Osmotic pressure curves

The slower diffusion coefficient derived from the dynamics of the proton anion reactions, measured under osmotic pressure (curve B in Figure 2), implies a complex relationship between the external pressure and the ordering of water in the hydration layer. As the width shrinks, the capacity of protons to diffuse within the space by a random walk is diminished. 

Fig. 38.—Plots of w/c against c for a series of polyisobutylene fractions M =38,000 to 720,000) in cyclohexane ( ) and in benzene (O), both at 30°C. The osmotic pressure tz is expressed in g./cm. and c in g./lOO cc. Curves have been calculated according to Eq. (13). (Krigbaum. )...

Fig. 116.—w/c plotted against c for several fractions of polystyrene in toluene at 30°C. Molecular weights of the fractions are indicated by the numbers appearing with each curve. The osmotic pressure n is expressed n g./cm.2 (Results of Krigaum. )... 

Equation (20-80) requires a mass transfer coefficient k to calculate Cu, and a relation between protein concentration and osmotic pressure. Pure water flux obtained from a plot of flux versus pressure is used to calculate membrane resistance (t ically small). The LMH/psi slope is referred to as the NWP (normal water permeability). The membrane plus fouling resistances are determined after removing the reversible polarization layer through a buffer flush. To illustrate the components of the osmotic flux model. Fig. 20-63 shows flux versus TMP curves corresponding to just the membrane in buffer (Rfouimg = 0, = 0),... 

The dissolution of a solute into a solvent perturbs the colligative properties of the solvent, affecting the freezing point, boiling point, vapor pressure, and osmotic pressure. The dissolution of solutes into a volatile solvent system will affect the vapor pressure of that solvent, and an ideal solution is one for which the degree of vapor pressure change is proportional to the concentration of solute. It was established by Raoult in 1888 that the effect on vapor pressure would be proportional to the mole fraction of solute, and independent of temperature. This behavior is illustrated in Fig. 10A, where individual vapor pressure curves are... 

The influence of neutral salts as well as of acids and bases on the swelling of gelatine which we have seen can be attributed to an apparent change in the solvation of the gel fibrils and may be interpreted in the light of Donnan s theory of the effect of a non-diffusible ion on the osmotic pressure differences between the two phases, is likewise to be noted in the alteration of the viscosity and alcohol precipitation values of protein solutions. From the considerations already advanced there should exist two well-defined maxima in the viscosity and alcohol precipitation curves when these properties are plotted as functions of the Ph, the maxima coinciding with the points of maximum dissociation of the salts... 

Fig. 2. Comparison between the scaled particle theory (solid curves) and experiment (circles and triangles) for osmotic pressure II of PBLG-DMF [56,57], For the samples with M = 6.6 x 104 and 15.5 x 104, the data at T = 15, 30, and 45 °C are plotted with the same symbols...

Why is it that the force of double-layer interactions for curved surfaces cannot be derived using osmotic pressure arguments as is done in the case of planar double layers ... 

The Maxwell construction would determine the condition of two phase coexistence or the points on the curves where the first-order phase change occurs [6,7]. It is the condition that the two phases have the same value of g or j d II = 0 from Eq. (2.6) at zero osmotic pressure, v2 and vx being the values of v in the two phases. However, this criterion is questionable in the case Kcritical point). This is because the shear deformation energy has not been taken into account in the above theory. See Sect. 8 for further comments on this aspect. 

The isoelectric regime (ct, > a3 Fig. 1, curve 3). Here the network remains in compressed state even in good solvent a. m-1/6. The attractive electrostatic interaction due to the term Fei s, < 0 (see Eq. (9)) and very small osmotic pressure of counter ions due to their low concentration are the reasons. 

In the polyelectrolyte regime, due to the presence of low-molecular salt, the osmotic pressure of ions becomes less pronounced because the concentration of salt within the network turns out to be less than the concentration of salt in the outer solution n [27]. As the concentration ns grows, the amplitude of the jump of the dependence a(x) decreases and the jump shifts to the region of better solvents (Fig. 2, curve 2). At some critical value of n, the jump on the curve a(x) disappears, i.e. collapse of the network becomes smooth (Fig. 2, curve 3). Under the subsequent increase of n, the curve a(x) becomes closer and closer to the swelling curve of corresponding neutral network (Fig. 2, curves 4). 

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. 

Fig. la, h. The elastic part (ne) and the negative of the mixing part (— Jtm) of the osmotic pressure as functions of polymer concentration < >. The intercepts of ae and — nm correspond to the equilibrium state of neutral gels. Numbers besides each curve of — represent Xi> which increases with temperature, (a) x2 = 0. Only one root at all temperatures, (b) Xi = 0.56. Three roots appear in the intermediate temperature range (around Xi = 0.465), which correspond to stable, unstable, and metastable states, respectively. (Reproduced with permission from Ref. 20)... 

The swelling behavior of poly(N-isopropylacrylamide) has been studied extensively [18,19]. It has been shown that this gel has a lower critical point due to the hydrophobic interaction. Such a swelling curve is schematically illustrated in Fig. 9. The gel is swollen at a lower temperature and collapses at a higher temperature if the sample gel is allowed to swell freely in water. The volume of the gel changes discontinuously at 33.6°C. The swelling curves obtained in this way correspond to the isobar at zero osmotic pressure. On the other hand, the friction coefficient is measured along the isochore, which is given in Fig. 9,... 

Fig. 9. The swelling curve of the poly(/V-isop-ropylacrylamide) gel is schematically shown. The isobar curve (thick line) corresponds to the zero osmotic pressure. The dotted line indicates the experimental path at which the volume is fixed at the initial volume V0 (the volume at which the gel is prepared)...

The molecular weight of the sodium salt of alginic acid has been determined by measurements of osmotic pressure in sodium chloride solution.88 The n/C versus C curve was found to be independent of salt concentration for values between 0.2 N and 0.5 JV, and the slope of the curve was the same for a series of seven fractions with values of molecular weight between 48,000 and 186,000 (220-860 D-mannuronic acid units). Intrinsic viscosity measurements showed the coefficient a in the modified Staudinger s equation88 to be 1.0 and the approximate value of Km to be 15(10)-4. 

Figure 3. Reduced osmotic pressure fve. reduced total amphlphllar concentration y. The curves are labeled for various values of the parameter A. The values of the other parameters are o — 4.5, n = 40, and n = 50.

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