Interactions between Sulfobetaine-Based Polyzwitterions and

J. Phys. Chem. B 2008, 112, 2299-2310

2299

Interactions between Sulfobetaine-Based Polyzwitterions and Polyelectrolytes Pascaline Mary† and Denis D. Bendejacq* Rhodia Centre de Recherche et de Technologie d’AuberVilliers, 52 rue de la Haie Coq, 93308 AuberVilliers, France ReceiVed: August 29, 2007; In Final Form: October 23, 2007

We investigate the interactions between sulfobetaine-based polyzwitterions and polyelectrolytes, either positive or negative ones, i.e., poly(DADMAC)s and poly(AA)s. Three different sulfobetaine motifs denoted SPE, SPP, and SHPP have been considered, presenting slight chemical changes either in the function carrying the zwitterionic group or in the zwitterionic motif itself. All three poly(sulfobetaine)s normally present critical temperatures (Tc) above which they become fully soluble. The association with polyelectrolytes directly affects the critical temperature in a highly nonmonotonic fashion as the mixture composition is varied. Thanks to layer-by-layer deposition in a reflectometric cell, we demonstrate that a selective attraction exists between polyzwitterions and polyelectrolytes, from which an association follows at a nanoscopic scale as demonstrated by small-angle X-ray scattering and atomic force microscopy. The association of polyzwitterions with polyelectrolytes, however, is site-specific since it exists only between positive polyelectrolytes (i.e., polycations) and polyzwitterions based on SPE or SPP motifs. The range in which the association affects the critical temperature, Tc, is found to largely depend on the molecular weights of both zwitterionic and cationic species. As a result, the complexation and the creation of a hybrid object, referred to as a complex, also depend on the same parameters. By varying the latter from a few thousands to several millions, we define rules for the existence of this complex. In particular, a minimum polyzwitterion molecular weight is needed to observe alterations of the critical temperatures and closure of the complexation cone. Finally, within a Flory-like approach, we consider the polyzwitterion/polyelectrolyte complex as an effective statistical copolymer, whose composition comprises a fraction φ j A of excess zwitterionic motifs as the majority species and a fraction 1 φ j A of complex motifs. We thereby reduce a polymer/polymer/solvent ternary system to a copolymer/solvent binary one, an assumption valid within the limit of small additions of cationic species. The approach predicts the reciprocal critical temperature 1/Tc to be quadratic in φ j A, which agrees very well with all experimental results, even for a large mismatch between the molecular weights of both species, and regardless of the zwitterionic motif, SPE or SPP.

1. Introduction In the living, the interactions between macroions, such as polyampholytes polyelectrolytes, and charged species such as charged micelles or colloidal objects, play a fundamental role. Numerous reports can be found on complexes of a polyelectrolyte and a species of opposite charge, such as another polyelectrolyte,asurfactantmicelle,1-3 orinorganicnanoparticles.4-7 The theoretical description of the complexation between conventional macroions has been the object of a recent review.8 Proteins, RNA strands, and DNA strands generally interact in complex ways, which are often site-specific. Protein/polyelectrolyte complexations have been reported experimentally by several teams active in this field over the past decade9 (in particular those of Dubin et al.10 and Prausnitz et al.11) with valuable practical outcomes. Protein separation12 and their controlled release,13 for instance, can benefit from complexation with polyelectrolytes. Such an association mainly relies on a genuine polarization-induced attraction between protein and polyelectrolyte species, as demonstrated by recent simulations,14 and on the entropic gain originating from the phenomenon of counterion release.15 From an experimental viewpoint, several * Corresponding author. E-mail: [email protected]. † Current address: Ecole Supe ´ rieure de Physique et Chimie Industrielles (ESPCI), 10, rue Vauquelin, 75005 Paris, France.

studies have evidenced the role of different structural parameters in protein/polyelectrolyte associations. In practice, the characteristics of the polyelectrolyte species are more easily tunable than those of the protein, and constitute the majority of the reports. The polyelectrolyte molecular weight,8 its persistence length,16 and its stiffness17,18 were all found to affect the association with proteins, although the latter remains highly site specific. Recently, polyampholytes (which may be considered as model proteins) have attracted a lot of attention. As was found with proteins, the interaction of polyampholytes with polyelectrolytes depends on the microstructure of the polyampholyte species itself:14,19,20 the association is a function of the polyampholyte/polyelectrolyte charge balance, and also of the blocky, statistical, or alternated character of the charge sequences. This strongly resembles the concept of site specificity in the binding of proteins with polyelectrolytes, yet remains to be verified. The first experimental reports of their association with polyelectrolytes dates back to the early 1990s, with several reviews over the past decades.21,22 However, there is little understanding of the structure at a microscopic level, and only recent simulations have started exploring this aspect of the problem. Although the association of polyzwitterions with polyelectrolytes has not been considered yet, we foresee that similar concepts may apply. The principle of site specificity, for

10.1021/jp0769274 CCC: $40.75 © 2008 American Chemical Society Published on Web 01/30/2008

2300 J. Phys. Chem. B, Vol. 112, No. 8, 2008 instance, could be explored with polyzwitterions far more easily than with polyampholytes, whose synthesis and preciseness (in terms of microstructure) remain a true challenge. As pointed out in our previous study,23 fundamental structural differences exist between polyzwitterions and polyampholytes. While polyampholytes bear positive and negative charges borne by different monomers not necessarily in equal numbers or evenly distributed along the backbone, polyzwitterions bear both charges on the same monomer, therefore de facto in equal numbers and evenly distributed. Even more importantly, the fundamental difference between polyzwitterions and polyampholytes resides in the asymmetry of the dipoles borne by the polymer backbone.24 For these reasons, polyzwitterions can be expected to have very selective, charge-specific interactions resembling those of proteins with other charged species, such as salts, surfactants, and polyelectrolytes. In a recent publication,23 we explored the interaction of sulfobetaine-based polyzwitterions with simple monovalent salts. Electrolytes indeed generally lead to an enhancement of the solubility of polyzwitterions. The macroscopic consequence of this feature, known as the “anti-polyelectrolyte effect”, is the decrease of the upper critical solution temperature (UCST) displayed by these polymers. However, because of the site specificity of the associations, the types of zwitterionic group and electrolytes used often dictate the extent of solubility promotion. In the present study, we investigate whether replacing a monovalent salt with a polymeric one matters. Early on, poly(sulfobetaine)s were indeed reported25 to have a specific interaction with polyelectrolytes and to form a complex, although no structural proof was provided. The conditions for the existence of a complex were not fully elucidated at the time, and no microscopic vision of the association is available. In recent years, however, several studies pertaining to the interactions between polyelectrolytes and proteins, polyampholytes, or polyzwitterions have started and tried to elucidate these features. Mincheva et al.26 or Ibraeva et al.27 have considered complexes between pH-dependent polyampholytes and polyacids or polybases. Schwarz et al.28 investigated mixtures of a weak polyzwitterion, i.e., poly(carboxybetaine), and a weak polyanion, i.e., poly(maleic acid-co-propene), which is the only report in the literature close to our investigations. Here, we explore the interaction between poly(sulfobetaine)s as model polymers bearing positive and negative charges and either negative or positive polymeric electrolytes, i.e., poly(acrylic acid)s and poly(diallyldimethylammonium chloride)s, respectively. We demonstrate the existence of an attraction using layerby-layer deposition thanks to a reflectometric setup. We explore the dependence of this association and map the conditions for the existence of polyzwitterion/polycation complexes, by varying (i) the molecular weights of the two species, mostly that of the polyzwitterion, by varying its degree of polymerization by 2 orders of magnitude; (ii) the type of zwitterionic motif, i.e., poly(SPE), poly(SPP), or poly(SHPP), presenting slight variations in the zwitterion chemical structure (see Table 1); and (iii) the ionic force of the solution. In solution, the association leads to the formation of a nanometer-sized object, as evidenced by small-angle X-ray scattering (SAXS) and atomic force microscopy (AFM). An interaction therefore exists, although not necessarily in the vicinity of the 1:1 stoichiometry between electrolytic and zwitterionic motifs. We will demonstrate that the polyzwitterion/polyelectrolyte association is site-specific since it appears only with the polycations tested, and not with weak polyanions of acrylic acid. In addition, both the existence and strength of the association depend on the zwitterionic motif

