Osmotic pressure, light scattering and

Physicochemical methods. The physicochemical methods (though mainly of historical interest) from which molecular weights of most biomacromolecules have been determined earlier include osmotic pressure, light scattering and sedimentation. 

The third virial coefficient A3 is defined as the coefficient of in eq 1-2.13 for osmotic pressure II. Theoretically, it reflects the excess interaction of ternary bead clusters, while experimentally its knowledge is important for accurate determination of A2 by analysis of osmotic pressure, light scattering, and sedimentation equilibrium data. However, accurate measurement of A3 is not a simple task, and the available data are as yet neither abundant nor systematic. 

Equation 1.15 may be regarded as the defining equation for the parameter y, since Ago can be evaluated by use of such standard techniques as osmotic pressure, light scattering, and sedimentation equilibrium. In the classic FH theory, y is taken as the strength of the polymer-solvent interaction. However, in the Koningsveld-Staverman formalism, it has no such meaning but is an empirical function which absorbs all the deviations of Ago in an actual quasibinary solution from that in the reference FH solution. 

However, eq 2.3 predicts more accurately x derived from osmotic pressure, light scattering, and sedimentation equilibrium measurements on one-phase solutions [12]. 

Methods of determining molecular weight include osmotic pressure, light scattering, gel permeation chromatography, dilute solution viscosity, vapor pressure, freezing temperatures, and others. Odian GC (2004) Principles of polymerization. John Wiley and Sons Inc., New York. Ehas HG (2003) An introduction to plastics. John Wiley and Sons, New York. Slade PE (2001) Polymer molecular weights, vol 4. Marcel Dekker, New York. 

Beyond adsorption saturation, the lyophobic parts of the amphiphilic molecules may associate to avoid unfavorable solute-solvent contacts. Then, upon further addition of the amphiphilic compound to the solution, the concentration of free monomeric molecules hardly increases anymore, so that, according to Equation 3.88, y remains essentially constant. Thus, the onset of the association process is marked by a discontinuity in the interfacial tension. In addition, a discontinuity is observed in other physical properties, for example, osmotic pressure, light scattering, electric conduction (in case of ionic amphiphiles), and so on. 

Due to the composition dependence of X/ different techniques determine different quantities. Chemical potentials (osmotic pressure, light scattering) involve first-order derivatives (cf. eqns [23a] and [23b]) and scattering experiments involve second-order derivatives of the free energy. For a -dependent X, Afj.1 and Afi2 can be catched in the same form as eqns [31] and [32] for a -independent X/ but now involving two parameters Xii and x Lll respectively. These are related to the free energy/by... 

The critical micelle concentration of a surfactant solution can be determined by measuring surface tension, electric conductivity, osmotic pressure, light scattering, viscosity, dye solubilization, and other physical properties [107] (see Chapter 9). The cmc in aqueous solution can be determined also from a change in the chemical environment indicated by the -NMR chemical shift (5) [140), plotted as a function of inverse surfactant concentration (Fig. 6.14). The intersection in the lines indicates the cmc. 

Theta temperature is one of the most important thermodynamic parameters of polymer solutions. At theta temperature, the long-range interactions vanish, segmental interactions become more effective and the polymer chains assume their unperturbed dimensions. It can be determined by light scattering and osmotic pressure measurements. These techniques are based on the fact that the second virial coefficient, A2, becomes zero at the theta conditions. 

Equation (22) has been confirmed by a variety of techniques including neutron scattering, dynamic light scattering, and osmotic pressured measurements [23]. As concentration increases the concentration blob decreases in size until the Kuhn length is reached and the coil displays concentrated or melt Gaussian structure. The coil accommodates concentrations between the overlap and concentrated through adjustment of the concentration blob size. 

Table I shows the molecular weight and the degree of end group substitution of the monofunctional polystyrene samples obtained. In Table II the corresponding data for the bifunctional samples are given. The samples were characterized by GPC in THF. and were calculated. Comparison with the corresponding nonfunctionalized control samples show good agreement. The results of the light scattering and osmotic pressure experiments with the acid form of the sulfonated polystyrenes were in agreement. No association was observed for THF solutions.

Polystyrene can be prepared as follows A mixture of styrene, detergent (Na-dodecanoate), and water is agitated ultrasonically to produce a fine emulsion. On the addition of hydrogen peroxide (initiator), PS is obtained as a polymer, which can be extracted after filtration. The polymer molecular weight is determined by various methods (such as light scattering and osmotic pressure). 

Analysis of polyelectrolytes in the semi-dilute regime is even more complicated as a result of inter-molecular interactions. It has been established, via dynamic light-scattering and time-dependent electric birefringence measurements, that the behavior of polyelectrolytes is qualitatively different in dilute and semi-dilute regimes. The qualitative behavior of osmotic pressure has been described by a power-law relationship, but no theory approaching quantitative description is available. 

This equation was then applied to a variety of experimental data on solvent activity as related to vapor pressure (40), osmotic pressure in dilute and concentrated solutions (41), and light scattering (42). 

C 26 Cowie, J. M. G., D. J. Worsfeld and S. Bywater Light-scattering and osmotic pressure study on solutions of polystyrene of narrow molecular-weight distribution produced by anionic catalysis. Trans. Faraday Soc. 57,705 (1961). 

If the molecular weight of a protein is known from measurements of osmotic pressure, of sedimentation and diffusion, of sedimentation equilibrium, of light scattering, or by any other inethod, and if its partial specific volume is also known, then the frictional ratio fjf may be determined either from its sedimentation constant or its diffusion constant. The frictional coefficient / is that characteristic of a spherical unhydrated molecule of the same molecular weight and partial specific volume as the protein under consideration. If r is the radius of tliis hypothetical sphere and rj the viscosity of the medium, then... 

Molar masses and molar mass distributions are usually measured in dilute solutions. Osmotic pressure measurements determine and light scattering measurements determine M. The entire molar mass distribution can be measured using properly calibrated SEC. 

Methods for the determination of the molecular weight of a polysaccharide include gel-filtration (Andrews, 1970), ultracentrifugation, light scattering, and osmotic pressure determinations (Banks and Greenwood,... 

Osmotic pressure and vapor pressure methods are used to determine absolute values of M , while light scattering and sedimentation velocity are used to determine However, if the GPC equipment is coupled with different detection techniques, such as light scattering, viscometry, refractive... 

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