Separation of Storage and Loss Modulus of Polyelectrolyte

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Separation of storage and loss modulus of polyelectrolyte multilayers on a nanoscale: – a dynamic AFM study – Johannes Hellwig, Samantha Micciulla, Julia Strebe, and Regine von Klitzing Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.6b02764 • Publication Date (Web): 09 Sep 2016 Downloaded from http://pubs.acs.org on September 13, 2016

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Separation of storage and loss modulus of polyelectrolyte multilayers on a nanoscale: – a dynamic AFM study – Johannes Hellwig, Samantha Micciulla, Julia Strebe, and Regine v. Klitzing∗ Stranski-Laboratorium, Department of Chemistry, TU Berlin, Strasse des 17. Juni 124 D-10623 Berlin, Germany E-mail: [email protected]

Abstract Atomic force microscopy (AFM) is used to carry out rheology measurements on the nanoscale and to determine the mechanical properties of poly(L–lysine) (PLL)/hyaluronic acid (HA) multilayer films. Storage (G’) and loss modulus (G”) of the films are calculated and compared with the values obtained from quartz crystal microbalance with dissipation monitoring measurements (QCM-D). A predominant elastic behavior independently of the applied frequencies (5-100 Hz) is observed for native HA/PLL films consisting of 36 double layer. If the layers are cross-linked, the value of G’ increases by 2 order of magnitude while the loss modulus becomes negligible, making these films a purely elastic chemical gel. The values of G’ and G” extracted from QCM-D measurements on native films are much higher, due to the different frequency regime of the applied shear stress. However, the viscoelastic ratio from the two methods is the same, and proves the elastic dominated response of the multilayer in both frequency regimes.

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Introduction Nowadays the assembly of complex molecules onto a solid substrate is a widely used method to prepare thin films to be applied to numerous applications. The assembly process can be carried out by using the Layer-by-Layer technique introduced by Decher and co-workers. 1,2 By this method thin layers are achieved by alternate adsorption of oppositely charged polyelectrolytes to produce polyelectrolyte multilayers (PEMs). A large number of studies has been published over the last decade, dealing with growth behavior, swelling, roughness and effect of relative humidity. Furthermore, many different PEM systems have been studied with the most common being poly–(styrene-sulfonate) (PSS)/poly(diallyl–dimethylammonium chloride) (PDADMAC), 3 PSS/poly(allylamine) (PAH) 4 or poly(acrylic acid) (PAA)/PAH. Such a method is not limited to simple synthetic molecules, but also more complex materials like viruses, 5,6 polysaccharides 7 or hydrogels 8–10 have been adsorbed and characterized on surfaces to understand their mechanical properties. Understanding and tuning the mechanics of various coatings opens a lot of different applications like drug delivery, 11–14 cell adhesion, 15–17 superhydrophobic surfaces, 18 cell and protein resistance coatings 19–21 or bioresponsive sensors. 22 This work is focused on a bio compatible polyelectrolyte multilayer made of poly(L-lysine) (PLL) and hyaluronic acid (HA). Their bicompatibility and the possibility to load the HA/PLL films with drugs and other molecules make them suitable as drug delivery systems. 23,24 Studies on HA/PLL films as template for cell growing showed that chondrosarcoma cells adhere very well on crosslinked films while the native films are highly anti adhesive. 17 Also smooth muscle cells deposited on HA/PLL films show an increase in spreading when adsorbed on a stiffer film. 15 Therefore a change in the stiffness of the films can be used to trigger the cell adsorption. 25–27 The stiffness of these HA/PLL films can easily be changed by crosslinking the native films after the preparation. 16,17 Recent studies reported that native HA/PLL films show a viscoelastic behavior. 17,28,29 Viscoelastic properties were investigated by a falling sphere experiment through a HA/PLL film, showing that HA/PLL films can be described either as a viscoelastic liquid with zero 2


