Article pubs.acs.org/Macromolecules
Prediction of Polyelectrolyte Complex Stoichiometry for Highly Hydrophilic Polyelectrolytes Feriel Meriem Lounis, Joseph Chamieh, Philippe Gonzalez, Hervé Cottet, and Laurent Leclercq* Institut des Biomolécules Max Mousseron, IBMM, UMR 5247 CNRS, Université de Montpellier, Ecole Nationale Supérieure de Chimie de Montpellier, Place Eugène Bataillon, CC 1706, 34095 Montpellier Cedex 5, France S Supporting Information *
ABSTRACT: The interaction between two hydrophilic polyelectrolytes of opposite charges was investigated using poly(L-lysine) (PLL) as the polycation and a library of copolymers of acrylamide and 2-acrylamido-2-methyl-1-propanesulfonate (P(AM-co-AMPS)) with various chemical charge densities as polyanions. The formation of polyelectrolyte complexes (PECs) was comparatively studied by varying different parameters, such as the mixing order, the P(AM-coAMPS) chemical charge density and the initial polycation to polyanion molar ratio. PECs were then characterized in terms of charge stoichiometry and of stability toward ionic strength. The results showed a strong dependency of precipitated PEC stoichiometry on the P(AM-co-AMPS) chemical charge density and the initial polycation to polyanion molar ratio. In contrast, PEC stoichiometry was not affected by the mixing order of the two polyelectrolyte partners. A general rule capable of predicting the PEC stoichiometry is proposed.
1. INTRODUCTION Polyelectrolyte complexes (PECs) are generally formed by electrostatic interaction between two oppositely charged polyelectrolytes in solution.1,2 A great number of PECs has been already studied in literature and are present in a wide variety of application fields, such as drug and gene delivery,3−10 thin film coating for separation processes,11−16 food industry17−20 and water treatment.21−24 Different types of PECs can be formed: (i) soluble or hydrodispersed complexes, which form a macroscopically homogeneous system; (ii) turbid colloidal systems with suspended complex particles in the transition range of phase separation; (iii) precipitated complexes, which phase separated from the solution; (iv) coacervates, which are issued from liquid−liquid phase separation.25 The type of PECs depends on several parameters, such as the chain length of the two polyelectrolytes, their chemical structure, as well as the type and distribution of the charged groups along the polyelectrolyte chains. Besides these structural parameters, the concentration of the polyelectrolytes, the polycation to polyanion mixing molar ratio expressed in terms of charged monomers (NPC/NPA), the mixing order, the ionic strength and the pH of the medium play an important role.26−28 Extensive phase diagrams for poly(acrylic acid) (PAA)/poly(allylamine hydrochloride) (PAH) complexation, including the effects of the above parameters, was presented by Chollakup et al.29 Stoichiometric PECs contain equal amounts of positive and negative charges and are generally obtained by mixing solutions of strong polyelectrolytes. They usually precipitate upon formation.30 However, precipitation can be avoided if a hydrophilic block is attached to at least one of the © XXXX American Chemical Society
polyelectrolytes. In such a case, water-soluble PECs are formed, consisting of a neutral water-insoluble core surrounded and stabilized by a hydrophilic corona.31−33 In contrast, association of weak polyelectrolytes often leads to the formation of nonstoichiometric PECs30,34−38 which formed when polyelectrolytes are mixed with an excess of one type of polyion charge. Nonstoichiometric PECs are usually classified in two categories: (i) highly aggregated PECs formed by several polyelectrolytes chains stabilized by the polyion in excess that charges the PEC surface and prevents macroscopic precipitation; (ii) water-soluble PECs formed by mixing nonstoichiometric amounts of polyanions and polycations and having a net charge of the same sign as the polyion in excess.34,39−41 For example, Saether et al.42 studied chitosanealginate interaction and showed that positively charged particles can be obtained using an excess of polycation, whereas particles with an overall negatively charged surface formed when using an excess of polyanion. In contrast, when the polyanion and the polycation were mixed in an equimolar ratio, neutral aggregated objects were generally formed. Leclercq et al.43,44 studied the formation of PECs issued from the association between poly(L-lysine) (PLL) polycation and various weak polyanions in water according to a titration protocol. To assess the stability of the different precipitated complexes, the critical NaCl concentration (Irecomp) that corresponds to the salt concentration at which a solid PEC previously destabilized at high ionic strength, reformed when Received: March 4, 2016 Revised: April 21, 2016
