Pore partitioning hydrodynamic

Casassa and Tagami (50) have given a theory for the partition of macromolecules, linear and branched, between a solution and cavities (such as the pores of a GPC gel). They have calculated elution volumes from their results, which agree closely with those derived from the hydrodynamic volume assumption this gives theoretical support to the use of hydrodynamic volume as a correlating parameter for branched polymers. This parameter has been used in studies of branching in polyethylene (Section 10). 

Surprisingly, intuition fails to predict the behavior of the same solute and solvent in a membrane with a uniform pore size larger than both the solvent and solute. The expectation that such a membrane will provide no rejection of the solute has been refuted repeatedly. Indeed, careful experiments indicate that partial rejection of the solute occurs even when the solute is considerably smaller (say 1/1 Oth as large as the pore size) (Miller, 1992 Deen, 1987 Ho and Sirkar, 1992 Happel and Brenner, 1965). The extent of rejection increases monotonically to the total rejection limit as the solute size approaches the pore size. These effects arise both from entropic suppression of partitioning and from augmented hydrodynamic resistance to transport through the fine pores. Thus, in this case, for a porous membrane, thermodynamic partitioning can play a role in the physical chemical processes of transport. 

The characteristics of pore structure in polymers is a key parameter in the study of diffusion in polymers. Pore sizes ranging from 0.1 to 1.0 pm (macroporous) are much larger than the pore sizes of diffusing solute molecules, and thus the diffusant molecules do not face a significant hurdle to diffuse through polymers comprising the solvent-filled pores. Thus, a minor modification of the values determined by the hydrodynamic theory or its empirical equations can be made to take into account the fraction of void volume in polymers (i.e., porosity, e), the crookedness of pores (i.e., tortuosity, x), and the affinity of solutes to polymers (i.e., partition coefficient, K). The effective diffusion coefficient, De, in the solvent-filled polymer pores is expressed by ... 

To evaluate the solute diffusion coefficient in the stationary phase, and the solute partition coefficient, fCq, a model for the pore is required. A simple model where the pore is considered as an infinitely long cylinder and the solute is a rigid sphere adequately describes the elution process [58]. Using this model, Dg, the solute diffusivity within the porous particles, can be estimated from the hydrodynamic theory of hindered diffusion [59] ... 

Ideal SEC would imply that no interaction occurs between macromolecules and chromatographic resin. In practice, however, many interactions such as adsorption, hydrophobic or ionic interactions, affect the chromatographic separation. Therefore, it is important to identify and minimize these residual interactions. Nucleic acids are separated in SEC by partitioning them between mobile phase and stationary phase within the pores of a support. Those with a hydrodynamic diameter larger than the pore diameter are excluded and eluted with the void volume which represents the interstitial volume between the particles of the resin. Sm2dler nucleic acids partially penetrate the support pores and have an elution volume described by the equation V =Va + F with being the pore volume and being the... 

Transport through nanofiltration membranes is controlled primarily by electrostatic and steric interactions. The extended Nemst-Plank equation commonly is used with Donnan and steric partitioning to predict transport rates based on effective membrane charge density, pore radius, and thickness to porosity ratio [131-132]. Inclusion of solute-pore hydrodynamic interactions and a pore size distribution improves the predictive and correlative capabilities of the models [133]. 

Still, the use of the hydrodynamic volume, a size based on dynamical properties, in the interpretation of SEC data is not fully understood. This is because SEC is typically run under low flow rate conditions where hydrodynamic factor should have little effect on the separation. In fact, both theory and computer simulations assume a thermodynamic separation principle the separation process is determined by the equilibrium distribution (partitioning) of solute macromolecules between two phases — a dilute bulk solution phase located at the interstitial space and confined solution phases within the pores of column packing material. Based on this theory, it has been shown that the relevant size parameter to the partitioning of polymers in pores is the mean span dimension (mean maximal projection onto a line). Although this issue has not been fully resolved, it is likely that the mean span dimension and the hydrodynamic volume are strongly correlated. 

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