Effects of Ionic Strength on the Surface Tension and Nonequilibrium

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Effects of Ionic Strength on the Surface Tension and Nonequilibrium Interfacial Characteristics of Poly(sodium styrenesulfonate)/ Dodecyltrimethylammonium Bromide Mixtures Á gnes Á brahám,† Attila Kardos,† Amália Mezei,† Richard A. Campbell,*,‡ and Imre Varga*,† †

Institute of Chemistry, Eötvös Loránd University, Budapest 112, P.O. Box 32, H-1518 Hungary Institut Laue-Langevin, 6 rue Jules Horowitz, BP 156, 38042 Grenoble, Cedex 9, France

‡

S Supporting Information *

ABSTRACT: We rationalize the surface tension behavior and nonequilibrium interfacial characteristics of high molecular weight poly(sodium styrenesulfonate)/dodecyltrimethylammonium bromide (NaPSS/DTAB) mixtures with respect to the ionic strength. Excellent agreement is achieved between experimental data and our recent empirical model [Langmuir 2013, 29, 11554], which is based on the lack of colloidal stability of bulk aggregates in the phase separation region and has no free fitting parameters. We show that the size of a surface tension peak positioned at the edge of the phase separation region can be suppressed by the addition of inert electrolyte, which lowers the critical micelle concentration in relation to the phase separation region. Such manipulation of the peak is possible for the 100 ppm NaPSS/DTAB system because there is a high free surfactant concentration in the phase separation region. The close agreement of our model with the experimental data of samples in the phase separation region with respect to the ionic strength indicates that the surface tension behavior can be rationalized in terms of comprehensive precipitation regardless of whether there is a peak or not. The time scale of precipitation for the investigated system is on the order of one month, which emphasizes the need to understand the dynamic changes in the state of bulk aggregation in order to rationalize the surface properties of strongly interacting mixtures; steady state surface properties measured in the interim period will represent samples far from equilibrium. We show also that the surface properties of samples of low ionic strength outside the equilibrium phase separation region can be extreme opposites depending on the sample history, which is attributed to the generation of trapped nonequilibrium states. This work highlights the need to validate the underlying nature of oppositely charged polyelectrolyte/ surfactant systems prior to the interpretation of experimental data within an equilibrium framework.

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INTRODUCTION Oppositely charged polyelectrolyte/surfactant (P/S) mixtures are used to optimize the performance of common household products such as detergents, shampoos, cosmetics, paints, and foodstuffs.1,2 A number of reviews have described the properties and applications of synthetic P/S mixtures both in the bulk3−5 and at surfaces.6−9 Further, the interactions between surfactants and biomacromolecules such as proteins or DNA also play important roles both in biological processes10,11 and in biomedical applications such as drug or gene delivery.12,13 It is therefore important to understand the interactions in the bulk and at interfaces in order to predict their behavior. An important property of any solution is its surface tension. The surface tension of a liquid can determine its wetting14 and rheological15 behavior as well as the stability of foams.16 Furthermore, the surface tension of complex mixtures determines the fate of a range of processes such as the stability of aerosol droplets in clouds17 and the biological function of lung surfactants.18 It has therefore been a long-standing objective to be able to predict the surface tension of strongly interacting mixtures. Such an interpretation, however, is © 2014 American Chemical Society

complicated by the fact that Gibbs adsorption equation is related to the chemical potential of all the surface-active components of the system, and these are modified by interactions in the bulk.19 Strong association in oppositely charged P/S mixtures can lead to rich phase behavior.20−22 In particular, as a result of a lack of colloidal stability of complexes close to charge neutralization, there is the formation of aggregates, which with time can precipitate and sediment.23 It has been shown that nonequilibrium effects can be more pronounced in samples of low ionic strength24,25 and that these features can determine the physical properties of mixtures as a function of the sample history.24,26 Indeed, the production of kinetically trapped aggregates outside the equilibrium phase separation region, which are stable on experimentally accessible time scales, can be related to the way in which the components are mixed.27 Received: February 18, 2014 Revised: March 27, 2014 Published: April 8, 2014 4970

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region (cleft), and bulk surfactant concentration at point of charge neutrality (cneut); no surface measurements of the P/S mixtures are required. The surface tension of the mixture, γmix, may then be expressed as

