Effect of Temperature on the Buildup of Polyelectrolyte Multilayers

The Journal of Physical Chemistry B 2017 121 (1), 322-333. Abstract | Full Text HTML ..... ACS Applied Materials & Interfaces 0 (proofing),. Abstract ...
0 downloads 0 Views 123KB Size
Download PDF
11232

Langmuir 2005, 21, 11232-11240

Effect of Temperature on the Buildup of Polyelectrolyte Multilayers Mikko Saloma¨ki,*,†,‡ Igor A. Vinokurov,† and Jouko Kankare† Department of Chemistry, University of Turku, FIN-20014 Turku, Finland, and Graduate School of Chemical Sensors and Microanalytical Systems (CHEMSEM), Turku, Finland Received June 15, 2005. In Final Form: September 7, 2005 The effect of temperature on the buildup of polyelectrolyte multilayers consisting of poly(styrenesulfonate) (PSS), poly(diallyldimethylammonium) (PDADMA), and poly(allylamine) (PAH) was studied by using a quartz crystal microbalance. The increase of temperature in the deposition process was shown to have a considerable effect on the rate of the layer-by-layer buildup. The effect of temperature on the PDADMA/ PSS deposition was found to be stronger than on the PAH/PSS deposition. The increasing temperature was found to extend the exponential buildup regime in all of the studied systems. A buildup model was created to simulate the buildup and to explain the effect of temperature. The model is based on the assumption that each deposition step leads to a quasi-equilibrium between the concentration of the polymer repeating unit in solution and the composition of the layer. According to the model, the layer-by-layer buildup is inherently exponential, becoming linear whenever diffusion is not fast enough to carry the polymer within the entire thickness of the film. This buildup model is discussed jointly with the earlier published threezone model of the polyelectrolyte multilayers. The rate of the buildup is characterized by growth exponent β. The temperature dependence of the growth exponent is discussed in connection with the thermodynamic parameters of the deposition.

Introduction Multilayered polyelectrolyte films can be deposited onto a charged surface by exposing it to solutions of polyanions and polycations in an alternating manner.1 Generally, the resulting polyelectrolyte multilayer film contains highly interpenetrated polyelectrolyte chains without a strictly stratified structure.1,2 The mass and thickness increments in a single deposition step depend strongly on the ionic strength of the polyelectrolyte solution.2,3 Other important factors affecting the buildup of the polyelectrolyte multilayer are electrolyte type,4,5 polyelectrolyte charge density,6,7 pH (particularly in weak polyelectrolytes),8 deposition time,4 solvent quality,4,9 and polyelectrolyte chain length.10 The deposition temperature has also been found to have a significant effect on the layer thickness using both weak11 and strong polyelectrolytes.12 The effect of temperature on the buildup process has attracted relatively little attention, despite the fact that * Corresponding author. E-mail: [email protected]. † University of Turku. ‡ Graduate School of Chemical Sensors and Microanalytical Systems (CHEMSEM). (1) Decher, G. Science 1997, 277, 1232-1237. (2) Lo¨sche, M.; Scmitt, J.; Decher, G.; Bouwman. W. G.; Kjaer, K. Macromolecules 1998, 31, 8893-8906. (3) Decher, G.; Schmitt, J. Prog. Colloid Polym. Sci. 1992, 89, 160164. (4) Dubas, S. T.; Schlenoff, J. B. Macromolecules 1999, 32, 81538160. (5) Saloma¨ki, M.; Tervasma¨ki, P.; Areva, S.; Kankare, J. Langmuir 2004, 20, 3679-3683. (6) Schoeler, B.; Kumaraswamy, G.; Caruso, F. Macromolecules 2002, 35, 889-897. (7) Glinel, K.; Moussa, A.; Jonas, A. M.; Laschewsky, A. Langmuir 2002, 18, 1408-1412. (8) Shiatori, S. S.; Rubner, M. F. Macromolecules 2000, 33, 42134219. (9) Potoshev, E.; Schoeler, B.; Caruso, F. Langmuir 2004, 20, 829834. (10) Sui, Z.; Salloum, D.; Schlenoff, J. B. Langmuir 2003, 19, 24912495. (11) Bu¨scher, K.; Karlheinz, K.; Ahrens, H.; Helm, C. A. Langmuir 2002, 18, 3585-3591. (12) Tan, H. L.; McMurdo, M. J.; Pan, G.; Van Patten, P. G. Langmuir 2003, 19, 9311-9314.

