Hydrodynamic diameter curve

Figure 3.5 (a) Schematic represent of the aggregates of PAA-Cso in aqueous solution (b) hydrodynamic diameter curve of the PAA-Qo in water (c) TEM images of PAA-Cso film cast from water solution. (Reprinted with permission from Reference [74], copyright American Chemical Society.)... 

Fig. 16. Apparent average hydrodynamic diameter (upper curves) and total scattering intensity in arbitrary units (lower curves) as a function of time following the addition of chymosin ( ) or controls (O). From Walstra et al. (1981), reproduced with permission.

As an example of the use of Eq. (28) (p. 114), the data for fractions of cellulose carbanilate, the molecule of which can be represented by a partially drained worm-like coil, are plotted in Fig. 64. The dependence of the expression of the left-hand side of Eq. (28) on is approximated by a straight line the slope of whidi yields the length of the Kuhn segment A and the intercept the hydrodynamic diameter of the chain d. The curves in Fig. 64 provide the values of A = 160 A and d = 6 A for the cellulose carbanUate chain. 

Diblock copolymers were synthesised by two stepwise anionic polymerisation methods. One method produced diblock copolymer plus 30% of poly(2-vinylpyridine) homopolymer. The copolymers were dissolved in O.IM hydrochloric acid. When the pH was increased by the dropwise addition of 0.1 M sodium hydroxide, micelles with well-defined hydrodynamic diameters formed spontaneously at around pH 5. Further basification produced stable micelle structures and reacidification produced the mirror image of this titration curve. Blue swirls were observed when sodium hydroxide was added at pH4 or pH5. The micelle sizes were measured by quasielastic light scattering. It is shown that (1) it is possible to control micelUsation by pH and (2) formation of well-behaved micelles of variable hydrodynamic diameter is possible by titration of different ratios and different total polymer concentrations of poly(2-vinylpyridine/poly(2-vinylpyridine-block-PEO). Relevance to drug release systems that can remain intact and circulate for long periods within the vascular system is suggested. 17 refs. 

The empiric master curve for the DLS data of p3Togenic powders offers an opportunity to calculate the effective translational diffusion coefficient Deff,o or the effective hydrodynamic diameter from one DLS experiment, i.e. for DLS at one scattering angle. Babick et al. (2012c) gave the following implicit formulation ... 

The HdC calibration curves of different particle sizes, as shown in Fig. 22.12 (30), are similar to the calibration curves of different pore size columns the separation ranges of MW due to hydrodynamic chromatography depend on particle size. The larger the particle size, the higher the MW ranges. Stegeman et al. (30) proposed that a smooth calibration curve may be achieved by proper ratio of the particle diameter to the pore diameter. 

Schiesser and Lapidus (S3), in later studies, measured the liquid residencetime distribution for a column of 4-in. diameter and 4-ft height packed with spherical particles of varying porosity and nominal diameters of in. and in. The liquid medium was water, and as tracers sodium chloride or methyl orange were employed. The specific purposes of this study were to determine radial variations in liquid flow rate and to demonstrate how pore diffusivity and pore structure may be estimated and characterized on the basis of tracer experiments. Significant radial variations in flow rate were observed methods are discussed for separating the hydrodynamic and diffusional contributions to the residence-time curves. 

Extension of the hydrodynamic theory to explain the variation of detonation velocity with cartridge diameter takes place in two stages. First, the structure of the reaction zone is studied to allow for the fact that the chemical reaction takes place in a finite time secondly, the effect of lateral losses on these reactions is studied. A simplified case neglecting the effects of heat conduction or diffusion and of viscosity is shown in Fig. 2.5. The Rankine-Hugoniot curves for the unreacted explosive and for the detonation products are shown, together with the Raleigh line. In the reaction zone the explosive is suddenly compressed from its initial state at... 

The permeability Ps is a measure of the transport of a molecule by diffusion. The reflection coefficient a of a given component is the maximal possible rejection for that component (at infinite solvent flux). Various models have been proposed for the reflection coefficient [75-77]. In the lognormal model [78], a lognormal distribution is assumed for the pore size. No steric hindrance in the pores or hydrodynamic lag is taken into account, but it is assumed that a molecule permeates through every pore that is larger than the diameter of the molecule. Moreover, the diffusion contribution to the transport through the membrane is considered to be negligible. Therefore, the reflection curve can be expressed as ... 

Figure 12.5 shows the cluster size dependence of X-ray emission spectra. The top, middle, and bottom curves represent the spectra measured with a laser contrast of C = 4 x 10-4 at Ar gas pressures of 60, 50, and 40 bar, respectively. Note that no X-rays were observed at an Ar gas pressure of 40 bar. According to hydrodynamic calculations (see Fig. 12.2), at 40 bar, a cluster with an average diameter of 200 nm is one order of magnitude smaller than that with an average diameter of 1.5 pm at 60 bar. Thus, in the case of the 40-bar experiment, the clusters were almost completely destroyed by the prepulse. This result demonstrates the important role of big clusters, and the validity of the nozzle design. 

Figure 15 Tj (p, T) vs. temperature for the solvent carbon dioxide at the critical density and the theoretically calculated curve. The frequency u> and the hard sphere diameters are the same as those used in the fit of the 33°C data. The theory is scaled to match the data at 33°C and the critical density, 10.6 mol/L. Unlike ethane at the critical density, there is no inverted region, and the vibrational lifetime decreases nearly linearly with temperature. The theory does not quantitatively fit the data, but it does show the correct general behavior. Most importantly, the hydrodynamic/thermodynamic theory shows the existence of the inverted region in ethane and the lack of one in carbon dioxide.

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. 

Fig. 22, Hydrodynamic thickness vs. chain length plotted on a log-log scale. The points (squares and crosses) are data for PEO/PS latex/water measured through dynamic lightscattering (squares, Cohen Stuart et al., 1984c crosses, Kato et al., 1981). The curves are calculated by Ploehn and Russel (1989) using the SCF of Eqs. (71) and (72). Curves A and B denote frictions per segment equivalent to Stokes spheres of diameter l and 21, respectively. Curve C is the thickness based only on segments contained in loops (Stokes sphere diameter = /).

Aeeording to the hydrodynamic theory of reaction waves propagating in one dimension (see references to the Introduction. Volume I) the detonation velocity is expected to be less than ideal in samples of diameter d such that the observed velocity D will approach the ideal velocity, > as J oo. Eyring et al. [25] developed a model based on a curved shock front bounded by a burned... 

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