Intrinsic Properties of Polyelectrolyte Multilayer Membranes: Erasing

Mar 21, 2018 - Intrinsic Properties of Polyelectrolyte Multilayer Membranes: Erasing the Memory of the Interface. Kristopher D. Kelly , Hadi M. Fares ...
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Intrinsic Properties of Polyelectrolyte Multilayer Membranes: Erasing the Memory of the Interface Kristopher D. Kelly, Hadi M. Fares, Samir Abou Shaheen, and Joseph B. Schlenoff* Department of Chemistry and Biochemistry, The Florida State University, Tallahassee, Florida 32306-4390, United States ABSTRACT: Polyelectrolyte multilayers (PEMUs) are ultrathin membranes made by alternating adsorption of oppositely charged polyelectrolytes on substrates. Although PEMUs have shown exceptional selectivity for certain ionfiltering applications, they usually contain an excess of one of the polyelectrolytes due to the history- and condition-dependent mode of PEMU assembly. This excess charge provides fixed sites for ion exchange, enhancing the concentration of oppositely charged ions. Thus, the ion-permselective properties of PEMUs cannot be compared unless they are assembled under identical conditions. This work demonstrates the enhanced permeability of PEMUs as-made from poly(diallyldimethylammonium) (PDADMA), and poly(styrene sulfonate) (PSS) to ferricyanide as an example of an anion. Annealing by NaCl followed by pairing of excess PDADMA with additional PSS produces an almost stoichiometric film that better reflects the intrinsic transport properties of PEMUs. This pairing, observed in real time using electrochemical methods, occurs at the PEMU/solution interface under countercurrent transport of PSS from solution and excess PDADMA paired with a counterion, termed PDADMA*, from the PEMU bulk. A quantitative comparison of PSS and PDADMA* diffusion reveals the conditions under which PEMU assembly depends on PSS molecular weight and concentration.

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INTRODUCTION Polyelectrolyte complexes (PECs) form spontaneously, driven by the release of counterions, when oppositely charged polyelectrolytes, Pol+ and Pol−, are brought together.1 Films of polyelectrolyte complex have a long history for use in membranes for separations.2 More recently, Decher and coworkers have described a powerful processing method for making ultrathin films of PEC by alternately exposing a surface to pairs of polyelectrolytes.3,4 This “multilayering” method, which could be performed on microporous supports, offered a convenient route to high-flux membranes for the separation of gases5−8 and ionic species.9−11 Impressive selectivities, demonstrated for separations of ions using polyelectrolyte multilayers (PEMUs), depend on the relative charge and size of the species of interest. For example, nanofiltration of anions or cations through multilayers has been accomplished with a selectivity of chloride over sulfate12 of 27 and sodium over magnesium13 of 22. Reasons for the exceptionally high selectivity of diffusion dialysis (for example, K+/Mg2+ selectivities of >350) compared to nanofiltration through multilayers were discussed by Cheng et al.14 Sanyal and Lee have recently reviewed various strategies to implement membrane separations using PEMUs.15 For ion separation and devices or sensors16 made from PEMUs, permeability is controlled by the population and distribution of charged sites within the membrane and by the amount of free volume accessible to permeants. As an example of the latter, membranes that are more swollen with water are likely more permeable, whereas cross-linking not only reduces permeability but also tends to enhance selectivity.17 © XXXX American Chemical Society

Sites for ion transport within PECs and PEMUs are termed “extrinsic sites” to differentiate them from the ion pairing between Pol+ and Pol− that holds the amorphous polyelectrolyte complex together (see Scheme 1). These extrinsic sites appear in PECs in two forms. First, if the PEC contains nonstoichiometric amounts of Pol+ or Pol−, there is a persistent excess of one counterion to balance the polyelectrolyte in excess. Nonstoichiometry results from the normal process of making PEMUs layer-by-layer (LbL) (see below) or can be introduced into the film post synthesis using photochemistry,18 hydrolysis of functional groups,19 or changing the state of ionization of one of the polyelectrolytes.20 Second, under the chemical potential of salt, MA, in solution, some MA is “doped” into the PEC according to the following equilibrium21 Pol+Pol−PEC + MA aq → Pol+A−PEC + Pol−M+PEC

(1)

Persistent sites behave as a classical ion exchanger, including oppositely charged counterions and rejecting like-charged ions.22 Doped sites allow both negative and positive ions to traverse the PEC.23 It was initially assumed that PEMUs are simply stoichiometric thin films of PECs and only the outer surface contained counterions as a result of charge overcompensation of each polyelectrolyte needed to propagate the layer-by-layer Received: January 30, 2018 Revised: March 6, 2018

