Colloidal systems Brownian motion

Short-time Brownian motion was simulated and compared with experiments [108]. The structural evolution and dynamics [109] and the translational and bond-orientational order [110] were simulated with Brownian dynamics (BD) for dense binary colloidal mixtures. The short-time dynamics was investigated through the velocity autocorrelation function [111] and an algebraic decay of velocity fluctuation in a confined liquid was found [112]. Dissipative particle dynamics [113] is an attempt to bridge the gap between atomistic and mesoscopic simulation. Colloidal adsorption was simulated with BD [114]. The hydrodynamic forces, usually friction forces, are found to be able to enhance the self-diffusion of colloidal particles [115]. A novel MC approach to the dynamics of fluids was proposed in Ref. 116. Spinodal decomposition [117] in binary fluids was simulated. BD simulations for hard spherocylinders in the isotropic [118] and in the nematic phase [119] were done. A two-site Yukawa system [120] was studied with... 

Other than hydrodynamic flows one must also take into account Brownian motion.Brownian motion is observed as the random displacement of colloids caused by thermal energy. Batchelor deemed this force as a microhydrodynamic force because only small objects with a low Reynolds number exhibit Brownian motion. Low Reynolds numbers are present in microhydrod)uiamic systems because inertia forces are small with respect to viscous forces. 

One type of colloidal system has been chosen for discussion, a system in which the solid metal phase has been shrank in three dimensions to give small solid particles in Brownian motion in a solution. Such a colloidal suspension consisting of discrete, separate particles immersed in a continuous phase is known as a sol. One can also have a case where only two dimensions (e.g., the height z and breadth y of a cube) are shrank to colloidal dimensions. The result is long spaghettihke particles dispersed in solution—macromolecular solutions. 

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)]. 

As discussed in Chapters 1-7, diffusion, Brownian motion, sedimentation, electrophoresis, osmosis, rheology, mechanics, interfacial energetics, and optical and electrical properties are among the general physical properties and phenomena that are primarily important in colloidal systems [12,13,26,57,58], Chemical reactivity and adsorption often play important, if not dominant, roles. Any physical chemical feature may ultimately govern a specific industrial process and determine final product characteristics, and any colloidal dispersions involved may be deemed either desirable or undesirable based on their unique physical chemical properties. Chapters 9-16 will provide some examples. 

These trajectory methods have been used by numerous researchers to further investigate the influence of hydrodynamic forces, in combination with other colloidal forces, on collision rates and efficiencies. Han and Lawler [3] continued the work of Adler [4] by considering the role of hydrodynamics in hindering collisions between unequal-size spheres in Brownian motion and differential settling (with van der Waals attraction but without electrostatic repulsion). The results indicate the potential significance of these interactions on collision efficiencies that can be expected in experimental systems. For example, collision efficiency for Brownian motion will vary between 0.4 and 1.0, depending on particle absolute size and the size ratio of the two interacting particles. For differential... 

For monodisperse or unimodal dispersion systems (emulsions or suspensions), some literature (28-30) indicates that the relative viscosity is independent of the particle size. These results are applicable as long as the hydrodynamic forces are dominant. In other words, forces due to the presence of an electrical double layer or a steric barrier (due to the adsorption of macromolecules onto the surface of the particles) are negligible. In general the hydrodynamic forces are dominant (hard-sphere interaction) when the solid particles are relatively large (diameter >10 (xm). For particles with diameters less than 1 (xm, the colloidal surface forces and Brownian motion can be dominant, and the viscosity of a unimodal dispersion is no longer a unique function of the solids volume fraction (30). 

A colloidal system represents a multiphase (heterogeneous) system, in which at least one of the phases exists in the form of very small particles typically smaller than 1 pm but still much larger than the molecules. Such particles are related to phenomena like Brownian motion, diffusion, and osmosis. The terms microheterogeneous system and disperse system (dispersion) are more general because they also include bicontinuous systems (in which none of the phases is split into separate particles) and systems containing larger, non-Brownian, particles. The term dispersion is often used as a synonym of colloidal system. 

Colloidal particles in a dispersion medium are always subjected to Brownian motion with frequent collisions between them. Stability and other characteristics of dispersion are thus determined by the nature of the interactions between the particles during such collisions. When attractive forces dominate, the particles will aggregate and the dispersion may destabilize. When repulsive forces dominate, the system will remain in a dispersed state. 

Since the particles have colloidal dimensions, they will be colliding with one another due to the Brownian motion. The system can remain as individual particles only if some mechanism prevents the collisions from resulting in a permanent aggregation. If the particles have the same charge (either positive or negative) they will repel one another. This mechanism of colloidal stabilization is referred to as electrostatic stabilization. 

The sedimentation method belongs to the classical methods of characterization of the colloidal properties of disperse systems. These methods can be used for the analysis of colloidal solutions with size of colloidal particles between 1 and 100 micrometer. The analysis of solutions with smaller particles leads to relatively high errors as a result of Brownian motion. 

In free disperse systems, in particular those with low concentration of dispersed phase, the nature of colloid stability and conditions under which the collapse occurs, are to a great extent dependent on thermal motion of dispersed particles, which may contribute to both stability and destabilization. For example, the necessary condition for sedimentation stability is sufficiently small particle size, so that the tendency of particles to distribute within the entire volume of disperse system due to the Brownian motion (an increase in entropy) would not be affected by gravity. As a quantitative criterion for the presence of noticeable amount of dispersed particles in equilibrium with a sediment one, for instance, may use the... 

The range of disperse systems of interest in colloid science is very broad. These include coarse disperse systems consisting of particles with sizes of 1 pm or larger (surface area S < 1 m2/g), and fine disperse systems, including ultramicroheterogeneous colloidal systems with fine particles, down to 1 nm in diameter, and with surface areas reaching 1000 m2/g ( nanosystems ). The fine disperse systems may be both structured (i.e. systems in which particles form a continuous three-dimensional network, referred to as the disperse structure), and free disperse, or unstructured (systems in which particles are separated from each other by the dispersion medium and take part in Brownian motion and diffusion). 

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