulses, are used to pump tuneable lasers to generate wavelength variable ultra-short pulses. 

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