Mary and Bendejacq itself, very much like the interaction with simple salts.23 Therefore, the association of a polyzwitterion and a polyelectrolyte can be completely controlled, altered, enhanced, or suppressed by very small changes in the molecular structure of the zwitterionic function, or by carefully choosing which polyelectrolyte it must be mixed with. 2. Materials and Methods 2.1. Polymer Synthesis and Preparation of Polymer Mixtures. The synthesis and purification of the poly(sulfobetaine)s used have been described in our previous paper.23 To the two poly(SPE) and poly(SPP) families already reported on, we add the poly(SHPP) one (see Table 1). For these three families, we consider number-average molecular weights ranging from a few tens of thousand to several million grams per mole. Poly(DADMAC)s with molecular weights 150 and 450 kg/mol were purchased from Aldrich, dialyzed in a Spectra Por membrane of molecular weight cutoff 8 kg/mol to get rid of any electrolytes, and freeze-dried. Poly(acrylic acid)s, with molecular weights ranging from 2 to 3000 kg/mol, were purchased from Aldrich and used as received. Mixtures of polyzwitterions and polyelectrolytes were done by first dissolving the poly(sulfobetaine)s and then adding a known volume of a polyelectrolyte solution. For the sake of convenience, all mixtures were done at a constant poly(sulfobetaine) weight fraction, i.e., cpZ ) 0.3 wt %, while the polyelectrolyte concentrations were varied. The molar ratio

r ) nE /nZw

(1)

between the number nE of electrolyte monomeric motifs and that nZw of zwitterionic ones, was varied from 0 (i.e., a pure polyzwitterion solution) to +∞ (i.e., a pure polyelectrolyte solution). Considering the constant concentration of 0.3 wt % polyzwitterion, nZw is in fact set to about 10-2 mol/L. 2.2. Critical Temperature and Conductivity Measurements. The critical temperatures of the solutions of the poly(sulfobetaine)s, of the polyelectrolytes, and of their mixtures, were determined as described in our previous paper, using a homemade temperature-controlled Jackson turbidimeter. The conductivity was measured with a Orion conductimeter. 2.3. Reflectometry. The polymer solutions prepared for critical temperature measurements and for the SAXS experiments were diluted to 25 ppm and used for reflectometric experiments carried out at the Rhodia’s Centre de Recherches et de Technologies d’Aubervilliers (CRTA), France. Silicon wafers used had a 100 nm SiO2 top layer. The principles of reflectometry are briefly detailed. The method relies on a polarized He-Ne laser beam (wavelength λ ) 632.8 nm), which penetrates a cell through a prism at the Brewster angle for a water/silicon interface and hits the silicon wafer. The reflected beam is then separated into two components, one perpendicular and one parallel, whose intensities Is and Ip are measured with photodiodes. The reflection of the incident beam occurs at the stagnation point, where no flow exists, to prevent any coupling between the transport of the species and their organization at the surface of the wafer. The flow of the polymer solution must be laminar and on the order of a few milliliters per minute. The quantity measured as a function of time during the adsorption is ∆S ) S - So (in volts), where So is the value of ratio Ip/Is in the presence of solvent alone in the cell and S is the value when the polymer solution is flushed. To compute the adsorbed amount Γ, a sensitivity factor AS is determined by modeling the wafer, the SiO2 layer, the adsorbed polymer layer,

Polyzwitterion-Polyelectrolyte Interactions

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TABLE 1: Specimen Characteristics: Type, Chemical Names, Topological Formulas, Absolute Average Molecular Weights as Measured by MALLS, and Computed Degrees of Polymerization of the Different Families of Poly(sulfobetaine)s

and the above water layer (considered as infinite) as stacked diopters. The factor depends on the wavelength of the laser, the angle of incidence, the thickness of the adsorbed layer, the refractive indices of the solvent and the substrate layers, and the increment of refractive index ∂n/∂cpZ,pE of the different polymers and mixtures, determined here thanks to an absolute refractometer. AS is then computed using the Fresnel coefficient of each layer according to the Snell-Descartes refraction laws. From this, the calibration ratio AS was computed and the adsorbed amounts

Γ ) (1/AS)∆S/So

(2)

