Poly hydrodynamic volume

The presence of inorganic salts in solutions of poly(ethylene oxide) also can reduce the hydrodynamic volume of the polymer, with attendant reduction in intrinsic viscosity this effect is shown in Figure 7. 

Chain degradation in turbulent flow has been frequently reported in conjunction with drag reduction and in simple shear flow at high Reynolds numbers [187], Using poly(decyl methacrylate) under conditions of turbulent flow in a capillary tube, Muller and Klein observed that the hydrodynamic volume, [r ] M, is the determining factor for the degradation rate in various solvents and at various polymer concentrations [188], The initial MWD of the polymers used in their experiments are, however, too broad (Mw/Iiln = 5 ) to allow for a precise... 

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. 

The hydrodynamic volume separation mechanism of SEC, along with the different molecular size/weight relationships of branched and linear polymers of identical chemical composition, can be exploited with the SEC/LALLS method to gain information about polymer branching. In the studies described in this paper both conventional SEC and SEC/LALLS are used to obtain data about branching in samples of poly(vinyl acetate) (PVA) and polychloro-prene (PCP). 

Many synthetic water-soluble polymers are easily analyzed by GPC. These include polyacrylamide,130 sodium poly(styrenesulfonate),131 and poly (2-vinyl pyridine).132 An important issue in aqueous GPC of synthetic polymers is the effect of solvent conditions on hydrodynamic volume and therefore retention. Ion inclusion and ion exclusion effects may also be important. In one interesting case, samples of polyacrylamide in which the amide side chain was partially hydrolyzed to generate a random copolymer of acrylic acid and acrylamide exhibited pH-dependent GPC fractionation.130 At a pH so low that the side chain would be expected to be protonated, hydrolyzed samples eluted later than untreated samples, perhaps suggesting intramolecular hydrogen bonding. At neutral pH, the hydrolyzed samples eluted earlier than untreated samples, an effect that was ascribed to enlargement... 

For some polymers, like polystyrene or poly(methyl methacrylate), narrow standards of known molar mass and small polydispersity are commercially available, which can be used for calibration. Unfortunately, such standards are not available for all polymers and then the obtained true molar masses of a specific polymer might differ by a factor of two from the value obtained by calibration with, e.g., polystyrene [30] (see Section 9.1). This problem can be resolved by the so-called universal calibration, which is based on the finding that the retention volume of a polymer is a single-valued function of the hydrodynamic volume of the polymer, irrespective of its chemical nature and... 

The concept of a unique hydrodynamic volume for all rodlike polymers was derived from examination of the Mark-Houwink constants, K and a, of the equation [rj ] = KMa. Macromolecules with values of a greater than unity are commonly accepted to be stiff or rigid rods. However, it was also found that such molecules (even for values of a less than unity) obey a relation illustrated by close concordance with the curve in Fig. lb (13) flexible, branched or otherwise irregular polymers, on the other hand, show dispersion around the upper part of the curve. The straight line curve in Fig. lb implies that the constants K and a are not independent parameters for the regular macromolecules to which they apply. Poly (a- and polyQJ-phenylethyl isocyanide) fall on this line the former has a value of a > 1 while the latter has a value a < 1 (14) both polymers give linear concentration dependence of reduced specific viscosity for fractionated samples... 

The viscometric data of poly[(a-carboxymethyl)ethyl isocyanide] in simple solvents surprisingly also show a very slow temperature-dependent viscosity decay phenomenon (8,9). Still more surprising, gel permeation chromatography shows no evidence of changes in the hydrodynamic volume over the time periods of decay. 

The dependence of retention on thermodiffusion imparts an additional dimension to the thermal FFF separation that is not present in SEC. Although our understanding of thermodiffusion in solids and liquids is incomplete, certain aspects are clear. For example, thermodiffusion is very sensitive to the chemical composition of the polymer. As a result, thermal FFF is capable of separating components that differ in composition, even though they may have the same molecular-weight or diffusion coefficient. An example [4] of the separation of polystyrene and poly(methyl methacrylate) standards by thermal FFF is illustrated in Fig. 1. This separation cannot be accomplished with SEC because the diffusion coefficients (or hydrodynamic volumes) of the two materials are virtually identical. The ability of thermal FFF to separate materials by chemical composition has spurred additional research designed to increase our understanding of thermodiffusion [5], which, in turn, has led to the application of thermal FFF to polymer blends and copolymers [6]. 

The column packing in SEC comprises porous, spherical gel beads with a defined pore size distribution. Most often, these beads are made from poly(styr-ene-divinylbenzene). (For GFC, cross-linked dextran and agarose gels are often used. ) The sample is dissolved in a suitable solvent that is often used as the mobile phase as well. Separation occurs as a result of differences in accessibility of pore volume. Small molecules can freely access the whole pore volume as a result, the column retards these molecules the greatest. As molecular volume increases, less and less pore volume is accessible for molecules to sample, and elution times decrease. For all molecules with hydrodynamic volumes that are too large to penetrate into the pores of the packing, elution occurs at the (interstitial) void volume of the column. The retention volume for each solute can be described mathematically as ... 

In the case of an azobenzene-modified poly(arylether ketone amide) (see Chart 5.2), a pronounced volume contraction due to photo-induced trans-cis isomerization of the azobenzene groups was evidenced by means of size-exclusion chromatography (SEC) [25]. When irradiated in dilute N,JV-diethylacetamide solution, this polymer underwent a reduction in its hydrodynamic radius by a factor of 2.7, corresponding to a contraction of the hydrodynamic volume by a factor of about 20. This pronounced shrinkage effect is believed to be due to a large number of conformationally restricted backbone segments, because other more flexible polyamides and polyurea polymers exhibit much weaker contraction effects. 

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