A

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Scheme 1. (A) Illustration of How Charge Is Balanced within a Nonstoichiometric PEMU Showing a Mix of Classical Fixed-Site Exchanger and Doping-Induced Exchange Sites; (B) Structures of Polyelectrolytes Used

in Cl−/SO42− selectivity for these PEMUs used in nanofiltration.25 More recently, de Grooth et al. have further explored the history and condition-dependent permeability and selectivity of PEMUs employed for membrane separations.26 The objective of the present work is to show how the thicknessand condition-dependent separation properties of PEMUs, which are a result of the asymmetric nature of the interfacial assembly, may be eliminated to obtain a more convergent set of permeability properties that better reflect the intrinsic nature of PEMUs.

assembly.3 The true picture is more complex, wherein most multilayers are nonstoichiometric and therefore contain a certain amount of bulk fixed charge, marooned within the PEMU during buildup.24 This result, a consequence of the interfacial nature of the assembly, is illustrated in Figure 1,

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EXPERIMENTAL SECTION

Materials. PDADMA (molecular weight, 400 000−500 000 g mol−1, 21.3 wt% in water) was used as received from Aldrich. A selection of narrow-polydispersity poly(styrene sulfonate), sodium salt from Scientific Polymer Products, is listed in Table 1. PSS with a

Table 1. Molecular Weights of Narrow-Polydispersity PSS (Sodium Salt) Used, Polydispersity Index, and Solution Diffusion Coefficients

Figure 1. Thickness versus number of PDADMA/PSS bilayers (PSS on top) for a PEMU built in 0.25 M NaCl. Up to (PDADMA/PSS)6, the addition of PSS yields a uniform stoichiometric film. Beyond this thickness, an increasing amount of excess PDADMA, compensated by Cl− counterions, remains within the film. Adapted from ref 24.

which depicts the multilayering of poly(styrene sulfonate) (PSS) and poly(diallyldimethylammonium) (PDADMA). The even (PSS) layers only are shown. For the initial layers, the film remains stoichiometric on each even layer and overcompensation only occurs on the addition of PDADMA. After about six PDADMA/PSS bilayers, excess PDADMA, compensated by anions, builds up within the film. Figure 1 shows how the issue of ion transport through a PEMU may be more complex. The material contains persistent extrinsic sites, but they are not homogeneously distributed. In addition, even if the extrinsic sites were uniformly distributed, the transport mechanism also has to include any sites produced by doping. This mixture of sites may have advantages or disadvantages, but a fundamental understanding of the transport mechanism through PEMUs is muddied by faulty assumptions concerning the membrane composition. The influence of PEMU growth conditions on permeability was recognized by Adusumilli and Bruening, who noted changes in ion-exchange capacity during the growth of PDADMA/PSS PEMUs and the consequent sharp decrease

PSS name

PSS Mw

Mw/Mn

Daq (×10−7 cm2 s−1)a

PSS57.5 PSS122.4 PSS626 PSS615 PSS801 PSS2260

57 500 122 400 262 000 615 000b 801 000 2 260 000

1.10 1.17 1.20 1.05 1.16 1.11

4.3 2.78 1.79 1.10 0.95 0.52

a

In 0.5 M NaCl at room temperature from ref 28. bPrepared by sulfonating polystyrene. molecular weight of 615 000 g mol−1 was prepared by sulfonating polystyrene of narrow molecular-weight distribution according to a literature procedure.27 Wide-molecular-weight-distribution poly(styrene sulfonic acid) (Mw ∼ 70 000 g mol−1) from Scientific Polymer Products was neutralized with NaOH prior to use and is termed PSS70. Potassium ferricyanide, K3Fe(CN)6, was used as received from Mallinckrodt, Inc. Potassium ferrocyanide trihydrate (K4Fe(CN)6·3H2O) and sodium chloride were used as received. All solutions were made in 18 MΩ deionized water (Barnstead, E-pure). 35 SO42− (received as Na235SO4; half-life, 87.4 days; β-emitter; Emax = 167 keV) was purchased from PerkinElmer. It was supplied as 1 mCi in 1 mL of water with a specific activity of 1494 Ci mmol−1 and used as a stock solution. PEMU Characterization. Thicknesses of dry PEMUs on Si(100) wafers were determined using a Gaertner Scientific L116S Autogain B