the effects are reasonably large. In this article, we focus on the effect of temperature on the character of the buildup but also on the general mechanism of the buildup process. There are two main buildup regimes that are usually found in polyelectrolyte multilayers: linear and exponential. The linear buildup in polyelectrolyte multilayers is usually observed after the nonlinear initial buildup.13,14 The linear regime can be realized as a steady state where the deposition of a polyelectrolyte, with a finite interpenetration range, generates a constant mass and thickness increment to the developing film. In most cases, the layer-by-layer buildup is self-limited to constant increments and can be sustained in the linear regime for hundreds or even thousands of layers. The nonlinear buildup regime in the polyelectrolyte multilayer assembly is actually a relatively common feature. However, it has been rather demanding to explain the exact mechanism behind the phenomenon. There are studies that support the surface roughness mechanism. In that model, the nonlinear buildup is attributed to the continuous increase of surface roughness, which leads to an increase in the physical surface area available for adsorption. The exponential buildup attributed to surface roughening is proposed to take place when polymers of low charge are used.15,16 The same trend is also observed when the charges of a highly charged polymer are compensated for with a high salt concentration.17 The model, based on the assumption of increasing active surface area, does not take into account the possible extension of the active surface toward the interior of the film so that in addition to the increased surface area there might also be an increased penetration depth of the adsorbed polymer. (13) Ladam, G.; Schaad, P.; Voegel, J. C.; Schaaf, P.; Decher, G.; Cuisinier, F. Langmuir 2000, 16, 1249-1255. (14) Schlenoff, J. B.; Dubas, S. T. Macromolecules 2001, 34, 592598. (15) Schoeler, B.; Poptoshev, E.; Caruso, F. Macromolecules 2003, 36, 5258-5264. (16) DeLongchamp, D. M.; Kastantin, M.; Hammond, P. T. Chem. Mater. 2003, 15, 1575-1586. (17) McAloney, R. A.; Sinyor, M.; Dudnik, V.; Goh, M. C. Langmuir 2001, 17, 6655-6663.

10.1021/la051600k CCC: $30.25 © 2005 American Chemical Society Published on Web 10/08/2005

Temperature Effect on Multilayer Buildup

Instead of an active surface area, some models are concerned with the active volume of the polyelectrolyte multilayer. The active volume can be realized as a certain part of a film that is capable of adsorbing the depositing polymer. The active volume concept corresponds to zone III of the polyelectrolyte zone model,13 and the height of the active volume can be characterized in terms of charge penetration length, defined by the theory of Schlenoff and Dubas.14 The latter mentioned theory gives a fundamental picture of the buildup and parameters used to describe the exponential and linear buildup. The theory of the diffusion of polyions in and out of the film18 can be understood on the basis of the idea of active volume. It can be realized that in this theory the whole film acts as an active volume in which at least one of the polyelectrolytes can freely diffuse. The internal diffusion has been proposed and demonstrated for some polyelectrolytes of a biological nature.19-22 The buildup regime is usually considered to be an inherent property of a distinct polyelectrolyte. On the basis of the published data, one might get the idea that the conventional synthetic polyelectrolytes adopt mostly the linear buildup regime whereas polyelectrolytes of a biological nature might provoke the exponential buildup of the multilayer. We have chosen two polymer pairs for the study of temperature effects. The poly(styrenesulfonate) (PSS)/ poly(diallyldimethylammonium) (PDADMA) pair shows a mostly linear buildup, whereas some experimental aspects such as high ionic strength might induce an exponential initial buildup in this polyelectrolyte system.17 The PSS/poly(allylamine) (PAH) pair has been considered to be a model example of linear buildup.23,24 The buildup in this system is expected to be linear after two bilayers on the surface.23 The quartz crystal microbalance is widely used in the polyelectrolyte multilayer study. Most of the performed studies utilize the Sauerbrey equation25 to analyze the mass growth. The equation is valid up to a certain mass increment, depending on the viscoelastic properties of the deposited material. The limitations of the Sauerbrey equation are contemplated in some of the published measurements concerning a polyelectrolyte multilayer buildup. Actually, the deviation from the Sauerbrey equation for thin layers due to the viscoelasticity is less than commonly believed. If the layer is in contact with air, the deviation is negligible even for very viscous films until the acoustic film resonance is approached. Under liquid, if the imaginary part of the complex shear compliance of the film material is known, then the deviation can be calculated.26 For instance, hyaluronan/ poly(L-lysine) forms a very soft multilayer (Im J ≈ 1.3 × 10-6 Pa-1, unpublished result by the authors), but still the relative deviation from the Sauerbrey equation is only ca. 6%. It should be noted also that because of the (18) Lavalle, P.; Picart, C.; Mutterer, J.; Gergely, C.; Reiss, H.; Voegel, J.-C.; Senger, B.; Schaaf, P. J. Phys. Chem. B 2004, 108, 635-648. (19) Picart, C.; Lavalle, P.; Hubert, P.; Cuisiner, 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) Richert, L.; Lavalle, P.; Payan, E.; Zheng, X. S.; Prestwich, G. D.; Stolz, J. F.; Schaaf, P.; Voegel, J. C.; Picart, C. Langmuir 2004, 20, 448-458. (22) Boulmedais, F.; Ball, V.; Schwinte, P.; Frisch, B.; Schaaf, P.; Voegel, J. C. Langmuir 2003, 19, 440-445. (23) Caruso, F.; Niikura, K.; Furlong, D. N.; Okahata, Y. Langmuir 1997, 13, 3422-3426. (24) Ramsden, J. J.; Lvov, Y. M.; Decher, G. Thin Solid Films 1995, 254, 246-251. (25) Sauerbrey, G. Z. Phys. 1959, 155, 206-222. (26) Kankare, J. Langmuir 2002, 18, 8496-8502.