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DOI: 10.1021/acs.macromol.6b00463 Macromolecules XXXX, XXX, XXX−XXX
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and 2.69 g of AM (0.0375 mol) were prepared and dissolved in 70 mL distilled water. The solution was neutralized at pH 7 using 2 M NaOH. A volume of 20 mL of absolute ethanol, used as a transfer agent, was added. The reaction mixture was then degassed using oxygen-free nitrogen for 40 min. After that, 194.5 mg of potassium persulfate dissolved in 5 mL degassed deionized water were introduced. Three minutes later, 167 mg of N,N,N′,N′-tetramethylethylenediamine dissolved in 5 mL of degassed deionized water were added. This method has the advantage of initiating the system at room temperature.48 The polymerization reaction was immediate and slightly exothermic. The reaction mixture was left 4 h and then precipitated in a large excess of acetone. The precipitate was dissolved in deionized water, dialyzed against deionized water using a 50 kDa cutoff dialysis membrane and finally freeze-dried. 2.3. Measurement of P(AM-co-AMPS) Refractive Index Increment. Before carrying out the refractive index measurements, a 2.0 g L−1 mother solution in the eluent of each synthesized P(AM-coAMPS) was dialyzed using a cellulose ester dialysis membrane of 100 Da against the eluent. The eluent used was the same for dialysis, refractive index measurements and size exclusion chromatography (SEC) experiments. It was composed of 0.15 M sodium dihydrogen phosphate, 1 M sodium chloride and 4.6 mM sodium azide. pH was adjusted at 7.4 using sodium hydroxide solution. The eluent was finally filtered on Durapore membrane filters of 0.1 μm cutoff. The refractive index increment (dn/dc) of the various P(AM-co-AMPS) was determined at 35 °C using a Shimadzu RID-6A refractive index detector at 690 nm. P(AM-co-AMPS) solutions were prepared at 2.0, 1.5, 1.0, 0.75, 0.5, and 0.25 g L−1 by dilution of the dialyzed mother solution. A volume of 2 mL of each P(AM-co-AMPS) solution was injected into the refractometer. The refractive index increment was then calculated using the ASTRA software (v6.1.1.17, Wyatt Technology Corp., see Table S1 in Supporting Information for the results). 2.4. Determination of Molar Mass Distribution of P(AM-coAMPS) by SEC-MALLS. The molar mass and the polydispersity index of P(AM-co-AMPS) were determined using size-exclusion chromatography coupled with multiangle laser light scattering (SEC−MALLS). Samples at 2 g·L−1 of P(AM-co-AMPS) were eluted using a Thermoscientific Ultimate 3000 separations module at a flow rate of 0.8 mL.min−1 from OHpak SBG column guard and two SB-806M-HQ columns (SHODEX, Munich, Germany) connected in series at a 35 °C thermostated temperature. The eluent used for SEC-MALLS analysis was 0.15 M sodium dihydrogen phosphate, 1 M sodium chloride and 4.6 mM sodium azide. The eluted samples were detected using a mini DAWN-Treos multiangle laser light scattering detector with a laser at 690 nm (Wyatt Technology Corp., Santa Barbara, CA) and a RID-6A refractive index monitor (Shimadzu, Tokyo, Japan). The instrument was calibrated using NaCl solutions of various known concentrations (2.0, 1.5, 1.0, 0.75, 0.5, and 0.25 g L−1) to get a dn/dc value of 0.187). The data for molar mass determination was analyzed using the ASTRA software (v6.1.1.17, Wyatt Technology Corp.) 2.5. Determination of the P(AM-co-AMPS) Chemical Charge Density Distribution. Capillary zone electrophoresis (CZE) was used to determine the P(AM-co-AMPS) chemical charge density distribution. In free solution, the electrophoretic mobility of evenly charged polyelectrolyte is not dependent on the molar mass, and depends only on the chemical charge density.49 In this regime, which is called the free draining behavior, it is thus possible to get quantitative estimation of the dispersion in chemical composition (or chemical charge), as recently described.50 Experiments were carried out using a 3D-CE Agilent instrument (Waldbronn, Germany) equipped with a diode array detector set at 200 nm. Bare fused silica capillary (50 μm i.d. × 33.5 cm, 25 cm to the detector) was purchased from Polymicro Technologies (Phoenix, USA). P(AM-co-AMPS) solutions at a concentration of 2 g L−1 were prepared in a 200 mM borate buffer (pH 9.2). Samples were hydrodynamically injected by applying a pressure of 35 mbar for 3.0 s. The electrophoretic system was operated under normal polarity and a constant voltage of +20 kV. Capillary temperature was maintained at 25 °C. New capillaries were flushed with 1 M NaOH for 20 min and then with deionized water for 20 min.
