Langmuir 2003, 19, 2507-2513
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Transition Highly Aggregated ComplexessSoluble Complexes via Polyelectrolyte Exchange Reactions: Kinetics, Structural Changes, and Mechanism Arkadi Zintchenko,* Gudrun Rother, and Herbert Dautzenberg Max-Planck-Institute of Colloids and Interfaces, Am Mu¨ hlenberg, D-14476, Golm, Germany Received September 12, 2002. In Final Form: December 6, 2002 The dissolution of highly aggregated polyelectrolyte complex particles formed in water after addition of salt was studied. The dissolution of aggregates proceeded to soluble complexes on the molecular level of the long-chain component. The driving force of the process is the polyelectrolyte exchange reaction between the aggregates and the free long chains in excess. The kinetics of the process was studied by different light scattering techniques. The rate of dissolution showed a strong dependence on the salt concentration in the solution and on the concentration of the species. The dependence on concentration of the species in solution weakened with increasing salt concentration. Investigations of the structural changes during the dissolution process revealed the presence of only two generations of particles in solution: aggregates and soluble complexes. While the scattering intensity decreased strongly, the dimensions of the aggregates changed only slightly during dissolution, indicating a spontaneous disaggregation of the particles. A mechanism of the dissolution process was proposed, which is in agreement with the experimental findings and previous results in the literature. The process represents a two-step reaction: The first step consists of the release of the short-chain component from the aggregates by an exchange reaction via the free long-chain component in solution (second-order reaction). The second step is the destruction of the aggregates by increasing osmotic pressure in the particle (first-order reaction). The dissolution process may be understood as a model process for the release of DNA from polyelectrolyte complexes in gene therapy.
1. Introduction Polyelectrolyte complexes can be divided into two categories: (1) highly aggregated complexes with a stoichiometry near 1:1, which in solution form big particles on the colloidal level,1-3 and (2) soluble complexes on the molecular level related to the long-chain component.4-6 Soluble complexes can be formed only under special conditions: (1) one component with weak ionic groups, (2) a significant difference in the molecular weights of the oppositely charged chains, (3) a high excess of the longchain component, (4) the presence of salt in solution, and (5) a relatively narrow range of mixing ratios. Generally, the formation of soluble complexes corresponds to the thermodynamic equilibrium and results in a uniform distribution of the short-chain component among the chains of the oppositely charged long-chain component.5,7 If one or more of these conditions are not valid, complex formation results in highly aggregated complex particles in the colloid range. Especially, the nature of the polyelectrolytes used for complex formation plays an important role (some combinations, that is, the complexes with Na-poly(styrene sulfonate), have been shown to be unable to form soluble complexes1,8,9). Polyelectrolyte complex (PEC) formation can be described as two-step reaction, where the first fast step is * To whom correspondence should be addressed. (1) Dautzenberg, H.; Hartmann, J.; Grunewald, S.; Brandt, F. Ber. Bunsen-Ges. Phys. Chem. 1996, 100, 1024. (2) Dautzenberg, H.; Rother, G.; Hartmann, J. In Macro-Ion Characterization: From Dilute Solutions to Complex Fluids; Schmitz, K. S., Ed.; ACS Symposium Series 548; American Chemical Society: Washington, DC, 1994; p 210. (3) Brandt, F.; Dautzenberg, H. Langmiur 1997, 13, 2905. (4) Kabanov, V. A.; Zezin, A. B. Sov. Sci. Rev., Sect. B 1982, 4, 207. (5) Kabanov, V. A.; Zezin, A. B. Macromol. Chem. 1984, 6, 259. (6) Tsuchida, E.; Osada, Y.; Sanada, K. J. Polym. Sci., Polym. Chem. Ed 1972, 10, 3397. (7) Tsuchida, E.; Abe, K. Adv. Polym. Sci. 1982, 45, 1.
