Swelling pressure calculation

FIG. 10 Pressure curves for Na+-mica surfaces in a 2 mol/L NaCl solution calculated from Eq. (27) and converted for flat surfaces. Also represented is the swelling pressure for a Na-montmorillonite platelet system. Inset pressure curves measured using the direct force method [51]. 

McPhee (1959) suggests that the solvent pressure opposes swelling of the fiber and shows a direct relationship between the extent of swelling in 2 M salt solutions and the solvent pressure calculated from volume changes during solution of the salt. This view is open to a number of criticisms (Crewther, unpublished observations, 1964). 

Water vapour sorption isotherms for a 10% crosslinked sulfonic acid cation exchanger and a 0.4% crosslinked reference resin are shown in Figure 5.2 together with a calculation of the swelling pressure. The anomalous relative positions of the curves at low values of relative humidity P/Pq may be explained in terms of van der Waals type intramolecular forces which weakly bind adjacent polymer chains in de-swollen exchangers of low crosslinking. 

Figure 5.2 Water vapour sorption isotherms and calculation of swelling pressure (Reprinted with permission from B. R. Sundheim, M. H. Waxman, and H. P. Gregor, Phys. Chem., 1953, 57, 974. 1953 American Chemical Society)...

Calculate the maximum possible swelling pressure ofNa" -smectite during expansion from the monolayer hydrate to the two-layer hydrate based on the data in Figure 8.13. 

From a difference in chemical potential it is easy to calculate a clear quantity, the osmotic pressure. Flory has drawn the analogy between swelling equilibrium and osmotic equilibrium (Flory 1953). The difference between the osmotic pressure and the elastic response 71 / of the network chains in the swollen network is named swelling pressure Ures- H can be calculated as following ... 

In order to calculate swelling pressure, we propose the following algorithm ... 

Tuna, N.Y. and Finlayson, B.A. (1984) Exit pressure calculations from numerical extmdate swell results./. Rheai., 28 (2), 79-93. 

Fig. 5. Influence of pressure on swelling of two samples of partly ionized PAAm hydrogels in 0.01 N aqueous NaCl solution solid curve — uniaxial, dashed curves — isotropic swelling as obtained by calculation. Points on the y-axis correspond to the free swelling. From Dubrovskii etal. [22]...

Gee ° has applied this method to the determination of the interaction parameters xi for natural rubber in various solvents. Several rubber vulcanizates were used. The effective value of VelV for each was determined by measuring its extension under a fixed load when swollen in petroleum ether. Samples were then swollen to equilibrium in other solvents, and xi was calculated from the swelling ratio in each. The mean values of xi for the several vulcanizates in each solvent are presented in Table XXXVI, where they are compared with the xi s calculated (Eq. XII-30) from vapor pressure measurements on solutions of unvulcanized rubber in some of the same solvents. The agreement is by no means spectacular, though perhaps no worse than the experimental error in the vapor pressure method. 

Shiga and Kurauchi have explained that the swelling deformation of a PAANa gel is qualitatively induced by a change in the osmotic pressure based upon a difference in mobile ion concentrations between the inside and the outside of a gel [13]. A change in the osmotic pressure under an electric field has been calculated as follows. 

Shiga and Kurauchi have predicted that the swelling deformation of a gel in an electric field is caused by an increase in Flory s osmotic pressure. In order to prove this mechanism, the change in the osmotic pressure under an electric field has been calculated using a simple model for ion transport. The gel and the surrounding solution have been divided into four phases, the A phase (solution at the anode), B phase (gel at the anode), C phase (gel at the cathode), and D phase (solution at the cathode). A mobile cation in a dc field moves toward the... 

Flory osmotic pressures at the anode and cathode sides have been calculated using Eqs. 3-10. In a system of i cations and j anions, the osmotic pressures are given by a summation of Eqs. 3-10. When dn/dt > 0 in an electric field, the gel swells. It shrinks when dn/dt < 0. When n at the anode side becomes larger than that at the cathode side, the gel bends toward the cathode. 

The swelling data in Table IV can be used to calculate x parameters for the extract and O-methylated extract using Equation 1. The results are shown in Table V. The x parameters for both extracts are observed to be positive and independent of pressure or concentration of benzene. The magnitude of the parameters are much larger than that determined for the O-octylated extract (0.65) which is consistent with their lower solubilities in liquid benzene. The X parameters are much larger than those determined by Larsen el al. for the pyridine-extracted Illinois No. 6 coal, which was near 0.3.(6) The reason for this are not clear. However, we note that benzene is a very poor solvent for these pyridine-extracts so large x parameters are expected. 

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