Colloids dynamic structure factor

As particle concentration increases, particle interactions and multiple scattering invalidate Eq. (33). The cross terms (y /) in the static and dynamic structure factors. Eq. (29), no longer cancel out, and thus they lead to more complex relationships [l 15-119] for (l>(diffusive motion of interacting particles also becomes more complex, depending on colloidal and hydrodynamic interactions among the particles and their spatial configurations. DLS measurements of particle motion can provide information about suspension microstructure and particle interactions. 

The discussion of the large- tail in S(q) in Section 7.4.1.1, which is characteristic for a short-ranged attraction, enables one to formulate a simplified theory of bond formation within MCT with the result that the long-time limit of the dynamic structure factor is controlled by a single interaction parameter, F = fP-(p/b. Bond formation occurs at T, = 3.02... [34]. For small values of F, the dynamic structure factor decays to zero for all wavevectors. Physically, this means that concentration fluctuations decay into equilibrium at long times, just as expected for a colloidal fluid. However, for F > F, the solutions yield a nonzero glass form factor, namely, the system arrests in a metastable state. This simple result requires the approximate expression for S(q) given above and needs to be replaced by a full numerical solution whenever this approximation fails. 

The final chapter on applications of optical rheometric methods brings together examples of their use to solve a wide variety of physical problems. A partial list includes the use of birefringence to measure spatially resolved stress fields in non-Newtonian flows, the isolation of component dynamics in polymer/polymer blends using spectroscopic methods, the measurement of the structure factor in systems subject to field-induced phase separation, the measurement of structure in dense colloidal dispersions, and the dynamics of liquid crystals under flow. 

Fig. 10 Glass form factors fq as function of wavevector q in a colloidal glass of hard spheres for packing fractions as labeled. Data obtained by van Megen and coworkers by dynamic light scattering are qualitatively compared to MCT computations using the PY-5j at values chosen ad hoc to match the experimental data from [12]. The PY structure factor at the glass transition density = 0.58 is shown as broken line, rescaled by a factor 1/10...

A third system that is claimed to behave as a model hard sphere fluid is a dispersion of colloidal silica spheres sterically stabilized by stearyl chains g ted onto the surface and dispersed in cyclohexane ". Experimental studies of both the equilibrium thermodynamic and structural properties (osmotic compressibility and structure factor) as well as the dynamic properties (sedimentation, diffusion and viscosity) established that this system can indeed be described in very good approximation as a hard sphere colloidal dispersion (for a review of these experiments and their interpretation in terms of a hard sphere model see Ref. 4). De Kruif et al. 5 observed that in these lyophilic silica dispersions at volume fractions above 0.5 a transition to an ordered structure occurs. The transition from an initially glass like sediment to the iridescent (ordered) state appears only after weeks or months. 

Figure 13.12 Density autocorrelation functions f q, t) (probed at the same scattering vector). The dynamics is probed at a scattering vector corresponding to the peak maximum of the structure factor of the pure colloid suspension at its glass-transition volume fraction. The polymer reservoir volume fractions cj) are indicated by the numbers at the curves. The thick solid lines correspond to nonergodic (glassy) samples. (Reprinted with permission from Eckert T. and Bartsch E. Re-entrant glass transition in a colloid-polymer mixture with depletion attractions Phys. Rev. Lett, 89 125701, 2002. Copyright 2002 by the American Physical Society.)...

The use of optical methods to study the dynamics and structure of complex polymeric and colloidal liquids subject to external fields has a long history. The choice of an optical technique is normally motivated by the microstructural information it provides, its sensitivity, and dynamic range. A successful application of an optical measurement, however, will depend on many factors. First, the type of interaction of light with matter must be correctly chosen so that the desired microstructural information of a sample can be extracted. Once selected, the arrangement of optical elements required to perform the required measurement must be designed. This involves not only the selection of the elements themselves, but also their alignment. Finally, a proper interpretation of the observables will depend on one s ability to connect the measurement to the sample s microstructure. 

To make the significance of the NMR technique as an experimental tool in surfactant science more apparent, it is important to compare the strengths and the weaknesses of the NMR relaxation technique in relation to other experimental techniques. In comparison with other experimental techniques to study, for example, microemulsion droplet size, the NMR relaxation technique has two major advantages, both of which are associated with the fact that it is reorientational motions that are measured. One is that the relaxation rate, i.e., R2, is sensitive to small variations in micellar size. For example, in the case of a sphere, the rotational correlation time is proportional to the cube of the radius. This can be compared with the translational self-diffusion coefficient, which varies linearly with the radius. The second, and perhaps the most important, advantage is the fact that the rotational diffusion of particles in solution is essentially independent of interparticle interactions (electrostatic and hydrodynamic). This is in contrast to most other techniques available to study surfactant systems or colloidal systems in general, such as viscosity, collective and self-diffusion, and scattered light intensity. A weakness of the NMR relaxation approach to aggregate size determinations, compared with form factor determinations, would be the difficulties in absolute calibration, since the transformation from information on dynamics to information on structure must be performed by means of a motional model. 

To improve the structure-dynamics relationships of CLs, the effects of applicable solvents, particle sizes of primary carbon powders, wetting properties of carbon materials, and composition of the catalyst layer ink should be explored. These factors determine the complex interactions between Pt/carbon particles, ionomer molecules, and solvent molecules and, therefore, control the catalyst layer formation process. Mixing the ionomer with dispersed Pt/C catalysts in the ink suspension prior to deposition will increase the interfacial area between ionomer and Pt/C nanoparticles. The choice of a dispersion medium determines whether ionomer is to be found in the solubilized, colloidal, or precipitated forms. 

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