Viscoelastic Properties of Adsorbed Bottle-brush Polymer Layers

15028

J. Phys. Chem. C 2008, 112, 15028–15036

Viscoelastic Properties of Adsorbed Bottle-brush Polymer Layers Studied by Quartz Crystal Microbalance s Dissipation Measurements Joseph Iruthayaraj,*,† Geoffrey Olanya,† and Per M. Claesson†,‡ Department of Chemistry, Surface Chemistry, Royal Institute of Technology, Drottning Kristinas Va¨g 51, SE-100 44 Stockholm, Sweden and Institute for Surface Chemistry, YKI, P.O. Box 5607, SE-114 86 Stockholm, Sweden ReceiVed: May 19, 2008

Adsorbed layers of a series of bottle-brush polyelectrolytes with 45 units long poly(ethylene oxide) [PEO], side chains have been investigated by the quartz crystal microbalance technique with dissipation monitoring. The data have been evaluated with three different models, the Sauerbrey model, the Johannsmann model, and the Voigt model. It is found that all three models predict the same trend in the variations of sensed mass and hydrodynamic layer thickness with polymer architecture, that is, with the backbone charge to side chain density ratio. However, the simple Sauerbrey model underestimates the sensed mass by a factor of 1.15-1.45 compared to the more accurate Voigt model. By following the evolution of the layer dissipation, elasticity, and viscosity with increasing surface coverage it was concluded that the layers formed by brush polymers with intermediate charge densities undergo a structural change as the coverage is increased. Initially, the polymers are anchored to the surface via the PEO side chains. However, as the adsorption proceeds a structural change that brings the backbone to the surface and forces the side chains to extend from it is observed. The layer elasticity and viscosity as a function of surface coverage go through a maximum in this transition region. 1. Introduction The study of viscoelastic properties of soft thin films can contribute to increased understanding of structure-property relationships. Such studies are of great importance considering that a recent simulation study revealed that the Young’s modulus of a material departs significantly from its bulk value as the lengthsscale of the material reaches the order of few tens of nanometers.1 Some information on shear viscoelastic properties of adsorbed layers in the MHz frequency range can be obtained from quartz crystal microbalance measurements. For instance, investigations of adsorbed cross-linked gels and covalently bound brush layers using the quartz crystal microbalance-dissipation (QCM-D) technique demonstrated that the shear modulus of the gel layer was larger (∼105 Pa) than that of the brush layer (∼104 Pa) at the same surface coverage.2 This was attributed to the stiffness induced by the cross-linked network structure of the gel layer. Further, the shear modulus of adsorbed gel layers, formed by mussel adhesive protein, has been found to increase upon crosslinking in situ.3 Another interesting sequence of interfacial events monitored by studying the viscoelastic properties is the glucagon fibrillation process,4 that is, the ability of some polypeptides to aggregate into long, thin needle-shaped structures. Other techniques allow the study of rheological properties of thin films under confinement. For instance, viscoelastic properties of thin, adsorbed polybutadiene films confined between a sphere and a plane have been studied using a modified surface force apparatus.5 At a critical distance the storage modulus was found to exhibit a sharp transition, whereas the * Corresponding author e-mail; [email protected]. † Royal Institute of Thechnology. ‡ Institute for Surface Chemistry.

loss modulus increased steadily with decreasing separation. From these data it was envisaged that the two adsorbed layers in contact with solution exhibited a sharp liquid-solid-like transition at the critical distance.5 In another study, colloidal probe atomic force microscopy (AFM) was employed to study the viscoelastic properties of adsorbed gelatin on glass in the frequency range 20-1000 Hz. The data showed that the viscous response dominated at larger separation, whereas the elastic response became dominant at high compression of the layers.6 Another interesting approach to measure viscoelastic properties of thin spin coated films (200-5 nm) is, as referred to by the authors,7 “buckling-based methodology”. In this study the thin films were adhered to an elastic substrate (PDMS) whose modulus is known. The system was then subjected to a small uniaxial strain, and the buckling patterns of the PDMS-supported polymer films were used to extract their viscoelastic properties. It was shown that the elastic modulus of both poly(styrene) and poly(methylmethacrylate) thin films decreased by an order of magnitude as compared to their respective bulk value as the thickness was reduced below 40 nm. In our earlier studies on brush polymers having 45 units long PEO side-chains, we observed that the adsorption increases significantly, on silica, upon introduction of small amount of charges along the backbone. We also showed that there is a transition in the adsorption mechanism, from predominantly nonelectrostatic to electrostatic, as the ratio of charge to PEO along the backbone was increased by variation in the polymer architecture. In this study we investigate the viscoelastic properties of the same brush polymer layers. Apart from providing viscoelastic information, the data also allow us to draw conclusions about changes in layer structure occurring during the adsorption process.

