Doping and Diffusion in an Extruded Saloplastic Polyelectrolyte

May 1, 2013 - Equilibrium Overcompensation in Polyelectrolyte Complexes. Hadi M. Fares and Joseph B. Schlenoff. Macromolecules 2017 50 (10), 3968- ...
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Doping and Diffusion in an Extruded Saloplastic Polyelectrolyte Complex Ramy A. Ghostine, Rabih F. Shamoun, and Joseph B. Schlenoff* Department of Chemistry and Biochemistry, The Florida State University, Tallahassee, Florida, 32306-4390, United States S Supporting Information *

ABSTRACT: Doping constants and diffusion coefficients for an extruded, stoichiometric, dense polyelectrolyte complex, PEC, were determined for a Hofmeister series of anions. These thermodynamic and kinetic parameters describe the extent and speed to which a complex of poly(styrenesulfonate) and poly(diallyldimethylammonium) may be doped. Both parameters followed a Hofmeister ordering and covered a wide range of response. Differences between doping and undoping kinetics were observed, with the latter adhering well to classical diffusion from the cylindrical geometry employed. Tracer diffusion of radiolabeled Na+, compared with coupled diffusion of NaCl, revealed slightly faster diffusion of Na+ compared to Cl− ions within the PEC.

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where (1 − y) is the fraction of intrinsic sites and aMX is the activity of the salt MX. Doping controls a broad suite of PEC properties, including mechanical response. For many decades, it has been known that PECs become more rubbery when doped.2,3,8,11,12 It has also been shown that some salts are more effective than others at doping PECs in their bulk13 or multilayer14 formats. The influence of salt type on multilayer growth and mechanical properties was placed into a Hofmeister series15 and we used a few IR active anions to establish values for doping constants for a multilayer of poly(styrenesulfonate) (PSS) and poly(diallyldimethylammonium) (PDADMA).16 Because most of the salts used to dope PECs, most notably NaCl, are not IRactive, some of the most significant Kdop values are not known. Even less is known about the rate of transport of ions through PECs. Most of the reported data comes from measurements of ion permeability through multilayers,17−19 which cannot provide ion diffusion coefficients unless the concentration of ions within the PEC is known. The aim of the present work is thus 2-fold: first, we establish room temperature equilibrium doping levels for a common Hofmeister series of anions, including Cl−. Second, we follow the kinetics of undoping, which yields diffusion coefficients for each salt within the PEC. For both of these types of measurement the dense, uniform, stoichiometric nature of extruded PECs (exPECs) is particularly valuable, since it leads to physical data for bulk PEC, rather than porous or multiphase materials.

INTRODUCTION Polyelectrolyte complexes, PECs, are amorphous blends1 of oppositely charged polyelectrolytes held together by multiple ion pairings. PECs are brittle, salt-like materials when dry and are difficult to process, even when hydrated.2−4 Thus, the formation of thin, uniform films of PEC by the “multilayering” process was a major breakthrough.5,6 Recently, we showed that PECs plasticized by water and salt may be extruded using standard extrusion techniques and hardware.7 When hydrated, these “saloplastic” complexes are tough, 3-dimensional materials suitable for a variety of applications. The driving force for polyelectrolyte complexation comes mainly from the entropic release of counterions and water.8,9 The association of oppositely charged segments within a PEC may be gradually reversed by adding salt of increasing concentration to aqueous solutions in which the material is immersed10 Pol+Polc − + M aq + + X aq − ⇌ Pol+X c− + Pol−Mc+

(1)

where Pol+ and Pol− represent the positive and negative polyelectrolyte repeat units, respectively, M+ and X− are counterions (such as Na+ and Cl−), and the subscript “c” labels components in the complex phase. A Pol+Pol‑ ion pair is termed an “intrinsic” site whereas repeat units neutralized by a counterion are “extrinsic” sites. The equilibrium doping level, y, is the fraction of the PEC in the extrinsically compensated form. A doping constant, Kdop, which is the inverse of the polyelectrolyte association constant, is given by the following:10 Kdop =

y2 (1 − y)aMX 2

→

y2 aMX 2

Received: February 27, 2013 Revised: April 8, 2013

(for small y)