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Langmuir ellipsometer with 632.8 nm radiation at an incident angle of 70° and a refractive index of 1.55. Fourier transform infrared (FTIR) spectra of PEMUs on double-side-polished Si(100) wafers were obtained at a resolution of 4 cm−1 averaging 100 scans using a Thermo Avatar 360 equipped with a deuterated triglycine sulfate detector. The background was a bare Si wafer. All multilayer buildup and treatments were conducted at room temperature (23 ± 2 °C). Rotating Disk Electrode (RDE). A 100 mL electrochemical cell was equipped with a water jacket and a circulating thermostat set to 20 °C (±0.1 °C), a platinum-wire counter electrode, and a KCl-saturated calomel reference electrode (SCE), against which all potentials were measured. The working electrode was a rotating platinum disk (RDE, Pine Instruments model AFE3T050PT), with a diameter of 5 mm, mounted in a Pine AFMSRCE rotator and speed controller. A Pine AFTP1 WaveNow potentiostat was used to generate potential ramps, and the resulting voltammograms were recorded using AfterMath software. The platinum electrode was polished with 0.3 μm alumina (Buehler), rinsed with deionized water, and dried under a stream of N2. Layer-by-layer adsorption of polyelectrolytes to the electrode was performed at a rotation rate of 1000 rpm. The electrode was dipped in polyelectrolyte for 5 min, followed by three 1 min water rinse steps. This process was alternated between positive and negative polyelectrolyte up to the desired number of layers. The polyelectrolyte deposition solutions were 15 mL PDADMAC and PSS70 (10 mM each based on the repeat unit) in 0.25 M NaCl. The thickness of the PEMUs was determined ellipsometrically in a separate experiment using a 2.5 cm diameter single-side-polished Si wafer rotating at 1000 rpm. Cyclic voltammograms (CVs) were collected in solutions of 2 mM ferricyanide in 0.6 M NaCl at a scan rate of 20 mV s−1 in the range of +300 to −300 mV vs SCE at 1000 rpm. The electrolyte was purged and then blanketed with Ar to exclude oxygen. Chronoamperometry was performed at a potential of −300 mV. Following construction of the PDADMA-terminated PEMU, the film was annealed in 1 M NaCl for 15 min to evenly redistribute any excess positive charges. The film was then placed into the electrochemical cell and rotated at 1000 rpm in 0.6 M NaCl. After 5 min, 2 mM ferricyanide was added to the cell. Once the current had stabilized, a small aliquot of concentrated PSS was added to provide a concentration of 0.1 or 1.0 mM in the cell and the current was continuously measured. The current fell as PSS consumed excess PDADMA. Radiolabeling. Na235SO4 was used to quantify the total amount of positive extrinsic sites, PDADMA*. 35SO42− solution (20 mL) was prepared by diluting 30 μL of the “hot” Na235SO4 in 19.97 mL of “cold” 10−3 M Na2SO4. The resulting solution had a specific activity of about 1 Ci mol−1. The specific activity determines the accuracy and precision of the counting, and the solution concentration ensures an excess of radiolabel in the solution. For counting, a photomultiplier tube (PMT, RCA 8850) housed in a dark box was used. A 3.8 cm plastic scintillator disk was cut from 3 mm thick sheet (SCSN-81, Kuraray America). It was placed on the 5 cm diameter window of the PMT with a drop of immersion oil under it to ensure good optical contact between the scintillator and the PMT. A Bertran 313B high-voltage supply fixed at 2300 V was connected to the PMT. To record the counts, a frequency counter (Philips PM6654C) interfaced with a computer running LabView software was used. The pulse threshold was fixed at −20 mV, and the gate time was 10 s. For each data point, the total number of counts registered ranged from 9700 to 30 000 with respective counting errors of 1 and 0.6%. After building and rinsing the PEMU to 17 layers, it was dried under a stream of N2 and soaked in the radiolabeled 35SO42− solution for 30 min. It was then dried using N2 without rinsing and placed face down on the plastic scintillator. The counting was performed for 15 min, after which the film was placed in 10−2 M cold NaCl solution to exchange out the hot sulfate for around 15 min. The film was then rinsed quickly in water and dried. The same labeling/cleaning procedure was used for the next two steps: 15 min in 1 M NaCl and 5 min in 10 mM PSS in 1 M NaCl. A calibration curve was built by dispensing 1−5 μL aliquots of the radiolabel solution covered with

a bare Si wafer for good spreading on top of the scintillator. The curve (counts vs number of moles) was used to obtain the number moles for each time point. The surface area of the film was measured and used to obtain mol m−2.

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RESULTS AND DISCUSSION Thin films of PDADMA/PSS were constructed on platinum electrodes using the layer-by-layer adsorption method. This polyion pair has been used for nanofiltration membranes,14,26,29,30 anticorrosion coatings,31,32 and as polyelectrolyte complexes for a range of applications.33 Transport to and through a membrane at the rotating disk is a wellunderstood system with mass transport limited by solution convection-diffusion to the membrane surface and diffusion through the membrane itself,34 as illustrated in Scheme 2. Scheme 2. Scheme of Fe(CN)63− (Yellow Dots) Permeating through a PEMU Coating an RDEa

a

Next to the PEMU is a stagnant layer of solution of significantly greater thickness than the PEMU that adds a series resistance to ferricyanide transport to the RDE.