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equilibrium elasticity or as a viscoelastic solid with a very small equilibrium elastic modulus. 30 Furthermore measurements with different approach speeds demonstrate that the indentation modulus increases for higher indentation velocity, while relaxation measurements were used to investigate the viscoelastic behavior of these films showing a full relaxation to zero. 29 Also the effect of preparation conditions and crosslinking on the mechanical properties of the films was investigated. 16,28 HA/PLL films are considered as a model system for non-linear growing due to the high mobility of PLL, which can diffuse into and out of the entire multilayer film. However, a switch from exponential to linear growth is observed at 12 double layers where the diffusion zone reaches a limited and constant thickness. 31,32 The HA/PLL films used in this study consist of 36 double layers and are therefore in the linear regime. To summarize, static measurements or measurements at very low frequency indicate that the HA/PLL PEMs are very soft with a very low elastic modulus. This is in agreement with the ability for the polyelectrolytes to diffuse within the PEM. No quantitative separation into the elastic and viscous part using AFM was achieved so far. To compare the elastic and viscous behavior in more detail frequency dependent rheological measurements are needed. According to static measurements one would expect that the loss modulus G” is much larger than the storage modulus G’. The present study addresses the quantitative separation of the storage and loss modulus for non-crosslinked and crosslinked HA/PLL films. The mechanical properties of HA/PLL films were determined by dynamic force measurements using a colloidal probe atomic force microscope 33,34 to distinguish between the elastic and viscous properties of the films. Dynamic force measurements have previously been performed on biological samples such as cells. 35–41 It has been shown that the exact values of G’ and G”, as well as their relation, are dependent on the frequency used during the dynamic measurements. For these biological samples G’ is higher than G” at small frequencies (∼10 Hz) and shows a low positive relation with frequency. G” shows also a positive relation with frequency, but of higher magnitude, resulting in G” > G’ for higher frequencies. The crossover (G’ = G”) for theses

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samples occurs between 10 and 100 Hz. In this work for the first time, dynamic force measurements with an AFM were used to determine the mechanical properties of HA/PLL films and differentiate between the storage and loss modulus as function of the frequency and indentation depth. It was observed that the mechanical properties of these films are independent of the applied frequency in the range of 5–100 Hz, as well as on the indentation depth. However, higher viscoelastic moduli and loss ratio were found from QCM-D measurements, due to higher frequency applied to produce a shear stress in the direction parallel to the substrate. The knowledge of the film mechanics over a broad frequency range is fundamental for the proper design of biomimetic films where specific pressures are involved, which is the case of many biological processes.

Materials and Methods Materials Tris(hydroxymethyl)aminomethane (Tris buffer), Poly(ethylenimine) (PEI, MW = 750 kDa), N-(3-Dimethylaminopropyl)-N’-ethylcarbodiimide hydrochloride (EDC), N-Hydroxy-sulfosuccinimide (NHS) and Poly-L-lysine hydrobromide (PLL, MW = 22 kDa, MW /Mn = 1.3, purity = 96 %) were purchased from Sigma-Aldrich (Steinheim, Germany) and used without further purification. Sodium hyaluronate (HA, MW = 357 kDa, purity = 96 %) was purchased from Lifecore (Minnesota, US).

Preparation: HA/PLL Films Polyelectrolyte multilayer films P EI − (HA/P LL)n /HA were prepared with the layer-bylayer technique 1,2 using a dip robot (Riegler & Kirstein GmbH, Berlin, Germany). Silicon wafers, 15 x 30 mm, used as substrate were cleaned in a piranha solution (1:1 mixture of 35 % hydrogen peroxide and 98 % sulfuric acid) for 20 min followed by multiple rinsing with MilliQ before deposition of the polyelectrolytes. The film build-up was achieved by alternate dipping 4


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of the silicon wafers into the poly(L-lysine) and hyaluronic acid solutions (0.5 mg/mL in 10 mM Tris-buffer containing 15 mM NaCl, pH 7.4) for 10 min. Each polyelectrolyte solution was filtered through a 0.24 µm syringe filter before use. Rinsing was done between each adsorption step for 10 min in the pure Tris-buffers solutions. The dipping procedure was repeated until n = 36 with n corresponding to the number of deposited double layers of (HA/PLL). For better adhesion of the polyelectrolytes, a polyethylenimine PEI layer was adsorbed as precursor layer under the same conditions as the other polyelectrolytes. The films were stored in Tris-buffer solution containing 15 mM NaCl at 4 ◦ C prior to measurement. The films were never dried during all preparation and measurement steps.

