Effect of Relative Humidity on the Viscoelasticity of Thin Organic Films

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Effect of Relative Humidity on the Viscoelasticity of Thin Organic Films Studied by Contact Thermal Noise AFM Juan Francisco Gonzalez Martinez, Erum Kakar, Stefan Erkselius, Nicola Rehnberg, and Javier Sotres Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.8b04222 • Publication Date (Web): 09 Apr 2019 Downloaded from http://pubs.acs.org on April 10, 2019

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Effect of Relative Humidity on the Viscoelasticity of Thin Organic Films Studied by Contact Thermal Noise AFM Juan F. Gonzalez-Martinez 1, Erum Kakar 1,2, Stefan Erkselius 3, Nicola Rehnberg 3 and Javier Sotres 1,* 1

Biomedical Science Department & Biofilms-Research Center for Biointerfaces, Malmö University, 20506 Malmö, Sweden. 2

COE in Solid State Physics, University of the Punjab, QAC, Lahore 54590, Pakistan.

3 Bona

AB, 20021 Malmö, Sweden.

* Corresponding author: [email protected]; phone: +46 (0) 406657926.

ABSTRACT Material scientist are in need of experimental techniques that facilitate a quantitative mechanical characterization of mesoscale materials and, therefore, their rational design. An example is that of thin organic films, as their performance often relates to their ability to withstand use without damage. The mechanical characterization of thin films has benefited from the emergence of the Atomic Force Microscope (AFM). In this regard, it is of relevance that most soft materials are not elastic but viscoelastic instead. While most AFM operation modes and analysis procedures are suitable for elasticity studies, the use of AFM for quantitative viscoelastic characterizations is still a challenge. This is now an emerging topic due to recent developments in Contact Resonance AFM. The aim of this work was to further explore the potential of this technique by investigating its sensitivity to viscoelastic changes induced by environmental parameters, specifically humidity. Here we show that by means of this experimental approach it was possible to quantitatively monitor the influence of humidity on the viscoelasticity of two different thin and hydrophobic polyurethane coatings representative of those typically used to protect materials from processes like weathering and wear. The technique was sensitive even to the transition between the anti-plasticizing and plasticizing effects of ambient humidity. Moreover, we showed that this was possible without the need of externally exciting the AFM cantilever or the sample i.e., just by monitoring the Brownian motion of cantilevers, which significantly facilitates the implementation of this technique in any AFM setup.

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INTRODUCTION Thin films made from organic materials are ubiquitous. Many objects that we encounter in our daily life e.g., furniture, houses, tools and vehicles made use of organic films as coatings 1. The performance of these films often relates to their ability to withstand damage overtime. Moreover, this performance can be significantly affected by environmental conditions like humidity and temperature 2-3. Thus, the characterization of the mechanical properties of thin organic films, and of how these properties are affected by environmental conditions, is of major importance to predict their performance. In this context, this work focuses on the characterization of the effect of relative humidity (RH) on the viscoelasticity of thin supported organic films. The quantification of the mechanical properties of very thin (e.g., µm-sized) supported films is a difficult task. In this regard, Atomic Force Microscopy (AFM) stands out as a powerful technique. This does not only rely on its ability to simultaneously map the topography and mechanical properties of surfaces, but also on its high sensitivity to forces and displacements in the sub-nanometer scale. The most common way to probe mechanical properties by means of AFM is to perform force distance measurements, where the deflection of the cantilever (proportional to the force between the AFM probe and the sample) is monitored while ramping the relative distance between the sample and the base of the cantilever 4. A common procedure to analyze force distance measurements is by means of continuous mechanical models that provide e.g., a value for the elastic Young modulus of the investigated samples. However, when it comes to organic films this is a limited approach as they are not purely elastic but viscoelastic instead 2, 5. While AFM force distance measurements allow a qualitative estimation of the viscoelastic character of the investigated samples, how to quantify this character from these measurements remains unclear 6. A promising alternative is to monitor the resonances of the cantilever when in contact with the samples. This methodology, commonly known as Contact Resonance AFM (CR-AFM) was originally developed to investigate the elastic character of hard surfaces 7-8. However, recent developments have shown that by monitoring both the frequency and quality factors of resonance peaks it is possible to quantify viscoelastic properties of soft thin films in terms of parameters like the storage modulus, loss modulus and loss tangent 9. Typically, CRAFM is performed by externally exciting either the sample or the cantilever at a frequency close to that of one of the contact resonances of the cantilever. The presence of an interaction with the sample e.g., a viscoelastic contact, will induce changes in both the frequency and quality factor of the cantilever resonances that can be monitored and compared e.g., via lock-in methods. Externally induced excitations lead to high sensitivity. However, this approach has also drawbacks. Few commercial AFM setups are equipped with standard CR-AFM possibilities. Large excitation powers can also modify the vibrational spectra of the cantilevers 10. Moreover, when investigating viscous samples or operating in damping environments, external acoustic excitations can also result in spurious vibrations that complicate the identification of the cantilever resonances 11-12. A strategy to overcome these drawbacks is to monitor the thermally induced Brownian motion of cantilevers 5, 13-14. Monitoring the Brownian motion of cantilevers rather than acoustically exciting them offers an additional advantage for the study of soft materials. The amplitude of Brownian oscillations of free non-standing cantilevers is typically even below 1 nm. This amplitude is further reduced when mechanical 2 ACS Paragon Plus Environment

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contact is established. This low amplitude reduces the possibility of damaging soft materials. We recently showed that this approach was sensitive to differences in the viscoelasticity of two thin organic films (spin-coated waterborne polyurethane coatings) of similar chemistry that mainly differed in their cross-linking density 5. In this work, we investigated these same coatings by means of Contact Thermal Noise AFM at different controlled relative humidities (RH). The aim was to investigate whether this technique is sensitive enough to RH-induced viscoelastic changes of these inherently hydrophobic films.