The steady-state convection-diffusion-limited current at an uncoated electrode, ilev, of area A rotating at an angular velocity ω is given by the Levich equation35 2/3 1/2 −1/6 ilev = 0.620nFADaq ω v Caq

(2)

where n represents the number of electrons (1 for ferri/ ferrocyanide), F is the Faraday constant, Daq is the solution diffusion coefficient of the electroactive species, v is the kinematic viscosity of electrolyte solution (here ∼0.01 cm2 s−1), and Caq is the concentration of the electrochemical species in solution (mol cm−3). A membrane coating the electrode adds additional series resistance to mass transport. The limiting current decreases as follows34 C

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Langmuir 1 ilim

=

1 imem

+

1 ilev

population of excess PDADMA (extrinsic sites) compensated with anions (Figure 1). This persistent charge, acting as a classical ion exchanger, is able to adsorb additional ferricyanide and enhance the membrane flux. Referring again to Figure 3, another interesting feature is that the flux of electroactive ion appears to level off after about 20 layers even though the film is gaining thickness with each layer as in Figures 1 and 3 (inset). This unusual behavior is a consequence of the interfacial nature of the layer-by-layer assembly: material accrues at the surface due to a countercurrent transport and reaction of polyelectrolyte coming in from solution and polymer extrinsic sites coming out of the film. The process is represented in Scheme 3 for a film terminated with PDADMA immersed in a solution of PSS. Although the addition of a layer in Scheme 3 alternates between polyanions and polycations, the diffusion rates of PSS and PDADMA extrinsic sites are not the same at the same [NaCl].47 In the time allowed for multilayer formation, excess PDADMA accumulates as linear multilayer growth occurs. Linear growth is a signature of a diffusion-limited system. The steady-state membrane current depends on the membrane concentration of the redox-active probe (here, ferricyanide C̅ ferri), and its membrane diffusion coefficient D̅ ferri

(3)

where imem is the current limited by diffusion through the membrane only. Thus, measurement of ilim at an electrode under the same conditions with and without a membrane is a convenient method of reproducibly removing the contribution of resistance to mass transfer through the solution.23,34,36 Because it is highly charged, ferricyanide diffuses slowly enough through the PEMU to measure imem . The membrane concentration of ferricyanide is about 30 mM, and electron hopping between redox sites (electron diffusion) does not occur.23 The use of a rotating electrode also facilitates the deposition of polyelectrolytes during multilayering. Thus, PSS and PDADMA were sequentially adsorbed to the Pt disk at 1000 rpm. After the desired number of layers was deposited, the electrode was placed in the electrochemical cell containing the electroactive species in 0.6 M NaCl supporting electrolyte. An example of cyclic voltammetry in an equimolar mixture of 2 mM ferri- and ferrocyanide is shown in Figure 2, which depicts CVs of the bare electrode and after 17 (PDADMA on top) and 18 (PSS on top) layers.

imem =

nFAD̅ferri Cferri ̅ d

(4)

The membrane concentration of ferricyanide has contributions from the amount doped into the film according to eq 1, C̅ ferri,dope, and the amount that occupies the persistent fixed charge resulting from excess PDADMA (extrinsic sites), C̅ ferri,PDADMA* Cferri ̅ = Cferri, ̅ dope + Cferri,PDADMA ̅ *

(5)

From eq 5, C̅ ferri depends on the amount of excess PDADMA, which in turn is highly dependent on the way the multilayer was assembled. The inclusion of anions by excess polycation within PEMUs has been observed, and sometimes designed, previously.25,48 Kharlampieva and Sukhishvili49 used this principle for the inclusion and release of both cationic and anionic dyes in PEMUs containing weak polyelectrolytes. On addition of polyelectrolyte, the dye was released from the PEMU, suggesting use for the controlled release of certain molecules. This behavior was also observed by Hübsch et al.50 for the release of ferrocyanide from a PEMU composed of poly(glutamic acid) and poly(allylamine hydrochloride). Ferrocyanide was not released from the membrane when placed in a Tris−NaCl buffer solution, but immediately diffused out on immersion in a polyelectrolyte solution.50 Balachandra et al. templated a PEMU with Cu2+ to enhance anion selectivity.37 Eliminating Excess PDADMA. To eliminate the imbalance of charge within the membrane, we employed a recently described technique for producing stoichiometric films of complex:51 exposing the as-made multilayer to a solution of higher salt concentration (here, 1 M NaCl) mobilizes the polymer within the film and evenly redistributes the excess PDADMA. When PSS in 1 M NaCl is added, it can now access almost all of the excess PDADMA (as in Scheme 3) and the film becomes almost stoichiometric. Scheme 4 summarizes the two layer-by-layer buildup strategies. Figure 3 shows the effect of this simple annealing step, performed after each PSS layer, on the layer-by-layer transport

