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General Physical Description of the Behavior of Oppositely Charged Polyelectrolyte/Surfactant Mixtures at the Air/Water Interface Imre Varga*,†,‡ and Richard A. Campbell*,§ †

Institute of Chemistry, Eötvös Loránd University, P.O. Box 32, Budapest H-1518, Hungary Department of Chemistry, University J. Selyeho, Komárno, Slovakia § Institut Laue-Langevin, 71 avenue des Martyrs, CS20156, 38042 Grenoble, France ‡

S Supporting Information *

ABSTRACT: This work reports a unifying general physical description of the behavior of oppositely charged polyelectrolyte/surfactant mixtures at the air/water interface in terms of equilibrium vs nonequilibrium extremes. The poly(diallyldimethylammonium chloride)/sodium dodecyl sulfate system with added NaCl at two different bulk polyelectrolyte concentrations and the poly(sodium styrenesulfonate)/ dodecyltrimethylammonium bromide system have been systematically examined using a variety of bulk and surface techniques. Similarities in the general behavior are observed for all the investigated systems. Following the slow precipitation of aggregates in the equilibrium two-phase region, which can take several days or even weeks, depletion of surface-active material can result in a surface tension peak. The limiting time scale in the equilibration of the samples is discussed in terms of a balance between those of aggregate growth and settling. Bulk aggregates may spontaneously dissociate and spread material in the form of a kinetically trapped film if they interact with the interface, and a low surface tension then results out of equilibrium conditions. These interactions can occur prior to bulk equilibration while there remains a suspension of aggregates that can diffuse to the interface and following bulk equilibration if the settled precipitate is disturbed. Two clear differences in the behavior of the systems are the position in the isotherm of the surface tension peak and the time it takes to evolve. These features are both rationalized in terms of the nature of the bulk binding interactions.

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INTRODUCTION

At the start of this century, work was carried out by Thomas and co-workers to relate the interfacial structures of oppositely charged P/S mixtures from neutron reflectometry (NR) to the surface tension.21−24 They found that mixtures exhibited different types of behavior: substantial interfacial layers and a plateau in the surface tension isotherm (type 1) or more compact layers and a surface tension peak (type 2).17 An example of a “type 1” mixture is poly(sodium styrenesulfonate)/dodecyltrimethylammonium bromide (NaPSS/ DTAB)21,22 while an example of a “type 2” mixture is poly(diallyldimethylammonium chloride)/sodium dodecyl sulfate (Pdadmac/SDS).23,24 The phase behavior of samples was commented in the original papers, but it was stated in the case of Pdadmac/SDS that precipitation could not fully explain the surface tension peak.24 Nonequilibrium characteristics such as a lack of reproducibility in data recorded of certain samples21 and a lack of agreement of a common structural model to NR data recorded in different isotopic contrasts were also commented.22 Nevertheless, the core data interpretations were based on an

The physical properties of oppositely charged polyelectrolyte/ surfactant (P/S) mixtures at the air/water interface have been investigated for decades due to their widespread use in consumer products and the environment.1−4 Goddard and co-workers found in the 1970s that the behavior of these systems is very different to that of weakly interacting polymer/ surfactant mixtures as the addition of a small amount of polyelectrolyte can result in a significant lowering of the surface tension of dilute surfactant solutions.5,6 Buckingham and coworkers later described electroneutral adsorption layers formed by synergistic interactions.7 Langevin and co-workers in the 1990s related the shape of surface tension isotherms to characteristics of the polyelectrolyte.8−10 They also described an interfacial structure with stoichiometric P/S binding for linear flexible polyelectrolytes in certain cases.11 In a review in 2002, Goddard discussed deviations from ideal Gibbs adsorption behavior with respect to the formation of thick or viscoelastic films.12 Interestingly, he concluded by commenting on an increasing awareness of slow equilibrium effects. A number of subsequent reviews have described the properties of these systems both in the bulk13−16 and at interfaces.17−20 © XXXX American Chemical Society

Received: April 13, 2017 Revised: May 11, 2017 Published: May 11, 2017 A

DOI: 10.1021/acs.langmuir.7b01288 Langmuir XXXX, XXX, XXX−XXX

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equilibrium or not, and to study a “type 1” mixture with a lower molecular weight is to examine if the surface tension peak is missing with faster diffusion of complexes or not. Our overall aim is to see if a unifying general description of the behavior of these systems can be clearly set out.

