Micelles, hydrodynamic radius

In a solution of a larger polymer, PSt/PEO - 1730/170, with a polymer and water content of 1500 and 28 ppm, respectively, micelles with Rh of 34 nm were observed. Since the micelle Rh values measured at 30,60, and 90 °C were the same within experimental error, it was concluded that the micelles are relatively mon-odisperse. The micelle hydrodynamic radius increases from 34 to 48 nm as the water content is increased from 28 to 98 ppm in a 1500 ppm solution of the 1730/170 block copolymer. 

Figure 10. Micelle hydrodynamic radius versus reaction time for the three initiator concentrations from Figure 9 [AIBN] -. 92 mMole ( ) 1.35 mMole 1.85 mMole (A).

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) ... 

Before the coupling reaction, the self-assembly of PI-Z>-PS-Z>-PI triblock copolymer chains in w-hcxane was investigated by LLS. Figure 7 shows typical hydrodynamic radius distributions (/(Rh)) of individual PI-Z>-PS-Z>-PI triblock chains in THF, a good solvent for both the PI and PS blocks, and the core-shell micelles formed via the self-assembly of the triblock copolymer chains in -hexane, a solvent selectively good for the PI block. The shifting of the peak from... 

Figure 7. Typical hydrodynamic radius distributions (/(Rh)) of individual PI-6-PS-6-PI triblock copolymer chains end-capped with butyl bromide group (SI44) in THF and their self-assembled coreshell micelle in w-hexane, where C = 1.0 x 10 2 g/mL and T = 25.0 °C.

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. 

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. 

Fig. 3.4 Showing the coexistence of molecules and micelles via dynamic light scattering. Intensity fraction versus the apparent hydrodynamic radius for solutions of PBO, PEOwPBOs (120gem 3, 20 and 40°C) (Booth et al. 1997 Yang et al. 1996a). Here PBO denotes poly(oxybutylene) and PEO poly(oxyethylene). The peaks correspond to molecules (or molecular clusters) at small values of / hi>pp and to micelles at large values Ol f h.app ...

Abbreviations A H Huggins coefficient M, molar mass R, radius of gyration RD, core radius p, association number AmcH°, standard enthalpy of micellization, AmlcG°, standard Gibbs energy of micellization A2, second virial coefficient. Ru, hydrodynamic radius. 

Fig. 4.2. Mean radius of gyration plotted versus the mean hydrodynamic radius for different micelle shapes according to theoretical predictions (solid lines). Circles give experimental quasi-elastic light scattering results for SDS micelles at different temperatures in 0.6 M NaCl. (From Ref.34 )...

One aspect of the dynamics of micellar systems that has received a renewed interest during recent years is the translational motion of the micelles themselves. In the simplest approximation, the translational diffusion coefficient, D, of a spherical micelle is related to the hydrodynamic radius rM through the Stokes-Einstein relation... 

Fig. 17. Apparent average hydrodynamic radius (upper curve) and turbidity (lower curve) of casein micelles as a function of ethanol concentration. From Horne (1984b), reproduced with permission.

The decrease in the hydrodynamic radius coincides with the first inflection point of the potentiometric titration a further and significantly smaller decrease might be assumed at the second inflection point. At pH 4 spherical structures with a maximal radius of approximately 120 nm are observed. As the contour length of the polymer chain is only 140 nm these spherical aggregates most probably do not represent simple spherical micelles. More likely vesicles are formed. At pH 10 also spherical aggregates are found, which appear to be less uniform than the ones formed under acidic conditions. at basic conditions the maximal radius was determined to be about 100 nm. 

Hydrodynamic radius of micelles formed, RH Radius of gyration, RG... 

Ratio of hydrodynamic radius, Rr, to radius of gyration, Ru Micelle core radius, Rc Micelle corona thickness, C... 

Aggregation number Radius of gyration, RG Hydrodynamic radius, RH Core/corona size, micelle structure, overall micelle size... 

When the solute is spherical, or close to be so, its radius is easily obtained otherwise, estimations can be made on the basis of the geometry and arrangement of the constituting atoms or ions. For solutes having a complex stucture (e.g., micelles), a distinction should be made between the hydrodynamic radius (which appears in the Stokes-Einstein equation of the diffusion coefficient) and the reaction radius [98]. For Ps, RPs should represent the bubble radius. However, as shown in Table 4.4, the experimental data are systematically very well recovered by using the free Ps radius, RPs = 0.053 nm using the bubble radius results in a calculated value of kD (noted kDb) that is too small by a factor of 2 or 3. Table 4.4 does not include such cases where k kD, as these do not correspond to purely diffusion-controlled reactions. 

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