# Conformational and visometric behavior of quaternized polysulfone in dilute solution.

INTRODUCTIONPolysulfones (PSF) represent a class of polymers containing sulfone groups and aromatic nuclei, characterized by good optical properties, thermal and chemical stability, mechanical strength, and resistance to extremes of pH and low creep [1-3]. Chain rigidity is derived from the relatively inflexible and immobile phenyl and S[O.sub.2] groups, while toughness from the connecting ether oxygen [4]. The chemical modification of polysulfone, especially the chloromethylation reaction, is a subject of considerable research interest from both theoretical and practical points of view, including obtaining the precursors for functional membranes, coatings, ion exchange resins, ion exchange fibers, and selectively permeable films [2, 5, 6]. Thus, chemical modification is an efficient method to improve polymer properties. Polysulfones (PSF) and chloromethylated polysulfones (CMPSF) have shown many interesting properties that led to a wide spectrum of industrial and environmental applications [7-9]. Also, the different components of a block or graft copolymer may segregate in bulk, yielding nanometer-sized patterns or mesophasic structures. There are many applications for the nanodomained solids [10]. By matching the periodicity of the patterns with the wavelength of visible light, literature studies have demonstrated that block copolymers, including polysulfone, act as photonic crystals. Segregated block copolymers, including polysulfone, have been also used as precursors for the preparation of various nanostructures, including nanospheres, nanofibers, annotates, and thin films containing nanochannels. Thin films containing nanochannels have been used as membranes, pH sensors, or templates to prepare metallic nanorods. Therefore, one of the extremely important roles in polysulfone applications is played by the control balance between the solution properties of PSF and other chemically modified structure of theirs. Thus, chemical modification of chloromethylated polysulfone by the quaternization of ammonium groups is an efficient method for increasing the hydrophilicity. In this context, these copolymers can be utilized for multiple applications, e.g. as biomaterials and semipermeable membranes. Their solution properties are strongly affected by the quaternization degree of the ammonium groups. The polyelectrolyte effect is detected when the charge density per macromolecule reaches a critical value in terms of quaternization degree or molar mass [11].

Previous publications have presented the syntheses [12, 13] and some solution properties [14, 15] of a series of polysulfones. Studies have been carried out on the chloromethylation reaction for obtaining soluble chloromethylated polymers with different degrees of substitution. Influence of concentration and temperature on the coil densities and dimensions, as well as the influence of the chlorine content on unperturbed dimension parameters, were analyzed.

The objective of the present study was to provide information on the conformational behavior of quaternized polysulfones in dilute solution, with various amounts of ionic chlorine, obtained from chloromethylation processes. The experimental and theoretical results on the preferential and total adsorption coefficients versus solvent's composition are discussed in correlation with the variation of intrinsic viscosity.

EXPERIMENTAL

Materials

UDEL-1700 polysulfone (Union Carbide) (PSF) ([M.sub.n] = 39,000; [M.sub.w]/[M.sub.n] = 1.625) is a commercial product. It was purified by repeated reprecipitation from chloroform and dried for 24 h in vacuum, at 40[degrees]C, before being used in the synthesis of chloromethylated polysulfone. Mixture of commercial paraformaldehyde with an equimolar amount of chlorotrimethylsilane ([Me.sub.3]SiCl), as a chloromethylation agent, and stannic tetrachloride (Sn[Cl.sub.4]), as a catalyst, were used for the chloromethylation reaction of polysulfone at 50[degrees]C. Reaction time was varied from 24 to 140 h so as to obtain different degrees of substitutions of the chloromethylated polysulfones (CMPSF) [12]. Finally, the samples were dried under vacuum at 40[degrees]C. Table 1 presents the chlorine content, the degree of substitution (DS), the molecular weights of the structural units, [m.sub.0], the number-average molecular weights, [M.sub.n], of the chloromethylated polysulfones, determined from the polymerization degree of the polysulfone (DP = 90), and the molecular weights of the structural units of chloromethylated polysulfones. Table 1 also shows the intrinsic viscosity determined in DMF at 25[degrees]C [15].

CMPSF was dissolved in N,N-dimethylformamide (DMF) vacuum distilled over [P.sub.2][O.sub.5], and then the N,N-dimethylethanolamine (DMEA) quaternized derivative was poured into the reactor. The reaction time was 48 h, at 60[degrees]C. The characteristics of the obtained quaternized polysulfones (PSF-DMEA) are presented in Table 2. The content in ionic chlorine, [Cl.sub.i], was determined by potentiometric titration (Titrator TTT1C Copenhagen) with 0.02 N AgN[O.sub.3] aqueous solution. The potentiometric titration permits the determination of the low contents in ionic chlorine. The transformation degree was in the 94-98% range.

The general chemical structure of the quaternized polysulfone is presented in Scheme 1.

