Introduction

Polyion complexes formed by a wide variety of polyanions and polycations in aqueous solution have been studied for more than half a century by changing parameters, such as the mixing ratio, ionic strength and pH. Table 1 lists common polyanion−polycation pairs that have been investigated so far; a more comprehensive list can be found in ref. 1. Despite the long research history, the mechanism of polyion complexation is not yet fully understood. Fuoss and Sadek2 reported stoichiometric complexation between sodium poly(acrylate) (NaPA) or sodium poly(styrene sulfonate) and poly(4-vinyl-N-butylpyridinium) chloride, and other researchers3, 4, 5 later reported stoichiometric complexation for different polyelectrolyte pairs (Table 1). On the other hand, Tsuchida et al.6 and Nakajima and his group7, 8, 9 observed non-stoichiometric complexation of the polyion pairs listed in Table 1. The latter findings indicate that not only the electrostatic attraction but also the hydrophobic interaction among polyion chains has important roles in polyion complexation in aqueous solution.

Table 1 List of typical polyanion–polycation pairs investigated in aqueous solution
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In dilute solutions, polyion complexes often do not precipitate but become colloidal particles in the same way as hydrophobic colloids of low molar mass salts, such as AgI.10 Colloidal polyion complexes have also been studied for many years, mainly by viscometry and light scattering. Some colloidal polyion complexes3, 5, 11 were reported to decrease in size with increasing ionic strength, but the opposite ionic strength dependence has also been reported,12 demonstrating that polyion complexation is not a simple phenomenon. As discussed below, the irreversibility of the complexation makes the phenomenon more complicated.

In this study, we conducted static light scattering measurements on colloidal polyion complexes formed by NaPA and poly(vinyl ammonium) chloride (PVACl) in water of neutral pH. Although PVACl is a polycation of the simplest chemical structure bearing primary amine groups, only a few studies have been performed on polyion complexation of this polycation.12, 13 This study focuses on the dependences of the colloidal complex structure on the mixing ratio and polymer-chain-length ratio of NaPA and PVACl to elucidate the mechanism of complex formation.

Experimental procedure

Samples

Free radical polymerization of N-vinyl formamide was conducted in a mixed solvent of formamide/2-propanol (1:9, vol/vol) under an argon atmosphere at 70 °C using 2,2′-azobisisobutyronitrile as the initiator. The obtained polymer sample was divided into several fractions by repeated fractional precipitation with water as the solvent and acetone as the precipitant. The weight-average degrees of polymerization n+ and the polydispersity indices Mw/Mn of the three intermediate fractions of poly(N-vinyl formamide) were determined by size-exclusion chromatography equipped with an online multi-angle light scattering detector (SEC-MALS; DOWN DSP, Wyatt Technology, Santa Barbara, CA, USA) using 0.1 M aqueous NaCl as the eluent. The results are listed in Table 2.

Table 2 Molecular characteristics of NaPA and PVACl samples used
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The three intermediate fractions and an unfractionated sample were hydrolyzed in 1.5 M NaOH solution at 80 °C for 24 h under reflux, dialyzed against water for a week, and neutralized with HCl to convert the ions to their hydrochloric salts. For the unfractionated PVACl930 sample after hydrolysis, n+ was determined by the batch measurement of static light scattering (see below and Table 2).

The polymer of tert-butylacrylate was obtained by the reversible addition-fragmentation chain transfer polymerization in dimethyl formamide under an argon atmosphere at 70 °C, purified by reprecipitation using a methanol/water mixture as the precipitant, and hydrolyzed in 2 M HCl solution at 120 °C for 24 h under reflux. The obtained sample was dialyzed against water for a week and neutralized with NaOH to convert it to the sodium salt. The weight-average degree of polymerization n− and Mw/Mn of the NaPA sample (NaPA110) were determined by SEC-MALS (Table 2). Two stock NaPA samples14 (NaPA370 and NaPA600) and an anionically polymerized commercial NaPA sample (NaPA300; Polymer Source, Quebec, Canada) were added for the following experiments.