(in milligrams per square meter (mg/m2)) are deduced. Reflectometric curves are usually indicated in arbitrary units of ∆S/ So and have not been transformed into adsorbed amounts Γ in mg/m2 simply because the calibration factor AS for a multilayered system is much more difficult to assess since the thickness of each layer remains unknown to conventional reflectometry. For mathematical reasons related to the theory of reflectometry, AS is designed to be nearly independent of the adsorbed polymer layer when the deposit is made of a unique layer. It is not so when the system is multilayered, and ∆S/So cannot be easily transformed into adsorbed amounts, as often pointed out in the earlier reports on multilayers.29 A new method involving the use of two different oxidized substrates30 has been shown to

successfully allow the simultaneous measurements of thickness and adsorbed amounts by optical reflectometry. However, this goes far beyond the conventional experimental setup, and we restricted ourselves to ∆S/So signals when multilayers were involved, and to absolute deposited amounts only in the case of a monolayer. 2.4. Structural Characterizations in Solution and on Surfaces. Small-angle X-ray scattering experiments were carried out on 1 mm capillaries filled with selected solutions at 0.3 wt % poly(sulfobetaine), using the Nanostar setup at the Centre de Recherche Paul Pascal (CRPP) in Bordeaux, France. Selected silicon wafers resulting from the reflectometric experiments were simply taken out of the reflectometric cell, air-dried, and directly imaged using an atomic force microscope in tapping mode, at the Rhodia Centre de Recherches et de Technologies de Lyon, France. 3. Results and Discussion 3.1. Evidence of an Interaction between Polyzwitterions and Polycations. Figure 1a shows the example of a sequenced adsorption of polyzwitterion SPE1611 and polycation DADMAC2778. This allows the construction of layer-by-layer systems (as schematically represented in the inset) very much like what is known for polyanion/polycation multilayers both theoretically31 and experimentally.32 In the example shown, a poly-

2302 J. Phys. Chem. B, Vol. 112, No. 8, 2008

Mary and Bendejacq

Figure 2. Critical temperatures Tc’s of SPE1611/DADMAC2778 mixtures as a function of molar ratio r. We schematically represent the structure envisioned for the object formed: in the cone tip, a globular object; on either side of the cone tip, a core-shell object comprising a core made of the minority component, and a shell made of the minority one (see text for details).

Figure 1. (a) Example of a layer-by-layer deposition using reflectometry: relative signal ∆S/So detected upon sequential deposition of polyzwitterion SPE1611 and polycation DADMAC2778 each at NaCl background concentration 0.01 mol/L and polymer concentration of 25 ppm. Inset: Schematic representation of a multilayer system. (b) Superimposition of three different layer-by-layer depositions. For the sake of clarity, the curves have been vertically shifted with a constant of either +0.5 or +1.0 (in units of ∆S/So). Inset: Master curve obtained by appropriately shifting each section, according to the beginning of an injection sequence of a given polymer species (indicated by the arrows in both figures).

(SPE) is first flushed into the reflectometric cell and adsorbs onto the silicon wafer as already reported in the literature,33 and also onto silica particles.34 Beyond this first layer, the following poly(DADMAC) and poly(SPE) adsorptions are highly reproducible and present the same adsorption kinetics and plateaus. Figure 1b shows several curves coming from different layer-by-layer depositions, in which the injection times of each polymer species were varied. The curves completely superimpose (see the master curve in the inset) provided the different segments are appropriately shifted in time. This quite simple experiment irrevocably demonstrates the existence of an attractive interaction between the polyzwitterions and polycations used. We now consider polyzwitterion/polycation mixtures in water and investigate how the association of the polyzwitterion with a polycation impacts its apparent critical temperature. For instance, Figure 2 shows critical temperatures of SPE1611/ DADMAC2778 mixtures as a function of molar ratio r. The behavior is highly nonmonotonic: (i) for r e rmin the critical

temperature measured slowly increases from the critical temperature of the pure polyzwitterion solution initially prepared; (ii) for rmin e r e r*, Tc then rapidly decreases as r is further increased; (iii) for r* e r e rmax, Tc increases again with r; (iv) for rmax e r, Tc sharply decreases as r is further increased (note: in the case represented here, rmin ) 0.02, r* ) 0.48, and rmax ) 9.46). In the last regime, Tc eventually falls under 0 °C when r reaches 100, that is, for a solution containing a vast majority of polycations. Expectedly, a polycation is fully soluble in water regardless of temperature in the 0-100 °C range, and as a result, would never present a critical temperature. The shape of this curve is in fact general and characteristic of the association between polycations and polyzwitterions. The details of the curve, however, depend on the nature of the zwitterionic motif, the degree of polymerization of the polycation or that of the polyzwitterion, as will be seen later on. We point out that the cone tip, i.e., the locus r* of minimum Tc, can significantly deviate from the 1:1 stoichiometry (i.e., r ) 1) between positive and zwitterionic charges. Considering the case of polycarboxybetaine/polyanion mixtures investigated by Schwarz et al.,28 this does not seem coincidental and must be related to the size, compaction, or structure of the complex formed. For now, however, we have no microscopic vision of what the complex looks like, which would greatly help in understanding its physics. SAXS experiments allow characterizing the object formed in solution. Figure 3a shows the intensity I(q) scattered by different SPE1611/DADMAC2778 mixtures: (i) for r ) 0 (i.e., pure polyzwitterion solution) and r ) +∞ (i.e., pure polycation solution), the scattered intensity is very low and the SAXS spectra show no discernible pattern (not displayed here); (ii) for r ) 0.104, 0.195, 0.47, 1.38, and 2.92, the scattered intensity sharply increases, with a maximum detected around r ) 0.195 (see inset in Figure 3a). The existence of a Porod regime in the largest q-window, where I(q) ∝ q-4, is well-defined especially for central compositions r ) 0.195, 0.47, and 1.38, all in the vicinity of the cone tip r* ) 0.48. The Porod regime, usually associated with the existence of a sharp interface in the medium,35 suggests that the complexation leads in solution to an object dense enough to scatter X-rays much more than each of its polymeric constituents taken separately. There is a difference of almost 1 order of magnitude in the scattering



Figure 3. (a) SAXS spectra obtained on SPE1611/DADMAC2778 mixtures for molar compositions r ) 0.104, 0.195, 0.47, 1.38, and 2.92. All curves show a Porod regime where the scattered intensity scales as q-4, although the lower (0.104) and upper (2.92) r values display data much more noisy in the higher q-range, suggesting the Porod regime disappears as one goes away on either side of the cone tip (r* ) 0.48) toward polyzwitterionrich or polycation-rich compositions. For the sake of convenience, the curves have been vertically shifted by multiplying with factors 1, 1, 20, 100, and 5000, respectively. Inset: Absolute intensities scattered at zero wave vector, as a function of the molar composition r. (b) Corresponding Guinier plots Ln I(q)/I(q f 0) vs q2. The straight lines are least-square fits to the experimental data. Inset: Radius of gyration of the objects from the fitting of the SAXS curves, as a function of composition r.