equilibrium framework. Indeed, two thermodynamic models were later published,25,26 and parameters were extracted such as the critical aggregation concentration, surfactant aggregation number, and degree of dissociation based on the assumption of the equilibrium nature of the original experimental data. In the meantime, the bulk phase behavior of oppositely charged P/S mixtures attracted attention.27−29 It was shown that at bulk compositions close to where P/S complexes have stoichiometric binding (charge neutralization) they lack colloidal stability, and with time they aggregate, precipitate, and either sediment (down) or cream (up), leaving a depleted supernatant.30,31 These compositions signify the equilibrium two-phase region. At bulk compositions that are far from charge neutralization, the complexes either form an equilibrium onephase solution or have sufficient charge to hinder aggregation in the form of an electrostatically stabilized colloid dispersion. Kinetically trapped aggregates formed due to concentration gradients present while the components are mixed can persist outside the equilibrium two-phase region for weeks or even longer.32−34 Also, the order of addition of the components can result in different amounts of precipitate, which may be insoluble on experimentally accessible time scales. Such characteristics were shown to be most pronounced in samples of low ionic strength.35,36 These studies suggested that the accessibility of equilibrium in these systems is a great challenge. A few years ago, we described two nonequilibrium characteristics of the Pdadmac/SDS in 0.1 M NaCl system: slow evolution of the bulk and interfacial properties and tuning of the interfacial properties of equilibrated samples by the application of mechanical stress to the settled precipitate.37 The degree of mechanical stress applied resulted in different surface tension values. Indeed, the process of pouring an equilibrated sample into a measurement dish could lower the surface tension considerably. It was becoming evident how extremely challenging the equilibrium surface properties of such mixtures are to access. We went on to relate systematically the surface tension of oppositely charged P/S mixtures to the bulk phase behavior. We showed that the surface tension peak in the 100 ppm, 100− 200 kDa Pdadmac/SDS in 0.1 M NaCl system is positioned at the phase boundary, and in the equilibrium two-phase region the surface tension is quantitatively consistent with adsorption of surfactant after comprehensive precipitation of aggregates out of the supernatant.38 Later we revealed a surface tension peak also for the 100 ppm, 1000 kDa NaPSS/DTAB system after full bulk equilibration, which takes about 1 month.39 A simple way to predict the surface tension in the equilibrium two-phase region was also described,39 and the method was then applied to the same mixture at different ionic strengths.40 Even so, it was later speculated by Bahramanian et al. that the surface tension peak we had found for NaPSS/DTAB was the result of artifacts related to our experimental methodology and approach.26 A unifying framework to describe the general behavior of these systems was therefore still missing. The scope of the present work is to examine the general behavior of oppositely charged P/S mixtures at the air/water interface in terms of equilibrium vs nonequilibrium extremes. In relation to the reference system (A) 100 ppm, 100−200 kDa Pdadmac/SDS in 0.1 M NaCl, we examine (B) 10 ppm, 100− 200 kDa Pdadmac/SDS in 0.1 M NaCl and (C) 100 ppm, 17 kDa NaPSS/DTAB in pure water. The motivations to study a “type 2” mixture with a lower polyelectrolyte concentration is to see if a system with less obvious aggregation is closer to