EXPERIMENTAL SECTION Materials In this work we report investigations on coatings prepared from two different waterborne polyurethane (PU) dispersions further diluted in a film forming aqueous solution. The polyurethanes dispersions, from now on referred as PU1 and PU2, were kindly provided by Bona AB (Malmö, Sweden). The dispersions were prepared following the same protocols provided in 15. Specific details on their composition are provided in 5. Briefly, the hard segments of both polyurethanes were based on isophorone diisocyanates and on 2,2bis(hydroxymethyl)propanoic acid as a dispersing agent. The polyurethanes mainly differed in the composition of their soft segments. Those of PU1 consisted of a polyester made of a natural mixture of, mainly, C18 unsaturated fatty acids (linolenic and linoleic acid) that, on exposure to air, polymerize to form a cross-linked network 16. Those of PU2 consisted on a synthetic mixture of saturated C18 fatty acids that provide a similar hydrophobicity as the unsaturated polyester, but are inert towards air. Thus, there is no molecular weight build up after synthesis. Both PU dispersions were used to form coatings on clean silica surfaces. Before this, silica substrates were rinsed extensively with Ultra High Quality (UHQ) water, treated in a Hellmanex II 2% (v/v) water solution for 20 min. and subsequently rinsed again extensively with UHQ water. Finally, the surfaces were dried under nitrogen and plasma-cleaned for 5 min in low pressure residual air using a glow discharge unit (PDC-32 G, Harrick Scientific Corp., Ossining, NY, USA). Then, coatings were formed on the silica surfaces by spin-coating (1200 rpm, spincoater developed in-house) 20 µl of the PU dispersions and let them dry under room temperature and humidity conditions (T~22°C and RH~40%) for >1 month. The thickness of the coatings obtained by means of this procedure was ~2 µm (Supporting Information, Section S1). Atomic Force Microscopy A commercial atomic force microscope equipped with a sealed liquid cell (MultiMode 8 SPM with a NanoScope V control unit; Bruker AXS, Santa Barbara, CA, USA) was employed to mechanically characterize the polyurethane coatings. Relative humidity was controlled by flowing humid air generated with a GenRH-A setup (Surface Measurement Systems, Pragolab, Prague, Czech Republic) through the sealed liquid cell. The coatings were characterized by means of force distance measurements and contact thermal noise AFM as detailed below. In all experiments, the effective radius of AFM tips was estimated first by visualizing a clean granular silica surface and then by using the Tip Qualification algorithm of the NanoScope Analysis software (Bruker AXS, Santa Barbara, CA, USA) to analyze these images. Before each experiment, AFM tips were rubbed against clean mica surfaces in order to clean the tip apex and to remove asperities from it. This process, which is recommended for minimizing tip 3 ACS Paragon Plus Environment

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apex changes during experiments 17-18, proved to be crucial for obtaining reproducible results. This procedure resulted in tip radius values in the 200-250 nm range. Force Distance Measurements Force distance measurements is a widely used AFM operation mode well-described in the literature 4. In this mode the AFM cantilever and the sample, initially separated by a distance long enough so that interactions between them can be neglected, are approached towards each other until a defined cantilever deflection (proportional to tip-sample force) is achieved. Subsequently, they are withdrawn from each other. Specifically, in our setup the cantileversample position was varied by vertically displacing the sample. During the measurement, the deflection of the cantilever while ramping the vertical position of the sample is registered by monitoring a laser beam reflected at the backside of the free end of the cantilever with a position sensitive photodetector. Prior to analysis, raw data from force distance measurements was processed according to the following procedure. First, the photodetector signal corresponding to zero deflection was calculated by averaging its value over a window of sample vertical positions far enough from the sample. This value was then subtracted from all the photodetector signal values. Then, the photodetector signal was first transformed into cantilever deflection by scaling with the photodetector calibration factor (calculated as the slope of the photodetector signal monitored while pressing the AFM tip against a stiff sapphire surface). Subsequently, cantilever deflection was transformed into tip-sample force by scaling with the cantilever force constant (calculated by means of the Sader method 19). Sample vertical position was finally converted into real tipsample distance, d, by adding the corresponding cantilever deflection. Thus, the result from this process was a representation of the interaction force between tip and sample for different separations between both. Different quantities can be estimated from force distance measurements. Specifically, we focused on the effective Young modulus, E, obtained by fitting the contact (repulsive) region of the withdrawal force distance measurement with the DMT elastic contact model for a sphereplanar geometry 4, 20: 4

𝐸

3

𝐹(𝑑) = 𝐹𝑎𝑑ℎ + 31 ― 𝜐2 𝑅𝑡𝑖𝑝(𝑑0 ― 𝑑)

2

(Eq.1)

where Fadh is the maximum adhesion force, ν is the Poisson’s ratio of the tip (assumed to be 1/3 21), R is the tip radius (estimated as previously indicated) and d is the contact point, which is tip 0 also estimated from the fit. In order to average E over different lateral positions of the coatings, force distance measurements were collected by operating the AFM in the force volume mode 22, where a force distance curve is obtained at every point of an imaged area. In our experiments, we specifically probed 10 µm x 10 µm areas with a resolution of 16x16 points equidistant from each other. At each point, a force distance measurement was acquired at a maximum applied load of ~220 nN and at a sample-cantilever relative speed of 0.4 µm·s-1. For these experiments, rectangular silicon cantilevers were used (RTESPA-300, Bruker AFM Probes, nominal force constant of 40 N·m-1). Contact Thermal Noise AFM 4 ACS Paragon Plus Environment