A body of work is emerging on nonequilibrium aspects of the interaction of P/S aggregates with adsorption layers that result in modification to the interfacial properties. For example, there can be changes to the dynamic elasticity as a result of surface heterogeneities,28,29 spontaneous penetration or surface-trapping of aggregates depending on the solution pH,30 triggered redispersion of aggregates from sediment to reduce the surface tension,31 transport of nanostructured particles under gravity,32 and the activation of a convection/spreading mechanism under dynamic conditions to enhance the surface excess.33 Furthermore, there is experimental evidence that suggests an irreversibility to the adsorption process in the formation of a surface gel phase,34,35 which begs the question whether the interfacial layer is in equilibrium with the subphase or not. As a complement to this range of interesting nonequilibrium effects, the present paper focuses on the effects of depletion resulting from the precipitation of surface-active material which is sequestered into sediment that sinks away from the probed interface. It has been a challenge over the years to understand the surface tension behavior of oppositely charged P/S mixtures. An ion exchange model has been described where the synergistic lowering of the surface tension is independent of the bulk polymer concentration due to the formation of neutral complexes at the air/water interface,36 although this model is dependent on the flexibility of the polyelectrolyte to bind to the surfactant headgroups.37 Also, a sharp peak in the surface tension isotherm has been observed for some systemse.g., poly(diallyldimethylammonium chloride)/sodium dodecyl sulfate (Pdadmac/SDS)38 and poly(ethylene imine)/SDS (PEI/ SDS) at low pH39but not others−such as poly(sodium styrenesulfonate)/dodecyltrimethylammonium bromide (NaPSS/DTAB)40,41 and poly(vinylpyridinium chloride)/ SDS.41 In work on the surface tension peak by Staples et al., it was acknowledged to coincide with the two-phase region, but it was stated that precipitation could not explain the feature.38 Instead, the peak was attributed to a competition between a surface-active polymer/surfactant monomer complex and a non-surface-active polymer/surfactant micelle complex, and this physical picture was developed in a thermodynamic model by Bell et al. where both types of equilibrium solution complex were formalized as having single polymer chains, i.e., neglecting the effects of aggregation and precipitation.42 The model has been applied to describe the main features of a range of P/S systems,43 but as it involves fitting parameters that have not been measured independently, an approach to predict the surface tension was still missing. We have shown recently that the surface properties of the Pdadmac/SDS system can be rationalized by the comprehensive precipitation of polymer and most of the surfactant out of the liquid phase after dynamic changes in the bulk phase behavior have reached completion.44 Recently, we formalized this picture by describing an empirical method to predict the surface tension of aged P/S mixtures in the phase separation region based on that of a depleted surfactant solution.45 The method is based on the framework of a lack of colloidal stability of bulk complexes in compositions around the charge match point of the oppositely charged components, and it has no free fitting parameters. The input parameters required are the surface tension isotherm of the pure surfactant with respect to the bulk surfactant concentration (γsurf(csurf)), bulk polymer concentration in terms of monomer units (cpoly), bulk surfactant concentration at the left, low-csurf edge of the phase separation

γmix(csurf ) = γsurf (csurf − kc poly )

(1)

where k = 0.6 + 0.4[(csurf − cleft)/(cneut − cleft)] for csurf < cneut and k = 1 for csurf ≥ cneut. The binding isotherm correction k is particularly important when cbound > cfree, e.g., for 100 ppm Pdadmac/SDS; cf. 100 ppm NaPSS/DTAB where cfree ≫ cbound. The method achieved excellent agreement with the experimental data involving a surface tension peak for three different systems: NaPSS/DTAB in the absence of added inert electrolyte, Pdadmac/SDS with 100 mM NaCl, and DNA/ DTAB with 10 mM NaBr.45 This finding raises the question about whether one would expect a peak for all oppositely charged P/S mixtures after the dynamic changes in the bulk phase behavior have reached completion, and in our letter we discussed some general aspects that may affect its appearance. For example, a large peak should occur when the free surfactant concentration at the low-csurf edge of the phase separation region is much lower than the critical micelle concentration (cmc). In principle, the variation of ionic strength should affect the cmc greatly and the phase separation region minimally, but the implications on the surface tension behavior remained to be validated. The scope of the present paper is to rationalize the surface tension behavior of an oppositely charged P/S mixture in the phase separation region with respect to the ionic strength: NaPSS/DTAB samples in (1) pure water, (2) 100 mM NaCl, and (3) 100 mM NaBr. The NaPSS/DTAB system was chosen because even though it has been the subject of thorough experimental investigations in the past (e.g., refs 25, 28, 34, 37, and 40), it has been categorized as a system that does not have a surface tension peak,6 so it seemed an ideal candidate to challenge our existing understanding of the behavior of P/S mixtures. Two different types of salt at the same concentration were chosen to have the ability to tune the cmc while keeping the aggregation rate in the phase separation region roughly constant. High molecular weight polymer samples were used to enhance the range of bulk compositions over which aggregation occurs. Our approach is to characterize the P/S mixtures both in the bulk and at surfaces with respect to the sample age using a range of experimental techniques. Having rationalized the surface tension isotherms of the system, we conclude with an evaluation of the nonequilibrium behavior of the NaPSS/ DTAB system in relation to the ionic strength.

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EXPERIMENTAL SECTION

Materials. Pure H2O was generated by passing deionized water through a Milli-Q purification system (total organic content = 4 ppb; resistivity = 18 mΩ·cm). D2O for the neutron reflectometry measurements was used as received (Euriso-top, Saclay, France or Sigma-Aldrich). Poly(sodium styrenesulfonate) (1 MDa NaPSS; Aldrich) was purified by Amicon Ultra-15 centrifugal filter units (30 kDa molecular weight cutoff) in pure H2O to give a stock solution of ∼20 000 ppm (determined by gravimetric analysis) free of low molecular weight impurities. Hydrogenous dodecyltrimethylammonium bromide (DTAB or hDTAB; Sigma; 99.9%) was recrystallized twice in acetone, and each time the solutions were cooled over several hours to maximize the purity. Deuterated DTAB (dDTAB) was purchased from Canadian Isotopes Ltd. and was used as received. Sample Preparation Methods. The solutions made all comprised 100 ppm of NaPSS with DTAB at various concentrations 4971