the formation of the initial contacts, which proceeds during the diffusion time of the components and results in the formation of initial aggregates.10 The second step consists of structural rearrangements via a polyelectrolyte exchange reaction between the chains present in solution.11 For the formation of soluble complexes, both steps are active. In the formation of highly aggregated complexes, the exchange reactions are suppressed. This means that the exchange reaction between the polyelectrolytes is one of the most important aspects of the mechanism of polyelectrolyte complex formation. In the literature, a wide range of polyelectrolyte reactions were studied, either between chains of the same nature5,11,12 or between chains of different natures.13-15 Nearly all of these studies were focused on the investigation of the end products of the exchange reaction in order to elucidate the influence of the parameters (the molecular properties, the properties of the media, etc.) responsible for the shift of the equilibrium to one product or another. There are only a small number of papers concerning the proceeding of the reaction itself. Bakeev et al. studied the exchange reactions between the chains of soluble complexes and free polyelectrolyte chains, revealing that the exchange reactions obey second-order kinetics.11 (8) Karibyants, N.; Dautzenberg, H. Langmiur 1998, 14, 4427. (9) Karibyants, N.; Dautzenberg, H.; Co¨lfen, H. Macromolecules 1997, 30, 7803. (10) Bakeev, K. N.; Izumrudov, V. A.; Zezin, A. B.; Kabanov, V. A. Dokl. Akad. Nauk SSSR 1988, 299, 1405. (11) Bakeev, K. N.; Izumrudov, V. A.; Kuchanov, S. I.; Zezin, A. B.; Kabanov, V. A. Macromolecules 1992, 25, 4249. (12) Kabanov, V. A.; Zezin, A. B. Pure Appl. Chem. 1984, 56, 343. (13) Gulaeva, Z. G.; Zansokhova, M. F.; Razvodovskii, Y. F.; Yefimov, V. S.; Zezin, A. B.; Kabanov, V. A. Vysokomol. Soedin. 1983, A25, 1238. (14) Izumrudov, V. A.; Bronich, T. K.; Saburova, O. S.; Zezin, A. B.; Kabanov, V. A. Macromol. Chem., Rapid. Commun. 1988, 9, 7. (15) Margolin, A. L.; Sherstyuk, S. F.; Izumrudov, V. A.; Svedas, V. K.; Zezin, A. B.; Kabanov, V. A. Dokl. Akad. Nauk SSSR 1985, 284, 997.
10.1021/la0265427 CCC: $25.00 © 2003 American Chemical Society Published on Web 02/06/2003
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Table 1. Characteristics of the Polyelectrolytes PAMPS PEG content, mol % M of starting PEG block Mn expected Mn, osmometry Mw, SLS number of PEGs per chain mass per charge a
530000 207
DHP4a 52 2000 9000 27000 70000 ∼3 195
For a discussion of the structure of DHP4, see ref 25.
Despite the large number of publications about exchange reactions, studies of the transformations of highly aggregated complexes to soluble complexes via exchange reactions between the aggregated particles and the free polyelectrolyte chains are missing. However, these reactions are of great interest from the theoretical as well as the practical point of view. For example, polycation/DNA complexes can be used in gene therapy as transport vectors to the human cells.16-18 Mostly they are highly aggregated systems (the aggregation number ranges from several tens to several hundreds of DNA molecules per particle). The release mechanism of the DNA from the complex in the cell is supposed to be a polyelectrolyte exchange reaction with different polyions being present in a cell.19 Because the DNA used for gene transport is a long molecule associated with a number of the shorter polycation molecules, the most interesting point in this case is the release of the DNA from the complexes in the presence of long-chain polyanions. To bridge this gap, the kinetics and structural changes during the dissolution process of big primary aggregates and the formation of the soluble complexes via polyelectrolyte exchange reactions were studied in this work in detail. A mechanism of this process was proposed, which may explain all experimental facts. 2. Experimental Section 2.1. Materials. A radically polymerized poly(2-acrylamido2-methyl-1-propanesulfonic acid) (PAMPS) was used as the polyanion. A block copolymer between poly(diallyldimethylammonium chloride) (PDADMAC) and poly(ethylene glycol) (PEG) was used as the polycation. The characteristics of the polymers are presented in Table 1. The large difference in the Mn value expected from the information about the composition of the copolymer and the one determined from osmometry could be explained by the branched multiblock structure of the copolymer with approximately 3 PEG chains per 1 polymer chain (the expected Mn value was calculated under the assumption of a diblock structure of the copolymer). For a detailed discussion of the structure of DHP4, see ref 25. Deionized water and sodium chloride solutions were used as solvents. 2.2. Methods. 2.2.1. Preparation of Complexes. All complexes were prepared by fast mixing of the component solutions in pure water under strong stirring. The polyanion solution (10-2 monomol/L) served as the starting solution. The polycation solution (2 × 10-2 monomol/L) was added up to the desired mixing ratio. After that, the ionic strength of the medium was increased by addition of salt solution up to the desired level. For some experiments, the initially obtained complex solutions were diluted with water. (16) Seymour, L. W.; Kataoka, K.; Kabanov, A. V. In Self-Assembling Complexes for Gene Delivery, from Laboratory to Clinical Trial; Kabanov, A. V., Felgner, P. L., Seymour, L. W., Eds.; John Wiley and Sons: Chichester, 1998; p 219. (17) Wu, G. Y.; Wu, C. H. J. Biol. Chem. 1988, 263, 14621. (18) Boussif, O.; Lezoualch, F.; Zanta, M. A.; Mergny, M. D.; Scherman, D.; Demeneix, B.; Behr, J. P. Proc. Natl. Acad. Sci. U.S.A. 1995, 92, 7297. (19) Erbacher, P.; Roche, A. C.; Monsigny, M.; Midoux, P. Bioconjugate Chem. 1995, 6, 401.