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EXPERIMENTAL SECTION

Materials. Poly(diallyldimethylammonium chloride) (100−200 kDa Pdadmac; Sigma-Aldrich) was purified by dialysis (regenerated cellulose, 12−14 kDa molecular weight cutoff, Medicell International Ltd.) or by Amicon Ultra-15 centrifugal filters (30 kDa regenerated cellulose membrane) in pure water. These procedures gave stock solutions of ∼20 000 ppm free of low molecular weight impurities. Their concentrations were verified by gravimetric analysis. Poly(sodium styrenesulfonate) (17 kDa NaPSS; Sigma-Aldrich) was used as received. Sodium dodecyl sulfate (SDS, Sigma; 99.9%) was recrystallized twice from ethanol, and dodecyltrimethylammonium bromide (DTAB; Sigma; 99.9%) was recrystallized twice in a 4:1 v/v acetone/ethanol mixture; each time the solutions were cooled over several hours. Deuterated SDS and DTAB (CDN Isotopes, 99.9%), and D2O (Sigma-Aldrich) were used as received. Pure water was generated by passing deionized water through a Milli-Q purifier (total organic content = 4 ppb; resistivity = 18 mΩ·cm). Sample Preparation Methods. The Pdadmac/SDS mixtures were prepared in 0.1 M NaCl, and the NaPSS/DTAB mixtures were prepared in pure water. A “standard mixing” approach where equal volumes of polyelectrolyte and surfactant at double their intended final bulk concentrations were poured together simultaneously, and the solution was then swirled gently for a few seconds.41 This approach was used to limit the formation of kinetically trapped aggregates due to the presence of concentration gradients. For fresh samples, the mixtures were transferred at once into the measurement dish. For aged samples, fresh mixtures were transferred into 100 mL glass flasks (surface tension measurements of 100 ppm Pdadmac/SDS solutions in 0.1 M NaCl) or 4 mL glass vials (all other measurements), in which they were left for the stated period. Afterward, 30 mL of supernatant was pipetted from each flask in the former case and 1 mL from each vial in the latter case for immediate measurement. Care was taken not to agitate any settled precipitate at the bottom of the flasks in order to avoid the redispersion of surface-active material.37,38,42 All the measurements were performed at 23−25 °C. Electrophoretic Mobility. The electrophoretic mobility measurements were performed using a Malvern Zetasizer NanoZ instrument. The data were analyzed using the M3-PALS technique. The standard error in the values was around 10%, and measurements were performed on freshly mixed samples. UV−Vis Spectroscopy. The turbidity measurements were performed in a quartz cell with a 1-cm path length using a PerkinElmer Lambda 2 UV−vis spectrophotometer. The turbidity of the samples was determined by the optical density at 400 nm (OD400). Measurements were carried out 3 min after mixing (fresh) or after extraction of the supernatant. The polyelectrolytes and surfactants used do not have absorption bands above 350 nm. Surface Tensiometry. Surface tension measurements were performed using a Wilhelmy plate (100 ppm Pdadmac/SDS in 0.1 M NaCl system) or a home-built pendant drop apparatus (other systems). In the former case, an automated Krüss “K10” surface tension balance was used. A sand-blasted platinum plate of 20 × 10 × 0.1 mm was immersed in the liquid and then withdrawn until its lower edge was parallel with the surface. The plate was cleaned with water and ethanol and was then dried with a Bunsen burner immediately prior to each measurement. In the latter case, a pendant drop was created at the tip of a PTFE capillary joined to a gastight Hamilton syringe lodged in a computer-controlled syringe pump. Drops were formed in a closed chamber with an internal size of 1 × 2 × 5 cm. The side walls were covered with wetted filter paper to limit evaporation. A series of drops were formed at the tip of the capillary to ensure the creation of a fresh surface. The pump was stopped after the third drop, and monitoring of its shape commenced. The data represent a surface B


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Figure 1. Electrophoretic mobility of freshly mixed (A) 100 and (B) 10 ppm Pdadmac/SDS in 0.1 M NaCl and (C) 100 ppm NaPSS/DTAB in pure water. The arrows mark the bulk composition of charge equivalence, and the vertical dashed lines mark that of charge neutrality.

Figure 2. Optical density at 400 nm recorded using UV−vis spectroscopy of (A) 100 and (B) 10 ppm Pdadmac/SDS in 0.1 M NaCl and (C) 100 ppm NaPSS/DTAB in pure water with respect to the stated sample ages. Shaded areas mark the equilibrium two-phase regions.

PSS−:DTA+ 47 aggregates. We start with a comparison of the bulk binding interactions through characterization of the surface charge on the bulk complexes with respect to the bulk composition. Figure 1 shows electrophoretic mobility measurements for the three systems. The transitions from undercharged through neutral to overcharged complexes with increasing bulk surfactant concentration are qualitatively similar. The behavior can be rationalized in terms of the association of macroions with surfactant ions: there is an excess of polyelectrolyte segments in the complexes at low bulk surfactant concentrations, stoichiometric binding in charge neutral complexes, and excess surfactant ions on the complexes at high bulk surfactant concentrations. The difference in bulk composition between that of stoichiometric binding (charge neutralization; see vertical dashed lines) and stoichiometric mixing (or “charge equivalence”; see arrows) varies significantly from system to system. This difference is related to the efficiency of the binding interaction. We return to this issue in our description of the phase behavior below. Figure 2 shows UV−vis spectroscopy data as a function of the bulk composition and sample age for the three systems. The optical density may be taken as a measure of the turbidity of the sample, i.e., the scattering of light from aggregates suspended in the supernatant. Low values indicate samples that are either in the equilibrium one-phase region with a minimal number of kinetically trapped aggregates or are in the equilibrium twophase region where the aggregates have already precipitated to form sediment to the bottom of the flask. Certain characteristics in the optical densities are equivalent for the three systems. The values are high for freshly mixed samples at bulk compositions close to charge neutralization, and they decrease

age of 30 min, unless otherwise stated, and appeared to have reached steady state. To rule out the possibility that the application of the two different measurement methods caused systematic deviations in our results, we measured the surface tension of the 100 ppm Pdadmac/SDS in the 0.1 M NaCl system at selected concentrations using the pendant drop method. The values determined by the two methods after 30 min were equivalent to within the experimental error. Neutron Reflectometry (NR). NR measurements of the surfactant surface excess (ΓS) of adsorbed layers and spread films were performed using the FIGARO reflectometer at the Institut Laue-Langevin (Grenoble, France).44 An incident angle of θ = 0.62° was used. Neutrons with wavelengths of λ = 2−16 Å were measured, but only those of 4.5−12 Å were used to restrict the Qz range to 0.01−0.03 Å−1, where the momentum transfer Qz = 4π sin θ/λ, following an approach developed recently.45,46 This restriction maximized sensitivity of the measurements to ΓS and not the interfacial structure. Background was not subtracted from the data. Additional information about the NR data acquisition and analysis can be found in part 1 of the Supporting Information.

