Macromolecular solution

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. 

For many years, it was thought that the macro solute forms a new phase near the membrane—that of a gel or gel-like layer. The model provided good correlations of experimental data and has been widely used. It does not fit known experimental facts. An explanation that fits the known data well is based on osmotic pressure. The van t Hoff equation [Eq. (22-75)] is hopelessly inadequate to predict the osmotic pressure of a macromolecular solution. Using the empirical expression... 

One important class of integral equation theories is based on the reference interaction site model (RISM) proposed by Chandler [77]. These RISM theories have been used to smdy the confonnation of small peptides in liquid water [78-80]. However, the approach is not appropriate for large molecular solutes such as proteins and nucleic acids. Because RISM is based on a reduction to site-site, solute-solvent radially symmetrical distribution functions, there is a loss of infonnation about the tliree-dimensional spatial organization of the solvent density around a macromolecular solute of irregular shape. To circumvent this limitation, extensions of RISM-like theories for tliree-dimensional space (3d-RISM) have been proposed [81,82],... 

M. Daoud, P. G. de Gennes. Statics of macromolecular solutions trapped in small pores. J Physique 55 85-93, 1977. 

If a solution of protein is separated from a bathing solution by a semipermeable membrane, small molecules and ions can pass through the semipermeable membrane to equilibrate between the protein solution and the bathing solution, called the dialysis bath or dialysate (Figure 5A.2). This method is useful for removing small molecules from macromolecular solutions or for altering the composition of the protein-containing solution. 

The consideration made above allows us to predict good chromatographic properties of the bonded phases composed of the adsorbed macromolecules. On the one hand, steric repulsion of the macromolecular solute by the loops and tails of the modifying polymer ensures the suppressed nonspecific adsorptivity of a carrier. On the other hand, the extended structure of the bonded phase may improve the adaptivity of the grafted functions and facilitate thereby the complex formation between the adsorbent and solute. The examples listed below illustrate the applicability of the composite sorbents to the different modes of liquid chromatography of biopolymers. 

Isihara, A. and Guth, E. Theory of Dilute Macromolecular Solutions. Vol. 5, pp. 233-260. Janeschitz-Kriegl, H. Flow Birefringence of Elastico-Viscous Polymer Systems. Vol. 6, pp. 170-318. 

We note that the calculation of At/ will depend primarily on local information about solute-solvent interactions i.c., the magnitude of A U is of molecular order. An accurate determination of this partition function is therefore possible based on the molecular details of the solution in the vicinity of the solute. The success of the test-particle method can be attributed to this property. A second feature of these relations, apparent in Eq. (4), is the evaluation of solute conformational stability in solution by separately calculating the equilibrium distribution of solute conformations for an isolated molecule and the solvent response to this distribution. This evaluation will likewise depend on primarily local interactions between the solute and solvent. For macromolecular solutes, simple physical approximations involving only partially hydrated solutes might be sufficient. 

Peter Debye in 1944 further extended the work of Rayleigh and the fluctuation theory of Smoluchowski and Einstein to include the measurement of the scattering of light by macromolecular solutions for determining molecular size. 

For Molecular weight determination by viscometry we do not need absolute h value, viscosity measurements may be carried out in simple Ostwald Viscometer. Because of (the non-Newtonian behaviour of most macromolecular solutions at high velocity gradients in the capillary, the viscometer dimensions are chosen in such a manner that the viscosity gradient is the smallest possible. 

Particulate sorbents are available almost exclusively in the shape of micrometersized beads. These beads are packed in columns and represent currently the most common stationary phases for high-performance liquid chromatography (HPLC). Despite their immense popularity, slow diffusional mass transfer of macromolecular solutes into the stagnant pool of the mobile phase present in the pores of the separation medium and the large void volume between the packed particles are considered to be major problems in the HPLC of macromolecules, frequently impairing their rapid and efficient separation [1]. 

For ultrafiltration, the macromolecular solutes and colloidal species usually have insignificant osmotic pressures. In this case, the concentration at the membrane surface (C ) can rise to the point of incipient gel precipitation, forming a dynamic secondary membrane on top of the primary structure (Figure 7). This secondary membrane can offer the major resistance to flow. 

Equations 4 and 5 have been used to predict flux values for a variety of macromolecular solutions and channel geometries ( ). The theoretical values were in good agreement with the experimental values. Figure 13 illustrates the 0.33 power dependence on wall shear rate per unit channel length (U/dj L). 

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 initial objective of this paper is to identify, within the context of macromolecular solution modeling, the typical approximations, explicit and implicit, and to discuss the possible impHcations of such approximations. Secondly, we hope to demonstrate that modeling of carbohydrate high polymer solu-... 

Caroline, D. Jones, G. In Light Scattering in Liquids and Macromolecular Solutions. Degiorgio, V., Corti, M, Giglio,... 

Isihara, A. andGuTH,E. Theoiy of Dilute Macromolecular Solutions. Vol. 5, pp. 233—260. 

Jacobson, B., 1955. On the interpretation of dielectric constants of aqueous macromolecular solutions. Hydration of macromolecules, J. Am. Chem. Soc., 77, 2919-2926. 

Current investigations on dilute polymer solutions are still largely limited to the class of macromolecular solutes that assume randomly coiled conformation. It is therefore natural that there should be a growing interest in expanding the scope of polymer solution study to macromolecular solutes whose conformations cannot be described by the conventional random-coil model. The present paper aims at describing one of the recent studies made under such impetus. It deals with a nonrandom-coil conformation usually referred to as interrupted helix or partial helix. This conformation is a hybrid of random-coil and helix precisely, a linear alternation of randomly coiled and helical sequences of repeat units. It has become available for experimental studies through the discovery of helix-coil transition phenomena in synthetic polypeptides. 

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