Figure 2. Cyclic voltammetry of a mixture of 2 mM ferricyanide and 2 mM ferrocyanide at the rotating disk electrode on a PDADMAterminated PEMU (17 layers) (blue), PSS70-terminated PEMU (18 layers) (red), and on a bare electrode (green). When PSS terminated the PEMU, the film had no net charge and mobility of ferricyanide was diffusion-limited. Both PEMU CV experiments showed complete blocking of ferrocyanide through the film (the currents were less than 3 μA from 200 to 500 mV). Experiments were performed in 0.6 M NaCl at a platinum electrode with an area of 19.6 mm2 and a rotation rate of 1000 rpm.

The results in Figure 2, similar to those obtained previously,23 show approximately equal solution mass transport of ferricyanide and ferrocyanide and strongly preferred transport of ferri- over ferrocyanide. Selectivity of lower- over higher-charged ions through PEMU membranes is usually found.9,14,37−40 Current versus Layer Number. As-built PEMUs terminated with PDADMA always yielded higher currents than PSSterminated multilayers with similar numbers of layers. This results in a sawtooth pattern of current versus layer number, as seen in Figure 3. The up−down pattern of current versus permeability was first reported by Lvov41 and is one of a number of odd−even effects during multilayer buildup.26,42−46 For the PDADMA/PSS system, PDADMA-capped films are more permeable to anions because they contain a significant D

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Figure 3. Limiting current at −0.3 V at the rotating disk electrode vs number of layers for 1 mM ferricyanide, Fe(CN)63− in 0.6 M NaCl using a 20 mV s−1 sweep rate and 1000 rpm rotation rate, at room temperature. The first data point is the Levich current for the bare electrode. Two methods of buildup were performed, standard (red squares) and annealing (blue diamonds). The standard method consists of solution alternation by dipping with intermediate rinsing steps. The annealing method used 1 M NaCl following each PSS70 layer to redistribute charge within the film. The PEMU was rinsed again and then additional PSS was adsorbed from 1.0 M NaCl. This allows the film to grow at a higher rate than standard buildup procedures. The platinum electrode had an area of 0.196 cm2. PDADMA/PSS multilayers were built from 10 mM polymer solutions in 0.25 M NaCl.

Scheme 3. Illustration of the Adsorption of PSS to a PDADMA-Terminated PEMUa

a Excess positive charges (extrinsic sites) from PDADMA (PDADMA*) diffuse to the surface to meet PSS from solution at the PEMU/solution interface. The polymer charges pair, annihilating PDADMA* and giving a stoichiometric film.

In 1.0 M NaCl, DPDADMA * is 6 × 10−13 cm2 s−1. Using the following to estimate diffusion length, Δ, in time t

Scheme 4. Sequence of Immersion Steps for Films Assembled Following the “Standard” Method (A) for Layerby-Layer Assembly and (B) with an Additional “Annealing” and Second Immersion in PSS To Remove Almost All of the Excess PDADMA

Δ=

(7)

Δ = 3 × 10−5 cm, or 300 nm, after 15 min annealing in 1.0 M NaCl; 300 nm is more than the thickest films (see inset in Figure 3) showing that the annealing conditions should be enough to extract PDADMA*. The effectiveness of the annealing step at removing excess PDADMA was assessed using two methods.51 In the first method, Cl− ions were exchanged with the infrared active ion NO3−, which provided a semiquantitative measure of PEMU anion content. The method is illustrated in Figure 4, which shows the strong NO stretch at 1350 cm−1 following exchange of Cl− in a 17-layer film. A 15 min soak in 1.0 M NaCl removed the nitrate ion and allowed charge redistribution (Figure 4). When PSS in 0.25 M NaCl was added, depositing the 18th layer, the amount of PSS increased and NO3− labeling revealed almost no excess PDADMA extrinsic sites. At this point, the PEMU is almost stoichiometric. Peak areas, normalized to the PDADMA peak, from Figure 4 are shown in Figure 5A. The relative area of PDADMA compared to PSS does not change significantly on annealing in 1 M NaCl. With the addition of PSS (layer 18), the PSS area increases. The area of the nitrate peak decreases by about 90%

of ferricyanide. When the current was recorded after each annealing step, the flux of Fe(CN)63− was greatly reduced for the PSS layer. PDADMA addition continues to leave excess PDADMA behind, so the flux through the PDADMAterminated PEMU is initially higher. Thickness as a function of layer number, shown as the inset in Figure 3, increases more steeply when the annealing step is employed because more PSS is included in the film. According to our previous studies with these same polyelectrolytes,47 the diffusion coefficient for the excess PDADMA, D*PDADMA, is given by * DPDADMA = (2.60 × 10−14) e3.12[NaCl]