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RESULTS Reproducible steady state properties of oppositely charged P/S mixtures can result in samples that are far from equilibrium. We examine the investigated systems(A) 100 ppm, 100−200 kDa Pdadmac/SDS in 0.1 M NaCl, (B) 10 ppm, 100−200 kDa Pdadmac/SDS in 0.1 M NaCl, and (C) 100 ppm, 17 kDa NaPSS/DTAB in pure waterwith respect to two nonequilibrium processes: the slow approach to and the perturbation from equilibrium. Slow Approach to Equilibrium. Bulk Properties. The size and surface charge of aggregates have been characterized for the Pdadmac/SDS35 and NaPSS/DTAB36 systems, as has the hexagonal internal structure of Pdadma + :DS − 46 and C


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interaction efficiency in 100 ppm, 17 kDa NaPSS/DTAB mixtures in pure water is even lower as a large excess of surfactant is required for neutralization of the bulk complexes: in this case cneut,free/cneut,bound is 13. It is interesting that this ratio is correspondingly high for the larger 100 ppm, 1000 kDa NaPSS/DTAB systems both without39 and with40 added inert electrolytes. Effects of the molecular weight and ionic strength on the relatively poor binding efficiency of this system are therefore minor. Instead, the much poorer binding efficiency for NaPSS/DTAB than for Pdadmac/SDS can be attributed to the less efficient wrapping of the polyelectrolyte chains around the surfactant aggregates. The origin may be related to the greater separation of the charged groups from the backbone in NaPSS than Pdadmac, the higher relative rigidity of the PSS chains, possible slower chain dynamics, or a combination these factors. However, further work, outside the scope of the present study, would be required to resolve the reasons. Note that it was not necessary for these differences to be considered in the phase mapping of the NaPSS/DTAB system by Hansson and co-workers,48 as that work was conducted in the semidilute regime where cfree ≪ cbound, so the total bulk surfactant concentration could be approximated as cbound; the same simplification is not valid in the dilute regime of 10 and 100 ppm. It is interesting to note therefore that the effects of these differences in the binding efficiency of the two systems, which result in the equilibrium two-phase region falling at different bulk compositions, will be much less pronounced in samples with higher bulk polyelectrolyte concentrations that are of key relevance to many technological applications.1−3 The second difference between the systems is the time scale of the evolution of the bulk: while the 100 ppm, 100−200 kDa Pdadmac/SDS in 0.1 M NaCl system takes a few days, the other two systems take about 1 month. We attribute the extremely slow bulk equilibration of these systems to different reasons. The time scale itself is related to the aggregate growth and settling processes, which in turn are determined by a combination of the collision frequency and size of the aggregates and their density difference with the supernatant, respectively. For the system involving 10 ppm Pdadmac, as there is the lowest concentration of aggregates, the collision rate is slow; thus, it requires a longer time to form large enough aggregates to settle. As such, the slow equilibration is primarily due to slow aggregate growth. For the system involving NaPSS/DTAB, two pieces of evidence indicate that the slow equilibration is determined by slow aggregate settling. First, the difference in the time scales is present at charge neutralization

with time as aggregate growth and settling increases the transparency of the supernatant. These characteristics signify the equilibrium two-phase region for each system, which is shaded. The values remain low at bulk compositions far below charge neutralization as complexes form an equilibrium solution. Lastly, at intermediate bulk compositions close to the phase boundaries, the values remain high as kinetically trapped aggregates formed during mixing are insoluble on experimentally accessible time scales. Two main differences between the systems are clear. The first difference is that the equilibrium two-phase region lies at very different bulk compositions for the two different systems that have 100 ppm polyelectrolyte. This difference can be understood in terms of the relative efficiencies of the binding interactions for surfactant to neutralize the polyelectrolyte. Table 1 lists some bulk surfactant concentrations of relevance Table 1. Noteworthy Bulk Surfactant Concentrations in the P/S Mixtures Investigated quantity

