Controlling the Growth Regime of Polyelectrolyte Multilayer Films

Jan 27, 2004 - Eric Hu¨bsch,†,‡ Vincent Ball,‡ Bernard Senger,† Gero Decher,‡,§. Jean-Claude Voegel,† and Pierre Schaaf*,‡. Institut N...
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Langmuir 2004, 20, 1980-1985

Controlling the Growth Regime of Polyelectrolyte Multilayer Films: Changing from Exponential to Linear Growth by Adjusting the Composition of Polyelectrolyte Mixtures Eric Hu¨bsch,†,‡ Vincent Ball,‡ Bernard Senger,† Gero Decher,‡,§ Jean-Claude Voegel,† and Pierre Schaaf*,‡ Institut National de la Sante´ et de la Recherche Me´ dicale, Unite´ 595, Faculte´ de Chirurgie Dentaire, Universite´ Louis Pasteur, 11, rue Humann, 67085 Strasbourg Cedex, France, Centre National de la Recherche Scientifique, Institut Charles Sadron, 6, rue Boussingault, 67083 Strasbourg Cedex, France, and Universite´ Louis Pasteur, 1, rue Blaise Pascal, 67008 Strasbourg Cedex, France Received November 21, 2003. In Final Form: December 17, 2003 When multilayer films are built up with polycations and polyanions, their thickness can grow either linearly or exponentially with the number of deposited layer pairs, depending for example on the nature of the polyelectrolytes used. We investigate in the present work the construction of a film using a binary mixture of polyanions as polyanion solution. The two anionic components are chosen such that one of them causes the film to grow linearly while the other causes the film to grow exponentially. It is observed that a mixture of both components leads to a hybrid growth law, depending on its composition. At the beginning of the construction, the thickness of the film increases exponentially with the number of deposited bilayers. Once a given thickness is reached, one observes the crossover to a linear growth regime. This finding is discussed on the basis of the diffusion coefficients of the polyanions that are assumed to diffuse “in” and “out” of the film.

Introduction The alternate deposition of polyanions and polycations on a charged surface leads to the formation of a film called “polyelectrolyte multilayer”. Because of their widespread potential applications ranging from electrooptical devices to ultrafiltration and biomaterials,1-8 these films have received considerable attention since their discovery in 1991 by Decher and co-workers.9,10 Schematically, two kinds of multilayers have been reported. The first class of multilayers encompasses the multilayers whose mass and thickness grow linearly with the number of deposition steps. These are the most common and most widely studied and will be called “linearly growing films”. Multilayer films composed of poly(styrene sulfonate) (PSS) and poly* Address correspondence to this author. E-mail: schaaf@ ics.u-strasbg.fr; phone: +33-388-414012; fax: +33-388-414099. † Institut National de la Sante ´ et de la Recherche Me´dicale, Universite´ Louis Pasteur. ‡ Centre National de la Recherche Scientifique, Institut Charles Sadron. § Universite ´ Louis Pasteur. (1) Eckle, M.; Decher, G. Nano Lett. 2001, 1, 45-49. (2) Kim, B. Y.; Bruening, M. L. Langmuir 2003, 19, 94-99. (3) Onda, M.; Lvov, Y.; Ariga, K.; Kunitake, T. J. Ferment. Bioeng. 1996, 82, 502-506. (4) Rmaile, H. H.; Schlenoff, J. B. J. Am. Chem. Soc. 2003, 125, 66026603. (5) Sinani, V. A.; Koktysh, D. S.; Yun, B. G.; Matts, R. L.; Pappas, T. C.; Motamedi, M.; Thomas, S. N.; Kotov, N. A. Nano Lett. 2003, 3, 1177-1182. (6) Mendelsohn, J. D.; Yang, S. Y.; Hiller, J.; Hochbaum, A. I.; Rubner, M. F. Biomacromol. 2003, 4, 96-106. (7) Chluba, J.; Voegel, J. C.; Decher, G.; Erbacher, P.; Schaaf, P.; Ogier, J. Biomacromol. 2001, 2, 800-805. (8) Serizawa, T.; Yamaguchi, M.; Matsuyama, T.; Akashi, M. Biomacromol. 2000, 1, 306-309. (9) Decher, G.; Hong, J. D.; Schmitt, J. Thin Solid Films 1992, 210, 831-835. (10) Decher, G. Science 1997, 277, 1232-1237.

