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Describing the sorption characteristics of a ternary system of benzene (1) and alcohol (2) in a nonporous polymer membrane (3) by the Flory-Huggins model.

INTRODUCTION

Mixed solvents are widely used to adjust solvent properties according to the specific needs of chemical engineering processes and chemical research [1-9]. One type of chemical engineering process, where mixed solvents have found broad use is separation of components from mixtures. Our research is focused on membrane separation processes [10-18] and, as a further challenge, on the separation of single enantiomers from their racemic mixtures. The preparation of single enantiomers is important in the pharmaceutical industry and in pharmacology because two enantiomers may exhibit completely different biological or pharmacological activities, pharmacokinetic profiles or effectiveness, or they may exhibit different potency, as the interacting molecules in biological systems are also chiral [19-25]. A direct artificial preparation of a single enantiomer can be possible when using enantioselective catalysis using chiral catalysts or enzymes; however, such approaches are expensive and time consuming. It could be much easier and cheaper to prepare the racemic mixture by classical simple nonenantioselective chemical synthesis and this mixture would be separated in a following step by enantioselective physical methods. Therefore development of cheap and effective methods for the separation of the desired enantiomer is a challenging task encountered in many fields of research and industry. Because pharmacologically important enantiomers are typically large molecules, they are mostly not volatile and are often in the solid state. Therefore, popular membrane separation techniques, namely permeation and pervaporation, cannot be used, and membrane separation based on transport from a liquid solution into a liquid solvent is required. Donan dialysis, a process related to the transport of charged particles, and pertraction, where a liquid membrane is used to separate nonelectrolytes or electrolytes, are examples [26, 27]. Denomination pertraction is also used for membrane process involving transport from a liquid into the liquid phase through a nonporous solid membrane (a liquid membrane is an example of a nonporous membrane). In addition to using the appropriate pertraction apparatus for the separation of nonvolatile compounds, it is necessary to use suitable nonpolar or polar solvents according to the physical properties of the polymer membrane, solvent, and dissolved mixture that should be separated. To be able to describe both the sorption equilibrium of this system and, in the case of a concentration (chemical potential) gradient, the component flux through the membrane adequately, it is necessary to use suitable thermodynamic and diffusion models. Because we use the mixed solvent of benzene and alcohol in our pertraction experiments, we studied the sorption equilibrium with both polar and nonpolar membranes in these liquid mixtures to ascertain whether we would be able to describe the sorption equilibrium in different combinations of polar and nonpolar liquids and membranes using a single model.

A treatment of the experimental data on sorption of liquids (pure or mixtures) in an immersed nonporous polymer membrane can be based on purely empirical or semiempirical equations or on theoretical models. In the sorption description, the polymer membrane is treated either as a homogenous amorphous surrounding where solute molecules are dissolved, or as surrounding including amorphous and the crystalline phases, where molecules of solutes are dissolved only in the homogenous amorphous phase and crystalline phase behaves as an inert phase [28]. Examples of the models used to describe these systems include: (i) the Flory-Huggins equation [29-32]; the Flory-Rehner equation [28, 33-37], which is a modified form of the original Flory-Huggins equation; (iii) the UNIFAP model [28, 38-12], which is based on the UNIFAC model [43, 44]. A different approach for highly concentrated polymer solutions and swelled membranes immersed into liquid solutions was given by van de Witte et al. [45] and Young et al. [46], in which the ternary interaction parameter in the Flory-Huggins equation was used. This approach was used in this article.

MATERIALS

2-Butanol (puriss p.a. min. 99.5 % grade) and methanol (puriss p.a. min 99.8 % grade) were supplied by Sigma-Aldrich. Benzene (p.a. min 99.8 %) was supplied by Penta, Czech Republic. No additional purification treatment was applied.