2.2.2. Analytical Ultracentrifugation (AUC). For AUC measurements, the Beckman Optima XL-I ultracentrifuge (Beckman, Spinco Division, Palo Alto, CA) equipped with integrated Rayleigh interference and UV adsorption optics was applied. The sedimentation velocity measurements were performed at a speed of 40 000 rpm. 2.2.3. Static Light Scattering (SLS). SLS measurements were carried out at 25 °C with a Sofica 42000 instrument (Wippler and Scheibling, Strasbourg, France), equipped with a 1 mW He-Na laser as the light source. The instrument was modified for data capture by SLS Systemtechnik Freiburg, Germany. The accuracy of the measurements was better than 1%. For kinetic studies, time-resolved SLS measurements were carried out with a multiple-angle laser light scattering (MALLS) instrument Dawn EOS (Wyatt, Santa Barbara, CA), equipped with a 30 mW gallium-arsenide laser diode and able to detect the scattering intensity at 18 angles simultaneously every second. To improve the accuracy of measurements, a cylindrical cell and an index matching bath with plan-parallel windows (Hellma, Germany) were used. The refractive index increments of the polyelectrolytes were measured with an interferometric scanning refractometer ScanRef (Nanofilm Technology GmbH, Goettingen, Germany). The refractive index increments and the concentrations of the solutions of the soluble complexes were calculated under the assumption of uniform distribution of the short chains (DHP4) between the chains of the high molecular weight polymer (PAMPS) and full release of the counterions, using the following equations:
dnPEC dn/dcPAMPSmPAMPS + dn/dcDHP4mDHP4X ) dc mPAMPS + mDHP4X
(1)
and
CPEC )
CPAMPSVPAMPS + CDHP4VDHP4(1 - MNaCl/MDHP4) (VDHP4 + VPAMPS)
(2)
where dn/dcPEC, dn/dcPAMPS, and dn/dcDHP4 are the refractive index increments of the PEC, PAMPS, and DHP4, respectively; MNaCl and MDHP4 are the molar masses of NaCl and of a charged unit of DHP4; mPAMPS and mDHP4 are the average masses of the charged units without counterions; and VPAMPS and VDHP4 are the volumes of the PAMPS and DHP4 solutions, respectively. CPEC and CDHP4 are the concentrations of the PEC and DHP4 solutions. X is the mixing ratio (ratio between the number of positive and negative charges in the complex solution). The scattering curves were analyzed by a Zimm plot (Kc/R(q) versus q2) or by a special fitting algorithm, based on a comparison of the experimental curves with theoretically calculated ones in a scaled double logarithmic plot (log R(q) versus log q, compare refs 20 and 21), which allows us to assess the structure type and polydispersity of the particles and to determine their mass, size, and structural density. To describe the polydispersity, for spherical particles a special logarithmic distribution of radii was used. The polydispersity parameter σ of this distribution corresponds for smaller values to the relative standard deviation; the radius parameter am is related to the weight-average molecular mass by the expression
Mw )
4π FNAam3 3
(3)
where NA is Avogadro’s number and F is the structural density of the complex particles. 2.2.4. Dynamic Light Scattering. Dynamic light scattering was measured with the instrument SIMULTAN (ALV, Langen, Germany), equipped with a correlator 5000 and a 400 mW YAG laser DPSS 532-10 (Coherent, Santa Clara, CA) as the light source. The correlation functions were measured at 30° and 90° (20) Dautzenberg, H.; Rother, G. Makromol. Chem., Macromol. Symp. 1992, 61, 94. (21) Dautzenberg, H.; Rother, G. J. Polym. Sci., Part B: Polym. Phys. 1988, 26, 353.
