Brownian motion, intramolecular

Rg. Increasing the temperature will induce an increase in the Brownian motions and the intramolecular fluctuations. Therefore, deactivation of the excited singlet state Si via nonradiative processes will be favored, and there will be fewer emitted photons. This induces a decrease in the quantum yield. 

Haas E, Katchalski-Katzir E, Steinberg I. Brownian motion of the ends of oligopeptide chains in solution as estimated by energy transfer between the chain ends. Biopolymers 1978 17 11-31. Haas E, Steinberg I. Intramolecular dynamics of chain molecules monitored by fluctuations in efficiency of excitation energy transfer. Biophys. J. 1984 46 429-437. 

The general principle of BD is based on Brownian motion, which is the random movement of solute molecules in dilute solution that result from repeated collisions of the solute with solvent molecules. In BD, solute molecules diffuse under the influence of systematic intermolecular and intramolecular forces, which are subject to frictional damping by the solvent, and the stochastic effects of the solvent, which is modeled as a continuum. The BD technique allows the generation of trajectories on much longer temporal and spatial scales than is feasible with molecular dynamics simulations, which are currently limited to a time of about 10 ns for medium-sized proteins. 

Figure 2. Two-dimensional potential surface for reaction in the Sumi-Maicus scheme along the coordinate X for diffusive Brownian motions and the coordinate q for much faster intramolecular vibrational motions, and an example of reactive trajectories there.

In order for the reaction to take place with the mechanism in the Grote-Hynes theory as well as in the Kramers theory, the reactant must surmount over the transition-state barrier only by diffusional Brownian motions regulated by solvent fluctuations. In the two-step mechanism of the Sumi-Marcus model, on the other hand, surmounting over the transition-state barrier is accomplished as a result of sequential two steps. That is, the barrier is climbed first by diffusional Brownian motions only up to intermediate heights, from which much faster intramolecular vibrational motions take the reactant to the transition state located at the top of the barrier. 

The viscoelastic properties of dilute polymer solutions offer an opportunity to bring some rigor to both the theory and the experiments. In a dilute polymer solution, the individual chain molecules adopt a statistical ensemble of conformations which is constantiy changing. This intramolecular Brownian motion is incessant. During flow, the molecules are subjected to forces that change the distribution of chain conformations and lead to measurable birefringence in the solution. The subject of the intrinsic viscosity immediately raises the question of the vahdity of the Staudinger Law. The discussion by Alfrey leaves no doubt about the outcome the Law is empirically unjustified and theoretically offensive. 

Intcrmolecular dipole-dipole relaxation depends on the correlation time for translational motion rather than rotational motion. Intermolecular dipole-dipole interactions arise from the fluctuations which are caused by the random translational motions of neighboring nuclei. The equations describing the relaxation processes are similar to those used to describe the intramolecular motions, except is replaced by t, the translation correlation time. The correlation times are expressed in terms of diffusional coefficients (D), and t, the rotational correlation time and the translational correlation time for Brownian motion, are given by the Debye-Stokes-Einstein theory ... 

The intramolecular motions which relax the total dielectric increment, As = So — b oo, or in other words the mean square dipole moment , can generally be divided into two classes (i) fast local motions and (ii) large-scale, slower Brownian motions of chains. The former are responsible for the jS-process, and the latter for the a-process. The mean square dipole moment, = l, where the sum is taken over... 

In general, the motion of a polymer chain in solution is governed by intermolecular interaction, hydrodynamic interaction, Brownian random force, and external field. The hydrodynamic interaction consists of the intra- and intermolecular ones. The intramolecular hydrodynamic interaction and Brownian force play dominant roles in dilute solution, while the intermolecular interaction and the intermolecular hydrodynamic interaction become important as the concentration increases. 

To demonstrate the potential of two-dimensional nonresonant Raman spectroscopy to elucidate microscopic details that are lost in the ensemble averaging inherent in one-dimensional spectroscopy, we will use the Brownian oscillator model and simulate the one- and two-dimensional responses. The Brownian oscillator model provides a qualitative description for vibrational modes coupled to a harmonic bath. With the oscillators ranging continuously from overdamped to underdamped, the model has the flexibility to describe both collective intermolecular motions and well-defined intramolecular vibrations (1). The response function of a single Brownian oscillator is given as,... 

To provide an example of the two-dimensional response from a system containing well-defined intramolecular vibrations, we will use simulations based on the polarized one-dimensional Raman spectrum of CCI4. Due to the continuous distribution of frequencies in the intermolecular region of the spectrum, there was no obvious advantage to presenting the simulated responses of the previous section in the frequency domain. However, for well-defined intramolecular vibrations the frequency domain tends to provide a clearer presentation of the responses. Therefore, in this section we will present the simulations as Fourier transformations of the time domain responses. Figure 4 shows the Fourier transformed one-dimensional Raman spectrum of CCI4. The spectrum contains three intramolecular vibrational modes — v2 at 218 cm, v4 at 314 cm, and vi at 460 cm 1 — and a broad contribution from intermolecular motions peaked around 40 cm-1. We have simulated these modes with three underdamped and one overdamped Brownian oscillators, and the simulation is shown over the data in Fig. 4. 

Eq. (14.17) is called the Langevin equation of motion, and gives rise to stochastic or Brownian dynamics " The magnitude of the friction coefficient determines the importance of the intramolecular forces compared with the friction term, and large values of C, lead to the Brownian dynamics limit. 

The anisotropy of segmental motion exhibited in Fig. 19 may arise, as noted above, either from the intramolecular or from the intermoleoilar ccmstraint to the rotational motion. The anisotropy d orioitational condadon decay was indeed noted already by Weber and Helfand [47] in their Brownian dynamics simulation of polyethylene of infinite chain length. Their orioitational time-correlation function of the chord vector ( = 0°) decayed much more slowly than those of either the bisector vector ( = 0°, = 0°) or the out-of-plane vector ( = 0°, = 90°). What they modeled was a phantom chain having no... 

Dynamics of the mesogenic unit and of the backbone in the mesomorphic and isotropic states. Above the static glass transition two new intramolecular motions become active in side-chain liquid crystal polymers. Firstly, as in flexible-chain polymers, the micro-Brownian segmental motions of the backbone chain are successively liberated. The increased mobility of the backbone chain enables in turn large-scale reorientations of the long axis of the pendant mesogenic units. As a result, new DR relaxation processes appear. ... 

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