High-pressure low-density polyethylene (LDPE) BRALEN FB 2-30 (Slovnaft, Bratislava) in the form of a foil (thickness 0.046 mm--measured by an Inductive Dial Indicator, Mahr, Germany) was used as an example of a nonpolar membrane. Its density ([rho] = 0.940 g [cm.sup.-3]) was determined by weighing of a sample of known area and thickness. Prior to experiments, the foil was washed with distilled water, dried in a drying box for 20 hours at 60[degrees]C and then kept in a vacuum desiccator.

Nafion N-112, N-115, and N-117 (each having different thickness but density of 1.97 g [cm.sup.-3]--as determined by weighing a sample of known area and thickness) was used as received (DuPont). These are examples of highly polar membranes. Moreover, Nafion is a polymer with chiral carbons and a highly reactive acidic hydrogen cation ([H.sup.+]), and it is possible to modify Nafion membrane by substituting the [H.sup.+] for a cation with chiral properties to obtain a membrane suitable for chiral separation.

EXPERIMENTAL

The total amount of the sorbed liquid per 1 g of dry membrane, ([Q.sub.m]), has been determined by a gravimetric method [14, 15, 28, 47]. A preweighed circular disc-shaped membrane sample of the dry polymer (diameter of 6 cm) was immersed into an excessive amount ([m.sub.solution]/[m.sub.polymer] [approximately equal to] 300) of the respective solvent mixture of an exactly known composition in a tightly sealed flask and allowed to reach sorption equilibrium. The wet membrane sample was then transferred into a weighing bottle lined with filter paper and arranged in such a position that only its edges touched the paper. The full bottle was weighed after approximately 1 h when the paper had drained off the excess liquid from the membrane and equilibrium in the bottle was established. The foil was then quickly taken out and the bottle with the wet paper was weighed again. The difference represented the weight of the swollen foil (m). This procedure was found to be reproducible to [+ or -]2 mg. The results are expressed as the mass swelling degree ([Q.sub.m])

[Q.sub.m] = [m - [m.sub.0] / [m.sub.0] (1)

where [m.sub.0] and m are the masses of the dry and swollen polymer membrane, respectively.

To determine the preferential sorption, the change in benzene concentration in the bulk solution brought about by its contact with polymer was measured. Exactly weighed amounts of the dry polymeric foil cut in small pieces and of the binary liquid solution with a known composition ([m.solution]/[m.sub.polymer] [approximately equal to] 3) in a tightly sealed bottle were kept at constant temperature for 24 hours and stirred often. The difference in benzene mole fraction in the initial and equilibrium liquid solutions with the immersed membrane, [x.sup.l.sub.1,0] - [x.sup.l.sub.1], was then determined using a Rayleigh-Haber-Lowe differential interferometer (Carl Zeiss, Germany) with a 0.5-cm double cell [(maximum difference in the molar fractions [+ or -] 0.02).sup.18]. The preferential sorption was calculated from

[[OMEGA].sub.1] = [n.sup.l.sub.0] x ([x.sup.1.0] - [x.sup.l.sub.1] (2)

where [n.sub.0] is the number of moles of the initial binary solution per 1 g of dry polymer, and [x.sup.l.sub.1,0] and [x.sup.l.sub.1] are the molar fractions of benzene in the bulk initial and equilibrium solutions, respectively. The total amount of binary liquid absorbed in 1 g of a dry polymer ([n.sup.sm.sub.(12)]) can be expressed from the weight uptake and average molar mass of absorbed liquid ([[bar.M].sup.s])

[n.sup.sm.sub.(l2)] = [Q.sub.m]/[[bar.M].sup.sm.sub.(12)]] = [Q.sub.m]/[x.sup.sm.sub.1(12)] [M.sub.1][M.sub.1] + (1 -[x.sm.sub.1(12))) [M.sub.2] (3)

where [x.sup.sm.sub.1(12) is mole fraction of benzene in liquid absorbed in the swelled membrane and [M.sub.1 and [M.sub.2] denote molar masses of substances 1 and 2, resp:

The preferential sorption can be expressed also as

[[OMEGA].sub.1].= [n.sm.](12)([x.sup.sm].sub.1(12)] - [x].sup.l.sub.1]) (4)

and [x.sup.S.sub.1] can be calculated from experimental data merging Eqs. 3 and 4:

[x.sum.1(12) = [Q.sub.m] [x.sup.l.sub.1] [[OMEGA].sub.1][M.sub.2]/[[OMEGA].sub.1] ([M.sub.2] - [M.sub.1]) + [Q.sub.m] (5)

where preferential sorption is obtained from Eq. 2.