10.1021/jp804395f CCC: $40.75  2008 American Chemical Society Published on Web 08/27/2008

Viscoelastic Properties of Bottle-brush Polymer Layers

J. Phys. Chem. C, Vol. 112, No. 38, 2008 15029

TABLE 1: The Copolymers Used in This Studya brush polymers poly(PEO45MEMA) PEO45MEMA:METAC-2 PEO45MEMA:METAC-10 PEO45MEMA:METAC-25 PEO45MEMA:METAC-50 PEO45MEMA:METAC-75 poly(METAC)

METAC Cl-(wt %) METAC (mol %) in yield in (mol %) copolymer copolymer (%) Feed 0 2 10 25 50 75 100

0 0.03 0.20 0.57 1.62 3.93 15.9

0 2.0 10.6 25.8 51.3 75.0 99.3

92 90 92 93 92 95 89

a The columns denote the composition (mol %) of the feed in terms of METAC monomers, chloride content of the copolymer (in wt %, and hence the amount of METAC segments in the copolymer). The last column reports the yields of the various copolymers.

CHART 1: Molecular structures of the PEO45MEMA and METAC segments present in the brush polymers, where X denotes the mol % of the charged METAC unit

2. Materials and Methods The series of bottle-brush polymers of varying charge densities used in this work (see Table 1), represented as PEO45MEMA:METAC-X, were synthesized by free-radical copolymerization of PEO45MEMA and METAC monomers in polymerization tubes under nitrogen atmosphere using AIBN as the thermal initiator.8 In the polyelectrolyte representation “X” denotes the molar percentage of the permanently charged METAC segments, see Chart 1. 2.1. Quartz Crystal Microbalance-Dissipation. QCM-D measurements were performed using a q-sense E4 microbalance (q-sense Gothenburg), employing quartz crystals (AT-cut with 5 MHz fundamental frequency) coated with 50 nm silica. The silica crystals were cleaned with 2% Hellmanex (Hellma GmbH) for 30 min, followed by rinsing with copious amount of Milli-Q water. The surfaces were left overnight in Milli-Q water before the measurement. The resonance frequency (f) and the energy dissipation (D) of the crystal are accurately determined as described by Rodahl et al.9 The dissipation is measured by switching off the driving power to the sensor and monitoring the amplitude decay profile of the oscillator. The amplitude decays as an exponentially damped sinusoidal function with a characteristic decay time (τ). The decay constant is related to the dissipation by eq 1,

D)

2 ωτ

(1)

where ω (ω ) 2πf) is the angular frequency of the oscillating crystal. By recording the amplitude of oscillation as a function

of time and fitting a decaying exponential profile, both τ and ω are obtained and, hence, the dissipation. The frequency change (∆f) and the dissipation change (∆D) due to adsorption were recorded at six different overtones (15, 25, 35, 45, 55, and 65 MHz) using the Q-tools program (q-sense, Gothenburg). 2.2. Theoretical Modeling of QCM-D Data. In QCM measurements, a quartz crystal oscillator is set to oscillate at its resonance frequency. The shift in frequency due to formation of an adsorption layer is typically between 10-100 Hz. The frequency change and the dissipation change can be related to the mass oscillating with the crystal and the viscoelastic properties of the layer through various models. 2.2.1. The Sauerbrey Model. The Sauerbrey10 equation (eq 2) relates the frequency change (∆f) of the oscillating quartz crystal, due to the presence of a thin film, to the mass of the film (∆mf).

f0 ∆f ∆mf ) -C∆mf )n tqFq

(2)

Where n, f0, tq, and Fq represent the overtone number, the fundamental frequency of the quartz oscillator, the thickness, and the density of quartz (2650 kg m-3), respectively. The value for C for our crystal is 17.7 ng Hz-1 cm-2. The above equation is strictly valid only for thin films in air. As the film thickness increases, the damping of the oscillating crystal also increases due to viscous dissipation in the film. For this reason, the frequency change, even when measured in air, is a consequence of both the mass change and the viscoelastic properties of the film.11,12 Therefore, theoretical models are required to relate the measured quantities to the mass and the viscoelasticity of the adsorbed film. Adsorbed films can either be modeled as an electrical component with characteristic impedance (The Johannsmann model) or as a linear viscoelastic Voigt solid (continuum mechanics approach). 2.2.2. The Johannsmann Model. In the Johannsmann model the quartz resonators are modeled as equivalent electrical circuits.13 In this approach the adsorbed layer is described in terms of a generalized impedance (Z/). There exists a relationship between the generalized impedance (Z/) and the acoustic impedance of the film (Zf) and the acoustic impedance (Zf ) √FfGf ) is related to the viscoelasticity of the film as shown in the parenthesis, where Ff and Gf are the density and the complex shear modulus of the film. For an adsorbed film on a quartz resonator measured in air or vacuum, the complex frequency change is given be eq 3,

( )

∆f * ) Im

Z/ 1 )Z tan(kfdf) 2πtqFq 2πtqFq f

(3)

where kf (kf ) √Ff ⁄Gf × ω) is the wave vector of the shear waves inside the film, and df is the film thickness. It can be shown from eq 3 that in the thin film limit (tan x ≈ x) the equation results in the Sauerbrey equation and for a slightly thicker film the tangent is Taylor expanded to the third order, resulting in the final expression:

[

m * ) m0 + ˆj

]

Ff2df3 × ω2 3

(4)

where m* is the equivalent mass (m* ) -2πtqFqδf/f) and ˆj ) 1/G is the shear compliance of the adsorbed film. Thus, the plot of the equivalent mass versus the square of the angular frequency gives the true mass as the intercept, and the shear compliance is deduced from the slope, assuming that the compliance is independent of ω.