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at 25 °C. All mixtures were prepared in pure water or with 100 mM NaBr or NaCl. A standard mixing approach was used to ensure that the mixing of the oppositely charged components took place under reasonably well-defined conditions.30 These protocols were used to limit the formation of kinetically trapped aggregates due to concentration gradients present during mixing.24 To mix each solution, equal volumes of 200 ppm polyelectrolyte and double the intended concentration of DTAB were poured together simultaneously. The solution was then swirled gently for a few seconds. For fresh samples, the mixtures were transferred at once into the measurement vessel. For aged samples, fresh mixtures were transferred into 4 mL glass vials (UV−vis spectroscopy and surface tensiometry) or 100 mL glass bottles (NR), in which they were left for the stated time. Afterward, 1 mL of supernatant was pipetted from each vial (UV−vis spectroscopy and surface tension) or 30 mL was pipetted from each bottle (NR) for immediate measurement. Care was taken not to agitate any sediment on the bottom of the flask given that in principle such agitation could redisperse surface-active material.31 Electrophoretic Mobility. A Malvern Zetasizer NanoZ instrument was used to measure the electrophoretic mobility of the NaPSS/ DTAB complexes using the M3-PALS technique. The standard error in the values of the electrophoretic mobility was around 10%. Measurements were always performed on freshly mixed samples. UV−vis Spectroscopy. The turbidity of NaPSS/DTAB solutions was measured using a PerkinElmer Lambda 2 UV−vis spectrophotometer with a semimicro quartz cell having a 1 cm path length. In each case the optical density of the samples was determined at 400 nm (OD400). Measurements were carried out 5 min after mixing (fresh) or immediately after extracting the supernatant (aged). Since neither the polymer nor the surfactant has an adsorption band above 350 nm, increasing OD400 values indicate the presence of larger aggregates. Gravimetric Analysis. NaPSS/DTAB solutions (300 mL) were prepared in 500 mL glass bottles and were left to age and settle for one month. After this time 209 mL of the supernatant was transferred by glass pipet into a glass dish with known mass. It was dried through heating by steam from a water bath and then was placed in a vacuum drier at 60 °C for a few hours. The dish was removed warm from the drier and was placed to cool to ambient temperature in a desiccator (above dry calcium chloride) for 15 min. The heating and drying procedure was repeated for 3 or 4 cycles until constant mass was reached. This calculation takes the simple approach of assuming an average stoichiometry of polyelectrolyte/surfactant in the precipitate of unity; i.e., all of the sodium counterions in the polyelectrolyte are replaced by dodecyltrimethylammonium ions. Surface Tensiometry. The surface tension measurements were done using a home-built pendant drop apparatus. The experimental setup has been described elsewhere.46 The pendant drop was created at the tip of a PTFE capillary which joined a gastight Hamilton syringe placed in a computer-controlled syringe pump. The drops were formed in a closed, temperature-controlled chamber with an internal size of 1 × 2 × 5 cm. To avoid the evaporation of the pendant drop, the side walls of the chamber were covered with wetted filter paper. The applied experimental procedure was as follows: by turning on the syringe pump, a series of drops were formed at the tip of the capillary, thus ensuring the creation of a fresh surface. The time required for the formation of a drop was approximately 1 s. After the formation of the third drop, the syringe pump was stopped and the monitoring of the shape started. A picture of the pendant drop was taken every ∼2 s, and the recorded sequential digital images were used for the calculation of the temporary surface tension values, giving rise to the surface tension versus time function. The surface tension values were read after 30 min to describe the local surface equilibrium characteristic for the investigated state of the system (freshly mixed or aged). Neutron Reflectometry (NR). NR measurements were performed on the supernatant of NaPSS/DTAB samples without added inert electrolyte that had been aged for two months. This sample age maximized the chances that the dynamic changes in the state of bulk aggregation had reached completion The measurements were made on the neutron reflectometer FIGARO at Institut Laue-Langevin (Grenoble, France).47 The time-of-flight instrument was used with a

chopper pair giving neutron pulses with 7.0% dλ/λ in the wavelength range 2−30 Å. Data acquisitions were carried out at an incident angle of 0.62°. Samples were left to reach steady state for around 2 h prior to each measurement. The neutron reflectivity profiles presented in the Supporting Information show the intensity ratio of neutrons in the specular reflection to those in the incident beam with respect to the momentum transfer, Q, defined by

Q=

4π sin θ λ

(2)

where θ is the incident angle and λ is the wavelength. For a layer on air contrast matched water (ACMW; 8.1 vol % D2O in H2O) of zero scattering length density, ρ, the specular reflectivity, R, at low-Q values is related to the square of the scattering intensity. For a thin homogeneous layer of a single component, the R(Q) profile may be fitted to a one-layer model to derive ρ and the layer thickness, d. The surface excess, Γ, may then be calculated Γ=

ρd NAb

(3)

where b is the scattering length of the component and NA is Avogadro’s number. For mixed films at the air/water interface the surface excess is a linear combination of the contributions from the different components to ρd, fitted to a single layer at low-Q values where it is insensitive to structural details of a more complex model. The NaPSS/DTAB mixtures were recorded in two isotopic contrasts: NaPSS/cmDTAB/ACMW (contrast 1) and NaPSS/ dDTAB/ACMW (contrast 2); see the relevant scattering length densities in Table 1. This choice of contrasts may seem unconven-

Table 1. Scattering Length Densities of Materials Used material a

dDTAB NaPSSa air

ρ (×10−6/Å−2) 5.13 1.85 0.00

material b

ACMW cmDTABc hDTAB

ρ (×10−6/Å−2) 0.00 0.00 −0.23

a

The molecular volume of DTAB was taken as 485 Å3 and the value for NaPSS was taken as 275 Å3, both from ref 40. bThe composition of ACMW is 8.1 vol % D2O in H2O. cThe composition of contrast matched DTAB (cmDTAB) is 4.5 vol % dDTAB in hDTAB.

tional, but they allowed us to carry out a direct determination of the interfacial composition without the application of a detailed structural model. The data were reduced at low-Q values only (0.007−0.04 A−1) without background subtraction using the program Cosmos, and they were fitted using the program Motofit.48 First, the background was refined to the value 2.3 × 10−5, which was the lowest value possible where zero surface excess was fitted to a fictional layer on a clean air/ ACMW measurement. The data from the two isotopic contrasts were then fitted to a single layer model at low-Q values only. The derived products of scattering length density and thickness were related to the interfacial composition through the solving of the following equations

