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Stiffening of Soft Polyelectrolyte Architectures by Multilayer Capping Evidenced .... This analysis will reveal that the parameters of the SK model de...
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J. Phys. Chem. C 2007, 111, 8299-8306

8299

Stiffening of Soft Polyelectrolyte Architectures by Multilayer Capping Evidenced by Viscoelastic Analysis of AFM Indentation Measurements Gre´ gory Francius,†,‡ Joseph Hemmerle´ ,†,‡ Vincent Ball,†,‡ Philippe Lavalle,†,‡ Catherine Picart,§ Jean-Claude Voegel,†,‡ Pierre Schaaf,| and Bernard Senger*,†,‡ Institut National de la Sante´ et de la Recherche Me´ dicale, Unite´ 595, 11 rue Humann, 67085 Strasbourg Cedex, France, UniVersite´ Louis Pasteur, Faculte´ de Chirurgie Dentaire, 1 place de l’Hoˆ pital, 67000 Strasbourg, France, UniVersite´ de Montpellier II, Laboratoire de Dynamique des Interactions Membranaires Normales et Pathologiques, Centre National de la Recherche Scientifique, UMR 5235, Place Euge` ne Bataillon, 34095 Montpellier Cedex 5, France, and Centre National de la Recherche Scientifique, UPR 22, Institut Charles Sadron, 6 rue Boussingault, 67083 Strasbourg Cedex, France ReceiVed: January 18, 2007; In Final Form: March 22, 2007

The mechanical properties of polyelectrolyte multilayer films built up with poly-L-lysine (PLL) and hyaluronan (HA) can be tuned using a chemical cross-linker. The present study is aimed at showing that the viscoelasticity can also be changed by exposing a (PLL/HA)m film alternatively to a solution of poly(sodium 4-styrene sulfonate) (PSS) and a solution of poly(allylamine hydrochloride) (PAH), thus forming (PLL/HA)m-(PSS/ PAH)n-PSS films. Force curves have been recorded with an atomic force microscope using a micrometric spherical probe and different approach velocities ranging over 2-3 orders of magnitude. These curves are analyzed in the framework of the Hertzian mechanics corrected for the finite thickness of the film deposited on a hard (glass) substrate, with the indentation limited to 50 nm to preserve material linearity. The force curves cannot be reproduced satisfactorily when the probed films are assumed to be elastic bodies. Better agreement is achieved when the films are depicted as Maxwell bodies, and further improvement is reached when they are represented as a spring in series with a Kelvin unit (referred to as “SK model”, where S stands for “spring” and K for “Kelvin”). The evolution of the SK model parameters with n reveals that the successive depositions of PSS and PAH onto the (PLL/HA)m stratum, at a fixed value of m, increase the dynamical stiffness of the films. This effect is attributed to the penetration of PSS into the (PLL/HA)m stratum, which is evidenced by infrared spectroscopy. This study thus shows that the deposition of successive polyelectrolyte multilayers can affect the mechanical properties of the underneath multilayers, an effect that has not been described until now.

Introduction Over the past 10 years, it has been recognized that biological cells, deposited on a substrate, are sensitive to its mechanical properties, such as adhesion, viability, proliferation, and mobility.1-8 However, the hardest substrates are not necessarily the most favorable, depending on the cell type and the biological process under consideration.6,7,9 Therefore, it is of great importance to be able to prepare substrates with different mechanical characteristics especially if they are intended to be used as biomaterials.10 Furthermore, the adhesion to the substrate may induce a modification of the cell itself. This point motivated pathophysiological-oriented measurements of the mechanical properties of adhering and nonadhering neutrophils.11 It should be noticed that the preparation of the substrate includes eventual functionalization. Indeed, functionalization is potentially likely to alter the mechanical properties of the substrate measured before functionalization.12 The discovery of the polyelectrolyte multilayer (PEM) films in the 1990s13,14 has opened a valuable route to the formation * Corresponding author: Phone: +33-(0)390-243258. Fax: +33-(0)390-243379. E-mail: [email protected]. † Institut National de la Sante ´ et de la Recherche Me´dicale. ‡ Universite ´ Louis Pasteur. § Universite ´ de Montpellier II. | Centre National de la Recherche Scientifique.

