Langmuir 1993,9, 1370-1377
1370
Osmotic Properties of Polyelectrolyte Membranes: Positive and Negative Osmosis H.Rottger and D.Woermann* Institut fiir Physikalische Chemie, Universitiit Kbln, Luxemburger Strasse 116, 0-5000 Kbln 41, Germany Received December 10, 1992. In Final Form: February 4, 1993
The osmotic properties of two types of hydrated polyelectrolyte membranes with negatively charged fixed ionic groups in aqueous solutionsof NaCl and SrCl2 are studied. The membranes are condensation products of p-hydroxybenzenesulfonicacid and formaldehyde(abbreviated-SO3- gel) and (hydroxypheny1)methanesulfonicacid and formaldehyde (abbreviated-CH2S03-gel),respectively. Theosmoticproperties are characterizedby measurements of the reflection coefficientusand its concentrationdependence. The system-CH2S03-/SrC12showsnegative osmosis in concentratedsolutions (negativeosmosisis the transport of water across the membrane under isobaric conditions ainst its gradient of the chemical potential). For the other systems (-CH2S03-/NaC1,-SO3-/SrC12,-S 3-/NaC1) positive osmosis is observed at all concentrations. The experimentally determined concentration dependence of usis compared with that predicted by the model of the membrane with narrow pores. The values of the parameters of the model are determined by independent experiments. A satisfactory agreement between the experimental u,(c,) data and the prediction of the model is found when an effectivef i e d ion concentrationof the gels is used for the calculation instead of the analytically determined value. The experimentsindicate that the gels have an inhomogeneous structure.
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1. Introduction
It is the aim of this investigation to analyze the osmotic properties of two types of hydrated polyelectrolyte gels with negatively charged groups. The gels have slightly different chemical structures but differ greatly in their osmotic properties. The simplified chemical structure of the two gels is shown in Figure 1. The osmotic properties are studied in systems in which a membrane formed from these gels separates two homogeneous aqueous solutions of a single electrolyte of slightly different concentrations (Le., Ac,J(c,) 0; anion, zi < 01,F is the Faraday number, R is the universal gas constant, T i s the thermodynamic temperature, (p is the electric potential in the membrane phase, P i s the hydrostatic pressure in the membrane phase, the pressure jump (P - P, at the two-phase boundary membrane phase/bulk phase is given by P- P = RTC(Cj - ci), Xisthe concentration of fixed ionic groups per unit volume of the solution within the pores, w is the sign of the charge of the fixed ionic groups (cation exchange membrane, w = -1; anion exchange membrane, w = +l),and x is the space coordinate running perpendicular to the phase boundary membrane phase/bulk phase. An analysis of eqs 5 and 6 in terms of the thermodynamics of irreversible processes reveals14 that j v is the barycentric velocity of the medium within the pores averaged over the membrane area. For dilute solutions it can be approximated by the mean volume velocity of the pore fluid. It can be identified with the changes of the volume of the bulk phases of the membrane as functions of time (i.e., j v = Vwjw,where V , is the partial volume of water and j , is the molar flow density of water; see also ref 22). The molar flow density ji of species i is also measured relative to the membrane. Equations 5 and 6 show that the model of the membrane with narrow- pores contains only four system-specific parameters, Di, dh, w, and X . They can be determined by independent experiments. The concentrations Ci can be calculated from the concentrations C i of the ionic species i in the bulk phase using the Donnan relation (see eqs 7 and 8). The integrated form of eq 6 GV= (dh/G)(hP-FwX (1, -1) valent electrolyte (e.g., NaC1)
(2, -1) valent electrolyte (e.g., SrC1,)
c+/x- [C+/(2X)l+ w / 2 = 0
(8)
RBttger and Woermann
1372 Langmuir, Vol. 9, No. 5, 1993 s
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Figure 3. Concentrationdependenceof the reflection coefficient u8 of a cation exchange membrane for a (1, -1) and a (2, -1) electrolyte in aqueous solution calculated on the basis of the model of the membrane with narrow pores (see eq 9).
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model of membranes with narrow pores. For a cation exchange membrane it is given by eq 9. The quantities
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Figure 2. Schematic representation of the conditions under which positive and negative osmosis is observed with a cation exchange membrane on the basis of the model of the membrane with narrow pores under isobaric conditions (P= P').A single capillary-likepore is shown. The positionof the symbols s (solute) and w (water)in the schematic representationof the membrane system indicates that the concentrationof the solute in the left bulk pase (single prime) is larger than that in the right bulk phase (double prime) @e., c,' > c,"). m indicates membrane, j,(h& = (dh/6)O,jv(A(p) = (dh/G)(FXA(p) (see eq 6 for w = -l), A single primed variable minus double primed variable, d h is th_e mechanical permeability,6 is the thickness of the_membrane, P is the hydrostaticpressure inside the membrane, (pisthe electric potential in the membrane phase, j v is the volume flow density across the membrane, X is the concentration of the fiied ionic groups per unit volume of the pore fluid, and F is the Faraday number.
