Aggregate size, determination

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. 

Figure 18-10. Size of fractal silica aggregates as a function of silica concentration. SAXS-spectra were recorded 5 days after initial mixing. The dashed line presets the maximum aggregate size determinable with the experimental set-up.

By request of the owner, two concrete test cores (0 15cm) were drilled out of the building. The wall thickness was determined at 25cm, with the maximum aggregate size being about 32mm. 

Before beginning a size determination, it is customary to look at the material, preferably under a microscope. This examination reveals the approx size range and distribution of the particles, and especially the shapes of the particles and the degree of aggregation. If microscopic examination reveals that the ratios between max and min diameters of individual particles do not exceed 4, and indirect technique for particle size distribution based on sedimentation or elutria-tion may be used. Sedimentation techniques for particle size determination were first used by Hall (Ref 2) in 1904, He showed that the rate of fall of individual particles in a fluid was directly related to the particle size by the hydrodynamic... 

Table 2.7 lists techniques used to characterise carbon-blacks. Analysis of CB in rubber vulcanisates requires recovery of CB by digestion of the matrix followed by filtration, or by nonoxidative pyrolysis. Dispersion of CB within rubber products is usually assessed by the Cabot dispersion test, or by means of TEM. Kruse [46] has reviewed rubber microscopy, including the determination of the microstructure of CB in rubber compounds and vulcanisates and their qualitative and quantitative determination. Analysis of free CB features measurements of (i) particulate and aggregate size (SEM, TEM, XRD, AFM, STM) (ii) total surface area according to the BET method (ISO 4652), iodine adsorption (ISO 1304) or cetyltrimethylammonium bromide (CTAB) adsorption (ASTM D 3765) and (iii) external surface area, according to the dibutylphthalate (DBP) test (ASTM D 2414). TGA is an excellent technique for the quantification of CB in rubbers. However, it is very limited in being able to distinguish the different types of... 

Light scattering technique was used in determining the oil solubilization rate. Debye s equation ( ) was used in the interpretation. The basic principle involves the measurement of the surfactant aggregate size during the solubilization. As the oil goes into the surfactant micelle, the increased size will be reflected by the turbidity of the solution. 

In many situations the dispersed phase is present as aggregates, not as primary particles. In such cases, it is the size, shape, and concentration of the aggregates that determine the properties of the dispersion itself. As a matter of fact, some substances —for example, those carbon blacks known as channel and furnace blacks —possess rigidly fused, aggregatelike structures as their primary particles. 

The three parameters, mean primary particle size (or specific surface area), structure (or aggregate size), and surface chemistry (e.g. surface oxides), largely determine the application characteristics of carbon blacks. A summary of how these parameters affect color and performance appears in Table 31. 

Summarizing the statements of these three most commonly used models, it appears that the so-called mass action and phase-separation models simulate a third condition which must be fulfilled with respect to the formation of micelles a size limiting process. The latter is independent of the cooperativity and has to be interpreted by a molecular model. The limitation of the aggregate size in the mass action model is determined by the aggregation number. This is, essentially, the reason that this model has been preferred in the description of micelle forming systems. The multiple equilibrium model as comprised by the Eqs. (10—13) contains no such size limiting features. An improvement in this respect requires a functional relationship between the equilibrium constants and the association number n, i.e.,... 

Both vapour pressure osmometry and depression of the freezing point are the standard techniques probably most frequently used to determine the apparent number average molecular weight of the aggregates. The former method is preferred since the temperature of the sample is easily varied, thus allowing the investigation of the temperature dependence of the aggregate size. The accuracy of the commercially available equipment is rather different, and this has to be carefully considered below... 

In a similar approach, the aggregation of phenyl-acetylene macrocycles 65 (Chart 1) in solution have been studied with H NMR spectroscopy.169 170 They have determined the association constant for dimerization, iCssoc, by curve fitting the concentration dependence of the proton chemical shift to a model for monomer—dimer equilibrium. The results obtained from NMR studies, e.g., aggregation constants and aggregate size, have independently been verified by vapor pressure osmometry experiments. Further, it has been well documented in the literature that... 

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