of thin films,15,16 with the aim, among others, of coating almost any material,17,18 notably those to be brought into contact with biological tissues.19-25 One way to harden a PEM film may consist of cross-linking it. This procedure has been applied to poly(L-lysine)/hyaluronan (hereafter abbreviated as PLL/HA) films using 1-ethyl-3-(3-dimethylaminopropyl)carbodiimide (EDC) and N-hydrosulfosuccinimide (sulfo-NHS).26-29 Cross-linking can also be obtained by heating the film. This has been exemplified with the combination of poly(allylamine hydrochloride) (PAH) and poly(acrylic acid) (PAA). When a PAH/ PAA film is heated at 150 °C for 6 h, and then rehydrated, the final Young modulus is about 6-fold the initial one.30 The elasticity of a film can also be controlled via the assembly pH.30-32 In particular, the compliance of a PAH/PAA film increases when the pH is decreased.31 Furthermore, the effects of chemical cross-linking and temperature elevation can be combined. Thus, a poly(N-isopropylacrylamide) gel, cross-linked with N,N-methylenebis(acrylamide), undergoes a strong stiffening when heated above the lower critical solution temperature (∼33 °C).33 A change in salt concentration can also alter the hardness of a polyelectrolyte film as was exemplified by the dramatic softening of a poly(sodium 4-styrene sulfonate) (PSS)/ PAH film when the NaCl concentration exceeds 3 M.34 Another route to the preparation of high-strength thin films consists of the fabrication of a nanostructured composite from cellulose

10.1021/jp070435+ CCC: $37.00 © 2007 American Chemical Society Published on Web 05/22/2007

8300 J. Phys. Chem. C, Vol. 111, No. 23, 2007 nanocrystals35 or clay platelets36 and poly(dimethyldiallylamonium chloride). It has already been observed that adhesion of HT29 cells on PLL/HA films is enhanced when the (PLL/HA)m multilayer film is successively capped with PSS, (PSS/PAH)-PSS, and (PSS/ PAH)2-PSS.37 It was anticipated without proof that this might be due to changes in the mechanical properties of the films induced by capping. Indeed, these composite films were originally built up with the goal of forming a stratum constituted by PLL and HA, which acts as a reservoir of a cytotoxic drug (paclitaxel) surmounted by a barrier allowing the access to the drug to be delayed.37 It was incidentally observed that the barrier consisting of PSS and PAH also has an influence on the adhesion of the cells as mentioned above. In the present study, we shall examine the modifications of the mechanical properties of a (PLL/HA)m film made of m ) 24 pairs of layers by exposing it alternatively to PSS and PAH a number of times, n, ranging from 0 up to 24. In addition, the buildup will always end in the adsorption of PSS, leading to (PLL/HA)24-(PSS/ PAH)n-PSS architectures deposited on glass slides. The mechanical properties of the soft (PLL/HA)24 film will thus be changed without cross-linking28 but just by deposition of another type of multilayer film. These composite films will be submitted to nanoindentation tests using a homemade atomic force microscope (AFM) equipped with a cantilever terminated by a spherical probe. The cantilever deflection will be recorded as a function of the piezodrive position at several different approach velocities spanning 2-3 orders of magnitude. The force curves, that is, the relations between the force applied on the probe and the indentation, will be derived from these raw data. They will be analyzed using as material model a spring in series with a Kelvin unit (referred to as “SK model”, where S stands for “spring” and K for “Kelvin”) in order to extract characteristic quantities permitting the different films to be compared. This analysis will reveal that the parameters of the SK model depend upon the number of PSS and PAH layers deposited onto the (PLL/HA)24 stratum, at a fixed approach velocity. Moreover, for a fixed value of n, the parameters depend on the approach velocity. This has, to our knowledge, not been taken into account in previously published mechanical studies on polyelectrolyte multilayer films. Thus, it appears essential to take this velocity dependence of the measured parameters into account for these parameters to be physically relevant. Therefore, it is important to perform the measurements over a velocity domain as large as possible. This is a general rule whenever the material investigated does not predominantly behave as a pure elastic solid. However, applying this precaution does not seem to be the common practice in the literature until now although “all materials display both elastic and viscous properties”.38 The paper is organized as follows. The next section summarizes the preparation of the polyelectrolyte and rinsing solutions, the film buildup, the AFM manipulations already described in detail elsewhere,28 and the infrared spectroscopy in the attenuated total reflection mode, which is aimed at probing the PSS content evolution of the (PLL/HA)24 stratum as a function of the number of deposited PSS/PAH layer pairs. The theoretical approach is described in the Computational Background Section. Then, we present and discuss the experimental results (Results and Discussion Section). A brief conclusion closes the article. Materials and Methods Polyelectrolyte Solutions and Film Buildup. The preparation of solutions of poly(L-lysine) (PLL, 27 kg/mol, Sigma,

Francius et al. SCHEME 1: Schematic Representation of a Composite (PLL/HA)24-(PSS/PAH)n-PSS Film, (a) When the Two Strata are Well Separated, (b) When PSS (and Perhaps Also PAH) is Assumed to Diffuse into the (PLL/HA)24 Stratum (indicated by “-” within it) as Suggested by the Infrared Measurements (See Below)a

a For the sake of clarity, the thickness of the upper stratum is exaggerated with respect of the thickness of the lower stratum. The actual thickness ratio is on the order of 1:50 or less.

