Colloid osmotic coefficient

In Fig. 8b, we show the osmotic coefficients for PAA stars that differ with respect to the numbers of arms at the given degree of neutralization. In accordance with theoretical predictions, the osmotic coefficient (j> decreases (i.e., the degree of localization of counterions increases) upon an increase in the number of arms, p, in the star. Note that in the case of star polymers with relatively small number of arms, the osmotic coefficient is significantly larger (by two orders of magnitude) than that measured previously in the solutions of colloidal PE brushes [44,45]. 

Study of anomalies in a large number of physicochemical properties of solutions of soaps and detergents, e.g., equivalent conductivity, osmotic coefficient, viscosity, and transference numbers, has revealed that the detergents exist both as simple ions and as colloidal aggregates known as micelles. The transition from simple strong electrolytes to micelles begins rather abruptly in dilute solution at a critical concentration char-... 

Kakehashi R, Yamazoe H, Maeda H (1998) Osmotic coefficients of vinylic polyelectrolyte solutions without added salt. Colloid Polym Sci 276 28 33... 

Das B, Guo X, BaUaufF M The osmotic coefficient of spherical polyelectrolyte brushes in aqueous salt-free solution, Progr Colloid Polymer Sd 121 34—8, 2002. 

Now if we adhere strictly to the conception (sec 3d, p 125) that a potential difference between different phases cannot be determined cq (121) has no practical signifi-cance Eq (119) can be used to determine /+ in the colloidal system when the anal3rtical data are available and/+ in the colloid-free solution has been determined. Likewise the osmotic coefficient g can be determined from eq. (122) if all other quantities (notably the molar fraction of the colloid) are known. But as there is no simple relation between /+ and g in this case, that would mean nearly the end of all practical application of the Donnan equilibrium. 

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 ... 

S. Matsumoto and M. Kohda The Viscosity of W/OAV Emulsions An Attempt to Estimate the Water Permeation Coefficient of the Oil Layer from the Viscosity Changes in Diluted Systems on Aging under Osmotic Pressure Gradients. J. Colloid Interface Sci. 73,13 (1980). 

Here, the quantities jn ° and ji are, respectively, the chemical potentials of pure solvent and of the solvent at a certain biopolymer concentration V is the molar volume of the solvent and n is the biopolymer number density, defined as n C/M, where C is the biopolymer concentration (% wt/wt) and M is the number-averaged molar weight of the biopolymer. The second virial coefficient has (weight-scale) units of cm mol g. Hence, the more positive the second virial coefficient, the larger is the osmotic pressure in the bulk of the biopolymer solution. This has consequences for the fluctuations in the biopolymer concentration in solution, which affects the solubility of the biopolymer in the solvent, and also the stability of colloidal systems, as will be discussed later on in this chapter. 

RTfVw) nNw because yw was set equal to 1. For an exact treatment when many interfaces are present (e.g., in the cytosol of a typical cell), we cannot set yw equal to 1 because the activity of water, and hence the osmotic pressure (n), is affected by proteins, other colloids, and other interfaces. In such a case, Equation 2.11 suggests a simple way in which a matric pressure may be related to the reduction of the activity coefficient of water caused by the interactions at interfaces. Equation 2.11 should not be viewed as a relation defining matric pressures for all situations but rather for cases for which it might be useful to represent interfacial interactions by a separate term that can be added to Fly, the effect of the solutes on FI. 

The recent synthesis of model PMMA-grafted SiO2 nanoparticles with the flexibility of tuning grafting density and tc/L [112] provided a means to continue the investigations of along the already discussed path of parameter space. Their dynamic response should display common and distinct features compared with the established equilibrium dynamics of hard sphere colloids. The similarities should include the three aforementioned diffusion coefficients which are, however, expected to be quantitatively different because of the significant alteration of tire interaction potential. In addition, tlie curvature-dependent brush-like nature of the polymeric shell should be manifested in the osmotic pressure of the suspension and the associated dynamics of the total density fluctuations. 

The linear relationship between scattering intensity (excess Rayleigh ratio) and particle concentration holds true only for extremely dilute suspensions. For fine, colloidal particles, a declining concentration impact can be observed, which is related to the osmotic pressure in the colloidal suspension and, therefore, depends on the virial coefficients (Einstein 1910 Zimm 1945 Debye 1947) ... 

Matsumoto, S., and Kohda, M., 1980, The viscosity of water-in-oil-in-water emulsions An attempt to estimate the water permeation coefficient of the oil layer from the viscosity changes in diluted systems on ageing under osmotic pressure gradients, J. Colloid Interface 73 13-20. 

Even in 1928, Harman (34) concluded from conductivity, transfer numbers, activity coefficients, hydrolysis, osmotic activity, freezing point data, phase relations, and diffusion experiments that there are only two simple silicates, NajSiOj and NaHSiOa, and that silicates in the SiO rNajO ratio range of 2 1 to 4 1 become increasingly colloidal. ... 

The osmotic second virial coefficient represents an experimentally accessible thermodynamic parameter to evaluate colloidal stability. This parameter reflects the overall attraction or repulsion between molecules such that a positive value represents net repulsion and vice versa. measurements have been used extensively in the field of protein crystallization to screen for solution conditions favorable to crystallization. In contrast, good pharmaceutical stability seeks strong protein-solvent interactions (positive 22 values) representing conditions under which protein molecules should be less likely to associate. Measurements of 22 h ve proven helpful in developing formulation conditions to minimize aggregation. However, in cases where aggregation proceeds via the formation of a small fraction of a partially unfolded species, the B measurement is not likely to adequately reflect the aggregation propensity of the system [14]. 

The influence of polymer architecture on intermolecular interactions in dilute solutions was investigated by membrane osmometry in toluene (good solvent for polystyrene), cyclohexane (theta or 0 solvent), and methylcyclohexane (poor solvent Striolo et al., 2001). The osmotic second virial coefficient (B22) measured for arborescent polystyrene in toluene was lower than for homologous linear polymers, as expected due to their smaller Rg. In a 0 solvent (cyclohexane), branching lowered the 0 temperature from 34.5 °C (linear homolog) to 32.2 °C (GO polymer). The 0 temperature for the GO polystyrene sample in methylcyclohexane was likewise lowered to 36 °C, as compared to values estimated between 60 and 70 °C for linear polystyrene samples. The experimental osmotic pressure data were successfully fitted with a molecular-thermodynamic equation suitable for colloids, indicating that the behavior of arborescent polystyrene molecules in dilute solution corresponds to a perturbed (weakly interacting or interpenetrable) hard sphere. 

In the applications it is however rarely possible to apply the Donnan theory for ideal systems, at least if more than qualitative results are wanted. From the eq. (115, 116, 117 and 118) it is possible to determine the charge on the colloid in three independent ways. This means, that two relations between the three phenomena (distr. of ions, membrane potential, osmotic pressure) should exist. Now usually, when the osmotic pressure is calculated either from analytical data or from the membrane potential it is found to be too low (Hahmarsten effect ). This clearly indicates the need for a more exact treatment of the Donnan equilibrium, in the first place the introduction of activity coefficients. 

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