Diffusion of particles in solution

Molecules in solution are in constant motion. The trajectory of the center of mass of a macromolecule in solution can be described in terms of a vector, If the origin of coordinates is chosen as the location of the particle at f = 0, the squared displacement is given hyR R. If the trajectory is followed many times for some elapsed time x, the mean-squared displacement is found to be proportional to the elapsed time. The Brownian diffusion law is 

The solvent is treated as a viscous continuum of viscosity T) and temperature T. A particle in such a solution is subject to three types of forces  

Particle motion is resisted by a viscous force equal to -t v, where v is the particle velocity relative to the solvent, and is called the 

External forces such as gravity or electric or magnetic fields. 

The trajectory of a particle can then be calculated in terms of the Lan-gevin equation  

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To make the significance of the NMR technique as an experimental tool in surfactant science more apparent, it is important to compare the strengths and the weaknesses of the NMR relaxation technique in relation to other experimental techniques. In comparison with other experimental techniques to study, for example, microemulsion droplet size, the NMR relaxation technique has two major advantages, both of which are associated with the fact that it is reorientational motions that are measured. One is that the relaxation rate, i.e., R2, is sensitive to small variations in micellar size. For example, in the case of a sphere, the rotational correlation time is proportional to the cube of the radius. This can be compared with the translational self-diffusion coefficient, which varies linearly with the radius. The second, and perhaps the most important, advantage is the fact that the rotational diffusion of particles in solution is essentially independent of interparticle interactions (electrostatic and hydrodynamic). This is in contrast to most other techniques available to study surfactant systems or colloidal systems in general, such as viscosity, collective and self-diffusion, and scattered light intensity. A weakness of the NMR relaxation approach to aggregate size determinations, compared with form factor determinations, would be the difficulties in absolute calibration, since the transformation from information on dynamics to information on structure must be performed by means of a motional model. 

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