Colloidal forces scaling

The formation of complexes is not restricted to mixtures of polyectrolytes and surfactants of opposite charge. Neutral polymers and ionic surfactants can also form bulk and/or surface complexes. Philip et al. [74] have studied the colloidal forces in presence of neutral polymer/ionic surfactant mixtures in the case where both species can adsorb at the interface of oil droplets dispersed in an aqueous phase. The molecules used in their studies are a neutral PVA-Vac copolymer (vinyl alcohol [88%] and vinyl acetate [12%]), with average molecular weight M = 155000 g/mol, and ionic surfactants such as SDS. The force measurements were performed using MCT. The force profiles were always roughly linear in semilogarithmic scale and were fitted by a simple exponential function ... 

While in the case of noninteracting dispersions one needed to consider only the effect of the particle concentration, in interacting dispersions one needs to consider the time over which the flow behavior is observed and its magnitude relative to the time scales over which either shear or colloidal forces alter the local structure of the dispersions. What the flow behavior is, which interaction effects dominate the behavior, and how they do depend on the competing influences of the applied shear and interaction effects. In this section, we outline some of the important parameters one can formulate to judge the relative effects of various colloidal interactions and the physical significance of those parameters. 

The van der Waals forces scale up from atomic distances to colloidal distances undiminished. How the molecular forces scale up in the case of large objects, expressions for such forces, definition of the Hamaker constant, and theories based on bulk material properties follow in Sections 10.5-10.7. 

We have also to say a few words about a smeared out analogue utilized in our consideration to represent the surface charge distribution. There was an indication in the literature that the image interaction within this adsorption layer may influence the interaction on a macroscopic scale, i.e., which is being commensurate with the range of colloidal forces [29]. However, later results... 

We group the forces that control the suspension rheology into two main categories colloidal forces and viscous forces. The colloidal forces include Brownian diffusion forces and the surface forces of electrostatic repulsion and van der Waals attraction. In order to define the dimensionless scaling parameters that characterize the relative magnitude of these forces we assume the particles are separated by a distance of the order of the particle radius a, which is in turn assumed to be close to the smallest particle separation... 

In suspensions, it is common to consider particles whose sizes range down to the submicron scale, where Brownian motion and colloidal forces have pronounced effects (Russel et al. 1991). The influence of Brownian motion relative to shear flow is captured through a P clet number given by Pe = ( fl )/Do = (67tTioy )/fcT, where Do = kT/ 6ny Qa) is the Stokes-Einstein diffusion coefficient, k is Boltzmann s constant, and T is the temperature. The first form shows that Pe may be interpreted as a ratio of the hydrodynamic diffusion scaling with the shear rate and particle size ya ) as well as a dimensionless function of the volume fraction not shown. It is more common, however, to interpret Pe as the ratio of a diffusive timescale u IDq, relative to the flow timescale given by When Pe = 0, a Brownian suspension will approach a true equilibrium state through its thermal motions. Interparticle forces of many sorts are possible in a liquid medium. 

The possible relevance of this quadrupole-quadrupole force at colloidal length scales was advanced in references [9,46,47]. As emphasized in reference [9], the natural surface roughness in the nanometer scale of a micrometer-sized spherical particle could conceivably cause a force of this kind. It was also proposed as an explanation of the structures observed experimentally [47] in 2D colloids of nonspherical micrometer particles at a fluid interface. This motivated the theoretical investigation of the anisotropic capillary forces The main difficulty lies in the determination of the capillary charges in terms of given properties of the particles (e.g., wettability and shape). Different simplifications were applied the contact line is approximated by a circle [48-50] or by an expansion in small eccentricity [45] highly elongated shapes are dealt with numerically [51]. 

