Volume fraction adsorption onto

To illustrate how the effect of the adsorption on the modulus of the filled gel may be modelled we consider the interaction of the same HEUR polymer as described above but in this case filled with poly(ethylmetha-crylate) latex particles. In this case the particle surface is not so hydrophobic but adsorption of the poly (ethylene oxide) backbone is possible. Note that if a terminal hydrophobe of a chain is detached from a micellar cluster and is adsorbed onto the surface, there is no net change in the number of network links and hence the only change in modulus would be due to the volume fraction of the filler. It is only if the backbone is adsorbed that an increase in the number density of network links is produced. As the particles are relatively large compared to the chain dimensions, each adsorption site leads to one additional link. The situation is shown schematically in Figure 2.13. If the number density of additional network links is JVL, we may now write the relative modulus Gr — G/Gf as... 

Despite many years of interest in the phase distribution of POPs, few predictive models are available. A Langmuir-type relationship, which Junge (1977) first proposed and Pankow (1987) later reviewed and critically evaluated, is the most popular model for estimating adsorption onto aerosols. The Junge-Pankow equation relates the fraction of particulate POPs (c >) to the saturation liquid-phase vapor pressure of the compound ( P Pa) and the surface area of particles per unit volume of air (8, cm2 aerosol / cm3 air). 

For adsorption onto colloidal particles two approaches are possible. The first is to determine vlscometrlcally the increase in the effective particle volume fraction upon adsorption, and the second is to measure the decrease in the particle diffusion coefficient. 

SEC technique, in which polymers are separated in an SEC column using a good solvent and fractions are then switched into a second SEC column using a poorer solvent as the mobile phase. If compositional heterogeneity is present, components that have similar molecular hydrodynamic volumes in the good solvent may have diflFerent hydrodynamic volumes in the poorer solvent and thus will be size separated in the second column. Additionally, adsorption onto the packing may occur in the second dimension, giving rise to selective retention of components. 

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). 

The adsorption of a non-ionic surfactant onto latex particles was studied by small-angle X-ray scattering(SAXS). The analysis of the process of adsorption by S AXS was examined in detail. It was shown that SAXS allowed monitoring of the gradual build-up of the surface layer with increasing amount of added surfactant. SAXS also allowed the radial volume fraction of the hydrophilic tails of the surfactant to be obtained. Possible limitations of this method of analysis are discussed. 21 refs. (7th Dresden Polymer Discussion, Characterization of Sorption Phenomena from Solution to the Surface, Meissen, Germany, April 1999)... 

The same concepts apply to column chromatography, where the stationary phase is normally small particles of silica, Si02, or alumina, A1,0 . These substances are not very reactive and have specially prepared surfaces to increase their adsorption ability. The column is saturated with solvent, and a small volume of solution containing the solutes is poured onto the top. As soon as it has soaked in, more solvent is added. The solutes travel slowly down the column and are eluted (removed as fractions) at the bottom (Fig. 2). If the mobile phase is less polar than the stationary phase, the less polar solutes will be eluted first and the more polar ones last. 

For example, a 10-mL aliquot can be loaded onto a 1-mL column bed, with collection of two 5-mL spent fractions. The column is then washed with water (2 mL) and bound material eluted see Subheading 4.5.). The purpose of collecting two or more spent fractions is to monitor for sample breakthrough. An important factor in resin selection is loading capacity. One may wish to load as much broth as possible per unit volume of resin in order to render the isolation process practical. This becomes especially important when scaling up to larger fermentation processes. A well-chosen resin can allow for very selective adsorption/elution of the desired compound and for an efficient process. 

If the gas around the adsorbent solid occupies some fraction e of a volume V, and if this volume contains an adsorbing gas i, then the rate of adsorption of the gas onto the adsorbent... 

The formation of floes due to bridging flocculation has a dramatic effect on sedimentation rates, sediment volumes and on the ease of filtration. Effective flocculation may occur over a narrow range of polymer concentration because too little polymer will not permit floe formation, while too much polymer adsorption will eliminate the fraction of free particle surface needed for the bridging action (i.e. the polymer molecules will adsorb onto single particles in preference to bridging several particles). It has been proposed that the optimum degree of bridging flocculation may occur when particle surfaces are half covered with adsorbed polymer. 

Before casting Equation 7.1 in dimensionless form, the inclusion of terms to describe adsorption and velocity enhancement of the transported species will be considered. These phenomena are, of course, more appropriate to polymer transport than tracer transport but the form of the equation is very similar. The velocity enhancement referred to concerns the effect of the excluded volume or inaccessible pore volume effect which the polymer shows (Chauveteau, 1982, Dawson and Lantz, 1972) and which is discussed in more detail below. However, the physical observation on polymer transport is that there appears to be a fraction of the pore space—either the very small pores (Dawson and Lantz, 1972) or regions close to the wall of the porous medium (Chauveteau, 1982)—which is inaccessible to polymer transport. This leads to an enhancement of the average velocity of the polymer through the porous medium. When there is both adsorption of transported polymer onto the rock matrix and a fraction of the pore volume is apparently inaccessible to the polymer, Equation 7.1 must be extended to ... 

When a diffusing solute partitions or adsorbs onto a solid matrix, we can often use standard solutions for nonsorbing solids to follow the course of adsorption by suitably modifying one of the solution parameters. For the case of adsorption by spherical particles from a well-stirred solution of limited volume, for example, the parameter Soi n/ spheres io Figure 4.4 is replaced by Vsoi-n/f Vspheres/ where K is the partition coefficient or Henry s constant. Assume the following parameter values K = 10, Vgoi-n/V spheres = 10, D = 10 cm /s, R = 0.46 cm. Whaf is the fractional saturation of the adsorbent after 1 h ... 

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