INPUT DATA FOR CORRELATION

Experimental sorption data for benzene (1), methanol (2), and polymer membrane (3) systems were published in Randova et al. [14]. Experimental sorption data for the system containing benzene (1), 2-butanol (2), and LDPE (3) measured in this work are given in Table 1. Vapor-liquid equilibrium data were taken from Gmehling et al. [48] This reference is a comprehensive database collecting primary experimental data. Because some primary references were difficult to obtain, the data were taken from this secondary reference.

CORRELATION PROCEDURE

The Flory-Huggins equation [29, 30] was used for correlation of data. Because Flory's original article [30] is for a binary diluted system, we used the equations for the calculation of chemical potentials given by Young et al. [46]. These equations are valid for highly concentrated polymer solutions and incorporate a description of concentration dependence of interaction parameters for a ternary system with a swollen membrane. Note that there is an error in the form of the original Eq. 2 in Young's articles [46, 49]. To obtain the right form of the equation it is necessary to delete the term - [[phi].sub.1], [[phi].sup2.sub.3] ([partial derivative][[chi].sub.13]/[partial derivative][[phi].sub.2] from the original equation for the chemical potential of compound 1. The equation used for Gibbs energy of mixing ([DELTA][G.sup.M]) and the derived equations for the activities of substances ([a.sub.i]) in the ternary system were

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (6)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (7)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (8)

The symbols [[mu].sub.i], and [[mu].sup.0.sub.i] denote the values of the chemical potential and the chemical potential in the standard state, respectively. Activities ([a.sub.i]) are expressed as a function of the volume fractions [[phi].sub.i] ([a.sub.i] = [[gamma].sub.i][[phi].sub.i]. Volume fractions are defined as

[[phi].sub.i] = [V.sup.*.sub.i]/[[summation].supn.sub.j=1][V.sup.*.sub.j] (9)

where the volume of the pure i-th solute ([V.sup.*.sub.j]) is divided by the sum of the volumes of pure compounds (no excess volume taken into account). The binary interactions parameters ([x.sub.ij]) and the ternary interaction parameter ([[chi].sub.T]) are concentration dependent. The symbol [V.sub.mi] denotes molar volumes of the substances. The fractions [h.sub.1(12)] and /[h.sub.2(12)] are defined as

[h.sub.1(12] = [[phi].sub.1]/[[phi].sub.1] + [[phi].sub.2]; [h.sub.2(12)] = [[phi].sub.2]/[[phi].sub.1] + [[phi].sub.2] (10)

and they represent the volume fractions in the binary sub-system of substances (1) and (2).

To achieve higher quality correlation results, the polymer sorption data were supplemented with literature vapor-liquid equilibrium (VLE) data for the benzene-alcohol system. This approach enabled us to adjust the parameters related to benzene-alcohol interactions independently of the polymer sorption data, decreasing the number of adjustable parameters. The Flory-Huggins equation was chosen for correlation of the binary VLE data to keep consistency using the same equation as for description of the ternary system.

The correlation of the binary VLE data was performed using thermodynamic conditions at equilibrium where the chemical potentials are equal. Because the standard states are the same in bulk phases for benzene and the alcohols studied in this work, the equilibrium conditions can be written as an equality of activities

[a.sup.l.sub.1,i] = [a.sup.g.sub.1,i]

[a.sup.l.sub.2,i] = [a.sup.g.sub.2,i] (11)

where the superscripts 1 and g denote liquid and vapor phases, respectively, and the subscripts 1,2, and i denote the activity of benzene, alcohol, and a consecutive number of an experimental points, respectively.

