Volume model, hydrodynamic

Hydrodynamic volume refers to the combined physical properties of size and shape. Molecules of larger volume have a limited ability to enter the pores and elute the fastest. A molecule larger than the stationary phase pore volume elutes first and defines the column s void volume (Vo). In contrast, intermediate and smaller volume molecules may enter the pores and therefore elute later. As a measure of hydrodynamic volume (size and shape), SE-HPLC provides an approximation of a molecule s apparent molecular weight. For further descriptions of theoretical models and mathematical equations relating to SE-HPLC, the reader is referred to Refs. 2-5. 

Advanced computational models are also developed to understand the formation of polymer microstructure and polymer morphology. Nonuniform compositional distribution in olefin copolymers can affect the chain solubility of highly crystalline polymers. When such compositional nonuniformity is present, hydrodynamic volume distribution measured by size exclusion chromatography does not match the exact copolymer molecular weight distribution. Therefore, it is necessary to calculate the hydrodynamic volume distribution from a copolymer kinetic model and to relate it to the copolymer molecular weight distribution. The finite molecular weight moment techniques that were developed for free radical homo- and co-polymerization processes can be used for such calculations [1,14,15]. 

Apart from one compound (II), the lignin model compounds that had free phenolic groups eluted at close to the retention times predicted by the calibration curve from the polymer standards and not from the derive tized model compounds. This could simply be a result of the underivatized models having a similar variation in hydrodynamic volume with molecular weight as the polymer standards. However, it is to be expected that solvation of the underivatized model compounds should occur with THF as solvent (10), with hydrogen bonding of one THF molecule to each under-... 

Grubisic et al. (3) showed that for many polymers a single calibration curve can be drawn through a plot of the product of intrinsic viscosity and molecular weight ( [7/] M) vs. retention volume. This relationship certainly supports the model of molecular separation based on hydro-dynamic volume since [77] M is proportional to the hydrodynamic volume of the molecule in solution. Hence, molecular weights of the two polymers (calibration standard polymer and sample) which have identical retention volume under identical GPC analytical conditions can be expressed in terms of each other by combining the Grubisic relationship ... 

Table II. Viscometric and GPC Weight Average Molecular Weight Data Using the Hydrodynamic Volume (Universal Calibration Model)...

Recent studies based on comparison between gel permeation chromatography and ultra/micro-filtration [119] have shown that whatever the chemical nature and shape of the model macromolecule used, it is possible to predict the cut-off value of a membrane by considering the hydrodynamic volume of the macromolecule. This parameter provides an appropriate definition of the effective solute size to be considered in hydrod)mamic models. 

The orientation autocorrelation function P2[cos 0(t)] is given by r(t) and reflects the motion undergone by the fluorescent chromophore (2,14). A number of models for Brownian motion have been proposed (14) but in the simple case of a rigid sphere, r(t) is described by a single exponential decay where Tf., the rotational correlation time is related to the hydrodynamic volume of the sphere and the viscosity of the medium through the Stokes-Einstein relation (14,16). More complex motions of fluorophores necessitate the development of models which fit the functional form of r(t) experimentally obtained (14). 

Stepanov and Shliomis [80] have proposed an egg model akin to a three-dimensional form of the itinerant oscillator model [72]. (We recall [72] that in the itinerant oscillator, one relaxation mechanism occurs due to rotation of the oscillator as a whole, the other due to jumping of the inner rotator over a potential barrier) whereby the interdependence of the two relaxation mechanisms is taken into account. In the egg model [80], the ferrofluid particle is represented as an egg of volume V (the hydrodynamic volume) embedded in the liquid with viscosity 17. The magnetic moment of the ferroparticle is modeled by the yolk of volume V magnetic torque acts directly on the yolk but due to the viscosity of the white it is also transmitted to the eggshell. Such a model allows one to take into account the coupling between the two mechanisms in a quantitative way so that its influence on and may be estimated. 

Figure 10. The egg model of Stepanov and Shliomis a>, is angular velocity of yolk, to, is angular velocity of eggshell, ft is local angular velocity of the surrounding fluid, IX = magnetic viscosity represented by the viscosity of the white, r is the viscosity of the surrounding fluid, v is the volume of the yolk. V is the hydrodynamic volume.

The model proposed above suggests that the differential exclusion of the solute molecules was achieved on the basis of their hydrodynamic volumes, that is, their size and shape. This model has been extended by Porath [28], who considered the pores in dextran gels to be conical in nature. A further approach [29], which considers the gel to be composed of randomly arranged rigid rods, shows good correlation between the molecular radius and retention volume of the solute. 

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