Aggregates linear

Altliough tire tlieories of colloid stability and aggregation kinetics were developed several decades ago, tire actual stmcture of aggregates has only been studied more recently. To describe tire stmcture, we start witli tire relationship between tire size of an aggregate (linear dimension), expressed as its radius of gyration and its mass m ... 

A spectrophotometric investigation of the ground-state absorption of benzophenone in pure SC CO2 and in the presence of 2-propanol was performed in order to determine both benzophenone solubility and the potential for solute/solute or co-solvent/solute aggregations. Linear Beer s law plots of absorbance versus concentration of benzophenone over a concentration range of 1-15 mM in SC OO2 insured that the ketone was fully disolved and in a non-associated form under the conditions of the laser experiments (- 10 mM). Analysis of the absorption spectrum of benzophenone in SC CO2 ranging from high to low pressure, resulted in absorption bands nearly... 

The variation of this standard ehemical potential with aggregate size is important in determining whether micelles or aggregates will form. This reference potential also determines polydispersity and aggregate shape. For the sake of discussion we consider the formation of (one-dimensional aggregates) linear ehains of surfactants. We approximate the pairwise binding energy (relative to separated speeies) as akT. The standard reference potential is then written ... 

Lipps et al. (10,11) assumed a system mix of three types of aggregates (linear, planar, and close-packed three dimensional) in deriving form factors for singlet multiplicities up to 13. In coagulation experiments on polystyrene latex, Lips et al. (10) concluded that aggregates consisting of more than 13 singlets accounted for less than 0.5% of the... 

Pertsev, N.A., Zembilgotov, A.G., and Waser, R. 1998. Aggregate linear properties of ferroelectric ceramics and polycrystalline thin films calculation by the method of effective piezoelectric medium. Journal of Applied Physics 84 [3] 1524-1529. 

The next example, which we discuss in some detail, is a MD study of the self-assembly and liquid-crystal phase behavior of reversibly aggregating linear model polymers. In this model, a detailed description can be found in Ref. 68, the particles, that is, the monomers, interact via a Lennard-Jones-like potential with anisotropic attraction ... 

Maointosh F C, Safran S A and Pinous P A 1990 Self-assembly of linear aggregates the effeot of eleotrostatios on growth Europhys. Lett. 12 697-702... 

CMC hydrates rapidly and forms clear solutions. Viscosity buUding is the single most important property of CMC. DUute solutions of CMC exhibit stable viscosity because each polymer chain is hydrated, extended, and independent. The sodium carboxylate groups are highly hydrated, and the ceUulose molecule itself is hydrated. The ceUulose molecule is linear, and conversion of it into a polyanion (polycarboxylate) tends to keep it in an extended form by reason of coulombic repulsion. This same coulombic repulsion between the carboxylate anions prevents aggregation of the polymer chains. Solutions of CMC are either pseudoplastic or thixotropic, depending on the type. 

It was shown in Chapter 3 that in the absenee of erystal aggregation, the produet erystal size distribution is log-linear, as illustrated in Figure 6.11(a). 

It was shown in Chapter 6 that if the erystals are suffieiently small, for whieh the aggregation rate is determined by the perikinetie meehanism, then the mean partiele volume inereases linearly with time ... 

The reversible aggregation of monomers into linear polymers exhibits critical phenomena which can be described by the 0 hmit of the -vector model of magnetism [13,14]. Unlike mean field models, the -vector model allows for fluctuations of the order parameter, the dimension n of which depends on the nature of the polymer system. (For linear chains 0, whereas for ring polymers = 1.) In order to study equilibrium polymers in solutions, one should model the system using the dilute 0 magnet model [14] however, a theoretical solution presently exists only within the mean field approximation (MFA), where it corresponds to the Flory theory of polymer solutions [16]. 

Beyond the CMC, surfactants which are added to the solution thus form micelles which are in equilibrium with the free surfactants. This explains why Xi and level off at that concentration. Note that even though it is called critical, the CMC is not related to a phase transition. Therefore, it is not defined unambiguously. In the simulations, some authors identify it with the concentration where more than half of the surfactants are assembled into aggregates [114] others determine the intersection point of linear fits to the low concentration and the high concentration regime, either plotting the free surfactant concentration vs the total surfactant concentration [115], or plotting the surfactant chemical potential vs ln( ) [119]. 

---