Polymer concentration, effect hydrodynamic volume

The concentration dependence of the zero shear viscosity, (normalized to the solvent viscosity, r/s], is given in Figure 37. The concentration is expressed as the effective hydrodynamic volume fraction, Hard sphere data, taken from the literature, are included for comparison. It is obvious that with increasing the star functionality the polymer behavior ranges from entangled polymers (f= 32) to soft colloidal spheres (f = 128).1 1... 

In 1959, Maron considered polymer coils as a whole with an effective hydrodynamic volume B(j)2 in dilute solutions (Maron 1959 Maron and Nakajima 1960). Here e is a prefactor for the effective polymer volume, which exhibits an empirical dependence on polymer concentrations as... 

Figure 3 represents the effect of added electrolyte concentration on the [nl obtained from the modified Huggins plot for poly(4VMP/pSS) and poly(MPTMA/AMPS), and the usual Huggins plot for poly(METMA/MES). The intrinsic viscosity increases with increasing salt concentration for all three ampholytic systems. Similar results are also reported for other polyampholyte-salt systems (6,13,27,28). This behavior may be rationalized on the basis of chain expansion which results in increased solute-solvent interaction. The [ri] is related to the hydrodynamic volume of macromolecules in solution (29). An expansion of the chain results in the viscosity increase due to an increase in effective hydrodynamic volume of the solute in the given solvent. It is expected that the added electrolyte would disrupt the intramolecular and intermolecular interactions and allow the polymers to behave more freely. Thus, the increase in [n] may be related to extended chain conformations resulting from the increased polymer-solvent interactions. 

In the mucosal environment, effects of salt, pH, temperature, and lipids need to be taken into consideration for possible effects on viscosity and solubility. A pH range of 4-7 and a relatively constant temperature of 37°C can generally be expected. Observed solution properties as a function of salt and polymer concentration can be referred to as saline compatibility. Polyelectrolyte solution behavior [27] is generally dominated by ionic interactions, such as with other materials of like charge (repulsive), opposite charge (attractive), solvent ionic character (dielectric), and dissolved ions (i.e., salt). In general, at a constant polymer concentration, an increase in the salt concentration decreases the viscosity, due to decreasing the hydrodynamic volume of the polymer at a critical salt concentration precipitation may occur. 

The effect of polymer concentration on the hydrodynamic volume also was considered in the generation of the hydrodynamic volume curve. The computational procedure Includes an option for correcting the concentration effect through Rudin s equation.(37)... 

Shape effect of PFPE molecules or magnetic particles in suspension, including agglomeration phenomena at low concentration, interaction among these particles, and effects of floes can be examined via solution viscosity (r ) measurement. For a very dilute polymer solution [108], there is no interaction among polymer molecules, and the solution viscosity results from the contribution of the solvent plus the contribution of the individual polymer molecules. The intrinsic viscosity, therefore, is a measure of the hydrodynamic volume of a polymer molecule as well as the particle aspect ratio. Figure 1.24 shows the determination of the intrinsic viscosity for Zdol4000 in three different solvents. 

Note that the universal calibration relations apply to polymeric solutes in very dilute solutions. The component species of whole polymers do indeed elute effectively at zero concentration but sharp distribution fractions will be diluted much less as they move through the GPC columns. Hydrodynamic volumes of solvated polymers are inversely related to concentration and thus elution volumes may depend on the concentration as well as on the molecular weights of the calibration samples. To avoid this problem, the calibration curve can be set up in terms of hydrodynamic volumes rather than molecular weights. A general relation [20] is... 

Molecular-weight averages calculated with calibration curves of varying concentrations may differ in value. As the influence of the sample concentration on the retention volume is based on the essential nature of the hydrodynamic volume of the polymer in solution, it is necessary to select experimental conditions that will reduce the errors produced by the concentration effect. 

In concentrated solutions, with the increase of the polymer concentration, the screen effect of hydrodynamic interactions is enhanced due to the interpenetration of polymer chains. We can assume that the hydrodynamic screening length is close to the screening length of volume exclusion of monomers as given by... 

Rudin and Hoegy [43] have considered the assumption, inherent in the universal calibration procedure, that the hydrodynamic volume of a polymer at the concentration range adopted in SEC analysis is that which pertains at infinite dilution, and discuss whether this can account for apparent failures in some instances. A model is presented to estimate hydrodynamic volumes of polymers at finite concentrations and provide a universal calibration. Polypropylene is one of the examples used to illustrate the size of the effect. 

Fig. 3 Plot of the preferential solvation coefficient. A, as a function of the volume fraction of polymer(2), (f>2, at three hydrodynamic volumes, Vij = 10 (O ) lO ( ). and 10 (AA.) ml/mol for different systems (a) Tol/PDMS/PS (b) Bz/ PDMS/PS and (c) CHX/PDMS/PS eluted in p.-Styragel (empty symbols) and TSK Gel Hhr (solid symbols) columns. Solid line has been calculated with equations and 3 values given in Ref. 28. Source From An analysis of the concentration effects on elution volumes through the preferential solvation parameter in two SEC packings, in Macromol. Chem. Phys. ...

THF > Bz > Diox, and for PDMS, the order is Tol > Bz > CHX. In this sense, the effect of the injected polymer concentration on the magnitude of the hydrodynamic volume should also follow the mentioned order, and it should be expected for the respective slopes of the vs. 

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