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This AFM operation mode was used to probe the influence of RH on the viscoelastic character of the investigated coatings. It is based on monitoring how the Brownian motion of cantilevers are modified due to the mechanical contact with the investigated samples 13-14 (Figure 1). For this, the vertical deflections of the cantilevers were monitored with an external data acquisition board (PCI-6132, National Instruments Sweden AB) at a sampling frequency of 1 MHz and a resolution of 2048 points while raster scanning the coatings in the contact mode in order to easily average viscoelastic measurements over different positions of the sample (scan area 2 µm, scanning speed 1 µm·s-1). Rectangular silicon cantilevers (OMCL-AC240TS, Olympus, Japan, nominal force constant of 2 N·m-1) were used. The actual value of the force constant was always measured before each experiment by means of the thermal noise method 23. In these experiments, the applied load was set to ~3.5 nN (corresponding to an indentation depth of ~5 nm, Fig. 2). This value was lower than that for which the investigated coatings could be damaged as shown in a previous work 5. For each experiment, the thermal fluctuations of the cantilever were also registered far from the sample. Then, the Power Spectral Density (PSD) for the registered thermal fluctuations of the AFM cantilevers was calculated. The first resonance peaks from the PSD (both that corresponding to the free non-supported cantilever and that corresponding to the cantilever supported by the samples) were fitted with Lorentzian functions in order to obtain the corresponding frequencies and quality factors. These parameters were then used to quantify the viscoelasticity of the coatings in terms of their loss tangent by means of the procedure detailed below. Theory and Analysis of Contact Resonance AFM Several previous works addressed the theoretical analysis of Contact Resonance AFM data (e.g., 7, 9-10, 24-26 and references therein). However, a comprehensive review of the basis of these theories within a single work is not yet available. Thus, we present here the derivations behind one of the most currently used theoretical schemes for the analysis of viscoelasticity by means of Contact Resonance AFM. The starting point is usually the Euler−Bernoulli model that states that the flexural vibrations of a rectangular cantilever can be described by the following equation 27: ∂4𝑍

∂2𝑍

𝐸𝐼∂𝑦4 +𝜌𝐴𝐿2 ∂𝑡2 = 0

(Eq. 2)

where Z(y,t) is the vertical deflection of the cantilever along its longitudinal direction y at time t, E is the Young modulus, I is the area moment of inertia, A is the cross section of the cantilever and ρ its mass density. Z(y,t) can be separated in their spatial and temporal contributions so that Z(y,t)=z(y)cos(ωt+δ). Then, Eq. 2 can be expressed as: ∂4𝑧 ∂𝑦4

+ 𝜅4 𝑧 = 0

where 𝜅4 =

𝜌𝐴𝜔2 𝐸𝐼

(Eq. 3) . The general solution for Eq. 3 has the form:

𝑧(𝜉) = 𝐴cos (𝑘𝜉) +𝐵sin (𝑘𝜉) +𝐶cosh (𝑘𝜉) +𝐷sinh (𝑘𝜉)

(Eq. 4)

where 𝜉 = 𝑦/𝐿 (L, length of the cantilever) and 𝑘 = 𝜅𝐿. This equation can be solved for different sets of boundary conditions that reflect different possible situations of the cantilever. In general, all these situations have in common three boundary conditions. The first one is that the deflection at the base of the cantilever is zero, 𝑧(0) = 0. The second boundary condition 5 ACS Paragon Plus Environment

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reflects that the slope of the deflection of the cantilever at its base is also zero,

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∂𝑧

|

∂𝜉 (𝜉 = 0)

= 0.

The third boundary condition reflects the fact that the torque at the free end of the cantilever is ∂2𝑧

also zero, ∂𝜉2

|

= 0. (𝜉 = 1)

The fourth boundary condition needed to solve Eq. 3 and that will, therefore, determine the value of 𝑘 and the frequency of each flexural vibration mode, is specific for each of the situations that a cantilever can encounter. For instance, for a free non supported cantilever one ∂3𝑧

makes use of the boundary condition 23 ∂𝜉3

|

= 0 that expresses that the force on the free (𝜉 = 1)

end of the cantilever is zero. Using this boundary condition, we arrive at the characteristic equation for the free non supported cantilever: 1 + cos (𝑘)cosh (𝑘) = 0 (Eq. 5) Solving this equation numerically leads to 𝑘𝑛 = 1.88, 4.69, 7.85… (n=1, 2, 3, …) or,

(

)

1

approximately, 𝑘𝑛 = 𝑛 ― 2 𝜋. For a cantilever supported on an infinitely hard surface, 𝑧(1) = 0 applies as the last fourth boundary condition, which reflects the fact that the deflection of the free end of the cantilever does not change. This leads to the following characteristic equation for the supported cantilever: sin (𝑘)cosh (𝑘) ― cos (𝑘)sinh (𝑘) = 0 (Eq. 6) Which, when solved numerically, leads to 𝑘𝑛 = 3.93, 7.07, 10.21, … (n = 1, 2, 3, …) or,

(

)

1

approximately, 𝑘𝑛 = 𝑛 + 4 𝜋. The fourth boundary equation can be generalized for the case of an interaction acting on the free end of the cantilever. In this case, the last boundary condition should reflect a transition between the case of the free non supported cantilever and that of the supported one 26 i.e., ∂3𝑧 ∂𝜉3

|

= 𝛼 ⋅ 𝑧(1), which reflects that the forces acting at the free end of the cantilever are (𝜉 = 1)

proportional to its deflection. For the case of an AFM cantilever in mechanical contact with a viscoelastic sample, this proportionality can be modeled e.g., with a Kelvin-Voigt model. This model considers that the interaction between the free end of the cantilever and the sample consists of a conservative element (a spring) and a dissipative element (a dashpot) in parallel (Figure 1c). Within this model, α is the harmonic damped oscillator differential operator given by: 1