The form of the minimization function was

S = [N.summation over (i=1)] {[([a.sup.g.sub.1i] - [a.sup.l.sub.1i]/[a.sup.l.sub.1i]).sup.2] + [([a.sup.g.sub.2i] - [a.sup.l.sub.2i]/[a.sup.l.sub.2i]).sup.2]} (12)

where the activity terms in the denominators are in place to increase the weight of points from dilute regions, where activities are low. The symbol N denotes overall number of experimental points.

VLE data were correlated using the Flory-Huggins equation assuming that interaction parameter [[chi].sub.12] was dependent on concentration (expressed by volume fraction [[phi].sup.l.sub.i] in binary liquid solution). The polynomial and rational functions

[[chi].sup.l.sub.12] = [A.sub.12] + [B.sub.12][[phi].sup.l.sub.2] + [C.sub.12][[phi].sup.l.sub.2] [[chi].sup.l.sub.12] = [A.sub.12] + [B.sub.12]/1 + [C.sub.12][[phi].sup.l.sub.2] (13)

were tested. The quality of the correlation using the three-parameter polynomial equation was not satisfactory. The correlation using the three-parameter rational equation in the Flory-Huggins equation was plausible, as shown in Fig. 1. The obtained values of the parameters [Al.sub.2], [B.sub.12], and [C.sub.12] of the rational function were 1.8960, 5.6330, and 7.2051 for benzene (1) + methanol (2) sub-system and 1.1824, 0.72840, and 2.3618 for benzene (1) + 2-butanol (2) sub-system, respectively. The result of the correlation using the Flory-Huggins equation was slightly better than that from the Margules three-parameter equation. The values of the limiting activity coefficients were not fixed to particular values during correlation because their values are not known with sufficient precision. We constrained the values of the parameters in such a way that the limiting activity values had to be within 10 % of the most probable value. The experimental literature data and estimation by the modified UNIFAC method show that the most probable values for the limiting activity coefficient at 298.15 K (using volume fraction convention [a.sub.i] = [[gamma].sub.i][[phi].sub.i]) are 3.4 for benzene in methanol [50-52], 48.3 for methanol in benzene as estimated by the modified UNIFAC method [43, 53-55], 4.2 for benzene in 2-butanol and 6.9 for 2-butanol in benzene.

Correlation for ternary data was performed using the same thermodynamic conditions at equilibrium as in the case of the VLE data because it is assumed that the standard states for methanol and benzene are the same in both bulk phases (liquid and swelled polymer)

[a.sup.l.sub.1i] = [a.sup.sm.sub.1i]

[a.sup.l.sub.2i] = [a.sup.sm.sub.2i] (14)

where the superscripts 1 and sm denote the liquid and swelled polymer membrane, respectively. There are only two equations because the polymer is not dissolved in the liquid. Activities in the swollen polymer were calculated using Eqs. 7 and 8 for chemical potentials in the ternary system. The terms with [V.sub.m3] values in the denominators could be neglected because the molar volume of the polymer is much higher than the molar volume of benzene or alcohol with only one or four carbon atoms. The volume of the pure polymer membrane used in the determination of the volume fractions was calculated from the mass of the sample and the density of the polymer. The volume fractions were calculated in two ways. First, no crystallinity was assumed, and the volume of the whole membrane sample was used in the volume fraction calculation (as in the Table 1). Second, the extent of crystallinity reported in the literature was taken into consideration (45.5 % in the case of LDPE [56], 25 % in the case of Nafion [57]). It was assumed that the crystalline part is not affected by liquid, and, therefore, the volume of membrane used in the calculations of volume fractions was obtained by multiplication of the dry membrane volume by the relative fraction of the amorphous phase (0.545 for LDPE and 0.75 for Nafion membranes).