2Dt

(6) E

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accuracy and precision, a radiolabeling technique was employed, where PEMUs were dipped in 35SO42− solution to exchange the Cl− ion with radiolabeled ions. The results in Figure 5B show a decrease in extrinsic sites from 50 to 10 μmol m−2. Membrane Permeability. The membrane current may be converted to membrane flux, Jmem, as follows52 Jmem =

imem D̅ C̅ = ferri ferri nFA d

(8)

The raw electrochemistry results from Figure 3 are converted to flux in Figure 6, which shows how the history-dependent Figure 4. Extrinsic site labeling by NO3− using FTIR. The nitrate ion was added after each processing step (17 layers, NaCl annealing, and PSS70 addition). (A), (B), and (C) show the respective peak locations for PDADMA, NO3−, and PSS. Following the 17th layer (17L), which is PDADMA, the addition of NO3− showed an excess of extrinsic sites within the film. Annealing in 1 M NaCl (17L+) allowed the even redistribution of positive extrinsic sites. The addition of PSS (18L) removed almost all extrinsic sites shown by the near disappearance of NO3−. Spectra have been displaced along the y-axis for clarity.

Figure 6. (A) Membrane flux of ferricyanide through PEMUs constructed by two different methods. The standard layer-by-layer (LbL) PDADMA/PSS PEMU is represented by red squares, which shows greater membrane flux due to inclusion of ferricyanide by positive extrinsic sites (PDADMA*). Annealing the PEMU with 1 M NaCl, followed by an extra PSS70 adsorption step removes the excess positive charge and shows a decrease in membrane flux demonstrated by blue diamonds. (B) Data from (A) converted to permeability.

interfacial assembly method of making membranes from multilayers can lead to rather high flux. Because ilev and ilim are initially so close (see Figure 3), there is substantial uncertainty about imem (eq 3) for the first few layers. Thus, Figure 6 plots five layers onward. A better comparison between nonstoichiometric and stoichiometric PEMUs is made by normalizing the flux by membrane thickness, d, to provide permeability, P

Figure 5. Extrinsic site labeling by (A) NO3− and (B) 35SO42− using FTIR and radiolabeling, respectively. In (A), FTIR peak areas from Figure 4 are normalized to the PDADMA area. (A) shows that the relative areas of PDADMA and PSS70 do not change on annealing in salt but PSS area increases when PSS is added (layer 18). The use of radioactive 35SO42− labeling in (B) accurately tracks both the amount and decrease in positive sites.

after this treatment, showing almost complete removal of extrinsic positive sites. Although this FTIR technique shows the trends in relative amounts of PSS, nitrate, and PDADMA, it does not provide the absolute amounts. In addition, a decrease in the relative amount of nitrate to PDADMA was observed, which suggested a slight loss of PDADMA. To measure the ion content with greater

P=

Jmem d Cs − Ce

(9)

where Cs is the solution concentration and Ce is the concentration at the electrode, which is zero at the limiting current.52 The units of permeability depend on whether a difference in pressure or concentration is the driving force. The F

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The kinetics of capture and annihilation of PDADMA* by solution PSS at the PEMU/solution interface illustrated in Scheme 3 depends on countercurrent transport of PSS from solution and PDADMA* from the PEMU bulk. It is assumed that one of these processes must be rate-limiting under certain conditions. For example, if the solution concentration of PSS is high enough, the rate should be limited by PDADMA* diffusion. For most of the experiment, the flux of PDADMA* from bulk to surface, JPDADMA*,m, is given by semi-infinite diffusion out of a plate53

permeability of the PEMU shows great variability from the presence of PDADMA*. If the composition of the PSSannealed film were truly independent of thickness, its permeability should remain constant, whereas there is a slight decrease (Figure 6B) perhaps due to less water in thicker films. Kinetics of Eliminating Excess Charge. The dynamics of PDADMA* pairing with PSS in solution, shown in Scheme 3, may be tracked by monitoring the current in real time. This experiment was performed on the 17th layer, motivated by the large decrease in current (Δ = −42 μA) between the 17th (PDADMA) and 18th (PSS) layers from Figure 3. The potential of the rotating disk was held at −300 mV, corresponding to the limiting current, and an aliquot of dilute PSS was added. Figure 7 shows that the membrane current drops significantly as the PSS pairs with, or annihilates, PDADMA* within the multilayer.