© XXXX American Chemical Society

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EXPERIMENTAL METHODS

PECs from another popular combination, poly(allylamine) and PSS, are glassy over a wide range of [NaCl] and require high [NaCl] before they start to soften.24,25 The doping range of PSS/PDADMA conveniently spans the 0−1 M NaCl range.23 In addition, the starting materials have low cost and low toxicity and are widely available. Both the equilibrium doping levels and the undoping kinetics were followed by measuring the conductivity versus time of solutions in which doped samples were immersed. This simple technique offered high precision and accuracy: the rate of undoping was provided by the slope and the plateau values give the original amount of salt within the complex. Sodium salts were used to compare counterions usually listed in the Hofmeister series.26 Because concentration is dilute, conductivity = k[NaX] (in concentrated solutions the proportionality constant decreases). The minimum conductivity (0.2 μS cm−1), regulated by autoionization of water and dissolved CO2, allowed a minimum measurable doping level of y = 0.003. Figure 1 presents an example of concentration versus time for samples of exPEC doped in NaCl, then allowed to undope

Materials and Methods. PSS was from AkzoNobel (VERSA TL 130, MW 200 000 g mol−1) and PDADMAC from Ondeo-Nalco (SD 46104, MW of 400 000 g mol−1). The complex was prepared and extruded in the form of continuous rod with a diameter of ca. 0.66 mm as previously described.7 Sodium nitrate (NaNO3), sodium fluoride (NaF), sodium iodide (NaI), and sodium thiocyanate (NaSCN) were from Fisher Scientific; sodium chloride (NaCl) and sodium bromide (NaBr) from SigmaAldrich; and sodium chlorate (NaClO3), sodium acetate (NaCH3COO), and sodium perchlorate (NaClO4) from Mallinckrodt. Radiolabeled sodium was from Perkin-Elmer Life Sciences: 22Na+ as NaCl, half-life 950 d, Emax = 0.546 MeV (positron), supplied with a specific activity of 1722 mCi mg−1. Solution Preparation. All salts were prepared using 18 MΩ deionized water (Barnstead, E-pure). The concentrations of all solutions were checked by conductivity using a four probe conductivity electrode and meter (Orion 3 Star, Thermo). Stock solutions of each salt at 1.0 activity were prepared. Tabulated values were used of the densities, solution conductivities, activities and concentrations.20,21 The radiolabeled solution was prepared by spiking 1 mL nonlabeled 0.5 M NaCl with 4 μCi 22NaCl to yield a specific NaCl activity of 8 × 10−3 Ci mol−1. Conductivity Measurements. The conductivity meter, equipped with a water jacket and temperature controlled to 25 ± 0.1 °C, was standardized with NaCl solutions. After two consecutive extrusions, the stoichiometric (1:1 PSS:PDADMA) exPECs were annealed in 1.5 M NaCl for 24 h, then soaked in excess water to remove all ions. The exPEC rods were cut into samples approximately 1 cm long, dabbed dry with a paper wipe and immersed separately into solutions of various salts at different concentrations. Each sample was allowed to dope to equilibrium at room temperature (23 ± 2 °C) for at least 24 h. PECs were wiped then dropped into 50 mL of water in the conductivity cell equipped with a small stir bar. Conductivity values were recorded every 30 s for 90 min and sent to a computer. After release of salt, exPECs were dried at 110 °C for 6 h to obtain the dry mass of the complex. Radiocounting Measurements. Plastic scintillator sheets, 3 mm thick (SCSN-81, Kuraray America, Inc.) were cut into 1.5 in. diameter disks. These disks were placed on the 2 in. window of a photomultiplier tube (PMT, RCA 8850) in a dark box biased to 2300 V with a Bertan 313B high voltage supply. A frequency counter (Philips PM6654C) interfaced to a computer running LabView recorded counts with a 10 s gate time. ExPEC was doped with radiolabeled 0.5 M 22NaCl for 24 h, dried with a wipe, and placed on top of a sheet of parafilm on the scintillator to measure the counts. Then the complex was dropped into 4 mL nonradiolabeled 0.5 M NaCl to exchange the labeled 22Na+ ions with unlabeled Na+ ions. 200 μL aliquots were withdrawn from the exchanging solution at intervals and counted later. After this self-exchange the exPEC itself was counted to verify all 22Na+ had been exchanged. For each data point, the total number of counts ranged from 7,000 and 90,000 giving respective counting errors of 84 (1.2%) to 300 (0.3%).