HA/PLL crosslinking Crosslinking of HA/PLL films is based on the reaction between the primary amine (PLL) and activated carboxylic groups (HA). Activation of carboxylic groups is achieved by using water soluble 1-ethyl-3-(3-dimethylamino-propyl)carbodiimide EDC and N-hydrosulfosuccinimide sulfo-NHS. 16,17 A 1:1 EDC/sulfo-NHS solution was prepared using 400 mM EDC and 100 mM sulfo-NHS solutions containing 15 mM NaCl at pH 5. A volume of 1 mL of the prepared mixture of EDC/sulfo-NHS was deposited in a petri dish containing the prepared native HA/PLL films. Crosslinking of the HA/PLL films was achieved over 12 h at 4 ◦ C followed by multiple rinsing with Tris-buffer solution. All samples were measured and stored in Tris-buffer solution to prevent them from drying out.

Atomic Force Microscopy Force measurements on all samples were performed at room temperature with an MFP–3D BIO AFM (Asylum Research, Oxford Instruments, Santa Barbara, CA). To get a reliable statistic of the measured properties at least three different positions of each sample were measured, recording spatially resolved force maps on 90 x 90 µm2 with 5 x 5 points. The built-in force map mode of the MFP–3D AFM was used to measure force-distance and force5


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time curves which provide information about the local mechanical response of the PEMs. The approach velocity of the measurements was kept constant at 800 nm/s. Moreover, all measurements were done in Tris-buffer solution using a CoolerHeater cell (Asylum Research) to ensure a constant temperature of 25 ◦ C.

Cantilever calibration and Microsphere attachment Two different cantilevers were used for measurements: a soft cantilever (k = 0.05 N/m, HQ:CSC38/tipless/CR–AU, MikroMasch, USA) with an attached colloidal silica particle for the native PEMs and a stiffer cantilever (k = 2.8 N/m, HQ:NSC18/CR–AU, MikroMasch, USA) with a tip (length = 12–18 µm, full tip cone angle = 40 ◦ , radius = 35 nm) for the crosslinked films. The use of different cantilevers was necessary because of the huge difference in stiffness between native and crosslinked films, making the use of the same cantilever unsuitable. The colloidal silica particles with a radius of 3.35 µm (Bangs Laboratories, Inc., USA) were manually glued on the soft cantilevers using a two-component epoxy adhesive (UHU plus endfest 300, UHU GmbH, Germany). Placement of the adhesive and silica particle on the cantilever was achieved by using a micromanipulator and a microscope. The used cantilevers were calibrated before each measurement. For this the optical lever sensitivity of the cantilevers was determined against a cleaned silicon wafer, followed by the calculation of the spring constants by fitting the thermal noise spectra of the cantilevers (build–in procedure in the MFP–3D).

Dynamic Force Measurements Dynamic force measurements can be used to determine the complex modulus of a sample. 36,37,39,42 For these measurements the cantilever is sinusoidal excited using the Z-piezo of the AFM. The excitation of the cantilever takes place at low frequency, small amplitude and below its resonance frequency, while the deflection and the excitation signal are detected over time. Depending on the surrounding medium of the cantilever the deflection and excitation 6


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signals of the cantilever can show different phase shifts to each other: If the cantilever is placed on a purely elastic surface, deflection and excitation signal are in phase (i.e. 0 ◦ phase shift). If the cantilever is surrounded by a purely viscous medium, excitation and deflection signals show a 90 ◦ phase shift. The measurement on a sample can show a phase shift between 0 ◦ and 90 ◦ behaving more like an elastic solid or like a viscous liquid, respectively. In a static force measurement the cantilever is pushed into a sample surface until a certain trigger point is reached (e.g. deflection, force, Z-movement, etc.) and immediately retracted afterwards. An apparent indentation modulus can be determined from the force curve. In a dynamic force measurement the oscillation of the cantilever will be applied during a dwell in the sample surface after reaching the trigger point and before retracting the cantilever from the sample surface. In this work the trigger point was set to three different indentation depths, namely 100, 150 and 200 nm. During this dwell the cantilever was kept indented in the sample until the sample relaxed into a steady state, as shown in Fig 1. After relaxation the cantilever was excited for approx. 10 s to a sinusoidal movement using the Z-piezo. Frequency and amplitude of the excitation were set to 5-100 Hz and 10 nm, respectively. After the measurement the cantilever was retracted from the sample surface. Force and indentation signals were measured for further analysis of the complex modulus of the samples. The detected signals include the amplitudes AD , AF , Aδ , AZ and the phases ϕD , ϕF , ϕδ , ϕZ for the deflection (D), force (F ), indentation (δ), and Z-piezo (Z) over time. The deflection signal in this work is used to calculate the force signal by multiplying it with the spring constant of the cantilever (Hooke’s law). The indentation signal is calculated by subtracting the deflection from the Z-piezo signal, which is set to zero at the contact point between the probe and the surface of the sample. All settings for the dynamic measurements were done by using the built-in indenter panel of the Asylum Research MFP–3D software.

