Micelles diffusion coefficients

Ka <1, where k is the Debye screening length and a is the radius of the micelle, diffusion coefficients at the critical micelle concentration (cmc), Dcmc. decrease with decreasing ionic strength, i.e., Ka. With further decrease in m from 0.24 to 0.18, the Dcmc value does not decrease. This fact suggests that the drag of ionic atmosphere reaches maximum when xa becomes ca. 0.2. 

Figures 1 and 2 show diffusion coefficients of pyrene solubilized in C igTAC and C14TAB micelles, respectively, at 35 °C. Because essentially all pyrene molecules are solubilized in the micelles, the diffusion coefficients can be interpreted as tracer diffusion coefficients of the micelles. Diffusion coefficients decrease with increasing concentration of the micelles, and increase with increasing concentration of the salts added. Diffusion coefficients at erne s, Dcmc> obtained by extrapolation, and are listed in Table 1...

Figure 5. Micelle diffusion coefficients for various alkanes as a function of pressure measured by DLS. T - 25 Cf W - 5, Yaot 0.015 (mole fraction.)...

The apparent diffusion coefficient, Da in Eq. (11) is a mole fraction-weighted average of the probe diffusion coefficient in the continuous phase and the microemulsion (or micelle) diffusion coefficient. It replaces D in the current-concentration relationships where total probe concentration is used. Both the zero-kinetics and fast-kinetics expressions require knowledge of the partition coefficient and the continuous-phase diffusion coefficient for the probe. Texter et al. [57] showed that finite exchange kinetics for electroactive probes results in zero-kinetics estimates of partitioning equilibrium constants that are lower bounds to the actual equilibrium constants. The fast-kinetics limit and Eq. (11) have generally been considered as a consequence of a local equilibrium assumption. This use is more or less axiomatic, since existing analytical derivations of effective diffusion coefficients from reaction-diffusion equations are approximate. 

The micelle diameter can be calculated by measuring the micelle diffusion coefficient using the technique of dynamic light scattering (DLS). If one assumes that aU micelles are spherical in shape, the radius of a micelle in solution may be calculated by using the Stokes-Einstein relation ... 

It was shown that the diffusion coefficient was decreased by micelle inclusion related to the P i constant [6]. The overall solute diffusion coefficient, D , in a micellar solution depends on the micelle diffusion coefficient, D, and the solute diffusion coefficient in the aqueous phase, D, ... 

Konak, et a/. (34) report on the diffusion of block copolymer micelles through solutions of linear polystyrene, as shown in Figure 9.20. The block copolymer was a 74 kDa Kraton G-1650 polystyrene-hydrogenated polybutadiene-polystyrene that forms 4.8 MDa 23 nm radius micelles. The matrix polymers were 110 and 200 kDa polystyrenes having M /Mn = 1.4. The micelle diffusion coefficient Dp and the... 

Reference 115 gives the diffusion coefficient of DTAB (dodecyltrimethylammo-nium bromide) as 1.07 x 10" cm /sec. Estimate the micelle radius (use the Einstein equation relating diffusion coefficient and friction factor and the Stokes equation for the friction factor of a sphere) and compare with the value given in the reference. Estimate also the number of monomer units in the micelle. Assume 25°C. 

Micellization is a second-order or continuous type phase transition. Therefore, one observes continuous changes over the course of micelle fonnation. Many experimental teclmiques are particularly well suited for examining properties of micelles and micellar solutions. Important micellar properties include micelle size and aggregation number, self-diffusion coefficient, molecular packing of surfactant in the micelle, extent of surfactant ionization and counterion binding affinity, micelle collision rates, and many others. 

Mechanisms of micellar reactions have been studied by a kinetic study of the state of the proton at the surface of dodecyl sulfate micelles [191]. Surface diffusion constants of Ni(II) on a sodium dodecyl sulfate micelle were studied by electron spin resonance (ESR). The lateral diffusion constant of Ni(II) was found to be three orders of magnitude less than that in ordinary aqueous solutions [192]. Migration and self-diffusion coefficients of divalent counterions in micellar solutions containing monovalent counterions were studied for solutions of Be2+ in lithium dodecyl sulfate and for solutions of Ca2+ in sodium dodecyl sulfate [193]. The structural disposition of the porphyrin complex and the conformation of the surfactant molecules inside the micellar cavity was studied by NMR on aqueous sodium dodecyl sulfate micelles [194]. 

Ionic, polar and amphiphilic solubilizates are forced to reside for relatively long times in very small compartments within the micelle (intramicellar confinement, compart-mentalization) involving low translational diffusion coefficients and enhancement of correlation times. 

The limitation of using such a model is the assumption that the diffusional boundary layer, as defined by the effective diffusivity, is the same for both the solute and the micelle [45], This is a good approximation when the diffusivities of all species are similar. However, if the micelle is much larger than the free solute, then the difference between the diffusional boundary layer of the two species, as defined by Eq. (24), is significant since 8 is directly proportional to the diffusion coefficient. If known, the thickness of the diffusional boundary layer for each species can be included directly in the definition of the effective diffusivity. This approach is similar to the reaction plane model which has been used to describe acid-base reactions. 