(ρd)1 = NAbNaPSS ΓNaPSS

(4)

(ρd)2 = NA(bNaPSS ΓNaPSS + bdDTAB ΓdDTAB)

(5)

where contrast 1 (eq 4) is sensitive only to the polymer surface excess and contrast 2 (eq 5) is sensitive to both components but primarily the surfactant surface excess. The solving of simultaneous eqs 4 and 5 results in a direct measure of the interfacial composition without the need to apply a detailed structural model, which increases the precision of the measured polyelectrolyte surface excess over traditional methods (in the absence of deuterated polyelectrolyte) while saving both neutron beam time and D2O. 4972

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the different hydrodynamic size of the counterions51,52 and/or van der Waals forces.53 To investigate the dynamic changes in the state of bulk aggregation of 1 MDa NaPSS/DTAB samples with respect to the ionic strength, we performed turbidity measurements at four different sample ages (Figure 2).

RESULTS AND DISCUSSION Bulk Behavior with Respect to the Ionic Strength. In order to explain the surface properties of strongly interacting P/S mixtures, it is necessary to understand both the nature of the bulk interaction and the dynamic changes in the state of bulk aggregation. First we carried out electrophoretic mobility measurements of fresh samples of 100 ppm, 1 MDa NaPSS and with respect to different bulk concentrations of DTAB and the presence of added inert electrolyte (Figure 1). The

Figure 1. Electrophoretic mobility of 100 ppm, 1 MDa NaPSS/DTAB complexes as a function of csurf in pure H2O (blue circles), 100 mM NaCl (red upward triangles), and 100 mM NaBr (green downward triangles). The vertical dashed line indicates the point of charge neutrality.

polyelectrolyte is anionic so at low csurf values the NaPSS molecules have a net negative charge. As csurf increases, the binding of surfactant to the oppositely charged polyelectrolyte reduces its negative charge density until stoichiometric binding is reached. Charge reversal then occurs at higher csurf values, and the aggregates develop a net positive charge. The point of charge neutrality of the bulk complexes occurs at the same csurf values (4.8 mM) regardless of the ionic strength. As the equivalent monomer concentration of 100 ppm of NaPSS is 0.48 mM, the free surfactant concentration (cfree = ∼4.3 mM) is an order of magnitude larger than the bound amount at stoichiometric binding. This is a much higher value of cfree compared with that for the same bulk polymer concentrations of the Pdadmac/SDS31 or PEI/SDS24,49 systems (cfree = ∼0.2 mM), where stoichiometric binding involves values of cfree that are more than an order of magnitude lower. This difference may be related to the stiffness of the polymer chain that strongly influences how efficiently the polyelectrolyte can wrap the surfactant aggregates in the P/S complex. In the presence of salt the absolute value of the electrophoretic mobility measured at a given value of csurf is smaller than in pure water. This is in agreement with the expectation that with increasing ionic strength the electric double layer of colloidal particles is compressed leading to reduced zeta potential and electrophoretic mobility.50 Despite the fact that the ionic strengths in NaCl and NaBr are the same, the electrophoretic mobility in NaBr is lower than in NaCl, indicating that ion specific effects also play a role. These effects may be related to

Figure 2. Optical density at 400 nm of 100 ppm, 1 MDa NaPSS/ DTAB solutions as a function of csurf in (A) pure H2O, (B) 100 mM NaCl, and (C) 100 mM NaBr. The samples were measured immediately after mixing (blue) and after 1 day (green), 1 week (red), and 1 month (purple). The pale blue shaded areas indicate the phase separation regions.

In pure water (Figure 2A), the high optical density of fresh samples at compositions close to the point of charge neutrality shows that complexes lack colloidal stability and aggregate to form macroscopic particles. Far away from stoichiometric binding, the turbidity of fresh samples is lower, indicating that the complexes are sufficiently charged to suppress aggregation. A reduction in the turbidity of these samples occurs over several weeks due to precipitation and sedimentation; hence the supernatant becomes clear, and these compositions mark the equilibrium phase separation region. The aggregation rate 4973

