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Competitive/Cooperative Electrostatic Interactions in Macromolecular Complexes: Multinuclear NMR Study of PDADMAC-PMANa Complexes in the Presence of Al3+ Ions J. Krˇ´ızˇ,*,† H. Dautzenberg,‡ J. Dybal,† and D. Kurkova´† Institute of Macromolecular Chemistry, Academy of Sciences of the Czech Republic, Prague, Czech Republic, and Max-Planck-Institute for Colloids and Interfaces, Golm, Germany Received June 21, 2002. In Final Form: August 19, 2002 Interaction of Al3+ ions with electrostatic complexes of poly(N-diallyldimethylammonium chloride) (PDADMAC) and sodium polymethacrylate (PMANa) in D2O were studied by using 1H, 27Al, 23Na, and 35Cl NMR, relaxations, and pulsed-gradient stimulated echo (PGSTE) self-diffusion experiments. Al3+ ions are shown to enter the complex structure, substituting up to about 20% of the DADMAC groups in their electrostatic links. The structure of the complex somewhat changes, the free PDADMAC chains being pushed to the outer area of the complex, but remains otherwise intact. This process has an equilibrium nature and larger excess of Al3+ ions does not perceptibly influence its product. It is shown to be an interesting example of a combination of competitive and cooperative interaction: Al3+ ions compete with DADMAC groups in their electrostatic coupling with the polyanion and, at the same time, cooperate with them in the stabilization of the complex.
Introduction Electrically charged macromolecules such as polycations and polyanions are known to produce macromolecular complexes primarily based on long-range electrostatic interactions of opposite charges1-19 (for fuller scope of the field, see in particular reviewsin refs 1-3 and the references therein). According to the structure of polyions * Corresponding author. E-mail:
[email protected]. † Academy of Sciences of the Czech Republic. ‡ Max-Planck-Institute for Colloids and Interfaces. (1) Kabanov, V. A. In Macromolecular Complexes in Chemistry and Biology; Dubin, P., Bock, J., Davies, R. M., Schulz, D. N., Thies, C., Eds.; Springer-Verlag: Berlin, 1994; Vol. 10, p 151. (2) Dautzenberg, H.; Koetz, J.; Linow, K. J.; Philipp, B.; Rother, C. In Macromolecular Complexes in Chemistry and Biology; Dubin, P., Bock, J., Davies, R. M., Schulz, D. N., Thies, C., Eds.; Springer-Verlag: Berlin, 1994; Vol.8, p 119. (3) Philipp, B.; Dautzenberg, H.; Linow, K. J.; Koetz, J.; Dawydoff, W. Prog. Polym. Sci. 1989, 14, 91. (4) Tsuchida, E.; Osada, Y.; Sanada, K. J. Polym. Sci., Polym. Chem. Ed. 1972, 10, 3397. (5) Tsuchida, E.; Osada, Y.; Ohno, H. J. Macromol. Sci. 1980, B17 (4), 683. (6) Kabanov, V. A.; Zezin, A. B. Makromol. Chem. Suppl. 1984, 6, 259. (7) Hone, J. H. E.; Howe, A. M.; Cosgrove, T. Macromolecules 2000, 33, 1206. (8) Izumrudov, V. A.; Zhiryakova, M. V.; Kudaibergenov, S. E. Biopolymers 1999, 52, 94. (9) Babak, V. G.; Merkovich, E. A.; Desbrieres, J.; Rinaudo, M. Polym. Bull. 2000, 45, 77. (10) Buchhammer, H. M.; Petzold, G.; Lunkwitz, K. Colloid Polym. Sci. 2000, 278, 841. (11) Dragan, S.; Cristea, M. Eur. Polym. J. 2001, 37, 1571. (12) Peyratout, C.; Donath, E.; Daehne L. J. Photochem. Photobiol. A-Chem. 2001, 142, 51. (13) Dragan, S.; Cristea, M. Polymer 2002, 43, 55. (14) Moller, M.; Nordmeier, E. Eur. Polym. J. 2002, 38, 445. (15) Zelikin, A. N.; Izumrudov, V. Macromol. Biosci. 2002, 2, 78. (16) Mende, M.; Petzold, G.; Buchhammer, H. M. Colloid Polym. Sci. 2002, 280, 342. (17) Lin, X. J.; Zhong, A. Y.; Chen, D. B.; Zhou, Z. H.; He, B. B. J. Appl. Polym. Sci. 2002, 85, 638. (18) Reschel, T.; Konak, C.; Oupicky, D.; Seymour, L. W.; Ulbrich, K. J. Control Release 2002, 81, 201. (19) Kovacevic, D.; van der Burgh, S.; de Keizer, A.; Stuart, M. A. C. Langmuir 2002, 18, 5607.