The form of the minimization function for membrane sorption data was analogous to the Eq. 12

S = [N.summation over (i=1)] {[([a.sup.sm.sub.1i] - [a.sup.l.sub.1i]/[a.sup.l.sub.1i]).sup.2] + [([a.sup.sm.sub.2i] - [a.sup.l.sub.2i]/[a.sup.l.sub.2i]).sup.2]} (15)

During correlation, three parameters ([A.sub.12], [B.sub.12], [C.sub.12]) describing the concentration dependence of [[chi].sup.sm.sub.12] (obtained from the VLE data correlation) were kept fixed and [[chi].sup.sm.sub.12] values were calculated from the equation

[[chi].sup.sm.sub.12] + [A.sub.12] + [B.sub.12]/1 + [C.sub.12][h.sup.m.sub.2(12)] (16)

where

[h.sup.sm.sub.2(12)] = [[phi].sup.sm.sub.2]/[[phi].sup.sm.sub.1][[phi].sup.sm.sub.2] (17)

These equations assume that [[chi].sup.m.sub.12] values are not influenced by the third substance. The values of the binary interaction parameters [[chi].sup.m.sub.13] and [[chi].sup.m.sub.23] were calculated using either the rational or polynomial functions

[[chi].sup.sm.sub.i3] = [A.sub.i3] + [B.sup.i3]/1 + [C.sub.i3][h.sup.sm.sub.3(i3)] (18)

or

[[chi].sup.sm.sub.i3] = [A.sub.i3] + [B.sup.i3][h.sup.sm.sub.3(i3)] + [C.sub.13][([h.sup.sm.sub.3(i3)]).sup.2] (19)

where

[h.sup.sm.sub.3(i3)] = [[phi].sup.sm.sub.3]/[[phi].sup.sm.sub.i] + [[phi].sup.sm.sub.3] (20)

Choosing between Eqs. 18 or 19 depended on the type of polymer membrane and the i-th solute. For a polar membrane (Nafion), Eq. 18 was preferred for description of benzene--Nafion interactions and Eq. 19 was prepared for methanol--Nafion interactions because of relatively low values of [[chi].sup.sm.sub.23] where a fractional form of the equation is not suitable. Analogously, in the case of a nonpolar LDPE membrane, Eq. 19 was preferred because of relatively low values of [[chi].sup.sm.sub.13] for description of benzene-LDPE chain interactions, and eq. 18 was preferred for LDPE chains--polar methanol interactions. In the case of 2-butanol in LDPE, polynomial Eq. 19 was used because 2-butanol is much less polar than methanol. Note that Nafion was treated as a nonionic membrane because the liquid is nonionic, and therefore, there is no exchange of hydrogen cations between Nafion and the liquid solution (i.e. the hydrogen cation--sulfonic group ionic bond persists).

The ternary interaction parameter ([[chi].sup.sm.sub.T]) was defined as [46]

[[chi].sup.sm.sub.T] + [A.sub.T] + [B.sub.T][[phi].sup.sm.sub.2] + [C.sub.T][[phi].sup.sm.sub.3] (21)

The values of the parameters [A.sub.13] and [A.sub.23] were constrained following the sorption data in pure liquids (i.e., membrane in pure benzene or pure alcohol). The activity of pure solvent in the liquid phase is 1; in such a case, [A.sub.13] and [A.sub.23] are determined from the corresponding equilibrium condition. The parameters [B.sub.13], [B.sub.23], [C.sub.13], [C.sub.23], [A.sub.T], [B.sub.T], [C.sub.T] were adjusted or set to zero by the correlation procedure. The values of parameters obtained by the correlation procedure are given in Table 2.

