Hydrodynamic size, polymers

There is usually an ionic strength above which there is no more effect on hydrodynamic size or, worse yet, there are hydrophobic interactions of the polymer with the stationary phase. Thus, the optimum 1 is usually at the low 1 end of the plateau of size vs 1. This concentration will minimize ionic strength effects while also minimizing wear on the pump seals and pistons. 

TTiis ion exclusion effect can sometimes be exploited beneficially. For example, by purposefully choosing a column with some carboxyl groups and a pH that ionizes them (greater than approximately 6.5), it may allow separation of a charged and an uncharged polymer that have the same hydrodynamic size. Alternatively, one may be able to fine-tune elution of a polymer by adjusting pH. 

The major advantage of the capillary hydrodynamic chromatography is that the mobile phase does not need to have similar solubility parameter as the sample and packing material. (In SEC, nonsize exclusion effects may be observed if the solubility parameter of the sample, packing material, or mobile phase is considerably different.) Therefore, the hydrodynamic size of polymers can be studied in a 0 solvent and even in a solvent that is not compatible with any currently available SEC packing material (9). Figure 22.4 is an example of polystyrene separation in both THF and diethyl malonate. Diethyl malonate is the 0 solvent of polystyrene at 31-36 C. 

The length of monomer unit of MA is taken to be 0.25 nm [71]. The length of the polymer chain equal to the turn or the diameter of the protein globule is calculated taking into account the hydrodynamic size of the protein molecule via Stockes radius (Rsl). 

The results are discussed in terms of collision rate theories where the shear rate in the system and the hydrodynamic sizes of the particles and the polymer molecules are considered. 

Note Soluble recombinant interleukin-2 (IL-2) was modified with various lengths of polyethylene glycol (PEG) polymers with average molecular weight listed. The final PEG to IL-2 ratio is listed as molar ratio, and their respective hydrodynamic size was determined based on their sendimentation coefficient. Hence the molecular weight listed in Effective Size is not the sum of the PEG and IL-2 with consideration of molar ratio of the PEG-IL-2 conjugates. 

Under a variety of conditions, plasmid DNA undergoes a dramatic compaction in the presence of condensing agents such as multivalent cations and cationic polymers. Naked DNA coils, typically with a hydrodynamic size of hundreds of nanometers, after condensation it may become only tens of nanometer in size. Contrary to proteins which show a unique tertiary structure, DNA coils do not condense into unique compact structure. Cationic polymers execute their gene carrier function by their condensation effect on gene materials and, furthermore, their protection effect on DNA from nuclease digestion. Currently, the most widely used cationic polymers in research include linear or branched PEI (poly (ethyleneimine) (161-165), polypeptides such as PLL (poly-L-lysine) (166-169), PLA (poly-L-arginine) (170). 

Figure 8 illustrates the relationship between inherent viscosity (IV) and concentration for PBI/PAr/NMP solutions. It is interesting to note that the IV of all solution blends exhibited normal polymer solution characteristics. At a fixed concentration (0.5%), it was noted that the IV of the solution blends exceeded the rule of mixtures (see Fig. 9) suggesting that PBI and PAr exhibit specific interactions in a dilute solution, such that the resulting hydrodynamic sizes of the blends were greater than that of the calculated averages based on each component. 

Since size exclusion chromatography separates polymer molecules by their size (especially hydrodynamic size), plotting the molecular size vs. the retention volume should be universal, regardless of the polymer molecular weight. The universal calibration curve is given as ... 

Fl-FFF is most attractive for water-soluble polymers [59] and can directly deliver the diffusion coefficient distribution and also a molar mass distribution via the relationship D=AM b. This was exploited for poly(ethylene oxide), poly(styrene sulfonate) and poly(vinyl pyrrolidone) and other polymers using published Mark-Houwink constants [361 ]. Many papers just report on the fractionation of polymers or the determination of the hydrodynamic size distribution of polymers. Examples include poly(styrene sulfonates) [59,165,243],poly(acrylic acid) [243] and poly(2-vinylpyridine) [59]. 

Structure of each nonlinear polymer molecule can be estimated, most simply in a 0 solvent, using the structural information shown in Fig. 19. By determining the hydrodynamic size of each polymer molecule, we can also estimate the size exclusion chromatography (SEC) elution curve [302-306]. 

The first pathway is the formation of mixed micelles or hemimicelles, composed of polymer-bound hydrophobes comicellized with surfactant molecules. Intermolecular physical cross-links often enhance the viscosity of the micellar solutions. The second pathway is intramolecular comicellization so that the hydrodynamic size of the associates contracts. 

SEC-ESIMS is a valuable tool for polymer characterization. Compounds are separated based on their hydrodynamic size in solution, but upon detection, an absolute molecular weight is also furnished. Only 1% of the SEC effluent is required for ESIMS analysis, thereby accommodating the popular SEC detectors. SEC-ESIMS provides an attractive solution to the calibration of SEC without the use of external calibrants. Chemical composition distribution information on copolymers is easily afforded provided the individual monomers differ in molecular weight. The successively acquired mass spectra contain narrow fractions of the overall distribution that simplifies the analysis of complex formulations. Unfortunately, we have not been able to provide structured details on materials beyond 5000 Da due to the low resolution of the quadrupole mass spectrometer. Nevertheless, SEC-ESIMS is an exciting hyphenated techniques for polymer characterization. 

Fig. 10.4. (a) Gel filtration chromatograms of multidentate polymer coated CdTe quantum dots showing direct size comparison with protein standards ferritin (440 kDa), aldolase (158 kDa), ovalbumin (43kDa), and carbonic anhydrase (29kDa). (b) Fluorescence emission spectra from the corresponding quantum dots. The quantum dot hydrodynamic sizes are 5.6 nm (2.5 nm core, blue), 6.6 nm (3.1 nm core, green), 7.8nm (4.0nm core, red), and 9.7nm (6.0nm core, brown)... 

In summary, we have reported a new strategy to minimize the hydrodynamic size of QDs by using multifunctional, multidentate polymer ligands. A novel finding is that a balanced composition of thiol and amine groups yields... 

Polymer molecules tend to spread out to a larger hydrodynamic size in a good solvent than they do in a poor solvent, which results in a reduced diffusion coefficient D as the Stoke-Einstein equation shows ... 

The block of data concerned with this area generally does not consider the developments concerning the solution behavior of nonmobility control polymers which has been reported in the polymer literature. Implicitly, one is led to believe that the mobility control polymer solutions are unique and have little in common with more conventional polymer solutions. This study will show that there is a direct qualitative correlation between the behavior of mobility control polymer solutions and other solutions of macromolecules. In particular, it is demonstrated that the viscous properties are directly related to the hydrodynamic size of the polymer chain and the influence of system characteristics such as salt concentration, shear rate, etc., can be correlated with the effective size of the polymer molecule in solution. Consequently, this study suggests that more emphasis should be placed on the measurement of the molecular size of mobility control polymers in solution if a fundamental understanding of these solutions is to be developed. 

The dominate factor which controls the solution properties of mobility control polymers is the configuration (and hence size) that the molecule assumes in a given environment. Although the viscosity of a polymer solution is related to the hydrodynamic size of the polymer molecules, it is difficult to determine the unique relationship between viscosity and size. However, exten-... 

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