Apparent hydrodynamic radius

Fig. 27 Apparent hydrodynamic radius (Rh) of the mesoglobules formed by quickly heated aqueous solutions of the homopolymer PVCL or the graft copolymers with varying concentrations. (Reprinted with permission from Ref. [180] copyright 2005 Elsevier)...

Figures 22,23 and 24, respectively, depict the apparent hydrodynamic radius distributions f(Rh) for STVPh-3, STVPh-9, and STVPh-15, as well as their blends with PEMA in toluene. Here, the STVPh unit fraction Fr is defined as the total moles of styrene and vinylphenol monomer units of STVPh relative to those of PEMA plus STVPh. In LLS experiments done, PMMA cannot be seen , because its dn/dc in toluene is close to zero. As seen in Fig. 22, the f(Rh) of the STVPh-3/PEMA (50 50, w/w) blend is similar to that of pure STVPh-3, indicating that...

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 ...

Fig. 3.12 Intensity contribution function, extracted from dynamic light scattering intensities, versus apparent hydrodynamic radius for PBO PEO PBOiz in aqueous solution at 10 °C and different concentrations (indicated) (Zhou el al. 1996c),...

Measurements of the diffusion coefficients of globular protein molecules in solution yield values for molecular size that are greater than the corresponding radii determined by x-ray crystallography. The apparent hydrodynamic radius can be calculated from the Stokes-Einstein relation ... 

Fig. 32 a Temperature dependence of the intensity of scattered light (J) (filled symbols) and the apparent hydrodynamic radius (J h) (open symbols) obtained at 90° scattering angle. Data collected for equilibrium heated PVME of Mw = 12 800 g mol (squares) and of Mw = 19600gmol" (triangles) with 1.00 gL polymer concentration, b Corresponding hydrodynamic radius distributions obtained for PVME of Mw = 19 600 g mol for selected temperatures above and below the LCST. (Reprinted with permission from Ref. [147] copyright 2005 Elsevier)... 

Our studies of the thermal transition In xanthan solutions were done using the spectrum analyzer, which was not sufficiently sensitive to allow us to perform experiments at high temperatures for concentrations below c. Nevertheless, we were able to look at the thermal properties of higher concentration solutions. Figure 5 shows the hydrodynamic radii determined from the Stokes-Einstein equation plotted as a function of temperature for a 0.1% salt-free (NREL) xanthan solution. This concentration corresponds to semidllute conditions (c < c < C2) However, we would expect that the behavior of the apparent hydrodynamic radius, which... 

Thus, if the particle has no permanent dipole moment, the rise and decay signals of the birefringence are symmetrical [cf Eqs. (13) and (14)]. The rotational diffusion coefficient 9 is usually obtained directly from the decay curve, Eq. (14) and Eq. (11), together with the apparent hydrodynamic radius Vf, determined in light scattering experiments, can be used to obtain information about the size and eccentricity alb of the rotating ellipsoid. 

Nordskog et al. observed a behavior similar to that found by Bronstein et al. for mixed systems of PEO62- -PB40 with DTAB [29]. In this work, worm-like BCP micelles were characterized by SANS, DLS, and Cryo-TEM, Upon addition of the cationic surfactant, the apparent hydrodynamic radius (/ h) calculated for these block copolymer solutions started to decrease until a plateau value of approximately 15 nm was reached. Further addition of surfactant did not lead to any further change in size of the mixed polymer/surfactant micelles. Using SANS it was possible to show that above a certain threshold concentration, excess micelles of the surfactant were formed. Below this threshold, all added surfactant is incorporated into mixed BCP/DTAB micelles and, hence, the change in size is due to structure reorganization induced by the DTAB. 

The same polymer was also studied in mixtures with SDS [30]. With this anionic surfactant, the observed change in the apparent hydrodynamic radius was similar. In Fig. 6 the change is plotted schematically. 

Fig. 6 Apparent hydrodynamic radius (/ h) of the mixed BCP/DTAB micelles as obtained from a second-order cumulant analysis of the intermediate scattering fimctions of the PEO62-b-PB40 surfactant mixtures in water. The above behavior was observed for SDS, CTAB, and also for C12E5...

Fig. 5. For concentrations below 10 gm/cm, 2Rp is independent of concentration consistent with the interpretation of the data in terms of single polymer chains in dilute solution. At higher concentrations (> 10 gm/cm ) the apparent hydrodynamic radius increases, indicative of the onset of cluster growth precursor to gelation. The dilute limit, therefore, is apparently achieved for concentrations below 10 gm/cm. The concentration independence...

Evaluating the first cumulant in this approximation, we find that the apparent hydrodynamic radius is given by the following ... 

In order to estimate the actual size of the shrunken DNA in comparison with the elongated DNA coil ((A) in Figure 23.1), the Brownian motion has been analyzed Figure 23.2. From the slope of curve (b), the apparent hydrodynamic radius / h of the DNA outside the liposome is evaluated as 0.58 0.03 pm (in the presence of... 

Figure 32 Solubilization of oil (diisopropyl benzene) in 8 mM solution of SDP-2S in the presence of added electrolyte (NaCl, CaClz, or AlCl,) of fixed ionic strength, / = 24 mM. The volume of solubilized oil per unit volume of solution, Vou/ soiuiion> is plotted against the valence of the counterions (Na", Ca ", or Al " ). The measured apparent hydrodynamic radius of the swollen micelles, Rh, is also plotted versus the counterion valence.

Here ks is Boltzmann s constant, T is the absolute temperature, and q is the experimentally-measured macroscopic solution viscosity. When D and / or j are known, this equation may be inverted to yield an apparent hydrodynamic radius rn or a microviscosity q, namely... 

This equation may be inverted to give an apparent hydrodynamic radius r or a microviscosity rip. as determined by Dp and other parameters. For probes in polymer solutions, t]p often differs greatly from the directly-measured q, typically with Ppconcentration dependence of Dp will primarily be compared with... 

Lin and Phillies in a series of three papers measured Dp of polystyrene spheres in aqueous nonneutralized poly acrylic acid (PAA)(8-10). Lin and Phillies(8) report Dp of nominal 38 nm carboxylate-modified spheres in solutions of 300 kDa PAA at polymer concentration 0.37 < c < 171 g/1 and a range of temperature. At each polymer concentration. Dp tracks T/rj with reasonable accuracy. In a further study, Lin and Phillies(9) compared Dp of probe spheres of various sizes (radius 20.4-1500 nm) in 300 kDa PAA for 0 < c < 145 g/1 polymer. As seen in Figure 9.2, for each probe Dp/Dpo falls markedly with increasing c, for large spheres by as much as three orders of magnitude. For each probe, Dp(c) had a stretched-exponential concentration dependence. The apparent hydrodynamic radius rh (Figure 9.2) of... 

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