water was added. The stepwise addition of PLL to the polyanion in solution led to the. formation of stoichiometric PECs when using poly(β-malic acid) (PMLA), poly(L-lysine citramide) (PLCA), or poly(L-lysine citramide imide) (PLCAI) polyanions, and nonstoichiometric complexes when using poly(acrylic acid) (PAA) polyanions.45,46 Reversely, the stepwise addition of PAA into PLL led to the formation of stoichiometric PECs, whereas the addition of PMLA, PLCA, or PLCAI into PLL led to the formation of nonstoichiometric complexes.45,46 At a first glance, it seems difficult to establish a general rule predicting the stoichiometry of the precipitated polyelectrolyte complexes. This work aimed at predicting the excess of polymer charge in the polyelectrolyte complexes formed between two polyelectrolytes of opposite charges having hydrophilic backbones, knowing the initial molar ratio and the charge parameter of each partner. As an example, PLL was selected as the polycation and a library of statistical copolymers of acrylamide and 2-acrylamido-2-methyl-1-propanesulfonate (P(AM-coAMPS)) with various chemical charge densities were selected as polyanions. The formation of PECs was comparatively studied by varying different parameters, such as the mixing order, the P(AM-co-AMPS) chemical charge density and the initial polycation to polyanion (NPC/NPA) molar ratio. PECs were characterized in terms of charge stoichiometry and of stability toward ionic strength with the determination of the Irecomp parameter.
2. EXPERIMENTAL SECTION 2.1. Chemicals. Low polydisperse linear poly(L-lysine) under its chloride form (PLL) (degree of polymerization DP 50, molar mass Mw 8200 g·mol−1, polydispersity index PDI 1.04) was supplied by Alamanda Polymers (USA). 2-Acrylamido-2-methyl-1-propanesulfonic acid (AMPS), acrylamide (AM), N,N,N′,N′-tetramethylethyldiamine, potassium persulfate, sodium hydroxide, sodium tetraborate decahydrate, sodium dihydrogen phosphate, and sodium azide were purchased from Sigma-Aldrich (Steinheim, Germany). Absolute ethanol and sodium chloride were purchased from VWR (Leuven, Belgium). Nitrogen gas was obtained from Air Liquide (Paris, France). Deionized water was purified using a Milli-Q system (Millipore, Molsheim, France). D2O was purchased from Euriso-Top (Saint Aubin, France). Cellulose ester dialysis membrane of 100 Da (reference number: 131 018) and cellulose dialysis membrane of 50 kDa (reference number: 132 544) were purchased from Spectrum Laboratories (Rancho Dominguez, CA, USA). Durapore membrane filters were purchased from Merck Millipore (Darmstadt, Germany). All chemicals were used without any further purification. 2.2. P(AM-co-AMPS) Synthesis. Copolymers of acrylamide (AM) and 2-acrylamido-2-methyl-1-propanesulfonate (P(AM-co-AMPS)) with different chemical charge densities of 5%, 15%, 20%, 30%, 55%, 70%, and 100% were synthesized by radical copolymerization, according to the procedure described by McCormick et al.47 The chemical charge density f is defined as the molar fraction of charged monomer
f=
n n+m
(1)
where n (respectively m) is the molar quantity of AMPS (respectively AM) monomers in the chain. The chemical structures and synthetic route leading to the copolymers are represented in Figure S1 in the Supporting Information. Each free radical polymerization was conducted at room temperature in a three-necked flask equipped with a mechanical stirrer, a nitrogen inlet tube, and a rubber septum. As an example, the procedure of the synthesis of the P(AM30-coAMPS70) copolymer is described. The molar feed ratio of AMPS to AM was 0.7/0.3. Mixture of 8.13 g of AMPS (0.0875 mol) in acid form B
DOI: 10.1021/acs.macromol.6b00463 Macromolecules XXXX, XXX, XXX−XXX
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Macromolecules Before each run, the capillary was washed with deionized water (2 min) and fresh buffer (3 min). Electropherograms were collected using the Agilent ChemStation software and then exported to Microsoft Excel for subsequent data treatment. 2.6. Preparation of the Polyelectrolyte Complexes. Three different methods were used to prepare the PECs to study the impact of the mixing order (see Figure 1). During complexation, pH remains
Measurement of optical density was carried out using Lambda 20 PerkinElmer spectrophotometer (Waltham, MA). 2.8. Determination of PECs Stoichiometry by 1H NMR Spectroscopy. Solid PECs were dissolved in D2O in the presence of NaCl and the resulting solutions were analyzed by 1H NMR on a Brücker 400 MHz spectrometer. Charge stoichiometry within the PECs fractions was determined from the relative integrations of PLLCH and P(AM-co-AMPS)−CH2−SO3− resonances of the respective protons as shown in Figure 2 for a stoichiometric introduced charged
Figure 1. Schematic representation of (i) PECs formation protocols and (ii) PECs characterization: determination of Irecomp and charge stoichiometry by 1H NMR. Figure 2. 1H NMR spectrum of (A) P(AM45-co-AMPS55) in D2O and (B) PEC formed by adding PAMPS into PLL (DP 50). [NaCl] = 0.5 mol·L−1 and (NPC/NPA)intro= 1.0.