Measurements

Viscosity measurements of the obtained quaternized polysulfones (3) were carried out in DMF, methanol (Me) and in solvent mixtures DMF (1)/Me (2) in the range of 20-55[degrees]C ([+ or -]0.01[degrees]C), on an Schott viscometer AVS 350, with an Ubbelohde suspended-level viscometer. The kinetic energy corrections were found as negligible. The flow volume of the used viscometer was above 5 mL, making drainage errors unimportant. Flow times were obtained with an accuracy of [+ or -]0.035%, for different measurements. Intrinsic viscosities [[eta]] were determined by Huggins equation [16] and Rao equation, [17] the latter being only slightly sensitive to the possible errors that may occur in the determination of relative viscosity, [[eta].sub.rel]

[GRAPHIC OMITTED]

[[eta].sub.sp]/c = [[eta]] + [k.sub.H][[eta]][.sub.Huggins.sup.2]c (1)

1/[2([[eta].sub.rel.sup.1/2] - 1)] = [1/[[[eta]][.sub.Rao]c]] - [(a-1)/2.5] (2)

where [[eta].sub.sp] is the specific viscosity, [k.sub.H] is the Huggins constant, c is the concentration of polymer solution, a = 1/[[PHI].sub.m] and [[PHI].sub.m], is the maximum volume fraction to which the particles can pack, expressed by [[PHI].sub.m] = [[[eta]]/2.5][c.sub.m].

The preferential adsorption coefficients, [[lambda].sub.1], were directly accessible from the experiments, through interferometry (Zeiss interferometer) at 25[degrees]C and dialysis equilibrium, according to Eq. 3

[[lambda].sub.1] = [(dn/dc)[.sub.[mu]] - (dn/dc)[.sub.u]]/[dn/d[[phi].sub.1]] (3)

where (dn/dc)[.sub.u] is the refractive index increment of the polymer in the solvent mixture, (dn/dc)[.sub.[mu]] is the refractive index increment of the polymer in the DMF/Me solvent mixture, after establishing dialysis equilibrium, and (dn/d[[phi].sub.1]) is the variation of the refractive index increment of the solvent mixture as a function of DMF volumetric composition.

The preferential and total adsorption coefficients were also determined from theoretical approximations.

Equilibrium dialysis experiments were carried out in a dialyser with a total volume of about 15 mL. The semipermeable cellophane membrane was conditioned in each of the solvent mixtures before use. Dialysis equilibrium was obtained in 6 h.

RESULTS AND DISCUSSION

Viscometric behavior of quaternized polysulfones in DMF/Me solvents

It must be emphasized that viscometry represents probably the most widely used experimental method to assess the conformational modification of charged polymers in solution. Indeed, viscometric behaviors are related to the chemical structure of the polycation, to its size and charge density, but also to environment properties such as ionic strength, pH, and addition of other solvent or salts [18].

[FIGURE 1 OMITTED]

Figure 1 shows the linear dependencies with positive slopes from Huggins plots (Eq. 1) for PSF, CMPSF1, and CMPSF2, as expected for neutral polymers [14, 19]. Also, a decrease of [[eta].sub.sp]/c with increasing polymer concentration and a sharp increase of the [[eta].sub.sp]/c at low concentration range for quaternized polysulfones appear. This specific comportment of polyelectrolyte is presented too in Fig. 1 for PSF-DMEA1 and PSF-DMEA2.

The polyelectrolyte effect is due to an expansion of the polyionic chain, as caused by the progressively enhanced dissociation of ionizable groups as concentration decreases, and therefore the intensification of intramolecular repulsive interactions between the ionized groups, i.e. ammonium groups, spread all along the chain. Moreover, one can note that the reduced viscosity sharply increases when the quaternization degree increases; this effect results from the higher electrostatic repulsions and steric hindrance, which led to more expanded hydrodynamic volume and some increase of long range repulsive interactions. On the other hand, the reduced viscosity changes with solvent mixtures. Thus, parts (a) and (b) of Fig. 1 show the influence of the solvent mixture compositions on [[eta].sub.sp]/c; increasing the quaternization degree augments the solubility in Me. The affinity of the DMF, Me, or DMF/Me for the quaternized samples depends on the neutral segment and on the charged groups. Thus, an increase in the quaternization degree of tertiary ammonium groups leads to higher reduced viscosity values, due to a higher hydrodynamic volume and some increase of long range repulsive interactions.

The curves shown in Fig. 1 for quaternized samples can be linearized by applying the Rao approximation (Eq. 2) for the determination of intrinsic viscosity. Fig. 2 presents the Rao plots for PSF-DMEA1 and PSF-DMEA2 in DMF/Me at different compositions.

The values of intrinsic viscosity are affected by the charged groups from the studied quaternized samples. Figure 3 shows the variation of intrinsic viscosity with the composition of DMF in DMF/Me mixtures for quaternized polysulfones. It is observed that polymer's coil dimension increases with increase in the quaternization degree, attaining a maximum value at DMF composition, which decreases with increase in ionic species density. Moreover, for volume fractions of Me higher than 0.75, the PSF-DMEA1 precipitates, while for volume fractions of DMF higher than 0.75, it is the PSF-DMEA2 that precipitates. Thus, the precipitation phenomenon is due to the high content of nonsolvent in the system.