intensities of the SPE1611/DADMAC2778 mixture, which scatters the most (r ) 0.195), and its pure constituents (cf. inset in Figure 3a). On the other hand, for the lower (r ) 0.104) and upper (r ) 2.92) edge compositions shown, a Porod regime is difficult to assess because the data are much noisier.36 Figure 3b shows Guinier plots Ln I(q) vs -q2/3 at different r values. The radius of gyration Rg of the object formed can be extracted from the slope of the linear dependences observed at low enough wave vector so that qRg , 1.37 The values found are all on the order of a few nanometers (see lower inset in Figure 3b), with a minimum gyration radius Rg ) 6.9 nm measured at r ) 1.38, i.e., close to the 1:1 equimolar situation.38 Considering the absence of form factor oscillations (usually expected in the large q-window for objects well-defined in terms of shape and size), we conclude that the object is rather polydisperse, in either shape or size, although well-defined in terms of scattering profile. AFM is finally used to confirm the existence of well-defined objects. Reflectometry was first used to adsorb, on a silicon wafer, the mixture SPE1611/DADMAC2778 at r ) 2.92. After a plateau was reached in the adsorption isotherm, the wafer was taken out of the reflectometric cell, rapidly air-dried at room temperature, and directly imaged at the stagnation point using AFM. Figure 4a shows micrographs at different length scales. The deposit is not a homogeneous polymer layer but consists of nanometric aggregates evenly distributed on the surface. AFM also showed that flushing a pure polyzwitterion solution at the same concentration leads to a homogeneously covered surface (see Figure 4b) and not a patterned one. The existence of individualized nanoscopic objects in solution seems undeniable. An average radius RAFM ) 17.6 nm in this dry state, with a standard deviation σAFM ) 4.6 nm, is found using the 120

measurements of core radii (from Figure 4a). The values in the dry (AFM) and dispersed (SAXS) states are rather consistent. An estimation of the number of objects per unit area yields N ≈ 100 core-shell objects/µm2. The adsorbed quantity then reads

Γ ≈ dN(4πRcore3)/6

(3)

where d is the density of the object formed, approximated to unity given the densities dpoly(SPE) ) 1.38 g/cm3 and dpoly(DADMAC) ≈ 1.0 g/cm3 of its polymeric constituents. We then find an average deposit Γ ) 1.4 ( 0.9 mg/m2, while the adsorption isotherm of the SPE1611/DADMAC2778 mixture at r ) 2.92 gave Γ ) 3.4 mg/m2 (see Figure 5b). The discrepancy may have several origins, among which is the theory of reflectometry itself, which assumes a homogeneous polymer layer deposited on the surface, which is obviously not the case here with a nanostructured deposit. The agreement, however, is satisfactory. Until now, we have given examples using poly(SPE) and poly(DADMAC) polymers. In the following, we detail the site specificity of the interaction, by showing that the nature of the polyelectrolyte ingredient (anionic vs cationic), the nature of the zwitterionic group (SPP vs SPE), and, finally, the molecular weights of both species all contribute to modifying not only the position (in composition r and in temperature Tc) of the complexation cone, but also its very existence. 3.2. Rules for the Existence of a Complex. Polyanions Vs Polycations. In the present section, we set the poly(sulfobetaine) to SPE6442 for the sake of convenience and adopted a molar ratio r between acidic and zwitterionic motifs equal to 1 (i.e., 1:1 stoichiometry). On the other hand, we varied the degree of polymerization NpAA and ionization R of the polyanion family


Mary and Bendejacq

Figure 4. 5 × 5 µm2 AFM imaging in tapping mode (height contrast), of reflectometric deposits on a silicon wafer, of a SPE1611/DADMAC2778 mixture at r ) 2.92 (a) and pure SPE1611 at r ) 0 (b). In (a), the deposit is structured at a nanoscopic scale; the inset corresponds to a portion of a 2 × 2 µm2 picture, zooming in on individualized objects. In (b), the deposit is homogeneous on the surface. In each figure, the colors scale from 0 to 15 nm in height.

Figure 6. Reciprocal critical temperatures Tc’s vs conductivity σ of SPE6442/AAx mixtures at uncontrolled ionic force, where x corresponds to the polymerization degree of poly(acrylic acid)s, ranging from NpAA ) 28 to 41 667. In all measurements, the molar ratio r between acrylic acid and zwitterionic motifs is equal to 1 and the ionization degree R of the polyanions is equal to 1. The line is a guide for the eye.

Figure 5. (a) Number of objects found as a function of core radius RAFM, as extracted from the AFM pictures. The full line is a leastsquare fit to the experimental data according to a normal law D(R) ) [1/(2πσAFM2)1/2] exp[-(R - RAFM)2/(2σAFM2) for the distribution. The fit leads to an average core radius RAFM ) 17.6 nm and a standard deviation σAFM ) 4.6 nm. (b) Adsorption isotherm of the corresponding SPE1611/DADMAC2778 mixture at r ) 2.92, on an oxidized silicon wafer.

chosen, i.e., poly(acrylic acid)s. Two series of experiments were carried out: (i) for R ) 1 (i.e., full ionization of all acrylic acid motifs), NpAA was varied by 2 orders of magnitude, from NpAA ) 28 to 41 667; (ii) for a constant NpAA ) 41 667, R was varied from 0 to 1, by adding a strong base (i.e., NaOH) or a strong acid (i.e., HCl). No relation between Tc and NpAA or R could be deduced from both types of experiments; the results present no correlation between the two variables and the critical temperature measurements. However, measuring the conductivity σ of the mixtures, the correlation between Tc and σ becomes clear (cf. Figure 6). As the pAAs purchased were used as received, they contain uncontrolled amounts of salts. Varying their ionization by additions of NaOH or HCl cannot be done without modifying the ionic force as well. In other words, ionic force was not kept constant in either series of experiments. When ionic force is set to 0.1mol/L with a background addition of NaCl, all poly-

(SPE)/poly(AA) mixtures display the same critical temperature (on the order of 10 ( 0.5 °C), regardless of NpAA or R. The decrease in the Tc of a polyzwitterion upon a mixture with polyanions is thus only due to the increase in the ionic force of the solution. The idea of an interaction between polyzwitterions and polyanions and the existence of a complex are challenged. We selected the SPE6442/AA6250 mixture at r ) 1, R ) 1, and no background addition of NaCl. Its critical temperature being above room temperature, this mixture macroscopically phase separated when centrifuged at 20 000 rpm/min during 1 h. The clear water-rich upper phase was separated from the whitish lower one (supposedly polymer-rich) and titrated with a HCl solution at 0.1 mol/L. The titration revealed that all of the poly(acrylic acid) added resides in the upper phase, which irrevocably demonstrates that no interaction, and no complex, exists in the polyzwitterion/polyanion mixture investigated. Finally, polyzwitterions interact with polycations, yet not with polyanions of acrylic acid. This contradicts the work of Schwarz et al.,28 although the reactive species are not identical. Our understanding of the phenomenon, however, is that the interaction may also be selective precisely because the zwitterionic group is asymmetric: the negative sulfonate charge of the zwitterionic motif is located far from the backbone and is free to interact with a positive DADMAC motif coming from a polymeric species. On the contrary, the positive ammonium