The methodology discussed previously can be applied to the study of colloidal suspensions where a number of different molecular forces and hydrodynamic effects come into play to determine the dynamics. As an illustration, we briefly describe one example of an MPC simulation of a colloidal suspension of claylike particles where comparisons between simulation and experiment have been made [42, 60]. Experiments were carried out on a suspension of AI2O3 particles. For this system electrostatic repulsive and van der Waals attractive forces are important, as are lubrication and contact forces. All of these forces were included in the simulations. A mapping of the MPC simulation parameters onto the space and time scales of the real system is given in Hecht et al. [42], The calculations were carried out with an imposed shear field. 

J. T. Padding and A. A. Louis, Hydrodynamic interactions and Brownian forces in colloidal suspensions coarse-graining over time and length scales, Phys. Rev. E 74, 031402 (2006). 

The top-down approach involves size reduction by the application of three main types of force — compression, impact and shear. In the case of colloids, the small entities produced are subsequently kinetically stabilized against coalescence with the assistance of ingredients such as emulsifiers and stabilizers (Dickinson, 2003a). In this approach the ultimate particle size is dependent on factors such as the number of passes through the device (microfluidization), the time of emulsification (ultrasonics), the energy dissipation rate (homogenization pressure or shear-rate), the type and pore size of any membranes, the concentrations of emulsifiers and stabilizers, the dispersed phase volume fraction, the charge on the particles, and so on. To date, the top-down approach is the one that has been mainly involved in commercial scale production of nanomaterials. For example, the approach has been used to produce submicron liposomes for the delivery of ferrous sulfate, ascorbic acid, and other poorly absorbed hydrophilic compounds (Vuillemard, 1991 ... 

Leong, Y.K., Scales, P.J., Healy, T.W., Boger, D.V. (1995). Interparticle forces arising from adsorbed polyelectrolytes in colloidal suspensions. Colloids and Surfaces A Physicochemical and Engineering Aspects, 95, 43-52. 

The attractions of interest in colloid stability usually arise from the van der Waals forces, and we see below that they are scaled-up versions of the same intermolecular attractions discussed in the following section and that contribute to the nonideality and ultimately liquefaction of gases. In view of Figure 10.1a, we are interested in both the magnitude and the distance dependence of these attractive forces. 

ULTRAFILTRATION. Ultrafiltration is a pressure-driven filtration separation occurring on a molecular scale. See also Dialysis Filtration Hollow-Fiber Membranes Membrane Separations Technology and Reverse Osmosis. Typically, a liquid including small dissolved molecules is forced through a porous membrane. Large dissolved molecules, colloids, and suspended solids that cannot pass through the pores are retained,... 

In this chapter the thermal motion of dissolved macromolecules and dispersed colloidal particles will be considered, as will their motion under the influence of gravitational and centrifugal fields. Thermal motion manifests itself on the microscopic scale in the form of Brownian motion, and on the macroscopic scale in the forms of diffusion and osmosis. Gravity (or a centrifugal field) provides the driving force in sedimentation. Among the techniques for determining molecular or particle size and shape are those which involve the measurement of these simple properties. 

Abstract In this paper we report on AFM force spectroscopy measurements on hollow polymeric spheres of colloidal dimensions made from polyelectrolyte multilayers of polyal-lylamine and polystyrenesulfonate in water. We find that the shells show a linear force-deformation characteristic for deformations of the order of the shell wall thickness. This experimental outcome is discussed in terms of analytical results of continuum mechanics, in particular the scaling behaviour of the shell spring constant with wall thickness, shell radius and speed of the deformation is analysed. The experimental results agree well with the predictions of Reissner for thin shells and allow... 

As a result, the image forces within the adsorption layer have no influence on the colloidal interaction on a nanometer scale. However, there can be some effect due to discreteness of the surface charge if particles approach each other closely. 

These experiments are an attempt to imitate, on a scale large enough to be visible, the adhesional forces which control the stability of suspensoid colloids, and are of very great interest. Protective action has been investigated to some extent also, but. the results published so far are rather meagre. 

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