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a)

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10

Time [s]

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40 Approach and Indentation

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-1 -2 4 2 0 -2 -4 8.6

20

10

Measurement Retract

1

Force [nN]

2

Measurement

Relaxation

Force [nN]

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Indentation [nm]

6

Retract

8

Force [nN]

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0

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9.0

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c)

0

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10 Time [s]

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Figure 1: Schematic example of a dynamic force measurement on a) native and c) crosslinked HA/PLL films shown as force over time profile. Including the approach and indentation of the cantilever into the HA/PLL film surface, the relaxation of the film and the measurement where the cantilever oscillates with a given frequency and amplitude. b) The change in the force signal [nN] and the change in the indentation [nm] measured at an indentation depth of 100 nm.

Quartz Crystal Microbalance with Dissipation Monitoring The use of Quartz Crystal Microbalance with Dissipation monitoring (QCM-D) is well established to study the adsorption and viscoelastic properties of thin polymer films onto solid substrates. 43–48 The working principle of the technique is based on the piezo-electric properties of quartz, which is driven to oscillate to its resonance frequency and higher overtones by the application of a driving sinusoidal potential. When the driving potential is cut off, the amplitude of the freely decaying crystal oscillation is recorded described by the relation

A(t) = A0 · exp(−π/τ ) · sin(2πf t + ψ)

(1)

with A0 being the amplitude of oscillation at t=0 and ψ the phase shift, f the resonance frequency and τ the decay time constant. 49 The dissipation factor D is obtained from the relation D = 1/πf τ . Literature on the topic can be found in References 43,48–51. The frequency shift ∆fn = (fn − fn0 ) and the dissipation change ∆Dn = (Dn − Dn0 ) are typically reported by QCM-D measurements, and they describe the change of adsorbed mass and the energy dissipated by the system. Since they allow to directly correlate adsorption processes and dissipative losses, QCM-D measurements can support the interpretation of the 8


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viscoelastic behavior of a film in response to the applied shear stress. Using the Voigt model, Voinova et al. 52 described the physical features of a viscoelastic film, which is characterized by a complex shear modulus,

G∗ = G′ + iG′′ = µf + i2πf0 ηf

(2)

with shear modulus µf and shear viscosity ηf correlated to the corresponding storage (G’) and loss (G”) moduli. The viscoelastic parameters can be obtained by proper modeling of the measured ∆f and ∆D on a viscoelastic system, given that some parameters for the quartz crystal and the bulk liquid are known. QCM-D measurements reported in this work were carried out on the instrument E1 from Q-Sense (Sweden). Polyelectrolyte multilayers of PEI(HA/PLL) were prepared on a silicon coated substrate (QSX3030, Q Sense). A solution flow of 0.1 mL/min was used to mimic the conditions of the dipping process. The adsorption time was set to 10 min, each step followed by rinsing with Tris-buffer solution for 5 minutes. The viscoelastic modeling of the measured signals for 3th , 5th and 7th overtone was performed using the software Q-Tools from Q-Sense. Density and fluid viscosity of the bulk medium were fixed to 997 kg/m3 and 0.9 mPa·s, 53,54 respectively. The film density was fixed to 1400 kg/m3 .

Data Analysis Dynamic force measurements were previously reported in the work of Alcaraz et al. 36,37 and Rother et al. 39 Based on the Hertzian contact mechanics model 55,56 its is possible to calculate the complex modulus of the sample by 1−ν G = G (ω) + i G (ω) = 3 δ tan (φ) ∗

′

′′

9

F (ω) − iωb (h0 ) δ (ω)


(3)

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where ν is the Poisson ratio of the sample, which is set to 0.5, δ the indentation depth and φ is the half opening angle of the pyramidal tip of the cantilever. The force F (ω) and indentation signals δ(ω) as a function of the angular frequency are given by F (ω) AF (ω) i (ϕF (ω) −ϕδ(ω) ) = e δ (ω) Aδ (ω)

(4)

′

The complex modulus consists of a real part G (storage modulus) and an imaginary part ′′

G (loss modulus). The real part gives information about the energy stored in the sample and the imaginary part about the energy that is dissipated in the sample. For the spherical indenter used for the native PEMs the prefactor of the equation is changed to 38

∗

′

1−ν

′′

G = G (ω) + i G (ω) =

4 (R δ)1/2

F (ω) − iωb (h0 ) δ (ω)

(5)

When applying a sinusoidal oscillation to a cantilever which is surrounded by a viscous medium, in this work Tris-buffer, the cantilever experience a hydrodynamic drag due to the viscosity of the medium. 36,37 This hydrodynamic drag can be corrected by a drag coefficient b0 (h0 ) which is already included in equations 3 and 5.