Figure 7. Layer-by-layer deposition of DADMAC2778 and three types of zwitterionic motifs, i.e., SPE1611, SPP1404, and SHPP1654. Note that all polyzwitterions have similar polymerization degrees. For the sake of clarity, the curves have been vertically shifted with a constant of either +0.5 or +1.0 (in units of ∆S/So).

charges are located closer to the backbone: the interaction with a negative AA motif coming from a polymeric species is sterically hindered. As a result, the complexation of polyzwitterions with polyelectrolytes is site-specific. Effect of the Zwitterionic Group. Figure 7 shows the layerby-layer deposition of DADMAC2778 and two other types of polyzwitterions, namely SPP1404 and SHPP1654, whose zwitterionic motifs slightly differ from the SPE one presented until now. For the sake of comparison, the layer-by-layer deposition of SPE1611 and DADMAC2778 shown in the very beginning of the first section is superimposed. The three polyzwitterion chemistries SPE, SPP, and SHPP have similar degrees of polymerization: no parameter other than the nature of the zwitterionic group is varied. The layer-by-layer deposition of poly(SPP) and poly(DADMAC) strongly resembles that of poly(SPE) and poly(DADMAC), from which we conclude that an attractive interaction also exists between a SPP-based polyzwitterion and a polycation. Critical temperatures were also measured on SPP1404/DADMAC2778 mixtures as a function of composition r and compared to those of SPE1611/DADMAC2778 mixtures (cf. Figure 8). Both couples present a complexation cone with identical characteristic values of rmin, r*, and rmax. The only difference between the two sets of measurements is a vertical shift on the critical temperatures axis, nearly constant in the whole composition range. As shown in our previous study, poly(SPP)s have Tc’s systematically smaller than those of their poly(SPE)s equivalents. The constant shift in Tc in the SPP1404/DADMAC2778 mixtures is inherited from the nature of the zwitterionic motif itself. The complexation with a polycation therefore seems a general feature of SPE and SPP polyzwitterions. The strength of the complexation, however, could depend on the zwitterionic motif considered, although it is impossible for now to assess it. Only a quantitative analysis of the multilayering, implying the determination of the layer thicknesses, could help characterize this strength. On the contrary, the adsorption isotherm remains at the same plateau in spite of several alternated poly(DADMAC) and poly(SHPP) injections. No multilayering occurs with the SHPP chemistry, and we conclude that no interaction exists between a SHPP-based polyzwitterion and a polycation. It appears that the presence of an extra -OH group in the SHPP motif,


Figure 8. Critical temperatures Tc’s for SPP1404/DADMAC2778 and SPE1611/DADMAC2778 mixtures, as a function of composition r. For two polyzwitterions of similar degrees of polymerization and of SPE and SPP chemistries, the positions of the critical compositions r* and rmax are rather close.

compared to the SPP one, is sufficient to hinder the association with a cationic polymeric species. Note that, very much like usual polyelectrolytes, poly(SHPP)s are all fully soluble in water in the 0-100 °C range, even in salt-free conditions and regardless of the concentration in water. Although the attraction between ammonium and sulfonate groups is responsible for the phase separation in polyzwitterion solutions, the -OH function sufficiently alters the electronic environment to reduce the attraction and suppress phase separation. It seems logical that the drive responsible for the association of poly(SPE)s and poly(SPP)s with polycations is also suppressed in poly(SHPP)s. Impact of the Species Molecular Weights. We varied both molecular weights of the zwitterionic and cationic species, in order to investigate the evolution of the complexation cone. Figure 9a shows the evolution of the critical temperature of SPEy/DADMAC2778 mixtures, where the degree of polymerization y ) 177, 429, 1611, and 6442 of the SPE polyzwitterion was varied and that of the poly(DADMAC) kept constant. Figure 9b shows the evolution of the critical temperature of SPE6442/ DADMACx mixtures, where the degree of polymerization x ) 926 and 2778 of the DADMAC polycation was varied and that of the poly(SPE) kept constant. The features of the complexation cone obviously evolve as the polymerization degree of either species is varied. More precisely, in Figure 10, we plot as a function of the polymerization degree of the poly(SPE) species the positions rmax and r*. However, the data on the lower boundary rmin (not shown here) are not as well-defined; rmin roughly increases as NSPE is decreased from 6442 to 177. In the meantime, the upper boundary rmax of the cone decreases in the process. In other words, the complexation cone closes as the degree of polymerization of the polyzwitterion is decreased. On the other hand, the position r* of the cone tip increases. The three sets of data can be extrapolated to obtain the intersect, which corresponds to the minimum value NSPE* necessary to completely close the cone: we thereby determine that the polyzwitterion polymerization degree must be larger than ca. NSPE* ≈ 60. Similar results are obtained with the second poly(DADMAC) used. In particular, the critical value NSPE* seems general and independent of the polycation polymerization degree. The plots of r* and rmax show the well-defined scaling law r ∝ NSPEγ. The exponent γ ) +0.23 observed for rmax, however, seems independent of the polycation polymerization degree, while that observed for r* does: we find that γ ) -0.56


Mary and Bendejacq compositions, scaling arguments may be irrelevant to account for their evolution with the polymerization degrees of both species. We turn to a phenomenological Flory-like approach, able to explain the evolution of Tc with composition r over the whole range of the complexation cone. This mean-field approach relies on modeling how the complexation between zwitterionic and cationic motifs may alter the effectiVe interaction between the polyzwitterionic chains and the solvent water molecules, as explained in the following. 3.3. Modeling and Understanding the Shape of the Complexation Cone. General Remarks. The case of a binary system consisting of a polymer/solvent mixture, is well-known and has been treated in detail by Flory.40 His approach to the thermodynamics of polymers in solution relies on the simple balance between the chain entropy of mixing and the enthalpic cost of contacting monomer and solvent segments. The Gibbs free energy then reads

∆FM/kBT ) nS ln φS + nP ln φP + χS/PnSφP

Figure 9. Critical temperatures Tc’s vs composition r for (a) SPEy/ DADMAC2778 mixtures, with y ) 177, 429, 1611, and 6442; (b) SPE6442/ DADMACx mixtures, with x ) 926 and 2778. The lines are guides for the eye.