used and conditions of their mixing, different complex formations starting from molecular complexes up to nanoparticles, physical networks, and gels can be produced. Among the possible polycations, which offer themselves as parts of such complexes, poly(N-diallyldimethylammonium chloride) (PDADMAC) or poly(2-Ntrimethylammonioethylmethacrylate)(PTMAEMA)proved to be suitable both for theoretical study and preparation of practically interesting particles. They are known do produce electrostatic complexes20-27 with polyanions such as sodium poly(styrenesulfonate) (PSSNa), polyphosphate (PPNa), or polymethacrylate (PMANa). The interaction between complementary polyions has been shown to be cooperative,21-27 the driving force being the entropy gain in the liberated small counterions and water molecules, although hydrophobic interaction could also play a role in some cases.27 According to the underlying cooperativity (and probably to other factors), the complexes have varying stability in media with high ionic strength. Strong cooperative interaction resists competition of small ions and the effect of charge screening. However, the effect of low-molecular-weight electrolytes on the complexes is far from simple. In the case of PDADMAC-PMANa complexes (usually containing excess of one type of ionic groups, which ensures solubility of the complex particle), excess of NaCl in the system completely destroys the complex. In contrast to it, addition of salts with trivalent ions such as Al3+ not only leaves the complex particles virtually intact but (20) Brand, F.; Dautzenberg, H.; Jaeger, W.; Hahn, M. Angew. Makromol. Chem. 1997, 248, 41. (21) Brand, F.; Dautzenberg, H. Langmuir 1997, 13, 2905. (22) Dautzenberg, H. Macromolecules 1997, 30, 7810. (23) Krˇ´ızˇ, J.; Kurkova´, D.; Dybal, J.; Oupicky´, D J. Phys. Chem. A 2000, 104, 10972. (24) Krˇ´ızˇ, J.; Dautzenberg, H. J. Phys. Chem. A 2001, 105, 3846. (25) Krˇ´ızˇ, J.; Dybal, J.; Dautzenberg, H. J. Phys. Chem. A 2001, 105, 7486. (26) Krˇ´ızˇ, J.; Dybal, J.; D. Kurkova´ J. Phys. Chem. B 2002, 106, 2175. (27) Dautzenberg, H.; Zintchenko, A.; Krˇ´ızˇ, J. paper in preparation for Langmuir.
10.1021/la0205809 CCC: $22.00 © 2002 American Chemical Society Published on Web 11/02/2002
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apparently stabilizes them against cleavage by subsequently added excess NaCl. This effect can only be observed in complexes with excess of PDADMAC (such as 1:0.6 mol/mol with PMANa). In complexes with prevailing PMANa, the addition of multivalent cations results in immediate flocculation. In the former case, Al3+ ions presumably compete with PDADMAC cations in binding to PMA anions but, after their insertion into the complex, cooperate with the rest of them in stabilizing the complex. The aim of this work is to clear the interaction of these ions with the complex.
