Micelle/monomer relaxation times

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). 

The relaxation time of the dissociation for the micelle-monomer exchange process (fast relaxation process) [75] is given by... 

Ultrasonic relaxation spectroscopy (URS) is nothing but a special treatment of data from ultrasonic absorption measurements. Micelle dynamics involves characteristic relaxation processes, namely micelle-monomer exchange and micelle formation-breakdown. Ultrasonics can provide information about the kinetics of the latter, the fast relaxation process also, theoretical expressions for the relaxation time and relaxation strength such as those derived by Teubner [76] provide self-consistent estimates of both. 

The quadrupolar 2H spin-lattice relaxation of specifically deuterated surfactants, such as the methyl deuterated n-alkyl phosphocholine surfactants, also shows a concentration dependence. The CMC of dodecyl phosphocholine was determined by exploiting the difference in the 2H spin-lattice relaxation times of the monomers versus the micellar state.68 Quadrupole splittings of 14N were also used to characterize the micellization process of short-chain perfluoro-carboxylic acid salts.69... 

Telgmann and Kaatze studied the stmcture and dynamics of micelles using ultrasonic absorption in the 100-KHz to 2-GHz frequency range [100]. They detected several relaxation times in the long (ps), intermediate (10 ns), and fast (0.1-0.3 ns) time scale. The longest relaxation time has been attributed to the exchange of monomer between bulk and the micelles, and the fastest to the rotation of the alkyl chains of the surfactants in the core of the micelle. The intermediate relaxation time has not been assigned to any particular motion. We will discuss later that the intermediate relaxation times in the 10-ns time scale may well be due to solvent relaxation in the Stem layer. 

Two well separated relaxation times can always be observed by relaxation measurements on micellar systems. (1) The best model that can account for the two processes has been proposed by Aniansson and Wall. (2) For the derivation of the relaxation expressions, the micellar distribution curve was divided into three different regions The monomers and oligomers, the nuclei in the distribution minimum and finally the proper micelles around the distribution maximum. If the equilibrium is suddenly perturbed, the reequilibration process between the proper micelles of different size can proceed rapidly. The number of the micelles is not changed by this process. Aniansson showed that the monomer relaxation leads exactly to a single relaxation time... 

The theory of step-wise micelle association and disinter-gration has heen extended to mixed micelles. The relaxation process will again split into a fast and a slow one. During the first one internal (pseudo-)equilibrium is established in the micellar and monomer regions at a constant total number of micelles and characterized by a number of relaxation times equal to the number of components in the micelles. The slow process will be characterized by a single relaxation time the value of which is mainly determined by the properties at a saddle-shaped narrow passage between the micellar and monomer regions. Closed expressions for the relaxation times are deduced and their concentration dependence discussed. 

For the formation of micelles in these solutions, such a model would allow faster relaxation times than the pure surfactant because the dissociation-association process has been restricted to the one dimension along the polymer chain these micellar aggregates are formed by diffusion of monomers along the polymer chain. In this model the polymer acts as a nucleus for surfactant aggregates by promoting clusters of monomers in the form of premicellar aggregates or sub-micelles. 

As with surfactant monomers, the solubilisate molecules are not rigidly fixed in the micelle, but have a freedom of motion that depends on the solubilisation site. The lifetime of a solubilisate in the micelle is very short, usually less than 1 ms. These short relaxation times have been determined using NMR and ultrasonic techniques. 

As mentioned above, the most important adjuvants are surface active agents of the anionic, nonionic or zwitterionic type. In some cases polymers are added as stickers or antidrift agents. The production of spray droplets (from a spray nozzle) is determined by the adsorption of surfactants under dynamic conditions (with time in the region of 1 ms). The droplet adhesion to the target surface and its wetting and spreading is also determined by the dynamic contact angle which is also determined by the rate of surfactant adsorption to the surfeice. Above the critical micelle concentration (cmc), the supply of monomers is determined by the relaxation time of micelle formation and its breakdown. The dynamics of surfactant adsorption is determined by the monomer concentration and the diffusion coefftcient of the surfactant molecules to the interface. 

Many different kinetic models have been described which allow the evaluation of an expression for the various relaxation times. Sams et al. [220] have proposed a two-state model which considers a monomeric state and an associated state consisting of all species larger than the monomer unit. This model describes only the fast process and makes the assumption that the rate constants for association and dissociation of the monomer from the micelle are independent of micellar size. The association process is regarded as a collision between a small particle and a large sphere. The rate of monomer association was considered to be proportional to the concentration of monomers, the concentration of micelles... 

In Equation 3.26, T is the equilibrium surface excess, C the bulk concentration, t the time, and D the surfactant monomer diffusion coefficient. Eastoe et al. have measured the time dependence of the DST and the relaxation time %2 for solutions of many surfactants nonionic, dimeric, and zwitterionic. In all instances the fitting of the data to Equation 3.26 with the experimentally determined value of %2 was poor. The authors concluded that the micelle dissociation may have an effect on the measured DST only if the concentration of monomeric surfactant in the subsurface diffusion layer is limiting or when the micelle lifetimes are extremely long. No surfactant for which this last condition is fulfilled was evidenced by the authors. They also concluded that the rapid dissociation of monomers from micelles present in the subsurface was not likely to limit the surfactant adsorption and thus the DST. 

In Equation 6.1, N is the average micelle aggregation number, k is the exit rate constant of a monomer from the micelle, and c is the half-width of the micelle size distribution. Equation 6.1 predicts that the reciprocal of the fast relaxation time should vary linearly with surfactant concentration C above the critical micelle concentration (cmc). 

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