(

∂2

∂

)

(Eq. 7)

𝛼 = 𝐸𝐼 𝑘𝑖𝑛𝑡 + 𝛾∂𝑡 ― 𝑚𝑡𝑖𝑝∂𝑡2

where kint is the interaction elastic constant, γ is the damping factor, and mtip the mass concentrated at the free end of the cantilever (i.e., that of the AFM tip). Typically, mtip can be ignored. In this case, Eq. 7 can be approximated by: 1

(

∂

)

𝛼 ≈ 𝐸𝐼 𝑘𝑖𝑛𝑡 + 𝛾∂𝑡

(Eq. 8)


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Thus, in this situation we need to consider again the time dependence of the cantilever ∂3𝑧

deflection, 𝑍(𝑦,𝑡) = 𝑧(𝑦)𝑒𝑖𝜔𝑡, and the fourth boundary condition can be rewritten as ∂𝜉3

|

(𝜉 = 1)

𝑒𝑖𝜔𝑡 = 𝛼 ⋅ 𝑍(1,𝑡). Applying 𝛼 on 𝑍(1,𝑡): 𝛼 ⋅ 𝑍(1,𝑡) =

𝑧(1) 𝐸𝐼

By using 28 𝐼 =

(𝑘𝑖𝑛𝑡 + 𝑖𝛾𝜔)𝑒𝑖𝜔𝑡

𝑤𝑡3 12

and 𝑘𝑐𝑎𝑛𝑡 =

(Eq. 9)

𝐸𝑤𝑡3 4𝐿3

(where w is the width of the cantilever and t its thickness),

Eq. 9 can be expressed as: 𝛼 ⋅ 𝑍(1,𝑡) =

3 𝑧(1) 𝑘𝑐𝑎𝑛𝑡

(𝑘𝑖𝑛𝑡 + 𝑖𝛾𝜔)𝑒𝑖𝜔𝑡

(Eq. 10) ∂3𝑧

and, therefore, the forth boundary condition can be rewritten as ∂𝜉3

|

= (𝜉 = 1)

3 𝑧(1) 𝑘𝑐𝑎𝑛𝑡

(𝑘𝑖𝑛𝑡 + 𝑖𝛾𝜔).

Thus, in this case the wavenumber is a complex number. Therefore, we note it from now on as 𝑘𝑛 (for each flexural mode). In this case, we end up with the following characteristic equation for the flexural vibrations of the cantilever: 3

cos ( 𝑘𝑛)sinh ( 𝑘𝑛) ― sin (𝑘𝑛)cosh ( 𝑘𝑛) =

𝑘𝑛

(

3

𝑘𝑖𝑛𝑡 𝑘𝑐𝑎𝑛𝑡

+ 𝑖 𝛾𝑘

(1 + cos ( 𝑘𝑛)cosh (𝑘𝑛))

)

𝜔𝑛

𝑐𝑎𝑛𝑡

(Eq. 11) From this equation, the complex wavenumber 𝑘𝑛 = 𝑎𝑛 +𝑖𝑏𝑛 can be obtained. The real part of 𝑘𝑛 2

( ) ⇒𝜔

the complex wavenumber is related to the frequency of the vibration mode 𝜔𝑛 = 𝜔𝑓 𝑎𝑛 2

()

= 𝜔𝑓

𝑘𝑓

𝑘𝑓

𝑛

1

⇒𝑎2𝑛

=

( ) 𝜔𝑛

2 𝜔𝑓 𝑘𝑓⇒𝑎𝑛

=

( ) 𝜔𝑛 𝜔𝑓

2

𝑘𝑓. Note that the index 𝑛 is related to the n-vibration

mode in contact while 𝑓 indicates the first free vibration mode. The imaginary part of the complex wavenumber is related to the dissipation. The relation between damping and the vibrational mode can be explained as follows. We first consider the modal expansion of 𝑍(𝜉,𝑡) 29, 𝑍(𝜉,𝑡) =

𝐹𝐷𝑒𝑖𝜔𝑡 𝑚𝑐𝑎𝑛𝑡

𝑧𝑛(1)𝑧𝑛(𝜉)

∞

∑𝑛 = 1

𝑁𝑘4𝑛

― 𝜔2 + 𝑖𝜔𝛾𝑛

(Eq. 12)

(𝐹𝐷 is an harmonic force excitation with frequency 𝜔, 𝑚𝑐𝑎𝑛𝑡 is the mass of the cantilever, 𝑘4𝑛 is the mode wavenumber, 𝑧𝑛(𝜉) are the spatial functions that define the shape of the eigenmode, previously defined, 𝑁 = 𝐸𝐼/(𝑚𝑐𝑎𝑛𝑡𝐿)), and assuming that 𝑏𝑛 ≪ 𝑎𝑛, and that the response of the cantilever is near one of the eigenmodes n, so the nth-mode dominates, 𝑍(𝜉 = 1,𝑡) (assuming that the AFM tip is at 𝜉 = 1) can be approximated by 𝑍(1,𝑡) ≈

𝐴𝑛𝑒𝑖𝜔𝑡

(

(𝜔2𝑛 ― 𝜔2) + 𝑖

𝜔𝛾𝑓 +

4𝜔2 𝑛𝑏𝑛 𝑎𝑛

)

(Eq. 13)

(𝐴𝑛 = 𝐹𝐷 𝑧2𝑛(1)/𝑚𝑐𝑎𝑛𝑡). From this equation the complex part shows that the damping factor 𝛾𝑛 at an eigenmode frequency (𝜔 = 𝜔𝑛) is 𝛾𝑛 = 𝛾𝑓 +

4𝜔𝑛𝑏𝑛 𝑎𝑛

. This is, the dissipation at a viscoelastic


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contact can be considered as an increasing value from 𝛾𝑓, the dissipation of the free fundamental 𝛾𝑛 ― 𝛾𝑓

eigenmode mode in air. From this relation the value for 𝑏𝑛, could be obtained: 𝑏𝑛 = 𝑎𝑛

4 𝜔𝑛

.