Langmuir, Vol. 21, No. 24, 2005 11233

viscoelasticity the real mass is always higher than that calculated from the Sauerbrey equation. In some cases, the film was made so thick, with respect to its viscoelastic properties, that a maximum in the change of resonance frequency was already approached.19 In the region near the maximum, it is understandable that the Sauerbrey equation cannot be used. The analysis of the film buildup by means of the Sauerbrey equation has to be terminated before the maximum, and in some cases the range of the exponential buildup cannot be determined. Instead of the generally used resonance frequency change, we utilize the imaginary part of the local acoustic impedance (Im ζ0, given in units of Rayl ) kg m-2 s-1) to describe the mass increment at the surface of the quartz crystal. The local acoustic impedance can be derived from the electrical impedance of the quartz crystal resonator.27 The imaginary part of the local acoustic impedance has a first-order proportionality to the areal mass density Γ of the deposited material in the “Sauerbrey regime”:

∆Γ ≈

∆Im ζ0 ω

(1)

Here ω is the nominal angular resonance frequency of the quartz resonator (2πf). Although eq 1 looks formally different, the approximations leading to it are essentially the same, and it will be also called the “Sauerbrey equation”. Experimental Section Materials. Poly(sodium 4-styrenesulfonate) (PSS, 70 kDa, from Aldrich), poly(allylamine hydrochloride) (PAH, 70 kDa, from Aldrich), and 2-mercaptoethanesulfonic acid, sodium salt (MESA, from Aldrich) were used as received. Poly(diallyldimethylammonium chloride) (PDADMA, 100-200 kDa, from Aldrich) was dialyzed against electrolyte solutions to exchange the counteranions as described in our earlier article.28 The viscosities of the polymer solutions were measured on an Anton Paar AMVn automated microviscometer. The densities of the solutions were measured on an Anton Paar DMA 45 density meter. Multilayer Preparation. The polished quartz crystals with gold plating (10 MHz, Lap-Tech, Inc., South Bowmanville, Ontario) were rinsed with water and dried. The crystals were cleaned in oxygen and hydrogen plasma before use.29 The MESA primer layer was deposited at the gold surface of the crystal to obtain a negative ionic charge on the surface (a droplet of 1 mM water solution of MESA for 1 h on the gold surface of the crystal). After that the crystal was placed in a flow cell. The multilayer films were made by using an automated multilayer deposition system described earlier.30 The deposition sequence was following: Sequentially, a 1.5 mL portion of a 10 mM (referring to monomer concentrations) solution of PDADMA, PSS (in 0.1 M aq solution of NaBr or NaF), or PAH (in 1 M aq solution of NaCl) was injected into the cell and allowed to adsorb for 15 min. The crystal was then rinsed for 5 min with 20 mL of the corresponding electrolyte solution and allowed to stabilize for 15 min before the measurement. The solutions were adjusted to the deposition temperature prior to the injection into the cell. The crystal parameters were measured as described in detail in our previous publications28,30 using a prototype crystal analyzer with impedance detection.31 (27) Lucklum, R.; Behling, C.; Cernosek, R. W.; Martin, S. J. J. Phys. D: Appl. Phys. 1997, 30, 346-356. (28) Saloma¨ki, M.; Laiho, T.; Kankare, J. Macromolecules 2004, 37, 9585-9590. (29) Hickman, J. J.; Laibinis, P. E.; Auerbach, D. I.; Zou, C.; Gardner, T. J.; Whitesides, G. M.; Wrighton, M. S. Langmuir 1992, 8, 357-359. (30) Saloma¨ki, M.; Loikas, K.; Kankare, J. Anal. Chem. 2003, 75, 5895-5904. (31) Kankare, J.; Loikas, K. Patent pending.

11234

Langmuir, Vol. 21, No. 24, 2005

Figure 1. PSS/PDADMA multilayers deposited in 0.1 M NaBr at different temperatures.

Saloma¨ ki et al.

Figure 2. PSS/PDADMA multilayers deposited in 0.1 M NaF at two different temperatures.

Results and Discussion Buildup vs Temperature. Figure 1 shows the PSS/ PDADMA multilayer buildup at different temperatures using NaBr as an electrolyte. It can be seen that the temperature has a remarkable effect on the apparent mass of the films. It is also interesting that the character of the buildup process is altered because of the temperature increase. A predominantly linear buildup is observed when the multilayer is deposited at 15 and 25 °C. The increasing temperature brings along some progression in the multilayer buildup. Although the multilayer deposited at 35 °C shows some slight progression in the buildup, the multilayers deposited at 45 and 55 °C have a clear exponential buildup regime. The multilayers deposited at high temperatures also have apparent differences between the buildup of polycation and polyanion layers. PDADMA gains more temperature-induced mass growth than PSS, which has also been observed.12 The temperature dependence in the polyelectrolyte multilayer buildup is actually very large, and it should not be neglected even at near room temperature. With a crude approximation taken from Figure 1, it can be said that the increase in mass is 5% for the 30-bilayer PSS/ PDADMA film deposited in 0.1 M NaBr if the buildup temperature is increased only by 1 °C near room temperature. Most of the multilayer depositions described in the literature are made without accurate temperature control. On the basis of the observation here, it is favorable to have temperature control in the deposition process. The PSS/PDADMA deposition in 0.1 M NaF produces a much thinner film with apparently different internal structure. The film deposited in NaF is evidently much softer than the film deposited in NaBr.28 Figure 2 also shows that under these conditions the progressive buildup can be generated by increasing the deposition temperature. The buildup at 55 °C is clearly exponential during a large number of layers. The exponential buildup regime in this film consists of nearly 100 bilayers. In Figure 3, there are PSS/PAH multilayers deposited at relatively high temperatures. It is seen in Figure 3 that the buildup of this film also follows the trend influenced by temperature. The multilayer buildup is seemingly exponential for the first five bilayers at 55 °C. If the temperature is increased to 80 °C, then slightly more progression in the buildup is observed. At that temperature, approximately the first eight bilayers adopt exponential growth. The exponential buildup in this system cannot be extended to a much greater number of layers because of the restriction by the temperature range. However, this experiment also shows

Figure 3. PSS/PAH multilayers deposited in 1 M NaCl at two different temperatures.

