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Hydrodynamic radii relationship

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... [Pg.349]

The architecture of hypeibranched polymers and dendrimers is connected with difficulties in determining molar mass. Many of the common characterization techniques—e.g. size exclusion chromatography (SEC)—used for polymers are relative methods where polymer standards of known molar mass and dispersity are needed for calibration. Highly branched polymers exhibit a different relationship between molar mass and hydrodynamic radius than their linear counterparts. [Pg.12]

Knowing these functions, the mean-square radius of gyration (S2)z and the translational diffusion coefficient Dz can easily be derived eventually by application of the Stokes-Einstein relationship an effective hydrodynamic radius may be evaluated. These five... [Pg.4]

Second, an equivalent hydrodynamic radius can be defined from the diffusion coefficient via a Stokes-Einstein relationship... [Pg.79]

The refractive index of the ethane/propane mixture, needed for calculation of the scattering vector, was determined from experimental density measurements and an empirical Lorentz-Lorenz relationship (12). Incorporating the errors from the viscosity and refractive index calculations into the Stokes-Einstein relation results in a maximum error in the hydrodynamic radius of approximately 5%. [Pg.187]

Diffusion coefficients may be converted to the molecular parameters (25.) In dilute solution where each molecule is separated, the diffusion coefficient is the translational diffusion coefficient of individual molecules and is related to the hydrodynamic radius, Rj,by the well-known Stokes-Einstein relationship (20)... [Pg.448]

Figure 18. Reciprocal relationship between the hydrodynamic radius of multicomponent borosilicate species and the corresponding refractive index of films prepared from borosilicate sols as a function of root aging time at 50 °C and pH —3. (Reproduced with permission from reference 1. Copyright 1988.)... Figure 18. Reciprocal relationship between the hydrodynamic radius of multicomponent borosilicate species and the corresponding refractive index of films prepared from borosilicate sols as a function of root aging time at 50 °C and pH —3. (Reproduced with permission from reference 1. Copyright 1988.)...
Universal Calibration In the conventional calibration (described above), there is a problem when a sample that is chemically different from the standards used to calibrate the column is analyzed. However, this is a common situation for instance, a polyethylene sample is run by GPC while the calibration curve is constructed with polystyrene standards. In this case, the MW obtained with the conventional calibration is a MW related to polystyrene, not to polyethylene. On the other hand, it is very expensive to constmct calibration curves of every polymer that is analyzed by GPC. In order to solve this problem, a universal calibration technique, based on the concept of hydrodynamic volume, is used. As mentioned before, the basic principle behind GPC/SEC is that macromolecules are separated on the basis of their hydrodynamic radius or volume. Therefore, in the universal calibration a relationship is made between the hydrodynamic volume and the retention (or, more properly, elution volume) volume, instead of the relationship between MW and elution volume used in the conventional calibration. The universal calibration theory assumes that two different macromolecules will have the same elution volume if they have the same hydrodynamic volume when they are in the same solvent and at the same temperature. Using this principle and the constants K and a from the Mark-Houwink-Sakurada equation (Eq. 17.18), it is possible to obtain the absolute MW of an unknown polymer. The universal calibration principle works well with linear polymers however, it is not applicable to branched polymers. [Pg.359]

Even within the group of dynamic methods, one can find in the recent literature entirely different hydration numbers, for instance, those presented in Table 12.2 for biologically important ions [157]. Surprisingly, the fundamental Stokes-Einstein relationship between the hydrodynamic radius and the diffusion coefficient of the ion is being used in several different manners in the calculation of the effective hydrated radius of an ion (compare [158] and [159]). [Pg.458]

According to the theory of SEC, aU partially excluded analytes elute in a relatively narrow window between the interstitial volume and the hold-up volume of the column. The interstitial volume of a column packed with a beaded material of broad bead size distribution amounts to about 40% of the column volume [144]. In addition to this volume, the mobile phase (water) also occupies the porous volume within the sorbent. In the case of our polymeric packings, the total pore volume amounted to about half of the polymer volume. AU analytes are thus expected to elute in the window between 40 and 70% of the column volume. (The size of the separation window equals the total pore volume in the column packing.) Each analyte must have a fixed position in this window corresponding to the portion of the pore volume that is accessible to its molecules. In analytical SEC, the hydrodynamic radius of a species thus can be directly read from the calibration plot showing the relationship between the analyte sizes and their elution volumes. Importandy, the distance between the elution volume of a totally excluded analyte and that of a small species of the size of a water molecule should not exceed the above one-third of the bed volume. This is the maximum separation selectivity that can be expected for the pure size exclusion mechanism of separation. [Pg.464]

