Orientation autocorrelation function anisotropy

The relationship between the structure of a polymer chain and it dynamics has long been a focus for work in polymer science. It is on the local level that the dynamics of a polymer chain are most directly linked to the monomer structure. The techniques of time-resolved optical spectroscopy provide a uniquely detailed picture of local segmental motions. This is accomplished through the direct observation of the time dependence of the orientation autocorrelation function of a bond in the polymer chain. Optical techniques include fluorescence anisotropy decay experiments (J ) and transient absorption measurements(7 ). A common feature of these methods is the use of polymer chains with chromophore labels attached. The transition dipole of the attached chromophore defines the vector whose reorientation is observed in the experiment. A common labeling scheme is to bond the chromophore into the polymer chain such that the transition dipole is rigidly affixed either para 1 lei (1-7) or perpendicular(8,9) to the chain backbone. 

Time-resolved optical experiments rely on a short pulse of polarized light from a laser, synchrotron, or flash lamp to photoselect chromophores which have their transition dipoles oriented in the same direction as the polarization of the exciting light. This non-random orientational distribution of excited state transition dipoles will randomize in time due to motions of the polymer chains to which the chromophores are attached. The precise manner in which the oriented distribution randomizes depends upon the detailed character of the molecular motions taking place and is described by the orientation autocorrelation function. This randomization of the orientational distribution can be observed either through time-resolved polarized fluorescence (as in fluorescence anisotropy decay experiments) or through time-resolved polarized absorption. 

The experimental anisotropy contains information about molecular motion, but is independent of the excited state lifetime. Equation 4 indicates that the orientation autocorrelation function can be obtained directly and unambiguously (within the multiplicative constant r(0)) from the results of a transient grating experiment. 

The fluorophore was modeled by two beads that are attached as a short pendant side-chain (tag). Both the absorption and emission dipole moments of the fluorophore are defined by the direction of the tag (parallel), as indicated by the vector in Fig. 19, and the fluorescence anisotropy was calculated from its orientation autocorrelation function. For simplicity, we assumed that the reorientaional motion of the fluorophore is the only source of fluorescence depolarization. We neglected energy transfer and other processes that might occur in real systems. The fluorescence anisotropy decays were interpreted using the mean relaxation time, defined as ... 

In polymers, due to the constraint resulting from the connectivity of the chain, the local motions are usually too complicated to be described by a single isotropic correlation time x, as discussed in chapter 4. Indeed, fluorescence anisotropy decay experiments, which directly yield the orientation autocorrelation function, have shown that the experimental data obtained on anthracene-labelled polybutadiene and polyisoprene in solution or in the melt cannot be represented by simple motional models. To account for the connectivity of the polymer backbone, specific autocorrelation functions, based on models in which conformational changes propagate along the chain according to a damped diffusional process, have been derived for local chain... 

Among the various expressions that are based on a conformational jump model and have been proposed for the orientation autocorrelation function of a polymer chain, G t), the formula derived by Hall and Helfand (HH) [4] leads to a very good agreement with fluorescence anisotropy decay data. It is written as... 

In time-resolved fluorescence anisotropy studies the orientational motion of a fluorescent label rigidly affixed to a point on the chain, or that of a probe dissolved in the system, are studied. These experiments yield directly the time decay of the second orientational autocorrelation function, MaCx), associated with the unit vector m(x) along the transition moment of the chromophore at time X. M2(x) is given by... 

ABSTRACT - The fluorescence anisotropy decay (FAD) technique is first described, then the different expressions ich have been proposed for the orientation autocorrelation function (OACF) of polymer chains are presented. Typical FAD curves of dilute and concentrated solutions of polystyrene labelled with an anthracene group in the middle of the chain are compared to the various OACF expressions and discussed. In the case of bulk polybutadiene, FAD results obtained either on anthracene labelled chains or on 9,10 dialkylanthracene probes free in the polymer matrix, show that the same type of OACF as for polymer solutions can account for the experimental data. Besides, the temperature dependence of the correlation time of the labelled polybutadiene appears to agree with the WLF equation derived from macroscopic viscoelastic measurements, proving that the segmental motions of about 20 bonds which lead to the FAD of labelled polybutadiene participate in the glass transition processes of this polymer. 

It appears that there is no effect of the polymer concentration on the shape of the anisotropy decay curves and the same conclusions as on dilute solutions are obtained about the most appropiate expression of the orientation autocorrelation function. 

In this paper we have shown that the fluorescence anisotropy decay technique is a powerful tool to examine the orientation autocorrelation function of labelled chains in solution or in bulk polymers, as well as at of free probes in a polymer matrix. It clearly appears that OACF of polymer chains has a specific nature due to the chain connectivity. This implies a non exponential short time term characteristic... 

Formally, when the exchange intensity Hgure 13(b) is plotted as 1 - (tmix NtR)/ it is identical to an orientation autocorrelation function of the process. In the case of CODEX, the recoupling (encoding) time NIr determines the angular sensitivity ((S is the anisotropy parameter of the chemical shift tensor), and the exact mathematics is somewhat involved due to the MAS. In case of static stimulated-echo experiments mentioned above, one obtains essentially analogous, but a mathematically even simpler signal function, that is, the sine-sine correlation function of P2,... 

From a theoretical point of view, the experimentally accessible time-resolved anisotropy, r(f), represents the autocorrelation function of orientations of the emission transition dipole moment at time t and the absorption transition dipole moment fiA(t = 0) at the instant of excitation, t = 0, and can be expressed as... 

Szabo proposed an interesting model-free formula for the time-resolved anisotropy in a macroscopically isotropic system [112]. He expressed r(f) as the autocorrelation function of orientations of the emission dipole moment at time t and absorption dipole moment at time t = 0 in a form suitable for general treatment of various systems, and particularly those with possible internal rotation ... 

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