15030 J. Phys. Chem. C, Vol. 112, No. 38, 2008

Iruthayaraj et al.

2.2.3. Voigt Model12 (Continuum Mechanics Approach). In this model the frequency (∆f) and the dissipation changes (∆D) are related to the viscoelastic properties of the adsorbed film through the β parameter,14 as shown in eqs 5 and 6.

(

∆f ) Im

)

(5)

β πftqFq

(6)

β 2πtqFq

( )

∆D ) -Re

The β parameter introduced in this model is analogous to the complex impedance (Z/) of the adsorbed layer introduced in the equivalent circuit model (Johannsmann model),13 as shown in eq 3. Eventually, it is the β parameter or the complex impedance (Z/) that contains the information on the adsorbed layer viscoelasticity, and both approaches result in the same equations. To relate β to the viscoelastic quantities (such as elasticity and viscosity), a relevant viscoelastic model should be chosen to describe the adsorbed film. In this respect the adsorbed film is modeled as a Voigt solid. The Voigt model is a simple linear viscoelastic model in which the total stress acting on the material is the summation of stresses due to the elastic (Hooke’s law) and the viscous (Newton’s law of viscosity) components of the material, as shown in eq 7.

σxy ) µf

∂ux(y, t) ∂Vx(y, t) + ηf ∂y ∂y

(7)

The first term is Hooke’s law (the differential term is the strain), and the second term is Newton’s law of viscosity (the differential term is the strain rate); thus, µf and ηf denote the elasticity modulus and the viscosity of the film, respectively. The terms ux and Vx refer to displacement and velocity in the x-direction, respectively. Within this model, the adsorbed film of thickness df and density Ff is characterized by a complex shear modulus (µ/)15

µ/ ) µ ′ + iµ ″ ) µf + i2πfηf ) µf(1 + i2πfτ)

(8)

Where µf is the elastic shear modulus (storage modulus), ηf is the shear viscosity (loss modulus) of the film, and τ is the characteristic relaxation time of the film (τ ) ηf/µf). The β parameter is obtained by solving the wave equation for bulk shear waves propagating in a medium whose viscoelaticity is described by a Voigt model. The final expression for a single viscoelastic layer in a liquid medium is given below.12

∆f ) -

{

( )} ( )}

ηfω2 ηb 1 dfFfω - 2df 2 2 δ 2πFqtq µf + ω ηf

∆D )

{

µfω ηb 1 2df 2 2 2 2πfFqtq µf + ω ηf δ

2

(9)

2

(10)

The symbols have the same meaning as before. The subscript b represents the bulk liquid, and ω is the angular frequency. The viscous penetration depth δ is defined as:

δ)

2ηb Fbω

Figure 1. Frequency change (∆f) and dissipation change (∆D) during the adsorption of PEO45MEMA:METAC-25 on silica from water. The polymer concentration was 10 ppm. The frequency and the dissipation plots are represented as f and D, respectively. the numerals represent the overtone number.

3. Results The changes in frequency (∆f) and dissipation (∆D) during the adsorption process of PEO45MEMA:METAC-25 on a silicacoated quartz oscillator is shown in Figure 1. The data were collected at 6 different frequencies, but only 3 of them are shown for the sake of clarity. 3.1. ∆f-∆D Plots. The change in layer dissipation (∆D) is plotted as a function of the frequency change (∆f) during the adsorption of PEO45MEMA:METAC-X polymers in Figure 2, panels a and b. These plots can be used for drawing conclusions about structural transitions occurring as the adsorbed layer grows in mass. The interpretation of these plots is discussed in the next section. 3.2. Preliminary Analysis. As a first step in the analysis of the data the adsorbed layer was treated as a thin, rigid film, and the Sauerbrey model was used to calculate the sensed mass (mSauerbrey). In the second step the layer was assumed to be viscoelastic, as described by eq 4. Here, the equivalent sensed mass (m/) was calculated using the Sauerbrey model (eq 2) at different overtones, and the obtained masses were plotted against the square of the oscillation frequency in accordance with the eq 4. The results are shown in Figure 3, and it is obvious that the plots are nonlinear when the whole frequency range is considered, suggesting that the shear compliance is frequencydependent. However, a linear fit was approximated to the first three frequencies, and the frequency-independent sensed mass (m0) was obtained by extrapolation to zero frequency. The effective hydrodynamic thickness of the film (df) was calculated from the sensed mass (obtained from the Sauerbrey model and the Johannsmann model), the adsorbed mass (obtained from reflectometry (Γrefl)) and the bulk density of the polymer (Fpolymer)16 using the expression shown below;17

df )

mQCM ) Feff

(

mQCM Γrefl Γrefl Fpolymer × + Fwater × 1 mQCM mQCM

)