(allylamine hydrochloride) (PAH) constitute one example of such films.11 During each layer deposition step, the polyelectrolytes from the solution are electrostatically attracted by the oppositely charged polyelectrolytes constituting the last layer of the film on the solid substrate. This polyelectrolyte deposition then leads to charge overcompensation at the solid/liquid interface,12-14 which, in turn, causes electrostatic repulsion with excess material in solution and limits the adsorbing layer to monolayer coverage. The surface is then rinsed with pure buffer and the film is brought into contact with the polyelectrolyte solution of opposite charge, which starts a new deposition cycle. It was shown that such films exhibit a somewhat “fuzzy” but layered structure, each polyelectrolyte layer interpenetrating with its neighboring layers.15 Thus, there is typically no “communication” between a polyelectrolyte deposited at step i and a polyelectrolyte deposited at step i ( p with p larger than 2 or 3. It should be emphasized that p depends on the chemical nature of the polyions involved and both larger and smaller values were reported. The thickness per layer lies typically between 1 and 10 nm depending on various parameters such as the ionic strength of the polyelectrolyte solutions,12,14 their pH (for weak polyelectrolytes),16 and, to some extent, on the molecular weight of the polyelectrolytes.17 (11) Ramsden, J. J.; Lvov, Y. M.; Decher, G. Thin Solid Films 1995, 254, 246-251. (12) Ladam, G.; Schaad, P.; Voegel, J. C.; Schaaf, P.; Decher, G.; Cuisinier, F. Langmuir 2000, 16, 1249-1255. (13) Caruso, F.; Lichtenfeld, H.; Donath, E.; Mohwald, H. Macromolecules 1999, 32, 2317-2328. (14) Schlenoff, J.; Ly, H.; Li, M. J. Am. Chem. Soc. 1998, 120, 76267634. (15) Lo¨sche, M.; Schmitt, J.; Decher, G.; W. G., B.; Kjaer, K. Macromolecules 1998, 31, 8893-8906. (16) Shiratori, S. S.; Rubner, M. F. Macromolecules 2000, 33, 42134219.

10.1021/la0361870 CCC: $27.50 © 2004 American Chemical Society Published on Web 01/27/2004