[FIGURE 2 OMITTED]

[FIGURE 3 OMITTED]

The intrinsic viscosities and their dependence on temperature for the PSF-DMEA in DMF, Me and solvent mixture DMF/Me are shown in Fig. 4. The obtained linear dependencies with positive and negative slope have been interpreted in terms of a conformational change of the polymer chain. These results seem to indicate that the predominant factor is the polarity of solvent in solvation power. Thus, DMF solvates PSF-DMEA1 with a content in ionic chlorine, [Cl.sub.i] = 2.15%, more strongly than the mixed solvent DMF/Me with a high content of methanol. On the other hand, Me solvates PSF-DMEA2 with a content in ionic chlorine [Cl.sub.i] = 5.71%, more strongly than the mixed solvent DMF/Me with a high content of DMF.

[FIGURE 4 OMITTED]

[FIGURE 5 OMITTED]

Therefore, for a given composition of the DMF/Me mixture, the DMF or Me components are adsorbed preferentially to the quaternized polysulfone molecules in the direction of a thermodynamically most effective mixture.

Preferential and total adsorption coefficient in the quaternized polysulfone/DMF/Me system

Experimental results of the preferential adsorption coefficients. Figures 5 and 6 show the variation of the preferential adsorption coefficient [lambda] with the solvent composition for PSF-DMEA1 and PSF-DMEA2 in the binary mixture DMF/Me, as determined from refractive index increments, both before (dn/dc)[.sub.u] and after (dn/dc)[.sub.[mu]] establishing dialysis equilibrium (Table 3) from Eq. 3.

The value of dn/d[[phi].sub.1] = 0.101 was obtained from the linear dependencies [20]:

[n.sub.0] = 1.328 + 0.101[[phi].sub.1] (4)

where [n.sub.0] is the refractive index of solvent mixtures.

In these systems, the experimental results indicate that the preferential adsorption is markedly influenced by the charged groups attached to the polymer backbone, as well as by the solvent mixture. Generally, for solvent/nonsolvent mixtures, the addition of precipitant decreases solvent quality. However, there are some particular mixtures, called "synergistic solvents," in which the addition of precipitant causes the increase of the dissolving power of the mixture [21, 22]. According to the present data, DMF is a good solvent, Me is a nonsolvent for samples with a small content in ionic chlorine-PSF-DMEA1 sample, while Me is a good solvent and DMF is a nonsolvent for samples with a high content in ionic chlorine-PSF-DMEA2 samples. Addition of nonsolvent Me (for PSF-DMEA1) or DMF (for PSF-DMEA2) increases the quality of solvent mixtures. Thus, the DMF/Me mixture forms a structure with much better solvation properties than DMF or Me, while for [[phi].sub.1] [congruent to] 0.7 from [[eta]] or [[phi].sub.1] [congruent to] 0.5 from [[lambda].sub.1] for PSF-DMEA1, and for [[phi].sub.1] [congruent to] 0.5 from [[eta]] or [[phi].sub.1] [congruent to] 0.33 from [[lambda].sub.1] for PSF-DMEA2, it exhibits a maximum value.

[FIGURE 6 OMITTED]

Binary polymer--solvent interaction parameters. To determine the theoretical preferential and total adsorption coefficients, knowledge of the [g.sub.12], [g.sub.i3] and [[chi].sub.12], [[chi].sub.i3] parameters is necessary. Subscript "i" refers to solvent 1 -DMF or 2 -Me, and subscript 3 refers to quaternized polysulfone.

The quaternized polysulfone-solvent interaction parameters, [[chi].sub.13], were calculated by considering the entropic and enthalpic contributions [23]:

[[chi].sub.i3] = [[V.sub.1]/RT]([[delta].sub.1,2] - [[delta].sub.3])[.sup.2] + 0.34 (5)

where [[delta].sub.1,2] is the solubility parameter for DMF [1] or Me [2], and [[delta].sub.3] is the solubility parameter for the polymer, R is the gas constant, T is the Kelvin temperature, [V.sub.1] is the molar volume of solvent 1. Also, the quaternized polysulfone--solvent interaction parameter, [g.sub.i3], results from equation

[[chi].sub.i3] = (1 - [2/z])[g.sub.i3] (6)

with the coordination number of lattice z = 8.

For the determination of the solubility parameters there were applied, too, the theoretical methods with the following steps [24]:

* Calculation of the zeroth-order connectivity indices [.sup.0.[chi]] and [.sup.0.[chi].sup.v] and of the first-order connectivity indices [.sup.1.[chi]] and [.sup.1.[chi].sup.v] described in Appendix A. The values of the atomic simple connectivity indices, [delta], and of the valence connectivity indices, [[delta].sup.v], used in the calculations are listed in Table 4. Table 5 presents the values obtained for [.sup.0.[chi]], [.sup.0.[chi].sup.v], [.sup.1.[chi]], and [.sup.1.[chi].sup.v].

* Calculation of cohesive energy by two methods (Appendix B) by applying the group contributions of Fedors (Eqs. B1-B3) and the group contributions of van Krevelen and Hoftyzer (Eqs. B4, B5);

* Calculation of the molar volume [V.sub.3] at room temperature (298 K) according to Appendix C. Table 6 shows cohesive energy, [E.sub.coh](1) or [E.sub.coh](2), and molar volume, [V.sub.3].