The complex wavenumber (for each vibration mode) 𝑘𝑛 = 𝑎𝑛 +𝑖𝑏𝑛 can be also expressed using the above relations for 𝑎𝑛 and 𝑏𝑛, and the relation 𝛾𝑛 = 𝜔𝑛/𝑄𝑛, as 𝜔𝑛 1/2

1 1

𝜔𝑓

4 𝑄𝑛

( ) ⋅ (1 + 𝑖 (

𝑘𝑛 = 𝑘𝑓

))

𝜔𝑓

― 𝜔𝑛𝑄

(Eq. 14)

𝑓

where 𝜔𝑛 and 𝑄𝑛 are the contact resonance frequency and quality factor and 𝜔𝑓 and 𝑄𝑓 are the fundamental resonance frequency and quality factor of the free non-supported cantilever and 𝑘𝑓 is the fundamental wavenumber of the free non-supported cantilever. 𝑘𝑖𝑛𝑡

and uses 𝜔𝑛 = 𝜔𝑓 𝑘2

𝑐𝑎𝑛𝑡 𝑓

3

𝜃+𝑖𝛽⋅

2 𝑘𝑛

𝑘𝑛

(1 + cos (𝑘𝑛)cosh (𝑘𝑛))/3 𝑛

𝑛

𝑘𝑓

(Eq. 15)

= cos (𝑘 )sinh (𝑘 ) ― sin (𝑘 )cosh (𝑘 ) 𝑛

𝑘𝑛 2

( ) , Eq. 11 can be rewritten as:

𝛾 𝜔𝑓

If one notes 𝜃 = 𝑘𝑐𝑎𝑛𝑡 and 𝛽 = 𝑘

𝑛

By using this equation, it is possible to obtain the storage and loss moduli of the sample ( 𝐸′ and 𝐸′′, respectively), as these quantities can be expressed as 30: 1

𝐸′ = 2𝑘𝑖𝑛𝑡

𝜋

𝐴;

1

𝐸′′ = 2𝜔𝛾

𝜋 𝐴

(Eq. 16)

where 𝐴 is the contact area. Determining 𝐴 is a difficult problem. It does not only require knowledge on the geometry of the tip-sample interface but also requires the assumption of a contact model (e.g., Hertz, DMT, JKR, etc.). A strategy to partially overcome this problem is to use a reference sample with known 𝐸′𝑟𝑒𝑓 and 𝐸′′𝑟𝑒𝑓 values 7, 30-31. By doing so, it follows from Eq. 15 that: 𝑚

( )

𝐸′ = 𝐸′𝑟𝑒𝑓

𝜃

𝜃𝑟𝑒𝑓

(

; 𝐸′′ = 𝐸′′𝑟𝑒𝑓

𝜔𝑛𝛽

𝑚

)

𝜔𝑛,𝑟𝑒𝑓𝛽𝑟𝑒𝑓

(Eq. 17)

where 𝐸′𝑟𝑒𝑓 and 𝐸′′𝑟𝑒𝑓 are the known values for the storage and loss moduli of the reference sample; 𝜃𝑟𝑒𝑓 and 𝛽𝑟𝑒𝑓 refer to the values obtained from Eq. 15 for the reference sample and 𝜔𝑛,𝑟𝑒𝑓 is the contact resonance frequency of the nth mode measured as well on the reference sample. This approach avoids the need to assume a geometry for the tip-sample interface, but still requires knowledge on the contact model, as this choice will determine the exponent 𝑚 in the equations above. Within the framework of the Hertz contact model, for a planar sample interacting with a spherical tip 𝑚 = 3/2, whereas if a planar tip is assumed 𝑚 = 1 30. However, to the best of our knowledge, similar expressions have not been reported for other contact models. A different approach for CR-AFM viscoelastic characterization that does not require assumptions on the nature or geometry of the contact between tip and sample has been recently developed 24. This approach allows characterizing the viscoelasticity of samples in terms of their loss tangent i.e., the ration between the loss and storage moduli. It makes use of the expression 32 where the loss tangent of viscoelastic materials is expressed in terms of the following force-displacement ratio: 8 ACS Paragon Plus Environment

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𝜔𝑛𝛾

tan 𝛿𝑛 = 𝑘𝑖𝑛𝑡

(Eq. 18)

that, according to the expressions reported above can be rewritten as 9, 24: 𝛽𝜔𝑛

tan 𝛿𝑛 = 𝑘2𝑓𝜃𝜔𝑓

(Eq. 19)

Thus, from Eqs. 14, 15 and Eq. 19 it is clear that by experimentally measuring 𝜔𝑛, 𝑄𝑛 , 𝜔𝑓 and 𝑄𝑓 it is possible to determine tan 𝛿𝑛 . A Matlab® code for performing this calculation is provided in Supplementary Information, Section S2.

Figure 1. Contact Thermal Noise AFM: This AFM operation mode is based on the comparison between the resonance frequencies of AFM cantilevers measured a) far from the sample so no interactions are present and b) in mechanical contact with the sample, a situation where the amplitude of the vibrational modes is reduced but their frequencies incremented. c) If the sample is viscoelastic, the mechanical contact can be modelled in terms of a Kelvin-Voigt equivalent, which considers that the tip-sample interaction consists of a conservative element (a spring) and a dissipative element (a dashpot) in parallel.