between 6.6 and 7.2. At this pH, both polyelectrolytes are fully ionized and PLL helicity did not occur. In the first route, 500 μL of P(AM-coAMPS) solution in NaCl of concentration equal to 30% Irecomp (see section 2.7) was added to 500 μL of PLL solution in NaCl of the same concentration. The final PLL concentration was fixed at 10 g L−1 and the P(AM-co-AMPS) concentration was adjusted depending on the chemical charge density f and the initial molar ratio (NPC/NPA)intro. All the concentration data are summarized in Table S2 (see Supporting Information). PECs were prepared at different molar ratios initially introduced (NPC/NPA)intro = 0.2, 0.35, 0.6, 1.0, 1.6, 3.5, and 10.0. In the second route, the reverse process was carried out to determine the influence of mixing order. The precipitate formed after each stepwise addition was collected by centrifugation using a Sigma 302 K centrifuge at 10 000 rpm for 15 min, then washed once with 20 μL of fresh salted (30% of Irecomp) solution. The washing solution was systematically combined to the supernatant phase. In all cases, the precipitated PECs collected by centrifugation were finally washed using deionized water to remove the salt, and then freeze-dried. PECs were also prepared by a third route called “in situ”. In that case, the oppositely charged polyelectrolytes were mixed at the desired molar ratio in a high concentrated NaCl to prevent PEC formation (above Irecomp). Then, pure water was added into the resulting solution to get the final desired NaCl concentration and to enable complex formation. The precipitate formed was collected by centrifugation, washed with fresh salted (at the same final NaCl concentration) solution and then with deionized water to remove the salt, and finally freeze-dried. 2.7. Determination of the Ionic Strength of Recomplexation (Irecomp). Irecomp values were determined using turbidity method at 520 nm. Solid PECs were first decomplexed in 1 mL NaCl solutions, at concentrations slightly higher than Irecomp and adapted to each P(AMco-AMPS) chemical charge density. The optical density of the salted solution at 520 nm was close to zero. At this wavelength, the selected polyelectrolytes did not absorb light, and thus, the value of optical density reflected the light scattered by PECs particles only. Pure water was then successively added to dilute the salted solution. The Irecomp was deduced from the NaCl concentration corresponding to an optical density of 0.03 absorbance in a 1 cm path length quartz cuve. For accurate measurements, the amount of pure water necessary to cause turbidity due to recomplexation was limited to a maximum of 100 μL, i.e. less than 10% of initial volume so that dilution could be neglected.
ratio (NPC/NPA)intro= 1.0 in the case of P(AM45-co-AMPS55). Stoichiometric PECs were obtained for PLL-CH area (chemical shift of proton number 5) equal to half of P(AM-co-AMPS)−CH2−SO3− area (chemical shift of proton number 1′).