Figure 1. Concentration of NaCl released versus time after immersion of doped PSS/PDADMA exPEC in water at 25 °C. Samples were first doped to equilibrium for 24 h in 1.0 (a), 0.80 (b), 0.60 (c), 0.25 (d), and 0.10 (e) activity NaCl at room temperature. Concentration was obtained directly from conductivity every 30 s. Precision and accuracy ±2%.

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in water at room temperature. Similar plots for a range of NaX salts are shown in Supporting Information (Figure S1). It is assumed that all the NaX within samples is released into water since the relative volumes of water (50 mL) and sample (0.009 cm3) were high. This assumption was verified by radiotracer analysis of 22Na+ remaining in samples after release: ex-PEC was doped to equilibrium for 24 h in 0.5 M NaCl spiked with 22 Na+. The radiolabel in the sample was measured by scintillation counting before and after releasing the NaCl into water. The count rate was 123 ± 0.4 cps before release and 1.05 ± 0.02 cps after immersion in H2O for 90 min, showing that release was 99.2% complete (i.e., less than 0.8% of the original Na+ remained in the sample). Plateaus in Figure 1 were reached after about an hour. Individual samples were then dried and weighed. The amounts released, calculated from the plateau concentration and the

RESULTS AND DISCUSSION Doping Constants. The salt-plasticized22 extruded materials used here are a dense, stoichiometric morphology of polyelectrolyte complex. Our previous work has shown that these saloplastic PECs have few pores.7 In addition, because they are stoichiometric (1:1 PSS:PDADMA repeat units) they have no excess counterions (extrinsic charge) after rinsing in pure water.7 These properties allow transport and equilibrium measurements on well-defined bulk complex. The choice of PSS and PDADMAC to illustrate PEC doping was not arbitrary. The response of PECs to salts covers a wide range, depending on the combination of polyelectrolytes. For example, PECs from poly(acrylic acid) and PDADMAC are quite soft and dissolve in a rather low [NaCl].23 In contrast, B

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larger K’s for higher doping levels due to loss of cooperativity between neighboring ion pairs.27 Because the cation is the same for all the salts listed in Table 1 the only differences in doping efficiency are due to the anions which may be ordered according to a Hofmeister series (weaker to stronger doping)

solution volume, were compared to the amounts of PEC in the sample using the molecular weight of the PSS/PDADMA ion pair (309 g mol−1). Doping levels vs. salt activity (converted from concentration using tabulated activity coefficients) are plotted in Figure 2 for a range of NaX salts. The slopes provide

F− < CH3COO− < ClO3− ≤ Cl− ≤ NO3− ≤ Br − < I− < ClO4 − < SCN−

We avoid using the classification of ions as chaotropic (structure breaking) or kosmotropic (structure making) since there are questions as to the actual extent of structuring differences between ions.28,29 The ranking of ions follows an approximate trend in hydration. Differences in hydration are thought to cause differences in doping: fewer waters of hydration mean less loss of entropy when an ion dopes the complex.16 PDADMA+PSS−·aH 2O(c) + Na +·bH 2O(aq) + X−·c H 2O(aq) ⇌ PDADMA+X−·d H 2O(c) + PSS−Na +·e H 2O(c) + f H 2O(aq)