Preparation of test solutions

Freeze-dried samples of NaPA and PVACl were dissolved into pure water separately to make dilute solutions of the same initial concentration c0 at neutral pH. Then, the solutions of NaPA and PVACl with volumes V− and V+, respectively, were mixed at room temperature to form the polyacrylate–poly(vinyl ammonium) (PA–PVA) complex. In the following text, the polymer composition in the mixed solution is expressed in terms of the mole fraction x− of the carboxy group calculated from x−=(V−/M0,−)/[(V−/M0,−)+(V+/M0,+)], with M0,− and M0,+ representing the molar masses of the NaPA and PVACl monomer units, respectively.

Nuclear magnetic resonance measurements

Two pairs of aqueous NaPA and PVACl solutions with a relatively high concentration (c0=5.0 × 10−4 g cm−3) were mixed with different x− and kept standing for ∼12 h. The mixed solution was slightly turbid and was therefore centrifuged at 9000 r.p.m. for 1.5 h. The obtained precipitate was dried in vacuo overnight and dissolved in D2O with NaOD (pD≡−log [D+]=13) to make a 1H-nuclear magnetic resonance (NMR) measurement at 30 °C using a JEOL JNM EX270 MHz or GSX400 spectrometer (JEOL Ltd, Tokyo, Japan). Chemical shifts were determined using 2,2-dimethyl-2-silapentane-5-sulfonic acid as the internal reference.

Light scattering

When the total polymer concentration c0 was less than 1 × 10−4 g cm−3 and x− was not close to 0.5, the aqueous NaPA−PVACl mixtures were almost transparent. Static and dynamic light scattering measurements were performed on these mixtures at 25 °C using an ALV/SLS/DLS-5000 light scattering instrument (ALV, Langen, Germany) with an Nd:YAG laser operating at 532 nm or an Otsuka Electronics DLS-7000DL instrument (Otsuka Electronics Co. Ltd, Hirakata, Japan) with an He–Ne laser of 633 nm. Each of the NaPA and PVACl solutions was filtered with a 0.20-μm cellulose acetate membrane filter before mixing. The measurements were performed at least 6 h after mixing, and the scattered light intensity did not change with time.

NMR analyses indicated that the NaPA and PVACl solutions formed a stoichiometric complex consisting of equal numbers of PA and PVA monomer units in the aqueous solution of the NaPA–PVACl mixture with any x−. Therefore, the mixture solution contains the (almost) neutral PA−PVA complex (component 2) and the excess component (that is, PVACl at x−<0.5 and NaPA at x−>0.5; component 1). Light scattering theory gives us the following equation for the dilute ternary solution:15

On the left-hand side, K is the optical constant, c is the total polymer mass concentration and Rθ is the excess Rayleigh ratio at the scattering angle θ of the mixture solution over that of the solution containing only the excess component. On the right-hand side, wi, Mi, Pi(θ) and γi are the weight fraction (of the total polymer), molar mass, particle scattering function and refractive index increment of species i (=1, 2), respectively, and A2,ij is the second virial coefficient between species i and j. If the complex (component 2) is stoichiometric, the following equations hold for w2 and γ2:

By differential refractometry, γ− of NaPA and γ+ of PVACl were determined to be 0.185 cm3 g−1 and 0.234 cm3 g−1, respectively, and γ2 was calculated to be 0.207 cm3 g−1 from equation (2), which was used to calculate the optical constant K in equation (1).

The scattering intensity was enhanced by mixing the NaPA and PVACl solutions to such a degree that Rθ in equation (1) was approximated by the excess Rayleigh ratio of the mixture solution over that of the solvent, and the A2,12 term in parentheses on the right-hand side of equation (1) was neglected. For polydisperse colloidal solutions, M2 and P2(θ) should be regarded as the weight-average value and z-average function, respectively. In what follows, M2 and the radius of gyration obtained from P2(θ) are denoted as Mw and 〈S2〉z1/2, respectively, and A2,22 simply as A2.

Dynamic light scattering provides the intensity autocorrelation function g(2)(t). The first cumulant Γ and the hydrodynamic radius RH were determined from g(2)(t) using the equations

where kBT is the Boltzmann constant multiplied by the absolute temperature, and η0 is the solvent viscosity.

