Osmotic pressure experimental

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. 

First, we consider the experimental aspects of osmometry. The semiperme-able membrane is the basis for an osmotic pressure experiment and is probably its most troublesome feature in practice. The membrane material must display the required selectivity in permeability-passing solvent and retaining solute-but a membrane that works for one system may not work for another. A wide variety of materials have been used as membranes, with cellophane, poly (vinyl alcohol), polyurethanes, and various animal membranes as typical examples. The membrane must be thin enough for the solvent to pass at a reasonable rate, yet sturdy enough to withstand the pressure difference which can be... 

Osmotic pressure experiments provide absolute values for Neither a model nor independent calibration is required to use this method. Experimental errors can arise, of course, and we note particularly the effect of impurities. Polymers which dissociate into ions can also be confusing. We shall return to this topic in Sec. 8.13 for now we assume that the polymers under consideration are nonelectrolytes. 

What makes the latter items particularly important is the fact that the charge and electrolyte content of an unknown polymer may not be known hence it is important to design an osmotic pressure experiment correctly for such a system. It is often easier to add swamping amounts of electrolyte than to totally eliminate all traces of electrolyte. Under the former conditions a true molecular weight is obtained. Trouble arises only when the experimenter is indifferent toward indifferent electrolyte this sort of carelessness can be the source of much confusion. 

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... 

This kinetic explanation of osmotic pressure has recently received experimental support in the beautiful researches of Perrin on the Brownian movement (Urcwnian Movement and Molecular lteality, J. Perrin, trails. F. Soddy, 1910). 

In physical chemistry, we apply the term colligative to those properties that depend upon number of molecules present. The principal colligative properties are boiling point elevation, freezing point depression, vapour pressure lowering, and osmotic pressure. All such methods require extrapolation of experimental data back to infinite dilution. This arises due to the fact that the physical properties of any solute at a reasonable concentration in a solvent are... 

The various physical methods in use at present involve measurements, respectively, of osmotic pressure, light scattering, sedimentation equilibrium, sedimentation velocity in conjunction with diffusion, or solution viscosity. All except the last mentioned are absolute methods. Each requires extrapolation to infinite dilution for rigorous fulfillment of the requirements of theory. These various physical methods depend basically on evaluation of the thermodynamic properties of the solution (i.e., the change in free energy due to the presence of polymer molecules) or of the kinetic behavior (i.e., frictional coefficient or viscosity increment), or of a combination of the two. Polymer solutions usually exhibit deviations from their limiting infinite dilution behavior at remarkably low concentrations. Hence one is obliged not only to conduct the experiments at low concentrations but also to extrapolate to infinite dilution from measurements made at the lowest experimentally feasible concentrations. 

Van t Hoff introduced the correction factor i for electrolyte solutions the measured quantity (e.g. the osmotic pressure, Jt) must be divided by this factor to obtain agreement with the theory of dilute solutions of nonelectrolytes (jt/i = RTc). For the dilute solutions of some electrolytes (now called strong), this factor approaches small integers. Thus, for a dilute sodium chloride solution with concentration c, an osmotic pressure of 2RTc was always measured, which could readily be explained by the fact that the solution, in fact, actually contains twice the number of species corresponding to concentration c calculated in the usual manner from the weighed amount of substance dissolved in the solution. Small deviations from integral numbers were attributed to experimental errors (they are now attributed to the effect of the activity coefficient). 

Experimental measurements must be interpreted in connection with all external influences, including fluid flow, bulk viscosity, and pH of the system. Consideration must be given to whether the mass transport is occurring in one or more dimensions and whether mass transport is affected by pressure gradients and/or osmotic pressure gradients. 

Osmose plays an essential role in a wide technological and especially in biological systems represented by solutions of biopolymers. That is why understandable is interest of scientists to the problem of osmotic pressure of polymeric solutions which permits comparatively easy experimentally to determine the advantages and deficiencies of theoretical imaginations about thermodynamical properties of polymeric solutions. 

The experimental techniques for the study of conformational branched properties in solution are the same as used for linear chains. These are, in particular, static and dynamic light scattering, small angle X-ray (SAXS) and small angle neutron (SANS) scattering methods, and common capillary viscometry. These methods are supported by osmotic pressure measurements and, nowadays extensively applied, size exclusion chromatography (SEC) in on-line combination with several detectors. These measurements result in a list of molecular parameters which are given in Table 1. 

Activity data for electrolytes usually are obtained by one or more of three independent experimental methods measurement of the potentials of electrochemical cells, measurement of the solubility, and measurement of the properties of the solvent, such as vapor pressure, freezing point depression, boiling point elevation, and osmotic pressure. All these solvent properties may be subsumed under the rubric colligative properties. 

Mauritz et al., motivated by these experimental results, developed a statistical mechanical, water content and cation-dependent model for the counterion dissociation equilibrium as pictured in Figure 12. This model was then utilized in a molecular based theory of thermodynamic water activity, aw, for the hydrated clusters, which were treated as microsolutions. determines osmotic pressure, which, in turn, controls membrane swelling subject to the counteractive forces posed by the deformed polymer chains. The reader is directed to the original paper for the concepts and theoretical ingredients. 

Rgure 4.5. The computed shear modulus G (stars) and osmotic pressure (line), compared with the experimental values for (squares) and n (full circles). All data are normalized by Kint/a- (Adapted from [21].)... 

---