Scheme 1
Experimental Section
amounts to 0.25 × 10-3 mol/L of observable DADMAC. Like in our previous studies, all NMR measurements thus were technically challenging due to extreme dilution of the samples. Taking into account the line widths of 10 Hz or more, such concentration is near to the sensitivity limit of NMR. A number of NMR techniques were thus excluded and those which could be used amounted to timeconsuming experiments taking from hours (for simple 1D spectra) to days (relaxation and PFG measurements). Despite these drawbacks, NMR proved to be unique in providing insight into the structure of the complexes and behavior of small ions. In our study, we used complexes of PDADMAC having Mw ) 56 × 103, 106 × 103, 200 × 103, 435 × 103, and 700 × 103 g/mol with PMANa having Mw ) 205 × 103 and 7 × 103 g/mol. For different combinations of Mw of the two components, some of the results slightly varied quantitatively, but they followed quite analogous trends. To make the results and their discussion easily comprehensible, we reproduce here (unless stated otherwise) as an example the behavior of the PDADMAC-PMANa complex (DADMAC/PMANa ) 1/0.6 mol/mol) with the respective Mw of the components 56 × 103 and 205 × 103 g/mol. 1. 1H NMR and Relaxations. As already shown in our previous studies,24,25 protons in groups immobilized by strong electrostatic interactions give rise to extremely broadened signals, which avoid detection by high-resolution NMR. This effect can also be partly observed on free PDADMAC in its dilute regime28 in the absence of added electrolyte. 1H NMR spectrum of the PDADMAC-PMANa 1/0.6 complexes thus does not contain signals of PMANa and the absolute intensity of those of PDADMAC is strongly diminished. Figure 1 shows the dependence of cumulative intensity of the N-methyl signals on the skeletal CH2 groups of PDADMAC in the complex and their dependence on the concentration of added Al3+ ions. The intensity is expressed as a ratio of the actual absolute intensity to that obtained for the equivalent concentration of free PDADMAC (i.e., 0.25 mmol/L DADMAC in the typical case where 2 mmol/L PDADMAC and PMANA solutions were mixed in a 1:0.6 ratio) at the same ionic strength (i.e., 0.375 mmol/L NaCl, liberated by the electrostatic coupling, and the given concentration of Al3+) ions. As one can see, this ratio is less than 1.0 for both types of groups for the original complex and grows over 1.0 (in particular for CH2 groups) in the mixtures containing 2 mmol/L or more of Al3+ ions. However, the dependence is convergent, indicating thus that the intensity of PDADMAC signals never achieves the value of a fully liberated PDADMAC (theoretical value of the corresponding ratio being 2.5). Figure 1 also shows complementary dependences of transverse relaxation rates for both kinds of proton groups. Only the leading terms (amounting to 0.7 of the whole intensity) in polyexponential relaxation decays are given, the rest being faster components.
Materials and Sample Preparation. Poly(N-diallyldimethylammonium chloride) (PDADMAC) was prepared by radical polymerization using a procedure published earlier.1 The Mw values were 56 × 103, 106 × 103, 200 × 103, 435 × 103, and 700 × 103 g/mol. Poly(sodium methacrylate) (PMANa) with Mw ) 205 × 103 and 7 × 103 g/mol and poly(sodium styrenesulfonate) (PSSNa) with Mw ) 48.1 × 103 g/mol were products purchased from Polymer Source Inc., Canada. In the typical example, 1.2 mL of a 2 mmol/L solution of PMANa (Mw ) 1.46 × 105 g/mol) in D2O was added by a syringe pump to 2.0 mL of a vigorously stirred 2 mmol/L solution of PDADMAC in D2O during 2 h at ambient temperature. In the experiments with Al3+ ions, the appropriate quantity of 0.1 mol/L solution of Al2(SO4)3 was slowly added under vigorous stirring to the sample. The slightly opalescent but stable solution was then transferred into the NMR tube, degassed, and sealed. NMR Measurements. All measurements were done on an upgraded 300-MHz NMR spectrometer Bruker Avance DPX300. 1H NMR spectra and relaxations were measured at 300.13 MHz by using a sensitive inverse-detection probe, collecting typically 80 scans with 16 kilopoints. For transverse relaxation, a CPMG sequence with 1-ms delay between alternately phased π pulses was used. In this case, typically 240 scans (in some cases 800 scans) for each of the 32 points were collected. 23Na, 27Al, and 35Cl NMR spectra and relaxations were measured at 79.39, 78.21, and 29.41 MHz, using the broad-band probe. 3200-8000 scans were collected according to sensitivity, the typical spectrum being taken in 8 kilopoints. Exponential weighting functions were applied to the FIDs before FT, with the line-broadening coefficient of 1.0 Hz for 23Na, 3.0 Hz for 27Al, and 5.0 Hz for 35Cl. Selfdiffusion experiments were measured with a water-cooled inverse-detection probe and a special PFG unit, with z-field gradients varied in 16 steps from 100 to 600 (or maximum 1200) G/cm. A Tanner stimulated-echo sequence with 1-ms gradient pulses and 20-ms diffusion delay was used.