* Calculation of solubility parameters [[delta].sub.3], at room temperature:

[[delta].sub.3](298 K) [equivalent to] [[E.sub.coh]/[V.sub.3](298 K)][.sup.1/2]. (7)

Solubility parameters from the theoretical data calculated for quaternized polysulfones with cohesive energy, [E.sub.coh](1) or [E.sub.coh](2) and molar volume, [V.sub.3], are presented in Table 6. Table 6 also shows the solubility parameters of DMF and Me [23].

Thus, the polymer-solvent interaction parameters calculated with the solubility parameters from Eqs. 5 and 6, are presented in Table 7.

Solvent-solvent interaction parameters. The DMF/Me interaction parameters were determined by Flory-Huggins equation [25]:

[g.sub.12] = ([[G.sup.E]/RT] + [x.sub.1]ln([x.sub.1]/[[phi].sub.1]) + [x.sub.2]([x.sub.2]/[[phi].sub.2]))[1/[[x.sub.1][[phi].sub.2]]] (8)

where [x.sub.1,2] are the mole fractions of the mixture solvents, [[phi].sub.1,2] are the volume fractions of the mixture solvents, and [G.sup.E] is the Gibbs free energy of mixing, calculated from the following equation, described in ref. 26:

[G.sup.E]/[[V.sub.m][[phi].sub.1][[phi].sub.2]] = ([[delta].sub.1] - [[delta].sub.2])[.sup.2] (9)

where [V.sub.m] is the volume of mixture solvents and [[delta].sub.1,2] are the solubility parameters of solvents: [delta] = 24.7 [square root of (J/cc)] for DMF and [delta] = 29.7 [square root of (J/cc)] for Me. Figure 7 depicts the excess free energy, [G.sup.E] > 0, for the liquid mixtures, as a function of the volume fraction, [[phi].sub.1]. A positive strong deviation from the ideality, caused by an unfavorable solvent-solvent interaction, appears with a maximum at [[phi].sub.1][congruent to]0.6. Moreover, a decrease in [G.sup.E] from the maximum value to zero leads to a more thermodynamically stable system. Thus, the preferential adsorption coefficient is related to this variation and to a magnitude that quantifies the polymer-binary solvent interaction, for instance, intrinsic viscosity.

The obtained [g.sub.12] function at T = 298 K, presented in Fig. 7, is

[g.sub.12] = -0.69 + 3.29[[phi].sub.1] - 2.61[[phi].sub.1.sup.2] (10)

Theoretical interpretation of the preferential and total adsorption coefficients. The theoretical values of the preferential and total, Y, adsorption coefficients can be calculated from the equations

[[lambda].sub.1] = -[v.sub.3][[M.sub.13]/[M.sub.11]] (11)

Y = [[V.sub.1]/2RT]([M.sub.33] - [[M.sub.13.sup.2]/[M.sub.11]]) (12)

where [M.sub.ij] are

[[M.sub.11][V.sub.1]]/RT = [1/[[phi].sub.1]] + [l/[[phi].sub.2]] + [[[[partial derivative].sup.2]([[phi].sub.1][[phi].sub.2][g.sub.12])]/[[partial derivative][[phi].sub.1.sup.2]]] (13)

[[M.sub.13][V.sub.1]]/RT = l - 1 + [g.sub.13] - lg[.sub.23] - [[[partial derivative]([[phi].sub.1][[phi].sub.2]([g.sub.12] - [g.sub.T]))]/[[partial derivative][[phi].sub.1]]] (14)

[[M.sub.33][V.sub.1]]/2RT = [1/2]([[phi].sub.1] + l[[phi].sub.2]) - [[chi].sub.13][[phi].sub.1] - l[[chi].sub.23][[phi].sub.2] + [[phi].sub.1][[phi].sub.2]([g.sub.12] - [g.sub.T] - [[chi].sub.T]) (15)

where [v.sub.3] = [V.sub.3]/[m.sub.0] is the partial specific volume of the quaternized polysulfones (Table 7), [V.sub.1] and [V.sub.1] are the molar volume of solvent 1 and 2 and l(= [V.sub.1]/[V.sub.2]) = 1.928.

In Eqs. 11-15, there appear the ternary interaction parameters [g.sub.T] and [[chi].sub.T], defined as

[FIGURE 7 OMITTED]

[g.sub.T]([[phi].sub.1]) = [a.sub.g][g.sub.12]([[phi].sub.1]) (16)

[[chi].sub.T]([[phi].sub.1]) = [a.sub.[chi]][g.sub.12]([[phi].sub.1]) (17)

where [a.sub.g] and [a.sub.[chi]] have different expressions, according to different theories. In the present study, the Flory-Huggins-Pouchly model [27, 28] was used. The [a.sub.g] and [a.sub.[chi]] coefficients in the FHP model, calculated from Eqs. 18-21, and the ternary interaction parameters [g.sub.T] and [[chi].sub.T] are presented in Table 8.

[a.sub.g] = [[g.sub.13][g.sub.23]]/[1 - D] (18)

[a.sub.[chi]] = [2[g.sub.13][g.sub.23] - D]/[2(1 - D)] (19)

or

[a.sub.g] = [[g.sub.13][g.sub.23]]/[1 - D'] (20)

[a.sub.[chi]] = [[g.sub.13][g.sub.23](1 - [D'/2])]/(1 - D') (21)

where

D = [g.sub.13]([g.sub.23] - [[chi].sub.23]) + [g.sub.23]([g.sub.13] - [[chi].sub.13]) (22)

and

D' = D/[2[g.sub.13][g.sub.23]]. (23)

Figures 5, 6, and 8 plot graphically the theoretical values of the preferential and total coefficients calculated from Eqs. 11-23.