France) and hyaluronan (HA, 412 kg/mol, Bioiberica, Spain) and the buildup of (PLL/HA)24 films was described in a former article.28 Poly(sodium 4-styrene sulfonate) (PSS, 70 kg/mol, Sigma, France) and poly(allylamine hydrochloride) (PAH, 70 kg/mol, Sigma, France) were used for the buildup of the (PSS/ PAH)n-PSS top films (where n is the number of layer pairs), which were deposited over the (PLL/HA)24 stratum. PLL, HA, PSS, and PAH were dissolved at 1 mg/mL in a buffer solution containing 150 mM NaCl and 20 mM of tris(hydroxymethyl)aminomethan (TRIS, 121 g/mol, Merck, Germany) at pH 7.4. During the film construction, all of the rinsing steps were performed with a 150 mM NaCl/20 mM TRIS aqueous solution at pH 7.4. The (PLL/HA)24-(PSS/PAH)n-PSS architectures were prepared with a dipping machine (Dipping Robot DR3, Riegler & Kirstein GmbH, Germany) on 14-mm glass slides (VWR Scientific, France). Cleaning of the slides and film buildup were described in detail previously.8,37 The rinsing time of the substrate was about 10 min, the adsorption time of PLL and HA was also about 10 min, and that of PSS and PAH about 4 min. All of these durations were chosen because no further adsorption was observed for longer contact times. The thickness of the films, as measured with confocal laser scanning microscopy using fluorescein-labeled PLL, was about h ) 5 µm, essentially due to the (PLL/HA)24 stratum (Scheme 1). Atomic Force Microscope. The experiments were performed using a homemade AFM working in the indenter-type mode (IT-AFM).39 The probe was a borosilicate sphere (5 µm in diameter) fixed to a cantilever having a nominal spring constant of 0.06, 0.38, or 0.58 N/m (Bio-Force Nanosciences Inc., Ames, IA). Before each measurement, the cantilever was cleaned during 15 min in a UV-tip cleaner (Bio-Force Nanosciences Inc., Ames, IA) and the spring constant was checked with the thermal fluctuation technique.40 The measurements of the dynamic elastic modulus of the films were performed at various approach velocities in the range of 10-104 nm/s, and the force curves were obtained as described previously.28 All experiments were performed in liquid environment, that is, the films were immersed in a drop of the 150 mM NaCl/20 mM TRIS aqueous solution already used during the film buildups. Infrared Spectroscopy. A trapezoidal zinc selenide (ZnSe) crystal was used as the substrate for FTIR-ATR measurements. It was cleaned for 15 min using a Hellmanex solution at 2% (v/v), rinsed with ethanol and ultrapure water, and put in contact with a 0.1 M HCl solution for 15 min. Finally, the ZnSe crystal was rinsed again with ultrapure water. Before the deposition of the (HA-PLL)24-HA film, the ZnSe crystal was modified by the adsorption of a layer of poly(ethylene imine) (PEI, 750 kg/

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mol, Sigma), which was a prerequisite for the subsequent buildup of the multilayer film. All of the polyelectrolytes were dissolved at a concentration of 1 mg/mL in a 150 mM NaCl /Tris 20 mM buffer in D2O whose pH was adjusted to 7.9 (equivalent to pH 7.4 in H2O). This was mandatory in order to avoid the overlap between the strong absorption of water around the spectral position of the amide I band (1620-1700 cm-1) characteristic of PLL and around the band centered at 1610 cm-1, which is attributed to the carboxylate groups of HA. Concerning the deposition of the (HA/PLL)24-HA stratum, each deposition time was held constant at 10 min as for the film deposition on the glass slides used for the force-indentation curves. The rinsing time with buffer was also of 10 min, and the infrared spectra (from 512 accumulated interferograms) were taken regularly at a resolution of 2 cm-1 between 650 and 4000 cm-1 using a liquid-nitrogen-cooled mercury cadmium telluride detector on a Bruker IFS 55 spectrometer (Bruker, Wissembourg, France). The transmitted intensity was then compared to that of the PEI-covered ZnSe crystal to calculate the absorbance spectra. Concerning the deposition of the (PSS/ PAH)n-PSS strata on top of the PEI-(HA/PLL)24-HA film, the deposition time was held constant at 4 min. This was particularly important during the first deposition of PSS in order to avoid a PSS-triggered dissolution of the PEI-(HA/PLL)24-HA film (data not shown). The infrared spectra were acquired during the buffer rinse steps following the exposition to the last PSS solution in the sequences (PSS/PAH)n-PSS (with n ranging from 0 up to 24) in order to evaluate the change in PSS content of the PEI(HA/PLL)24-HA stratum. Indeed, this film is about 5 µm thick, which exceeds substantially the penetration depth of the evanescent wave originating from the total internal reflection at the ZnSe-film interface (the penetration depth, λ, equals about 1 µm at 1650 cm-1, i.e., at the central position of the amide I band due to PLL). Consequently, if the (PSS/PAH)nPSS film deposited on top of the PEI-(HA-PLL)24-HA film as a sharply defined stratum, that is, without penetration of PSS (and eventually of PAH) in the PEI-(HA-PLL)24-HA stratum, then the characteristic strong vibrational bands ascribed to PSS at 1007 and 1035 cm-1 should not be detected. Computational Background Elastic Medium. The indentation of a soft, homogeneous, and infinitely thick material by a rigid spherical punch of radius R has been described by Sneddon.41,42 The indentation, δ, and the force, F, are given separately as a function of the radius of the contact area, a, the elastic modulus, E, and the Poisson ratio, ν:41,43