JPDADMA*,m =

1/2 D̅ PDADMA *C̅ PDADMA*,m

π 1/2t 1/2

(10)

where C̅ PDADMA*,m is the concentration of PDADMA* in the PEMU. The flux of PSS from solution to the surface, JPSS,aq (mol s−1 cm−2), is under the same convection field as the ferricyanide 2/3 JPSS,aq = 0.620DPSS,aq ω1/2v−1/6C PSS,aq

(11)

CPSS is again based on the concentration of the repeat unit and remains constant because it is present in excess over the amount adsorbed in a layer. The total amount, QPSS (mol cm−2), that reaches the PEMU as a function of time is 2/3 Q PSS = t 0.620DPSS,aq ω1/2v−1/6C PSS,aq

(12)

Assuming all other parameters except C̅ ferri are constant, the rate at which the membrane current decreases in Figure 7 depends on the rate that PDADMA* is annihilated from the film. The midpoint slopes of Figure 7 are shown in Figure 8.

Figure 8. Slope of current decrease for a range of narrow molecular weights of PSS to the PDADMA-terminated PEMU at 1 and 0.1 mM in 2 mM ferricyanide/0.6 M NaCl. There was a significant reduction in rate from 262k to 615k molecular-weight PSS due to the slower rate of solution PSS diffusion. The slopes were calculated from the chronoamperometry plots in Figure 7.

Figure 7. Six narrow molecular weights of PSS at (A) 0.1 mM and (B) 1 mM in 2 mM ferricyanide/0.6 M NaCl were used to determine the effects of molecular weight on polyelectrolyte adsorption kinetics using the RDE. As PSS chains bind to the PDADMA-terminated PEMU, PDADMA* is consumed reducing the concentration of fixed sites in the PEMU and reducing the membrane current. As molecular weight increases, the rate at which PSS diffuses through solution to the PEMU decreases. PSS addition is noted by the dashed line at 30 s. Every 10 points were averaged.

There is a transition in slope between the 262 and 615 kDa Mw 1 mM PSS samples. The slope is independent of 1 mM PSS molecular weight below 262 kDa. This slope is interpreted to be the maximum annihilation rate of PDADMA*, which corresponds to the diffusion-limited maximum transport rate of PDADMA*. From Figure 7A, it takes about 30 s to extract PDADMA* from the film under PDADMA* diffusion-limited conditions. The dry thickness of the film is about 40 nm, and the wet thickness is thus about 80 nm, assuming that it is swelled by water to double its dry thickness.54 Using eq 7 and a wet thickness of 80 nm, a diffusion coefficient of 1 × 10−12 cm2 s−1

The chronoamperometry (current versus time) experiment in Figure 7 used six narrow-molecular-weight PSS standards at two concentrations. The 17-layer as-built multilayer on the RDE required annealing in 1 M NaCl for 15 min for a stable initial current. The electrode was then immersed, under Ar, in 0.6 M NaCl with 2 mM ferricyanide. Then, PSS with desired concentration and molecular weight was injected into the solution. G

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Langmuir is calculated. This rough estimate is somewhat higher than D for PDADMA* in PDADMA/PSS determined with eq 647 (1.6 × 10−13 cm2 s−1). Scheme 3 shows that the PDADMA*/PSS reaction zone moves down, which would make the process somewhat faster than simple PDADMA* diffusion to the PEMU/solution interface and give higher apparent DPDADMA* Molecular-Weight-Limited Addition of Polyelectrolyte. If the flux of PSS is limiting, an estimate for the time taken to remove 50 μmol m−2 PDADMA* by pairing with 50 μmol m−2 of PSS may be made using eq 12 (QPSS = 50 × 10−10 mol cm−2) and values of DPSS from Table 1. The times are compared with the intercepts on the time axis from Figure 7 and summarized in Table 2.

The ratio JPSS,aq/JPDADMA*,m for unstirred conditions (Figure 9B) suggests that in the absence of vigorous stirring JPDADMA*,m

Table 2. Calculated versus Experimental Times for PSS from 0.1 mM PSS Solution (Figure 7A) To Neutralize PDADMA* in PEMU, Assuming Rate Is Limited by Mass Transport of PSS from Solution (eq 12) PSS name

PSS Mw

tcalculated (s)

texperimental (s)

PSS57.5 PSS122.4 PSS626 PSS615 PSS801 PSS2260

57 500 122 400 262 000 615 000 801 000 2 260 000

65 87 120 160 180 270

74 71 74 140 170 420

Figure 9. Ratio of estimated JPSS,aq/JPDADMA*,m at different [NaCl]. (A) Convective transport of PSS to the interface at the rotating disk electrode (1000 rpm, see eq 13). (B) Transport of PSS to the interface by diffusion only (see eq 15). In both panels, CPSS,aq is 10 mM (solid line), 1 mM (dash), 0.1 mM (dot-dash), and DPSS,aq is assumed constant at 10−7 cm2 s−1. Ratios >1 indicate that transport is limited by diffusion of PDADMA* within the film.