The experimental results for [[lambda].sub.1] are better fitted by the FHP model for PSF-DMEA1 with a small content of charged groups. The most important deviations appear for PSF-DMEA2 with a higher content of charged groups, due to the electrostatic interactions that were negligible in the calculation of the polymer-solvent interaction parameters.

The theoretical total adsorption coefficient characterizes the degree of swelling of the polymer coil and makes the difference in the composition of the mixed solvent inside and outside the coil. The curves describing the dependence of Y on solvent composition [[phi].sub.1] can depict typical shapes directly related to parameter [g.sub.12]. Thus, a high value of Y appear in the sorption equilibrium when [g.sub.12] > 0 for good solvent mixtures, and a minimum values appear when [g.sub.12] < 0, signifying that the solvent mixtures become poor [29].

[FIGURE 8 OMITTED]

CONCLUSIONS

Modification of intrinsic viscosity and preferential and total adsorption coefficients of quaternized polysulfones in solvent mixtures DMF/Me was investigated. The observed polyelectrolyte effect from Huggins plots is due to the progressively enhanced dissociation of ionisable groups as concentration decreases. The reduced viscosity changes with solvent mixtures and with temperature, thus the affinity of the DMF, Me, or DMF/Me for the quaternized samples depends on the neutral segment and on the charged groups. The intrinsic viscosity obtained from Rao equation shows that the polymer coil dimension increases with increase in the quaternization degree, attaining a maximum value at a DMF composition, which decreases with increasing the ionic species density. The influence of temperature indicates that the polarity of the solvent influenced the conformational change of the polymer chain.

The experimental results concerning the preferential adsorption in mixed solvent systems, based on the measurements of refractive increments, yielded values that agreed well with the viscometric results.

The theoretical determination of [[lambda].sub.1] by the FHP model required the knowledge of the polymer-solvent interaction parameters and of the Gibbs free energy of solvent mixtures. The most important deviations between theoretical and experimental data appear for quaternized polysulfones with a higher content of the charged groups, due to the electrostatic interactions that were negligible in the calculation of the polymer-solvent interaction parameters.

The swelling degree of the polymer coil and the difference in composition of the mixed solvent inside and outside the coil, as observed from the total adsorption coefficient, were correlated with the solvent-solvent interaction parameters.

APPENDIX A: CALCULATION OF THE ZEROTH-ORDER CONNECTIVITY INDICES AND OF THE FIRST-ORDER CONNECTIVITY INDICES

[.sup.0.[chi]] [equivalent to] [SIGMA](1/[square root of [delta]]) (A1)

[.sup.0.[chi].sup.v] [equivalent to] [SIGMA](1/[square root of [[delta].sup.v]]) (A2)

[[beta].sub.ij] [equivalent to] [[delta].sub.i][[delta].sub.j] (A3)

[[beta].sub.ij.sup.v] = [[delta].sub.i.sup.v][[delta].sub.j.sup.v] (A4)

[.sup.1.[chi]] [equivalent to] [SIGMA](1/[square root of [beta]] (A5)

[.sup.1.[chi].sup.v] [equivalent to] [SIGMA](1/[square root of [[beta].sup.v]]) (A6)

APPENDIX B: CALCULATION OF THE COHESIVE ENERGY

a. Calculation of cohesive energy applying the group contributions of Fedors

[E.sub.coh](1) [approximately equal to] 9882.5([.sup.1.[chi]]) + 358.7(6[N.sub.atomic] + 5[N.sub.group]) (B1)

[N.sub.atomic] [equivalent to] 4[N.sub.(-S-)] + 12[N.sub.sulfone] - [N.sub.F] + 3[N.sub.Cl] + 5[N.sub.Br] + 7[N.sub.cyanide] (B2)

[N.sub.group] [equivalent to] 4[N.sub.1hydroxyl] + 12[N.sub.amide] + 2[N.sub.(nonamide-(NH)-unit)] + 4[N.sub.(nonamide-(C=O)-next to nitrogen)] + 7[N.sub.(-(C=O)-in carboxylic acid, ketone, or aldehyde)] + 2[N.sub.(other-(C=O)-)] - [N.sub.(alkyl ether-O-)] - [N.sub.C=C] + 4[N.sub.(nitrogen atoms in six-membered aromatic rings)] (B3)

b. Calculation of cohesive energy applying the group contributions of van Krevelen and Hoftyzer

[E.sub.coh](2) [congruent to] 10570.9([.sup.0.[chi].sup.v] - [.sup.0.[chi]]) + 9072.8(2([.sup.1.[chi]]) - [.sup.1.[chi].sup.v]) + 1018.2 [N.sub.VKH] (B4)