Growth Regime of Polyelectrolyte Multilayer Films

More recently, a second class of films whose mass and thickness grow exponentially with the number of deposition steps were reported.18,19 These films will be called “exponentially growing films”. Their buildup is based on the diffusion “in” and “out” of the whole film during each layer pair deposition step of at least one of the polyelectrolytes constituting the film. A detailed description of such a buildup process was reported recently.20 The structure of these films is quite different from that of linearly growing ones. For example, these films, in contrast to linearly growing ones, do not give Bragg peaks in neutron reflection experiments when deuterated polyelectrolytes are used to label certain layers in the film architecture.21 This indicates that they are not as structured but can more be seen as gels of polyanion/polycation complexes. Exponentially growing films were mainly observed with polypeptides and polysaccharides. Poly(glutamic acid)(PGA)/poly(allylamine hydrochloride)(PAH) constitutes an example of such films.22 Up to now, almost all existing reports on polyelectrolyte multilayer films are based on the deposition of a single compound in each individual layer. To the authors’ knowledge, only three publications describe the buildup of polyelectrolyte multilayers in which the film is exposed to a solution containing a mixture of polyelectrolytes of the same charge so that two different polyions (either two polycations or two polyanions) are competing for their incorporation into the film. Leporatti et al. have briefly mentioned the use of PAH-chitosan and PSS-chitosan sulfate mixtures to construct multilayer capsules but they did not check how the different polyelectrolytes were incorporated into the films and did not mention the reasons for using such mixtures in their study.23 Sui and Schlenoff used a mixture of poly(diallyldimethylammonium chloride), PDADMA, and a random copolymer of diallyldimethylammonium chloride with acrylic acid, PDADMAco-PAA, to construct pH responsive polyelectrolyte multilayers.24 The first systematic study of films constructed from polyelectrolyte solutions containing two polyions was reported by Debreczeny et al. who investigated the construction of multilayer films using mixtures of poly(L-glutamic acid) (PGA) and poly(L-aspartic acid) (PLA) as polyanions and poly(L-lysine) (PLL).25 They found, in particular, that both polyanions (PGA and PLA) are incorporated simultaneously in the film, though with a ratio different from the one present in the solution containing the polyanion mixture. The incorporation of PLA was favored over that of PGA. In this report, we investigate the construction of multilayer films by exposing a charged surface consecutively to a solution of PAH and to a solution containing both PGA and PSS. This system was chosen because (PSS/ PAH) represents a linearly growing system, whereas (PGA/PAH) shows an exponential film growth. We investigate the film growth by different methods as a (17) Sui, Z.; Salloum, D.; Schlenoff, J. B. Langmuir 2003, 19, 24912495. (18) Elbert, D. L.; Herbert, C. B.; Hubbell, J. A. Langmuir 1999, 15, 5355-5362. (19) Picart, C.; Lavalle, P.; Hubert, P.; Cuisinier, F. J. G.; Decher, G.; Schaaf, P.; Voegel, J. C. Langmuir 2001, 17, 7414-7424. (20) Picart, C.; Mutterer, J.; Richert, L.; Luo, Y.; Prestwich, G. D.; Schaaf, P.; Voegel, J. C.; Lavalle, P. Proc. Natl. Acad. Sci. U.S.A. 2002, 99, 12531-12535. (21) v. Klitzing, R. private communication. (22) Boulmedais, F.; Ball, V.; Schwinte, P.; Frisch, B.; Schaaf, P.; Voegel, J. C. Langmuir 2003, 19, 440-445. (23) Leporatti, S.; Gao, C.; Voight, A.; Donath, E.; Mo¨hwald, H. Eur. Phys. J. 2001, 5, 13-20. (24) Sui, Z.; Schlenoff, J. B. Langmuir 2003, 19, 7829-7831. (25) Debreczeny, M.; Ball, V.; Boulmedais, F.; Szalontai, B.; Voegel, J. C.; Schaaf, P. J. Phys. Chem. B 2003, 107, 12734-12739.