100 ppm Pdadmac/SDS in 0.1 M NaCl

10 ppm Pdadmac/SDS in 0.1 M NaCl

100 ppm NaPSS/DTAB in pure water

cneuta (mM) cneut,boundb (mM) cneut,freec (mM) cneut,free/cneut,boundd

0.82 0.62 0.20 0.32

0.26 0.062 0.20 3.2

6.0 0.48 5.5 13

a

cneut is the total bulk surfactant concentration to produce charge neutral complexes (from Figure 1). bcneut,bound is the concentration of surfactant bound in the charge neutral complexes, which is approximated to the bulk polyelectrolyte concentration in monomer units. ccneut,free is the free bulk surfactant concentration when there are charge neutral complexes, which is equal to cneut − cneut,bound. dcneut,free/ cneut,bound is the ratio of the free surfactant to that bound in the charge neutral complexes.

for these mixtures, where cneut,free/cneut,bound is the ratio of the free surfactant to that bound in charge neutral complexes, which may be taken as a measure of the binding interaction efficiency to produce charge neutral complexes (see more details in the footnote). The bulk interactions on the approach to charge neutralization in 100 ppm Pdadmac/SDS mixtures in 0.1 M NaCl are very efficient, as cneut,free/cneut,bound is just 0.32. When the bulk polyelectrolyte concentration is reduced to 10 ppm, cneut,free (which is required to provide the chemical potential of the surfactant in equilibrium with the stoichiometric complex) remains roughly the same while cneut,bound decreases, so cneut,free/cneut,bound increases to 3.2. The binding

Figure 3. Surface tension of freshly mixed and aged samples of (A) 100 and (B) 10 ppm Pdadmac/SDS in 0.1 M NaCl and (C) 100 ppm NaPSS/ DTAB in pure water. D


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Figure 4. Application of our surface tension prediction for aged samples of (A) 100 and (B) 10 ppm Pdadmac/SDS in 0.1 M NaCl and (C) 100 ppm NaPSS/DTAB in pure water. The details of the calculations are provided in part 3 of the Supporting Information.

Figure 5. Surface tension of aged samples of (A) 100 and (B) 10 ppm Pdadmac/SDS in 0.1 M NaCl and (C) 100 ppm NaPSS/DTAB in pure water without and with inversion of the flasks immediately prior to the measurement of the supernatant.

where both the Pdadmac/SDS and NaPSS/DTAB aggregates fully lack colloidal stability (i.e., there is no electrostatic potential barrier), so the collision rate cannot be the limiting factor. Second, the time scale is roughly equivalent for the 100 ppm 17 kDa and 1000 kDa NaPSS/DTAB systems,39 where the number of aggregates and hence the collision frequency are very different. These factors imply that a smaller density difference between the aggregates and the supernatant leads to slower settling. The origin of this difference may be related to the more hydrated structure of the precipitate as has been observed for mixtures where the surfactant has a longer chain.47 It is evident that any steady state physical measurements of 10 ppm Pdadmac/SDS mixtures in 0.1 M NaCl or 100 ppm NaPSS/DTAB mixtures carried out only within hours or days of mixing must be far from equilibrium. Interfacial Properties. As the time scale of bulk equilibration has now been resolved for each system, we may examine the surface tension of fresh and aged samples to see the direction to which it evolves. Figure 3 shows that a surface tension peak occurs after bulk equilibration for all three systems. Interestingly, in contrast to the more concentrated Pdadmac/ SDS in 0.1 M NaCl system studied, a surface tension peak appears also for the fresh mixture at 10 ppm. We recall that these data are reported on a time scale of 30 min and appeared to have reached steady state. However, for the same samples on a time scale of 4 h, the peak in fact disappears. Kinetic data are presented in part 2 of the Supporting Information showing that there is a sharp drop in the surface tension after a characteristic delay. We rationalize these results by recalling that in these more dilute samples the concentration of dissolved complexes or suspended aggregates is much lower. It follows that on a time scale of 30 min the interface is dominated by the

adsorption of free surfactant, and the surface tension is high because the free surfactant concentration is low. However, with sufficient time for the transport of complexes or aggregates to the interface, a mixed P/S layer forms and the surface tension drops to the low values seen for the more concentrated system. Slow kinetics of adsorption have been observed previously as well for the Pdadmac/SDS system in pure water.49 We infer that this surface tension peak is a transient feature that is steady state on a time scale of 30 min for fresh samples where the bulk has not yet equilibrated. It is curious that the system evolves first to low surface tension values yet once the bulk has equilibrated there is an even more pronounced surface tension peak. This emphasizes that steady state physical measurements, even if accessed reproducibly, need not necessarily represent equilibrium. We may now apply our surface tension model,39 based on a depleted surfactant solution in the equilibrium two-phase region, to all three systems. Figure 4 shows its application to the experimental data, and details of the calculations are provided in part 3 of the Supporting Information. Agreement of the model with the experimental data is excellent in all cases, which supports its general applicability to systems that are more dilute or have lower molecular weight polyelectrolytes than those to which it had previously been applied. Perturbation from Equilibrium. In our first publication on the surface tension peak,37 we demonstrated a nonequilibrium method to tune the interfacial properties of equilibrated samples. A mechanical stress exerted on the settled precipitate results in a “snowstorm” of particles in the depleted supernatant, and the surface tension decreased. Nevertheless, we did not resolve the physical basis of this process. Does the redispersion result in dissolution of surface-active complexes E