Figure 4. Acoustic impedance vs number of bilayers in PSS/ PDADMA deposition in 0.1 M NaBr. The temperature was changed twice during the deposition.

that in the PSS/PAH system the character of the buildup can be changed by temperature. Temperature changes performed in the middle of the deposition seem to bring about changes in the buildup regime of the polyelectrolyte multilayer, as seen in Figure 4. The reason to do this experiment was somewhat analogous to the multicompartment deposition by Garza et al.32 In the multicompartment film, there are regions of polymer layers formed by different buildup processes

Temperature Effect on Multilayer Buildup

(i.e., there has been switching between the linear and the exponential buildup). Figure 4 shows that the deposition, started at 45 °C, has a clearly exponential buildup pattern during the first 15 bilayers. After that, the temperature is lowered to 25 °C, and the film buildup seems to reach a linear phase after a slight downward bend. The buildup rate in the middle section, at 25 °C, corresponds to the film that has been deposited completely at 25 °C (Figure 1). If the temperature is raised back to 45 °C, then the buildup does not adopt the exponential pattern, but a seemingly linear phase with higher mass increments is observed. It seems that the buildup in the final section would continue in a same manner as the first section was finished. The situation here is slightly different from that in the films of Garza et al.32 They changed the polyelectrolytes during the deposition; therefore, the underlying film provides a semisolid impermeable substrate for the new compartment of the multilayer to grow. In our case, the properties of the underlying film are inevitably changed because of the temperature change, and no isolated compartments are formed. The slight downward bend that takes place at the start of the second section is evidently caused by the large amount of polymer deposited during the previous step at a higher temperature. The deposition in the second section, after approximately 10 layers, adopts the characteristic buildup rate for that temperature. The change back to the higher temperature in the third section again causes structural changes within the previously deposited film, allowing the new polyelectrolytes to penetrate deeper into the bulk film. Also, the underlying film is thick enough for a maximum intake of the depositing polyelectrolyte, allowing the linear buildup almost immediately after the temperature change. Character of the Temperature Effect. The initial growth in the multilayer seems to be independent of temperature. This temperature independence in singlelayer films has already been observed by Tan et al.12 In fact, it would seem that practically the first 8 bilayers in the NaBr deposition and up to 20 bilayers in the NaF deposition of PSS/PDADMA are equal in mass growth. In the PSS/PAH system, the first four bilayers are equal in buildup. The temperature independence in the primary layers indicates that the initial multilayer growth is not significantly related to the temperature of solution but to the thickness of the underlying film. It has been suggested that the elevation in temperature would eventually precipitate the polyelectrolytes in solution11 and moving toward the point of precipitation would gain the deposited thickness.33 However, the effect is apparently not visible after the first couple of layers. It has also been stated that the precipitation of linear highly charged PSS, for example, would not take place upon heating,12 whereas cooling precipitates the polymer solution at high ionic strength.34 Actually, a sharp phase transition of polymers upon heating is observed for some polymers. This rather unusual phase transition is considered to be related to a delicate balance between hydrophobic and hydrophilic interactions in some polymers of very low charge, uncharged water-soluble polymers, and polymer blends.35 These kinds of polymers undergo a phase transition at temperatures that are higher than their defined lower critical solution temperature (32) Garza, J. M.; Schaaf, P.; Muller, S.; Ball, V.; Stoltz, J.-F.; Voegel, J.-C.; Lavalle, P. Langmuir 2004, 20, 7298-7302. (33) Gopinadhan, M.; Ahrens, H.; Gu¨nther, J.-U.; Steitz, R.; Helm, C. A. Macromolecules 2005, 38, 5228-5235. (34) Takahashi, A.; Kato, T.; Nagasawa, M. J. Phys. Chem. 1967, 71, 2001-2010. (35) Fujishige, S.; Kubota, K.; Ando, I. J. Phys. Chem. 1989, 93, 33113313.

Langmuir, Vol. 21, No. 24, 2005 11235

Figure 5. Reduced viscosities of 10 mM PSS in 0.1 M NaBr and 10 mM PDADMA in 0.1 M NaBr and NaF solutions at different temperatures. The inset shows a magnification of the PDADMABr data.