Here X is the salt anion, a is the number of water molecules hydrating the intrinsic ion pair, b and c are the water hydrating salt counterions in solution, d and e are the hydration numbers of the extrinsic ion pairs, and f represents the balance of water molecules which can be positive or negative. The range of doping constants is quite wide, varying by a factor of 400 from F− to SCN−. Values of Kdop agree in general with those determined using FTIR for multilayers made from PSS and PDADMA. K’s for PEMUs were 3.8 and 0.27 for ClO4− and NO3−, respectively, while KSCN− deviated more for PEMUs (0.42).16 Table 1 lists constants for non-IR active ions, including the most widely used NaCl. K’s reported here should be considered more precise and valid for stoichiometric PSS/PDADMA complex. Kinetics: Doping vs Undoping. The time-resolved data in Figure 1 provide an opportunity to evaluate the rate at which PECs are undoped. Using this data, it should be possible to estimate the diffusion coefficient for NaX in the PEC if the geometry is known. There are two caveats to doing this. First, because the composition of the PEC changes as NaX leaves the PEC the system is a reactive-diffusion one.30 Second, for the same reason, undoping kinetics may not be the same as doping kinetics. A comparison between doping and undoping kinetics is presented in Figure 3 for PEC samples that either are being doped by, or have been doped in, 0.5 M NaCl. The progress of (un)doping is given by the fraction f, between 0 and 1, where 1 is fully doped or fully undoped for the respective samples. This fraction is plotted versus t1/2 because the rate (slope) should be linear at early times for a diffusion process (see below). Figure 3 shows that although it takes about the same time for samples to reach equilibrium, whether they are doping or undoping, the process is not symmetrical. Whereas undoping adheres to a simple diffusion model ( f ∼ t1/2), doping shows slower kinetics at the beginning with acceleration later on. The reason for this difference: for undoping NaX travels out from the middle of the complex through regions that already have NaX in them, whereas for doping the ions encounter glassy, NaX-free complex as they enter the PEC. A D̅ that depends on doping

Figure 2. Doping level, y, in PSS/PDADMA exPEC versus salt activity: NaF (red ●); NaCH3COO (green ◇); NaClO3 (red ▲); NaCl (blue ■); NaNO3 (violet △) NaBr (○); NaI (gray ◆); NaClO4 (green ×); NaSCN (□). Room temperature. Correlation coefficients are listed in Table 1.

Table 1. Doping Constants (Kdop) and Diffusion Coefficient in PSS/PDADMA exPEC at 0.6 Salt Activity (D̅ NaX, a=0.6), and at y = 0.5 Doping Level (D̅ NaX, y=0.5)a X: anionb

Kdop (r2)

D̅ NaX,a=0.6 (×10‑7cm2 s‑1)

D̅ NaX,y=0.5 (×10‑7 cm2 s‑1)c

SCN− ClO4− I− Br− NO3− Cl− ClO3− CH3COO− F‑

3.20 (0.998) 2.40 (0.989) 1.00 (0.992) 0.42 (0.981) 0.41 (0.995) 0.30 (0.999) 0.18 (0.995) 0.02 (0.970) 0.008 (0.978)

10.7 12.8 9.67 6.70 6.10 5.73 5.67 3.77 1.87

6.0 4.6 5.9 8.0 7.5 10.8 13.0 15.9 4.0

(3)

−

Precision, ±5%, accuracy ±10%. X− is the anion with Na+ as a common cation. Kdop are from slopes in Figure 2 with r2 correlation coefficients listed. bCation is Na+ cCalculated from the slope of D vs y. a

doping constants listed in Table 1. Figure 2 shows that doping level is proportional to solution activity and that there is no NaX when samples are immersed in pure water (y→0). In contrast, experiments on polyelectrolyte multilayers usually show a residual population of anions, even after rinsing in pure water.16 This residual extrinsic charge is due to nonstoichiometric composition of polyelectrolytes within PEMUs. In Figure 2 no doping levels beyond y = 1, the theoretical maximum, are reported, since the curves become nonlinear and complexes were sticky and hard to handle close to y = 1. The data in Figure 2 are linear to higher levels of y than expected from eq 2. Such behavior, seen previously, was attributed to C

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Figure 3. Fraction, f, of NaCl taken up (doped) (red ●) or released (undoped) (blue ◆) vs t1/2 from exPEC. For the doping kinetics, several undoped samples were immersed in 0.5 M NaCl labeled with 22 Na+, then samples were removed at various times for counting (precision ±5%). For the undoping kinetics, a piece of exPEC was first doped in 0.5 M NaCl for 24 h then immersed in 50 mL water as in Figure 1 (precision ±3%).