Agreements between calculated and measured times are reasonable, given the assumptions and the fact that the polymers are not perfectly monodisperse. Whether the addition of polymer to the growing PEMU is limited by PDADMA* diffusion or PSS solution transport may be deduced by comparing eqs 10 and 11. For example, convective (stirred) solution transport of PSS to the interface is rate-limiting under the following conditions 1/2 D̅ PDADMA *,m C̅ PDADMA*,m

π 1/2t 1/2

can exceed JPSS,aq and changes in DPSS (molecular weight) or CPSS can limit the layer buildup rate.55 For PDADMA/PSS PEMUs, Nestler et al. found a dependence of film thickness on molecular weight for PSS Mw lower than 25 000 g mol−1 and Cpss = 1 mM in unstirred solutions.56 In a typical multilayering experiment, the solution is stirred gently (e.g., with a stir bar), which means the solution transport is somewhere between steady-state convection and pure diffusion. Under these conditions, there should be little influence of PSS molecular weight as long as CPSS exceeds 10 mM. A recent study of layer adsorption kinetics in PDADMA/ PSS PEMUs demonstrated the lack of dependence of kinetics on PSS molecular weight up to 588 kDa in 1 M NaCl: these solutions were vigorously stirred.47 If wide-molecular-weightdistribution PSS is used (usually the case), an interesting consequence of multilayers built under the conditions of eq 13 or 15 is that the PEMU should contain a higher fraction of lowmolecular-weight polyelectrolyte than in the solution because smaller chains reach the surface faster.

2/3 > 0.620DPSS,aq ω1/2v−1/6C PSS,aq

(13)

A rough estimate of whether JPSS,aq or JPDADMA*,m is greater uses eq 6 to predict D̅ PDADMA*,m as a function of [NaCl] and assumes DPSS,aq remains of order 10−7. A 35% excess of PDADMA translates to C̅ PDADMA*,m ∼ 0.001 M cm−3. Typical values for CPSS,aq range from 0.1 to 10 mM. Comparison of a steady-state (eq 11) with a time-dependent (eq 10) flux is somewhat awkward, but a t of 1 min represents the lowest limit of multilayering time. Using 1000 rpm and ν = 0.01, Figure 9A shows the ratio JPSS,aq/JPDADMA*,m as a function of [NaCl] for three CPSS,aq. Under these conditions, the ratio is almost always >1, meaning the flux of PSS is higher than that of PDADMA*, the condition in eq 13 does not hold, and there should be no dependence of the rate of layering on CPSS,aq or the molecular weight (i.e., DPSS, aq). However, if the PSS solution is not stirred and transport to the interface is by diffusion only, layer formation is limited by solution diffusion if 1/2 D̅ PDADMA *,m C̅ PDADMA*,m

π 1/2t 1/2

>

■

CONCLUSIONS Polyelectrolyte multilayers are thin films of polyelectrolyte complex assembled at an interface. Over the past few years, it has become clear that the bulk composition of PEMUs, i.e., the ratio of Pol+ to Pol−, is not 1:1, as initially assumed. This variable stoichiometry, usually with Pol+ in excess, leads to variable transport properties when PEMUs are employed as membranes for selective transport of ions. Restoring the stoichiometry of PEMUs to 1:1 yields more consistent and uniform compositions and therefore more predictable transport properties. Nonstoichiometry should not necessarily be considered detrimental to separations, however. The excess of Pol+ produces fixed charge, which enhances counterion flux through the membrane. Membrane performance requires optimizing this amount of fixed charge.

1/2 DPSS,aq C PSS,aq

π 1/2t 1/2

(14)

i.e., 1/2 1/2 D̅ PDADMA *,m C̅ PDADMA*,m > DPSS,aq C PSS,aq

(15) H

DOI: 10.1021/acs.langmuir.8b00336 Langmuir XXXX, XXX, XXX−XXX

Article

Langmuir

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Molecular weight has been a poorly understood variable in multilayer assembly. The proper representation of layer formation as countercurrent transport and reaction of extrinsic sites and solution polymer at the interface allows a quantitative analysis of the effects of molecular weight on layer assembly kinetics. Conditions under which the molecular weight controls assembly, producing thinner films, have been established. Multilayers which are grown under conditions not limited by the rate of (multilayer) site transport or solution (polymer) transport are not kinetically limited and are expected to grow exponentially.47

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Hadi M. Fares: 0000-0003-4009-2037 Joseph B. Schlenoff: 0000-0001-5588-1253 Notes

The authors declare no competing financial interest.

■ ■

ACKNOWLEDGMENTS This work was supported by grant DMR 1506824 from the National Science Foundation. REFERENCES

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J

DOI: 10.1021/acs.langmuir.8b00336 Langmuir XXXX, XXX, XXX−XXX