DISCUSSION AND CONCLUSION

As seen in Figs. 2 and 3, the description of the sorption equilibrium using the chosen equation and the fitted parameters (given in Table 2) is of good quality, and there is no significant difference between calculations assuming zero and nonzero crystallinity. Of course, there is a significant difference in the phase diagrams for zero and nonzero crystallinity where volume fractions of polymers are calculated by taking the amorphous part of polymer into account, only (see Fig. 4 and 5). The calculations assuming zero crystallinity are reasonable if a chemical engineering perspective (i.e., total chemical composition without distinguishing between crystal and noncrystal phase of polymer) is preferred and obtaining parameters with thermodynamic background is of low importance. If it is preferable to account only for the interacting parts of the systems and it is assumed that the crystal part of the polymer is inert (i.e., from the point of view of interactions between the polymer chains and the absorbed liquid), then only the amorphous part of the polymer needs to be taken into account in the calculation. The concentration dependence of [[chi].sup.sm.sub.13] and [[chi].sup.sm.sub.23] as a function of the pseudo-binary mixture composition ([h.sup.sm.sub.i(i3)]) is shown in Figs. 6 and 7. As was anticipated, the parameter values are low for benzene vs. nonpolar LDPE interactions and alcohol vs. polar Nafion interactions. There is no significant difference among the different Nafions. They differ only by thickness values of the membrane, which in fact supports the idea that preferential adsorption at the surface is negligible compared to absorption in the membrane (or the preferential adsorption at the surface is the same as in the membrane). Figure 7 shows the difference between the values calculated for data assuming zero-crystallinity and data assuming nonzero crystallinity of the polymers. It can be seen that the differences are very low. This finding is reasonable, reflects positively on our data and correlation procedure because the parameters are shown as a function of a pseudobinary solute (i)-polymer (3) system. Of course, if the volume fractions [[phi].sup.sm.sub.i] would be considered as independent properties, the form of the dependences would be different, but the values of the parameters at the concentration edges would be the same. Finally, limiting activity coefficients of benzene and alcohols in swelled LDPE calculated from constants in Table 2 were compared with values estimated from the modified UNIFAC [43, 53] assuming that the solvent is a hypothetical liquid hydrocarbon that has the same density as LDPE. To obtain the limiting activity coefficient values from the UNIFAC method, we extrapolated the densities of liquid n-hydrocarbons at 298.15 K as a function of carbon atom number. We found that the necessary hypothetical liquid hydrocarbon would have 60 carbon atoms. Then, we estimated the limiting activity coefficients of benzene and the alcohols in this C60 hydrocarbon, and after conversion into values corresponding to the use of volume fractions for the calculation of activity, we compared them to values from our data. The agreement was reasonable. The value of 4.9 for benzene in this hypothetical C60 hydrocarbon is close to the value of 6.6 obtained from our data assuming nonzero crystallinity, albeit more distant from the value of 12 obtained from our data assuming zero crystallinity. The value of 390 for methanol in the hypothetical C60 hydrocarbon is relatively close to the value of 365 obtained from our data assuming zero crystallinity and more distant from value the 260 obtained from our data assuming nonzero crystallinity. In the case of 2-butanol in the hypothetical C60 hydrocarbon, the modified UNIFAC method gave a value of 90. The resulting values for the limiting activity coefficient of 2-butanol in LDPE from the parameters obtained by our correlation are 110 assuming nonzero crystallinity and 140 assuming zero-crystallinity. The agreement between the corresponding values is not excellent, but is rather good when considering the number of simplifying assumptions that were performed (e.g. no branching of the carbon chain was assumed). Therefore we plan to develop this concept in future studies.

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Stepan Hovorka, (1) Alena Randova, (1) Petr Sysel, (2) Libuse Brozova, (3) Jan Zitka, (3) Pavel Drasar, (4) Lidmila Bartovska, (1) Jan Storch, (5) Lucie Cervenkova-Sfastna, (5) Pavel Izak (5)

(1) Faculty of Chemical Engineering, Department of Physical Chemistry, Institute of Chemical Technology Prague, Technicka 5, CZ 166 28, Prague 6--Dejvice, Czech Republic

(2) Faculty of Chemical Technology, Department of Polymers, Institute of Chemical Technology Prague, Technicka 5, CZ 166 28, Prague 6--Dejvice, Czech Republic