Results and Discussion As already known from earlier studies,7-9 densely charged polyelectrolytes not containing electrically neutral hydrophilic segments, such as PDADMAC and PMANa, produce physically stable complex particles only if one of them is in substantial excess. In such a case, electrically charged segments of the excess polyion give both the hydrophilicity of the particles and their electrostatic repulsion, thus their resistance to aggregation. In the present case, we have chosen the DADMAC/MANa molar ratio 1.0/0.6, which ensures comparatively good stability of the systems. The complex thus contains segments of PDADMAC-PMANa couplings and segments of free PDADMAC as depicted in Scheme 1. In addition to their right molar ratio, low concentration of the mixed components is one of the most important factors in producing stable complex systems. According to our experience, the highest concentration of the polycation affording reproducible results was 2 × 10-3 mol/L for both DADMAC and PMANa in the mixed solutions. In a 1/0.6 PDADMAC-PMANa complex, it
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Figure 1. DADMAC N-CH3 and skeletal CH2 signal intensities (relative to the equivalent free DADMAC at the same ionic strength) and transverse relaxation rates (leading terms) in DADMAC-PMANa complexes under various concentrations of Al3+ ions (D2O, 300 K).
These results clearly indicate the following features. (i) PDADMAC is immobilized in the complex to a higher degree than could be expected by mere electrostatic coupling. This can be due a neighboring effect of the electrostatic links, i.e., PDADMAC and PMANa do not combine strictly in a ladder-like way, leaving long segments of PDADMAC free, but the complex has rather a scrambled-egg21,22 collapsed structure (see below). (ii) Interaction with Al3+ ions liberates part of the DADMAC groups into a mobile state. As the actual/theoretical intensity ratio exceeds 1.0, this liberation is only partly due to a restructuring of the complex, but, in addition to it, some of the existing DADMAC-MA bonds must be cleaved. The course of transverse relaxation rate shows that both the originally free and the liberated DADMAC groups adopt higher mobility in this process. However, the convergence of the intensity ratio to values much lower than the theoretical limit 2.5 (as well as the course of transverse relaxation) indicates that the complex is not destroyed even at a large excess of Al3+ ions. Another evidence of this conclusion comes from the fact that PMA signals remain missing in 1H NMR spectrum even at large excess of Al3+ ions. This contrasts with the behavior of 1H NMR spectra of equivalent solutions of PMANa: when Al3+ ions are added, the signals of PMA are somewhat broadened but their intensity decreases very slowly due to gradual precipitation of the PMA-Al complex. 2. 27Al Longitudinal Relaxation. The most probable cause of the cleavage of electrostatic bonds in the complex is the partial substitution of DADMAC cations by Al3+ ions. Such a process must be accompanied by relative immobilization of inserted Al ions in a position surrounded by an electric field of lower symmetry, compared with that around a hydrated ion in a dilute solution. Due to a comparatively high quadrupole moment of the 27Al nucleus (I ) 5/2), this should lead to a very marked increase in the corresponding quadrupolar relaxation rate. In principle, two extremes of behavior of the inserted Al ions could be expected: (i) relatively long residence time with only occasional exchange and (ii) fast exchange (with τex < 10-4 s) with the free ions in solution. In the first case, polyexponential and very fast relaxation of the bound 27Al nuclei is probable; if the relaxation of bound ions is very fast, the bound ions avoid detection and only free
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Figure 2. Dependence of longitudinal relaxation rates R1 of 27 Al on the statistical fraction of bound Al ions φb in the systems of Al2(SO4)3 with PMANa, DADMAC-PMA, and DADMACPSS (D2O, 300 K).