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Langmuir, Vol. 19, No. 6, 2003 2509 Table 2. Molecular Characteristics of the DHP4/PAMPS Complexes
Figure 1. Distribution of the sedimentation coefficients in 0.01 N NaCl for the complexes DHP4/PAMPS at mixing ratios of (9) X ) 0, (b) X ) 0.2, (2) X ) 0.4, and (1) X ) 0.6. during 1 min every 5 min. For the analysis of the correlation functions, the fitting algorithm REPES was used, which is similar to the CONTIN algorithm, but directly minimized the intensity correlation function.22 The apparent hydrodynamic radius RH was calculated from the average collective diffusion coefficient D, using the Stokes-Einstein equation:
RH ) kT/6πηD
(4)
where k is the Boltzmann constant, T is the absolute temperature, and η is the viscosity of the solvent.
3. Results and Discussion 3.1. The Molecular Characteristics of the Complexes. The mixing of the solutions of the oppositely charged polymers in pure water resulted in extremely turbid solutions, indicating the formation of very big particles on the colloidal level. However, after addition of salt the turbidity of the solutions decreased in time, and after a certain period (several hours for a 0.01 N NaCl solution) the turbidity reached a level that corresponds to the equilibrium state of the system. In the literature, there are two different explanations for such kinds of processes. The first one is the dissolution of the big aggregates into the soluble complexes on the molecular level, corresponding to the thermodynamic equilibrium.11 The second one is the disaggregation of the big secondary aggregates into smaller primary aggregates.23 Therefore, the first step of this work was to make clear what type of equilibrium state was reached in our systems. One of the differences between highly aggregated complexes and molecularly dispersed complexes is the distribution of the short chains of the component in deficiency between the long chains of the component in excess. For soluble complexes, the distribution is uniform and the system is monomodal.4,5 For highly aggregated complexes, one can distinguish between two modes: the big aggregates of nearly 1:1 charge stoichiometry and the free polyelectrolyte in excess. AUC can give information about the distribution of the species in the system. Figure 1 presents the AUC studies for free PAMPS and for complexes of different degrees of charge compensation in the equilibrium state. The polyelectrolyte complexes were first formed in pure water, and then the ionic strength of the solution was increased by addition of salt up to the concentration of 0.01 N NaCl. After about 1 day (the time needed to reach equilibrium), the AUC measurements were performed. One can see that only one, relatively slow sedimentation mode is present (22) Jakes, J. Czech. J. Phys. 1988, 38, 1305. (23) Dautzenberg, H.; Karibyants, N. Macromol. Chem. Phys. 1999, 200, 118.