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function of the composition of the polyanion solution and we propose a mechanism for the observed complex growth behavior. Materials and Methods Polyelectrolyte Solutions. Polyelectrolytes from commercial sources were used for the buildup of the (PGAx-PSS1-x/PAH)n multilayer architecture. Poly(allylamine hydrochloride) (PAH, M ) 70 000 g mol-1, CAS: 71550-12-4; cat. no.: 28,322-3) was purchased from Aldrich, poly(L-glutamic acid) (PGA, M ) 17 000 g mol-1, CAS: 26247-79-6; cat. no.: P-4761) was obtained from Sigma and poly(styrene sulfonate) (PSS, M ) 70 000 g mol-1, CAS: 25704-18-1; cat. no.: 24,305-1) was purchased from Aldrich. Branched polycation poly(ethylene imine) (PEI, M ) 750 000 g‚mol-1, CAS: 25987-06-8; cat. no.: 18,197-8) was purchased from Aldrich. All the polyelectrolytes were used without further purification. The polyelectrolyte solutions were prepared by dissolving the appropriate amounts of polyelectrolytes in filtered (0.22 µm Millex GV) 0.15 M sodium chloride (NaCl, Prolabo, France, R. P. Normapur) aqueous solutions prepared with Millipore water (resistivity ) 18.2 MΩ cm, Milli Q-plus system). The pH of all the solutions was adjusted to pH 7.4 ( 0.05 by addition of appropriate volumes of either HCl solution (Prolabo, France, R. P. Normapur) or NaOH solution (Prolabo, France, R. P. Normapur) immediately before use. The (PGAx-PSS1-x/PAH)n films were constructed by using a 1 mg mL-1 PAH solution as polycation solution and a polyanion solution obtained by mixing x mL of a 0.733 mg mL-1 PGA solution and (1 - x) mg mL-1 of a 1 mg mL-1 solution of PSS. The mixed PGAx-PSS1-x solution thus has a total monomer repeat unit concentration of 4.85 × 10-3 mol L-1, and x represents the molar percentage of the monomer repeat unit of PGA. For instance, a (PGA0.25-PSS0.75/PAH)n film is constructed from a polyanion solution containing 0.18 mg mL-1 PGA and 0.75 mg mL-1 PSS. The film construction was performed as follows. The substrate was first brought in contact for at least 1 h with the 0.15 M NaCl aqueous solution at pH 7.4. The surface was then brought in contact with a 1 mg mL-1 PEI solution for 10 min. The solution was then rinsed 10 min by the 0.15 M NaCl aqueous solution. The deposition of this PEI precursor layer was only performed once. The surface was then brought in contact with the mixed polyanion solution for 10 min followed by 10 min of rinsing with the 0.15 M NaCl aqueous solution, followed by 10 min of contact with the PAH solution, again followed by 10 min of rinsing with the aqueous solution. This four-step procedure was repeated n times. Optical Waveguide Lightmode Spectroscopy. Optical waveguide lightmode spectroscopy (OWLS) is an optical technique that allows determining the optical thickness and the refractive index of an adsorbed layer on a Si0.8Ti0.2O2 waveguide.26 A laser beam is directed on a diffraction grating imprinted in the waveguide. The incoupling angles for both transverse electric (TE) and transverse magnetic (TM) waves are determined by changing the incident angle of the laser beam. To each incoupling angle corresponds an effective refractive index, either NTE or NTM, depending on the polarization. The knowledge of these indexes allows calculating the optical thickness and the refractive index of the film. The film deposited on the waveguide is sensed by an evanescent wave with a typical penetration depth of 200 nm. When the film thickness exceeds largely this depth, the film behaves optically as a semi-infinite medium. All experiments were performed on a home-built experimental setup equipped with a He-Ne laser and ASI 2400 waveguides made of Si0.8Ti0.2O2 (Artificial Sensing Instruments, Zu¨rich, Switzerland). All the details about the analysis of the data and further experimental details about the apparatus can be found elsewhere.27 The multilayers were constructed as described above. Each polyelectrolyte deposition step was performed by flushing 100 µL of the polyelectrolyte solution into the cell compartment of volume 37 µL. The injection took approximately 30 s out of the 10 min of contact. Each rinsing step was performed by flushing continu(26) Tiefenthaler, K.; Lukosz, W. J. Opt. Soc. Am. B: Opt. Phys. 1989, 6, 209-220. (27) Picart, C.; Ladam, G.; Senger, B.; Voegel, J.-C.; Schaaf, P.; Cuisinier, F. J. G.; Gergely, C. J. Chem. Phys. 2001, 115, 1086-1094.

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Hu¨ bsch et al.

Figure 2. Resonance frequency shifts measured with QCM-D at 15 (triangles), 25 (squares), and 35 (diamonds) MHz, divided by the overtone number (ν ) 3, 5, and 7, respectively). These experimental data correspond to the buildup of the multilayer film with the PGA0.5-PSS0.5 polyanion mixture.

Figure 1. Resonance frequency shifts (A) and dissipations (B) as obtained by QCM-D at 15 MHz. These experimental data correspond to the buildup of the multilayer film with PGAxPSS1-x polyanion mixtures, where x ranges from 0 to 1 as indicated by the labels on the curves. The results corresponding to x ) 0 and x ) 0.1 are practically indistinguishable. The symbols in panel B are in correspondence with those in panel A. ously the aqueous NaCl solution through the cell for 10 min with a flow rate of 10.1 mL h-1. Quartz Crystal Microbalance. Experiments with the dissipation quartz crystal microbalance (QCM-D) were performed on a Q-Sense D 300 apparatus (Q-Sense AB, Go¨teborg, Sweden) by monitoring the resonance frequencies of silica coated crystals, as well as the dissipation factors at four frequencies (the fundamental at 5 MHz and the 3rd, 5th, and 7th harmonics at 15, 25, and 35 MHz). These data give, in principle, information on the adsorption process, as well as on certain viscoelastic properties of the adsorbed film.28,29 In a first approximation, the resonance frequency shifts are proportional to the mass of the film deposited on the crystal per unit area.30 However, this approximation holds only in homogeneous, quasi-rigid films with a thickness that is not too high. The multilayers were constructed as described above. Each polyelectrolyte deposition step and rinsing step was performed by flushing 1.5 mL of the solution (polyelectrolyte or aqueous NaCl solution) into the cell compartment of volume 100 µL. The injection took approximately 90 s out of the 10 min of contact.