[N.sub.VKH] [equivalent to] [N.sub.Si] + 3[N.sub.(-S-)] + 36[N.sub.sulfone] + 4[N.sub.Cl] + 2[N.sub.Br] + 12[N.sub.cyanide] + 16[N.sub.(nonamide-(C=O)-next to nitrogen)] + 7[N.sub.(nitrogen atoms in six-membered aromatic rings)] + 12[N.sub.cyanide] + 2[N.sub.(nitrogen with [delta] = 2. but not adjacent to C=O, and not in a six-membered aromatic rings)] + 20[N.sub.(carboxylic acid)] + 33[N.sub.HB] - 4[N.sub.cyc] + 19[N.sub.anhydride] + [SIGMA](4 - [N.sub.row])[.sub.(substituents with [delta] = 1 attached to aromatioic rings in the backbone)] (B5)

where in Eq. B2: [N.sub.(-S-)]-number of sulfur atoms in the lowest (divalent) oxidation state; [N.sub.sulfone]-number of sulfur atoms in the highest oxidation state (commonly in -[SO.sub.2]); [N.sub.F]-number of fluorine atoms; [N.sub.Cl]-number of chlorine atoms; [N.sub.Br]-number of bromine atoms; [N.sub.cyanide]-number of -C=N groups;

in Eq. B3: [N.sub.hydroxyl]-number of -OH; [N.sub.amide]-number of amide groups; [N.sub.(nonamide-(NH)-unit)]-number of NH units from the nonamide structure; [N.sub.(nonamide-(C=O)-next to nitrogen)]-number of C=O units from the nonamide structure next to nitrogen; [N.sub.(-(C=O)-in carboxylic acid, ketone or aldehyde)]-number of C=O groups in carboxylic acid, ketone, or aldehyde structures, [N.sub.(other-(C=O)-)]-number of other C=O groups; [N.sub.(alkyl ether-O-)]-number of alkyl ether-O-groups, [N.sub.C=C]-number of carbon-carbon double bonds, excluding any such bonds found along the edges of the rings; [N.sub.(nitrogen atoms in six-membered aromatic rings)]-number of nitrogen atoms in six-membered aromatic rings;

in Eq. B5: [N.sub.Si]-number of silicon atoms; [N.sub.(carboxylic acid)]-number of carboxylic acid; [N.sub.HB]-total number of strongly hydrogen-bonding structural units, such as alcohol-type or phenol-type hydroxyl (-OH) groups and amide groups (the -OH groups in carboxylic acid and sulfonic acid moieties are not counted in [N.sub.HB]); [N.sub.cyc]-number of nonaromatic rings (i.e., "cyclic" structures) with no double bonds along any of the ring edges. When more than one such ring shares the edges, [N.sub.cyc] is determined by using simple counting rules, which avoid double counting of any of the shared edges, and may result in a noninteger value of [N.sub.cyc]; [N.sub.anhydride]-number of anhydride groups, [N.sub.row]-row of an atom in the periodic table. Methyl (-C[H.sub.3]) groups and halogen atoms are substituents with [delta] = 1, i.e., bonded to only one nonhydrogen atom, commonly encountered in polymers; [N.sub.(nitrogen with [delta] = 2, but not adjacent to C=O, and not in a six-membered aromatic rings)]-number of nitrogen atoms with specification from subscript.

APPENDIX C: CALCULATION OF THE MOLAR VOLUME

[V.sub.3](298 K) [congruent to] 3.642770([.sup.0.[chi]]) + 9.798697([.sup.0.[chi]]) - 8.542819([.sup.1.[chi]]) + 21.693912([.sup.1.[chi].sup.v]) + 0.978655[N.sub.MV] (C1)

[N.sub.MV] [equivalent to] 24[N.sub.Si] - 18[N.sub.(-S-)] - 5[N.sub.sulfone] - 7[N.sub.Cl] - 16[N.sub.Br] + 2[N.sub.(backbone ester)] + 3[N.sub.ether] + 5[N.sub.carbonate] + 5[N.sub.C=C] - 11[N.sub.cyc] - 7([N.sub.fused] - 1) (C2)

(last term only to be used if [N.sub.fused] [greater than or equal to] 2) where [N.sub.(backbone ester)]-number of ester (-COO-) groups in the backbone of the repeating units; [N.sub.ether]-total number of ether (-O-) linkages in the polymeric repeating unit. Note that only the (-O-) linkages between two carbon atoms will be counted as ether linkages in [N.sub.ether]; [N.sub.carbonate]-number of carbonate (-OCOO-) groups; [N.sub.fused]-number of rings in fused ring structures. A "fused" ring structure is defined in the present context as any ring structure containing at least one aromatic ring that shares at least one edge with another ring and with all the other rings with which it shares an edge.

REFERENCES

1. M. Barikani and S. Mehdipour-Ataei, J. Polym. Sci. Part A: Polym. Chem., 38, 1487 (2000).

2. P. Vaisanen and M. Nystrom, Acta Polytechnica Scand., 247, 25 (1997).

3. A. Higuchi, M. Harashima, K. Shirano, M. Hara, M. Hattori, and K. Imamura, J. Appl. Polym. Sci., (a) 36, 1753 (1988); (b) 41, 1973 (1990); (c) 46, 449 (1992).

4. R.N. Johnson, "Polysulfones. Plastics, Resins, Rubbers, Fibers," in Encyclopedia of Polymer Science and Technology, Vol. 11, F.M. Herman, G.G. Norman, and M.N. Bikales, editors, Wiley, New York, 447 (1969).