Figure 10. Positions rmax and r* which define the tip and upper boundary of the complexation cone vs polymerization degree Npoly(SPE) of the poly(SPE) species, for the two poly(DADMAC) polymerization degrees investigated Npoly(DADMAC) ) 926 and 2778 (see Figure 8). The lines are power-law fits to the experimental data. Contrary to the position of the upper boundary, that of the cone tip seems to depend on the polycation degree of polymerization, although displaying welldefined power laws in all cases.

for NDADMAC ) 2778 and γ ) -0.34 for NDADMAC ) 926. In this latter case, we suspect that the scaling observed is only apparent. Even if scaling laws are observed with these particular

(4)

where nS and nP are the number of solvent and polymer molecules, φS and φP are their volume fractions, and kBTχS/P = SP - (1/2)[SS + PP] is the Flory-Huggins (FH) interaction parameter between solvent molecules and polymer segments; SP, SS, and PP are the solvent/monomer, solvent/solvent, and monomer/monomer contact energies, respectively. The FH parameter thus corresponds to the change in energy associated with the formation of an unlike contact pair between polymer and solvent segments. Critical temperatures Tc’s are then often considered to be linked to the reciprocal FH parameter via χS/P = δH/Tc - δS, where δH and δS are the split enthalpic and entropic contributions, only depending on the chemistry of the species and its interaction with the solvent. In the phase diagram showing Tc as a function of the polymer volume fraction φP, the binodal curve has a very recognizable dumbbell shape which was already observed for poly(sulfobetaines) in water.23 Polymer/polymer mixtures are another example of binary mixtures. In the latter, however, the entropic gain of mixing the two species is considerably larger than that of polymer/ solvent ones, a specific feature pointed out by Flory. Indeed, in the polymer/solvent case, the number of polymer solutes is small compared to that of solvent molecules, and large first-neighbor attractive interactions between monomeric and solvent species are required to obtain complete miscibility. On the contrary, for polymer/polymer mixtures, even a small first-neighbor attractive interaction between two unlike monomeric species is sufficient to induce miscibility, especially for high molecular weight polymers. In high molecular weight polymer blends, miscibility is in fact the exception, and can only follow from a favorable negative interaction free energy. Pairs of polymers comprising polar or ionic moieties with a favorable interaction are the principal exception. In the present study, the situation consists of a ternary system comprising a solvent (i.e., water) and two polymers (i.e., the polyzwitterion and the polycation) respectively denoted S, A, and B for the sake of clarity. The Gibbs free energy of the system reads

∆FM/kBT ) nS ln φS + nA ln φA + nB ln φB + (χABφAφB + χASφAφS + χBSφBφS)(mAnA + mBnB + mSnS) (5) (where mA ) VA/V0 and mB ) VB/V0 are molar volume ratios of the polymers to a reference volume V0, generally taken as that of the solvent molecules) and takes into account the two solvent/ polymer interaction parameters χAS and χBS, as well as the



polymer-polymer one χAB. Scott has investigated the case of two polymers having the same molecular weight, placed in a common good solvent yet immiscible, i.e., presenting a repulsive FH polymer-polymer contribution. All three interaction parameters are then positive. Nevertheless, the thermodynamics in a ternary system are such that deriving exact (or even approaching) equations for the binodals is generally not possible, and one must resort to numerical methods as pointed out by Flory. Thanks to advances in computing, Hsu and Prausnitz41 considered the impact of a molecular weight mismatch, as well as a FH parameter mismatch, including the case of a slight attraction between the two polymers, although the authors always considered both polymers to be in good solvent conditions, i.e., a negative χAB, while χAS and χBS are positive. In our case, the solvent conditions for one polymer (i.e., the polyzwitterion) depend on temperature and concentration, because of the existence of a UCST in its binary phase diagram. On the other hand, this first polymer also has an attractive interaction with the second one (i.e., the polycation), which is in good solvent conditions in the whole concentration range. In such a situation, predicting even in an approaching way, how the apparent critical temperature Tc of the polymer-rich phase should evolve as a function of the mixture composition, is impossible using Flory’s formalism. Yet it is precisely what we intend to do: our aim is to understand why the critical temperature of a two-component complex made of a polyzwitterion and a polycation evolves with composition r in such a highly nonmonotonic fashion. Phenomenological Flory-like Mean-Field Model. First, it is profitable to explore the case of a binary mixture consisting of a solvent and a statistical copolymer A-stat-C, made of two different chemical species. The unique ingredient changing in Flory’s approach is the FH interaction parameter. Taking its entropic part δS as negligible, the parameter of a statistical copolymer with a solvent rewrites to an effectiVe quantity:42

χS/A-stat-C ≡ φAχS/A +(1 - φA)χS/C - φA(1 - φA)χA/C

(6)

The latter is a function of the relative amount of either of the two constituents in the statistical copolymer (in the present case, the fraction φA ) φA/(φA + φB) of component A), their respective interactions with the solvent molecules, and that with each other, i.e., χS/A, χS/C, and χA/C as the FH parameters of S/A, S/C, and A/C couples, respectively. Taking the usual reciprocal law between the FH parameter and the critical temperature of the statistical copolymer χS/A-stat-C ∝ 1/Tc, one can finally derive

1/Tc ∝ aφA2 + bφA + c

(7)

quadratic in φA, where a ) χA/C, b ) χS/A - χS/C - χA/C, and c ) χS/C. For a statistical copolymer, one expects 1/Tc to follow a parabolic law function of the copolymer composition, and whose coefficients only depend on the different FH parameters involved. We now assume that the complexation between zwitterionics (A motifs) with cationics (B motifs) is total, meaning each cationic site introduced contributes to producing a complex site (C motif). This assumption greatly simplifies the whole approach without loss of generality. We point out that, considering the constant concentration cpZ ) 0.5 wt % at which the mixtures are carried out, all polyzwitterions are above their crossover concentration cpZ* regardless of their degree of polymerization NZw.43 Therefore, any cationic motif introduced is always

Figure 11. Schematic representation of the selective association between a polymer and another species, effectively leading to a copolymer microstructure.

