Osmotic pressure applications

The phenomena we discuss, phase separation and osmotic pressure, are developed with particular attention to their applications in polymer characterization. Phase separation can be used to fractionate poly disperse polymer specimens into samples in which the molecular weight distribution is more narrow. Osmostic pressure experiments can be used to provide absolute values for the number average molecular weight of a polymer. Alternative methods for both fractionation and molecular weight determination exist, but the methods discussed in this chapter occupy a place of prominence among the alternatives, both historically and in contemporary practice. 

As noted above, all of the colligative properties are very similar in their thermodynamics if not their experimental behavior. This similarity also extends to an application like molecular weight determination and the kind of average obtained for nonhomogeneous samples. All of these statements are also true of osmotic pressure. In the remainder of this section we describe osmotic pressure experiments in general and examine the thermodynamic origin of this behavior. 

The most important application of semi-permeable membranes is in separations based on reverse osmosis. These membranes generally have pores smaller than 1 nm. The pressure across the semi-permeable membranes for reverse osmosis is generally much larger than those for ultrafiltration, for example. This is because reverse osmosis is usually used for small molecules which have a much higher osmotic pressure, because of the higher number density, than the colloids separated in ultrafiltration. As a result reverse osmosis membranes have to be much more robust than ultrafiltration membranes. Since the focus of our discussion in this chapter will be on reverse osmosis based separations, we will describe these membranes in greater detail. 

The deduction adopted is due to M. Planck (Thermodynamik, 3 Aufl., Kap. 5), and depends fundamentally on the separation of the gas mixture, resulting from continuous evaporation of the solution, into its constituents by means of semipermeable membranes. Another method, depending on such a separation applied directly to the solution, i.e., an osmotic process, is due to van t Hoff, who arrived at the laws of equilibrium in dilute solution from the standpoint of osmotic pressure. The applications of the law of mass-action belong to treatises on chemical statics (cf. Mel lor, Chemical Statics and Dynamics) we shall here consider only one or two cases which serve to illustrate some fundamental aspects of the theory. 

Hence, as the pressure difference is increased, the solvent flow increases. The pressure difference used varies according to the membrane and the application, but is usually in the range 10 to 50 bar but can also be up to 100 bar. The osmotic pressure in Equation 10.25 for dilute solutions can be approximated by the Van t Hoff equation ... 

It can now be used for the extremely important purpose of calculating calcium sulphate and 4,000 dyne/cm. for barium sulphate. These figures entirely confirm the conclusion to which we have come on general grounds, that the surface tensions of solids must have high values. The applicability of the Ostwald-Hulett formula is limited, since it is based on Van t Hoff s equation for osmotic pressure, which only holds for small concentrations and, therefore, in the present case, for low solubilities. 

In support of the association theory, colloid chemists cited non-reproduceable cryoscopic molecular weight determinations (which were eventually shown to be caused by errors in technique) and claimed that the ordinary laws of chemistry were not applicable to matter in the colloid state. The latter claim was based, not completely without merit, on the ascerta-tion that the colloid particles are large aggregates of molecules, and thus not accessible to chemical reactants. After all many natural colloids were shown to form double electrical layers and adsorb ions, thus they were "autoregulative" by action of their "surface field" (29). Furthermore, colloidal solutions were known to have abnormally high solution viscosities and abnormally low osmotic pressures. 

Two main approaches for osmotic pressure of polymeric solutions theoretical description can be distinguished. First is Flory-Huggins method [1, 2], which afterwards has been determined as method of self-consistent field. In the initial variant the main attention has been paid into pair-wise interaction in the system gaped monomeric links - molecules of solvent . Flory-Huggins parameter % was a measure of above-said pair-wise interaction and this limited application of presented method by field of concentrated solutions. In subsequent variants such method was extended on individual macromolecules into diluted solutions with taken into account the tie-up of chain links by Gaussian statistics [1]. 