(LCST). Nevertheless, it is apparent that all of the polyelectrolytes utilized in this study are fully soluble in the used temperature range. It has been proposed that the increase in temperature is somewhat equal to adding more salt to the polyelectrolyte solution.12 In general, the increased temperature and the increased ionic strength have been found to generate gradually thicker films. It has been shown both theoretically and experimentally that increasing ionic strength reduces the radius of gyration of polyelectrolytes.36,37 To study the effect of temperature on polyelectrolytes in solution, we have measured the reduced viscosities (ηred) of the solutions of PDADMA and PSS at the temperatures and concentrations used in deposition (ηred ) (η - ηs)/ηsc, where η is the viscosity of solution, ηs is the viscosity of solvent, and c is the mass concentration of polymer). It can be seen in Figure 5 that the increase in temperature in the PSS solution decreases the reduced viscosity and the solution becomes more waterlike. A similar monotonic decrease in reduced viscosity with increasing temperature is shown by PDADMA fluoride. The solution of PDADMA bromide, however, has a maximum in reduced viscosity at 30 °C. Nevertheless, this solution also generates a lower reduced viscosity when heated. The apparent conclusion is that the polyelectrolytes are liable to adopt more globular forms and do not give as great a contribution to the viscosity as at lower temperatures. This observation gives evidence of the similarity between the effect of high temperature and high ionic strength. The large difference between the reduced viscosities of PDADMA bromide and fluoride reflects the difference in the site binding of these anions. When studying multilayer formation, the attention must be also focused on the film and the polyelectrolyte complexes that are formed under different conditions. A common feature in the effect of the increased temperature and ionic strength is smoothing the previously adsorbed polyelectrolyte multilayer films. Polyelectrolyte material that is deposited at low temperature and low ionic strength is probably bound to the surface of the previously adsorbed film. It can be considered that the added polymer is trapped in a local energy minimum very close to the film-solution interface. It is supposed that the increased temperature (36) Tanahtoe, J. J.; Kuil, M. E. J. Phys. Chem. 1997, 101, 1083910844. (37) Joanny, J.-F.; Castelnovo, M. In Multilayer Thin Films; Decher, G., Schlenoff, J. B., Eds.; Wiley: Weinheim, Germany, 2003; p 87.

11236

Langmuir, Vol. 21, No. 24, 2005

Saloma¨ ki et al.

as well as the increased ionic strength brings about interference in the electrostatic binding between the oppositely charged polyelectrolytes, causing breakage of the bonds inside the film and allowing the oppositely charged polymers to form new energetically more favored bond configurations.38,39 That reorganization would produce increasingly entangled and interpenetrating polymer chains, meaning that the polymer chains would eventually reach configurations that are closer to the global energy minimum. This particular change in the polyelectrolyte multilayer would be seen in the healing and smoothing of the film surface together with a slight swelling of the film.39,40 The increased ionic strength, for example, has been found to swell the walls of the PSS/PDADMA microcapsules, and further swelling is observed when the temperature is raised.41 However, it is notable that the effect of temperature is found to be reversed when there is no salt present in solution. The swelling in a surfacebound material is apparently smaller than in a freestanding material that is free to swell in all three dimensions. It can be realized correspondingly that if the temperature (or ionic strength) is high during the deposition then the adsorbed polymers with increased mobility in the film would have a greater ability to penetrate deep inside the polyelectrolyte multilayer to find the energetically optimal binding sites already at the deposition stage. There is a great difference between films that are obtained by increasing the temperature after or before deposition. This was observed in a simple experiment where the temperature was raised after the deposition. The mass of a 60-layer PSS/PDADMA multilayer deposited in 0.1 M NaBr at 45 °C is approximately three times higher than that of a multilayer deposited at 25 °C. If the multilayer, deposited at 25 °C, is kept in solution and heated to 45 °C, then the increase in mass is only about 3%. The increase in mass can probably be explained by water diffusing inside the film, causing minor swelling. The properties of polyelectrolyte multilayers are very strongly dependent on the deposition conditions, and the total configuration change afterward in the multilayer is a very slow process. Layer-by-Layer Buildup Model. In the LbL process, the polymer layer that is actually a blend of cationic and anionic polyelectrolytes is in contact alternately with the aqueous solutions of the same polycation and polyanion. We assume that the concentrations of these polymers (in terms of the repeating units) in the solutions are c+ and c-, respectively. The mole fractions of these polymers in the blend are denoted by x+ and x-. In terms of molar amounts per unit area, n, we have then

x( )

n( n( + n-

(2)

The basic assumption is that at least one of the polymers is relatively freely diffusing in the domain of thickness h within the polymer blend at the polymer-solution interface. In principle, this domain would correspond to zone III in the nomenclature of Ladam et al.13 Another assumption is that each concentration of the cationic or anionic polyelectrolyte in the solution corresponds to a (38) Leporatti, S.; Gao, C.; Voigt, A.; Donath, E.; Mo¨hwald, H. Eur. Phys. J. E 2001, 5, 13-20. (39) McAloney, R. A.; Dudnik, V.; Goh, M. C. Langmuir 2003, 19, 3947-3952. (40) Ko¨hler, K.; Shchukin, D. G.; Sukhorukov, G. B.; Mo¨hwald, H. Macromolecules 2004, 37, 9546-9550. (41) Gao, C.; Leporatti, S.; Moya, S.; Donath, E.; Mo¨hwald, H. Chem.s Eur. J. 2003, 9, 915-920.