5. A. Higuchi, K. Shirano, M. Harashima, B.O. Yoon, M. Hara, M. Hattori, and K. Imamura, Biomaterials, 23, 2659 (2002).

6. M. Tomaszewska, A. Jarosiewicz, and K. Karakulski, Desalination, 146, 319 (2002).

7. S. Savariar, G.S. Underwood, E.M. Dickinson, P.J. Schielke, and A.S. Hay, Desalination, 144, 15 (2002).

8. K. Sotiroiu, S. Pispas, and N. Hadjichristidis, Macromol. Chem. Phys., 205, 55 (2004).

9. A.F. Ismail and W.A. Hafiz, J. Sci. Technol., 24, 815 (2002).

10. Z. Lu and G. Liu, Macromoleculecules, 37, 174 (2004).

11. I. Ydens, S. Moins, P. Degee, and P. Dubois, Eur. Polym. J., 41, 1502 (2005).

12. E. Avram, E. Butuc, and C. Luca, J. Macromol. Sci. Pure Appl. Chem., 34, 1701 (1997).

13. E. Avram, Polym, Plast. Technol. Eng., 40, 275 (2001).

14. L. Ghimici and E. Avram, J. Appl. Polym. Sci., 90, 465 (2003).

15. S. Ioan, A. Filimon, and E. Avram, J. Macromol. Sci. Phys., 44, 129 (2005).

16. M.L. Huggins, J. Am. Chem. Soc., 64, 2716 (1942).

17. M.V.S. Rao, Polymer, 34, 592 (1993).

18. O.O. Kotlyarevskaya, V.A. Navrotskii, M.V. Orlyanskii, A.V. Navrotskii, and I.A. Novakov, Polym. Sci. Series A, 47, 313 (2005).

19. S. Ioan, A. Filimon, and E. Avram, J. Appl. Polym. Sci., in press.

20. S.R. Gooda and M.B. Huglin, Eur. Polym. J., 29, 365 (1993).

21. J. Pouchly, Pure Appl. Chem., 61, 1085 (1989).

22. C.I. Simionescu, S. Ioan, M. Bercea, N. Mitu, and B.C. Simionescu, Eur. Polym. J., 29, 183 (1993).

23. E.A. Grulke, "Solubility Parameter Values," in Polymer Handbook, 4th ed., J. Brandrup and E.H. Immergut, editors, Wiley, New York, Ch. VII, 675 (1999).

