Adsorbed layer, thickness

Rheological methods of measuring the interphase thickness have become very popular in science [50, 62-71]. Usually they use the viscosity versus concentration relationships in the form proposed by Einstein for the purpose [62-66], The factor K0 in Einstein s equation typical of particles of a given shape is evaluated from measurements of dispersion of the filler in question in a low-molecular liquid [61, 62], e.g., in transformer oil [61], Then the viscosity of a suspension of the same filler in a polymer melt or solution is determined, the value of Keff is obtained, and the adsorbed layer thickness is calculated by this formula [61,63,64] ... 

PVA and TaM -for the 88%-hydrolyzed PVA. The same dependence was found for the adsorbed layer thickness measured by viscosity and photon correlation spectroscopy. Extension of the adsorption isotherms to higher concentrations gave a second rise in surface concentration, which was attributed to multilayer adsorption and incipient phase separation at the interface. The latex particle size had no effect on the adsorption density however, the thickness of the adsorbed layer increased with increasing particle size, which was attributed to changes in the configuration of the adsorbed polymer molecules. The electrolyte stability of the bare and PVA-covered particles showed that the bare particles coagulated in the primary minimum and the PVA-covered particles flocculated in the secondary minimum and the larger particles were less stable than the smaller particles. 

Effect of PVA Molecular Weight on Adsorbed Layer Thickness. Figure 4 shows the variation of reduced viscosity with volume fraction for the bare and PVA-covered 190nm-size PS latex particles. For the bare particles, nre(j/ is independent of and the value of the Einstein coefficient is ca. 3.0. For the covered particles, rired/ t increases linearly with tp. Table IV gives the adsorbed layer thicknesses calculated from the differences in the intercepts for the bare and covered particles and determined by photon correlation spectroscopy, as well as the root-mean-square radii of gyration of the free polymer coil in solution. The agreement of the adsorbed layer thicknesses determined by two independent methods is remarkable. The increase in adsorbed layer thickness follows the same dependence on molecular weight as the adsorption density, i.e., for the fully hydrolyzed PVA s and... 

Table IV. Adsorbed layer thickness 5 and the rms radius of gyration (S2) 5...

Effect of PS Latex Particle Size on Adsorbed Layer Thickness. Figure 6 shows the variation of reduced viscosity with volume fraction for 190, 400, and HOOnm-size bare and PVA-covered PS latex particles. The viscosity variation of the different-size bare particles was the same, with an Einstein coefficient of ca. 3.0. The... 

Table V Adsorbed layer thickness 6 and the effective flat layer thickness 6eff...

The adsorbed layer thickness for the llOOnm-size particles could not be measured by photon correlation spectroscopy because of the lOOOnm upper limit of this instrument. Again, the agreement between the two methods is excellent. It is interesting that the adsorbed layer thickness increases with increasing latex particle size and that these values vary with the 0.5 power of the particle radius, i.e., where R is the particle radius. This re-... 

Approximate limits to the adsorbed layer thickness can be defined. The lower limit is about twice the radius of gyration for particles of the appropriate size. This particle size can b culated from the radius of gyration and the relationship <5aR The adsorbed layer thickness increases with increasing particle size, and the measured thicknesses are always greater than twice the radius of gyration, the difference increasing with increasing particle size. The upper limit cannot be defined at present. Moreover, these limits are conjectural and require more experimental evidence for their verification. 

Table I. Adsorbed Layer Thickness of Soluble Calf Skin Collagen on Glass as a Function of pH and Temperature, (thicknesses a7.7°C and a15°C are given in A)...

The force-distance profiles Al, A2 appear to show the relaxed, or quasi-equilibrium limit for the interaction between the mica plates bearing the PEO in the good solvent conditions of the present study. The adsorbed layer thicknesses 6 are then about half the value of D at which onset of repulsion (A curves) is first noted. 6 thus corresponds to some 3Rg for both polymers in the present investigation, a value comparable to that obtained for hydrodynamic layer thickness of PEO absorbed on latex particles in water, for similar molecular weights, from light scattering studies. 