Results and Discussion Film Construction. The evolution of the resonance frequency shifts ∆f and dissipation values D measured with QCM-D during the construction of films with different compositions are given in Figure 1, as a function of the number of deposited layers. For reasons of clarity, we report QCM-D data only for the third harmonic (15 MHz). The resonance frequency of the crystal in contact with buffer is used as reference value. Therefore, ∆f ) 0 prior to the deposition of the first layer. As can be seen, the evolution of the frequency is almost indistinguishable for films constructed from polyanion solutions characterized by x ) 0 and x ) 0.1 (i.e., polyanion solutions with small (28) Voinova, M. V.; Rodahl, M.; Jonson, M.; Kasemo, B. Phys. Scr. 1999, 59, 391-396. (29) Rodahl, M.; Kasemo, B. Sens. Actuators, A 1996, 54, 448-456. (30) Sauerbrey, G. Z. Phys. 1959, 155, 206-222.

PGA contents). In striking variance, it is seen that when the PGA content of the polyanion solution varies from x ) 1 to x ) 0.88, corresponding respectively to 1 - x ) 0 and 1 - x ) 0.12 (i.e., polyanion solutions with small PSS contents), the evolution of the frequency shift during the buildup of the films is markedly different. This observation emphasizes the fact that the two polyanions constituting the mixture play highly different roles during the film construction. The evolution of ∆f/ν, for the three odd harmonics ν ) 3, 5, and 7, is plotted in Figure 2 as a function of the number of layers for the film built up from a polyanion solution containing 50% of PGA. As can be seen, the curves corresponding to the three overtones are very close. This result is typical for all systems investigated in the present work. The coincidence of the three curves displayed in Figure 2 shows that, in a first approximation, ∆f is proportional to the mass per unit area, m, of the film deposited on the vibrating quartz crystal. This mass includes the water molecules entrapped within the film. It is calculated within this approximation by the Sauerbrey relation:30

∆f ν

m ) -C

(1)

where C is a constant characteristic of the crystal plate (C ≈ 17.7 ng cm-2 Hz-1 for the quartz plates used here). By assuming that the density of the film is close to 1 g.cm-3, one deduces the evolution of the film thickness, d, during the buildup (Figure 3). To go beyond the Sauerbrey approximation, the experimental data (∆f and D) can be analyzed by using the framework developed by Voinova et al.28 Under the hypothesis that the film is a homogeneous and isotropic viscoelastic layer, a unique series of thickness values, d, is derived from ∆f and D corresponding to ν ) 3, 5, and 7. Figure 3 shows that the values of d obtained by this more refined analysis are in good agreement with those derived by using eq 1. In addition, the analysis based on Voinova’s model yields a shear elastic modulus, µ, and a shear viscosity, η, of the film that are very large. This suggests that the film is nearly a solid. This conclusion is fully coherent with the observation that Sauerbrey’s relationship gives a good estimate of the thickness. Moreover, high values of µ and η favor a great penetration depth of the acoustic wave which allows measuring the thickness up to several hundreds of nanometers as seen in Figure 3. As expected, the thickness of the film built up with a PSS polyanion solution (x ) 0) depends linearly on the number of layers, whereas it increases exponentially in

