Brownian motional narrowing

Polymerization in microemulsions allows the synthesis of ultrafine latex particles in the size range of 5 to 50 nm with a narrow size distribution [33], The deposition of an ordered monolayer of such spheres is known to be increasingly difficult as the diameter of such particles decreases [34], Vigorous Brownian motion and capillary effects create a state of disorder in the system that is difficult... 

Narrowing of NMR lines has been observed in colloidal suspensions of ultrafine particles, presumably by Brownian motion. A suggestion related to this principle is to take small solid particles into a liquid medium and induce sufficient reorientational motion of these particles to produce narrowing (Satoh and Kimura 1990). Ultrasound induces translational motion and collisions of the particles produce rotation. This sonically induced narrowing has been observed for Al in aluminium sulphate, with the advantage that no spinning sidebands were observed (Homer et al. 1991). The experiment depends on the frequency and the power of the ultrasound and the liquid medium. Although the first reports of this approach appeared in 1989 there have been few developments in this field. 

We consider ditTu.sion in one dimension alone. Suppose that a cloud of line panicles, all the same size, is released overa narrow region luround the plane corresponding io.r = 0. The concentration everywhere else in the gas is zero. With increasing lime, the panicles diffuse as a result of the Brownian motion. The spread around the plane. v = 0 is symmetrical (Fig. 2.2) in the absence of an external force field acting on the particles. 

The factor of appears in equation (21-19) because molecules confined to narrow channels probably collide with the walls of a tube, for example, that are separated by 2(raverage), and the dimensionality of the system is 3 for random Brownian motion in three dimensions. In many cases, the factor of /3 in (21-19) is replaced by the kinetic theory prediction of y/S/jt when Knudsen is based on the average speed of the gas molecules (i.e., (u, ) = SRT/ttMW,). Now the Knudsen diffusion coefficient is given by 92% of (21-19) (see Moore, 1972, p. 124 Bird et al., 2002, pp. 23, 525 Dullien, 1992, p. 293 and Smith, 1970, p. 405). If the average pore size is expressed in angstroms and the temperature... 

Major relaxations are characterized by a decrease in modulus over a narrow temperature range. Their presence is ascribed to the micro-Brownian motion of the amorphous polyol segments. Relaxation temperatures and magnitudes of tan d are given in Table 3.18a. The a... 

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