RESULTS AND DISCUSSION Force distance measurements were performed on both PU1 and PU2 coatings in the RH 0-98% RH range. Representative examples at RH 80% are shown in Figure 2a for PU1 and in Figure 2b for PU2 coatings (examples for all investigated RH values are shown in Section S3 of the Supporting Information). Force distance measurements allowed quantifying the stiffness of the coatings in terms of an effective Young Modulus, E, by fitting the repulsive region of the retract curves with the DMT mechanical contact model (Eq. 1). Mean and standard deviation E values obtained from this analysis are shown in Figure 2c for both coatings. It should be noted that these Young Modulus values did not exhibit a significant dependence on the maximum applied load or on the cantilever-sample relative speed during force measurements (Supporting Information, Section S4). It follows from this analysis that, for the whole investigated RH range, PU1 coatings i.e., those containing unsaturated fatty acids that could cross-link, were stiffer than PU2 coatings i.e., those containing saturated fatty acids without the ability to cross-link. Thus, cross-linking was associated with higher stiffness in agreement with previous reports 5, 9 ACS Paragon Plus Environment

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33-34. Adhesion forces support this conclusion. The gradual and long-range detachment observed

during withdrawal indicates that an additional process different than just the rupture of a water capillary took place in our experiments. Successive force distance measurements obtained on the same spot of the coatings revealed similar adhesion profiles. Thus, the measured adhesions indicate a significant stretching of the coatings upon probe-sample separation. Figure 2 shows that PU2 coatings could be stretched up to longer distances than PU1 coatings, supporting the stiffening induced by cross-linking. The reported E values also support the plasticizing effect of RH on the coatings in the 20-98 % range i.e., the coatings became softer when RH was increased. However, from 0% RH to 20% RH a slight, but statistically non-significant, stiffening of both investigated coatings was observed.


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Figure 2. Representative force distance measurements obtained on a) PU1 and b) PU2 coatings at RH 80%. c) Mean and standard deviation values for the effective Young Modulus of PU1 and PU2 coatings calculated by fitting the contact region of force distance measurements (dashed lines in Figures 2a and 2b) with the DMT model (Eq. 1). In the force distance measurements shown in Figure 2, a hysteresis between the repulsive forces measured while approaching and separating tip and sample can be observed. This reflects that the samples were not elastic but viscoelastic instead 6. Therefore, the Young moduli obtained from the DMT analysis should be handled carefully, as they were obtained by applying an elastic contact model that does not take into account the viscoelasticity of the samples. The 11 ACS Paragon Plus Environment

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quantification of viscoelasticity from AFM force distance measurements is in fact a problem not yet resolved 6. However, the quantification of the viscoelastic character of thin films can be addressed instead by experimentally determining how the natural frequencies of an AFM cantilever change from a free non-supported situation far from the sample to a situation where the cantilever is in mechanical contact with the sample 9, 24, 35. We have used this approach to estimate RH-induced changes in the viscoelastic character of the investigated coatings. Figure 3a shows representative fundamental resonance peaks for the free non-supported cantilevers monitored at different RH values. As observed, these peaks were not influenced by RH, indicating that this environmental parameter had no significant effect on the cantilevers. Figures 3b and 3c show the fundamental resonance peak of the cantilevers in contact with PU1 and PU2 coatings respectively. These peaks exhibited a similar qualitative relationship with RH for both investigated coatings. The transition from 0% RH to 20% RH led to narrower resonance peaks at higher frequencies. However, while ramping from 20% RH to 98% RH the resonance frequencies shifted to smaller values and the peaks became wider. Figure 3 also shows that the resonance peaks for PU1 coatings (Figure 3b) were characterized by higher frequencies and quality factors than those observed for PU2 coatings. Fitting these peaks to a Lorentzian function provides fundamental resonance frequencies and quality factors. As detailed above, different theoretical frameworks are available for relating these experimental quantities into viscoelastic parameters of the samples. If the contact area was known, the storage and loss moduli of the samples could be obtained separately (Eq. 16). However, this would require knowledge on the geometry of the tip and on its contact interaction with the sample. Even if a reference sample is used, obtaining relative values of the storage and loss moduli still requires knowledge on how tip and sample interact upon mechanical contact. So far, expressions for this approach have only been derived for cases where the contact can be modelled with the Hertz model (Eq. 17). This model is only valid in the absence of adhesion, which is not the case for the reported experiments (Fig. 2). Accordingly, in this work we use instead Eq. 19 for data analysis, which allows estimating the loss tangent of the samples, tan ( 𝛿), without the need of any assumption on the nature or geometry of the contact between tip and sample. Values for tan ( 𝛿) of PU1 and PU2 coatings at different RH values are shown in Figure 4.


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Figure 3. PSD (averaged from all registered measurements) for a) a free standing cantilever, and a cantilever in mechanical contact with b) PU1 and c) PU2 coatings for all investigated RH conditions. In the figure, Z is the photodiode vertical signal and Δ𝜔 is the bin size.