a R+a δ ) ln 2 R-a F)

(1a)

R+a E (R2 + a2) ln - 2aR R-a 2(1 - ν 2)

[

]

(1b)

In the limit when a tends to zero (thereby also δ) at fixed R, eq 1a reduces to the Hertz relation a2 ) Rδ.42 This suggests that a can be expanded as

a ) R δ (1 + b1δ + b2δ + b3δ + b4δ + ...) 1/2 1/2

2

3

4

(2)

Inserting eq 2 into eq 1a leads to b1 ) -1/6R, b2 ) -1/360R2, b3 ) 11/5,040R3, b4 ) 1,357/1,814,400R4, and so forth. Then, inserting eq 2 into eq 1b leads to

F)

(

4R1/2 1 δ2 1 δ Eδ3/2 1 + 2 10 R 840 R2 3(1 - ν ) 11 δ3 1357 δ4 + + ... (3) 15 120 R3 6 652 800 R4

)

where the expression in front of the parentheses is the Hertzian force for a paraboloidal punch.44 Part of the above computations has been performed with the commercial software “Maple” (Maple V release 5.1, Waterloo Maple Inc., Waterloo, Ontario, Canada). It follows from eq 3 that using the Hertz law instead of the exact Sneddon formalism for a spherical punch should not induce an appreciable bias in the estimation of the viscoelastic parameters of the films when δ is limited to some percent of R. To account for the finite thickness of the film, h, deposited on an “infinitely” hard substrate (Eglass ≈ 70 GPa),45 the Hertz force is multiplied by the Dimitriadis corrective factor, fD:

F)

4R1/2 Eδ3/2fD 3(1 - ν2)

(4)

Conversely, if F is prescribed, eq 4 may be rewritten as

δ3/2fD )

3(1 - ν2) F 4R1/2 E

(5)

The corrective factor has the form46

fD ) 1 + R1χ + R2χ2 + R3χ3 + R4χ4

(6)

with χ ) (Rδ)1/2/h. Viscoelastic Medium. When the elastic solution is known (namely, the Hertz-Dimitriadis force-indentation relation, eq 4 or 5), the viscoelastic solution can be obtained. If the load history is known, that is, if F ) F(t) is known (where t means the time), then the compliance, 1/E, is replaced by the creep compliance function, J(t), corresponding to the assumed viscoelastic model of the material under consideration.47 Then, upon replacing the ratio F/E in eq 5 by the Boltzmann superposition integral (or integral operator),47,48 eq 5 becomes

δ(t)3/2 fD[δ(t)] )

3(1 - ν2) 4R

1/2

∫0t J(t - t′)

dF(t′) dt′ dt′

(7)

To simplify the notation, we shall write Xm(t) instead of δ(t)3/2 fD[δ(t)] when this quantity is evaluated with the model as expressed by eq 7. The experimental counterpart will be denoted by Xe(t). In the case of the AFM indentation experiments, the force, F(t), is derived from the cantilever deflection, d(t), recorded as a function of time during the approach phase of the piezodrive, using F(t) ) kC d(t), where kC is the cantilever stiffness. For a Maxwell unit, consisting in a spring of elastic modulus E1 in series with a dashpot of viscosity η2, the creep compliance function is47

J(t) )

t 1 + E1 η2

(8)

Note that the creep compliance of the Maxwell unit increases indefinitely with t. This means, conversely, that its equilibrium modulus is zero, which is the characteristic feature of a viscoelastic liquid. In the limiting case when the viscosity tends