Hydrodynamic Drag Correction The measure of the hydrodynamic drag acting on a cantilever can be done by exciting the cantilever at several frequencies and small amplitudes as a function of cantilever-sample separation. These measurements were performed in a Tris-buffer solution at room temperature against a cleaned silicon wafer. A sinusoidal oscillation at different frequencies ranging from 10–100 Hz with an amplitude of 10 nm was applied to the cantilever at different separations of 0.2 − 2 µm above the silicon surface. In these measurements only the interaction between the surrounding medium and the cantilever is detected. The signals detected for calculation of the hydrodynamic drag are the Z–piezo signal, AZ and ϕZ , as well as the force signal, AF and ϕF as shown in fig 2. 10


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15

40

10 Force [pN]

Z-Sensor [nm]

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5 0 -5

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-10 -15 6.0

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Time [s]

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Figure 2: Fits of the Z-sensor and force signals of a cantilever oscillation at 60 Hz in liquid to determine the hydrodynamic drag acting on the cantilever. Before correction of the hydrodynamic drag it is necessary to correct a phase shift between the phases ϕZ and ϕF . Water as pure viscous medium leads to a phase shift of 90 ◦ between the Z-piezo and force signal. Deviations between the measured phase shift and 90 ◦ is corrected by a phase lag ϕlag which is already included in following equations:

H ∗ = H ′ (f ) + i H ′′ (f ) =

Hα =

kHα (f ) k − Hα (f )

A∆F i(ϕF (ω) −ϕZ(ω) −ϕlag(ω) ) e A∆Z

(6)

(7)

′ ′′ where k is the spring constant of the cantilever. Calculation of HD and HD using the mea-

sured signals at different separations is shown in Figure 3. The real part of the hydrodynamic ′ ′′ drag HD shows no dependency on the increasing oscillation frequency while HD shows a lin-

ear increase. The drag coefficient b(h) at a fixed separation can be determined by linear ′′ ′′ fitting of the HD with m = 2 π b(h). Fitting HD for each separation gives a dependency of

the drag coefficient on the separation, showing a higher drag at smaller separations, as shown in Figure 4. A scaled spherical model, Eq. 8, can be used to fit these data and determine

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H'D and H''D [mN/m]

5

H'D (Real part) H''D (Imaginary part) z = 2000 nm

4 3 2 1 0 40

60 80 100 Frequency [Hz]

Figure 3: Calibration of the drag coefficient by plotting the real H’ and imaginary part H” of the hydrodynamic drag function vs oscillation frequency. H” shows the linear dependency of the hydrodynamic drag on the oscillation frequency and is fitted with the equation: m = 2 π b(h) to obtain the drag coefficient for a probe-sample distance of 2000 nm the drag coefficient 37 at 0 separation b(h0 ).

b (h) =

2 6 π η αef f h + hef f

(8)

55 50

b(h) [nNs/m]

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45 40 35 30 25

0

500

1000

1500

2000

2500

Distance [nm]

Figure 4: Dependency of the drag coefficient on the probe-sample distance. Fitting of the data was done by using a scaled spherical model eq. 8. The fit is extrapolated to the probe-sample distance of 0 to get the drag coefficient b(h0 ).