3. RESULTS AND DISCUSSION 3.1. Characterization of the Synthesized P(AM-coAMPS) Polyanions. The chemical charge density distribution of all P(AM-co-AMPS) samples was determined by CZE as previously described.49,50 The obtained raw electropherograms were subsequently treated to transform the time-scale axis into a mass relative distribution of the chemical charge density50 based on the correlation between the electrophoretic mobility and the average chemical charge density f. The quantitative data relative to the polydispersity in chemical charge density of the P(AM-co-AMPS) samples are shown in Table 1, where σf is the standard deviation of the chemical charge density distribution and σf /f is the relative standard deviation (see also Figure S2 in the Supporting Information for the complete charge density distributions). It is worth noting that the asymmetrical charge density distributions observed at high chemical charge densities are due to different reactivity ratios during the radical copolymerization (1.06 for AM and 0.52 for AMPS).51 The refractive index increment of the synthesized P(AM-co-AMPS) (see Figure S3 in the Supporting Information for dn/dC variation with P(AM-co-AMPS) chemical charge density), as well as the weight-average molar mass Mw and polydispersity index (PDI = Mw/Mn) determined by SEC-MALS are also reported in Table 1 (see Figure S4 in the Supporting Information for the molar mass distributions). As expected, free radical copolymerization leads to the formation of copolymers having relatively large polydispersity indexes between 1.8 and 2.8. Table 1 shows that the molar mass of P(AM-co-AMPS) increases with the chemical charge density C
DOI: 10.1021/acs.macromol.6b00463 Macromolecules XXXX, XXX, XXX−XXX
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Macromolecules Table 1. Physico-Chemical Characteristics of P(AM-co-AMPS) Samples Used in This Worka P(AM-co-AMPS) f (%) dn/dc Mw × 105 (g/mol) PDIb σf (%) σf/f
5 0.166 3.20 1.9 0.74 0.15
15 0.162 3.22 2.1 1.48 0.10
20 0.160 3.49 2.8 1.40 0.07
30 0.155 4.37 2.4 2.24 0.07
55 0.143 6.41 2.8 3.44 0.06
70 0.137 8.42 2.8 3.71 0.05
100 0.123 9.55 1.8 − −
a The refractive index increment dn/dc, weight average molar masses Mw and polydispersity index PDI were determined by SEC-MALLS. The standard deviation σf of the chemical charge density distribution and its relative standard deviation was obtained by CE. bPolydispersity index.
between ∼3 × 105 and 1 × 106 g mol−1. The weight-average degree of polymerization DPw was relatively constant ∼3900 ± 415 (±1 SD) whatever the chemical charge density (see Figure S5 in Supporting Information). On the contrary, it was also found that the polydispersity in charge density is rather low for all the P(AM-co-AMPS) samples (standard deviations σf below 10% of the average charge density, for all samples except P(AM95-co-AMPS5)). It can be concluded that all P(AM-coAMPS) are polydisperse in molar masses, but their chemical charge density distribution is relatively narrow. 3.2. Variation of Irecomp with the Chemical Charge Density f . The Irecomp value is an important parameter because it is directly related to the interaction strength (or binding constant, or the Gibbs free energy) between the two polyelectrolytes of opposite charges. There is no stable complex when the ionic strength of the medium is above Irecomp as demonstrated by the turbidity measurements displayed in Figure S6 (see Supporting Information). As expected, Irecomp increases with the chemical charge density of P(AM-co-AMPS) (see Figure 3). When increasing the chemical charge density of
a break in the plot seems to occur at f = 35% that is reminiscent of the critical Manning condensation threshold for vinylic copolymers. In the Manning theory, the parameter ξ defined as the ratio of the intercharge distance (b) between two adjacent charged monomers to the Bjerrum length (0.71 nm in water at 25 °C) is a dimensionless measure of the polyelectrolyte charge density. For values of ξ > 1, counterions condense on the chain reducing its net value to unity. For values of ξ < 1, there is no counterion condensation and the effective charge density corresponds to the chemical (or nominal) charge density. 3.3. Stoichiometry of the Polyelectrolyte Complexes. 3.3.1. Effect of the Polycation on Polyanion Mixing Molar Ratio and on the Chemical Charge Density. The charge composition of the precipitated PEC was systematically investigated for different (NPC/NPA)intro ratios and for different P(AM-co-AMPS) chemical charge density f. First, the addition order corresponding to the addition of P(AM-co-AMPS) into PLL was investigated. Mixing P(AM-co-AMPS) and PLL either in pure water or in salted medium (30% of Irecomp) led to the formation of nonsoluble precipitated PECs. All the precipitated PECs were analyzed by 1H NMR to get the (NPC/NPA)PEC charge stoichiometry in the PEC. Hydrodispersed PECs were obtained only when PLL was initially introduced in excess ((NPC/NPA)intro = 10) with PAMPS, and when PLL was initially introduced in default ((NPC/NPA)intro = 0.2) with P(AM85-coAMPS15). 1H NMR analyses in these cases were not possible. The (NPC/NPA)PEC charge stoichiometry, which represents the number of lysine residues bound per AMPS monomer in the precipitated PECs for different P(AM-co-AMPS) chemical charge densities and for different initial polycation to polyanion mixing molar ratios (NPC/NPA)intro is given in Table S3 (see Supporting Information). When PLL was introduced in default (NPC/NPA)intro < 1 in the presence of a low charge density P(AM-co-AMPS) (typically 15% of AMPS units), the positive charges of lysine residues were compensated, leading to the formation of stoichiometric PECs. In contrast, nonstoichiometric negatively charged PECs were obtained with P(AM-co-AMPS) of high charge density. When PLL was introduced in excess (NPC/ NPA)intro > 1, nonstoichiometric positively charged PECs were obtained with P(AM-co-AMPS) of low charge density. In contrast, stoichiometric PECs were obtained with P(AM-coAMPS) of high charge density; all the positives charges were almost compensated. Figure 4 shows that for a given P(AM-co-AMPS) chemical charge density, the (NPC/NPA)PEC charge stoichiometry increases when increasing the initial polycation to polyanion mixing molar ratio (NPC/NPA)intro. The more the PLL is introduced in excess, the more the PECs are enriched in positive charges.