ions with virtually unaffected relaxation are observed. In the second case, approximately monoexponential decay (in particular in the longitudinal regime) can be observed, with relaxation rate increased (in comparison with that of free ions at the same concentration) proportionally to the statistical fraction of the bound ions. The second of these cases is observed with our systems: there is only one comparatively narrow 27Al NMR signal, which decays monoexponentially (in the limits of experimental error) in the inverse-recovery experiment. The change of relaxation rate with varying Al3+ concentration in our systems is rather complex. To present it in an easily comprehensible way, we plot its’ dependence on the formal molar fraction of the bound Al ions φb, which is constructed in the following way. In the system with the respective concentrations of carboxyl, Na, and Al3+ ions CCOO, CNa, and CAl, the concentration Cb of the bound Al ions under their purely statistical competition with Na ions is Cb ) (1/3)CCOO3CAl/(CNa + 3CAl). Thus we have φb ) Cb/CAl ) CCOO/(CNa + 3CAl). In reality, “bound” means rather a distribution of states near the anion group. Also, the competition between Al3+ and Na+ or DADMA+ ions cannot be purely statistical. From a purely electrostatic point of view, Al3+ must be preferred due to its large specific charge. Also, substitution of three Na+ ions by one Al3+ should lead to an entropy gain, which should influence the statistics. However, there are steric constrains to full utilization of all three Al valences, as will be shown later in this article. Figure 2 shows dependence of the longitudinal relaxation rate R1 on φb for PDADMAC-PMANa complex and, for comparison, for PMANa and PDADMAC-PSS at equivalent concentrations of the polyanions. Whereas the dependence for PMANa is reasonably linear, that for PDADMAC-PMANa and PDADMAC-PSS shows deviations from linearity for low values of φb (i.e., large excess of Al3+ ions). In addition to it, linear parts of these dependences decrease in the order PMANa, PDADMACPMANa, and PDADMAC-PSS. These results can be interpreted in the following way. Whereas the fraction of bound Al ions follows the statistical expectation in PMANa, both complexes resist excessive uptake of these ions at their larger excess. Hence the deviation from linearity at small φb. Lower slope of the dependence for PDADMACPMANa and in particular for PDADMAC-PSS means
Electrostatic Interactions in Macromolecular Complexes
27
Figure 3. Longitudinal relaxation rates R1 of Al in dependence on the statistical fraction of bound Al ions φb in the systems of DADMAC-PMA with Al2SO4 added after (1) or before (2) the addition of PMANa (D2O, 300 K).