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Results Force measurements were carried out, spatially resolved, on two different samples: 1) a native HA/PLL film that shows an indentation modulus lower than hundred kPa (static measurements) and 2) a HA/PLL film that is cross-linked with EDC/sulfo-NHS, showing an indentation modulus of several MPa. Dynamic force measurements were performed at different frequencies, f = 5, 10, 20, 40, 60, 80, 100 Hz, and three different indentation depths δ = 100, 150 and 200 nm. Native HA/PLL films show no dependency either in the storage modulus G’ nor in the loss modulus G” on the applied frequencies, as shown in Figure 5. Furthermore, G” show values around 23–27 kPa, nearly 3 times lower than the G’ values at 75–85 kPa. Measurements at different indentation depths 100, 150 and 200 nm show the same values for the native HA/PLL films, as shown in Figure 5. To summarize for native HA/PLL films no dependence of storage and loss modulus on the frequency and indentation depth was found. 6

10

G' & G'' [Pa]

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G' G''

(Storage modulus) (Loss modulus)

5

10

4

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3

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4

6 8

2

10

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6 8

100

Frequency [Hz] Figure 5: Native HA/PLL films: Storage modulus G’ (filled symbols) and loss modulus G” (open symbols) as function of the used oscillation frequency for three different indentation depths of 100 nm (circles), 150 nm (squares) and 200 nm (triangles). Cross-linked HA/PLL films were also measured at the same frequencies and indentation depths as the native ones. Figure 6 shows that the storage modulus G’ of the cross-linked films is around two orders of magnitude higher than the values for the native PEMs. In contrast the G” values are just 4 times higher. Analogous to the behavior of native HA/PLL 13


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films, the moduli are independent of frequency and indentation depth, showing constant values around 3 MPa and 80 kPa, respectively. The loss tangent (η = G ′′ /G ′ ) of the native 8

G' & G'' [Pa]

10

G' G''

7

(Storage modulus) (Loss modulus)

10

6

10

5

10

4

10

4

6 8

2

10

4

6 8

100

Frequency [Hz] Figure 6: Crosslinked HA/PLL films: Storage modulus G’ (filled symbols) and loss modulus G” (open symbols) as function of the used oscillation frequency for three different indentation depths of 100 nm (circles), 150 nm (squares) and 200 nm (triangles). HA/PLL films is higher than for the crosslinked HA/PLL films. As shown in fig. 7, for the native films G”/G’ ≈ 0.3 while the crosslinked ones show a much lower G”/G’ ratio of 0.05.

loss tangent (G''/G')

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0.6

100 nm indentation 150 nm indentation 200 nm indentation

0.5 0.4 0.3 0.2 0.1 0.0 20

40

60

80

100

Frequency [Hz] Figure 7: Loss tangent for the native (filled symbols) and crosslinked (open symbols) HA/PLL films as function of the frequency. The modeling of QCM-D data on a Voigt viscoelastic element was performed on native HA/PLL films with a different outermost layer, containing either 15 or 16 layers. The analysis of thicker PEMs, comparable to those studied by AFM, was not possible due to the detection limits (60 − −250 nm depending on the overtone number) of the technique, 14


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which is determined by the penetration depth δ of the acoustic wave in the bulk liquid. 57 In fact, the values of δ in aqueous media was estimated between 90 and 140 nm from 3th to 7th overtone, which corresponds to the thickness of a PEI(HA/PLL)8 swollen in water. In Table 1 shear thickness df , shear modulus µf , shear viscosity ηf of HA and PLL- terminated films, 15 and 16 layer, respectively, are reported. From these values and according to eq. 2, storage G′ , loss G′′ moduli and the corresponding loss tangent G′′ /G′ were calculated. First of all, minor differences were found between HA and PLL termination. This indicates that

Table 1: Viscoelastic parameters obtained by modeling of QCM-D data for PEI(HA/PLL) multilayers according to a Voigt element. Termination HA PLL

µf (·105 ) [Pa] 15.0±0.1 10.6±0.2

ηf (·10−3 ) [Pa ·s] 13.2±0.1 8.6±0.1

df [nm] 141.1±0.2 172.3±0.4

G’ [kPa] 1500±10 1060±20

G” [kPa] 410±2 269±4

G”/G’ 0.27 0.25

the internal structure mostly determines the viscoelastic response of the system to the shear stress. A minor influence on G’ and G” might be given by the different water content of the outermost layer, in particular with a slightly more flexible and hydrated structure for PLL layer (lower G’ and G”). Second, the viscoelastic moduli are roughly 1 order of magnitude higher than the values measured by AFM, likely due to the higher frequency applied for the shear stress (in the range of from 25 to 45 MPa for QCM-D measurements). However, the loss tangent is similar to AFM, which means that the elastic and viscous components increase proportionally under the increased applied frequency, leading at the end to the same material properties as found by AFM. QCM-D measurements on crosslinked films were not carried out, due to the high film rigidity. This makes the viscoelastic models (Maxwell and Voigt models) unsuitable to the description of the mechanical properties of these systems.