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to infinity, the creep compliance of the Maxwell unit, for any finite time, reduces to that of a pure spring. Because the Maxwell model cannot represent a viscoelastic solid (nonzero equilibrium modulus), it is useful to consider the slightly more complicated model obtained by adding a spring in parallel with the dashpot of the Maxwell model (Scheme 1 in the Supporting Information). In this way, the model consists of a spring (modulus E1) in series with a Kelvin unit (modulus E2, viscosity η2). This model will be referred to as the “SK model” (the denomination “Voigt model” is sometimes used in literature49). Its creep compliance is given by47

J(t) )

( )]

[

E2 t 1 1 + 1 - exp E1 E2 η2

(9)

where the ratio η2/E2 defines the retardation time τ2. Then, the explicit expression of eq 7 is

Xm(t) )

3(1 - ν2) 4R1/2

∫0t

[

(

(

))]

1 1 t - t′ + 1 - exp E1 E2 τ2

dF(t′) dt′ (10) dt′

If η2 tends to zero, then J(t) reduces to 1/E1 + 1/E2. Then, the SK model represents an elastic solid. If E2 tends to zero, then J(t) reduces to the Maxwell creep compliance (eq 8). Therefore, it represents a viscoelastic liquid, and even a viscous liquid if, in addition, E1 tends to infinity. In summary, the SK model is the minimalist model capable of adapting, at least qualitatively, to all types of materials. The modeling can be enriched further. For instance, the combination in series of a Maxwell unit and a Kelvin unit constitutes the Burgers model.50 Burgers model, in turn, can be extended51 to an arbitrary number of Kelvin units. As for the Maxwell unit, the creep compliance of the Burgers model and the extended Burgers model increases indefinitely with t. Thus, they do again represent a viscoelastic liquid.52 If no steadystate flow takes place (“arrheodictic” material49), then the dashpot of the Maxwell unit is simply omitted38,53 with the consequence that the equilibrium modulus does not vanish (viscoelastic solid52). To eliminate undesirable fluctuations, the experimental deflection values (see an example in Figure 1a and b), beyond the contact point where d ) 0 and t is arbitrarily set to zero, have been smoothed by a polynomial of degree 3 (Figure 1a and b)

ds(t) ) d1t + d2t2 + d3t3

(11)

where the subscript “s” means “smoothed” to be distinguished from the raw experimental deflection, d(t). It has been systematically checked that the first time derivative of ds(t) never became negative. This is a sufficient condition for the radius of the contact circle not to diminish, as required by the theory summarized above.47 The force F(t) is therefore redefined by F(t) ) kCds(t) and is also expressed as a polynomial. The integration in eqs 9 and 11 can then be performed analytically. The experimental indentation, δe(t), is obtained by subtracting the smoothed deflection from the piezodrive position (Figure 1c), provided that the contact point has been identified and that the piezodrive position is set to zero at the contact point, as are the time and the cantilever deflection. The analysis of the force curves has been restricted to δe e δe,max ) 50 nm (i.e., ≈ 1% of the film thickness) in order to avoid nonlinear effects that

Figure 1. (a) Irregular line: cantilever deflection, d, measured on the film (n ) 2), at the approach velocity VA ) 10,000 nm/s, continuous line: smoothed deflection, ds (eq 13), dashed line: piezodrive position, zP . (b) Magnification of the small-time region of part a corresponding to the experimental indentation limited to δe,max ) 50 nm. (c) Experimental indentation obtained by subtracting the cantilever deflection from the piezodrive position: the dots indicate the indentations obtained using the raw deflections shown in part b, whereas the line is obtained using the smoothed deflections shown in part b.

may manifest for imposed strains that are too large.54 Strictly speaking, the linear theory of material deformation outlined above should apply for infinitesimal strains. In practice, however, it may be valid up to some percent of the material thickness.38 In addition, one can compute Tabor’s indentation strain given by  ) 0.2a/R or 0.2 xδ/R if Hertz’s relation a2 ) Rδ is used. With 0 e δe e 50 nm and R ) 2,500 nm,  ranges from 0 to 0.028. Thus, for all indentations taken into consideration,  is smaller than the limit of 0.032 where plasticity begins to play a role.55 Curve Fitting. Whatever the mechanical description chosen for the probed material, the model quantity Xm is to be fitted to its experimental counterpart Xe. The agreement between Xm and Xe can be quantified by

q2 )

1

n

(i) 2 (X(i) ∑ m - Xe ) n i)1

(12)

where n is the number of experimentally available indentation values from δ ) 0 up to δ ) δe,max, corresponding to t ) 0 and t ) T, respectively, where T is the time necessary for the probe starting from the contact point to reach the prescribed maximum indentation.