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in the phase separation region depends on the bulk composition: the maximum rate is observed at 4.8 mM, which is the point of charge neutrality where the complexes have the lowest colloidal stability (cf. Figure 1). Peaks in the optical density of aged samples toward the edges of the phase separation region indicate the long-term stabilization of kinetically trapped aggregates formed as a result of concentration gradients during mixing. In the cases of added NaCl (Figure 2B) and NaBr (Figure 2C), the P/S complexes again lack colloidal stability in the phase separation region as shown by the high turbidity of fresh samples. In these cases, however, the samples are turbid even at the highest values of csurf measured, since the thickness of the electric double layer stabilizing the P/S colloidal particles decreases due to the increased ionic strength; thus, the interaction barrier among the formed complexes also decreases, resulting in reduced colloidal stability and enhanced aggregation. (cf. Figure 1). Over several weeks, the reduction in optical density occurs at a similar rate across the entire phase separation region. This indicates that fast coagulation occurs regardless of the stoichiometry of the bulk aggregates; i.e., the interaction barrier among the aggregates is smaller than kT for samples over the entire precipitation range at the investigated ionic strength (100 mM), except those at the extreme low-csurf edge. Further, in the presence of added inert electrolyte the aggregates precipitate at a similar rate to that of the sample measured at charge neutralization in pure water, i.e., in the fast coagulation regime limited by the collision rate rather than an energy barrier. Interfacial Behavior with Respect to the Ionic Strength. To characterize the surface tension behavior of the 1 MDa NaPSS/DTAB system, we measured data with respect to the sample age and ionic strength (Figure 3). A period of one month was chosen since the turbidity measurements indicated that this period is required for complete sedimentation over the entire precipitation range. In pure water (Figure 3A), the isotherms of fresh and aged mixtures may be compared to data for the pure surfactant. The cmc of the surfactant of 15.5 mM is in good agreement with the literature value.41 The surface tension isotherm of the fresh mixture shows a plateau in the range csurf = 1−7 mM, above which the data decrease while tracking closely those of the pure surfactant. According to the classical interpretation of the effect of the P/S interaction on the surface tension istherms,54 the plateau indicates the negligible change in cfree as added surfactant binds to the polyelectrolyte in the bulk; further decrease of the surface tension occurs as saturation of surfactant binding to the polyelectrolyte chains is reached. The closeness in the data of the mixture with those of the pure surfactant is due to the very low amount of surfactant bound to the polyelectrolyte in relation to cfree. The observed trends are in close agreement with both published data on low molecular weight NaPSS/DTAB samples40 and the surface tension isotherm observed for freshly mixed Pdadmac/SDS samples.31,44 In the latter case the surface tension peak emerged after 3 days when the dynamic changes in the bulk had finished. Here for the NaPSS/DTAB system, the general behavior is the same but the precipitation time is much longer. Just like in the Pdadmac/SDS case, the peak maximum coincides with the lowcsurf edge of the phase separation region, as opposed to the point of charge neutrality of the bulk complexes (see Figure 1), after comprehensive precipitation has taken place.

Figure 3. Surface tension of 100 ppm, 1 MDa NaPSS/DTAB solutions as a function of csurf in (A) pure H2O, (B) 100 mM NaCl, and (C) 100 mM NaBr. The samples were measured immediately after mixing (blue) and after one month (green). Pure DTAB solutions are shown for comparison (red). The pale blue shaded areas indicate the phase separation regions.

To assess the effects of added inert electrolyte on the surface tension behavior, we also measured isotherms with respect to the sample age in the presence of 100 mM NaCl (Figure 3B) and 100 mM NaBr (Figure 3C). The surface tension isotherms of fresh mixtures are similar in appearance to that of the samples recorded in pure water: there is a plateau above which the data almost merge into those of the pure surfactant. However, in the case of the mixtures aged for one month, the measured isotherms with added inert electrolyte are very different to the one recorded in pure water: in 100 mM NaCl the surface tension peak is smaller, and in 100 mM NaBr the peak is absent. The suppression and then extinction of the peak in the trend from pure water to 100 mM NaCl to 100 mM NaBr matches a trend in the reduction of the cmc from 15.5 to 8.0 to 4.5 mM. We will return to this point in the discussion of the factors which affect the peak for a given system. 4974

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Validation of Comprehensive Precipitation. Prior to the application of our empirical model for the surface tension in the phase separation region of NaPSS/DTAB samples with respect to the ionic strength, we scrutinize the major underlying assumption that comprehensive precipitation of the polyelectrolyte out of the liquid phase means that the system can be reduced to a depleted surfactant solution. In the bulk, we performed gravimetric analysis on the supernatant of NaPSS/DTAB samples in the absence of added inert electrolyte after one month. This allowed us to determine the proportion of polyelectrolyte that remained either dissolved as complexes or suspended as aggregates in the bulk liquid in relation to that present in the sediment (Figure 4A). The data

that of a depleted surfactant solution after comprehensive precipitation of P/S aggregates, we may go ahead and apply our prediction method to the experimental surface tension data. Application of Our Surface Tension Prediction Model. To apply our surface tension model (eq 1) to the experimental data from NaPSS/DTAB samples aged for one month, we require primarily the surface tension isotherms of the pure DTAB in pure water, 100 mM NaCl, and 100 mM NaBr (Figures 3A−C, respectively) and the polymer concentration in monomer units (cpoly = 0.48 mM). Additionally, for the binding correctionsmall in these cases due to the low bound amount of surfactant compared to cfreewe require the point of charge neutrality of the bulk complexes (cneut from Figure 1) and the bulk surfactant concentration at the left, low-csurf edge of the phase separation region (cleft from Figure 2). The height of the surface tension peak is linked to the ratio of the lowest free surfactant concentration in the phase separation region (i.e. on the left, low-cSDS edge) to the critical micelle concentration (i.e. the free surfactant concentration at which free micelles form in solution; cmc). The peak is higher when this ratio is smaller and is related to the spatial separation between the two bulk surfactant concentrations when data are displayed on a logarithmic scale. As cbound ≪ cfree in the phase separation region for the 100 ppm NaPSS/DTAB system, this ratio may be approximated to that of the total surfactant concentration at the low-cSDS edge of the phase separation region (cleft = cfree,left + cbound,left) to the total surfactant concentration at which free micelles form in solution marked by the final kink in the surface tension isotherm (cmc* = cmc + cbound). In order to demonstrate the significance of this ratio, we apply our prediction to the experimental data by normalizing both terms in parentheses in eq 1 by cmc* (Figure 5). The resulting predictions involve neither any physical surface measurements of the NaPSS/DTAB mixtures nor any free fitting parameters, and the agreement with the experimental data is outstanding. The model has therefore been validated on a single system where the existence and magnitude of a surface tension peak can be tuned by changing the ionic strength. Factors That Affect the Surface Tension Peak. Here we discuss factors that affect the existence and magnitude of the surface tension peak for a given system with respect to the ionic strength following comprehensive precipitation and the resulting loss of polyelectrolyte from the liquid phase. While the plateau value of the surface tension isotherm just outside the phase separation region will determine the relative height of any peak compared with its base, the maximum surface tension value at the low-csurf edge of the phase separation region marks the absolute height of the peak. This value is determined by the concentration of free surfactant at the low-csurf edge of the phase separation region in relation to the cmc after comprehensive precipitation has taken place. The cmc can be varied to a large extent by the addition of inert electrolyte: the value falls from 15.5 to 8.0 to 4.5 mM for pure water to 100 mM NaCl to 100 mM NaBr due to electrostatic screening of the headgroups and specific counterion effects. Indeed, it is found that the value correlates well for different salts at the same ionic strength with hydrodynamic radius and polarizability of the added counterions.55,56 As such, the surface tension isotherm is shifted to lower concentrations on an absolute scale (Figure 3). In contrast, the nature of bulk binding close to charge neutrality is practically unaffected by the addition of inert electrolyte (Figure 1), and the width of the phase separation is also not affected greatly by the changes in the

