Orientation autocorrelation function correlation time

Our experimental measurements of the orientation autocorrelation function on sub-nanosecond time scales are consistent with the theoretical models for backbone motions proposed by Hall and Helfand(ll) and by Bendler and Yaris(12). The correlation functions observed in three different solvents at various temperatures have the same shape within experimental error. This implies that the fundamental character of the local segmental dynamics is the same in the different environments investigated. Analysis of the temperature dependence of the correlation function yields an activation energy of 7 kJ/mole for local segmental motions. 

The orientation autocorrelation function P2[cos 0(t)] is given by r(t) and reflects the motion undergone by the fluorescent chromophore (2,14). A number of models for Brownian motion have been proposed (14) but in the simple case of a rigid sphere, r(t) is described by a single exponential decay where Tf., the rotational correlation time is related to the hydrodynamic volume of the sphere and the viscosity of the medium through the Stokes-Einstein relation (14,16). More complex motions of fluorophores necessitate the development of models which fit the functional form of r(t) experimentally obtained (14). 

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... 

Here 6(t) is the angle between the C-H bond vector at time zero and time t. This particular correlation function is referred to as a second order orientation autocorrelation function. 

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. 

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,... 

Diffusion. - Distribution of the diffusivitity of fluid in a horizontally oriented cylinder was demonstrated by NMR imaging in two papers on a granular flow system and in the earth s magnetic field. Correlation time (ic) and diffusion coefficient (D = Xc) imaging (CTDCI) was applied to a granular flow system of 2 mm oil-filled sphere rotated in a half-filled horizontal cylinder, ie. to an Omstein-Uhlenbeck process with a velocity autocorrelation function. Time dependent apparent diffusion coefficients are measured, and Tc... 

When a second rank potential is considered, the previous description must be modified, particularly when odd rank autocorrelation functions are involved, as we have pointed out above. We present results here that confirm our previous interpretation [40]. In Table IV we show correlation times and eigenmodes for a first rank observable. As in Table II, two dominant modes are present for D2 s 1 the fast one is again a FRD of the solute body, whereas the slow one is a thoroughly mixed nature (i.e., dynamic interactions), and may be loosely related, for very slow cages, to the jump motion of body 1 from one metastable orientation to another (cf. the cases in Table IV for Dj = 0.01, V2 = 2 and Vj = 4). 

The velocity autocorrelation function is an example of a single-particle correlation function, in which the average is calculated not only over time origins but also over all the atoms. Some properties are calculated for the entire system. One such property is the net dipole moment of the system, which is the vector sum of all the individual dipoles of the molecules in the system (clearly the dipole moment of the system can be non-zero only if each individual molecule has a dipole). The magnitude and orientation of the net dipole will change with time and is given by ... 

Other orientational correlation coefficients can be calculated in the same way as the correlation coefficients that we have discussed already. Thus, the reorientational correlation coefficient of a single rigid molecule indicates the degree to which the orientation of a molecule at a time t is related to its orientation at time 0. The angular velocity autocorrelation function is the rotational equivalent of the velocity correlation function ... 

The detailed analysis of carbon-13 spin-lattice relaxation times of a number of polymers either in solution or in bulk at temperatures well above the glass-transition temperature has led to a general picture involving several types of motions. The segmental reorientation can be interpreted in terms of correlated conformational jumps which induce a damped orientation diffusion along the chain. It is satisfactorily described by the well-known autocorrelation functions derived from models of conformational jumps in polymer chains [4,5] which have proven to be very powerful in representing fluor-... 

Mobility in this region is dominated by short-time motion, typically < 2 ps. After that time, all correlation of molecular motion is lost due to frequent collisions with the cavity walls. The center-of-mass velocity autocorrelation function of the penetrant exhibits typical liquid-like behavior with a negative region due to velocity reversal when the penetrant hits the cavity wall [59]. This picture has recently been confirmed by Pant and Boyd [62] who monitored reversals in the penetrant s travelling direction when it hits the cavity walls. The details of the velocity autocorrelation function are not very sensitive to the force-field parameters used. On the other hand, the orientational correlation function of diatomic penetrants showed residuals of a gas-like behavior. Reorientation of the molecular axis does not have the signature of rotational diffusion, but rather shows some amount of free rotation with rotational correlation times of the order of a few tenths of a picosecond, although dependent in value on the Lennard-Jones radii of the penetrant s atoms. 

One of the first applications of RQMC was to the rotational dynamics of carbonyl sulfide (OCS) molecules solvated in helium clusters, for cluster sizes (tV = 3,10) [42]. This and related work, described shortly, rest on the absorption spectrum given by the Fourier transform of the reptilian imaginary time electric dipole correlation function. Similarly, the optical activity is extracted from the autocorrelation of the molecular orientation vector. This work by Moroni and coworkers and/or Boroini and co-workers was closely followed by several other investigations of rotational dynamics in doped clusters, summarized as follows ... 

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