The thermodynamic approach does not make explicit the effects of concentration at the membrane. A good deal of the analysis of concentration polarisation given for ultrafiltration also applies to reverse osmosis. The control of the boundary layer is just as important. The main effects of concentration polarisation in this case are, however, a reduced value of solvent permeation rate as a result of an increased osmotic pressure at the membrane surface given in equation 8.37, and a decrease in solute rejection given in equation 8.38. In many applications it is usual to pretreat feeds in order to remove colloidal material before reverse osmosis. The components which must then be retained by reverse osmosis have higher diffusion coefficients than those encountered in ultrafiltration. Hence, the polarisation modulus given in equation 8.14 is lower, and the concentration of solutes at the membrane seldom results in the formation of a gel. For the case of turbulent flow the Dittus-Boelter correlation may be used, as was the case for ultrafiltration giving a polarisation modulus of ... 

Feed characterization, particularly for nondesalination applications, should be the first and foremost objective in the design of a reverse osmosis plant. This involves the determination of the type and concentration of the main solutes and foulants in the stream, temperature, pH, osmotic pressure, etc. Once the feed has been characterized, a realistic process objective can be defined. In most cases, some level of pretreatment is needed to reduce the number and concentration of foulants present in the feed stream. Pretreatment necessitates the design of processes other than the RO module, thus the overall process design should use the minimum pretreatment necessary to meet the process objective. Once the pretreatment steps have been determined and the final feed stream defined, the RO module can be selected. 

Elementary and advanced treatments of such cellular functions are available in specialized monographs and textbooks (Bergethon and Simons 1990 Levitan and Kaczmarek 1991 Nossal and Lecar 1991). One of our objectives in this chapter is to develop the concepts necessary for understanding the Donnan equilibrium and osmotic pressure effects. We define osmotic pressures of charged and uncharged solutes, develop the classical and statistical thermodynamic principles needed to quantify them, discuss some quantitative details of the Donnan equilibrium, and outline some applications. 

As mentioned above, the primary focus of this chapter is on osmotic pressure and its basis in solution thermodynamics. We consider both classical and statistical thermodynamic interpretations of osmotic pressure. The next three sections are devoted to this. The last two sections describe osmotic effects in charged systems and a few applications of osmotic phenomena. 

We conclude the chapter with a discussion of the Donnan equilibrium and the thermodynamic behavior of charged colloids, particularly with respect to osmotic pressure and molecular weight determination (Section 3.5), and some applications of osmotic phenomena (Section 3.6). 

The easiest way to extend these considerations to the osmotic pressure of nonideal solutions is to return to Equation (22), which relates ir to a power series in mole fraction. This equation applies to ideal solutions, however, since ideality is assumed in replacing activity by mole fraction in the first place. To retain the form and yet extend its applicability to nonideal solutions, we formally include in each of the concentration terms a correction factor defined to permit the series to be applied to nonideal solutions as well ... 

Rayleigh X Rs, particle size Applicable for (R/X) < 1/20 extension of the Rayleigh equation to solutions allows the measurement of osmotic pressure, molecular weight, and turbidity of colloidal or polymer solutions see Section 5.3... 

One can also recognize that application of sufficient pressure (above the equilibrium osmotic pressure n) to the right-hand chamber in (7.67) must cause the solvent flow to reverse, resulting in extrusion of pure solvent from solution. This is the phenomenon of reverse osmosis, an important industrial process for water desalination. Reverse osmosis is also used for other purification processes, such as removal of H20 from ethanol beyond the azeotropic limit of distillation (Section 7.3.4). Reverse osmosis also finds numerous applications in wastewater treatment, solvent recovery, and pollution control processes. 

Tn the previous papers of this series (1, 2, 3, 4) calibration and repro- ducibility of gel permeation chromatography (GPC) have been extensively examined. This paper describes the application of GPC to two selected samples of linear polyethylenes, one having a narrow molecular weight distribution (NMWD) and another a broad molecular weight distribution (BMWD). These samples were distributed by the Macro-molecular Division of IUPAC (5) for the molecular characterization of commercial polymers. The average molecular weights by GPC are compared with the data obtained from infrared spectroscopy, osmotic pressure, melt viscosity, and intrinsic viscosity. Problems associated with data interpretation are discussed. 

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