(

) (12)

(11)

Equation 9 reduces to the Sauerbrey equation (eq 2) in the absence of layer viscoelastic contributions. In the analysis of the data, the measured frequency change and dissipation change are fitted using eqs 9 and 10, respectively, as described below.

where mQCM is the QCM mass calculated using either the Sauerbrey model or the Johannsmann model, and Feff is the effective density of the adsorbed layer. The plots comparing the thicknesses obtained from various models using QCM data are shown later in Figure 10. The large difference between mQCM and Γrefl (see Table 2) shows that the water content of the layer



Figure 2. (a) ∆f-∆D plots for the PEO45MEMA:METAC-X series: (a1) Poly(PEO45MEMA), (a2) X ) 50, (a3) X ) 75. (b) ∆f-∆D plots for the PEO45MEMA:METAC-X series: (b1) X ) 2, (b2) X ) 10, (b3) X ) 25.

assumption was tested using two frequencies and the corresponding dissipation at a time to calculate the elasticity (µf), viscosity (ηf), and thickness (df) of the film. The results of this analysis are shown in Figure 4. The values reported here correspond to the equilibrium situation, that is, when the adsorbed layer is fully formed at the end of the adsorption process. The plot clearly illustrates, in agreement with the data reported in Figure 3, that the viscoelastic properties of the adsorbed film are dependent of the frequency of the oscillation and thus a more involved analysis is required. 3.4. Extended Viscoelastic Model. In order to account for the frequency dependence of the viscoelastic properties, the data were fitted with the extended viscoelasticity model in which the frequency dependence of the film elasticity and the film viscosity is taken into account by introducing a frequencydependent parameter, as shown in eqs 13 and 14:

Figure 3. Plot of equivalent mass (m/) vs frequency squared (f2) for the PEO45MEMA:METAC-X series: X ) 2% (0), X ) 10% (•), X ) 25% (O), X ) 50% (2), X ) 75% (∆), and poly(PEOMEMA) (9). (Inset) The frequency-independent sensed mass obtained by a linear fit to the mass calculated using the first three overtones.

is high; with 80-90% of the mass sensed by QCM being due to water associated with the layer. 3.3. Voigt Analysis. From the preliminary analysis it is clear that the solvent uptake by the adsorbed layer is significant, which results in a swollen state. Hence, the analysis procedure relevant to liquid medium must be used to analyze the data; therefore, we used the Voigt model to fit our data. The measured change in frequency (∆f) and dissipation (∆D) due to adsorption of PEO45MEMA:METAC-X polymers from aqueous solution were fitted using eqs 9 and 10 employing the Q Tools software. As shown in Table 3, we performed the analyses by making use of three fitting parameters and three other parameterssthe film density, the bulk viscosity, and the bulk densitysthat were kept fixed. The last two parameters are known, and as the water content of the film is high, the film density is close to that of bulk water, see Table 2, and we choose to keep this parameter fixed as well. The experiments deliver data from 6 different overtones, and at each overtone both the frequency change (∆f) and the dissipation change (∆D) are monitored, amounting to 12 experimental parameters. The simplest assumption is that the viscoelasticity of the adsorbed film is independent of the oscillation frequency, and if this indeed is the case, any combination of data from different overtones should yield the same value for the film elasticity and film viscosity. This

ηf(n) ) ηf(f0) × [1 + (n - 1) × R]

(13)

µf(n) ) µf(f0) × [1 + (n - 1) × β]

(14)

Here, f0 and n refer to the fundamental frequency and the overtone number, respectively. R and β are fitting parameters, in addition to those shown in Table 3, which amounts to five variables in total (µf, ηf, df, R, and β). In the extended model, frequency and dissipation data from all overtones are fitted at once. From this fit one obtains the film elasticity at the fundamental frequency µf(f0), the film viscosity at the fundamental frequency ηf(f0), the film thickness (df), and the constants R and β. The shear viscosity and elasticity of the film are calculated as a function of overtone number (i.e., frequency) using eqs 13 and eq 14, respectively. The film elasticity and the film viscosity are assumed to vary linearly based on the premise that the deformation of the adsorbed layer is low (amplitude of oscillation is ∼1 nm) in QCM experiments. Also, the linear variation of these parameters with frequency is reasonable, as indicated by the data displayed in Figure 4. The dependence of film elasticity (µf) on frequency for the brush polymers of varying charge densities is shown in Figure 5. Clearly, the elasticity increases with frequency in all cases. The fact that all curves are linear is a consequence of the fact that a linear viscoelastic model has been used to fit the data. We note the trend that the film elasticity increases with the brush polymer charge density, except for the neutral brush that does not conform to the general trend. This will be discussed further below. Similarly, Figure 6 shows the dependence of film viscosity (ηf) on frequency. In this case the frequency dependence is small, and both situations where the film viscosity increases slightly with frequency (X ) 75) and decreases slightly


Iruthayaraj et al.