Electrophoretic light scattering measurements on some NaPA–PVACl mixture solutions (c0=c=1 × 10−4 g cm−3) were conducted using an Otsuka Electronics zeta-potential analyzer ELSZ-2 (Otsuka Electronics Co. Ltd). From the Doppler shift frequency, Δω, obtained by electrophoretic light scattering, the apparent electrophoretic mobility, Uapp, was estimated using the equation

where E is the strength of the applied electric field and k is the magnitude of the scattering vector. The true electrophoretic mobility U was obtained after correcting for the electro-osmotic effect.16

The zeta potential of the colloid surface was calculated using the Smoluchowski equation17

where ɛ0 is the electric constant and ɛr is the relative permittivity of the solvent. The Fujita–Hermans theory18 gives us the following equation for the electrophoretic mobility U of spherical particles

where nC, e and κ are the total charge number of a spherical particle, the elementary charge and the inverse of the Debye length, respectively.

Results

Stoichiometry of the PA–PVA complex

Figure 1 shows the 1H-NMR spectra of the PA–PVA complex precipitated from aqueous solutions of NaPA600 and PVACl630 mixtures with different x− and then dissolved in alkaline D2O. From the peak areas around δ=1.5 p.p.m. (methylene group of PA and PVA; Aa), 2.2 p.p.m. (methine group of PA; Ab) and 3.0 p.p.m. (methine group of PVA; Ac), we have estimated the amounts of the PA and PVA monomers in the precipitated complexes. As shown in Table 3, the PA and PVA monomers are equimolar in the complex irrespective of x−. The same result was also obtained for the complex formed from NaPA110 and PVACl930 mixtures, demonstrating that the PA–PVA complex is stoichiometric, in agreement with the reports for many other polyion complex systems.

Figure 1
figure 1

1H-nuclear magnetic resonance spectra of polyacrylate–poly(vinyl ammonium) complexes formed in aqueous solutions of NaPA600 and PVACl630 mixtures with different x− values. NaPA, sodium poly(acrylate); PVACl, poly(vinyl ammonium) chloride.

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Table 3 Ratio of carboxy to ammonium groups in precipitates of the PA–PVA complex from aqueous solutions with different n−, n+ and x−, estimated by 1H-NMR in alkaline D2O solution
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Table 4 lists the zeta potential ψζ of colloidal PA–PVA complexes calculated from the electrophoretic mobility U obtained by electrophoretic light scattering at c0=c=1 × 10−4 g cm−3. The sign of the zeta potential is the same as that of the excess polymer component, indicating that the PA–PVA complex is charged by the excess components from the NaPA–PVACl mixture solution. This appears to be inconsistent with the 1H-NMR results listed in Table 2. To check for consistency, we calculated the number of net charges nC for a polyion complex from equation (7) and the value of [COO−]/[NH3+]=(N0,w−nC)/(N0,w+nC) contained in a polyion complex from nC and the total number N0,w of monomer units per polyion complex; N0,w can be calculated from the molar mass Mw of the complex (see below) by N0,w=2Mw/(M0,−+M0,+). The calculated values of [COO−]/[NH3+] listed in Table 3 are very close to unity, being consistent with the results of NMR measurements within experimental error. Thus, we conclude that the PA–PVA complex is almost stoichiometric and then neutral, but a tiny amount of the excess polyelectrolyte component is adsorbed on the neutral polyion complex colloids.

Table 4 Electrophoretic light scattering results for colloidal complexes formed from NaPA110 and PVACl930 at c0 (=c)=1 × 10−4 g cm−3
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Dependence on the method used to prepare polyion complex solutions

Because the polyion complex is formed by mixing NaPA and PVACl solutions, the mixing method may affect light scattering results. To determine the effect of the mixing method, we prepared the complex solutions using the following two methods prior to light scattering measurements:

Method 1: A NaPA solution was added dropwise into a PVACl solution rapidly (during ∼20 s) to prepare test solutions, and the mixture was stirred vigorously for ∼1 h.

