Molecular motion Brownian

Symmetrical application of magnetic field gradients around the refocusing pulse in a spin echo will refocus the signal from static molecules. However, microscopic molecular motion (Brownian motion) will cause dephasing of individual magnetic moments to a degree which is dependent on the freedom of the molecular motion of the water in cells. Freedom of the molecular motion... 

Doi, M. and Edwards, S.F., 1978. Dynamics of concentrated polymer systems 1. Brownian motion in equilibrium state, 2. Molecular motion under flow, 3. Constitutive equation and 4. Rheological properties. J. Cheni. Soc., Faraday Trans. 2 74, 1789, 1802, 1818-18.32. 

Diffusion The mixing of substances by molecular motion to equalize a concentration gradient. Applicable to gases, fine aerosols and vapors. (See Brownian diffusion.)... 

Sometimes the theoretical or computational approach to description of molecular structure, properties, and reactivity cannot be based on deterministic equations that can be solved by analytical or computational methods. The properties of a molecule or assembly of molecules may be known or describable only in a statistical sense. Molecules and assemblies of molecules exist in distributions of configuration, composition, momentum, and energy. Sometimes, this statistical character is best captured and studied by computer experiments molecular dynamics, Brownian dynamics, Stokesian dynamics, and Monte Carlo methods. Interaction potentials based on quantum mechanics, classical particle mechanics, continuum mechanics, or empiricism are specified and the evolution of the system is then followed in time by simulation of motions resulting from these direct... 

If excited molecules can rotate during the excited-state lifetime, the emitted fluorescence is partially (or totally) depolarized (Figure 5.9). The preferred orientation of emitting molecules resulting from photoselection at time zero is indeed gradually affected as a function of time by the rotational Brownian motions. From the extent of fluorescence depolarization, we can obtain information on the molecular motions, which depend on the size and the shape of molecules, and on the fluidity of their microenvironment. 

Diffusion here refers to the movement of ions and/or neutral species through the deposition bath or solution as a consequence of concentration gradients. It is primarily the result of random (Brownian) molecular motion, and it serves to produce more uniform distribution of the various component species in the bath. Depletion of ions next to the cathode will result in movement of the species from the (nearly unchanged) bulk of the bath toward the cathode. 

Kinetics is concerned with many-particle systems which require movements in space and time of individual particles. The first observations on the kinetic effect of individual molecular movements were reported by R. Brown in 1828. He observed the outward manifestation of molecular motion, now referred to as Brownian motion. The corresponding theory was first proposed in a satisfactory form in 1905 by A. Einstein. At the same time, the Polish physicist and physical chemist M. v. Smolu-chowski worked on problems of diffusion, Brownian motion (and coagulation of colloid particles) [M. v. Smoluchowski (1916)]. He is praised by later leaders in this field [S. Chandrasekhar (1943)] as a scientist whose theory of density fluctuations represents one of the most outstanding achievements in molecular physical chemistry. Further important contributions are due to Fokker, Planck, Burger, Furth, Ornstein, Uhlenbeck, Chandrasekhar, Kramers, among others. An extensive list of references can be found in [G.E. Uhlenbeck, L.S. Ornstein (1930) M.C. Wang, G.E. Uhlenbeck (1945)]. A survey of the field is found in [N. Wax, ed. (1954)]. 

Molecular motions in low molecular weight molecules are rather complex, involving different types of motion such as rotational diffusion (isotropic or anisotropic torsional oscillations or reorientations), translational diffusion and random Brownian motion. The basic NMR theory concerning relaxation phenomena (spin-spin and spin-lattice relaxation times) and molecular dynamics, was derived assuming Brownian motion by Bloembergen, Purcell and Pound (BPP theory) 46). This theory was later modified by Solomon 46) and Kubo and Tomita48 an additional theory for spin-lattice relaxation times in the rotating frame was also developed 49>. 

However, the three-component analysis becomes possible again at 100 °C, giving reduced wb and increased vn as shown in Fig. 12. It is thought that at 100 °C the micro-Brownian molecular motion has spread over the whole of the noncrystalline regions and the medium component due to the interfacial region has disappeared. 

As the temperature further rises, this sample shows a very enhanced change in the spectrum at temperatures between 35 and 40 °C. The wb begins to decrease and the wm suddenly disappears with increasing w . Thus, the spectrum at 60 °C could be well analyzed into two components, the broad and narrow. It may correspond to a two-phase structure composed of the crystalline region and a noncrystalline region with micro-Brownian molecular motion. 

In this chapter we consider dynamical solvent effects on the rate constant for chemical reactions in solution. Solvent dynamics may enhance or impede molecular motion. The effect is described by stochastic dynamics, where the influence of the solvent on the reaction dynamics is included by considering the motion along the reaction coordinate as (one-dimensional) Brownian motion. The results are as follows. 

M. Doi and S. F. Edwards, Dynamics of concentrated polymer systems. Part I. Brownian motion in the equilibrium state, J. Chem. Soc. Faraday Trans. II, 74, 1789 (1978) M. Doi and S. F. Edwards, Dynamics of concentrated polymer systems. Part 2. Molecular motion under flow, J. Chem. Soc. Faraday Trans.II, 74, 1802 (1978) M. Doi and S. F. Edwards, Dynamics of concentrated polymer systems. Part 3. The constitutive equation, J. Chem. Soc. Faraday Trans. II, 74,1818 (1978) M. Doi and S. F. Edwards, Dynamics of concentrated polymer systems. Part 4. Rheological properties, J. Chem. Soc. Faraday Trans. II, 75,38 (1979). 

High-resolution NMR in solution requires the sample to be soluble in a solvent such that the various nuclear spin interactions can be averaged or removed by molecular micro-Brownian motions. Unfortunately, elastomers used in various applications are normally crosslinked materials and therefore not soluble in any solvent. Thus, solid state NMR with magic angle-spinning technique has been used with great success in the study of cured elastomers. However, this technique demands extended instrument facilities and expertise. 

Figure 3 is a clear example of the ability of the two-dimensional fifth-order Raman response to deconvolve the intermolecular spectral density based on the degree of coupling between motions on different time scales. Although the association of the generalized time scales represented by Brownian osciallators with specific molecular motions is certainly imperfect, it is... 

University, Krak6w [i]. He described Brownian molecular motion independently from Einstein considering the collisions explicitly between a particle and the surrounding solvent molecules [ii], worked on colloids [iv-v], and obtained an expression for the rate with which two particles diffuse together (-> Smoluchowski equation (b)) [iii-v]. He also derived an equation for the limiting velocity of electroosmotic flow through a capillary (-> Smoluchowski equation (a)). 

Dynamically raised processes in the dispersion, such as Brownian molecular motion, cause variations in the intensities of the scattered light with time, which is measured by PCS. Smaller the particle, higher the fluctuations by Brownian motion. Thus, a correlation between the different intensities measured is only possible for short time intervals. In a monodisperse system following first-order kinetics, the autocorrelation function decreases rather fast. In a half logarithmic plot of the auto correlation function, the slope of the graph enables the calculation of the hydrodynamic radius by the Stokes-Einstein equation. With the commercial PCS devices the z-average is determined, which corresponds to the hydrodynamic radius. 

Gans, R. The Theory of Brownian Molecular Motion. Ann. Physik 86, 628... 

Particles are transported in an atmospheric airflow via two mechanisms diffusive transport, associated with the molecular motion of the medium, and advective transport, resulting from the bulk motion of the airflow. For particulate species, diffusive transport arises as a result of the (random) Brownian motion experienced by particles... 

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