TABLE 2: Adsorbed Layer Thicknesses Obtained by Using Different Models to Evaluate QCM Data; Sauerbrey Model (SM), Johannsmann Model (JM), and Voigt Model (VM)a df (nm) brush polymer

Feff (k gm-3)

QCM (SM)

(JM)

QCM (VM)

∆D3 106

∆D3/mVM (m2 mg-1)

Γrefl (mg m-2) optical method18

poly(PEO45MEMA) PEO45MEMA:METAC-2 PEO45MEMA:METAC-10 PEO45MEMA:METAC-25 PEO45MEMA:METAC-50 PEO45MEMA:METAC-75 poly(METAC)

1028 1030 1017 1020 1028 1028 1000

3.7 14.1 16.2 11.7 5.9 4.0 0.4

3.7 14.6 17.8 11.9 6.2 4.1 0.4

4.3 18 20.5 13.1 8.3 4.8

1.8 9.5 10.8 5.3 2.6 1.2 0.1

0.42 0.53 0.51 0.40 0.31 0.25

0.7 2.14 2.02 1.54 1.38 0.79 0.21

a Feff is the effective density of the layer. The last three columns report the dissipation change at the third overtone, the ratio of the dissipation change and the Voigt mass at the third overtone, and the adsorbed mass determined by reflectometry, respectively.

TABLE 3: Parameters Used to Fit the QCM-D Data Using the Simple Viscoelastic Modela parameters

min

film elasticity (µf)Pa film viscosity (ηf) kg/ms film thickness (df) m film density (Ff) kg/m3 bulk density (F) kg/m3 bulk viscosity (η) kg/ms

1 × 10 0.001 1 × 10-10

varied varied varied 1000 1000 0.001

max 5

1 × 109 3 1 × 10-6

a The minium and maximum values allowed for the variables are provided in columns 3 and 4, respectively.

Figure 5. Film elasticity (µf) as a function of frequency (f) for the PEO45MEMA:METAC-X series: (9) uncharged, (0) X ) 2, (•) X ) 10, (O) X ) 25, (2) X ) 50, and (∆) X ) 75.

Figure 4. Film elasticity (µf) (open circles) and film viscosity (ηf) (filled squares) of PEO45MEMA:METAC-50 obtained by fitting the measured data at different frequency combination. The numbers in the x-axis correspond to the following overtone combinations 1 ) F3F5, 2 ) F3F7, 3 ) F5F7, 4 ) F5F9, 5 ) F7F9, 6 ) F7F11, 7 ) F9F11, and 8 ) F11F13.

with frequency (X ) 25 and X ) 50) can be found. In the high frequency limit the film viscosity increases with the charge density of the brush polymer, except for the neutral brush polymer, which again is an exception. In the extended model the hydrodynamic film thickness (df) is assumed to be independent of frequency. The internal consistency of the data returned by the model can be tested by individually fitting each frequency/dissipation. In this consistency test the film elasticity and the film viscosity for each frequency were fixed at the values reported in Figures 5 and 6, thus leaving the film thickness as the only variable. By separately fitting the data in the plateau region for each frequency/ dissipation pair, the film thickness can be obtained as a function of frequency. Indeed, Figure 7 shows that the film thickness obtained in this way is independent of oscillation frequency and is in agreement with that returned by the extended model. Thus, the data analysis process appears to be internally consistent.

Figure 6. Film viscosity (ηf) as a function of frequency for the PEO45MEMA:METAC-X series: (9) uncharged, (0) X ) 2, (•) X ) 10, (O) X ) 25, (2) X ) 50, and (∆) X ) 75.

3.5. Film Elasticity and Viscosity. The film elasticity and the film viscosity corresponding to the third overtone are plotted as a function of polymer charge density in Figure 8. It can be seen that both the elasticity and the viscosity decreases as the charge density of the brush polymer is slightly increased from 0 to 2 mol %. The elasticity increases monotonically with further increase in polymer charge density. The variations in film elasticity and viscosity during the adsorption process of PEO45MEMA:METAC-X polymers from aqueous solutions are shown in Figure 9. The dissipation change accompanying the adsorption process is also shown in the graphs.


Figure 7. Film thickness (df) as a function of frequency for the PEO45MEMA:METAC-X series in aqueous solution: Poly(PEO45MEMA) (9), PEO45MEMA:METAC-10 (•), PEO45MEMA:METAC25 (O), PEO45MEMA:METAC-50 (2), and PEO45MEMA:METAC75 (∆). The lines correspond to the thickness obtained from the extended viscoealstic model.

Figure 8. Film elasticity (9) and film viscosity (•) at the third overtone as a function of polymer charge density.