Figure 4. (A) Gravimetric analysis of 100 ppm, 1 MDa NaPSS/DTAB solutions as a function of csurf in pure H2O aged for one month revealing the percentage of polyelectrolyte remaining soluble or suspended in the bulk solution of the supernatant. A simple assumption that the precipitate comprised stoichiometric P/S complexes was made. (B) The surface excess of polyelectrolyte in the interfacial layer determined directly by multicontrast NR measurements at low Q values of samples aged for two months. The pale blue shaded area indicates the phase separation region.

show clearly that there has been comprehensive precipitation of NaPSS out of the liquid phase by the time the dynamic changes in the bulk have reached completion. For the air/water interface, we performed NR measurements of samples that had been stored for two months to calculate the polyelectrolyte surface excess (Figure 4B; fitted reflectivity profiles may be found in the Supporting Information). A rather narrow range of compositions was measured due to the limitations of deuterated surfactant and neutron beam time. Nevertheless, the surface excess of NaPSS clearly converges to zero at compositions just inside the phase separation region. As a result of these confirmations that NaPSS/DTAB system conforms to 4975

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the addition of inert electrolyte to a given system will reduce the magnitude and ultimately eliminate the peak altogether. As an approximate measure of the free surfactant concentration at the edge of the phase separation region, which is difficult to determine experimentally, we may compare values of cfree at the bulk composition marking charge neutralization for different systems. This concentration is determined principally by the chemical nature of the interacting polyelectrolyte and surfactant, i.e., by the structure, charge density and chain stiffness of the polyelectrolyte as well as the alkyl chain length and headgroup size of the surfactant.57−59 In this respect, there is a major difference between the bulk behavior of the NaPSS/DTAB system studied here and the widely investigated Pdadmac/SDS system.29,32,38,44 While charge neutralization occurs at values of cfree that are 28, 54, and 96% of the cmc for 100 ppm NaPSS/DTAB samples in pure water, 100 mM NaCl, and 100 mM NaBr, respectively, it occurs already at only 14% of the cmc for 100 ppm Pdadmac/ SDS samples in 100 mM NaCl. Thus, even when the two systems have the same ionic strength (100 mM NaCl), the values of cfree required for equivalent binding to the polyelectrolyte around charge neutralization differ by more than an order of magnitude. This large difference explains why a large surface tension peak occurs for NaPSS/DTAB samples only in the absence of added inert electrolyte, yet a large peak occurs for Pdadmac/SDS samples even in the presence of added inert electrolyte. As a consequence, the ionic strength can be used to suppress the existence of a peak in the surface tension for a given system only when the binding at the point of charge neutrality is relatively weak, such as for NaPSS/DTAB. Equilibrium vs Nonequilibrium Nature of the System. Our results demonstrate that the interfacial properties of an oppositely charged P/S system can evolve extremely slowly as a result of precipitation in the bulk. Interfacial properties measured in the interim period therefore represent samples that are far from equilibrium even if surface data appear to reach steady state. Complementary investigations of P/S mixtures in the bulk have, in addition, shown that samples outside the phase separation region can become trapped in nonequilibrium states as a result of their preparation pathway.24−26 As such, we may ask if the NaPSS/DTAB system also exhibits trapped nonequilibrium states that impact the interfacial properties and if they are affected by the ionic strength. We performed a series of tests where we measured the surface tension of 1 MDa NaPSS/DTAB samples aged for one month as a function of the sample history (Figure 6). The bold lines in Figure 6 are interpolated data from Figure 3 for the pure surfactant and the supernatant of mixed samples that had been stored for one month. The discrete data points refer to measurements of samples made in a two-step process: mixtures were made in the phase separation region using higher polyelectrolyte concentrations before storage (open symbols) and then subsequently dilution to final compositions outside the phase separation region (closed symbols). The latter samples are therefore chemically identical to those made in the one-step process represented by the bold green lines at the same values of csurf. The results are extremely revealing: the data points of the samples made in pure water coincide with the curve for the pure surfactant even after an equilibration period of 2 months (light symbols) while the data points of samples of elevated ionic strength coincide with the curve for the aged mixture.