X
Mw × 10-5, g/mol
0 0.2 0.4 0.6
5.3 5 6.5 220
0.01 N NaCl 70 60 55 47
4 × 10-3 1.3 × 10-3 3.5 × 10-4 1.1 × 10-6
0 0.2 0.4
5.3 5 22
0.05 N NaCl 65 45 38
1.3 × 10-3 3 × 10-4 1.3 × 10-5
Rg, nm
A2, mol mL/g2
in the systems for mixing ratios from 0 to 0.4. With increasing X, the mean position of the distribution shifted to higher sedimentation coefficients. Such behavior corresponds to soluble complexes. Increasing charge compensation in the complex particles increased somewhat the mass of the complexed chains and decreased the radius and the second virial coefficient of the complexed chains.5 All of these factors contribute to the observed increase of the sedimentation coefficient. In case of the mixing ratio 0.6, a second peak corresponding to a faster sedimentation rate appeared. The position of the slow sedimentation peak corresponds to the position of the complex at X ) 0.4. This means the system underwent disproportionation above a critical mixing ratio, which is typical for soluble complexes.4 The SLS data of the complexes obtained by a Zimm plot are presented in Table 2. With increasing X, the mass of the complexes practically did not change for X < 0.6 at a salt concentration of 0.01 N and for X < 0.4 at a salt concentration of 0.05 N. The decrease in radius and in the second virial coefficient with increasing mixing ratio is more pronounced at higher ionic strength and corresponds to the increasing compactness of the complexed chains. At higher mixing ratios, the complexes obtained are partly compact structures on a high level of aggregation. The small radius and the low virial coefficient also confirm this statement. The concentrations of the complex and the refractive index increments used for the calculation of the molecular masses were calculated using the eqs 1 and 2; that is, the complex concentration was calculated as the total concentration of all polymers in the solution. That is true for soluble complexes but not for disproportionated systems, where only the concentration of big particles must be taken into account in their characterization. According to Figure 1, this concentration is much lower than the total one. Therefore, the real masses of the aggregate particles are several times higher than the given ones. Increasing salt concentration in the solution decreased the stabilizing ability of the noncomplexed chain parts of the soluble complexes. From this point of view, it is understandable that the disproportionation of the system occurred at lower mixing ratios for the complexes in 0.05 N NaCl. Such behavior was already described by several authors.4,5,12,24 Summarizing the first part of the paper, one can state that in the studied system a transition from initially turbid systems of highly aggregated particles to molecularly dispersed complexes took place. Among several studied systems (compare ref 25), we observed this behavior only for this one polyelectrolyte combination under specific (24) Izumrudov, V. A.; Kharenko, O. A.; Kharenko, A. V.; Gulaeva, Z. G.; Kasaikin, V. A.; Zezin, A. B.; Kabanov, V. A. Vysokomol. Soedin. 1980, A22, 692. (25) Zintchenko, A.; Dautzenberg, H.; Tauer, K.; Khrenov, V. Langmuir 2002, 18, 1386.
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Figure 2. Relative scattering intensity at 90° as a function of time for complex DHP4/PAMPS X ) 0.2 and salt concentrations of (1) 0.015 N NaCl, (2) 0.02 N NaCl, and (3) 0.025 N NaCl.
conditions, which are well-known from the literature for the formation of soluble complexes.4-6 Surprisingly, the requirement of weak polyelectrolytes must not be fulfilled. Most likely, the double hydrophilic character of the used polycation plays an important part in the behavior of the complexes. 3.2. Kinetics of the Dissolution Process. The dissolution process of the aggregated particles runs from the bimodal system (aggregates and free chains of the excess polyelectrolyte) to the monomodal system (soluble complexes). In other words, the short-chain component redistributed between the long chains of the component in excess. Kinetic studies can contribute valuable information about the mechanism of this process. Therefore, the next section deals with the kinetic aspects of the dissolution process. It was already mentioned by Bakeev et al.11 that the transfer of the short-chain component from one long chain to another in the soluble complexes proceeds as a secondorder reaction. In this study, the detected process is the decrease of the fraction of the aggregated particles in solution. The process of dissolution of the initial aggregates into molecularly dispersed complexes taking place after addition of salt is very slow in the case of 0.01 N NaCl solution. The system needed up to 1 day to reach equilibrium. In the case of 0.05 N NaCl solution, all aggregates were completely dissolved after 5 min. Figure 2 presents the time dependence of the relative intensity at scattering angle 90° (normalized by the value corresponding to the equilibrium state) of the complexes after fast addition of salt. The dissolution rate increased strongly with increasing salt concentration in the complex solution. That is in good agreement with the data in the literature11 and the initial qualitative observations. Increasing the mixing ratio worked in the opposite direction (Figure 3), that is, a decreasing dissolution rate at a higher mixing ratio, indicating the important role of the excess component in the reaction. The concentration of aggregates in the solution increased with increasing mixing ratio, and the concentration of the free polyelectrolyte decreased accordingly. Therefore, the number of free polyelectrolyte chains, the partner in the exchange reaction, per one aggregated particle decreased. The dissolution rate increased strongly with increasing concentration of the reacting species in 0.01 N NaCl (Figure 4a). A higher salt concentration (0.02 N NaCl) in the reacting solution (Figure 4b) weakened the concentration dependence. It is evident that both factors, concentration and ionic strength, affect the kinetics of the dissolution process. Increasing salt content weakens the concentration de-
Zintchenko et al.