available for an interaction with a zwitterionic motif, although not necessarily on the same polyzwitterionic chain. We restrict ourselves to the portion r < 1 of the complexation cone where zwitterionic motifs are not all complexed and remain the majority species. The situation can then be considered as a perturbation to the solubility of a pure polyzwitterionic chain, correctly described with the theory of binary mixtures. The analogy with the statistical copolymer is as follows: the equivalent effectiVe copolymer (see sketch in Figure 11) consists of a polyzwitterion comprising NA motifs, bearing complex sites statistically distributed along the chain; their number NC is the same as that NB of cationic motifs added. Provided the following condition |NAr Ln(rφA)/NB Ln(φA)| , 1 is respected, the entropic contribution nB ln φB of the polycationic chains in the Gibbs free energy is negligible compared to that, nA ln φA, of the polyzwitterionic ones. For a polyzwitterionic fraction φA on the order of 0.3 wt %, the degree of polymerization NA of the polyzwitterionic species ranging from 177 to 6442, and that NB of the polycationic one ranging from 926 to 2778, the condition is in fact always well satisfied for r < 1. The rest of the thermodynamics thus remains unchanged and the binodal curve of this ternary system boils down to that of a binary one.44 Finally, Flory-like approaches consist in distributing different species (monomer and solvent molecules) on a grid, assuming the species have equal sizes. The method therefore requires volume renormalization when the species involved are different in size: water molecules, zwitterionic motifs, as well as cationic or complexed ones, all have different sizes, which we reasonably approximate at first to their respective molecular weights, taking all densities close to 1. Technically, one of the species (i.e., the solvent molecules) is set as the reference, while the other molar quantities are recomputed according to the ratio of their molecular weight and that of a solvent molecule, leading to effectiVe molar quantities. The effective zwitterionic molar fraction in the copolymer then reads

φ j A ≡ 1/(1 + βr)

(8)

where β = MCoac/MZw ) (MZw + MCa)/MZw is the rescaling factor for r < 1, originating from the motif size heterogeneities, equal to (279 + 162)/279 = 1.58 and (292 + 162)/292 = 1.55 for SPE/DADMAC and SPP/DADMAC couples, respectively. As a conclusion, we expect 1/Tc to be quadratic in 1/(1 + βr) for βr < 1, where zwitterionic motifs remain the majority component after the association with cationic ones. Within this picture, however, the polymeric nature of the cationic species is omitted: the cationic motifs are considered as separate entities, able to distribute statistically on the polyzwitterion chain in an independent way. However, this assumption is the main limitation of the model which follows from mean-field considerations: a statistical distribution of complex motifs is unlikely considering the topological constraints following from the polymeric nature of either species. Intuitively, we foresee that the model will become largely erroneous when the molecular weight of the polycation becomes much larger than that of the polyzwitterion (and vice versa), or when not enough polycation has been introduced. Because cationic monomers must be


Mary and Bendejacq

Figure 12. Plots of reciprocal critical temperatures 103/Tc’s vs 1/(1 + βr) within the limit βr e 1 for (a) SPE6442/DADMAC926, (b) SPE6442/ DADMAC2778, (c) SPE1611/DADMAC2778, and (d) SPP1404/DADMAC2778 mixtures. The thick lines are least-square parabolic fits to the experimental data.

located within a region corresponding to the radius of gyration of the polycation, one cationic species is not always close enough to a zwitterionic motif when the ratio Np(SPE),p(SPP)/ Np(DADMAC) of the polymerization degrees is not adapted and/ or when the relative amount βr is not large enough. Comparison between Theory and Experiments. The degree of polymerization of the polyzwitterion, that of the polycation, or the type of zwitterionic motif was varied. Figure 12 compares plots of 103/Tc vs 1/(1 + βr) for SPE6442/DADMAC926, SPE6442/ DADMAC2778, SPE1611/DADMAC2778, and SPP1404/DADMAC2778 mixtures for βr e 1. In all four plots, parabolas are observed, centered on φ j A ≈ 1/2 (more precisely, 0.60 in all cases shown). A difference between the molecular weights of poly(SPE)s and poly(DADMAC)s does not seem to significantly affect the position of the parabolas. Although foreseen as a limitation of the model, the parabolas are found at approximately the same position, even for an extensive molecular weight mismatch spanning over 1 order of magnitude, from approximately 7 (i.e., 6442/926, Figure 12a) down to 0.6 (i.e., 1611/2778, Figure 12c). When going from SPE1611 to SPP1404 at constant DADMAC2778 (see Figure 12c,d), very similar curves are obtained: the parabolas are positioned at nearly the same critical value of 1/(1 + βr) and appear to be shifted on the y-axis to larger 1/Tc values. The three coefficients of the parabolas have different values for SPE and SPP polymers of approximately the same degree of polymerization, which provides an insight into the affinity of any of the three species involved (water, zwitterion, and complex) for the two others. For instance, since φ j A is the fraction of excess zwitterionic motifs, the sum by a + b + c ) χZw/H2O is by definition equal to the reciprocal critical temperature 1/Tc(φ j A ) 1) of the pure polyzwitterion alone in water. We compute 1/Tc(φ j A ) 1) ) 3.0 × 10-3 K-1 for SPE1611 and 3.3 × 10-3 K-1 for SPP1404, implying critical temperatures of 60 and 30 ( 5 °C, respectively. The 30 °C difference has already been identified in our previous report: poly(SPP)s are always more soluble in water than poly(SPE)s of the same molecular weight, implying a smaller critical temperature Tc, hence, a larger reciprocal temperature 1/Tc. This effect, dependent on the zwitterionic/water couple considered, remains visible for zwitterion/cationic polymer complexes in their whole compositional range: a complex with poly(DADMAC) retains the characteristics of its zwitterionic constituent. The first coefficient a ) χZw/Coac, which measures the strength of the interaction between zwitterionic and complex sites, is

negative regardless of the zwitterionic chemistry, SPE or SPP, implying an attraction between the excess zwitterionic motifs and the complex ones already formed. This makes sense considering zwitterionics are de facto attracted to cationics; complex sites bear a net positive charge which zwitterionic motifs can again be attracted to. Such an attraction between zwitterionic and complex motifs explains why the complex formed by the two polymers gets denser and smaller as its composition approaches the cone tip. The absolute value |a| ) (1.4 ( 0.1) × 10-3 K-1 found for the SPP chemistry (cf. Figure 12d) is smaller than that, (2.1 ( 0.1) × 10-3 K-1, found for the SPE one for a similar molecular weight mismatch (cf. Figure 12c). This suggests an interaction between a SPP motif and its SPP-based complex, significantly less attractive than in the SPE case. Finally, the last coefficient, c ) χCoac/H2O, which measures the strength of the affinity of complex sites for water, is equal to c ) (3.1 ( 0.1) × 10-3 K-1 for the SPP chemistry (cf. Figure 12d) and is smaller than that, (2.6 ( 0.1) × 10-3 K-1, for the SPE one for a similar molecular weight mismatch (cf. Figure 12c), suggesting that the SPP-based complex motif is in better solvent conditions in water than the SPE-based one. A rough picture relying on a copolymer-like behavior seems to capture rather well the physics of the association, and provides a crucial, quantitative insight. In all cases, the maximum is found at approximately the same position, 1/(1 + βr) ≈ 1/2, implying βr ) 1. The derivative ∂(1/Tc)/∂φ j A ) 2aφ j A + b of eq 8 with respect to the fraction φ j A of excess zwitterionic motifs is equal to zero at -b/2a with a ) χZw/Coac and b ) χZw/H2O - χCoac/H2O - χZw/Coac. In practice, finding maxima located around 1/2 implies that b ≈ -a, meaning χZw/H2O ≈ χCoac/H2O. Surprisingly, the FH parameter between complex sites and water is not drastically different from that between zwitterionics and water. Complex sites are therefore not necessarily in good solvent conditions in water. Considering that the association between zwitterionic and cationic motifs leaves each complex site with a positive excess charge, i.e., the ammonium site, one would expect an increase of the solubility (conversely, the complex/ water interaction parameter χCoac/H2O should be found significantly smaller than the zwitterion/water one χZw/H2O). However, the complexation also leaves each complex site with an insoluble sulfonate/DADMAC ionic couple, from which one may expect a decrease of the solubility (conversely, an effectively larger interaction parameter χCoac/H2O). The reality seems to lie in between: a complex site comprises two antonymic moieties (i.e., the positive ammonium excess charge