4. Discussions 4.1. Comparison between Models Used to Evaluate QCM Data. The measured frequency change (∆f) in QCM experiments is due to both the mass change and the viscoelasticity of the adsorbed layer. The simplest assumption is that the effect of viscoelasticity is negligible, the thin-film scenario, which is applicable when inertial forces are too small to induce film shearing. In this case, the Sauerbrey model10 (eq 2) can be used to evaluate the mass change due to adsorption. The Johannsmann model13 is a better approximation because it also considers adsorbed layers that are thick enough to shear under its own inertia. In this respect the Johannsmann model derived for a viscoelastic film in air13 is applicable to deduce the mass change and the shear compliance of the adsorbed film as given by eq 4. In a liquid environment the adsorbed layer is swollen, and the uptake of solvent results in a situation where the measured frequency change is affected by both the mass change and the viscoelastic property of the film. There are two (equivalent) approaches to model thin films in liquid environment. One approach is to treat the adsorbed layer as a linear viscoelastic solid, the Voigt solid12 (eqs 9 and 10), and in the second approach, by Johannsmann,13 the adsorbed layer is divided into an infinite number of thin slabs, each of them given by a finite impedance value, and the impedances are related to the density

J. Phys. Chem. C, Vol. 112, No. 38, 2008 15033 and the shear compliance of each slab. The end result of both models is the same.12,13 Here we have fitted our data using the Voigt model. We are interested in comparing the results emanating from the three models (Sauerbrey, Johannsmann in air, and Voigt, which is equivalent to Johannsmann in liquid) for adsorbed brush polymer layer in water to illustrate the magnitude and type of errors that may be encountered using different models. We note that the Voigt model is expected to be the most accurate because it is the only model that has been derived for viscoelastic layers in liquid. The sensed mass and the hydrodynamic layer thickness obtained from all three models (Sauerbrey, Johannsmann in air, and Voigt) are presented in Figure 10. All models show the same trend in the thickness and the sensed mass as a function of polymer charge density. We also note that for our systems the Sauerbrey model and the Johannsmann (in air) model give quantitatively rather similar results, suggesting that the Johannsmann model in these particular cases are only marginally better than the Sauerbrey model. It should be emphasized that the plots of apparent sensed mass versus frequency squared (Johannsmann model) is nonlinear, especially in the case of layers with high dissipation (Figure 3). This behavior indicates that the shear compliance of the adsorbed layer is frequency-dependent, in conflict with the assumption in the Johannsmann model. The sensed mass and thickness obtained from the Voigt model is regarded as being most close to the true values. From this perspective we note that the other two models underestimate these two quantities, and the ratio between the mass calculated from the Voigt model and that calculated from the Sauerbrey model is in the range 1.15-1.45. 4.2. Adsorption Mechanism of Bottle-brush Polymers on Silica. Our earlier studies on the adsorption of bottle-brush polymers on silica18 led us to conclude that the adsorption of low charge density brush PEO45MEMA:METAC-X (X e 10) are dominated by PEO-surface interactions, whereas the polymers with higher charge density are adsorbed predominantly due to electrostatic interactions. This study provides more insights to the adsorption mechanism of PEO45MEMA: METAC-X on silica. We will discuss the characteristic features of the ∆D-∆f plots for the different polymers in terms of layer structure and relate it to the layer elasticity and viscosity obtained through the Voigt analysis. ∆D-∆f plots can be interpreted in terms of structural changes in the polymer layer during the adsorption process. In general, polymer adsorption can be regarded as a three-step process; transport to the surface and attachment of the macromolecule to the surface, followed by a change in conformation of the adsorbed macromolecule. In the initial state of adsorption, when the surface coverage is low, the change in polymer conformation is expected to result in an increased number of surface-polymer contacts, leading to a lower dissipation for the relaxed chain compared to that of a newly arrived one. A linear region in the ∆D-∆f plots indicates that the average conformation of the polymer on the surface is not changing as the adsorption increases (the dissipation per unit mass is constant). This behavior can be obtained when the relaxation to the preferred conformation on the surface is fast compared to the transport and attachment of new chains to the surface, as well as when the relaxation is slow compared to the time scale of transport and attachment. 4.2.1. Uncharged Bottle-brush. The dissipation change and the frequency change due to adsorption of the uncharged bottlebrush polymer are low, indicating that the adsorbed layer is compact. Further, the hydrodynamic thickness calculated from


Iruthayaraj et al.

Figure 9. Dissipation (∆D), film elasticity (µf), and film viscosity (ηf) as a function of frequency change during the adsorption of PEO45MEMA: METAC-X polymers from 10 ppm aquesous solutions: (a) uncharged, (b) X ) 2, (c) X ) 10, (d) X ) 25, (e) X ) 50, and (f) X ) 75.