Method 2: A NaPA solution was poured gently on a PVACl solution in a light scattering cell from the cell wall, and the layered solution was kept standing for 24 h before stirring.

Light scattering measurements were performed several times on test solutions prepared using Methods 1 and 2 (c0=c=3.0 × 10−5 g cm−3, x−≈0.3). R0/Kcw2 values were (0.94±0.19) × 108 g mol−1 and (15.5±11) × 108 g mol−1 for solutions prepared using Methods 1 and 2, respectively, where R0 is the value of Rθ extrapolated to the zero θ and R0/Kcw2 is approximately equal to the weight-average molar mass Mw in dilute solution. Although variance of the results were rather large for solutions prepared using Method 2, it is clear that Method 2 produces larger colloidal polyion complexes than Method 1. In Method 2, the solution is more heterogeneous, so that polyion complexes formed during the early stage may travel through the PA-rich and PVA-rich regions in the solution many times, growing by adsorbing PA and PVA chains each time.

Figure 2 presents light scattering results for solutions of NaPA110 and PVACl930 (c0=c=1.0 × 10−4 g cm−3) prepared using Method 1, with x− initially set to 0.25 and then changed between 0.25 and 0.45 by iterative additions of NaPA and PVACl solutions of the same polymer concentration c0. When the NaPA solution was added (unfilled circles), R0/Kcw2 increased and colloidal particles grew, but when the PVACl solution was added (filled circles), no colloidal growth was observed. The results shown in Table 4 show that the colloidal polyion complex is positively charged at x−<0.5, so that the complex can only adsorb the anionic PA added to grow and does not dissociate on PVACl addition.

Figure 2
figure 2

Change in the R0/Kc value for solutions of NaPA110 and PVACl930 with increasing and decreasing x−. NaPA, sodium poly(acrylate); PVACl, poly(vinyl ammonium) chloride.

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The results of the above two light scattering experiments indicate the irreversibility of the PA–PVA complexation and the importance of the method used to prepare the test solution.

Characteristics of the PA–PVA complex colloid

Taking into account the results mentioned above, we performed light scattering on test solutions prepared using Method 1 (c0=3.0 × 10−5 g cm−3) by adding NaPA solution to PVACl solution for x−<0.5 and adding PVACl solution into the NaPA solution for x−>0.5 and diluted with pure water to obtain different total polymer mass concentrations c. Figure 3 shows an example of the Zimm plot for a colloidal PA–PVA complex in aqueous solution. Similar Zimm plots were obtained for other mixtures of NaPA and PVACl samples with different compositions. The common intercept and slopes of the plots at c=0 and k=0 indicate the weight-average molar mass Mw, the z-average radius of gyration 〈S2〉z1/2 and the second virial coefficient A2 (cf. equation (1)).

Figure 3
figure 3

Zimm plot for colloidal polyion complexes formed by mixing aqueous solutions of NaPA110 and PVACl930 of c0=3 × 10−5 g cm−3 with x−=0.426. NaPA, sodium poly(acrylate); PVACl, poly(vinyl ammonium) chloride.

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In Figure 4, the results of Mw obtained for different pairs of NaPA and PVACl samples are plotted against the composition x−. The total aggregation numbers of the polymer chains calculated from Mw by Mw(n−−1+n+−1)/(M0,−+M0,+) range from 400 to 8000, indicating that polyion complexes consist of a large number of polymer chains.

Figure 4
figure 4

Dependence of the weight-average molar mass on the composition of different pairs of sodium poly(acrylate) and poly(vinyl ammonium) chloride samples. Curves indicate values calculated by equation (11) using MN=0 and Λ=3 × 1010 (g mol−1)2/3 at x−<0.5 and Λ=1 × 1011 (g mol−1)2/3 at x−>0.5.