Growth Regime of Polyelectrolyte Multilayer Films

Figure 3. Thickness of the multilayer film built up with the PGA0.5-PSS0.5 polyanion mixture. The three sets of data point (triangles, squares, and diamonds) are derived from the resonance frequency shifts (see Figure 2) measured at 15, 25, and 35 MHz, respectively, by using the Sauerbrey relationship (eq 1). The solid line represent the thickness derived by means of the monolayer model described in refs 28-29. The three sets of data points derived using Sauerbrey’s relationship have been fitted with -11.2 + 12.68 exp(0.119 i) up to the 26th layer (i is the number of layers). The insert shows d + 11.2 for the three frequencies (as in the mainframe) on a logarithmic scale to reveal the exponential growth up to about the 26th layer.

the film corresponding to x ) 1 (constructed from a pure PGA solution as polyanion solution). For films constructed with mixtures of polyanion solutions whose PGA content is not too small, the film thickness increases exponentially during the first deposition cycles. At a certain point, it abruptly changes to a linear growth regime, as shown by the frequency shifts in Figure 1 (see x ) 0.25, 0.50, 0.67, 0.75). Interestingly, for each mixture composition where the two regimes are visible, the slope observed in the linear growth regime is smaller than that observed at the end of the exponential phase. Moreover, the slope increases as the polyanion solution becomes richer in PGA and the difference between the slope at the end of the exponential phase and that in the linear regime decreases. One can expect that for the (PGA/PAH) film built from a pure PGA solution (x ) 1), the exponential regime ultimately also goes over into a linear one but without change in the slope. Unfortunately, we could not observe this behavior because the change of the deposition regime is expected to occur only at a film thickness exceeding the detection limit of both OWLS and QCM-D. A similar qualitative thickness evolution was observed by Radeva et al. for the system PSS/PDADMAC (poly(diallyldimethylammonium chloride)).31 During the exponential growth phase, the film thickness, as estimated from QCM-D data, increases mainly when the film is brought into contact with the polycation solution and remains almost constant (or even decreases slightly) after contact with the polyanion solutions. Qualitatively similar evolutions of the film thickness with the number of layers were obtained by OWLS for the (PGA0.25-PSS0.75/PAH)n multilayers. For films constructed by using polyanion solutions with a higher PGA content, the film thickness could only be followed in the exponential regime up to a film thickness of about 200-300 nm, which corresponds to the penetration length of the evanescent wave which senses the film. Polyelectrolyte Diffusion. Earlier, we proposed a model for the exponential growth regime that is based on (31) Radeva, T.; Milkova, V.; Petkanchin, I. J. Colloid Interface Sci. 2003, 266, 141-147.

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Figure 4. Effective refractive index of the multilayer film during construction measured in situ with OWLS as a function of time. The arrows oriented from top to bottom indicate the injection times of the PAH solution. The arrows oriented from bottom to top indicate the injection times of the mixed polyanion solution (PGA0.67-PSS0.33). The labels (9-16) on the lower arrows denote the number of the deposition cycle.

the free or almost free diffusion of an unknown fraction of at least one of the polyions within the multilayer film and across the film/solution interface.20 OWLS proved to be a very useful technique to investigate such diffusion processes because of its restriction of the detection of refractive index changes within the penetration depth of the evanescent wave.19 If the thickness of the film is larger than this depth (about 200-300 nm), OWLS detects dynamic structural changes only close to the waveguide/ film interface. Figure 4 shows the evolution of the effective refractive index, NTE, corresponding to the polarization perpendicular to the plane of incidence during the buildup of the (PGA0.67-PSS0.33/PAH)n multilayers at the end of the exponential growth regime and at the beginning of the linear phase. A similar evolution is observed for NTM, the effective refractive index corresponding to the polarization in the plane of incidence (data not shown). At the end of the exponential regime, one observes the typical “cycling evolution” where the effective refractive indexes vary in a cyclic way from one layer pair build-up step to the next. As the number of build-up steps corresponding to the onset of the linear regime is attained, the amplitudes of variation of NTE and NTM strongly diminish and the two effective refractive indexes remain almost constant after the deposition of about two to four further layer pairs. A likely explanation for this phenomenon is that polyelectrolytes diffuse “in” and “out” of the film, down to its bottom during each layer pair deposition step in the exponential growth phase as could be demonstrated for other exponentially growing films.20 This polyelectrolyte diffusion down to the penetration zone of the evanescent wave suddenly stops as the linear growth regime starts. Moreover, the large increase of the film thickness measured by QCM-D in the exponential growth phase during the contact of the film with the polycation solution and its almost constancy during contact with the polyanion solution suggest that the polyanions are the diffusing species, whereas the polycation (PAH) seems not to diffuse in and out of the film. Our experiments, however, do not allow determining the composition of the diffusing species. In the following, we shall assume that both polyanions diffuse in the film. Interpretation of the Two Growth Regimes. This paragraph is aimed at explaining (i) the origin of the transition from the exponential to the linear regime, which can potentially occur in any exponentially growing polyelectrolyte system, and (ii) why this transition is accompanied by a change of slope of the thickness as illustrated in Figure 3. Let us first assume that the two polyanions, PGA and PSS, diffuse in and out of the film