certain mole fraction of these polymers in the blend. This assumption implies that after each change of the polymer solution there is sufficient time for the layer to attain a close equilibrium or quasiequilibrium state. In the very beginning of the layering process, there is enough time for the diffusive mixing of the polymeric constituents within the very thin “multilayer”. By continuation of the process, the multilayer becomes so thick that diffusion is not able to transfer material everywhere below the layersolution interface. This is one factor that determines the thickness h of zone III. Another factor is the slow rearrangement of the polymer chains, which gradually causes the chains to be entangled in an impenetrable network that completely hinders diffusion. This process creates zone II, which apparently grows with the further continuation of layering while zone III starts to maintain a constant thickness. The rates of diffusion and rearrangement depend on the character of polymers. In certain cases, h is very small, and there is very little diffusion, whereas in some cases the diffusion rate is high and consequently during the whole layering process zone III continues its growth. As the third assumption, we assume that the desorption rate of the polymers is negligible. We assume first that we are in the initial growth process where after each change of the solution there is enough time for the entire multilayer to adapt a new equilibrium state. Let these equilibrium compositions be x+ eq and xeq after contacts with the cationic and anionic polyelectrolyte solutions, respectively. Without a loss of generality, we assume now that the first layer on the substrate surface is the polycation. Let us now assume that we have k bilayers on the substrate (i.e., the substrate has been contacted k times with the solutions of the cationic and anionic polyelectrolytes). When this multilayer is in contact with the polyanion solution, we have

xeq

)

nk

(3)

n+ k + nk

After the washing period where only a negligible amount of polymer is desorbed, the layer is contacted with the + is polycation solution; consequently, the amount ∆nk+1 incorporated:

x+ eq )

+ n+ k + ∆nk+1

+ nk+1 ) + + n+ nk+1 + nk + ∆nk+1 + nk k

(4)

This multilayer is now brought into contact with the is added: polyanion solution, and the amount ∆nk+1

xeq )

nk + ∆nk+1 + nk+1 + nk + ∆nk+1

)

nk+1 + nk+1 + nk+1

(5)

Equations 3 and 4 give + ) nk+1

x+ eqxeq

n+ k

(6)

nk

(7)

(1 - x+ eq)(1 - xeq)

and equations 4 and 5 similarly give ) nk+1

x+ eqxeq (1 - x+ eq)(1 - xeq)

Temperature Effect on Multilayer Buildup

Langmuir, Vol. 21, No. 24, 2005 11237

Figure 6. Acoustic impedance vs number of bilayers in PSS/PDADMA multilayer film deposited in 0.1 M NaBr at 15 (a), 45 (b), and 55 °C (c). The straight line corresponds to the fitting result of exponential buildup regime. The curved line corresponds to the fitting result of the linear buildup regime.

We define now a growth factor R

R)

x+ eqxeq (1 - x+ eq)(1 - xeq)

(8)

and we may now write the total areal mass density Γk+1 after k + 1 additions of cationic and anionic polyelectrolytes + + - Γk+1 ) nk+1 M+ + nk+1 M- ) R(n+ k M + nk M ) ) - + Rk(n+ 1 M + n1 M ) (9)

Here M( is the molar mass of the repeating unit. If now R > 1, eq 9 predicts exponential growth. Expression 9 is also convenient to use in an exponential form

Γk+1 ) Γ1 exp(βk)

(10)

where we have defined the growth exponent β ) ln R. We assume next that the growth process has achieved the state where the rates of diffusion and deposition counterbalance each other and limit the mixing of polymers to a constant volume Vh, corresponding to thickness h of zone III. Then after each addition of a bilayer both the composition and the volume of the active zone are identical to the previous values and consequently each

added bilayer should be identical. The growth then occurs linearly in zone II. The depositions of PDADMA/PSS films in NaBr are characterized using semilogarithmic plots (Figure 6). The buildup is in most cases divided into not two but three separate segments. First, there is an initial buildup that can be related to the formation of zone I. The measurements carried out at five different temperatures show almost identical buildup in the first four bilayers. The buildup is nearly exponential, but it is independent of temperature. The temperature independence can probably be explained by the fact that the film has to have a certain compactness in order to act as a separate phase and to have characteristic properties. The second buildup segment consists of exponential buildup that is dependent on temperature. The corresponding β values for the multilayers are presented in Table 1. The increments of bilayer mass in this segment are clearly dependent on the thickness of the underlying film. Therefore, it is assumed that in this buildup segment at least one of the depositing polyelectrolytes diffuses freely everywhere inside the film, forming a polymer blend zone that can be expressed as zone III. Eventually, when the film becomes adequately thick the complete mixing of the polymer blend becomes impossible, and the depositing polymer will have a finite interpenetration depth. As a result, the film adopts a linear buildup regime, and zones I and III become separated by

11238

Langmuir, Vol. 21, No. 24, 2005

Saloma¨ ki et al.