It is further possible to relate the hydrodynamic radius of a particle to its partial specific volume, V, which in turn allows one to correlate the diffusion coefficient of the particle with its molecular weight, M. Thus, for the case of a spherical particle the following relationship holds [30] ... [Pg.321]

It is pertinent to point out here that a corresponding universal scaling relationship is found [Aral et al., 1995 Tominaga et al., 2002] between ur and an, the chain expansion parameter for the hydrodynamic radius determined from translational diffusion. However, the scaling observed deviates substantially from the QTP theory when the latter is constructed using the Barrett equation for an [Barrett, 1984] ... [Pg.38]

For constant surfactant concentration there is a linear correlation between water concentration and the size of the water droplet in a W/O microemulsion [36]. Thus, droplet size is proportional to Wq. [For the most commonly used surfactant, AOT, the droplet radius, Rd, can be directly obtained from the Wq value from the relationship Rd (nm)=0.175 Wo [37].] In general, it seems that maximum activity occurs around a value of Wq at which the size of the droplet is equivalent to or slightly larger than that of the entrapped enzyme. Figure 5 shows data compiled for 17 different enzymes on the relationship between the hydrodynamic radius of the protein and droplet radius at optimum activity [38]. With only one exception (lipoxygenase), the correlation between the two radii is excellent. [Pg.719]

The function F(F) is expanded in a power series of r. The first moment (cumulant) in the expansion is the average decay constant Favg, which defines an effective diffusion coefficient A for the particle size distribution. A is converted to the effective hydrodynamic radius using the Stokes-Einstein relationship. [Pg.151]

Hence, measurements of intrinsic viscosity yield the hydrodynamic radius (or volume) of the chain molecule. Under 0 conditions and in a good solvent, respectively, we expect for solutions of flexible chain molecules after relationships Equations (36) and (37) of chapter 3... [Pg.50]

The symbols are as given above. Eastoe et al. [150] who studied the rotational dynamics of AOT in a variety of alkanes proposed a relationship between the hydrodynamic radius of the water pool, obtained by dynamic light scattering, and the value of w by the equation... [Pg.63]

The hydrodynamic radius is, of course, larger than the water core radius (R ) by the length of the surfactant molecule and any possible layer of the alkane oil phase. Eastoe and colleagues later showed [60] similar linear relationships up to around w = 40 also for analogs of AOT, namely, (a) sodium bis(2-propyl-l-pentyl) sulfosuccinate (analog 2 in Fig. 3.10) and (b) sodium bis(l-ethyl-2-methyl-l-pentyl) sulfosuccinate (analog 5 in Fig. 3.10) obviously, the slopes were slightly different. [Pg.63]

According to the Stokes-Einstein equation, diffusion coefficients have a reciprocal relationship to the dynamic viscosity of the host fluid (rj) and the hydrodynamic radius of the diffusing species (R). [Pg.136]

This pattern is characteristic of the relationship between the diffusion coefficient of individual molecules and their hydrodynamic radius the larger the molecules, the slower their motion (diffusion) if their aggregation and interaction with the pore and cell walls could be ignored. For example, the diffusion coefficients Dg of BPTI, BSA, and Fg molecules in the aqueous solution are equal to (0.8-1.9) x 10 , (0.6-1.0) x 10" , and (1.9-3.1)x 10" cmVs, (Young et al. 1980,... [Pg.635]

Relationships between hydrodynamic radius, some solutes. and molecular wei t, M, for ... [Pg.141]

Fig. 4.17 left Power law relationship between the aggregation number N and the hydrodynamic radius of translation l h,t for DLCA, RLCA, and hep aggregates right coeffieient of variation (CV) for differently defined aggregate sizes within populations of DLCA aggregates of uniform aggregation number N (for 100 aggregates per N)... [Pg.172]

Every particle or molecule in suspension is constantly in contact with solvent molecules that are moving due to thermal energy. In turn, this causes the molecules or particles to move in a particular manner, called Brownian motion, which depends on their size. When the sample is illuminated with a laser, the intensity of scattered light fluctuates depending on particle Brownian motion velocities—and, therefore, then-size. Through the analysis of intensity fluctuations. Brownian motion velocity can be acquired and the radius of the particle can then be determined by the Stokes-Ein-stein relationship. He and co-workers have developed a technique for hierarchical DNA self-assembly into polyhedral architectures, and, using DLS, they compared the hydrodynamic radius of the assembled complexes with the predicted ones. ... [Pg.235]


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