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With the SK model evoked above, the least-squares method aimed at minimizing q2 can be formulated such that it implies solving a system of linear equations. Indeed, the SK model involves three unknowns: E1, E2, and η2 or τ2. Equations 10 and 11 show that J(t), hence also Xm(t), is linear with respect to 1/E1 and 1/E2 if the argument of the exponential function is written -t/τ2, that is, if τ2 is taken as the third independent variable instead of η2. The retardation time τ2 is then varied over a wide interval. For instance, log τ2 is incremented by 0.01 from -6 up to 3, which corresponds to τ2 ranging from 10-6 up to 103 s. For each value of τ2, a system of two linear equations is solved leading to (E1, E2) and to the corresponding quality of fit, q2. The triplet (E1, E2, τ2) selected is that leading to the smallest value of q2. An analogous procedure can be envisioned for more complicated models such as SK...K consisting of a spring and two or more Kelvin units in series. However, each supplementary Kelvin unit adds a scanning loop over its retardation time. Because the retardation time loops are nested, the computer time increases rapidly with the number of Kelvin units, although this time can be reduced somewhat when 10-6 e τ2 < τ3 < ... e 103 s is imposed to avoid redundant units. The equation system corresponding to the model considered can be solved by the Gauss method with pivoting.56 However, the resulting mathematical solution is not necessarily a physical solution because some unknowns may be negative. This occurs more and more frequently when the number of free parameters is increased, that is, when the number of mechanical elements making up the material model is increased. Fortunately, the SK model applied to the analysis of the present experimental force curves led always to positive E1 and E2. This shows a posteriori that the model is not over-parametrized. Results and Discussion Modeling by the SK Model. We have first evaluated the possibility of representing the experimental data with the two models simpler than the SK model, namely, on one hand, a spring and, on the other hand, a spring and a dashpot in series (the Maxwell model) (see the Supporting Information). The model using a unique spring clearly fails in reproducing the experimental force-indentation curves. The Maxwell model is more appropriate, showing that the material representation should contain at least one viscous element. The SK model, where the dashpot of the Maxwell model is replaced by a Kelvin unit, clearly improves the reproduction of the experimental curves (Figure 2a) when compared to Figure S1 and even Figure S2 given in the Supporting Information. The ability of SK to adequately account for the experimental force-indentation curves is further illustrated in Figure 2b and c, corresponding to the films where n ) 6 and n ) 12, respectively. The small residual discrepancy visible at the smallest values of F (e.g., < 0.5 nN when n ) 2) could be reduced further by using a Burgers or an extended Burgers model (see Computational Background, above). However, for the purpose of comparison of the (PLL/HA)24 films capped with an increasing number of PSS/PAH layer pairs, it is advisable to keep the number of parameters at the lowest level for which the reproduction of the experimental force curves is acceptable. Using a model with only three parameters, namely, the SK model, seems to constitute a good compromise between reproduction quality and simplicity. Before analyzing the experimental force-indentation curves using the SK model, it may be interesting to observe the time, T, needed by the probe to reach the maximum indentation, δe,max

Figure 2. Force curves (open disks) for the two approach velocities indicated by the labels. The continuous lines represent the experimental, smoothed data. The dashed lines, nearly undistinguishable from the continuous lines, represent the model predictions derived with eq 10 and the definition of Xm indicated below eq 7, if the film is assumed to behave as an SK model. (a) n ) 2, (b) n ) 6, (c) n ) 12. The maximum indentation is fixed to δe,max ) 50 nm.

Figure 3. Indentation time, T, as a function of the approach velocity, VA, for the (PLL/HA)24-(PSS/PAH)n-PSS films: n ) 0 (black disks), 1 (white disks), 2 (black triangles), 6 (white triangles), 8 (black squares), 12 (white squares), 15 (black diamonds), and 24 (white diamonds). The dashed lines represent δe,max/VA (lower line) and 4 δe,max/VA (upper line), with the maximum indentation, δe,max, fixed to 50 nm.

) 50 nm, considered here. This time is shown in Figure 3 as a function of the approach velocity for the various architectures examined in the present work. It appears that T varies approximately as 1/VA and is between slightly more than δe,max,/VA (lower line in Figure 3) and about 4 δe,max/VA (upper line in Figure 3). Note that T > δe,max,/VA was expected because the indentation velocity is necessarily

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Figure 4. Elastic modulus E1 (a), elastic modulus E2 (b), and retardation time τ2 (c) of the SK model as a function of the approach velocity, VA, for the (PLL/HA)24-(PSS/PAH)n-PSS films: n ) 0 (black disks), 1 (white disks), 2 (black triangles), 6 (white triangles), 8 (black squares), 12 (white squares), 15 (black diamonds), and 24 (white diamonds). The maximum indentation is fixed to δe,max ) 50 nm. Note the general tendency of E1 and E2 to decrease when VA decreases. In the same time, τ2 increases with 1/VA.