Table 1. Parameters Obtained from Linear and Nonlinear Fits of Acoustic Impedance Curves of PDADMA-PSS in 0.1 M NaBr temperature (°C)

growth exponent β

bilayer mass in linear regime (µg cm-2)a

zone III thickness (nm)b

15 25 35 45 55

0.27 0.29 0.34 0.38 0.37

2.8 4.2 8.7 17 g270c

69 88 120 360 g6000c

a According to the Sauerbrey equation. b Assuming a film density of 1200 kg m-3. c The values for 55 °C are approximated from the end of the exponential buildup regime.

zone II. The mass increment of each bilayer in the linear buildup segment is also dependent on temperature (Table 1). Figure 6 shows that the exponential regime between the initial growth and the linear regime is barely detectable at 15 °C (Figure 6a). However, at 45 °C the exponential buildup regime is clearly noticeable (Figure 6b). The duration of the exponential buildup phase at 55 °C cannot be distinguished from Figure 6c because the value of Im ζ0 undergoes a sharp drop, reaching negative values, after a local maximum just after 20 bilayers. Up to that point, the buildup seems not to have reached the fully linear regime. That behavior can be explained by the acoustic film resonance, and unquestionably, the linear relationship between the mass and the frequency of the oscillator (Sauerbrey equation) is lost before the first local maximum. The acoustic film resonance and its utilization in the analysis of the films is the subject of our forthcoming paper. The detailed analysis of the buildup allows us to estimate certain dimensions of the films. If zone III is understood to be a zone in which polymer diffusion and blending takes place, then the thickness of zone III can be estimated in the same way as the charge penetration length by Schlenoff and Dubas.14 The thickness of zone III (Table 1) is estimated from the total mass of layers in the exponential regime. The thickness values of zone III show a strong temperature dependence, reaching an incredibly high value, 6 µm, for the film deposited at 55 °C. The value for 25 °C, 88 nm, is approximately twice the value of the charge penetration length in the film deposited in 1 M NaCl.14 That probably can be explained by the fact that bromide is superior to chloride in its ability to increase the mass of the PSS/PDADMA multilayer.5,28 It is noteworthy that both the bilayer mass in the linear regime and the thickness of zone III increase exponentially as the temperature increases. One feature in the suggested growth model that should be noted is that the growth exponent does not depend explicitly on the molecular weight of the polyelectrolytes (cf. eq 8). In a recent work by Kujawa et al.42 where the buildup of hyaluronan/chitosan multilayers was studied, this fact was experimentally verified. Although the molecular weights of the polyelectrolytes varied by factors of 5 to 10, the value of the growth exponent varied only between 0.41 and 0.51. These authors used SPR for their film thickness measurements. The same pair of polyelectrolytes has been used by Richert et al.21 using QCM as their main tool for determining the thickness of the films. The growth exponents were not presented in their publication, but their values can be calculated from the (42) Kujawa, P.; Moraille, P.; Sanchez, J.; Badia, A.; Winnik, F. J. Am. Chem. Soc. 2005, 127, ASAP.

published data. For a multilayer with eight bilayers, we get 0.32 for the pair 400 kDa hyaluronan/110 kDa chitosan and 0.33 for the pair 270 kDa hyaluronan/110 kDa chitosan. Within the experimental accuracy, the numerical values of β are identical. The seemingly different growth rates for the same polymers but different molecular weights depend on Γ1 in eq 10. According to eq 9, Γ1 is directly proportional to the molecular weights of repeating units, but in fact, its value depends on where we consider the exponential growth to start. As discussed above, growth before the fourth bilayer does not fit into the model, probably because the layers have not yet achieved lateral homogeneity. This is then layer number one, but its thickness depends on various conditions and not only on the molecular weight. Dependence on Temperature. The essential parameter determining the rate of multilayer growth is growth exponent β. Its temperature dependence can be studied by differentiating it with respect to T: x+ d dβ eqxeq ) ln ) dT dT (1 - x+ )(1 - x- ) eq

eq

d ln x+ d ln x1 1 eq eq + (11) dT dT 1 - x+ 1 x eq eq We assume now that the small counterions X( of polyelectrolytes in solution associate with the charged sites of the polymer. This association can be either territorial or site binding, according to the definition by Manning.43 Territorial binding is purely electrostatic whereas site binding is more or less specific “inner sphere” binding of counterions to the charged sites of the polymer without intervening water molecules. Territorial binding does not follow the mass-action law, in contrast to site binding. In the present case, we assume the presence of specific site binding. Consequently, the solution contains a large number of polymer molecules with different net charges. Without a loss of generality, we may reduce the process to the transfer of a bare (i.e., unassociated) repeating unit of the polymer into the membrane. The transfer of polyelectrolytes from solution into the multilayer is a process driven by the difference in the electrochemical potential of polymers in these phases. The process approaches the end as the electrochemical potentials tend to be equal: ( M °S ( S µ°M ( + RT ln aM ( Fφ( ) µ( + RT ln aS ( Fφ( (12)

Here φS( and φM ( are galvanic potentials in solution and the multilayer, respectively. The activities of polymers in ( the multilayer (a( M) and solution (aS ) can be expressed ( ( with activity coefficients f and γ and mole fractions and concentrations of repeating units, respectively. Let the concentration of polymer in solution be [P(], again in terms of repeating units. After some manipulation, we obtain from eq 12

ln

x( eq

°S °M F S γ ( µ ( - µ( ( (φ( - φM + - ln[P ] ) ln () RT RT f( (13) (

(43) Manning, G. Acc. Chem. Res. 1979, 12, 443-449.