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Figure 6. Surfactant surface excess for adsorbed layers and spread films of (A) 100 and (B) 10 ppm Pdadmac/SDS in 0.1 M NaCl and (C) 100 ppm NaPSS/DTAB in pure water measured using NR.

presence of a kinetic barrier to equilibrate to the lower surface excess generated by adsorption. Our methodology built on recent findings related to the importance of the role of aggregates in these systems,42,50−53 although it should be noted that the formation of robust films for this system had been described in previous studies.54,55 Figure 6 shows the application of this methodology to the three systems in the present work where the surfactant surface excess measured using NR for the adsorbed layers and spread films are shown for a period of 30 min. In every case, the resulting surface excess is much higher from the exploitation of aggregate dissociation and spreading than adsorption from the bulk. These results provide further evidence that the redispersion mechanism that we described for the first time back in 2010,37 and is now applied to different systems in the present work, results from the dissociation of and spreading from aggregates at the interface to generate kinetically trapped films. To summarize, if one aims to determine the equilibrium surface properties of an oppositely charged P/S mixture, one needs not only to consider the time scale required for bulk equilibration but also take measures to circumvent the generation of kinetically trapped films from aggregate dissociation and spreading during the sample handling.

that adsorb to the interface in a local equilibrium, or do aggregates interact directly with the interface to spread material in the form of a kinetically trapped film? To gain insight into the system-dependence of this issue, we applied our redispersion procedure to the systems in the present work. It was carried out by a simple, crude inversion of the flasks containing the equilibrated samples immediately prior to the measurement. Figure 5 shows that different effects result from this process. The surface tension peak of the 100 ppm, 100−200 kDa Pdadmac/SDS in 0.1 M NaCl system is extinguished, as was previously reported. 37,38 For the corresponding more dilute system (10 ppm polyelectrolyte), the surface tension values also decrease to their initial values, indicating the occurrence of the same redispersion mechanism. For the 100 ppm, 17 kDa NaPSS/DTAB system, however, the surface tension peak is almost unaffected by the mechanical stress applied. Interestingly, we observed that the consistency of the precipitate is different. It resembles a sticky film, and a “snowstorm” of particles did not occur. Tentatively, therefore, we attribute the absence of the redispersion mechanism for the NaPSS/DTAB system to a lack of redispersion of precipitate as a result of its morphology. An additional experiment is reported in part 4 of the Supporting Information where equivalent aged samples of 100 ppm, 100−200 kDa Pdadmac/SDS in 0.1 M NaCl with 0.6 mM SDS (i.e., the bulk composition at the top of the surface tension peak) are (1) inverted, and immediately measured, and (2) inverted, then centrifuged, and immediately measured. In the former case a low surface tension results while in the latter there is a high surface tension. This result supports the idea that the redispersion process does not liberate free complexes into the bulk for adsorption at the interface, as in such a case the surface tension should be almost equivalent in the two experiments. Instead, the process must result from the suspension of aggregates in the supernatant that can dissociate at the interface and spread material to form a kinetically trapped film. This physical concept was exploited explicitly in our recent paper on spread NaPSS/DTAB films.45 The approach used was to drop onto pure water an aliquot of a fresh suspension of aggregates formed at the bulk composition of charge neutralization. The spread films were then compared with adsorbed layers from samples that had the same overall bulk composition but where the components were diluted prior to mixing; hence, the system remained in the equilibrium onephase region and free of aggregates during its preparation. Any excess of material for the former samples could therefore be attributed to (1) the rapid dissociation of aggregates and Marangoni spreading of material to form a film and (2) the

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DISCUSSION In this section, we discuss first the generalities (similarities and differences) of the investigated systems, and then we outline characteristics of the extreme types of equilibrium vs nonequilibrium behavior exhibited. Generalities of the Investigated Systems. The investigated systems exhibit several similarities in their bulk behavior. Neutralization of a polyelectrolyte at fixed concentration occurs as the bulk surfactant concentration is increased. The equilibrium two-phase region lies at compositions around that of charge neutralization where aggregates lack colloidal stability, and with time they precipitate, leaving a depleted supernatant. Prior to bulk equilibration, aggregates can interact with the air/water interface as a result of diffusion or convection, and a kinetically trapped film is formed with a lower steady state surface tension than at equilibrium. Aggregate interactions can be exploited explicitly for the preparation of films out of equilibrium conditions. Following bulk equilibration, with care, the equilibrium properties can be accessed. Our prediction for the surface tension based on that of a depleted surfactant solution can then be applied in the equilibrium two-phase region. The peak F