the sensed mass is close to that of the cross-sectional radius of gyration of the polymer in aqueous solution as determined by SAXS.19 This indicates that the polymer is adsorbed with the backbone parallel to the surface, anchored to the surface by PEO side chains. For the uncharged brush (Figure 9a) the slope of the ∆D-∆f plot is linear up to about 50% of full coverage. At higher coverage the dissipation per unit adsorbed mass decreases, and eventually it completely flattens. Clearly, the layer becomes more compact with increasing coverage. A dramatic increase in layer elasticity is observed close to full coverage. We interpret this as being due to a stiffening of the PEO side chains due to excluded volume effects. 4.2.2. Low Charge Density Brush (PEO45MEMA:METAC2). In the case of PEO45MEMA:METAC-2 (Figure 9b) the ∆D-∆f plot is more complex as compared to that for the

uncharged brush. The initial linearity persists only up to 15% of full coverage. An inflection point can be noted at about 50% coverage, above which the dissipation per unit mass increases. Thus, in this case the polymers that arrive last are adopting more extended conformations or, alternatively, the whole layer expands as full coverage is approached. The high dissipation and the low elasticity of the layer indicate that the final adsorbed layer is extended, in agreement with the calculated hydrodynamic thickness. Thus, introduction of only a small number of charges in the polymer structure results in a very different evolution of the layer structure with increasing adsorption and in the final layer structure. This occurs despite that the adsorption decreases with increasing pH and ionic strength, in conformity with predominantly PEO-driven adsorption but contrary to adsorption predominantly driven by electrostatic forces.



Figure 10. Hydrodynamic layer thickness (a) and sensed mass (b) obtained using the Sauerbrey equation (9), the Johannsmann model (∆), and the Voigt Model (O).

4.2.3. High Charge Density Brush (PEO45MEMA:METAC75). It is interesting to compare the uncharged brush with PEO45MEMA:METAC-75 because both exhibit similar adsorbed mass on silica (Table 2). However, the structural evolution of the adsorbed layer is different for the uncharged brush and PEO45MEMA:METAC-75 (curves 1 and 3 in Figure 2a). The slope of the ∆D-∆f plot at low coverage for PEO45MEMA:METAC-75 is less steep than that for the uncharged brush, indicating that the high charge density brush readily adopts a flat conformation on the surface. This is due to the strong electrostatic affinity between the backbone and the surface. At high coverage the dissipation is insensitive to the coverage, and the elasticity increases as full coverage is approached, as in Figure 9f. Thus, the layer becomes more rigid and, as for the uncharged brush, we suggest that this is due to excluded volume effects that limit the flexibility of the PEO side chains. Finally, we note that although the adsorbed mass of the uncharged brush and PEO45MEMA:METAC-75 are same (see Table 2), the layer elasticity is higher for the 75% charged brush. This is due to the higher surface affinity of the backbone to the surface. 4.2.4. Intermediate Charge Densities (X ) 10, 25, and 50). An important feature of ∆D-∆f plots at the intermediate charge densities (X ) 10, 25, and 50) is the appearance of an initial region where the ∆D-∆f curves have a low slope (Figure 9, panels c-e), above which the slope again increases. The characteristic transition occurs around ∆f ) 20-25 Hz and ∆D ≈ 2. These values are similar to those found at full coverage for the uncharged polymer, suggesting that the chains arriving in the initial stage of adsorption, just as for the uncharged brush, lie parallel to the surface and that the initial attachment is mediated by the PEO side chains. During the later stage of the build-up process the layer obviously undergoes a change to a more extended structure. This transition is made feasible due to the strong electrostatic interaction between the backbone charges and the surface. This transition must also result in PEO side-chains being forced to protrude away from the surface. The values of ∆D at full coverage decrease with increasing backbone charge as the charge density is increased from 10 to 75 mol %. This suggests a more flat backbone conformation at higher charge densities. It is certainly of interest to know how the layer viscoelasticity changes in the transition region discussed above. It can be seen from Figure 9, panels c and d, and to some extent in panel e, that both the elasticity and the viscosity of the layer go through a maximum in the transition region. Clearly, the structural transition results in a layer that is less rigid, and this can be

identified with reorientation of some PEO side chains from being in direct contact with the surface to becoming stretched away from the surface. An interesting difference between PEO45MEMA: METAC-10 on the one hand and PEO45MEMA:METAC-25(50) on the other hand is that in the latter cases a plateau region is observed during the final stage of the build-up process. This indicates that the layer attains a flat and rigid conformation with the backbone relatively flat on the surface. On the other hand, in the case of PEO45MEMA:METAC-10 the value of ∆D increases strongly at the end of the build-up process. This means that the charge density of the backbone is not sufficiently large to drive the backbone flat to the surface, but the layer extension increases with packing density due to repulsive interactions between backbone tails (with grafted side chains). 4.3. Effects of Polymer Architecture. A thin, rigid layer, with many anchoring points to the surface, has a higher elasticity than a thick layer with few anchoring points. For the brush polyelectrolytes of concern in this report, the elasticity increases when the backbone charge density is increased from 2 to 75 mol %; see Figure 8. This is in line with the higher backbone affinity to the surface, resulting in formation of brush-like layers when both the charge density and PEO side chain density is sufficiently high (25 e X e 75). A lower charge density (2 e X e 10) results, due to decreased backbone-surface affinity, in backbone tails and loops and in more extended layers. For the uncharged brush there is no drive for bringing the backbone to the surface, but rather the PEO side chains attach the polymer to the surface, and a flat conformation of the polymer on the surface maximizes this interaction. Thus, the layer elasticity is higher than that of the low charge density brush polyelectrolytes. 5. Conclusions The frequency and the dissipation change due to adsorption of PEO45MEMA:METAC-X polymers on silica in water have been analyzed by using different models; the Sauerbrey, the Johannsmann, and the Voigt. All three models describe the trends in the variation of the sensed mass and the hydrodynamic layer thickness with polymer architecture in the same way. The Sauerbrey and Johannsmann models provide similar results, whereas the more accurate Voigt model predicts higher sensed mass and layer thickness. The ∆D-∆f plots combined with the Voigt analysis in terms of layer elasticity and viscosity allowed us to draw conclusions on the evolution of the layer structure during the adsorption process. Both the uncharged brush and the highly charged brush, PEO45MEMA:METAC-75 form flat and rigid layers. The former is anchored to the surface with