Polyzwitterion-Polyelectrolyte Interactions and the insoluble sulfonate/DADMAC ionic couple) which act differently on the solubility of the zwitterionic chain. In practice, when only a few zwitterionic sites are complexed with cationics, the effect of the cationic excess charge dominates: solubility is enhanced and the apparent Tc decreases. On the contrary, when too many zwitterionic sites are complexed, the effect of the insoluble ionic pairs dominates, the chain becomes less soluble, and the apparent Tc starts increasing again. The picture, of course, is completely reversible: the same principles apply when one starts with a pure polycation fully soluble in water. This certainly explains the highly nonmonotonic dependence of the critical temperature with the mixture composition. 4. Conclusions We have presented the results of our investigations on polyzwitterion/polyelectrolyte mixtures in water. As already suggested in the literature, a strong attractive interaction exists between polyzwitterions and polycations, yet the present study is the first one to present a microscopic picture of the object formed. The nature of the zwitterionic function was also varied via small chemical changes and its impact on coacervation with strong polycations was investigated. We found that, while SPP and SPE-based polyzwitterions behave the same, SHPP-based ones do not show associations with strong polycations. We thereby demonstrate that the association is site-specific. On the other hand, we found that, contrary to polycarboxybetaine, the sulfobetaine-based polyzwitterions of the present study do not form a complex with the weak polyanions used, namely poly(acrylic acid)s, regardless of pH, ionic force, zwitterionic site, and degree of polymerization of either species. This further supports the concept of molecular recognition and site specificity in such associations. The molecular weights of both polyzwitterionic and polycation species were also varied. The formation of a complex was found to be general, even for a large molecular weight mismatch between the two polymers, although rules for complexation were evidenced. In particular, one imposes a minimum molecular weight for the polyzwitterion, independent of the molecular weight of the polycation. Finally, we have presented a phenomenological Flory-like approach, which describes the complex formed as comprising excess zwitterionic and complex sites statistically distributed along the backbone. The model predicts that the reciprocal critical temperature of the mixture should be quadratic with the content in either species, which is quite remarkably verified with several sets of experiments. The model also provides a crucial insight into the details of the interactions between the different components of the complex. Exploring large molecular mismatches, we feel that the approach is robust and captures well the physics of the coacervation. Polyzwitterions bear positive as well as negative charges evenly distributed along the backbone, which makes them suitable as model polyampholytic systems, to investigate their interactions with small ions as shown in our previous study,23 and also with macroions, as shown in the present report. However, the polyzwitterions used lack the hydrophobic moieties which proteins also generally bear. The latter necessarily participate in their solubility and interactions with other charged entities, for instance, cell membranes. In the future, polymers comprising zwitterionic motifs mixed with hydrophobic ones could be considered as model systems to further investigate the analogy. Acknowledgment. D.D.B. is thankful to Rhodia for authorizing publication. The authors are indebted to Marie-Pierre

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2310 J. Phys. Chem. B, Vol. 112, No. 8, 2008 (34) Starck, P.; Mosse, W. K. J.; Nicholas, N. J.; Spiniello, M.; Tyrrell, J.; Nelson, A.; Qiao, G. G.; Ducker, W. A. Langmuir 2007, 23, 14, 75877593. (35) Porod, G. Small-Angle X-ray Scattering; Glatter, O., Kratky, O., Eds.; Academic Press: London, 1982. (36) The upper composition (i.e., the more polycation-rich) displays a q-1-scaling which one would expect from a polycation: electrostatic repulsion between like-charged sites along a polyelectrolyte usually results in a well-known stretching from which the q-1-scaling originates. None of the central compositions displayed this feature, which becomes visible only once a sufficient amount of cationic polymer has been added. (37) Guinier, A.; Fournet, G. Small-Angle Scattering of X-Rays; Wiley & Sons: New York, 1955. (38) Note that taking one chain of each constituent, the resulting volume in the dry state reads 4πR3/3 ) VSPENpSPE + VDADMACNpDADMAC, where VSPE ) 0.33 nm3 is the volume of an SPE motif1 and VDADMAC ) 0.27 nm3 is that of a DADMAC motif. We extract an equivalent radius R ) 6.7 nm, which agrees well with the SAXS estimation of Rg ) 6.9 nm at r ) 1.38. (39) Flory, P. J. Principles of polymer chemistry, 7th ed.; Cornell University Press: Ithaca, NY, 1969.

Mary and Bendejacq (40) Hsu, C. C.; Prausnitz, J. M. Macromolecules 1974, 7, 320-324. (41) (a) Dudowicz, J.; Freed, K. Macromolecules 2000, 33, 3467-3477. (b) Dudowicz, J.; Freed, K. Macromolecules 2000, 33, 9777-9781. (42) We denote cpZ*, the polyzwitterion concentration associated with the crossover from a dilute to a semidilute state. The latter is defined via the relation nchVch ) 1, where nch ) cpZ*NA/MZwNZw is the number of chains per unit volume (where the density of the solution is taken close to 1; MZw of order 290 g/mol is the molecular weight of the zwitterionic motif) and Vch ) 4πRg3/3 ) 4πa3NZw3/2 is the volume occupied by a single chain at the theta point which defines our measure of the critical temperature. Finally, we simply derive cpZ* ) 3MZw/(4πa3NZw1/2). (43) Symmetrically, for r > 1, the equivalent copolymer would consist in a polycation bearing complex sites statistically distributed along the chain, whose number is the same as the number of zwitterionic motifs present in the solution. However, this case cannot be reasonably considered as a small perturbation to the binary mixture theory, as the entropic contribution to the Gibbs free energy of possibly unattached polycationic chains becomes far from negligible.

Interactions between Sulfobetaine-Based Polyzwitterions and

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