Hydrodynamic coil radius

As described in Sect. 3.2, the size of the NaPA coils shrink drastically when the precipitation line is approached. This is revealed by a decrease of the radius of gyration Rg and the hydrodynamically effective radius Rh- In exploiting this effect, data from various approaches to phase boundaries belonging to different inert salt levels and NaPA samples had been collected. Facing such an extensive set of data, a meaningful tool for its interpretation seems highly desirable. 

The hydrodynamic radius reflects the effect of coil size on polymer transport properties and can be determined from the sedimentation or diffusion coefficients at infinite dilution from the relation Rh = kBT/6itri5D (D = translational diffusion coefficient extrapolated to zero concentration, kB = Boltzmann constant, T = absolute temperature and r s = solvent viscosity). 

Hyperbranched poly(ethyl methacrylate)s prepared by the photo-initiated radical polymerization of the inimer 13 were characterized by GPC with a lightscattering detector [51]. The hydrodynamic volume and radius of gyration (i g) of the resulting hyperbranched polymers were determined by DLS and SAXS, respectively. The ratios of Rg/R are in the range of 0.75-0.84, which are comparable to the value of hard spheres (0.775) and significantly lower than that of the linear unperturbed polymer coils (1.25-1.37). The compact nature of the hyperbranched poly(ethyl methacrylate)s is demonstrated by solution properties which are different from those of the linear analogs. 

In fact, the diffusion constant in solutions has the form of an Einstein diffusion of hard spheres with radius Re. For a diffusing chain the solvent within the coil is apparently also set in motion and does not contribute to the friction. Thus, the long-range hydrodynamic interactions lead, in comparison to the Rouse model, to qualitatively different results for both the center-of-mass diffusion—which is not proportional to the number of monomers exerting friction - as well as for the segment diffusion - which is considerably accelerated and follows a modified time law t2/3 instead of t1/2. 

Both Reynolds and Karim worked at neutral pH, with denatured proteins, and with reduced disulfide bonds. Under these conditions, proteins are in a random coil conformation (Mattice et al., 1976), so that their hydrodynamic radius is monotoni-cally related to their molar mass. Takagi et al. (1975) reported that the binding isotherm of SDS to proteins strongly depends upon the method of denaturing disulfide bonds. Presumably, protein-SDS complexes are not fully unfolded when disulfide bonds are left intact, which breaks the relationship between molar mass and hydrodynamic... 

Models of the polymer coil are based on the end-to-end distance, which is generally not directly available as a quantitative feature. Coils in dilute solution can be characterized in terms of the radius of gyration, Rg, which is a statistical measure of the distribution of mass about the center of gravity or in terms of the hydrodynamic radius, Rh, that is usually determined through the use of Stokes law and a measurement of a drag coefficient or friction factor, /drag/ for the coil,... 

The solution properties of dendrigraft polybutadienes are, as in the previous cases discussed, consistent with a hard sphere morphology. The intrinsic viscosity of arborescent-poly(butadienes) levels off for the G1 and G2 polymers. Additionally, the ratio of the radius of gyration in solution (Rg) to the hydrodynamic radius (Rb) of the molecules decreases from RJRb = 1.4 to 0.8 from G1 to G2. For linear polymer chains with a coiled conformation in solution, a ratio RJRb = 1.48-1.50 is expected. For rigid spheres, in comparison, a limiting value RJRb = 0.775 is predicted. 

Alternative expressions linking Vc -t to Mr have been developed1239 for peptides, based on the relationship between the radius of gyration, Rg, and the molecular mass, Mr, i.e. Rg oc Mra where a = l for prolate or rod-like peptides, a =1/2 for flexible coiled-coil peptides, and a =1/3 for spherical peptides. For compact coiled-coil peptides, the hydrodynamic volume, Vh, can be calculated as follows ... 

All factors related to the arrangement of the polymer chain in space are classified as tertiary structure. Parameters measurable directly (the radius of gyration RG, the end-to end distance h, the hydrodynamical radius RH, and the asymmetry in light scattering intensity) or indirectly (interaction parameters, the second virial coefficient A2) are related to the dimensions, such as size and shape of the polymer chain in a specific solvent under given conditions of temperature and pressure. For the exact determination of the coil size of macromolecules, it is necessary to ensure that measure-... 

Gel permeation chromatography of protein linear random coils in guanidinium chloride allows simultaneous resolution and molecular weight analysis of polypeptide components. Column calibration results are expressed in terms of a log M vs. Kd plot or of effective hydrodynamic radius (Re/). For linear polypeptide random coils in 6M GuHCl, Re is proportional to M0 555, and M° 555 or Re may be used interchangeably. Similarly, calibration data may be interpreted in terms of N° 555 (N is the number of amino acid residues in the polypeptide chain), probably the most appropriate calibration term provided sequence data are available for standards. Re for randomly coiled peptide heteropolymers is insensitive to amino acid residue side-chain composition, permitting incorporation of chromophoric, radioactive, and fluorescent substituents to enhance detection sensitivity. 

Gel permeation studies on agarose-GuHCl columns provide for high resolution and accurate molecular weight determination of linear randomly coiled polypeptide chains. For nonlinear random coils, gel permeation studies provide for accurate determination of the effective hydrodynamic radius of the components. 

Fig. 1 Typical angular dependence of KC/Ryy(q) of PNIPAM in water at two different temperatures, where the weight-average molar mass (Mw) and concentration (C) of PNIPAM are 1.3 x 107 g/mol and 6.7 x 10-7 g/mL, respectively. The insert shows the corresponding hydrodynamic radius distributions f(R ) of the PNIPAM chains respectively in the coiled and the globular states [38]...

Fig. 3 Dissolving kinetics (in terms of average hydrodynamic radius Rh) of collapsed single-chain PNIPAM globules, where t is the standing time after the solution temperature was quenched from 33.02 to 30.02 °C and the dashed line represents a stable average value of Rh of individual PNIPAM random coils at 30.02 °C. The weight-average molar mass (Mw) of the PNIPAM sample used is 1.08 x 107g/mol with a polydispersity index (Mw/Mn) less than 1.1 [32]...

Measurements of hydrodynamic radius (Rh) and intrinsic viscosity [in] of PVP in Na2SC>4 (0.55 M) have been performed by using Dynamic Light Scattering (DLS) and viscometry. From these results, a coil - to - globule phase transition was detected. 

Alternative expressions linking Ve, to Mr have been developed,70 based on the relationship between the radius of gyration Rg and the molecular mass Mr, i.e., Rg oc M , where a = 1 for prolate or rodlike proteins, a = 1/2 for flexible coiled coils, and a = 1/3 for spherical proteins. For a compact globular protein, the hydrodynamic volume, Vh can be calculated from... 

Ralf Kuriyel (Millipore Corporation) addressed some of the issues related to the use of Dean vortices, formed during the flow of fluids in curved conduits, to enhance the performance of cross-flow filters by increasing the back transport of solutes. Results were presented on coiled hollow fibers with a varying radius of curvature, fiber diameter, and solution viscosity, to characterize the relationship between the back transport of solutes and hydrodynamic parameters. A performance parameter relating back transport to the Dean number and shear rate was derived, and a simple scaling methodology was developed in terms of the performance parameter. The use of Dean vortices may result in membrane systems with less fouling and improved performance. 

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