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For all the pairs of NaPA and PVACl samples investigated, Mw mostly increases as x− approaches 0.5 from both sides. PA–PVA complexes formed in solutions with x− very close to 0.5 precipitated, and light scattering measurements were impossible. This is similar to hydrophobic colloids of low molar mass salts such as AgI, which precipitates in an equimolar reaction of AgNO3 and KI in water.10

The dependence of the Mw of the PA–PVA complex on composition seems to be asymmetric at x−=0.5 in Figure 4. We will discuss this asymmetry in the next section. On the other hand, the dependence of Mw on the degrees of polymerization n− and n+ is less clear than the dependence on composition. The PA–PVA complex consists of so many polyelectrolyte chains that the molecular characteristics of the component polyelectrolytes may not have a major role in the complexation.

Dautzenberg5 reported a similar composition dependence of Mw for the mixture of sodium poly(methacrylate) and poly(diallyl-dimethylammonium chloride) in water, but the opposite dependence for the mixture of sodium poly(styrene sulfonate) and poly(diallyl-dimethylammonium chloride) in water. The opposite dependence for the latter system appears to be inconsistent with his observation of macroscopic flocculation in stoichiometric mixtures of both systems (at x−=0.5). He prepared test solutions for static light scattering measurements by adding the polyanion or polycation solution into the counterpart solution slowly and stepwise approaching an x− value of 0.5. During the stepwise dosage, the free chain concentration of the excess polyelectrolyte component decreases, and highly aggregated polyion complexes might form at the first dosage for the more hydrophobic sodium poly(styrene sulfonate) and poly(diallyl-dimethylammonium chloride) system.

Figure 5a shows the Mw dependences of 〈S2〉z1/2 of the colloidal PA–PVA complexes prepared for different NaPA and PVACl sample pairs at different x− values. Although the data points are rather scattered, most seem to follow a common line with a weak slope. The line shown in the figure has a slope of 1/3, expected for uniform density spheres, and yields an internal polymer concentration cc (=3Mw/4πNA(5〈S2〉z/3)3/2; NA: the Avogadro constant) of the spherical colloidal complex of 4.5 × 10−3 g cm−3. Therefore, the PA–PVA complex colloid contains a large amount of water, in sharp contrast to the colloidal complex of sodium poly(styrene sulfonate) and poly(diallyl-dimethylammonium chloride), where cc is on the order of 0.5 g cm−3.5 This contrast may be due to the difference in hydrophobicity between the two polyion complexes.

Figure 5
figure 5

Molar mass dependences of (a) the radius of gyration and (b) the ratio ρ obtained for different sodium poly(acrylate) and poly(vinyl ammonium) chloride sample pairs at different x− values.

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Figure 5b presents the ratios ρ of 〈S2〉z1/2 to the hydrodynamic radius RH obtained by dynamic light scattering. The data points are scattered around 1.5. Although we expect ρ=0.775 for monodisperse uniform-density spheres, polydispersity increases ρ. Spheres with a logarithmic normal distribution of Mw/Mn=4 have a ρ-value of 1.5.19 Furthermore, a linear Zimm plot as shown in Figure 3 (instead of the Guinier plot) is expected for the polydisperse spherical system of Mw/Mn=4.

Second virial coefficients for the colloidal PA–PVA complexes in aqueous solution ranged from 0 to 1 × 10−4 cm3 mol g−2, irrespective of n−, n+ and x−. These values indicate that the colloidal complexes are almost neutral, consistent with the electrophoretic light scattering results shown in Table 4.

Discussion

In polyion complexation, the electrostatic and hydrophobic interactions among oppositely charged polymer chains interact to give rise to complicated dependences on various experimental conditions. This section uses a simple model schematically illustrated in Figure 6 to interpret the composition dependence of Mw shown in Figure 4. When mixed, polyanion and polycation chains form neutral complexes N, initially due to electrostatic interactions (step 1), followed by the aggregation of neutral complexes due to hydrophobic interactions (step 2). If the system is a non-stoichiometric mixture of polyanions and polycations, then the excess component chain E may adsorb on the growing aggregate Nm to form charged colloids N m E m E (step 3), and when the net charge nC of N m E m E attains a critical value nC*, the growth of N m E m E stops20 (step 4). The value of nC* should depend on the strength of the hydrophobic interactions of N m E m E and on the ionic strength. Steps 2 and 3 occur simultaneously.