(3) Institute of Macromolecular Chemistry AS CR, Fleyrovskeho namesti 2, CZ-162 06, Prague 6, Czech Republic

(4) Faculty of Food and Biochemical Technology, Department of Chemistry and Natural Compounds, Institute of Chemical Technology Prague, Technicka 5, CZ 166 28, Prague 6--Dejvice, Czech Republic

(5) Institute of Chemical Process Fundamentals, Rozvojova 135, CZ-165 02, Prague 6, Czech Republic

Correspondence to: Stepan Hovorka; e-mail: Stepan.Hovorka@vscht.cz

Contract grant sponsor: The Czech Science Foundation; contract grant number: P106/12/0569.

DOI 10.1002/pen.23990

Published online in Wiley Online Library (wileyonlinelibrary.com).

TABLE 1. Experimental sorption data (from this work) for the system
of benzene (1), 2-butanol (2), and LDPE (3) including the equilibrium
total sorption of liquid [Q.sub.m], the equilibrium composition of
swelled polymer given by volume fractions ([[phi].sup.sm.sub.i]), and
the equilibrium molar fraction of benzene ([x.sup.sm.sub.1(12)]) in
the binary liquid absorbed in the swollen membrane both as function
of equilibrium molar fraction of benzene ([x.sup.l.sub.1]) in the
binary solution of benzene (1) and 2-butanol (2), in which membrane
is immersed

                  [[OMEGA].sub.1] x
                  [10.sup.4] mol      [Q.sub.m] g
[x.sup.l.sub.1]     [g.sup.-1]        [g.sup.-1]    [x.sup.sm.sub.1(12)]

1                     0               0.2396             1
0.89099               0.65369         0.192153           0.91745
0.88689               1.78515         0.190099           0.96009
0.80104               2.60623         0.175502           0.91655
0.70044               4.0852          0.168625           0.88862
0.53959               4.70594         0.16122            0.76487
0.32278               4.83945         0.127227           0.61407
0.27204               4.50394         0.11228            0.57862
0.068086              3.28753         0.06135            0.47546
0.033402              2.51681         0.054047           0.38573
0                        0            0.050357           0

                  [n.sup.sm.sub.1]   [n.sup.sm.sub.2]
                  x [10.sup.4] mol   x [10.sup.4] mol
[x.sup.l.sub.1]      [g.sup.-1]         [g.sup.-1]

1                     30.671             0
0.89099               22.663             2.0390
0.88689               23.411             0.97311
0.80104               20.679             1.8828
0.70044               19.291             2.4180
0.53959               15.977             4.9116
0.32278               10.202             6.4120
0.27204                8.4997            6.1899
0.068086               3.8399            4.2330
0.033402               2.75530           4.38782
0                      0                 6.79392

[x.sup.l.sub.1]   [[phi].sup.sm.sub.1]   [[phi].sup.sm.sub.2]

1                       0.20496                0.00000
0.89099                 0.15761                0.01494
0.88689                 0.16324                0.00715
0.80104                 0.14600                0.01401
0.70044                 0.13700                0.01809
0.53959                 0.11402                0.03693
0.32278                 0.07505                0.04971
0.27204                 0.06343                0.04868
0.068086                0.03015                0.03505
0.033402                0.02181                0.03659
0                       0.00000                0.05676

[x.sup.l.sub.1]   [[phi].sup.sm.sub.3]

1                       0.79504
0.89099                 0.82744
0.88689                 0.82961
0.80104                 0.83999
0.70044                 0.84491
0.53959                 0.84904
0.32278                 0.87524
0.27204                 0.88789
0.068086                0.93480
0.033402                0.94160
0                       0.94324

The data are supplemented by corresponding preferential sorption
([[ohm].sub.1]) values and values of amount of benzene (1) and
2-butanol (2) in the swollen membrane (per 1 gram of the dry
membrane).