Any fundamental study of the rheology of concentrated suspensions necessitates the use of simple systems of well-defined geometry and where the surface characteristics of the particles are well established. For that purpose well-characterized polymer particles of narrow size distribution are used in aqueous or non-aqueous systems. For interpretation of the rheological results, the inter-particle pair-potential must be well-defined and theories must be available for its calculation. The simplest system to consider is that where the pair potential may be represented by a hard sphere model. This, for example, is the case for polystyrene latex dispersions in organic solvents such as benzyl alcohol or cresol, whereby electrostatic interactions are well screened (1). Concentrated dispersions in non-polar media in which the particles are stabilized by a "built-in" stabilizer layer, may also be used, since the pair-potential can be represented by a hard-sphere interaction, where the hard sphere radius is given by the particles radius plus the adsorbed layer thickness. Systems of this type have been recently studied by Croucher and coworkers. (10,11) and Strivens (12). 

In recent years, the measurement of thick adlayers has received an increasing interest in the field of so-called polyelectrolyte multilayer films. These films sometimes have a thickness of several micrometers. Such large thicknesses are obviously not easily monitored using conventional waveguide sensors because of the limited penetration depth into the adlayer. Simply, waveguide sensors loses their sensitivity when the adsorbed layer thickness exceeds 2 3 times the penetration depth of the evanescent field and cannot be used to monitor films thicker than 350 nm12. 

Busscher, H. J., H. M. Uyen, G. A. M. ICip, and J. Arends. 1987. Adsorption of aminefluorides onto glass and the determination of surface free energy, zeta potential and adsorbed layer thickness. Colloids and Surfaces 22 161-69. 

In the strong adsorption limit (X/b 1) the expression of the adsorbed layer thickness A, corresponding to the size of the largest loops or tails in the layer, reads in the mean field theory ... 

In order to be able to include a steric contribution in the interparticle energy calculation, an estimate of the adsorbed layer thickness is required. This is very difficult to access experimentally probably the only technique which might be able to provide an estimate is small-angle neutron scattering which was beyond the scope of this work. As a result, a theoretical estimation of the thickness was made, based on a few key observations. This is described below. 

Dissolved polymer molecules can be adsorbed by polymer particles via electrostatic attractive force or hydrophobic interaction. When polyelectrolyte is adsorbed on an opposite-charge particle, the polymer molecules usually have a loop-and-tail conformation and, as a result, inversion of charge occurs. For example, sulfatecarrying particles behave as cationic ones after they adsorb poly(lysine). Then poly(-styrene sulfonate) can be adsorbed on such cationic particles and reinvert the charge of particles to anionic (14). Okubo et al. pointed out that the alternate adsorption of cationic and anionic polymers formed a piled layer of polyelectrolytes on the particle, but the increment of adsorbed layer thickness was much less than expected. This was attributed to synchronized piling of two oppositely charged polyelectrolytes (15). 

On nonporous surfaces it has been shown that when W /W is plotted versus P/Po the data all approximately fit a common type II curve above a relative pressure of 0.3. This implies that when WJW = 3, for example, the adsorbed layer thickness t will be 10.62 A regardless of the adsorbent. The common curve is described closely by the Halsey equation which for nitrogen can be written as... 

Assume that a surface is covered by adsorbates with a distribution of layer thicknesses shown schematically in Fig. 11.6. A given surface site might be covered by 0, 1, or m layers of adsorbed molecules, with the adsorbed layer thickness on adjacent sites randomly distributed. An adsorption/desorption equilibrium will be assumed. 

It is clear that as [A] approaches [A]sat, x approaches 1, and the surface-adsorbed layer thickness Eq. 11.60 goes to infinity that is, there is an infinite reservoir of liquid in equilibrium with the vapor. This is the desired limiting behavior for the model. 

Surface layers (adsorbed, solvated, ionic) are of considerable importance in controlling the stability and rheological properties of colloidal systems. Sedimentation methods have proven effective in the measurement of adsorbed layer thickness using equations similar to Equation 1 when the density of the layer could be estimated ( 7,8). The equation can be considerably simplified if the density... 

Another interesting aspect is the conformational changes when the chains are under different concentration conditions isolated dilute or semidilute or melt. The adsorbed layer thickness increases with increasing concentration, mainly due to the contribution of tails. Figure 3.31 shows this behaviour. 

A reduction in poly electrolyte charge density to 10% results in further increase in adsorbed layer thickness. The steep steric repulsion is now... 

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