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Langmuir appears as a “cliff edge” positioned at the phase boundary with the low bulk surfactant concentration. There are striking differences that are system-dependent as well. The surface tension peaks for the two 100 ppm systems lie at very different bulk compositions. For the 100−200 kDa Pdadmac/SDS in 0.1 M NaCl system, the bulk interaction is efficient, there is a low free bulk surfactant concentration at charge neutralization, and the peak is at 0.55 mM. For the 17 kDa NaPSS/DTAB system, the bulk interaction is less efficient, around 8 times more bulk surfactant is required for charge neutralization, and the peak is at 3.8 mM. The peak position is determined by the bulk compositions of the equilibrium twophase region and therefore the efficiency of the bulk binding interactions. The time scale of bulk equilibration also varies from system to system. It is related to the rates of aggregate growth (i.e., the collision frequency) and settling (i.e., their density difference with the supernatant). For the 10 ppm, 100−200 kDa Pdadmac/SDS in 0.1 M NaCl system, slow equilibration is attributed to slow aggregate growth, as there are fewer aggregates than in more concentrated mixtures, which results in a lower collision rate. However, for the 100 ppm, 17 kDa NaPSS/DTAB system, slow equilibration is attributed to slow aggregate settling, which we suggest is related to a lower density difference between the aggregates and the supernatant. Lastly, perturbation of the systems from equilibrium by the redispersion of aggregates from the settled precipitate is observed for Pdadmac/SDS but not for NaPSS/DTAB. This discrepancy is attributed to different morphologies of the precipitate: Pdadmac/SDS is particle-like while NaPSS/DTAB has the consistency of a sticky film. We have suggested that this difference also may be related to the hydrated nature of the aggregates in the latter case. In summary, the three investigated systems exhibit similar general behavior as long as the bulk phase behavior and kinetics of aggregation are fully taken into account. However, there are differences between the interfacial properties, which can be rationalized in terms of the nature of the bulk binding interactions and characteristics of the precipitate. While the physical picture described above was formed on the basis of measurements of synthetic P/S mixtures, it may be extended to systems involving biologically relevant polyelectrolytes. A maximum in surface tension isotherms can be found in the literature for oppositely charged systems involving homopolypeptides,8 proteins,56−58 and DNA,59 and we have previously applied successfully our surface tension prediction model to DNA/surfactant mixtures.39 The physical origin of such maxima may also be related to precipitation and depletion, although the application of our model to those data would be applicable only if the samples had fully equilibrated and had not been perturbed from equilibrium due to aggregates interactions with the interface. Deviations in the application of our model to protein/surfactant mixtures may also be expected according to the solubility of the complexes at their isoelectric point, which is an issue that merits future work. Extreme Types of Behavior of the Investigated Systems. Two extreme types of behavior have been determined for oppositely charged P/S mixtures at the air/ water interface. If samples have equilibrated and are not perturbed from equilibrium, there is the depletion of surfaceactive material from the bulk in the equilibrium two-phase region, and a surface tension peak can result. These are equilibrium characteristics. However, if samples have not yet