Figure 5. Surface tension of 100 ppm, 1 MDa NaPSS/DTAB solutions as a function of csurf relative to the cmc (for definition see text) in (A) pure H2O, (B) 100 mM NaCl, and (C) 100 mM NaBr measured after one month (green circles). The lines show the modeled surface tension in the phase separation of the surface based on our new prediction method. The pale blue shaded areas indicate the phase separation regions.

ionic strength applied (Figure 2). As a result, with progression from pure water to 100 mM NaCl to 100 mM NaBr, the value of the cmc decreases relative to cleft; hence, the free surfactant concentration at the low-csurf edge of the phase separation region increases, and the surface tension peak is duly suppressed and then extinguished. We may now consider the surface tension isotherms displayed on a relative concentration scale with respect to the cmc (Figure 5) to highlight vividly the effects of added inert electrolyte on the surface tension peak: in relative terms the addition of added inert electrolyte moves the low-csurf edge of the phase separation region closer to the cmc, resulting in an increase in the free surfactant concentration at that composition and therefore a lower maximum surface tension. Therefore, even though the dynamic changes in the bulk phase behavior are faster toward the extremities of the phase separation region, 4976

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separation region without added salt, kinetically trapped aggregates that are formed due to concentrate gradients present during mixing coagulate with time, and the particles do not reequilibrate with the bulk as shown by a slow increase in the optical density. In contrast, for samples outside the phase separation region with added salt, the samples are in a single phase at equilibrium as shown by the low optical density. We note that the former nonequilibrium characteristics in the optical density data are present for the Pdadmac/SDS system even in the presence of added inert electrolyte,44 and this behavior is in keeping with nonequilibrium characteristics exhibited by aged samples subjected to a light mechanical stress where a low surface tension results.31 The fact that the surface properties of the NaPSS/DTAB system at low ionic strength can converge to very different states depending on the sample history highlights the trapped nonequilibrium nature of the system. We infer as a result that both the nonequilibrium nature of the surface properties of oppositely charged P/S systems resulting from slow precipitation and the prevalence of any trapped nonequilibrium states formed must be clearly understood for a given system prior to the rationalization of experimental data within an equilibrium framework.

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CONCLUSIONS In this paper we have shown that the surface tension in the phase separation region of NaPSS/DTAB mixtures can be predicted with respect to the ionic strength using a single empirical equation. We have also shown that a peak in the surface tension may be tuned for a single system: addition of salt lowers the cmc relative to the phase separation region, which means that the free surfactant concentration after comprehensive precipitation is higher, so the peak is suppressed or even extinguished. The agreement of our model with the experimental data for samples of high ionic strength indicates that the underlying physical process of comprehensive precipitation, however, occurs whether there is a surface tension peak or not. We have compared the behavior of NaPSS/DTAB mixtures with those of another oppositely charged mixture, Pdadmac/ SDS, which has a pronounced surface tension peak even for samples with elevated ionic strength. This difference in the surface tension behavior is attributed to the much lower free surfactant concentration of samples in the phase separation of the latter system as opposed to any difference in the interaction at the air/water interface. In both cases, however, the surface properties are absolutely determined by the bulk phase behavior and the time scale by which the dynamic changes take place. This study highlights the nonequilibrium nature of the NaPSS/DTAB system by the very slow dynamic changes in the state of bulk aggregation. Any surface measurements carried out in the month that it takes the bulk aggregation, precipitation, and sedimentation processes to reach completion may well reach steady state values, but the system is in fact far from equilibrium. This finding emphasizes the importance of appreciating the dynamic changes in the bulk and understanding the time scales involved to aid the interpretation of surface measurements of strongly interacting P/S mixtures. In addition to the slowly evolving nonequilibrium nature of the surface properties during the slow precipitation of P/S aggregates, we have demonstrated the existence of trapped nonequilibrium states for NaPSS/DTAB mixtures in the

Figure 6. Surface tension of 100 ppm, 1 MDa NaPSS/DTAB solutions as a function of csurf in (A) pure H2O and (B) 100 mM NaCl where data repeated from Figure 3 are represented as solid lines of the same colors; additional data are shown as discrete points where samples were made in two steps: initially at (A) 220, 300, 400, and 500 ppm and (B) 180, 250, and 400 ppm (open symbols from left to right), then stored for 1 month, then diluted to 100 ppm, and then stored for 1 week (dark closed symbols) or 2 months (light closed symbols) before measurement.

The results in pure water highlight a characteristic nonequilibrium feature of oppositely charged P/S mixtures where precipitate is formed irreversibly and is therefore not in equilibrium with the bulk liquid. As such, details of the sample history, such as the pathway by which the components are mixed, can have a marked effect on the surface properties. Further, we have shown that this can even be the case for samples with bulk compositions well outside the phase separation region because precipitate formed at a point in the sample history does not dissolve on experimentally accessible time scales. We attribute the prevalence of this effect in samples only of low ionic strength to the high entropy associated with the release of counterions into the bulk upon complex formation rendering the dissolution of the precipitate unfavorable. In contrast, the entropic barrier is suppressed at higher ionic strength, which explains why the system with added NaCl conforms more to an equilibrium system. This finding is consistent with those in the bulk study of Pojják et al., who showed that NaPSS/DTAB mixtures exhibited more pronounced nonequilibrium effects at low ionic strength.25 The impact on the interfacial properties, however, has been demonstrated in the present work for the first time. A consequence of this difference in behavior between samples with and without added salt can be seen in the optical density data in Figure 2. For samples outside the phase 4977