Figure 6
figure 6

Schematic illustration of the colloidal polyion complexation process. Polyelectrolyte chains and colloidal polyion complexes are symbolically represented as unrealistic segments and rectangular objects, respectively. A full color version of this figure is available at Polymer Journal online.

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Step 1 may occur rapidly just after mixing the polyanion and polycation solutions. We choose the end of this step to be time t=0 and assume N at t=0 to be monodisperse spheres of a molar mass MN. Step 2 may be treated as the rapid coagulation of colloidal particles, which can be explained by the Smoluchowski theory.21 This theory gives the time dependence of the weight-average molar mass Mw of colloidal particles N by the equation:

where kBT is the Boltzmann constant multiplied by the absolute temperature, c0 is the total polymer mass concentration and η0 is the solvent viscosity. The radius R of the colloidal particle can be calculated from 4πR3cc/3=Mw/NA, where cc is the polymer mass concentration inside the particle.

The excess component E adsorbs on the growing colloidal particle surface (step 3). The rate of adsorption dmE/dt should be proportional to the surface area 4πR2 of the colloidal particle and to the molar concentration CE of the E chain:

with the rate constant kads. So little adsorption occurs that the change in CE over time can be ignored, and the number mE of E chains adsorbed on a particle can be expressed as

In the late stage, both colloidal growth and E chain adsorption should slow down because of the charging of the colloidal particles (slow coagulation). Although Equation (10) applies to rapid coagulation, we use approximately the same relationship between mE and Mw for slow coagulation, assuming that the colloidal growth and E chain adsorption decelerate at the same rate. Finally, in step 4, the colloids stop growing when the net charge nC (=mE multiplied by the degree of polymerization nE of the E chain) reaches the critical value nC*. The Mw of the stable colloid particle is then given by

where M̄0 is the average molar mass of the monomer units [= x−M0,−+(1−x−)M0,+]. We used the relation CEnE=103∣1 – 2x−∣c0/M̄0.

In equation (11), kads should depend on the affinity between N and E as well as on the diffusivity of the E chain in the solution. That is, kads may be different at x−<0.5 (where E is PVA) and >0.5 (where E is PA) and dependent on nE. In Figure 4, solid curves indicate values calculated by equation (11) using MN=0 and Λ=3 × 1010 (g mol−1)2/3 at x−< 0.5 and Λ=1 × 1011 (g mol−1)2/3 at x−>0.5. Although the data points are scattered, the trend of composition dependence is almost reproduced by the curves. The smaller value of Λ at x−<0.5 implies that PVA has a greater affinity to the neutral complex N than does PA. The lack of importance of MN in equation (11) indicates that the unit neutral complex N formed in the early stage 1 is much smaller than the final stabilized colloids.

On the other hand, the dependences of Mw on n− and n+ are mostly not appreciable within experimental error, but the data points for (n−, n+)=(110, 930) (

) may be fitted by equation (11) with smaller Λ values than the data points for (n−, n+)=(370, 930) (□) and (600, 930) (▪) at x−>0.5. This may result from the high diffusivity of PA with the lowest n− among the three samples.

Conclusion

This study investigated colloidal polyion complexation by mixing aqueous solutions of NaPA and PVACl and characterizing the mixtures by static, dynamic, electrophoretic light scattering and 1H-NMR. The experimental results obtained here allowed us to propose a simple model for colloidal polyion complexation, illustrated in Figure 6.

The results of 1H-NMR indicated that the PA–PVA complex is almost stoichiometric, and we assumed that a neutral complex N was formed at the beginning. However, electrophoretic light scattering indicated that the PA–PVA complex is weakly charged by the excess polyelectrolyte component, from which we assumed the adsorption of excess polyelectrolyte chains onto growing colloids. This assumption was consistent with the composition dependence of the molar mass for the final stabilized PA–PVA colloid shown in Figure 4. The molar mass was not sensitive to the degree of polymerization of the constituent polyelectrolytes, and thus, the chain-length ratio of individual polyanions and polycations may not be important in the complexation.