Sorption swelling equilibrium

SORPTION OF SOLVENT MIXTURES IN ION EXCHANGE RESINS INFLUENCE OF ELASTIC PROPERTIES ON SWELLING EQUILIBRIUM AND KINETICS... 

In eomparison with all methods of determination of solvent aetivities from swelling equilibrium of network polymers, the gravimetrie vapor sorption/pressure measurement is the easiest applieable proeedure, gives the most reliable data, and should be preferred. 

The parameter x can be obtained by several techniques including osmometry, vapor sorption, gas-liquid chromatography, freezing point depression of solvent, swelling equilibrium, intrinsic viscosity, and critical solution temperatures... 

Flory has derived the elastic free energy of dilation of a network with account of restrictions of fluctuations of junctions. Quantitative agreement has been reported for vapor sorption measurements. Particularly impressive is reproduction of the observation that the product of the linear expansion ratiok and the elastic contribution (pi — p.i)e, to the chemkal potential of the dilumt in a swollen network exhibits a maximum with increase in k, which is contrary to previous theory It is convenient to compare the phantom modulus obtained by stress-str measurements to that obtained from swelling equilibrium studies... 

The volume fraction of polymer at equilibrium (maximum) swelling is designated i 2m- Then, equations (144) and (146) may be used to test the phenomenological or molecular theories of elasticity, and to characterize elastomeric networks by differential solvent vapor sorption and swelling equilibrium measurements, respectively. 

The anomalous increase of the water uptake observed in Fig. 10 when approaching equilibrium at 60 °C has been associated to the damage. The abrupt upturn of the sorption curve may be explained considering a possible crazing of the low crosslinked internodular matrix induced by the differential swelling stresses that can arise, at high water contents, between areas of different crosslinking density. 

The equilibrium swelling degree is the most important property of a hydrogel it directly influences the rate of water sorption, the permeability to drugs, and the mechanical strength of the gel. It also affects the biocompatibility of the... 

Pure PHEMA gel is sufficiently physically cross-linked by entanglements that it swells in water without dissolving, even without covalent cross-links. Its water sorption kinetics are Fickian over a broad temperature range. As the temperature increases, the diffusion coefficient of the sorption process rises from a value of 3.2 X 10 8 cm2/s at 4°C to 5.6 x 10 7 cm2/s at 88°C according to an Arrhenius rate law with an activation energy of 6.1 kcal/mol. At 5°C, the sample becomes completely rubbery at 60% of the equilibrium solvent uptake (q = 1.67). This transition drops steadily as Tg is approached ( 90°C), so that at 88°C the sample becomes entirely rubbery with less than 30% of the equilibrium uptake (q = 1.51) (data cited here are from Ref. 138). 

EQUILIBRIUM SORPTION VALUES. The equilibrium sorption values for the extracts at various pressures of benzene are shown in Table II. The results show that O-methylated extract sorbs the most benzene at the lower pressure and that the O-octylated extract sorbs the least. At the higher pressme, the order is reversed. We believe the data shown in Table II reflect changes in the relative amounts of adsorption and absorption (swelling) with increasing size of the added alkyl groups. This interpretation is based on surface area and solubility measurements described below. 

Through the uptake of a substance in a polymer matrix, time dependent changes in the polymer matrix can take place, particularly at high concentrations. As a consequence, the diffusion coefficient can be time- as well as concentration-dependent. One observes such behavior for example by the sorption of substances that lead to swelling at temperatures below the Tg. After a relatively rapid approach to an apparent state of equilibrium one observes a slow change towards the actual equilibrium (Fig. 9-2e). These two-step processes are caused by a gradual loosening of the cohesive forces between the macromolecules. 

Lipatov798 recognized that the sorption of Methylene Blue on starch is a heterogenous neutralization reaction of neutralization in which starch acts as an acid. Adsorption isotherms of Methylene Blue on starch indicate that it is an equilibrium process and that swelling as well as other internal structural factors are responsible for the sigmoidal shape of the isotherm.799-800 It is also known that the Langmuir isotherm is affected by equilibrium between the monomer and dimer forms of Methylene Blue, both of which are capable of adsorption on starch (Table XLV).801... 

Although the kinetics of liquid uptake to attain gel-saturation is history-dependent, the composition at the true end-state (i.e. thermodynamic equilibrium in excess liquid) is not therefore the observed end-state is usually reproducible [19]. Gel-saturation is attained when the restraining force (per unit area) of the polymeric crosslinked network becomes equal and opposite to the osmotic pressure that causes the system to swell [20], In other words saturation is achieved when the chemical potential of swelling liquid, p1 in the swollen network is equal to the chemical potential of the excess pure liquid, p , outside the network. It was logical to anticipate that the volume of liquid sorbed per gram of polymer, at this state of thermodynamic equilibrium with excess liquid, would correlate with the molecular structure of the liquid. In fact two parameters already exist which relate the sorption affinity to the molecular structure, namely the solubility parameter, 8, first proposed by Hildebrand [21], and the interaction parameter, %, introduced by Flory [22] and Huggins [23-26],... 

Equation 5.4 is the basis of a more detailed and fundamental study of the swelling process achieved through the study of resin-water vapour sorption isotherms obtained isopiestically i.e. at equal total pressures and equal resin water content). The isopiestic vapour pressure technique takes account of variable activity of the water in the resin (and therefore IT) by allowing the resin to come to equilibrium with water vapour at different partial vapour pressures P. It is assumed that two resins of the same structural type, but with different degrees of crosslinking, have the same water activity at the same equivalent water content. At equilibrium between resin and vapour phases the water activity in resins (1) and (2) are given by ... 

This simple relationship was derived before as equation 5.24, and was first used by Bauman and Eichorn in 1947 to predict selectivity sequences for simple monovalent cations from mean ionic activity coefficient data for pure aqueous electrolyte solutions containing a common anion. The inaccessibility of resin phase activity coefficients to direct measurement always remains a problem with thermodynamic equilibrium treatments. Therefore Glueckauf and others developed weight swelling and isopiestic water vapour sorption techniques to determine osmotic coefficients of pure salt forms of a resin, from which the mean ionic activity coefficients of mixed resinates could be computed using a modified form of Harned s Rule. Such studies predicted selectivity coefficient values which were in fair agreement with experiment and also demonstrated the fixed ion of the resin to be osmotically inactive. 

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