Micelle kinetics relaxation time

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. 

Equations (4) and (5) are the relations derived by Aniansson for mixed micelles and they relate the relaxation times to kinetic constants and other parameters as follows ... 

The experimental techniques used to obtain the properties necessary to derive the kinetic constants of interest from the ultrasonic relaxation times have been previously described in detail [2,3]. Briefly, the degree of micelle ionization (P) and the binding constant (Ka) of an alcohol to mixed micelles were obtained from specific conductivity measurements as a function of surfactant concentration at various fixed alcohol compositions. The binding constant was determined from the slopes of the curves above the cmc, as proposed by Abu-Hamdiyyah et al... 

The adsorption kinetics in micellar systems was studied first by Lucassen (1975). He defined a micelle relaxation time... 

Though this model was proposed first for nonionic surfactants, it has been applied frequently to dissociating surfactants. This can be justified if the counterions are mobile to a sufficient extent in order to arrange themselves almost instantaneously to the distribution of surface active ions or if they are in excess. There are attempts for a construction of a more general theory taking into account the surfactant dissociation. One approach is based on the consideration that counterions are a separate component and on the application of the kinetic theory of two-component micelles [119, 120]. The obtained relations for the relaxation times are essentially more cumbersome and contain a number of coefficients with uncertain concentration... 

We assume here that the kinetic constants kj,kj,k,k, are independent of the length of micelles and surfactant concentration. Therefore, the relaxation of concentration f)erturbation in solutions of wormlike micelles can be essentially more complicated. Moreover, the relaxation processes enumerated above can influence at a different extent various properties of the non-equilibrium micellar solution. This gives a general possibility to determine all these relaxation times. The first of these relaxation processes can be described by model (5.185). The fifth one corresponds obviously to the fast relaxation process in the Aniansson and Wall model. Recently Waton derived an equation for the relaxation times of fusion and fission in micellar solutions, which can be applied to an arbitrary size distribution of micelles [128]. In the limiting cases of short micelles with a narrow size distribution and wormlike micelles this theory leads to relations (5.192) and (5.194), respectively. 

The complex dielectric spectra of water/ChEOjo and water/ChEOi binary systems (at 5, 10, and 15 wt% water) were determined at 25 °C by time-domain reflectom-etry (frequency range of 0.1-20 GHz, [39]). The low-frequency process was assigned to the kinetics of the hydrophiUc layer of micelles, including the motion of hydrated oxyethylene chain and hydrated water. Additionally, the relaxation time of the high-frequency process was attributed to the cooperative rearrangement of the H-bond network of bulk water. Following various calculations, which are reported in the article, the effective hydration number of ethylene chain Zeo was estimated. 

We now turn to the kinetic results. Aniansson (29) has recently reported an extension to mixed micelles, made out of two detergents, of his theoretical treatment of the kinetics of simple micellar systems (8,25). The expressions given for and T2 can be used to qualitatively assess the effect of alcohol on these relaxation times, since the alcohol molecules can be considered to form mixed micelles with the detergent. The ratio C /cmc, where is the micelle concentration, appears in the predominant term in Aniansson s equation for 1/Tj. At constant detergent concentration, close to the cmc, an addition of alcohol brings about an increase of C and a decrease of cmc. The ratio C /cmc, and thus l/Tj should increase with the alcohol concentration, as is indeed observed. 

One of the rare works on the kinetics of the formation of mixed micelles of Pluronics and surfactants also treats the system L64/SDS [58]. In temperature-jump experiments, the authors identified three different relaxation times for the L64/SDS mixture. The fastest ps) is associated with the binding of additional L64 unimers to the micelles. The two slower relaxation processes are interpreted as structural rearrangement of the mixed micelles and micelle clustering. These findings are qualitatively in agreement with the first kinetic investigation of these mixtures by Hecht and Hoffmann [59]. 

The equilibrium is dynamic in the way that a continual exchange of solute molecules takes place between the micelles and the bulk water. It has been shown previously (1) that the exchange process involving the alcohols propan-l-ol to hexan-l-ol and CTAB micelles is characterized by a single relaxation time in the ultrasonic frequency range 0.7 - 105 MHz. The dynamics of this process was described in terms of the kinetic principles previously... 

Experimental investigations using fast kinetic methods such as stopped-flow, temperature and pressure jumps, and ultrasonic relaxation measurements have shown that there are two relaxation processes for micellar equilibrium [12-18], characterized by relaxation times ti and T2- The first, ri, is of the order of 10 s (10 to 10 s) and represents the life-time of a surface active molecule in a micelle, i.e. it represents the association and dissociation rate for a single molecule entering and leaving the micelle, which may be represented by Eq. (2.7). 

In kinetic measurements of micellization processes one generally obtains two relaxation times from which rate constants, the width of the micelle size distribution and information on the rarest intermediate single micelles can be deduced [1, 2]. From such measurements it is also possible, as we shall see, to calculate the mean lifetime of a micelle. Such a quantity is of course of interest in itself but further interest arises in connection with the role of the micelle as host for one or more solubilized or adsorbed molecules. 

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... 

The chapter is organized as follows. Section II briefly recalls the theoretical aspects of micellar dynamics and the expressions of the relaxation times characterizing the main relaxation processes (surfactant exchange, micelle formation/breakdown). Section III reviews studies of micellar kinetics of various types of surfactants conventional surfactants with a hydrocarbon chain, surfactants with a fluorinated chain, and gemini (dimeric) surfactants. Section IV deals with mixed micellar solutions. Section V considers the d5mamics of solubilized systems. Section VI reviews the dynamics of sur-... 

Other studies considered specifically the effect of the alcohol on the kinetics of micelle formation/break-down.92>i i -i 2 Spectacular changes of the relaxation time T2 were evidenced. Note, however, that the three relaxation processes expected for a mixed surfactant + alcohol system were evidenced and investigated for only the tetradecyltrimethy-lammonium bromide (TTAB)/l-pentanol system. ... 

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