level (see below) should change with time if (un)doping were to proceed uniformly. If undoping can be fit with a single D̅ , the process is heterogeneous i.e. a diffusion-limited wave of undoping from the center of the sample outward. Undoping was not only more amenable to analysis with a pure diffusion model but the experimental setup was also simpler. Monitoring the conductivity of the solution with a sample of PEC as it undoped provided continuous data, whereas doping kinetics were obtained from several individual samples doped with radiolabeled NaCl. Kinetics and Diffusion Coefficients. Undoping kinetics were treated with classical models for diffusion from a cylinder − the geometry of the exPEC samples. The fraction of NaX released from the exPEC f after time t is given by30 f=

Mt =1− M∞

∞

∑ n=1

4 −D̅ αn2t / a2 e αn 2

Figure 4. (A) Fraction f of NaCl released vs t1/2 from exPEC doped to equilibrium with 0.5 M NaCl. The solid curve is a fit according to eq 4 with a single D of 4.5 × 10−7 cm2 s−1. (B) Fraction of radiolabeled 22 Na+ self-exchanged from exPEC vs t1/2. The exPEC was doped to equilibrium (24 h) in 0.5 M NaCl labeled with 22Na+ then immersed in unlabeled 0.5 M NaCl. Solid curve is the corresponding fit with D̅ = 1.0 × 10−6 cm2 s−1.

(4)

where Mt is the amount of NaX which has diffused out after t seconds and M∞ the amount after infinite time. It is assumed that all the salt leaves the sample and M∞ was the amount originally present. D̅ is the diffusion coefficient of NaX in the exPEC, and a is the radius of the cylinder. αn are the roots of the Bessel function of the first kind of zero order. Equation 4 assumes no resistance to mass transfer in the stagnant layer of liquid around the sample and the concentration of salt in solution is negligible at all times (no transport back into the PEC). These assumptions are valid as the diffusion in solution is at least 10−100 times faster than in the PEC and the maximum solution concentration, less than 10−3 M, is at least 100 times lower than the solution used to dope the sample. For each salt concentration, data for f vs t were fit using eq 4 using a single D̅ and the first 10 Bessel roots, and the results presented as f vs t1/2 (eq 4 is shown expanded using the first 10 Bessel roots in Supporting Information). The example in Figure 4, for doping with 0.5 M NaCl, shows that fits were generally excellent over the whole time course.

Undoping kinetics were measured for a range of anions and a range of doping levels to obtain corresponding diffusion coefficients (see Figure S2 in Supporting Information). As an example, diffusion coefficients for NaCl from the data in Figure 1 are shown in Figure 5. It is clear that D̅ depends on the doping level. In this case D̅ is an approximately linear function of y. Diffusion coefficients for all the sodium salts in exPECs doped in the same activity (0.6) of NaX are summarized in Table 1. For better comparison, diffusion coefficients for exPECs doped to the same y (0.5) are also provided in Table 1. The trend in D̅ when samples with the same y are compared actually reverses the Hofmeister series with the exception of NaF and NaSCN. The more hydrated ions bring more water into the PEC providing greater free volume for ion motion and therefore greater ion mobility. It is probable that the PEC is also better plasticized and softer for the same reason.22 Coupled vs Tracer Diffusion in PECs. Diffusion coefficients reported in Table 1 are for coupled NaX, not the individual ions. In other words, the mass transfer of Na+ and X− D

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coefficient of Na+ (D̅ Na+) was found to be 1.0 × 10−6 cm2 s−1, and the coupled diffusion coefficient of NaCl (D̅ NaCl) 4.5 × 10−7 cm2 s−1. Using these values and eq 6 the PEC diffusion coefficient of Cl− (D̅ Cl−) would be 2.9 × 10−7 cm2 s−1. These coefficients may be compared to those for aqueous solution at 25 °C: 1.61 × 10−5 cm2 s−1, 1.33 × 10−5 cm2 s−1, and 2.03 × 10−5 cm2 s−1, for NaCl,35 Na+,36,37 and Cl−,36 respectively. In contrast to its behavior in water, Na+ diffuses faster than Cl− in the PEC, perhaps because it is less hydrated (smaller effective diameter) in the complex. Charge makes a significant difference. When PSS/PDADMA is doped with 0.6 M NaCl, NaCl diffusion is much faster in PSS/PDADMA (D̅ ∼7 × 10−7 cm2 s−1) than is ferricyanide, Fe(CN)63‑ (D̅ ∼2 × 10−9 cm2 s−1) under the same conditions.10 PECs doped with 0.5 M NaCl labeled with 22Na+ lost more than 99% of their radioactivity after both coupled and tracer diffusion experiments, showing all salt is exchanged or expelled from the sample by the end of the run. Figure S4 in the Supporting Information shows the doping level at 0.5 M NaCl (activity = 0.34) fits well with the rest of the y vs a plots for NaCl.

