Structure of Colloidal Aggregates

Explain why the force between a periodic array of charged colloidal particles is only approximately related to the charge density at the Wigner-Seitz cell boundaries — i.e., show how the derivation of this relation for charged plates in Chapter 5, breaks down for an array of spheres. When might it be a particularly good or bad approximation  

In Ref. 14 it is suggested that fractals with a finite extent, L, can be described phenomenologically by a real-space correlation function. 

The first term comes from the self-correlation of the particle. Discuss the motivation for the second term and relate a to df (the fractal dimension) and d (the dimension of space). What is the structure factor for scattering from this object and discuss it in the limits of small, intermediate, and large wavevectors. 

A theta solvent is one where the second virial coefficient (the coefficient, V in Eq. (7.25)) — which balances the hard-core repulsion and the polymer-polymer attraction — vanishes. This occurs for many solvents only at a particular value of the temperature. (When the second virial coefficient becomes negative, the solution is unstable to phase separation and eventually, to the collapse of the individual chains into compact objects.) The free energy per unit area of a brush in a theta solvent therefore does not have any terms quadratic in the concentration and is written  

Find the characteristics of the polymer brush in a theta solvent — i.e., the concentration profile and free energy. How do they differ from those in a good solvent where the second virial coefficient is positive  

---

In addition to giving information about the shape and internal structure of colloidal aggregates, SANS studies can also be used profitably to determine the thickness and conformation of polymer layers adsorbed onto the surface of colloidal particles such as latex nanoparticles, and in some special cases, the surface of emulsion droplets. ° In such studies, the particles on which the polymer is adsorbed must generally be very accurately contrast matched to the solvent so as to allow information to be obtained only about the adsorbed layer. SANS studies have also been recently used in combination with differential scanning calorimetry and visual inspection of the solutions, to draw up a (simplified) partial phase diagram of the aggregation behavior of a polymeric surfactant in water.t ... 

A.E. Gonzalez and G. Ramirez-Santiago Spatial Ordering and Structure Factor Scaling in the Simulations of Colloid Aggregation. Phys. Rev. Lett 74,1238 (1995). 

Amal, R. Raper, J.A. Waite, T.D. (1990) Fractal structure of hematite aggregates. J. Colloid Interface Sd. 140 158-168 Amal, R. Raper, J.A. Waite, T.D. (1992) Effect of fijlvic add adsorption on the aggregation... 

The highly dynamic colloidal structures described in this chapter result in considerable complexity in behaviors. This complexity has resulted in relatively slow improvement in our understanding of colloidal systems despite the fact that the structure of micelles was in essence described almost a century ago already. Results from a series of relatively recent approaches to describe colloidal aggregates are now beginning to coalesce into a model of colloidal structures incorporating the dynamic and nonhomogeneous structures of these aggregates. 

In contrast, the three- or two-dimensional morphologies of colloidal aggregates via Brownian particle trajectories show a fractal-like structure. One of the most prominent features of the surface deposits formed by the diffusion-limited aggregation mechanism is the formation of isolated treelike clusters (9). In our experiments, the surface morphology of the silica-coated polyethylene composite prepared by... 

Although DLS is most often used to size solid colloidal particles, the technique has also been applied to characterize aerosols [78,86,87], emulsion droplets [88,89], amphiphilic systems [90-92], and macromolecular solutions [12,16,93]. Another common application is the study of the fractal structure and kinetics of colloidal aggregation [94-102], More information about dynamic light scattering and its applications can be found in Refs. 23. 103 (104), and 105, in reviews, Refs. 11, 13, 36, 37, 49, 50, and 106, and in collections of papers Refs. 12. 14. 16. 93 (107), 105, and 108-114. 

When neutron scattering of a sample is combined with contrast variation, information can be obtained not only about the shape and size of the micelle but also about its detailed (internal) molecular architecture. Because of the unique level of information about micellar systems that can be obtained from SANS experiments, the technique is now an extremely well-established tool for investigating the shape, size, and, to a lesser extent, the internal structure of micellar aggregates with several hundreds of papers being published since the 1970s when micelles were the first colloidal systems to be studied using SANS. 

Schaefer, D.W. et al.. Fractal geometry of colloidal aggregates, Phys. Rev. Lett., 52, 2371, 1984. Hurd, A.J. and Flower, W.L., In situ growth and structure of fractal silica aggregates in a flame, J. Colloid Interface Set, 122, 178, 1988. 

The second part is devoted to adsorption of polyelectrolytes at interfaces and to flocculation and stabilization of particles in adsorbing polymer solutions. A recent theory of the electrostatic adsorption barrier, some typical experimental results, and new approaches for studying the kinetics of polyelectrolyte adsorption are presented in the first chapter of this part. In the following chapters, results are collected on the electrical and hydrodynamic properties of colloid-polyelectrolyte surface layers, giving information on the structure of adsorbed layers and their influence on the interactions between colloidal particles examples and mechanisms are analyzed of polyelectrolyte-induced stabilization and fragmentation of colloidal aggregates ... 

In this section we focus on the theory of stability of charged colloids. In section C2.6.5.1 it is shown how particles can be made to aggregate by adding sufficient electrolyte. The associated aggregation kinetics are discussed in section C2.6.5.2. and the structure of the aggregates in section C2.6.5.3. For more details, see the recent reviews [53. 54 and 55], or the colloid science textbooks [33. 39]. 

---