TABLE 2. The parameters describing the concentration dependence of
binary ([[chi].sup.sm.sub.13], [[chi].sup.sm.sub.23]) and ternary
([[chi].sup.sm.sub.T]) interaction parameters in the Flory-Huggins
equation [DELTA][G.sup.M] = RT([n.sub.1] In [[phi].sub.1] + [n.sub.2]
In [[phi].sub.2] + [[chi].sub.12] [n.sub.1] [[phi].sub.2] +
[[chi].sub.13] [n.sub.1] [[phi].sub.3] + [[chi].sub.23] [n.sub.2]
[[phi].sub.3] + [[chi].sub.T][n.sub.1][[phi].sub.2][[phi].sub.3]) for
the ternary mixture of benzene (1), alcohol (2), and swelled
nonporous polymer membrane (3) systems

Membrane         Crystallinity (a)   [A.sub.13] (b)   [B.sub.13] (b)

LDPE (d)                 0              0.91653          0.56648
                       0.455            1.04797          -0.15556
LDPE (e)                 0              0.91653          0.56648
                       0.455            1.04797          -0.15556
Nafion 112 (d)           0              0.94550          0.18680
                       0.25             0.75979          0.21300
Nafion 115 (d)           0              1.33994          0.18631
                       0.25             1.23036          0.21918
Nafion 117 (d)           0              0.87578          0.19853
                       0.25             0.72783          0.21985

Membrane         Crystallinity (a)   [C.sub.13] (b)   [A.sub.23] (b)

LDPE (d)                 0                 --            1.29524
                       0.455               --            0.90428
LDPE (e)                 0                 --            116.454
                       0.455               --            38.3734
Nafion 112 (d)           0              -0.95534         4.53101
                       0.25             -0.95575         2.96273
Nafion 115 (d)           0              -0.95943         3.04474
                       0.25             -0.95759         2.03704
Nafion 117 (d)           0              -0.95581         2.97301
                       0.25             -0.96531         2.01035

Membrane         Crystallinity (a)   [B.sub.23] (b)   [C.sub.23] (b)

LDPE (d)                 0              0.15225          -0.95775
                       0.455            0.23097          -0.93643
LDPE (e)                 0              -254.528         142.272
                       0.455            -87.6355         53.1249
Nafion 112 (d)           0              -12.1528         10.1745
                       0.25             -8.28468         7.67871
Nafion 115 (d)           0              -6.95264         5.93925
                       0.25             -4.44001         4.21034
Nafion 117 (d)           0              -7.22729         6.52657
                       0.25             -4.79466         4.83876

Membrane         Crystallinity (a)   [A.sub.T] (c)

LDPE (d)                 0              4.6836
                       0.455            4.8240
LDPE (e)                 0              0.3295
                       0.455            0.8915
Nafion 112 (d)           0              7.5269
                       0.25             7.1348
Nafion 115 (d)           0              5.7220
                       0.25             5.2927
Nafion 117 (d)           0              6.1101
                       0.25             4.8388

(a) Value of the relative portion of the crystalline phase in dry
polymer that was used in the evaluation process

(b) Parameters of eq. 18 or 19. The rational eq. 18 was used for
methanol--LDPE [[chi].sup.sm.sub.23] and benzene--Nafions
[[chi].sup.sm.sub.13] interaction parameters, the polynomial eq. 19
was used for benzene--LDPE [[chi].sup.sm.sub.13], methanol-Nafions
[[chi].sup.sm.sub.23] and 2-butanol--LDPE [[chi].sup.sm.sub.23]
interaction parameters.

(c) The parameter of eq. 21; the parameters [B.sub.T] and [C.sub.T]
were not used (their value was 0).

(d) System with methanol.

(e) System with 2-butanol.
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Author:Hovorka, Stepan; Randova, Alena; Sysel, Petr; Brozova, Libuse; Zitka, Jan; Drasar, Pavel; Bartovska,
Publication:Polymer Engineering and Science
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Date:May 1, 2015
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