Colloid aggregation number

Other properties of association colloids that have been studied include calorimetric measurements of the heat of micelle formation (about 6 kcal/mol for a nonionic species, see Ref. 188) and the effect of high pressure (which decreases the aggregation number [189], but may raise the CMC [190]). Fast relaxation methods (rapid flow mixing, pressure-jump, temperature-jump) tend to reveal two relaxation times t and f2, the interpretation of which has been subject to much disagreement—see Ref. 191. A fast process of fi - 1 msec may represent the rate of addition to or dissociation from a micelle of individual monomer units, and a slow process of ti < 100 msec may represent the rate of total dissociation of a micelle (192 see also Refs. 193-195). 

One major question of interest is how much asphaltene will flocculate out under certain conditions. Since the system under study consist generally of a mixture of oil, aromatics, resins, and asphaltenes it may be possible to consider each of the constituents of this system as a continuous or discrete mixture (depending on the number of its components) interacting with each other as pseudo-pure-components. The theory of continuous mixtures (24), and the statistical mechanical theory of monomer/polymer solutions, and the theory of colloidal aggregations and solutions are utilized in our laboratories to analyze and predict the phase behavior and other properties of this system. 

Figure 10.11 As the aggregate number n increases, so the fraction of the added surfactant that goes into the micelle (as y ) varies more steeply with total concentration of surfactant monomer (as V). The critical micelle concentration (CMC) is the midpoint of the region over which the concentration of the micelle changes (Reproduced by permission of Wiley Interscience, from The Colloidal Domain by D. Fennell Evans and Hakan Wennerstrom)...

The most rigorous evidence that proteins had defined structures was probably the molecular weight determinations of Adair and Svedberg. From 1900, however the crystallization of increasing numbers of proteins, while not a very reliable indication of purity, suggested to Schulz that proteins were not colloidal aggregates but large molecules with definite structures. 

T. M. Herrington and S. S. Sahi, Temperature dependence of the micellar aggregation number of aqueous solutions of sucrose monolaurate and sucrose monooleate, Colloids Surf, 17 (1986) 103-113. 

Fig. 2. Concentration dependence of apparent aggregation number of dinonylnaphthalene sulfonates (o) = NaDNNS, ( ) = Ba(DNNS)2 in benzene at 25 °C. Concentration in formula weight (F. W.) per liter (L.) [J. Colloid Sci. 10, 139 (1955)1...

Fig. 6. g-micelle volumes ( aggregation numbers = acid residues per aggregate) in ml as determined by fluorescence depolarization measurements versus sulfonate concentration in g-equiva-lents per liter of dinonylnaphthalene sulfonates at 25 °C in benzene saturated with water [J. Colloid Sci. 12, 465 (1957)]... 

Fig. 13. Aggregation numbers as function of number of carbon atoms in alkylchains of di- (n-alkyl) sodium-sulfosuccinates and dialkyldimethylammonium halides. [J. Colloid interface Sci. 35, 636 (1971))...

Fig. 16. Correlation diagram of the mean aggregation number per micelle of AOT(n oT) and sodium di-2-ethylhexylphosphate (npQ-j-) in different solvents, 25 °C. [J. Colloid Interface Sci. 46, 417 (1974) (corrected according to new results)]...

Fig. 18. Relation between apparent aggregation number and concentration of sorbitan monofatty acid esters at 40 °C in different solvents n-C7H] 6 (a), C6H12 (0), C6H6 (o). J. Colloid Interface Sci. 49, 383 (1974)]...

Various gel- and porous-type resins have been examined for use in the cation-exchange chromatographic separation of the transplutonium elements from the fission-product lanthanides with an eluent of 11.7 M hydrochloric acid (17). In the case of gel-type resins, very fine ones such as colloidal aggregate, are needed to perform good separation. The number of theoretical plate obtained... 

Colloids used for the study (List I) were defined in terms of their size and shape to allow reproducible quantification of aggregate numbers and sizes. As much as possible, the aggregates should resemble the solids encountered in water and wastewater treatment as to size, density, and chemical characteristics like surface charge and its change with variations in the composition of the suspending medium. 

Li, F. Li, G-Z. Chen, J.-B. Synergism in mixed zwitterionic-anionic surfactant solutions and the aggregation numbers of the mixed micelles. Colloid Surface A 1998, 145, 167-174. 

Vasilescu, M. Caragheorgheopol, A. Caldararu, H. Aggregation numbers and micro structure characterization of self-assembled aggregates of poly(ethylene oxide) surfactants and related block-copolymers, studied by spectroscopic methods. Adv. Colloid Interf Sci. 2001, 89, 169-194. 

FIG. 6.2 Calculated dependence of (a) the monomer concentration C and (b) the weight average aggregation number gw on the total surfactant concentration Ctot for decyl, dodecyl, tetradecyl, and cetyl trimethylammonium bromides in ethylene glycol solutions. (From Nagarajan, R. and Wang, C.-C., J. Colloid Interface Sci., 178, 471, 1996.)... 

Problem 7-24. Sedimentation of a Colloidal Aggregate. Colloidal particles often aggregate because of London-van der Waals or other attractive interparticle forces unless measures are taken to stabilize them. The aggregation kinetics are such that the aggregate formed has a fractal dimension Df, which is often less than the spatial dimension. The fractal dimension measures the amount of mass in a sphere of radius R, i.e., mass R D<. For a fractal aggregate composed of Aprimary particles of radius Op with mass mp, estimate the sedimentation velocity of the aggregate when the Reynolds number for the motion is small. What is the appropriate Reynolds number ... 

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