Figure 3. Relative scattering intensity at 90° as a function of time for complexes DHP4/PAMPS: (1) X ) 0.2 and (2) X ) 0.4. The salt concentration is 0.02 N NaCl; the PAMPS concentration is 3 × 10-4 M.
Figure 4. Relative scattering intensity at 90° as a function of time for complex DHP4/PAMPS X ) 0.2 in (a) 0.01 N NaCl and (b) 0.02 N NaCl. PAMPS concentration: (1) 1 × 10-3 M, (2) 5 × 10-4 M, and (3) 2 × 10-4 M.
pendence. Most likely, the process itself consists of a number of stages; one of them (the slowest step) is concentration dependent. Increasing salt concentration may lead to an increase of the rate of the slowest stage and consequently decreases the difference in the rates of the different stages. To prove this hypothesis, it is necessary to consider the structural changes of the complexes accompanying the dissolution process. The third part of our work was focused on this problem. 3.3. Structural Changes of the Complex during the Dissolution Process. To judge the structural changes during the dissolution process, we analyzed in detail the scattering curves measured at different times after the addition of salt. For this analysis, a special fitting algorithm, based on a comparison of the experimental curves with theoretically calculated ones in a scaled double logarithmic plot (see refs 20 and 21, experimental part), was used. All of the systems under study revealed a similar
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Figure 5. The scattering curves (points) and the theoretical model curves (lines) from the system DHP4/PAMPS X ) 0.2 for different times after addition of salt. The salt concentration is 0.02 N NaCl. The curves correspond to the times in Table 3. Table 3. Structural Parameters of the Particles during the Dissolution Process (N Corresponds to the Curves in Figure 5) N
time, min
σ
1 2 3 4 5 6 7 8
16 28 42 55 68 88 119 146
0.55
Mwc × 10-10, g2/(mol mL)
Rg, nm
25.1 17.0 9.79 5.64 3.61 2.02 0.81 0.58
157.6 203.3 267.5 272.4 283.2 290.6 277.4 308.4
behavior during the dissolution. Therefore, the discussion will be restricted only to the complex with X ) 0.2 at a salt concentration of 0.02 N NaCl. The scattering curves belonging to this system are presented in Figure 5. Because the big particles mainly contribute to the scattering intensity, all the scattering curves reflect more or less the aggregates. Because their concentration changed during the dissolution process in an unknown way, the molecular weights of the particles cannot be calculated correctly. Therefore, to evaluate the changes in scattering intensity from the aggregate particles only the product of their molecular weight and concentration can be used (Table 3). However, the angular dependence and the data about the radius of gyration are independent of concentration and reflect the real changes. The angular dependencies looked very similar for all curves and correspond quite well to the theoretical curves of polydisperse spheres in the small-angle region. The radii of gyration increased by nearly a factor of 2 (Table 3), indicating a swelling of the particles during the dissolution process. Since the scattering intensity is proportional to the product Mwc, the changes in scattering intensity correspond to the changes either in molecular mass or in concentration of the particles in solution. If we try to explain the change in Mw of a factor of 43 only by decreasing the real particle mass, about 85% of the material must be released from the particles. Then one should expect drastic changes in the particle structure and in the scattering curves. Most likely, the parameter undergoing the main changes in the dissolution process is the concentration of the aggregates. Therefore, under the assumption of only slight changes in the molecular weight of the aggregates, Mwc would correspond mainly to the changes in the concentration of the aggregates by the factor of 43. Additionally, a difference between the experimental curves and the model curves appeared in the wide-angle range. This difference increased with time, corresponding to an increase of the contribution of the
Figure 6. (a) The distribution functions of the complex solution DHP4/PAMPS X ) 0.2 for different times after addition of salt: (1) 0 min, (2) 150 min, (3) 250 min, (4) 350 min, (5) 1 day. (b) The ratio between peaks. The salt concentration is 0.02 N NaCl. Angle ) 90°.