The two-state mobility model82 83 was used to describe such system, Equation (23), which states that the phenol self-diffusion coefficient is a weighted average of free and micelle-bound ones ... 

The diffusion coefficients of this system were determined for disordered micelles and bcc spheres [47]. They were found to be retarded as compared to the disordered state. This retardation is consistent with a hindered diffusion process, D Do exp(- AxN ), with D0 being the diffusion coefficient in the absence of any interactions (i.e. for y -> 0), and A is a prefactor of order unity. Hence, the diffusion barrier increases with the enthalpic penalty xNa, where N represents the number of monomers in the foreign block. In the simplest description of hindered diffusion, the prefactor A remains constant. This model describes the experimental data poorly as A was found to increase with xNa [47]. 

An example of the use of PGSE NMR spectroscopy can be found in the studies of Selke et al. [33], who investigated the dependence of enantioselectivity on the distribution of a chiral hydrogenation catalyst between aqueous and micellar phases. When a compound is incorporated into a micelle, its mobility is much lower compared to its mobility in solution. This effect is exactly what is probed with PGSE NMR. The calculated diffusion coefficient is a time-averaged value of the lower diffusion coefficient of the catalyst incorporated into the micelles, and of the diffusion coefficient of the free catalyst. An increased amount of micelle-embedded catalyst was found to lead to an increased enantioselectivity. 

The translational diffusion coefficient of micelles loaded with a fluorophore can be determined from the autocorrelation function by means of Eqs (11.8) or (11.9). The hydrodynamic radius can then be calculated using the Stokes-Einstein relation (see Chapter 8, Section 8.1) ... 

Figure Bll.2.1 shows the normalized autocorrelation functions of various micelles loaded with octadecyl rhodamine B chloride (ODRB) at pH 7 (PBS buffer)3 . The differences in size of the micelles are clearly reflected by the differences in diffusion times td- The translational diffusion coefficients are reported in Table Bll.2.1, together with the hydrodynamic radii and the aggregation numbers.

Tab. Bll.2.1. Translational diffusion coefficients, hydrodynamic volumes and aggregation numbers of various micelles loaded with ODRB...

The diffusion coefficients obtained with another fhiorophore (NBD derivative) were slightly different. The values of the aggregations numbers were found to be often overestimated because incorporation of the fluorescent probe may require extra surfactant molecules. However, the relative size differences between the micelles are in good agreement with the values reported in the literature. In addition to the size of micelles, FCS can give information on the size distribution. 

PGSE diffusion measurements can also be presented as a 2D spectrum where the chemical shift is displayed in the first dimension and the diffusion coefficient in the second one. Such an experiment is called DOSY (Diffusion Ordered Spectroscopy) [274, 322, 323] and has also been referred to as NMR chromatography , for its ability to facilitate and visualize the resolution and assignment of complex mixtures. Although used in several areas of chemistry, such as micelles [324], polymers [325-328], resins [329], biochemistry [330-332] and organic chemistry [333-336],... 

An indirect indication of the presence of interactions between micellar phase and drugs is given by molecular and dynamic parameters of the drug and the micelles (ionic mobility, diffusion coefficient, hydrodynamic radius, apparent molecular mass), which are altered by the solubilization of lipophilic substances in a significant manner. 

Micelles in the Physical Chemistry Laboratory Diffusion Coefficients and Half-Wave Potentials of Ferrocene 84... 

Phosphatidylcholine micelles are spherical particles having a molecular weight of 97,000 g mole-1. Assuming that the density of the dry lipid (p = 1.018 g cm-3) applies to the micelles, calculate the radius Rs and the diffusion coefficient D for these particles in water at 20°C. The experimental value of the diffusion coefficient is 6.547 x 10 7 cm2 s-1 under these conditions/ Evaluate f/f and estimate the hydration of the lipid. 

Colloids (casein micelles) of two different particle sizes are isolated from skim milk by centrifugation under different conditions. The sedimentation and diffusion coefficients of the two preparations are as follows ... 

Lin et al. (1971) used inelastic scattering of plane-polarized light of 632.8-nm wavelength from a He-Ne laser to determine the diffusion coefficient and thereby the hydrodynamic radii of monodisperse caseinate micelle fractions from milk. The cumulative distribution curve of the weight fraction of micelles revealed that about 80% of the casein occurs in micelles with radii of 50 to 100 nm and 95% between 40 and 220 nm, with the most probable radius at about 80 nm. This method has the advantage that the micelles are examined in their natural medium. 

In dynamic light scattering (DLS), or photon correlation spectroscopy, temporal fluctuations of the intensity of scattered light are measured and this is related to the dynamics of the solution. In dilute micellar solutions, DLS provides the z-average of the translational diffusion coefficient. The hydrodynamic radius, Rh, of the scattering particles can then be obtained from the Stokes-Einstein equation (eqn 1.2).The intensity fraction as a function of apparent hydrodynamic radius is shown for a triblock solution in Fig. 3.4. The peak with the smaller value of apparent hydrodynamic radius, RH.aPP corresponds to molecules and that at large / Hs,Pp to micelles. 

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