Figure 3. Variation of Irecomp (respectively (Irecomp)1/2) of P(AM-coAMPS)/PLL (DP 50) complex according to the P(AM-co-AMPS) chemical charge density f.
P(AM-co-AMPS), the number of electrostatic interactions between P(AM-co-AMPS) and PLL chains increases and the interaction becomes stronger. Thus, the concentration of NaCl that is required to screen the electrostatic interaction increases. For the lowest P(AM-co-AMPS) chemical charge density (5%), the concentration of NaCl required to breakdown the PEC is very low (91 mM). As shown in Figure 3, Irecomp increases linearly for P(AM-co-AMPS) chemical charge densities ranging between 5% and 55%. Above 55%, Irecomp increases less rapidly. If one represents (Irecomp)1/2, which is more relevant in the Debye−Hückel formalism, as a function of f (see also Figure 3), D
DOI: 10.1021/acs.macromol.6b00463 Macromolecules XXXX, XXX, XXX−XXX
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Table 2, a general rule can be derived. If the polyelectrolyte of highest charge density is introduced in default, then stoichiometric PEC are obtained. Reversely, if the polyelectrolyte of highest charge density is introduced in excess, then the PEC stoichiometry will be in favor of this excess. This rule can be summarized by the diagram given in Figure 5, which applies for all the systems studied in this work, as well as those gathered in Table 2 issued from the literature. 3.3.2. Effect of the Mixing Order. Table 3 shows the values of charge stoichiometry of precipitated PECs prepared by adding either the polycation into the polyanion, or the polyanion into the polycation, or prepared in situ by dilution at ionic strength close to Irecomp as illustrated in Figure 2. This comparison was performed for two P(AM-co-AMPS) chemical charge densities of 15% and 100%. In both cases, the charge stoichiometry values (NPC/NPA)PEC were very close, whatever the method of preparation of the PECs. This was true for all the investigated initial molar ratios and ionic strengths. It was also verified for the PAMPS at zero ionic strength, for which the binding constant is supposed to be maximum for the PLLP(AM-co-AMPS) system. We can conclude that, in the case of the interactions between P(AM-co-AMPS) and PLL, charge stoichiometry and Irecomp values of the precipitated PECs were not affected by the way the PEC was prepared. These findings suggest that PLL-P(AM-
Figure 4. Dependence of (NPC/NPA)PEC charge stoichiometry in PLLP(AM-co-AMPS) precipitated complexes as a function of the P(AMco-AMPS) charge ratio and for various (NPC/NPA)intro ratios. All the complexes are issued from the addition of P(AM-co-AMPS) into PLL in NaCl solutions at concentrations corresponding to 30% of Irecomp.
At the first glance, it seems difficult to find, from Figure 4 and Table S3 (in Supporting Information), a general rule that could predict the stoichiometry of the precipitated PEC according to the introduced stoichiometry and the charge densities of the two polyelectrolyte partners. However, if we combine these results with those derived from the literature and reported in
Table 2. PECs Charge Stoichiometry Obtained by Mixing Oppositely Charged Polyelectrolytesa,b PE in excess
n+/n‑ charge stoichiometry expected from the rule
n+/n‑ charge stoichiometry obtained experimentally
PAA PLL PMLA PLCA PLL PLCAI PLL PSS
1 1 >1
