Aggregation equilibrium

Aggregation equilibrium of rhodamines (ineluding rhodamine 6G) are researehed by many seientists. The dimerization eonstants and speetral lumineseent properties of dimerie forms are well known. 

FIGURE 3.4 UV-VIS spectra of crocin 3.7 monomers (low concentration of crocin in water, A.=445 nm) and crocin aggregates (high concentration of crocin 3.7 in water, A,=410nm). Monomer-aggregate equilibrium concentration c= 1 mg/mL, cf. cM=0.8mg/mL from tensiometric determination. (Reprinted from Nalum Naess, S. et al., Helv. Chim. Acta, 89, 45, 2006. With permission.)... 

To understand why and how chemical reactions happen it is necessary to consider also intermolecular interactions. It is only in the hypothetical case of an ideal gas that intermolecular interactions are totally absent. In all other systems they represent an important factor that affects molecular conformation, reactivity and stability. Whenever molecules co-exist in equilibrium it means that intermolecular forces are not sufficient to pull the molecules apart or together into larger aggregates. Equilibrium implies a balance of thermodynamic factors, and when these factors change, intermolecular interactions may overcome the integrity of a partially holistic molecule, and lead on to chemical reaction. Onset of the reaction is said to be controlled by an activation energy barrier. This barrier must clearly be closely allied to the quanmm potential of the molecule. 

As shown above, the quasichemical approach to the micellisation is based on the condition of aggregation equilibrium (5.21), which allows us to obtain the mass action law (5.22) for the micellisation process. The simplest situation arises when monodisperse micelles (only with aggregation number ni), composed only of the non-ionic surfactant molecules (component 1), are formed. The corresponding reaction can be represented by the following equation... 

The kinetics of formation and disintegration of micelles has been studied for about thirty years [106-130] mainly by means of special experimental methods, which have been proposed for investigation of fast chemical reaction in liquids [131]. Most of the experimental methods for micellar solutions study the relaxation of small perturbations of the aggregation equilibrium in the system. Small perturbations of the micellar concentration can be generated by either fast mixing of two solutions when one of them does not contain micelles (method of stopped flow [112]), or by a sudden shift of the equilibrium by instantaneous changes of the temperature (temperature jump method [108, 124, 129, 130]) or pressure (pressure jump method [1, 107, 116, 122, 126]). The shift of the equilibrium can be induced also by periodic compressions or expansions of a liquid element caused by ultrasound (methods of ultrasound spectrometry [109-111, 121, 125, 127]). All experimental techniques can be described by the term relaxation spectrometry [132] and are characterised by small deviations from equilibrium. Therefore, linearised equations can be used to describe various processes in the system. 

Let us assume that the condition for the aggregation equilibrium (5.149) holds for the local concentrations cj of aggregates, which belong to the regions of premicellar aggregates and full micelles (j < 1, s < j) in an arbitrary point of the system. Then Eq. (5.174) holds also locally for the perturbations 5 Cj ... 

One of the reasons of the insufficient reliability of micellisation kinetics data determined from dynamic surface tensions, consists in the insufficient precision of the calculation methods for the adsorption kinetics from micellar solutions. It has been already noted that the assumption of a small deviation from equilibrium used at the derivation of Eq. (5.248) is not fulfilled by experiments. The assumptions of aggregation equilibrium or equal diffusion rates of micelles and monomers allow to obtain only rough estimates of the dynamic surface tension. An additional cause of these difficulties consists in the lack of reliable methods for surface tension measurements at small surface ages. The recent hydrodynamic analysis of the theoretical foundations of the oscillating jet and maximum bubble pressure methods has shown that using these techniques for measurements in the millisecond time scale requires to account for numerous hydrodynamic effects [105, 158, 159]. These effects are usually not taken into account by experimentalists, in particular in studies of micellar solutions. A detailed analysis of... 

Similar to most chemical systems of interest, the characterization of colloidal solutions requires the determination of the size, shape, structure, and stability of the particles present. This information is especially important for the understanding and utilization of organized assemblies of surfactants, in particular microemulsions, because the physical properties of the particles usually depend strongly on the thermodynamic conditions such as overall composition, temperature, and external force fields. This dependence is mainly due to the sensitivity to conditions of the monomer-aggregate equilibrium of the surfactant, which is responsible for the existence of the particles, and to the delicate balance of forces that maintain their integrity. For microemulsions, an additional complication arises from the compartmentalization of the systems, which is a source of possible phase transitions but is also a reason for most of their practical applications. 

The above results suggest that the behavior of asphaltenes in solutions is governed by some sort of aggregation equilibrium. Many factors such as the nature of solvent, the concentration of asphaltenes or resins, temperature, and so on, can influence the level of aggregation. 

Special specimen preparation as with tensile testing. However, the extraction of intrinsic mechanical parameters from creep indentation data is analytically complex [3, 4]. Confined compression or unconfined compression tests require preparation of cylindrical cored specimens of tissue and underlying bone. With unconfined compression, the free draining tissue edges and low aspect ratio, layered nature of the test specimen may introduce error. Compression of a laterally confined specimen by a porous plunger produces uniaxial deformation and fluid flow. Confined compression creep data has been analyzed to yield an aggregate equilibrium compressive modulus and permeability coefficient [5] and uniaxial creep compliance [6]. 

Adsorption equilibria for polymers out of concentrated solutions as function of concentration frequently exhibit very pronounced maxima (Fig. 12). These unusual curves can be accounted for if one assumes that the adsorbed species are in aggregation equilibrium in the solution, depending upon the amount of surface area per unit volume of solution. Hence one expects that the adsorption equilibrium out of concentrated polymer solution may not only be approached with "infinite slowness but is also a function of the system characteristics, and the definition of reproducible conditions contains many more variables than one is used to from the more common work with dilute solution. This complexity is particularly awkward when one deals with the important case of competitive adsorption of polymers out of concentrated multicomponent solutions, a common phenomenon in many industrial processes, such as paint adhesion, corrosion prevention, lubrication, especially wear prevention, etc. 

Tasso TT, Furuyama T, Kobayashi N (2013) Absorption and electrochemical properties of cobalt and iron phthalocyanines and their qrratemized dtaivatives aggregation equilibrium and oxygen reduction electrocatalysis. Inorg Chem 52(16) 9206-9215... 

In this chapter we mainly concentrate on the mechanism proposed by Anniansson and Wall ]9,10] and will not discuss other mechanisms [12,13,52]. Relaxation after a small perturbation of the aggregation equilibrium in micellar solutions consists of two well-separated steps. The fast process can be reduced to the release/incorporation of a single molecule Xj from/by the micelle, symbolized by ... 

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