lower readiness of these complexes to bind Al ions, in comparison with free PMANa. This is quite understandable in view of the advantage given to PDADMAC in competition with Al ions by its cooperative binding. The results discussed so far lead to a definite conclusion that Al3+ ions are included into the complex via substitution of DADMAC in some links, their number increasing to a certain limit under their larger excess. It is, however, difficult to express this conclusion quantitatively as the quadrupolar coupling constant of 27Al in a typical bound position remains unknown. Using the previous results from 1H NMR, up to 12% of the DADMAC links in the complex are substituted by Al3+ ions. Two notes to this result are necessary. First of all, most of the Al3+ ions included into the complex are in a fast exchange with the free ones in solution. Thus the structure is close to an equilibrium state. This is clearly demonstrated in Figure 3, where the already presented data are compared with those obtained for the systems where the same amount of Al3+ ions was added to PDADMAC prior to its mixing with PMANa. The only slight difference between these two sets of data, which is comparable to the experimental error, strengthens the view that the system is roughly at equilibrium. The second note concerns interaction of Al3+ ions with PMANa itself. The data presented in Figure 2 correspond to freshly prepared mixtures of PMANa with the Al2(SO4)3 solution. After 2-days storage of these solutions, a faint trace of precipitate appeared, which sedimented slowly. When the systems were measured again after 14 days of storage and subsequent centrifugation, the 27Al relaxation rate was almost exactly that of the free ions, but the absolute intensity of the signal was diminished, compared to the original one. Thus the partial substitution of Na+ by Al3+ ions in PMANa clearly proceeds in two stages. In the first, ions are simply exchanged, Al3+ ions being bound more strongly due to their larger specific charge. In the second, the structure clearly rearranges, producing larger and slowly precipitating solid phase. Exchange of Al3+ ions between the solution and the precipitate is no longer possible, hence the ions in solution relax like free ions. The precipitation of PMANaAl systems is most probably due to the binding of Al3+ ions to more than one PMA
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Figure 4. 35Cl transverse relaxation rates of Cl- ions in the systems DADMAC-PMANa (1/0.6) and the equivalent free DADMAC-NaCl at varying concentration of Al2(SO4)3 (D2O, 300 K).
Figure 5. Longitudinal (R1) and transverse (R2) 23Na relaxation rates (monoexponential fits) in the systems DADMAC-PMANa (2.0/1.2 mmol/L) or PMANa (1.2 mmol/L) with varying concentration of Al3+ ions (D2O, 300 K).
chain (lower energy is achieved, see below), which results in a physical network. One can speculate that the same principle is applied in the PDADMAC-PMANa complexes, too. The partial networking of the complex by Al3+ could be one of the reasons of its increased stability against cleavage by NaCl. 3. 23Na NMR Transverse and Longitudinal Relaxation. The relaxation of 23Na35Cl nuclei in this study serves as a double-check on the remaining Na+ and Cl- counterions. Figure 5 compares the dependence of both longitudinal and transverse relaxation rates on the presence of Al3+ ions for PDADMAC-PMANa and the native PMANa. In the former case, relaxation rates R1 (longitudinal) and R2 (transverse) are almost equal and correspond to free Na+ ions. In the absence of Al3+, the coupling degree of PMANa is thus very near 1.0. Increasing the presence of Al3+ ions clearly does not change this situation. This is in particular clear by comparison with the behavior of equivalent solutions of PMANa. It is well-
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known28 that the polyelectrolyte effect in dilute solutions of densely charged polyelectrolytes affects the relaxation in counterions such as Na+ in a peculiar way. Whereas R1 behaves very much like that of free ions, R2 and in h (0) - J h (2ω0)] (which can particular the quantity ∆R2 ∝ [J be obtained by a careful analysis of both R1 and R2 or from the double-quantum coherence) depend on the distribution and diffusion of the counterions. In our case, Na+ ions are partly pushed out of the vicinity of the polyanion by competing Al3+ ions, hence the observed decrease in R2 at growing Al3+ concentration. The sharp contrast in the relaxation behavior of 23Na in both systems shows that the partial transformation of the complex by Al3+ ions does not help the present Na+ ions to have a detectable share in competition with DADMAC units. This is fully in accord with the previous findings.27 4. 