Discussion Usually, a rheometer works in the dimension of hundreds of µm up to millimeter, whereas the AFM can probe the mechanical properties in the nanoscale using a colloidal probe or a tip with a radius in nanometer scale. The AFM was so far used to determine mechanical properties of native and

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crosslinked HA/PLL films by static force measurements. This method is not suited for films with a viscoelastic character. The calculation of the indentation modulus usually is done by using a Hertz based model. Since Hertz based models require a pure elastic behavior of the samples, the calculated values do not fully describe the investigated native HA/PLL films. On the other hand dynamic force measurements can be used to determine the elastic and the viscous properties of the films, as it is usually done by the use of a shear rheometer. Although dynamic force measurements are already used in cell biology due to the mostly viscoelastic behavior of cells, it is rarely used for polyelectrolyte multilayers. The storage and loss moduli of the native films are shown in Figure 5. The storage modulus is with a value between 50 - 80 kPa about 4 times higher than the loss modulus with 15 - 25 kPa, in contrast to our expectation. This indicates that the film responses more like an elastic solid in the used frequencies from 5 to 100 Hz. Also no crossover was found in the investigated frequency range, unlike to the biological samples. 36,38,39 Both the storage and loss moduli show no dependency on the used frequencies. Both curves are parallel to each other without giving any hint for a crossover at lower or higher frequencies. At the crossover (G’/G” = 1), which is called sol–gel transition, the film properties changes from viscous to predominant elastic behavior, giving these films a gel like character. In order to determine if a crossover can be observed at higher frequencies the moduli were also determined by QCM-D. The obtained values are reported in Table 1 for input stimuli of 15, 25 and 35 MHz. The storage modulus for both HA and PLL terminated films is roughly 4 times higher than the loss modulus, meaning that the mechanical response is always elastic-dominated. The absolute values of QCM-D-moduli, 1000–1500 kPa and 300–400 kPa for G’ and G”, respectively, are about 10 to 20 times higher than the values measured by AFM. This significant difference can be due to the following reasons: 1) QCM-D films were subjected to shear stress, i.e. in the horizontal direction, while AFM measurements apply a compression stress, in the vertical direction. The higher moduli under an applied shear stress indicate an enhanced strength against flow, likely due to interdigitation among subsequent layers. 2) The large difference in the frequency might also be responsible for the corresponding different moduli. Since both storage and loss modulus are frequency-dependent quantities, 58,59 it is likely that the viscoelastic moduli are higher at higher applied frequency and lower in the low frequency regime of AFM. To speculate about the reason,

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one might assume that the relaxation time at static experiments reflects the time which is needed to break the complexation sites on a sub-molecular scale. At higher frequencies the complexation sites have not enough time to break and rearrange, which reduces the yield and let the system appear stiffer and more elastic. 3) It is questionable if the different preparation methods might have induced structural differences, which in turn produce diverse mechanical properties in the film. While the HA/PLL films, which are measured using the AFM, are prepared by dipping, the preparation of the HA/PLL film in the QCM-D is done under a steady flow of the polyelectrolyte solution. During dipping the polyelectrolyte solution is not stirred and the polyelectrolytes have more time to adsorb and rearrange. In contrast during adsorption under flow more polyelectrolytes reach the surface at the same time, which leads to a more quenched chain conformation without enough time for rearrangement. This leads to a different all-over-all structure in both PEM types. Nevertheless, the loss tangent (η = G ′′ /G ′ ) of the native films shows values which are about 0.3 for both AFM and QCM-D measurements, as shown in Figure 7 and Table 1. These values are well below 1, meaning that the films behave more as an elastic system rather than a viscous one, in the observed frequency range. Considering the fact that the HA/PLL films do not show any dependence on the input frequencies, the following model can be deduced: PLL is highly mobile, it can move through the film and build complexation sites between its amino group and the carboxylic acid groups of the HA. This implies that the film behaves like a weak physical gel network which is stabilized due to the complexation sites. A similar behavior of the mechanical properties to HA/PLL films can be found in uncrosslinked polyacrylamide hydrogels (PAA). Compared to the HA/PLL films, PAA hydrogels are showing a similar behavior of its mechanical properties measured by shear rheology. At frequencies between 5 and 100 Hz the storage modulus is higher than the loss modulus, the same as HA/PLL films, and showing mostly no dependency on the frequencies. At very low frequencies at 0.04 – 0.05 Hz a crossover was reported by Suriano et al. 60 Frequencies lower than 1 Hz cannot be measured with the used AFM without further modifications. Instabilities of the piezo signal due to electrical and temperature fluctuations or noise over long times > 1 − 2 min makes it impossible to get enough stable oscillations for a qualitative analysis. The properties of the HA/PLL films (AF M : η = 0.32; QCM − D : η = 0.27) show similar loss tangent values compared to PAA hydrogels 60