Figure 5. Diffusion coefficients at 25 °C for NaCl in PSS/PDADMA exPEC versus doping level.

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into or out of the material is coupled − Na+ must move with X− along a concentration gradient to maintain local charge neutrality. Coupled diffusion is well-known in classical ion exchangers.31 The coupled diffusion coefficient, D̅ NaX is given by31 D̅ NaX =

D̅ Na D̅ X (z Na 2C̅ Na + z X 2C̅ X) z Na 2C̅ NaD̅ Na + z X 2C̅ XD̅ X

CONCLUSIONS Ion diffusion coefficients for monovalent ions in these solid materials are quite high, within a couple of orders of magnitude of those for aqueous solution. PEC ion diffusion is many orders of magnitude faster than diffusion of the polyelectrolyte components. For example, PSS of molecular weight ca. 105 g mol−1 exhibited a diffusion coefficient of about 3 × 10−17 cm2 s−1 within PSS/PDADMA doped with 0.8 M NaCl.38 A Hofmeister series for ion doping follows the usual ordering for anions. A Hofmeister series for diffusion is only indirectly related to thermodynamic properties, but is believed to result from the differences in equilibrium ion hydration within the exPECs. Diffusion coefficients for exPECs represent a minimum rate for ion transport at room temperature. They should increase as the porosity increases and strongly as temperature increases. For example, room temperature diffusion coefficients for NaCl in macroporous exPECs39 were on the order of 10−6 cm2 s−1.

(5)

where D̅ Na and D̅ X are individual (uncoupled) diffusion coefficients of ions, zNa and zX their charges and C̅ Na and C̅ X their concentrations, respectively. The diffusion coefficients and corresponding concentration of Na+ and X− are those within the exchanger. PECs are “reluctant” exchangers,27 where the number of ion exchange sites is controlled by doping by external salt ions. For such doping, C̅ Na = C̅ X = C̅ , and in our case all the salt ions are monovalent (zNa = zX = 1). Thus, the coupled diffusion coefficient simplifies to the following:

D̅ NaX =

2D̅ Na D̅ X D̅ Na + D̅ X

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(6)

ASSOCIATED CONTENT

S Supporting Information *

Of course, eq 6 does not reveal any dependence of D̅ NaX, D̅ Na, and D̅ X on concentration. The literature on PECs in the form of multilayers compares permeability for steady-state membrane transport of ions.17−19 For example, Bruening and co-workers have measured permeability coefficients through supported PEMUs.17,32−34 For such steady-state measurements the diffusion coefficients would be those of the salt. In the present work, individual or “tracer” diffusion coefficients for Na+ were determined by doping (to equilibrium) with 0.5 M NaCl spiked with 22Na+. These samples were immersed in 0.5 M NaCl (unlabeled) for ion self-exchange and aliquots were removed at intervals for counting later on (Figure S3 in Supporting Information shows count rates). Fractions exchanged versus t1/2 for the 22Na+ self-exchange in 0.5 M NaCl are shown in Figure 4 along with the fit for the diffusion model, where D̅ is the Na+ tracer diffusion constant. The fact that the same sample was used for both coupled (Figure 4A) and tracer (Figure 4B) experiments allows close comparison of the results. Tracer diffusion of Na+ was slightly faster than coupled diffusion of NaCl. The uncoupled diffusion

Undoping versus time curves for PSS/PDADMA exPEC for various salts and concentrations, expanded eq 4, diffusion coefficients versus doping level for various salts, counts vs time for self-exchange, and doping curve for NaCl. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*(J.B.S.) E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by a grant from the National Science Foundation (DMR-1207188). REFERENCES

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