Colloidal particles Brownian motion

Smoluhovsky, M. Three reports on Brownian molecular motion and concretion of colloidal particles Brownian motion. M ONTl. 1936b, 332-417, (in Russian). 

The invention of the ultramicroscope by Siedentopf and ZsigmoNUy in 1903 placed the fact that gold sols contain particles the siae of which depended on the method of preparation beyond all doubt When soon after this (1908), thanks to the investigations of Perrin the si2 e of molecules and atoms became known and indeed in a way which illustrated continuous transitions between molecules and larger particles (Brownian motion) the character of colloids as a dispersion intermediate between molecular dispersion and that of coarse suspensions was generally accepted. 

Sols are dispersions of colloidal particles in a Hquid. Sol particles are typically small enough to remain suspended in a Hquid by Brownian motion. 

Perikinetic motion of small particles (known as colloids ) in a liquid is easily observed under the optical microscope or in a shaft of sunlight through a dusty room - the particles moving in a somewhat jerky and chaotic manner known as the random walk caused by particle bombardment by the fluid molecules reflecting their thermal energy. Einstein propounded the essential physics of perikinetic or Brownian motion (Furth, 1956). Brownian motion is stochastic in the sense that any earlier movements do not affect each successive displacement. This is thus a type of Markov process and the trajectory is an archetypal fractal object of dimension 2 (Mandlebroot, 1982). 

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... 

Many precipitates, such as Fe(OH)3, form initially as colloidal suspensions. The tiny particles are kept from settling out by Brownian motion, the motion of small particles resulting from constant bombardment by solvent molecules. The sol is further stabilized by the adsorption of ions on the surfaces of the particles. The ions attract a layer of water molecules that prevents the particles from adhering to one another. 

Brownian motion The ceaseless jittering motion of colloidal particles caused by the impact of solvent molecules. 

Hydrophobic colloidal particles move readily in the liqnid phase under the effect of thermal motion of the solvent molelcnles (in this case the motion is called Brownian) or under the effect of an external electric field. The surfaces of such particles as a rule are charged (for the same reasons for which the snrfaces of larger metal and insnlator particles in contact with a solution are charged). As a result, an EDL is formed and a certain valne of the zeta potential developed. 

Friedlander, S. K., and Wang, C. S., The Self Preserving Particle Size Distribution for Coagulation by Brownian Motion, J. Colloid Interface Sci., 22 126-132(1966)... 

For small colloidal particles, which are subject to random Brownian motion, a stochastic approach is more appropriate. These methods are based on the formulation and solution of the diffusion equation in a force field, in the presence of convection... 

The main disadvantage of the perfect sink model is that it can only be applied for irreversible deposition of particles the reversible adsorption of colloidal particles is outside the scope of this approach. Dahneke [95] has studied the resuspension of particles that are attached to surfaces. The escape of particles is a consequence of their random thermal (Brownian) motion. To this avail he used the one-dimensional Fokker-Planck equation... 

Photon correlation spectroscopy (PCS) has been used extensively for the sizing of submicrometer particles and is now the accepted technique in most sizing determinations. PCS is based on the Brownian motion that colloidal particles undergo, where they are in constant, random motion due to the bombardment of solvent (or gas) molecules surrounding them. The time dependence of the fluctuations in intensity of scattered light from particles undergoing Brownian motion is a function of the size of the particles. Smaller particles move more rapidly than larger ones and the amount of movement is defined by the diffusion coefficient or translational diffusion coefficient, which can be related to size by the Stokes-Einstein equation, as described by... 

There are some very special characteristics that must be considered as regards colloidal particle behavior size and shape, surface area, and surface charge density. The Brownian motion of particles is a much-studied field. The fractal nature of surface roughness has recently been shown to be of importance (Birdi, 1993). Recent applications have been reported where nanocolloids have been employed. Therefore, some terms are needed to be defined at this stage. The definitions generally employed are as follows. Surface is a term used when one considers the dividing phase between... 

Once nanoparticles have been formed, whether in an early state of growth or in a more or less final size, their fate depends on the forces between the individual particles and between particles and solid surfaces in the solution. While particles initially approach each other by transport in solution due to Brownian motion, convection, or sedimentation, when close enough, interparticle forces will determine their final state. If the dominant forces are repulsive, the particles will remain separate in colloidal form. If attractive, they will aggregate and eventually precipitate. In addition, they may adsorb onto a solid surface (the substrate or the walls of the vessel in which the reaction is carried out). For CD, both attractive particle-sur-... 

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. 

The Peclet number compares the effect of imposed shear (known as the convective effect) with the effect of diffusion of the particles. The imposed shear has the effect of altering the local distribution of the particles, whereas the diffusion (or Brownian motion) of the particles tries to restore the equilibrium structure. In a quiescent colloidal dispersion the particles move continuously in a random manner due to Brownian motion. The thermal motion establishes an equilibrium statistical distribution that depends on the volume fraction and interparticle potentials. Using the Einstein-Smoluchowski relation for the time scale of the motion, with the Stokes-Einstein equation for the diffusion coefficient, one can write the time taken for a particle to diffuse a distance equal to its radius R, as... 

Colloids are particles with diameters of 1-500 nm. They are larger than molecules but too small to precipitate. They remain in solution indefinitely, suspended by the Brownian motion (random movement) of solvent molecules.2... 

TJhe aggregation of particles in a colloidal dispersion proceeds in two distinct reaction steps. Particle transport leads to collisions between suspended colloids, and particle destabilization causes permanent contact between particles upon collision. Consequently, the rate of agglomeration is the product of the collision frequency as determined by conditions of the transport and the collision efficiency factor, the fraction of collisions leading to permanent contact, which is determined by conditions of the destabilization step (2). Particle transport occurs either by Brownian motion (perikinetic) or because of velocity gradients in the suspending medium (orthokinetic). Transport is characterized by physical parame-... 

Perikinetic Coagulation. If colloidal particles are of such dimensions that they are subject to thermal motion, the transport of these particles is accomplished by this Brownian motion. Collisions occur when one particle enters the sphere of influence of another particle. The coagulation rate measuring the decrease in the concentration of particles with time, N (in numbers/ml.), of a nearly monodisperse suspension corresponds under these conditions to the rate law for a second order reaction (15) ... 

The equation derived by Troelstra and Kruyt is only valid for coagulating dispersions of colloids smaller than a certain maximum diameter given by the Rayleigh condition, d 0.10 A0. Equation 4 applies in cases where particles are transported solely by Brownian motion. Furthermore, the kinetic model (Equations 2 and 3) has been derived under the assumption that the collision efficiency factor does not change with time. In the case of some partially destabilized dispersions one observes a decrease in the collision efficiency factor with time which presumably results from the increase of a certain energy barrier as the size of the agglomerates becomes larger. 

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