smaller than the approach velocity. Moreover, at a given approach velocity, the value of T increases with n, evidencing already without computation that the resistance the film opposes to the probe penetration increases with n. The modulus E1, the modulus E2, and the retardation time τ2, derived from the analysis of the experimental force curves for each film as a function of the approach velocity, are given in Figure 4a-c. The equivalent elastic modulus, Eeq, defined by 1/Eeq ) 1/E1 + 1/E2, and the viscosity, η2 ) τ2E2, of the dashpot in the Kelvin unit are shown in Figure 5a and b. Because E1 (Figure 4a) is quite larger than E2 (E1 > 5 E2) for all cases, Eeq (Figure 5a) is dominated by the value of E2 (Figure 4b). Furthermore, it may be mentioned that the equivalent modulus represents the static equilibrium modulus, that is, the modulus when the dashpot does not play a role. It may also be noticed that the equivalent modulus does not tend clearly to a plateau when VA decreases within the velocity domain that could be explored. Therefore, the observed tendency of Eeq to decrease (Figure 5a) suggests that the films resemble more of a liquid than a solid when the probe velocity vanishes (Eeq ) 0 when VA f 0). Finally, it may be observed that the retardation time τ2 (Figure 4c) and the indentation time T (Figure 3) vary in a similar way and that the values of τ2 are on the same order of

Francius et al.

Figure 5. Equivalent elastic modulus Eeq (a) and viscosity η2 (b) of the SK model as a function of the approach velocity, VA, for the (PLL/ HA)24-(PSS/PAH)n-PSS films: n ) 0 (black disks), 1 (white disks), 2 (black triangles), 6 (white triangles), 8 (black squares), 12 (white squares), 15 (black diamonds), and 24 (white diamonds). The maximum indentation is fixed to δe,max ) 50 nm. Note the general tendency of Eeq to decrease when VA decreases. As a consequence of the variations of E2 and τ2, η2 increases slightly less rapidly than 1/VA when VA decreases. The two observations point to the fact that the explored domain corresponds to the viscoelastic regime and, conversely, that it would have been interesting to further decrease the approach velocity to check whether Eeq tends to a nonvanishing plateau (in the hydrodynamic regime). However, the film being not cross-linked, the limit is probably Eeq ) 0.

magnitude as those of T, though somewhat smaller. Indeed, for the dashpot to be active over the time frame corresponding to the indentation process, its characteristic response time must be comparable to T. If τ2 were significantly smaller than T, then the dashpot would have a large compliance so that its contribution to the compliance of the Kelvin unit would be minor. If τ2 were significantly larger than T, then the dashpot would have a small compliance so that the Kelvin unit would appear as practically blocked. It follows in both cases that the SK model would essentially behave as a spring with a modulus respectively equal to Eeq or E1. Now we know that the viscous element is required (see Figure 2 and the Supporting Information). It is therefore not surprising that τ2 adapts to the indentation time, hence to the approach velocity. Because E2 is a relatively slowly varying function of VA, η2 varies only slightly less rapidly than τ2. Physically, it may be suggested that the material probed in these experiments has a large variety of viscous deformation mechanisms characterized by a wide spectrum of retardation times. Despite the scattering of the results, it appears that the curves representing both Eeq and η2 (Figure 5a and b, respectively) shift upward when the number of PSS/PAH pairs of layers deposited on the (PLL/HA)24 stratum increases. This observation reflects the growing stiffness with added PSS/PAH capping layers felt by the colloidal probe. From a practical point of view, this finding shows that the dynamical viscoelastic properties of a (PLL/HA)m film can actually be altered over a large domain without chemical cross-linking but merely by the alternate

Viscoelasticity of Composite Polyelectrolyte Films

Figure 6. Equivalent elastic modulus Eeq of the SK model as a function of the number of PSS/PAH pairs of layers, n, in the (PLL/HA)24-(PSS/ PAH)n-PSS films. At a given value of n, the values of Eeq corresponding to the various approach velocities (see Figure 5a) are represented.

