Osmotic compressibility, polymer solutions

At least two different techniques are available to compress an emulsion at a given osmotic pressure H. One technique consists of introducing the emulsion into a semipermeable dialysis bag and to immerse it into a large reservoir filled with a stressing polymer solution. This latter sets the osmotic pressure H. The permeability of the dialysis membrane is such that only solvent molecules from the continuous phase and surfactant are exchanged across the membrane until the osmotic pressure in the emulsion becomes equal to that of the reservoir. The dialysis bag is then removed and the droplet volume fraction at equilibrium is measured. 

An emulsion that is, for instance, stable over many years at low droplet volume fraction may become unstable and coalesce when compressed above a critical osmotic pressure 11. As an example, when an oil-in-water emulsion stabilized with sodium dodecyl sulfate (SDS) is introduced in a dialysis bag and is stressed by the osmotic pressure imposed by an external polymer solution, coarsening occurs through the growth of a few randomly distributed large droplets [8]. A microscopic image of such a growth is shown in Fig. 5.1. 

This article reviews the following solution properties of liquid-crystalline stiff-chain polymers (1) osmotic pressure and osmotic compressibility, (2) phase behavior involving liquid crystal phasefs), (3) orientational order parameter, (4) translational and rotational diffusion coefficients, (5) zero-shear viscosity, and (6) rheological behavior in the liquid crystal state. Among the related theories, the scaled particle theory is chosen to compare with experimental results for properties (1H3), the fuzzy cylinder model theory for properties (4) and (5), and Doi s theory for property (6). In most cases the agreement between experiment and theory is satisfactory, enabling one to predict solution properties from basic molecular parameters. Procedures for data analysis are described in detail. 

For a binary polymer solution, the reciprocal of the osmotic compressibility 0n/0c at constant T and the solvent chemical potential p0 can be determined by sedimentation equilibrium through the relation [58,59] ... 

It is well known that the osmotic pressure of a solution of one polymer can be scaled with a single dimensionless variable "S" which is proportional to polymer concentration at least for the case of mixtures with good solvents in the dilute to semidilute regime (12, 17). This implies that the osmotic compressibility factor (ti/cRT) can be expressed as some function of "S" only as shown in Equation 11. 

In Chapter 5, we defined the osmotic pressure of a polymer solution, we indicated how it can be measured, and we described various effects concerning the compressibility and the preferential adsorption. When the polymers are very long and when the volume fraction occupied by the polymers in the solution is small, the complex reality can be represented by a simple model which is the standard continuous model, studied in Chapter 10 in the context of perturbation theory. This model is especially useful because it allows us to perform effective calculations. In particular, it can be used in the limit of long polymers to determine universal quantities because, then, the general properties of long polymers become independent of the chemical microstructure. Calculations are... 

Concentration fluctuations in polymer solutions that are in thermal equilibrium are well understood. The intensity of the polymer concentration fluctuations is proportional to the osmotic compressibility and the fluctuations decay exponentially with a decay rate determined by the mass-diffusion coefficient D. Probing these fluctuations with dynamic light scattering provides a convenient way for measuring this diffusion coefficient Z) [ 1],... 

In Eq. (4) v in the kinematic viscosity of the polymer solution, p the chemical potential difference between solvent and solute such that the derivative (6p/6w)p,T taken at constant pressure p and constant temperature T, is proportional to the inverse osmotic compressibility of the solution. 

This exclusion of polymers from the interior of the vesicles results in an osmotic compression of the water layers and a decrease in the water layer thickness and lamellar phase volume. This effect allows the control of bulk properties such as viscosity and also provides a probe of water layer dimensions in lamellar dispersions. The lamellar surfactant system used in this study is the sodium dodecyl sulfate (SDS)/dodecanol (Ci20H)/water system that has been used to prepare submicron diameter emulsions (miniemulsions) from monomers for emulsion polymerization (5) and for the preparation of artificial latexes by direct emulsification of polymer solutions such as ethyl cellulose (4). This surfactant system forms lamellar dispersions (vesicles) in water at very low surfactant concentrations (< 13 mM). 

The osmotic compressibility of a polymer solution in a good solvent was given in Sect. 4.3 and reads... 

Concentration effects in solutions of randomly branched polymers are similar to those in solutions of other types of branched macromolecules but exhibit some specific features. Similar to the case of star-branched polymers, in semidilute solutions of fairly monodisperse branched polymers beyond the overlap concentration cj ja,jched- / branched, individual macromolecules contract without significant interpenetration. Appearance of a sharp corrdation peak in the stmrture fartor and vanishing osmotic compressibility in the concentration range dose to are the concomitant effects. 

Osmotic Compressibility In Section 2.4, we learned that the molecular weight and concentration-dependent factor in the excess scattering intensity of the polymer solution is c/(511/5c). The denominator is the osmotic compressibility. See Eqs. 2.104-2.107. At low concentrations, 5ll/5c = NjJcqT/M, and therefore... 

Finally, analytic predictions for the osmotic pressure of polymers in good and theta solvents can be derived based on the Gaussian thread model, PRISM theory, and the compressibility route. The qualitative form of the prediction for large N is " pP °c (po- ), which scales as p for theta solvents and p " for good solvents. Remarkably, these power laws are in complete agreement with the predictions of scaling and field-theoretic approaches and also agree with experimental measurements in semidilute polymer solutions. ""... 

For an athermal case, the continuous deswelling of the network takes place (Fig. 9, curve 1) which in the result of compressing osmotic pressure created by linear chains in the external solution (the concentration of these chains inside the network is lower than in the outer solution, cf. Ref. [36]). If the quality of the solvent for network chains is poorer (Fig. 9, curves 2-4), this deswelling effect is much more pronounced deswelling to strongly compressed state occurs already at low polymer concentrations in the external solution. Since in this case linear chains are a better solvent than the low-molecular component, with an increase of the concentration of these chains in the outer solution, a decollapse transition takes place (Fig. 9, curves 2-5), which may occur in a jump-like fashion (Fig. 9, curves 3-4). It should be emphasized that for these cases the collapse of the polymer network occurs smoothly, while decollapse is a first order phase transition. 

The solution analogue of the compressibility factor of a gas is the reduced osmotic pressure (I7/C2). This quantity is shown sch aticaOy in Fig. 3.3 for polymer molecules under different solvency conditions. In a poor solvent for the polymer, negative deviations from ideality are apparent. This can be envisag as arising because the polymer molecules are in dynamic association under such solvency conditions. Since osmotic pressure is a coUigative... 

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