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with the same diffusion coefficient. As long as the thickness of the film is smaller than a certain value, all polyanion chains diffuse out of the film during the time of exposure to the PAH solution. The number of polyanion chains available for the formation of complexes with PAH chains at the film/solution interface is therefore proportional to the total thickness of the film (or size of the reservoir). This relationship between thickness and number of complexes formed (or additional thickness) leads immediately to the observed exponential growth law for the thickness. However, because of the finite value of the diffusion coefficient, the film eventually reaches a thickness, which no longer allows all “free” polyanions to diffuse out of the multilayer during the contact time with the polycation solution (10 min for the experiments described here). At this point, the in and out diffusion affects predominantly a zone beneath the film/solution interface whose thickness is about (Dpt)1/2, where Dp is the diffusion coefficient of both polyelectrolytes and t is the contact time of the multilayer with the polycation solution. Because the number of polyanion chains that participate in the formation of new complexes is now constant, the film thickness grows linearly from this point on and the thickness increment per layer pair deposition is the same at the end of the exponential regime and in the linear regime (for constant contact times). It is, however, expected that both polyanions diffuse out of the film with different diffusion coefficients. During the build-up process, one then reaches a critical film thickness above which the slowest diffusing polyanion can no longer diffuse out of the entire film during the limited contact time with the polycation solution. The composition of the newly forming outer layer that results from the formation of the polyanion/polycation complexes as the polyanions diffuse out of the film then changes too. This change in composition leads also to a change of the density of the outer layer when compared to that of the film beneath. The diffusion coefficients of the two polyanionic species should thus also become different in the new forming layers when compared to the film beneath. It seems that in our case the diffusion coefficients in the outer layer are significantly reduced. The outward diffusion flux of the two polyanions is thus also affected and the composition of the subsequent layers is changed in such a way that the polyanion diffusion is reduced. One then rapidly enters in the case discussed previously where the diffusion of each polyanion out of the film takes place over a limited but constant thickness, different for each polyanion, whose extension is about (Dp,jt)1/2, Dp,j being the diffusion coefficient of the polyanion of type j. This process is schematically represented in Figure 5. Because the diffusion coefficient through the outer part of the film is reduced, the slope of the thickness decreases too. This interpretation is supported by Figure 6 which shows the time evolution of the frequency shift, ∆f, during the buildup of a (PGA0.67-PSS0.33/PAH)n multilayer in the exponential to linear transition zone, at the 15-MHz resonance of the quartz crystal. As can be observed, in the exponential growth regime ∆f changes almost instantaneously after each new contact of the film with the PAH solution and the signal stabilizes far before the beginning of the rinsing step. The ∆f decrease that follows the contact of the film with the PAH solution then suddenly becomes slower and during the next layer pair deposition it is so slow that the signal does not reach a constant value during the 10 min of contact with the polycation solution. During the following build-up steps, the decrease of ∆f becomes linear with time over the entire contact period with the PAH solution and it is identical for each layer pair deposition

Hu¨ bsch et al.