15036 J. Phys. Chem. C, Vol. 112, No. 38, 2008 relatively weak PEO-surface interactions, and the latter have stronger electrostatic backbone-surface interactions. For the uncharged brush and for polymers with backbone charge density in the range 25-75 mol %, a stiffening of the adsorbed layer is observed as full coverage is approached. This is attributed to excluded volume interactions that limit the flexibility of the PEO side chains. In contrast, in the charge density range 2-10 mol % the layers are more extended, more dissipative, and less elastic, suggesting that backbone loops and tails are formed. In the case of intermediate charge densities (X ) 10, 25, and 50) the adsorption proceeds via two-step mechanism. Initially the molecules interact with the surface via the PEO side chains, followed by a structural change that brings the backbone to the surface and forces PEO side chains to extend further away from the surface. This conclusion is based on the transition region observed in the ∆D-∆f plot. Both the elasticity and the viscosity go through a maximum in the structural transition region. Acknowledgment. Ricardas Makuska at Vilnius University is thanked for supplying the polymer samples. The work was carried out within the MC network “SOCON”. P.C. acknowledges financial support from the Swedish Research Council, VR. References and Notes (1) Bo¨hme, T. R.; de Pablo, J. J. J. Chem. Phys. 2002, 116, 9939–51. (2) Dutta, A.; Belfort, G. Langmuir 2007, 23, 3088–94.

Iruthayaraj et al. (3) Hoö¨k, F.; Kasemo, B.; Nylander, T.; Fant, C.; Sott, K.; Elwing, H. Anal. Chem. 2001, 73, 5796–04. (4) Hovgaard, M. B.; Dong, M.; Otzen, D. E.; Besenbacher, F. Biophys. J. 2007, 93, 2162–69. (5) Pelletier, E.; Montfort, J. P.; Loubet, J. L.; Tonck, A.; Georges, J. M. Macromolecules 1995, 28, 1990–98. (6) Braithwaite, G. J. C.; Luckham, P. F. J. Colloid Interface Sci. 1999, 218, 97–111. (7) Stafford, C. M.; Vogt, B. D.; Harrison, C.; Julthongpiput, D.; Huang, R. Macromolecules 2006, 39, 5095–99. (8) Iruthayaraj, J.; Poptoshev, E.; Vareikis, A.; Makuska, R.; van der wal, A.; Claesson, P. M. Macromolecules 2005, 38, 6152. (9) Rodahl, M.; Hoö¨k, F.; Krozer, A.; Brzezinski, P.; Kasemo, B. ReV. Sci. Instrum. 1995, 66, 3924. (10) Sauerbrey, G. Z. Phys. 1959, 155, 206. (11) Johannsmann, D.; Mathauer, K.; Wegner, G.; Knoll, W. Phys. ReV. B 1992, 46, 7808. (12) Voinova, M. V.; Rodahl, M.; Jonson, M.; Kasemo, B. Phys. Scr. 1999, 59, 391. (13) Johannsmann, D. Macromol. Chem. Phys 1999, 200, 501–516. (14) Rodahl, M.; Kasemo, B. Sens. Actuators, A 1996, 54, 448. (15) Hoö¨k, F.; Kasemo, B. Springer Ser. Chem. Sens. Biosens. 2007, 5, 425. (16) Naderi, A.; Iruthayaraj, J.; Vareikis, A.; Makuska, R.; Claesson, P. M. Langmuir 2007, 23, 12222. (17) Larsson, C.; Rodahl, M.; Hoö¨k, F. Anal. Chem. 2003, 75, 5080– 87. (18) Olanya, G.; Iruthayaraj, J.; Poptoshev, E.; Makuska, R.; Ausvydas, V.; Claesson, P. M. Langmuir 2008, 24, 5341–49. (19) Dedinaite, A.; Bastardo, L. A.; Oliveira, C. L. P.; Pedersen, J. S.; Claesson, P. M.; Vareikis, A.; Makuska, R. Solution properties of bottlebrush polyelectrolytes. Proc. Baltic Polym. Symp. 2007, in press.

JP804395F

Viscoelastic Properties of Adsorbed Bottle-brush Polymer Layers

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