Diffusion macromolecular solutions

A key factor determining the performance of ultrafiltration membranes is concentration polarization due to macromolecules retained at the membrane surface. In ultrafiltration, both solvent and macromolecules are carried to the membrane surface by the solution permeating the membrane. Because only the solvent and small solutes permeate the membrane, macromolecular solutes accumulate at the membrane surface. The rate at which the rejected macromolecules can diffuse away from the membrane surface into the bulk solution is relatively low. This means that the concentration of macromolecules at the surface can increase to the point that a gel layer of rejected macromolecules forms on the membrane surface, becoming a secondary barrier to flow through the membrane. In most ultrafiltration appHcations this secondary barrier is the principal resistance to flow through the membrane and dominates the membrane performance. 

Rate equation analyses for classical size exclusion chromatography have been based on treating the porous matrix as a homogeneous, spherical medium within which radial diffusion of the macromolecular solute takes place (e.g. (28,30,31)) or If mobile phase lateral dispersion Is considered Important, a two dimensional channel has been used as a model for the bed (32). In either case, however, no treatment of the effects to be expected with charged Brownian solute particles has been presented. As a... 

The fluid resistance experienced by a macromolecular solute moving in dilute solution depends on the shape and size of the molecule. A number of physical quantities have been introduced to express this. Typical ones are intrinsic viscosity [ry], limiting sedimentation coefficient s0, and limiting diffusion coefficient D0. The first is related to the rotation of the solute, while the last two are concerned with the translational motion of the solute. A wealth of theoretical and experimental information about these hydrodynamic quantities is already available for randomly coiled chains (40, 60). However, the corresponding information on non-randomly coiled polymers is as yet rather limited in number and in variety. 

These conclusions differ somewhat from those of Pirkle and Siegell in their analysis of adsorption chromatography in a crossflow magnetically fluidized bed (14). They found the dominant effects to be the width of the feed band and the external mass transfer resistance. It is not surprising that the effect of internal diffusion would be more important in size exclusion chromatography with macromolecular solutes. 

In order to proceed it is necessary to determine either GS(R, t) or equivalently F (q, t) for the dilute macromolecular solution. This requires a model. The first model we discuss is based on simple diffusion theory. 

This equation is readily integrated in closed form, although we shall not write the solution. We only note that even though it is not necessary to impose any restriction on the value of Pe, it is physically necessary that Pe> 1 otherwise the effects of diffusion near the cell bottom will extend to the solution region, and the infinite cell approximation will be invalidated. Typical values of Pe for ultracentrifugation of macromolecular solutes range from 10 to lOl... 

Both the concentration polarization and osmotic pressure descriptions can be applied to polymer solutions that form well-defined gels at high concentrations. In a gel the thermodynamic osmotic pressure results from the solvent-mediated interactions between the randomly moving gel monomers, and this pressure tends to swell the gel. Both descriptions have been calculated in some detail for gelling macromolecular solutions and shown to produce similar behaviors (Probstein et al. 1979, Trettin and Doshi 1981). Actually a relatively simple argument shows that the two approaches are equivalent if the diffusion... 

PROBSTEIN, R.F., LEUNG, W-F. ALLIANCE, Y. 1979. Determination of diffusivity and gel concentration in macromolecular solutions by ultrafiltration. J. Phys. Chem. 83, 1228-1232. 

In a quasielastic light scattering study of macromolecular solutions, it is essential to establish a clear relationship between the experimental conditions and the type of relaxation phenomena manifest in the light scattering data. To accomplish this, one must perform experiments over a range of scattering angles and solution concentrations. One of our objectives is to determine the translational diffusion coefficient (D ) for xanthan, and to relate this parameter to a hydrodynamic size. 

As the radical polymerization model the authors [47] considered the reaction, in which polymer macromolecular coils P were diffused in solution, consisting of statistically located nonsaturating traps T, which were also DMDAACh coils. At coils P and T contact the coil P disappears, forming the larger coil T. Such reactions can be described with the aid of the Eqs. (86) and (88) of Chapter 1. 

As mentioned above, concentration polarisation can be very severe in ultrafiltration because the flux through the membrane is high, the diffusivity of the macromolecules is rather low and the retention is normally very high. This implies that the solute concentration at the membrane surface attains a very high value and a maximum concentration, the gel concentration (Cg), may be reached for a number of macromolecular solutes. The gel concentration depends on the size, shape, chemical structure and degree of solvation but is independent of the bulk concentration. The two phenomena, concentration polarisation and gel formation are shown in figure VII -12. 

The DLS technique involves measurement of the Doppler broadening of the Rayleigh-scattered light as a result of Brownian motion (translational diffusion) of the particles. This thermal motion causes time fluctuations in the scattering intensity and a broadening of the Rayleigh line. The Rayleigh line has a Lorentzian line shape. In macromolecular solutions, concentration... 

Dialysis Symmetric microporous membrane, 0.1 to 10 pA pore size Concentration gradient Diffusion in convection-ffee layer Separation of salts and microsolutes from macromolecular solutions... 

---