35Cl NMR Transverse Relaxation. In principle, quadrupolar relaxation of 35Cl nuclei contains a wealth of information about the behavior of Cl- ions and, derivatively, about the dynamic state of PDADMAC segments in the complex. Unfortunately, the complexity of behavior as well as low effective sensitivity (due to fast relaxation) of 35Cl nuclei makes our results merely indicative. Figure 5 compares transverse relaxation rates R2 of 35Cl nuclei in the PDADMAC-PMANa complex and in the equivalent solution of the free PDADMAC-NaCl system under growing concentration of Al2(SO4)3. In both systems there is a fast exchange between the free and bound (i.e., statistically distributed in the vicinity of the polycation) ions. Therefore, the relaxation is apparently monoexponential if very fast. In the PDADMAC-NaCl system, R2 decreases with increasing concentration of Al2(SO4)3 partly due to substitution of Cl- by SO42- in the vicinity of the polycation and partly because of weakening of the polyelectrolyte effect due to increasing ionic strength. Qualitatively the same behavior can be observed in the PDADMAC-PMANa system (containing, of course, roughly the same concentration of NaCl). However, R2 starts at a much higher value here and its decrease with higher Al concentration is much more pronounced. The initially high value of R2 indicates that the bound Cl- ions are in less mobile positions than those in a free PDADMAC. This is fully in accord with our above results from 1H NMR indicating the scrambled-egg structure of the complex. The decrease in R2 with increasing Al concentration, much faster than for free PDADMAC, clearly indicates regrouping in the complex and partial increase in mobility of DADMAC groups (again in accord with 1H NMR results). This effect on R2 apparently overshadows that of the partial uptake of Cl- ions by DADMAC groups, liberated by inserted Al3+ ions, which should lead to a relative increase in R2. 5. 1H PFG Self-Diffusion Measurements. Translational diffusion mobility of the molecular complex systems offers useful complementary information about the system under study because it points to their dimensions and shape. Pulsed field-gradient (PFG) NMR methods should reflect analogous physical phenomena as the scattering methods such as dynamic light scattering (DLS) do, with some delicate differences. Generally, PFG methods can be considered to reflect a true mass transport along the chosen (in our case the main, or z) axis of the magnetic field. In our study, we used two types of PFG experiments, namely, pulsed-gradient spin-echo (PGSE) and pulsedgradient stimulated echo (PGSTE). In PGSE, the spins (28) Halle, B.; Wennerstro¨m, H.; Piculell, L. J. Phys. Chem. 1984, 88, 2482.
Krˇ ı´zˇ et al.
are in a single-quantum coherent state during the diffusion period. Signals with very fast transverse relaxation thus do not contribute to the results. In PGSTE, the spins are aligned along the z-axis during diffusion time and are thus affected only by the slower longitudinal relaxation. In our study, the data from PGSE were generally of a lower quality and are thus not reflected in our results. PGSTE gave reasonably reproducible results (with a 7% scatter) but the decays were polyexponential (they could be approximated by a biexponential decay, the ratio of the corresponding diffusion coefficients being 2.5-3.1). The reason of the polyexponentiality is not quite clear. In principle, polyexponentiality could be due to two main phenomena: (i) mixing of the translation of the whole complex particle with semilocal (reptation) motions of its segments and (ii) distribution of sizes and/or shapes of the complex particles. With a typical value of Ds ) 2 × 10-11 m2 s-1 and diffusion time 0.02 s, the experiment reflects transport over 89 nm, which is several times larger than the diameter of the complex particle or comparable to it (according to the molecular weight of the PDADMAC used for the complex). In other words, semilocal motions of polymer segments have some effect on the results, which can be only marginal for the smallest particles, however. On the other hand, broad distribution of particle size (polydispersity σ in the interval 0.3-0.4) has also been observed by DLS.27 We believe this distribution to be the main cause of the polyexponentiality of the PGSTE decays. In its interpretation, we assume that the distribution pw(a) of the hydrodynamic radii a follows22 a logarithmic function
pw(a) )
a-5/2 exp[-(ln a - ln am)2/2σ2]
(1)
x2πσam-3/2 exp[9σ2/8]
where am is a structure parameter and σ represents the polydispersity. Using eq 1, we assume that the intensity decay induced by a gradient g can be expressed by
[ ]
≈
I(0)
∑i
ξg2
∫
I(g) ) I(0) dapw(a) exp -
a
[ ] ξg2
pw(ai) exp -
ai
(2)
where
ξ)
kTγ2δ2(∆ - δ/3) 6πη
(3)
The symbols in eq 3 have the following meaning: k the Boltzmann constant, T temperature, η viscosity, γ the gyromagnetic ratio, ∆ and δ the length (in s) of diffusion of the gradient pulse, respectively. The structure parameter can be said to a polydispersity-independent weight mean of the particle radius, i.e., the weight of the particle G(am) is
G(am) ) (4/3)πFam3
(4)
where F is the density of the particle. Figure 6 gives an example of fits of eq 2 (discrete form) to some of the experimental data (Mw of PDADMAC used was 56 × 103 g/mol). In all these fits, the value of σ was in the interval 0.31-0.37. The dependence of the corresponding am values of the complex particles obtained for the given Mw of PDADMAC used in its complex with
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differences should not be overestimated in view of the more or less unique nature of each complex product. The initial increase in the particle size is in full accord with the above-found partial freeing of DADMAC segments in the complex. The small decrease of particle radius at larger excess of Al3+ ions is almost within experimental error so that we prefer not to speculate on it. In the whole, our PGSTE strongly supports the view that Al3+ ions even at larger excess somewhat change but do not destroy the structure of PDADMAC-PMANa complexes.