Figure 5. Schematic representation of the polyanion diffusion depth (black bars). In the exponential phase, the polyanions are extracted over the whole film thickness during its contact with the polycation solution. In and after the transition zone, only the “upper” fraction of the film plays the role of effective polyanion reservoir. In the linear phase, the polyanions that contribute to the formation of new complexes originate from a zone of constant thickness that moves “up” in the film with increasing number of layers. The thickness of this zone is different for each polyanion in the film.

Figure 6. Resonance frequency shift at the 15-MHz detection frequency, measured with QCM-D as a function of time. The arrows oriented from bottom to top indicate the injection times of the PAH solution. The arrows oriented from top to bottom indicate the injection times of the solution of the polyanion mixture (PGA0.67-PSS0.33). The small vertical bars indicate rinsing times.

step. Such an evolution is characteristic of a linear growth induced by limited diffusion. The interpretation given above is also supported by Figure 4 which shows that as the linear regime sets on, the diffusion process no longer extends down to the deposition substrate and thus only affects the outer part of the film. A similar behavior is expected for a system consisting in a unique polycation associated with a unique polyanion, when at least one of the species is very polydispersed. Indeed, in this case, the low-mass polyelectrolytes are expected to diffuse with a much larger diffusion coefficient than the high-mass chains. This could eventually explain the thickness evolution of the PSS/PDADMAC system observed by Radeva et al.31 Finally, it is important not to confuse the linear growth described here with the linear growth observed in films, such as (PSS/PAH) in which all polyions stay trapped within the respective layer which they formed on the surface of the film during their adsorption. In the case described here, the new layers that form during each contact with the polycation solution are the consequence of the diffusion, in and out of the film, of the “free” polyanions. If the linear process would result solely from the direct interaction of the polyions from the solution with the polyions of opposite charge deposited previously and constituting the film/solution interface, then the

Growth Regime of Polyelectrolyte Multilayer Films

increase of the film thickness in the linear regime should be extremely slow as it is always observed for (PSS/PAH) linear type buildup. We observe, in contrast, a rapid but constant thickness increase during the time of contact of the film with the polycation solution in the linear regime (Figure 6), the thickness increase depending upon the composition of the polyanion solution. Conclusion In this article, we have investigated the buildup of polyelectrolyte multilayers from a polycation solution (PAH) and solutions containing a mixture of polyanions (PGA and PSS) of different composition. The pure (PSS/ PAH)n system was known to grow linearly with the number of deposited layer pairs and the pure (PGA/PAH)n was already known to grow exponentially. The present work reveals that the (PGAx-PSS1-x/PAH)n film buildup displays two distinct regimes: at first the thickness grows exponentially and once it reaches a certain value, it continues to grow linearly, the transition between both regimes being quite abrupt. The characteristic feature of this transition is that the growth rate in the linear regime is smaller than that at the end of the exponential regime. The changeover from an exponential to a linear regime is proposed to depend on a diffusion limit imposed by the time-controlled “out” diffusion of the polyanions. For fixed diffusion coefficients of the polyanions, and a fixed contact

Langmuir, Vol. 20, No. 5, 2004 1985

time of the film with the solution of the oppositely charged polymer, only the free polyanions present in a limited diffusion zone in the film, at the film/solution interface, are actually affected by the diffusion process out of the film. The number of polyanion chains that diffuse out of the film tends then to become constant and such also the increment for the layer thickness of newly formed layers. This geometrical effect induces the transition between the two growth regimes, but by itself it cannot explain the drop of the thickness increment beyond the transition point. The change in the slope of the thickness is explained by the fact that the two diffusing polyanions do not have the same diffusion coefficient in the film. As a critical film thickness is reached, only the slowest diffusing polyanion can no longer fully diffuse out of the film. This leads to a change in the composition of the new forming outer layers, which slows down the polyanion diffusion out of the film and thus reduces the film thickness increment. Acknowledgment. One of the authors (E. H.) acknowledges the financial support from the Ministe`re de la Jeunesse, de l’Education Nationale et de la Recherche. This work has been partly supported by the Action Concerte´e Incitative “Surfaces, interfaces et conception de nouveaux mate´riaux” from the Ministe`re de la Jeunesse, de l’Education Nationale et de la Recherche. LA0361870