Brownian motion adsorption

The two contrasting approaches, the macroscopic viewpoint which describes the bulk concentration behavior (last chapter) versus the microscopic viewpoint dealing with molecular statistics (this chapter), are not unique to chromatography. Both approaches offer their own special insights in the study of reaction rates, diffusion (Brownian motion), adsorption, entropy, and other physicochemical phenomena [2]. 

Behavior. Diffusion, Brownian motion, electrophoresis, osmosis, rheology, mechanics, and optical and electrical properties are among the general physical properties and phenomena that are primarily important in coUoidal systems (21,24—27). Of course, chemical reactivity and adsorption often play important, if not dominant, roles. Any physical and chemical feature may ultimately govern a specific industrial process and determine final product characteristics. 

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. 

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... 

Studies on orthokinetic flocculation (shear flow dominating over Brownian motion) show a more ambiguous picture. Both rate increases (9,10) and decreases (11,12) compared with orthokinetic coagulation have been observed. Gregory (12) treated polymer adsorption as a collision process and used Smoluchowski theory to predict that the adsorption step may become rate limiting in orthokinetic flocculation. Qualitative evidence to this effect was found for flocculation of polystyrene latex, particle diameter 1.68 pm, in laminar tube flow. Furthermore, pretreatment of half of the latex with polymer resulted in collision efficiencies that were more than twice as high as for coagulation. 

Particle collision frequency due to Brownian motion was estimated to be less than 1% of the collision frequency due to shear. The effects of Brownian motion could therefore be neglected in the flocculation rate calculations. However, for the smallest molecular size, radius of gyration 14 nm (see Table I), the effect of Brownian motion on the particle-polymer collision efficiency was of the same order of magnitude as the effect of shear. These two contributions were assumed to be additive in the adsorption rate calculations. Additivity is not fundamentally justified (23) but can be used as an interpolating... 

The polymer radius has to be larger than 80% of the particle radius to avoid adsorption limitation under orthokinetic conditions. As a rule of thumb a particle diameter of about 1 pm marks the transition between perikinetic and orthokinetic coagulation (and flocculation). The effective size of a polymeric flocculant must clearly be very large to avoid adsorption limitation. However, if the polymer is sufficiently small, the Brownian diffusion rate may be fast enough to prevent adsorption limitation. For example, if the particle radius is 0.535 pm and the shear rate is 1800 s-, then tAp due to Brownian motion will be shorter than t 0 for r < 0.001, i.e., for a polymer with a... 

Because polymer adsorption is effectively irreversible, and because adsorption and floe growth occur simultaneously, flocculation is a non-equilibrium process. As a result, performance is largely determined by the kinetics of adsorption and aggregation. Both of these can be regarded as collision processes involving solid particles and polymer molecules. In each case, collisions can arise due to either Brownian motion or agitation of the suspension. The collision frequency v between particles and polymer molecules can be estimated from °... 

Figure 2 Relative adsorption rates due to collisions resulting from Brownian motion and mechanical agitation. The lines represent conditions where the rates are equal. Agitation dominates to the right of the lines...

The second mechanism is capture by Brownian diffusion, which is more of a factor for smaller particles. Small particles are easily carried along by the moving fluid. However, because the particles are small, they are subject to random Brownian motion that periodically brings them into contact with the pore walls. When this happens, capture by surface adsorption occurs. 

In filtration of gas-borne aerosol particles by microfiltration membranes, capture by adsorption is usually far more important than capture by sieving. This leads to the paradoxical result that the most penetrating particle may not be the smallest one. This is because capture by inertial interception is most efficient for larger particles, whereas capture by Brownian motion is most efficient for smaller particles. As a result the most penetrating particle has an intermediate diameter, as shown in Figure 2.35 [55,56],... 

Suppose that the interaction forces establish an energy barrier that retards the motion of particles both toward and away from the collector. If this barrier reduces the adsorption and desorption rates significantly, particles near the primary minimum will have time to achieve a balance between the interaction forces and Brownian motion, before their population changes. Integration of Equation (6) with j 0 and D = mkT leads Lo a Boltzmann distribution... 

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). 

In the following we want to discuss, first, experiments on the motility of brush molecules based on stimulated desorption/adsorption. The stimulation is effected by the tip of a scanning force microscope as the molecules are probed. Essential questions are whether this can cause mobility different from Brownian motion but also different from dragging of the molecules. For comparison, we summarize results on the dragged motion of a A-phage DNA through an entangled solution and the Brownian motion of DNA molecules adsorbed on a fluid lipid membrane. 

FIGURE 5.1 Electric double layer in the vicinity of an adsorption layer of ionic surfactant, (a) The diffuse layer contains free ions involved in Brownian motion, whereas the Stem layer consists of adsorbed (bonnd) counterions, (b) Near the charged snrface there is an accnmnlation of counterions and a depletion of coions. 

The surface excess can be defined in various ways. Actually, there is no true dividing plane, but rather an AW interface that is not sharp, since molecules have a finite size and moreover exhibit Brownian motion. Flence the interface extends over a layer of some molecular diameters. In the derivation of Eq. (10.2), the position of the dividing plane has been chosen so that the surface excess of the solvent is zero. In Figure 10.5 the concentration of the solute is depicted as a function of the distance from the dividing plane (z). In Figure 10.5a, there is no adsorption the two hatched areas on either side of the dividing plane are equal. (Because of the definition... 

Mobile ions of the Gouy layer are distributed under the influence of Brownian motion forces and electrostatic field of the interface intrinsic charge. Brownian motion forces are distributed uniformly and the forces of electrostatic field increase toward the charged surface, according to Simeon Denis Poisson (1781-1840) equation. In the description of adsorption-desorption processes on a flat surface it is possible to consider a xmi-form field only along the x coordinate. In this case the Poisson equation has the format ... 

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