Temperature Effect on Multilayer Buildup

Langmuir, Vol. 21, No. 24, 2005 11239

This is differentiated with respect to T, giving

(

)

°M °S d ln x( d ln[P(] d ln(γ(/f () 1 d µ( - µ( eq ) + ( dT dT dT R dT T S M F d φ( - φ( R dT T

=

(

(

)

°( S M d ln [P(] ∆HSfM F d φ( - φ( ( + dT R dT T RT2

)

(14)

Here we have assumed that the ratio of activity coefficients has a negligible temperature dependence, and we used the Gibbs-Helmholtz equation to obtain the °( for the transfer process. enthalpy change ∆HSfM The site binding of the counterions can be described by the equilibria

P( + X- h P(X-

(15)

These equilibria have association constants K( that actually are the microscopic association constants for the multisite binding with the assumption that the interaction energy between the charged sites is negligible because of screening by the territorially bound counterions. Another implicit assumption is that the polymers within the membrane are not markedly associated with counterions or these association constants are imbedded in the activity coefficients f ( and their temperature dependence is considered to be negligible. These approximations are admittedly rough, but it is hoped that the equations still retain some of their predictive value. Using these association constants K( and the concentrations of counterions, we obtain for the total concentration of the monomer units (

(

(

(

c ) [P ](1 + K [X ])

(16)

Taking the logarithm and differentiating with respect to T, we obtain (remembering that c( is constant and [X(] is large enough to be nearly constant)

[X(] d ln [P(] dK( )) ( ( dT 1 + K [X ] dT -

K([X(]

d ln K( (17) 1 + K([X(] dT

But here we have the Bjerrum formation function for the complexation:

n j( )

K([X(] 1 + K([X(]

(18)

This parameter represents the average proportion of occupied sites, varying between 0 and 1. Let the change in the Gibbs free energy for this reaction be ∆G°( X . Then by using the Gibbs-Helmholtz equation we obtain °( °( 1 d(∆GX /T) ∆HX d ln K ( )) dT R dT RT2

(19)

Figure 7. Dependence of buildup growth exponent β on temperature in the PDADMA-PSS system in 0.1 M NaBr.

Combining equations 11, 14, 17, 18, and 19 and differentiating with respect to 1/T instead of T, we obtain

dβ ) d(1/T) -

(

(

))

°+ ∆HSfM -n j +∆H°X+ F d φS+ - φM 1 + R R d(1/T) T 1 - x+ eq

(

(

))

°S M ∆HSfM -n j -∆H°F d φ- - φ1 X + R R d(1/T) T 1 - xeq

-

(20)

1 If we assume x+ eq ≈ xeq ≈ /2, then we obtain a slightly simpler equation

(

2 dβ °+ °≈ - ∆HSfM + ∆HSfM -n j +∆H°X+ R d(1/T) S S M M d φ+ - φ- + φ- - φ+ F (21) n j -∆H°X T d(1/T)

)

Assuming that the expression within the parentheses is reasonably independent of temperature, we should have a straight line of β versus 1/T. We may assume that the enthalpy terms are nearly constant within the narrow temperature range between 15 and 55 °C. The temperature dependence of the potential term is more difficult to assess. If the interfacial potential difference is considered to be diffusional, then the potential is mainly determined by the small counterions because of their higher mobility. The transport numbers of counterions are close to 1 and not appreciably dependent on temperature. The temperature dependence is now mainly due to the logarithm of activity ratios and can be rather safely assumed to be small. As shown in Figure 7, there is a strong correlation between the values of β and 1/T in the temperature range of 15 to 45 °C. The β value for the film deposited at 55 °C shows a slight deviation in the plot, although presumably this value is the most accurate because of the greatest number of layers in the exponential buildup regime. The net “enthalpy” change for the polyelectrolyte deposition calculated from eq 21 is 1.2 ( 0.2 kJ mol-1. The obtained value seems to be quite small, but one must take into account that it is a net enthalpy change for a repeating unit. The actual net enthalpy change for a macromolecule is naturally orders of magnitude larger.

11240

Langmuir, Vol. 21, No. 24, 2005

Conclusions The experimental results show that the increase in temperature in the deposition process has a profound influence on the rate of the layer-by-layer buildup. In addition to the increase in bilayer mass, elevated temperature is shown to change the buildup regime from totally linear to partly exponential. A simple phenomenological model was derived on the basis of the one-toone correspondence between the polymer concentration in solution and the composition of the layer, resembling an extraction equilibrium between two immiscible liquids. This model predicts that every layer-by-layer buildup process is inherently exponential, turning linear whenever the diffusion rate is not fast enough to carry the polymer within the entire thickness of the layer. In this respect, the chosen polyelectrolyte pairs represent widely different behavior, with PAH/PSS growing mainly linearly and showing exponential behavior only in the very beginning of the process at relatively high temperatures and PDADMA/PSS buildup in NaBr being exponential at

Saloma¨ ki et al.

higher temperatures. In the case of PDADMA/PSS, the counteranion used during the layer-by-layer procedure has a strong influence on the growth process. The influence of bromide and fluoride as counterions on the viscosity of polymer solutions shows clearly the specific site binding of bromide in PDADMA whereas the apparently binding of fluoride is much weaker. The rate of buildup is determined by the growth exponent β. The study of its temperature dependence leads to an Arrhenius-like function where the energy term in the exponent is composed of five terms. Four of these terms are enthalpies, and the fifth is a potential term. The separate contribution of each of these terms is unknown, but further studies by varying the concentrations and character of counteranions are in progress. Acknowledgment. Financial aid from the Academy of Finland is gratefully acknowledged (grant no. 102279). LA051600K