Figure 6. PGSTE decays (points) and the fits (curves) using eq 2 for the PDADMAC-PMANa complex (PDADMAC Mw ) 5.6 × 104 g/mol) in the presence of the indicated concentration (mmol/L) of Al3+ ions (D2O, 297 K).
Figure 7. Optimized am parameters of PDADMAC-PMANa complexes with the indicated Mw of the used PDADMAC in the presence of the given concentration (mmol/L) of Al3+ ions (D2O, 297 K).
PMANa (1:0.6) on the concentration of Al3+ ions is shown in Figure 7. As can be seen, the addition of a small quantity of Al3+ ions somewhat increases the radius of the particles, whereas additional increase in Al concentration leaves it virtually intact. The course of these changes for different Mw of the used PDADMAC is quite analogous; the slight
Conclusions By 1H NMR spectra and relaxations, we have shown that interaction of Al3+ ions with PDADMAC-PMANa complexes leads to a partial freeing of motions of DADMAC groups but not to any cleavage of the complex. This conclusion is supported by the results of 1H PGSTE selfdiffusion experiments, which show a partial increase in the hydrodynamic radius of the complex particles but no sign of liberating PDADMAC or PMANa as a result of interaction with Al3+ ions. 27Al NMR quadrupolar relaxation indicates that these effects are due to a partial inclusion of Al3+ ions into the complex, achieved by loosening of a part of DADMAC electrostatic links with the polyanion. This was shown to be an equilibrium process, as its result is nearly independent of the order in which PMANa and Al3+ salt is added to PDADMAC. 23 Na NMR longitudinal and transverse relaxations give evidence that Al3+ ions are the only ions substituting or partially liberating the DADMAC groups in the complex. According to the results of 35Cl NMR relaxation, Clcounterions are partly taken up by the complex under the influence of Al3+ ions. In the modified complex, Cl- ions are bound in more mobile position than those in the original structure. The following model of the interaction of Al3+ ions with the PDADMAC-PMANa complex appears to be plausible. Al3+ ions enter the original scrambled egg structure of the complex and partly substitute DADMAC cations in their nearest electrostatic links. During structure stabilization, Al3+ ions physically cross-link the PMA chains and push the free parts of PDADMAC chains to the outer area of the complex. The whole structure is somewhat less dense but better shielded by its outer positive charge against both self-aggregation and cleavage. This model offers a rather unique case of a combined competitive and cooperative interaction: Al3+ ions compete with PDADMAC groups in their electrostatic binding to PMA anions but, in doing so, cooperate with them in stabilizing the complex. Acknowledgment. We thank the Grant Agency of the Academy of Sciences of the Czech Republic for financial support given under the Grant A4050206 and the Academy of Sciences of the Czech Republic for additional support (Project No. AVOZ4050913). LA0205809