A;), where 6 is the thickness of the membrane,A indicates the single primed variable minus the double primed variable) can be used to state the conditions under which positive and negative osmosis will be observed under isobaric conditions (P= P").2 Thme conditions are shown schematicallyin Figure 2 for the case of a cation exchange membrane (w = -1; j,(AP) = (dh/S) 0; jv(Acp) = FX Acp)). It is assumed that the left bulk phase is more concentrated than the right bulk phase (i.e., c; > c,"). In this ca8e the pressure difference @within the membrane phase always has negative values. Consequentlythe volume flow density is always directed from the more dilute to the more concentrated bulk phase. It would cause positive osmo!is if it would act in the absence of the contribution jv(Acp). jV(AG) changes direction with a change of sign of the diffusion potential Acp within the membrane phase. Positive osmosis is observed when the diffusion poten_tial A(p within the membrane phase has negati_vevalues Acp < 0 (i.e., D+ > f)J. Then, jv(AP) and j,(Acp) are directed from the diluted to the concentrated bulk phase (see Figure 2a). Positive osmosis will also be observed when is directed from the dilute to the concentrated bulk phase and at the s-pe time jv(AG) is directed in the opposite direction (Acp > 0, Le., f)+ < f)Jbut bv(Q)l > jv(A(p) (see Figure 2b). Negative osmosis will be observed when jv(Af? is directed from the _dilute to the concentrated bulk phase (0 < 0)and jv(Acp) is directed in the opposite direction (A;> 0, i.e.,D+ < b-)but [i,(AP)J ici(see Table 111). The values of ci/ci are calculated using the Donnan relation with X = X,ff (see Table VI).
of p-hydroxybenzenesulfonicacid during the cross-linking process. The production rate of phenol will be different locally because during the gelation process the reaction mixture is contained in a mold and the composition of its content cannot be maintained homogeneous. Furthermore, the oligomers which are formed by mixing molten p-hydroxybenzenesulfonicacid and formaldehydecontain a high amountof phenol (i.e., a high concentration of groups with the functionality 3) and can act as nuclei for the formation of highly cross-linked regions. This makes the generation of a -SO3- gel with homogeneously distributed cross-links unlikely. A similar analysis of the reaction steps during the gelation process generating the -CH2SO3- gel leads to the expectation that the extent of structural heterogeneities in that gel will be smaller than that in the -803- gel. The ratio of the amounts of substances np/nhp(subscript hp, hydroxybenzenesulfonic acid) is larger than that in the gel at the end of the gelation process (n,/nhp = 3). The gelation process is not influenced by the production rate of phenol. The product DiCi is determined directly in tracer flow experiments (see section 2.3) whereas the ratio C i / C i is obtained from ion exchange experiments under equilibrium conditions. The values of the ratio C i / C i obtained in this manner are not relevant to transport processesbecause the membrane matrix has an inhomogeneous structure (i.e., X,ff < Xa). The agreementbetween the experimentally determined concentration dependence of the reflection coefficient us and those values us calculated from the values of the parameters DiCi and C i / C i is improved considerably when the D$i data are taken from tracer flow experimentaand the CJci data are calculated from the Donnan relation (see eqs 7 and 8) using the value of the effective fixed ion concentration Xeff obtained from the electroosmotic measurements. The results of the calculations are shown in Figure 7. The agreement between the calculated and the experimental curves is better for the -CH2S03membrane than for the -S03- membrane. It is noteworthy that for the system -SO3-/SrClz the calculated reflection coefficients (using Xee) are negative for c,, > 0.1 mol-dm3 whereas they are found to be positive in the entire concentration range experimentally. This finding can be explained by assuming that the volume fraction of the highly cross-linked regions is larger in the
Langmuir, Vol. 9, No.5, 1993 1377
Osmotic Properties of Polyelectrolyte Membranes I
-803- gel than that in the -CH2SO3- gel and that the differently structured regions of the -SOs- gel are coupled together like the components of a mosaic membrane consisting of patches of highly cross-linked cation exchanges and patches of anion exchange material. In the case of the 4 0 3 - gel the components of the mosaic membrane are assumed to be patches of cation exchange material with a high fixed ion concentration and a low mechanical permeability (region 1)and patches of cation exchange material with a low fixed ion concentration and a high mechanical permeability (region 2) [X(region 1)>> X(region 2); &(region 1)