24. J. Bicerano, J. Macromol. Sci. Rev. Macromol. Chem. Phys., C36(1), 161 (1996).

25. A. Horta, D. Radic, and L. Gargallo, Macromolecules, 22, 4267 (1989).

26. I. Katime, J.R. Ochoa, L.C. Cesteros, and J. Penafiel, Polym. Bull., 6, 429 (1982).

27. J. Pouchly, A. Zivny, and K. Solc, J. Polym. Sci. Polym. Lett. Ed., 23, 2451 (1968).

28. G. Grigorescu, S. Ioan, and B.C. Simionescu, Eur. Polym. J., 32, 851 (1996).

29. C.M. Gomez, R. Garcia, V. Soria, and A. Campos, Colloid Polym. Sci., 271, 372 (1993).

Silvia Ioan, Anca Filimon, Ecaterina Avram

"Petru Poni" Institute of Macromolecular Chemistry, 700487 Iasi, Romania

Correspondence to: S. Ioan; e-mail: sioan@icmpp.ro

TABLE 1. Chlorine content, substitution degree, DS, molecular weights of structural units, [m.sub.0], number-average molecular weights, [M.sub.n], and intrinsic viscosities, [[eta]], of polysulfone and chloromethylated polysulfones in DMF at 25[degrees]C. Sample Cl, % DS [m.sub.0] [M.sub.n] [[eta]], (dL [g.sup.-1]) PSF 0 0 442.51 39,000 0.3627 CMPSF1 3.34 0.437 463.68 41,000 0.3929 CMPSF2 10.53 1.541 517.17 46,000 0.4703 TABLE 2. Ionic chlorine content, molecular weights of structural units, [m.sub.0], and number-average molecular weights, [M.sub.n], of quaternized polysulfones. Sample Obtained from [Cl.sub.i], % [m.sub.0] [M.sub.n] PSF-DMEA1 CMPSF1 2.15 479.47 42,000 PSF-DMEA2 CMPSF2 5.71 647.31 57,000 TABLE 3. Specific refractive index increments before and after attainment of the dialysis equilibrium for quaternized polysulfones in binary solvent mixture DMF/Me as a function of the DMF content, [[phi].sub.1]. Sample [[phi].sub.1] (dn/dc)[.sub.u] (dn/dc)[.sub.[mu]] PSF-DMEA1 0.75 0.218 0.231 0.50 0.026 0.045 0.25 0.038 0.024 PSF-DMEA2 0.75 0.206 0.306 0.50 0.145 0.269 0.25 0.128 0.154 TABLE 4. [delta] and [[delta].sup.v] values used for the calculation of zero- and first-order connectivity indices [24]. Atom Hyb [N.sub.H] [delta] [[delta].sup.v] C [sp.sup.3] 3 1 1 2 2 2 0 4 4 [sp.sup.2] 1 2 3 0 3 4 N [sp.sup.3] 0 3 5 O [sp.sup.3] 1 1 5 0 2 6 S [sp.sup.3] (a) 0 4 8/3 Cl - 0 1 7/9 (a) These numbers refer to sulfur in its highest oxidation state, as typically encountered in the bonding configuration R--S[O.sub.2]--R'. TABLE 5. Zero- order connectivity indices, [.sup.0.[chi]] and [.sup.0.[chi].sup.v], and first-order connectivity indices, [.sup.1.[chi]] and [.sup.1.[chi].sup.v]. Polymer [.sup.0.[chi]] [.sup.0.[chi].sup.v] PSF-DMEA1 25.106 20.533 PSF-DMEA2 34.741 29.812 Polymer [.sup.1.[chi]] [.sup.1.[chi].sup.v] PSF-DMEA1 17.053 12.288 PSF-DMEA2 23.212 18.060 TABLE 6. Solubility parameters from the theoretical data calculated with cohesive energy, [E.sub.coh](1) or [E.sub.coh](2) and molar volume, [V.sub.3], for quaternized polysulfones and solubility parameters for using solvents. Polymer or [E.sub.coh](1) X [10.sup.-5], [E.sub.coh](2) X [10.sup.-5], Solvent J/mol (Eq. B1) J/mol (Eq. B4) PSF-DMEA1 2.410 2.606 PSF-DMEA2 3.363 3.580 DMF -- -- Me -- -- V (298 K), [[delta].sub.3](1), [[delta].sub.3](2), Polymer or cc/mol [square root of (J/cc)] [square root of (J/cc)] Solvent (Eq. C1) (Eqs. B1, C1, 6) (Eqs. B4, C1, 6) PSF-DMEA1 411.589 24.2 25.2 PSF-DMEA2 599.446 23.7 24.4 DMF -- 24.7[.sup.a] -- Me -- 29.7[.sup.a] -- * Data from literature [23]. TABLE 7. Partial specific volume, [v.sub.3], and binary polymer-solvent interaction parameters. Sample [v.sub.3] [[chi].sub.13] [[chi].sub.23] PSF-DMEA1 0.867 0.347 0.804 PSF-DMEA2 0.922 0.370 0.895 Sample [g.sub.13] [g.sub.23] PSF-DMEA1 0.463 1.072 PSF-DMEA2 0.493 1.193 TABLE 8. Theoretical values of [a.sub.g] and [a.sub.[chi]] coefficients, and ternary interactions parameters [g.sub.T] and [[chi].sub.T] [g.sub.T] Sample [[phi].sub.1] Eqs. 16, 18 Eqs. 16, 20 PSF-DMEA1 0.2 -0.0955 -0.0958 [a.sub.g] = 0.660 (Eq. 18) 0.3 0.0497 0.0499 [a.sub.g] = 0.662 (Eq. 20) 0.4 0.1309 0.1312 [a.sub.[chi]] = 0.495 (Eq. 19) 0.5 0.1839 0.1843 [a.sub.[chi]] = 0.579 (Eq. 21) 0.6 0.2191 0.2197 0.7 0.2356 0.2361 0.8 0.2172 0.2177 0.9 0.0776 0.0078 1 Indefinite Indefinite PSF-DMEA2 0 Indefinite Indefinite [a.sub.g] = 0.835 (Eq. 18) 0.1 -0.3164 -0.2978 [a.sub.g] = 0.784 (Eq. 20) 0.2 -0.1205 -0.1134 [a.sub.[chi]] = 0.625 (Eq. 19) 0.3 0.0627 0.0590 [a.sub.[chi]] = 0.686 (Eq. 21) 0.4 0.1650 0.1553 0.5 0.2318 0.2182 0.6 0.2763 0.2601 0.7 0.2970 0.2796 0.8 0.2739 0.2578 [[chi].sub.T] Sample [[phi].sub.1] Eqs. 17, 19 Eqs. 17, 21 PSF-DMEA1 0.2 -0.0716 -0.0838 [a.sub.g] = 0.660 (Eq. 18) 0.3 0.0373 0.0436 [a.sub.g] = 0.662 (Eq. 20) 0.4 0.0981 0.1148 [a.sub.[chi]] = 0.495 (Eq. 19) 0.5 0.1378 0.1612 [a.sub.[chi]] = 0.579 (Eq. 21) 0.6 0.1643 0.1922 0.7 0.1766 0.2066 0.8 0.1628 0.1905 0.9 0.0582 0.0681 1 Indefinite Indefinite PSF-DMEA2 0 Indefinite Indefinite [a.sub.g] = 0.835 (Eq. 18) 0.1 -0.2374 -0.2606 [a.sub.g] = 0.784 (Eq. 20) 0.2 -0.0904 -0.0992 [a.sub.[chi]] = 0.625 (Eq. 19) 0.3 0.0470 0.0517 [a.sub.[chi]] = 0.686 (Eq. 21) 0.4 0.1238 0.1359 0.5 0.1739 0.1910 0.6 0.2073 0.2276 0.7 0.2229 0.2447 0.8 0.2055 0.2256