equilibrated or are perturbed from equilibrium as a result of the way they are handled, bulk aggregates can reach the interface and dissociate, which results in the production of a kinetically trapped film and a low surface tension plateau. These are nonequilibrium characteristics. This general physical picture applies both to the Pdadmac/SDS/NaCl and NaPSS/DTAB systems when the bulk phase behavior and time scale required for bulk equilibration are fully taken into account. In the original work on the interfacial properties of these systems, two extreme types of behaviors in terms of the surface tension were also found,21−24 and this contributed to a distinction of “type 1” and “type 2” systems.16 The experimental data were interpreted in the context of chemical equilibrium, and later two thermodynamic models were formulated and applied to extract thermodynamic parameters for different systems.25,26 In the latter of the two model publications,26 Bahramanian et al. attempted to reason how we had published results that appeared to be in contradiction to theirs. In spite of the numerous studies that highlighted both the slow approach to equilibrium of these systems12,33,37−40 and the importance of the mixing protocols such as the order of addition in the production of trapped nonequilibrium states,32−34,41 the equilibrium nature of the original experimental data was not objectively questioned. Instead, the authors chose to dismiss directly both our general approach and many of our results as experimental artifacts. We may now comment on the interpretations of the original data in the context of the new results reported in the present manuscript. We have shown that according to the relatively weak binding interaction efficiency of the NaPSS/DTAB system, a large excess of free surfactant is required to neutralize bulk aggregates (Figure 1). A relatively high free bulk surfactant concentration is therefore present in the equilibrium two-phase region (Table 1). The bulk takes weeks to equilibrate during which time there is a suspension of aggregates in the samples (Figure 2). The surface tension peak appears only after the bulk is fully equilibrated (Figure 3). Prior to bulk equilibration, aggregates can spread material at the interface to produce a kinetically trapped film that has a low surface tension (Figure 6). Although the following information related to the sample preparation was not reported in the original papers,21−24 we learned during recent discussions that to produce samples with different bulk compositions in the original work, P/S mixtures with high bulk surfactant concentrations were diluted with pure polyelectrolyte solution to produce those with lower bulk surfactant concentrations.60 The origin of the controversy becomes immediately clear. Because of the high free surfactant concentration in these mixtures, their dilution with polyelectrolyte must have created a fresh suspension of aggregates that could interact with and spread material at the interface to produce a low surface tension plateau. The original NaPSS/ DTAB data therefore must have represented the extreme type of nonequilibrium behavior rather than the assumed equilibrium. These factors made it inevitable that the surface tension peak was missed. Additional comments and data concerning our methodology and results are provided in part 5 of the Supporting Information. Therein we reason three main points, all supported by experimental data, in response to the dismissive remarks in Bahramanian et al.26 First, suppression of the surface tension peak through the application of mechanical stress to the precipitate of Pdadmac/SDS samples is not related to limitations in the definition of our samples but instead to the G


Article

Langmuir Notes

spreading of material from aggregates resulting in a kinetically trapped film. Second, the surface tension peak for the 1000 kDa NaPSS/DTAB system is not an artifact of the high molecular weight of the polyelectrolyte we used but instead, just as with the corresponding 17 kDa polyelectrolyte, is a feature that can be predicted using our model once equilibrium is achieved. Third, it is not limitations in our methodology but instead our careful definition of samples that allowed us to resolve the elusive surface tension peak for the NaPSS/DTAB system, even though it had been previously missed by others.

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS An exchange of views between R.A.C. and Bob Thomas took place during and after the “Symposium on Nanostructured Interfaces” in Lund, Sweden (25−26 September 2014). We thank Bob for his input and suggestions as well as Lennart Piculell, Tommy Nylander, Marianna Yanez Arteta, Anna Angus-Smyth, Boris Noskov, Andrea Tummino, and Malcolm Campbell for helpful discussions and Krisztina Sebestény for assistance with the measurements. This research has received funding from the People Programme (Marie Curie Actions) of the European Union’s Seventh Framework Programme FP7/ 2007-2013/under REA grant agreement no. 290251 and from the Hungarian Scientific Research Fund (NKFIH K116629), which is gratefully acknowledged.

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CONCLUSIONS In this work, we have described the general behavior of oppositely charged polyelectrolyte/surfactant mixtures at the air/water interface in terms of equilibrium vs nonequilibrium extremes. Pdadmac/SDS/NaCl mixtures at different bulk polyelectrolyte concentrations and NaPSS/DTAB mixtures were investigated using a combination of bulk and surface techniques. The slow approach to and perturbation from equilibrium were systematically examined. Similarities in the general behavior are exhibited in the investigated systems when the bulk phase behavior and the kinetics of aggregation are taken into account. These include interactions of bulk aggregates with the interface to spread material and lower the surface tension (a nonequilibrium effect) and depletion from precipitation in the equilibrium two-phase region to produce a peak in the surface tension isotherm (an equilibrium effect). At the same time, differences between the properties of the systems exist. These include the position in the surface tension isotherm of the peak, the time scale required for the system to equilibrate, and the ability to modify the interfacial properties during handling of the precipitate in equilibrated samples. Such features can be rationalized in terms of the nature of the bulk binding interactions and characteristics of the precipitate. A last comment is that intuitively one may interpret the relatively low turbidity in samples of the more dilute system studied in the present work as an indication that the system is closer to equilibrium. However, in spite of the reproducible steady state properties that could be measured for days and weeks, this system was in fact trapped far from the equilibrium for even longer.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.langmuir.7b01288. Additional information about the NR data acquisition and analysis, dynamic data on the transient surface tension peak, binding isotherm for the Pdadmac/SDS in 0.1 M NaCl system, additional data on the physical basis of the redispersion process, and additional data and comments on the surface tension peak controversy (PDF)

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REFERENCES

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AUTHOR INFORMATION

Corresponding Authors

*(I.V.) Tel +36 204 890 440, e-mail [email protected]. *(R.A.C.) Tel +33 476 207 097, e-mail [email protected]. ORCID

Richard A. Campbell: 0000-0002-6296-314X H


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