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Figure 4. Mean and standard deviation values for tan ( 𝛿) calculated from all registered spectra on PU1 and PU2 coatings for all investigated RH conditions. Table 1 summarizes mean and standard deviation values for the effective Young modulus, 𝐸, and loss tangent, tan ( 𝛿), values obtained for PU1 and PU2 coatings in the whole investigated RH range. At this point, it should be noted that there is not a straightforward relationship between both magnitudes. Young modulus values provide a relationship for the stress needed to achieve a given deformation of a purely elastic material. The loss tangent is instead the ratio of loss modulus to storage modulus i.e., the ratio between the ability of a viscoelastic material to dissipate energy and to elastically store it when deformed. As discussed above, characterizing the coatings in terms of their loss tangent rather than in terms of the storage and loss moduli presents certain advantages. However, this approach also presents a main drawback. It is uncertain whether changes in the loss tangent are originated by changes in the storage or in the loss modulus. Young moduli obtained from force distance measurements can shed light into this problem. Conceptually, Young moduli obtained from indentation experiments and storage moduli from oscillatory measurements are similar. Both quantities give an estimation of the ability of a material to elastically store energy. However, the values will not be similar. First, the Young moduli we obtained underestimate those that would have been obtained at infinitely slow force distance measurements 6. Moreover, considering the tip as a sphere probably overestimates the contact area and, therefore, further underestimates the Young modulus. Additionally, Young moduli were obtained at significant smaller frequencies than loss tangents (in our case 1 Hz vs 200 kHz). Nevertheless, while Young moduli usually underestimate storage moduli, relative changes in Young modulus measured in low frequency indentation experiments provide a reasonably good estimation of changes in storage modulus measured in high frequency oscillation experiments 36.

E (GPa) tan(δ) (10-2)

PU1 PU2 PU1 PU2

RH 0%

RH 20%

RH 40%

RH 60%

RH 80%

RH 98%

1.39±0.35 0.49±0.10 6.11±0.23 8.21±0.66

1.42±0.44 0.51±0.11 5.38±0.21 7.47±0.51

1.28±0.36 0.46±0.10 5.88±0.22 7.88±0.54

1.18±0.34 0.40±0.08 6.38±0.23 8.56±0.64

1.06±0.29 0.38±0.07 6.85±0.32 9.99±0.96

0.94±0.23 0.33±0.07 7.87±0.35 12.45±1.24

Table 1. Mean and standard deviation values for the effective Young modulus, 𝐸, calculated from force distance measurements and tan ( 𝛿) values calculated from contact thermal noise spectra for both PU1 and PU2 coatings.


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Overall, it can be observed that tan ( 𝛿) values estimated from Contact Thermal Noise AFM experiments followed the same trend as the effective Young moduli estimated from force distance measurements. For the whole investigated RH range, PU1 coatings exhibited lower viscoelasticity/elasticity ratios i.e., tan ( 𝛿) values, than PU2 coatings. This supports previous works that indicated that cross-linking results in smaller tan ( 𝛿) 5. It is also of relevance that the measured tan ( 𝛿) values are similar to those reported in the literature for polyurethane coatings, 37-39 supporting the validity of the technique. In the same way as the Young modulus, tan ( 𝛿) exhibited different RH-dependence in the 020% and 20-98% RH ranges. For both PU1 and PU2 coatings, tan ( 𝛿) decreased when ramping RH from 0% to 20% while it increased when ramping from 20% to 98%. In order to understand the effect of RH on the measured tan ( 𝛿) values, all possible origins need to be discussed. We first consider whether RH affected the mechanical properties of the AFM cantilevers and, therefore, the measured dependence for tan ( 𝛿) on RH. In this regard, Figure 3a evidences that RH had no influence on the resonances of the free non-supported cantilevers. This indicates that RH-induced water absorption on the cantilever did not have a significant influence on the reported data. It should also be discussed the influence of RH-induced changes in the viscosity of air and, subsequently, on the damping forces acting on the body of the cantilever while probe and sample are in mechanical contact. The density and viscosity of air decrease with humidity 40. Thus, damping forces acting on the cantilever will decrease with RH. In the 20-98% RH range we observed the opposite i.e., higher RH resulted in higher damping of the cantilever oscillations. This indicates that in this range the effect of RH on the viscoelasticity of the sample dominated over the effect on the body of the cantilever. At room temperature, variations in the viscosity of air in the 0-20% RH range can be neglected 40. Therefore, it is reasonable as well to neglect in this RH range the effect of viscous damping of the cantilever on the reported RH dependence of the mechanical properties of the coatings. RH-dependent capillary forces that take place when AFM tips and samples come into contact also have an influence on AFM Contact Resonance data 25, 41. It has been reported that capillary condensation leads to an effective stiffening of the surface i.e., higher contact resonance frequencies 25. We observed just the opposite in the 20-98 % RH range (the frequencies and quality factors of the resonances decreased with RH, Fig.3). Thus, the increase of tan ( 𝛿) and the decrease of the Young modulus, 𝐸, with RH in this range reflects the plasticizing effect of RH on the coatings. It is worth to note that both quantities are typically used to characterize the plasticizing effect of RH. This is typically reflected, in agreement with the reported results, by increasing tan ( 𝛿) 4243 and decreasing 𝐸 44-45 with RH. However, it needs to be discussed whether the decrease of tan ( 𝛿) in the RH 0-20 % range was a consequence of the effect of RH on the coatings or of the effect of the formation of water capillaries between tip and sample instead. An ideal way to investigate this would have been to compare cantilever resonances in contact with the coatings and with a stiff surface with negligible water absorption but with the same wettability as the investigated coatings. Unfortunately, a reference sample that would match these requirements was not available. As an alternative approach, we investigated tip-sample adhesion forces at different RH values. Capillary condensation is accompanied by an increase in adhesion forces and, therefore, their study is a standard way to investigate this phenomenon4. In our case, adhesion did not increase with RH in this range (Supporting Information Section S5). Thus, it is reasonable to state that the decrease of the viscosity/elasticity ratio of the coatings in this RH range was not an effect of water capillaries, but an effect of RH on the coatings. This interpretation is further supported by the fact that the effective Young modulus of the coatings 15 ACS Paragon Plus Environment