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(7) Langevin, D.; Monroy, F. Interfacial rheology of polyelectrolytes and polymer monolayers at the air−water interface. Curr. Opin. Colloid Interface Sci. 2010, 15, 283−293. (8) Bain, C. D.; Claesson, P. M.; Langevin, D.; Mészáros, R.; Nylander, T.; Stubenrauch, C.; Titmuss, S.; von Klitzing, R. Complexes of surfactants with oppositely charged polymers at surfaces and in bulk. Adv. Colloid Interface Sci. 2010, 155, 32−49. (9) Noskov, B. A.; Loglio, G.; Miller, R. Dilational surface viscoelasticity of polyelectrolyte/surfactant solutions: formation of heterogeneous adsorption layers. Adv. Colloid Interface Sci. 2011, 168, 179− 197. (10) La Mesa, C. Polymer−surfactant and protein−surfactant interactions. J. Colloid Interface Sci. 2005, 286, 148−157. (11) Chiappisi, L.; Hoffmann, I.; Gradzielski, M. Complexes of oppositely charged polyelectrolytes and surfactants - recent developments in the field of biologically derived polyelectrolytes. Soft Matter 2013, 9, 3896−3909. (12) Malmsten, M. Soft drug delivery systems. Soft Matter 2006, 2, 760−769. (13) Lapitsky, Y.; Zahir, T.; Shoichet, M. S. Modular biodegradable biomaterials from surfactant and polyelectrolyte mixtures. Biomacromolecules 2008, 9, 166−174. (14) von Klitzing, R. Effect of interface modification on forces in foam films and wetting films. Adv. Colloid Interface Sci. 2005, 114−115, 253−266. (15) Noskov, B. A. Dilational surface rheology of polymer and polymer/surfactant solutions. Curr. Opin. Colloid Interface Sci. 2010, 15, 229−236. (16) Petkova, R.; Tcholakova, S.; Denkov, N. D. Role of polymer− surfactant interactions in foams: effects of pH and surfactant head group for cationic polyvinylamine and anionic surfactants. Colloids Surf., A 2013, 438, 174−185. (17) Lohmann, U.; Feichter, J. Global indirect aerosol effects: a review. Atmos. Chem. Phys. 2005, 5, 715−737. (18) Zuo, Y. Y.; Veldhuizen, R. A. W.; Neumann, A. W.; Petersen, N. O.; Possmayer, F. Current perspectives in pulmonary surfactant Inhibition, enhancement and evaluation. Biochim. Biophys. Acta, Biomembr. 2008, 1778, 1947−1977. (19) Shchukin, E. D.; Pertsov, A. V.; Amelina, E. A.; Zelenev, A. S. In Colloid and Surface Chemistry, 1st ed.; Mobius, D., Miller, R., Eds.; Elsevier Science B.V.: Amsterdam, 2001; Vol. 12. (20) Piculell, L. Understanding and exploiting the phase behavior of mixtures of oppositely charged polymers and surfactants in water. Langmuir 2013, 29, 10313−10329. (21) Sitar, S.; Goderis, B.; Hansson, P.; Kogej, K. Phase diagram and structures in mixtures of poly(styrenesulfonate anion) and alkyltrimethylammonium cations in water: significance of specific hydrophobic interaction. J. Phys. Chem. B 2012, 116, 4634−4645. (22) Li, D.; Kelkar, M. S.; Wagner, N. J. Phase behavior and molecular thermodynamics of coacervation in oppositely charged polyelectrolyte/surfactant systems: a cationic polymer JR 400 and anionic surfactant SDS mixture. Langmuir 2012, 28, 10348−10362. (23) Bergfeldt, K.; Piculell, L.; Linse, P. Segregation and association in mixed polymer solutions from Flory-Huggins model calculations. J. Phys. Chem. 1996, 100, 3680−3687. (24) Mezei, A.; Mészáros, R.; Varga, I.; Gilányi, T. Effect of mixing on the formation of complexes of hyperbranched cationic polyelectrolytes and anionic surfactants. Langmuir 2007, 23, 4237−4247. (25) Pojják, K.; Bertalanits, E.; Mészáros, R. Effect of salt on the equilibrium and nonequilibrium features of polyelectrolyte/surfactant association. Langmuir 2011, 27, 9139−9147. (26) Naderi, A.; Claesson, P. M.; Bergstrom, M.; Dedinaite, A. Trapped non-equilibrium states in aqueous solutions of oppositely charged polyelectrolytes and surfactants: effects of mixing protocol and salt concentration. Colloids Surf., A 2005, 253, 83−93. (27) Mészáros, R.; Thompson, L.; Bos, M.; Varga, I.; Gilányi, T. Interaction of sodium dodecyl sulfate with polyethyleneimine: surfactant-induced polymer solution colloid dispersion transition. Langmuir 2003, 19, 609−615.

absence of added inert electrolyte. In this case, chemically identical samples made in one-step and two-step procedures experienced extreme opposite behavior: samples made outside the phase separation region had a surface tension value consistent with an interfacial layer of polyelectrolyte and surfactant while samples made inside the phase separation region that were later diluted to outside the equilibrium phase boundary had surface tension values consistent with a depleted layer of surfactant. These results can be rationalized straightforwardly within a nonequilibrium framework by the lack of dissolution of the precipitate upon chemical change due to the high entropy associated with the release of counterions during complex formation. However, the implications are less straightforward in that completely different surface properties can result even for samples that are outside the phase separation region according to details of the sample history. With knowledge of these ways in which the interfacial properties of oppositely charged P/S mixtures may be far from equilibrium, we conclude that equilibrium characteristics must be validated for a given system prior to the rationalization of experimental data using an equilibrium framework. After all, a simple demonstration that surface data have reached steady state may be wholly inadequate.

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ASSOCIATED CONTENT

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AUTHOR INFORMATION

S Supporting Information *

Examples of neutron reflectivity profiles and fits. This material is available free of charge via the Internet at http://pubs.acs.org. Corresponding Authors

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

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank Anna Angus-Smyth, Marianna Yanez Arteta, Tommy Nylander, and Erik Watkins for helpful discussions, the ILL for beam time on FIGARO, and Simon Wood for expert technical assistance. 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 (OTKA H-07A 74230 and K100762), which is gratefully acknowledged.

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