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(η = ∼ 0.35) or a similar PEM systems as chitosan/heparin 54 (η = 0.3 − 0.5). PAA hydrogels show smaller values for the storage and loss modulus (G′ = 110 P a, G′′ = 35 P a at 10Hz) while chitosan/heparin films in contrast show a similar stiffness in QCM-D (G′ = 0.5 − 1M P a) compared to HA/PLL films (AF M : G′ = 50 − 80 kP a, G′′ = 15 − 25 kP a ; QCM − D : G′ = 1000 − 1500 kP a, G′′ = 300 − 400 kP a). The storage and loss modulus was also measured and calculated for different indentation depths at 100, 150 and 200 nm. The values of the measurements at the three different indentation depths are quite similar, as shown in Figure 5, proving that the film has a homogeneous structure which does not change with the indentation depth. Crosslinked films in contrast show a really high storage modulus compared to the value for the native films, as shown in Figure 6. The calculated storage modulus at all indentation depths is around 2 MPa. This is a 25 fold increase in the modulus due to the crosslinking of the films. The ratio between the storage and loss modulus is shown in Figure 7, where the loss tangent drops to values around 0.01 - 0.05. These low values indicate that the films show no viscoelastic behavior anymore. The films are fully crosslinked and are now a chemical gel with a pure elastic behavior. The storage and loss modulus of the crosslinked film shows no dependency on the used frequencies, 5 to 100 Hz, as it was also observed with the native HA/PLL films. Due to the crosslinking over 12 hours after preparation of the films it was not possible to measure the mechanical properties of the film with the QCM-D. For a pure elastic crosslinked film of HA/PLL the storage and loss moduli are not expected to show a cross over at low frequencies.

Summary and Conclusion In this work, the mechanical properties of native and cross-linked HA/PLL films were measured by dynamic force measurements using an Atomic Force Microscope at frequencies between 5 and 100 Hz. Quartz Crystal Microbalance was used to study the mechanical response in the frequency range of tens of MHz and compare it with the behavior at low frequency. As obtained from AFM studies, native HA/PLL films have a much higher storage (75–85 kPa) than loss (23–27 kPa) moduli (η = G ′′ /G ′ = 0.32) giving these films a more elastic response to dynamic measurements. Both moduli were independent on the used frequencies, for AFM, showing no change in their values and

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furthermore no indication of a cross over. QCM-D measurements were used to determine if the film properties were showing a cross-over at higher frequencies. The measured moduli were much higher values those obtained by AFM (G’= 1000–1500 kPa and G”= 300–400 kPa) but they confirmed the elastic response and similar loss tangent (η = G ′′ /G ′ = 0.27). The difference between the values for AFM and QCM-D measurements was explained by the difference in preparation of the films, the different frequency regime of the applied stress and the scale of measurement from nanometer size for the AFM to micrometer size for the QCM-D. A cross-over of the storage and loss moduli is expected at frequencies much lower than 1 Hz, as it is reported for polyacrylamide hydrogels. Such low frequencies are not accessible with the used AFM. Cross linking of the HA/PLL films in comparison leads to a purely elastic response and a 25 fold higher value for the storage modulus (3 MPa). Also in this case, G’ and G” were independent of the used frequencies and the loss tangent is decreases to values around 0.01 - 0.05. It is shown that dynamic force measurements can be used to measure the rheological properties of HA/PLL films on a nanoscale. This method can be extended to probe the dynamics of many different systems, not only polymer thin films but also chemical crosslinked or physical stabilized gels, polymer brushes, as well as under different environments (water, organic solvent and gases). As solvent in these measurements it is not necessary to use water based solvents but it is also possible to use ambient air or other gases.

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Piezo

Polyelectrolyte Multilayer

Force & Indentation

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Time

QCMD Polyelectrolyte Multilayer Au

Quartz Au

Amplitude

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Time

Separation of Storage and Loss Modulus of Polyelectrolyte

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