small particles of the soluble complexes to the scattering intensity. To prove these data, dynamic light scattering measurements were performed and the distributions of the hydrodynamic radii as a function of time were obtained (Figure 6a). The systems consist of two peaks; one of them (small radii) corresponds to the molecularly dispersed complexes, and the other one (big radii), to the initial aggregates. During the dissolution process, the peak of the soluble complexes increased while the peak of the aggregates decreased, leading to strong changes of about 2 orders of magnitude for the ratio between the peak heights (Figure 6b). A very important result is the fact that the peak of aggregates did not disappear completely, even after several days, when the whole dissolution process is finished. Obviously, the dissolution of the aggregates reached an equilibrium state in which both species exist in a certain relation of concentrations. The ratio given in Figure 6b corresponds to the relation of the scattered intensities. Taking into account the differences in radii and assuming the model of spheres and equal densities for all species, one can roughly estimate the mass distribution. The concentration ratio between the soluble complexes and the aggregates would be about a factor of 100 higher than the intensity ratio; that is, only a very small part of the complexes remained in the aggregated state. The hydrodynamic radius of the aggregates also increased during the fast intensity changes, but after 1 day it decreased to the initial level again (Figure 7). This result confirms the swelling of the aggregated particles during the dissolution process. The hydrodynamic radii obtained at the angle of 90° are remarkably larger than the radii of gyration. The hydrodynamic radii extrapolated at the zero angle (corresponds to the z-average value) are about 2 times higher than the radius of gyration (at least for the stable starting system). This means that the characteristic ratio Fs between Rg and Rh, indicative for the structural type of
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Figure 7. The hydrodynamic radius of the aggregates and the relative intensity changes during the dissolution process in 0.02 N NaCl. X ) 0.2. Angle ) 90°. Table 4. Theoretical Gs Values for Different Density Gradients in Monodisperse Spherical Particles density gradient, Fg/F0
Fs factor
1 0.6 0.3
0.775 0.757 0.732
density gradient, Fg/F0
Fs factor
0.1 0.01
0.686 0.57
the particles, is about 0.5. This value is significantly smaller than the theoretical value for monodisperse spheres (0.775). Such values can appear either if the particles have a relatively thick highly swollen polymer shell or as a consequence of a density gradient in the particle. The Fs factor for a particle with a density gradient F(r) depends both on the magnitude of the gradient and on its type (linear, exponential).26 Using the definition of the radius of gyration,
∫0R 4πr4F(r) dr ) R ∫0 4πr2F(r) dr 0
2
Rg
0
(5)
where r is the distance between the center of a spherical particle and a mass element and R0 is the radius of the particle (in first approximation equal to the hydrodynamic radius), one can calculate Rg for a given density profile. For an exponential density gradient,
(
F(r) ) F0 exp
ln Fg/F0 r R0
)
(6)
where F0 and Fg are the densities in the center and at the surface of the particle, respectively, one obtains
Fs ) Rg/R0 )
x
Q-4 + 12/Q2 Q - 2 + 2/Q(1 - e-Q) with Q ) ln Fg/F0 (7)
The calculated Fs factors are given in Table 4. An appropriate Fs factor of 0.57 would correspond to a density gradient of 0.01. That seems to be reasonable: the normal density of the aggregates in this system is about 0.4 g/cm3 (center of the particle); the density on the surface is then about 0.004 g/cm3, which corresponds nearly to the density of polymer coils. The values in Table 4 were calculated for monodisperse particles. Polydispersity also affects the Fs values, and if the polydispersity is known (see Table 3), one can estimate this effect. On the other hand, the (26) Dautzenberg, H.; Rother, G. Plaste Kautsch. 1986, 33, 241.
polydispersity values presented in Table 3 were obtained using the model of homogeneous spheres. Interpretation by inhomogeneous spheres would lead to lower polydispersities.26 Therefore, an unambiguous explanation cannot be given. However, being only a roughly estimation, the values presented in Table 4 suggest the presence of a density gradient in the particles and reflect the right magnitude. 3.4. Mechanism of the Dissolution Process. The results obtained allow us to propose a mechanism of the dissolution process, presented by Scheme 1. Directly after mixing of the solutions of the oppositely charged polyelectrolytes, the system is bimodal: there are the highly aggregated complex particles with nearly a 1:1 charge stoichiometry and the free excess component of the long PAMPS chains. After the addition of salt, the dissolution process starts. At first, the free polyanion chains of the excess component remove some amount of the polycations from the aggregates. This process can be split into four other steps: (1) adsorption of a chain of the excess component on the complex particle, (2) transition of one or several polycation chains to the adsorbed polyanion chain, (3) desorption of this chain loaded with some polycation chains from the surface of the particle, and (4) exchange of polycations between the particle of soluble complex and the other free polyanion chains in the s olution. Because the polyanion chains are relatively long and in the initial particle physically cross-linked by the salt bonds with the polycation chains, one should expect that the main amount of polyanions forming the initial aggregates remain in them. In this case, the removal of the polycation chains out of the complex changes the stoichiometry of the particles and leads to an excess of the polyanions in an aggregate. The noncomplexed polyanion groups cause an increase in counterion concentration in the aggregates, resulting in higher osmotic pressure and swelling of the particles. Because the removal of the polycations starts from the region close to the surface of the aggregates, one should expect the formation of a density gradient in the particle, as indicated by the Rg/Rh ratio. Finally the particle becomes unstable because the number of linkages in the structure formed by complexed macroions decreases and the tension due to the swelling increases. When the particle reaches the state where it cannot sustain this tension anymore, it will be destroyed and disintegrate into small particles, which are close to the molecular level. This stage is the second and final step of the dissolution process.