exposition of the (PLL/HA)m film to aqueous, salty solutions of PSS and PAH. Furthermore, it may be noted that when the number of adsorbed PSS/PAH layers goes from n ) 1 to n ) 2, the curve representing Eeq in Figure 5a shifts upward by 1 order of magnitude, indicating a strong relative effect of the PSS/PAH deposition. However, this effect attenuates when n is increased further. As can be seen, a rise of Eeq also by 1 order of magnitude occurs when n increases from 4 up to as much as 24. The evolution of Eeq with n is illustrated further in Figure 6. Assume that the successive PSS/PAH deposits form a film on top of the PLL/HA stratum. The system is then composed of a glass substrate, the PLL/HA stratum, and the PSS/PAH stratum, that is, a three-layer system where the top layer is hard and thin, the second layer is soft and thick, and the third layer is virtually infinitely hard. From the point of view of purely elastic layers, it can be shown using the theory developed by Chen57 and Chen and Engel58 that the probe pressed against the upper, hard, and thin layer feels practically only the middle, soft layer. If this were the case in the present experiments, then the dynamical elastic modulus should remain on the order of a few kilopascals (about 3 kPa as follows from our former work28) even after the deposition of 24 PSS/PAH pairs of layers. The results shown in Figure 5 are in strong contrast with this prediction and therefore suggest that PSS and/or PAH do penetrate into the PLL/HA stratum and thereby alter its mechanical properties noticeably. Such a stiffening effect has been described recently for poly(acrylic acid)/polyacrylamide films exposed to a solution of PAH.12 The infrared spectroscopy observations discussed in the next subsection will support our assumption. Infrared Spectroscopy Results. The first observation is that, although the PEI-(HA/PLL)24-HA film is much thicker than the penetration depth (∼1 µm at 1650 cm-1) of the totally internally reflected beam at the ZnSe-film interface, a signal ascribed to the PSS molecules is detected even after the deposition of only one PSS layer, that is, after 4 min of the flow of the PSS solution above the HA-ending polyelectrolyte multilayer film. This evidences that PSS penetrates into the PEI-(HA/PLL)24-HA film. To evaluate the change in the PSS concentration close to the ZnSe-film interface as a function of the number of PSS/PAH pairs of layers, we subtracted the absorbance of the PEI-(HA/ PLL)24-HA stratum from the absorbance of the PEI-(HA/PLL)24HA-(PSS/PAH)n-PSS film. Strictly speaking, this is an approximation because the film underwent a small shrinking upon (PSS/ PAH)n-PSS deposition. This shrinking was detected by an increase of the intensity of the elongation band due to the COOgroups of HA (at 1610 cm-1, data not shown). Because this

J. Phys. Chem. C, Vol. 111, No. 23, 2007 8305

Figure 7. Evolution of the absorbance of the PSS molecules at 1007 cm-1 (9) and 1035 cm-1 (0) as a function of n.

increase did not exceed about 7%, the increase of the HA signal around 1007 and 1035 cm-1 does not markedly affect the increase in the band intensities due to PSS. A plot of the absorbance derived from the intensities of the elongation bands ascribed to PSS at 1007 and 1035 cm-1 shows that the concentration of this polyelectrolyte close to the ZnSe-film interface continuously increases with n (Figure 7). This increase is the strongest between n ) 0 and n ≈ 5 and is less pronounced beyond n ≈ 5; nevertheless, a plateau is not reached. Finally, it may be pointed out that it is also possible that PAH penetrates into the (HA/PLL)24-HA multilayer film. This, however, cannot be explored using infrared spectroscopy. Though, it is established that the changes of the mechanical properties are due to the penetration of at least one of the polyelectrolytes involved in the capping process. Conclusions In this article, PSS and PAH have been deposited onto a (PLL/HA)24 film. Using AFM indentation measurements and a viscoelastic material model encompassing only three elements (two springs and a dashpot), it has been shown that both the elastic modulus and the viscosity increase with the number of PSS and PAH adsorption steps. It appears that the parameters vary with the approach velocity. However, in the velocity domain that could be explored, the dynamic elastic modulus decreases with the velocity without observable tendency to level off at a nonzero value. This suggests that the films examined in the present work behave as viscoelastic liquids rather than viscoelastic solids that would display a nonvanishing equilibrium elastic modulus. The reason for the stiffening is ascribed to the penetration of PSS (and perhaps PAH) into the (PLL/HA)24 film, revealed by infrared spectroscopy. This mixing clearly alters its mechanical properties, even after several PSS/PAH adsorption cycles. Finally, it may be mentioned again that increasingly better adhesion of HT29 cells was observed on PLL/HA films when they were successively capped with PSS, (PSS/PAH)PSS, and (PSS/PAH)2-PSS.37 The stiffening of the whole film evidenced in the present article strengthens the hypothesis37 that the enhanced adhesion observed when n equals successively 0, 1, and 2 is attributable to the gradual modification of the mechanical properties of the substrate. Acknowledgment. G.F. is indebted to the Faculte´ de Chirurgie Dentaire of Strasbourg for financial support. G.F. and B.S. thank Philippe Martinoty and Dominique Collin (Institut de Me´canique des Fluides et des Solides, Strasbourg) as well as Jacques Ohayon (Universite´ de Savoie, Chambe´ry) for enlightening discussions. The AFM apparatus was built with the financial support of the Institut National de la Sante´ et de la Recherche Me´dicale (APEX 99-13). This work has been

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