The bond correlation function for a macromolecular model chain on a tetrahedral lattice is derived by considering elementary three‐bond and four‐bond motions. The method of calculation allows the conformational structure of the chain to be involved in the final equations. Moreover, when the three‐bond motions are considered alone, no linearization assumption is required; hence, the theory is valid at short times.
In other papers on dynamics of macromolecular chains1p2 the authors analyzed the behavior of chains confined in a tetrahedral lattice and subjected to three-bond and four-bond motions. When the three-bond motions are considered alone, the bond orientation autocorrelation function has a long-time dependence on t-1/2. If, in addition, four-bond jumps occur, an exponential contribution may be expected.' However, the slowest relaxation times are predominant at very long times and in every case, the relaxation of the chain obeys the t-'I2 dependence. As a matter of fact, the master differential equation reflecting the equalization of orientation probabilities along the chain expresses a very general conservation law.3Furthermore, to describe the real behavior of a chain, one has to take into account the fact that a chain is not strictly confined to motions within a tetrahedral lattice. The departures from a lattice model may result from the following, as was pointed out by Dubois-Violette et al.4. (a) valence angles can vary markedly from the ideal value of 109O28'; (b) internal rotation angles may deviate from 0,1120O; (c) owing to thermal agitation, there is some uncertainty concerning the angles of internal rotation. An exponential contribution due to these deviations is to be expected at long times.4In addition, motions involving a larger number of bonds than the elementary jumps should be mentioned. In order to account for these large-scale motions, Weill and Herman& proposed to add rotational diffusion motions of the lattice, the Contribution of which is also exponential.In conclusion, for a real chain, the bond orientation autocorrelation function derived from a lattice model has to be multiplied by an exponential term. Hence, the long-time behavior is a dependence on t-"* exp (-t/O).
A theory of polarized fluorescence is developed for uniaxial physical systems in which micro‐Brownian motion is not negligible. All experimental information is shown to reduce, with reasonable assumptions, to four quantities characterizing molecular orientation and reorientational molecular mobility. The geometrical properties of the mobility in uniaxial systems are studied and methods are given for correcting for the effects of the birefringence and for a possible delocalization of the fluorescence transition moments.
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