Transition Highly Aggregated Complexes
The proposed mechanism can explain all the dependencies experimentally found. It must be emphasized that the stage of reaction detected in our kinetic studies is the final step. The changes in the scattering intensity of the solution monitor the transition from the “activated” unstable aggregates to the particles close to the molecular level, that is, the decrease of the number of aggregates in the solution. The transition of the primary aggregates, obtained in pure water, to the activated aggregates (first stage in Scheme 1, nonobservable by SLS) is governed by the second-order reaction described by Bakeev et al.11 This first step is the time-consuming one and determines the rate of the whole process. It has to be discussed with respect to the effects of the ionic strength, polyelectrolyte concentration, and mixing ratio on the dissolution rate. The rate of this step increases with increasing ionic strength, for the following reasons: (1) the repulsive interactions between the negatively charged particles and anionic chains decrease, and the quality of the solvent for PEG chains decreases, enhancing the chance for polyanion adsorption; and (2) the ionic interactions become weaker, favoring exchange reactions. Both effects lead to a faster transition of the polycation chains from the polyanion chains in the particles to the free ones and a higher dissolution rate (Figure 2). The mixing ratio also has a drastic effect on the dissolution rate, as demonstrated in Figure 3. This can easily be understood by the increase of the number of free polyanion chains with decreasing mixing ratio. The influence of the polyelectrolyte concentrations, that is, of the partners in the transition reaction, changes strongly with the ionic strength. At low ionic strength (Figure 4a), the dissolution rate decreases drastically with increasing concentration. However, this effect is much less pronounced at higher ionic strength (Figure 4b), because of the fast dissolution rate in all systems due to the increase in the ionic strength. The second step is concentration independent. Because the osmotic pressure inside the particle and the number of physical cross-links due to complex formation govern
Langmuir, Vol. 19, No. 6, 2003 2513
the rate of this stage and the increase of the salt concentration decreases the osmotic pressure, the presence of salt in the solution should decrease somewhat the rate of this step. Despite the discussed two-step mechanism, we observed a steady decrease of the scattering intensity with time. Only in the first minutes did the scattering level remain nearly constant. Most likely, the polydispersity of the particle system in several aspects (particle size, structure density, density of physical cross-linking) causes a smoothing of the dissolution step. 4. Conclusions Molecularly dispersed soluble complexes were obtained in a system of two strong polyelectrolytes, where the shortchain component was a double hydrophilic polycation. The principles of formation of these complexes, the conditions under which they could be formed, and their behavior correspond to soluble complexes formed by two weak polyelectrolytes. Complex formation in pure water resulted in big aggregates. Addition of low molecular weight salt (NaCl) to the solution led to dissolution into complexes on the molecular level with regard to the high molecular weight polymer. Kinetic studies of the dissolution process showed strong dependencies of the dissolution rate on ionic strength, polyelectrolyte concentration, and mixing ratio. The effect of salt overlaps the dependence on concentration of the species in solution. The studies of structural changes during the dissolution process suggest a two-step reaction, where the first stage is the release of polycations from the initial aggregates due to the transition from polyanion chains in the primary aggregates to the free polyanion chains in solution. In the second step, the osmotic pressure appearing in the aggregates due to an increasing excess of polyanions inside completely destroys the aggregates. The proposed mechanism of the process may explain all the dependencies found. LA0265427