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slightly increased for the same RH range (Figure 2c). This might be seen as counterintuitive as water is typically regarded as a plasticizer that, by interacting with polar groups of the polymers, would both break intermolecular polar bonds between polymers and increase their free volume. This would result in increased chain mobility and in subsequent softening of the material 46. However, this is a simplified scheme. It is often reported that small amounts of low molecular plasticizers, including water, lead to the opposite effect. When the film contains voids or defects, low molecular weight plasticizers initially fill them and, therefore, reduce the available free volume. This results in an enhancement of the mechanical properties of the film that lasts until a certain threshold concentration of the low molecular weight compound is reached. From this value, the plasticizing mechanism takes over and a decrease of the mechanical properties is then observed 47-48. Thus, the different effect of RH on the viscoelasticity of the coatings in the RH 0-20% and 20-98% intervals could be attributed to a transition from the role of water as an anti-plasticizer to a plasticizer compound. This is of high relevance from the point of view of the sensitivity and applicability of the presented technique. Moreover, the fact that the viscoelastic character of both investigated coatings followed a similar dependence with RH in the whole investigated range correlates with the fact that they adsorbed similar amounts of water (Supporting Information, Section S1). This result supports associating the RH dependence of the measured tan ( 𝛿) values to the effect of RH on the coatings. The observation that at high RH values (>80%, Figure 4) the tan ( 𝛿) values of the not cross-linked (PU2) coatings increased more than those of the cross-linked (PU1) coatings could be explained in terms of the swelling prevention properties of cross-links.

CONCLUSIONS Quantitative viscoelastic characterization of micro- and nano-sized materials is an emerging topic due to the recent availability of suitable experimental techniques and, among these, Contact Resonance AFM. In this work we further explored the potential of this technique and showed that without externally exciting the AFM cantilever/sample i.e., just by monitoring the Brownian motion of cantilevers, it was possible to monitor how relative humidity influenced the viscoelastic properties of µm-thin organic (waterborne polyurethane) films. The values obtained for the loss tangent of the films by means of this experimental method were similar to those reported for polyurethane films in the literature, supporting the validity of the technique. Moreover, the technique showed sensitivity to the transition between the anti-plasticizing and plasticizing effects of water. These results provide further evidences of the potential of Contact Resonance AFM modes for the viscoelastic characterization and, therefore, for its use in the rational design of mesoscale materials.

ACKNOWLEDGMENTS This work was supported by the Knowledge Foundation (Grant No. 20150207), the Swedish Research Council (Grant No. 2016-06950) and NordForsk (Grant No. 87794).


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SUPPORTING INFORMATION The Supporting Information is available free of charge on ... ● Estimation of the thickness of the polyurethane coatings by means of QCM-D. ● Matlab® code for loss tangent calculations. ● Force distance measurements at different Relative Humidity values. ● Dependence of Young Modulus values with the maximum applied load and cantilever-sample relative velocity. ● Adhesion forces at different Relative Humidity values.

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(43) Obataya, E.; Norimoto, M.; Gril, J. The effects of adsorbed water on dynamic mechanical properties of wood. Polymer 1998, 39, 3059-3064. (44) Ishiyama, C.; Higo, Y. Effects of humidity on Young's modulus in poly(methyl methacrylate). J. Polym. Sci. B 2002, 40, 460-465. (45) Moon, S.-h.; Foster, M. D. Influence of Humidity on Surface Behavior of Pressure Sensitive Adhesives Studied Using Scanning Probe Microscopy. Langmuir 2002, 18, 81088115. (46) Levine, H.; Slade, L. Water as a plasticizer: physico-chemical aspects of low-moisture polymeric systems. In Water science reviews 3 Water dynamics; Franks, F., Ed.; Cambridge University Press: Cambridge, 1988. (47) Chamarthy, S. P.; Diringer, F. X.; Pinal, R. The Plasticization-Antiplasticization Threshold of Water in Microcrystalline Cellulose: A Perspective Based on Bulk Free Volume. In Water Properties in Food, Health, Pharmaceutical and Biological Systems; Reid, D. S.; Sajjaanantakul, T.; Lillford, P. J.; Charoenrein, S., Eds.; Blackwell Publishing: Singapore, 2010. (48) Dlubek, G.; Redmann, F.; Krause-Rehberg, R. Humidity-induced plasticization and antiplasticization of polyamide 6: A positron lifetime study of the local free volume. J. Appl. Polym. Sci. 2002, 84, 244-255.


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TABLE OF CONTENTS GRAPHIC (TOC)


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Figure 1. Contact Thermal Noise AFM: This AFM operation mode is based on the comparison between the resonance frequencies of AFM cantilevers measured a) far from the sample so no interactions are present and b) in mechanical contact with the sample, a situation where the amplitude of the vibrational modes is reduced but their frequencies incremented. c) If the sample is viscoelastic, the mechanical contact can be modelled in terms of a Kelvin-Voigt equivalent, which considers that the tip-sample interaction consists of a conservative element (a spring) and a dissipative element (a dashpot) in parallel.

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Figure 2. Representative force distance measurements obtained on a) PU1 and b) PU2 coatings at RH 80%. c) Mean and standard deviation values for the effective Young Modulus of PU1 and PU2 coatings calculated by fitting the contact region of force distance measurements (dashed lines in Figures 2a and 2b) with the DMT model (Eq. 1).


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Figure 3. PSD (averaged from all registered measurements) for a) a free standing cantilever, and a cantilever in mechanical contact with b) PU1 and c) PU2 coatings for all investigated RH conditions. In the figure, Z is the photodiode vertical signal and Δω is the bin size.


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Figure 4. Mean and standard deviation values for tan⁡(⁡δ ) calculated from all registered spectra on PU1 and PU2 coatings for all investigated RH conditions. 163x110mm (96 x 96 DPI)


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Effect of Relative Humidity on the Viscoelasticity of Thin Organic Films

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