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Imaging Channel Connectivity in Nafion Using Electrostatic Force Microscopy Austin Michael Barnes, and Steven K. Buratto J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.7b08230 • Publication Date (Web): 01 Jan 2018 Downloaded from http://pubs.acs.org on January 1, 2018

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The Journal of Physical Chemistry

Imaging Channel Connectivity in Nafion Using Electrostatic Force Microscopy

Austin M. Barnes†, Steven K. Buratto†* † Department of Chemistry and Biochemistry, University of California, Santa Barbara, California 93106-9510, United States

ACS Paragon Plus Environment

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Abstract: Channel connectivity is an important material property that is considered in making higher performance proton exchange membranes (PEMs). Our group has previously demonstrated that nearly 50% of the aqueous surface domains in Nafion films do not have a connected path to the opposite side of the membrane. These so called “dead-end” channels lead to a loss in the conductance efficiency of the membrane. Understanding the structure of these “dead-end” channels is an important step in improving the conductance of the membrane. While conductive atomic force microscopy (AFM) is able to provide insight into the connected channels it does directly report on the “dead-end” channels. To address this, we use electrostatic force microscopy (EFM) to probe channel connectivity in a Nafion thin film (100-300 nm) at ambient conditions. EFM provided an image of the capacitive phase shift which is influenced by the surface charge, dielectric permittivity, and tip-sample geometry. We studied several individual channels and measured the quadratic dependence of the EFM signal with the bias voltage. Applying a simple parallel plate model allowed us to assign differences in the EFM signal to particular channel shapes: connected cylindrical channels, “dead-end” cylinder channels, and bottleneck channels.


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Introduction: Over the past 40 years, proton exchange membrane (PEMs) fuel cells have attracted significant interest as a promising power-conversion technology with the potential of a high power zero-emission source. Nafion, the most prominent PEM, has remarkable performance and is chemically stable over a large range of relative humidity and temperature.1 Nafion is a perfluorosulfonic acid polymer that consists of a Teflon-like backbone and sulfonic side chain. When cast into thin films, the components phase separate into hydrophilic channels surrounded by a hydrophobic matrix. Proton transport occurs by both hopping and vehicular diffusion within the channels that extend from one side of the membrane to the other.2 Understanding proton transport within these channels requires detailed understanding of the membrane morphology on the nanometer scale; the size of an individual channel. Characterizing the nanoscale morphology of the channels has relied primarily on the use of bulk characterization techniques, particularly small angle x-ray scattering.3 While these methods probe the appropriate length scale, they are spatially-averaged and any detail regarding the individual channels is lost. Insight into the structure of individual channels can be gleaned from imaging techniques such as tapping-mode AFM4 or TEM,5 but the drawbacks to these methods is that they shed little light onto how the channel structure influences the ion transport. Furthermore, structural models developed from scattering and imaging data, have focused on the size, shape, and correlation lengths of hydrophilic and hydrophobic structures, which have shown to extend 10-100 nm in length.6,7 Relatively little is known about the connectivity of hydrophilic domains or how transport occurs over several microns.



The membrane’s ability to conduct protons from the anode to the cathode requires that channels connect from one side to the other. It has been heavily debated how the hydrophilic domains are arranged to support long range charge transport.6-10 Several models have been proposed to describe membrane morphology and conductance that are consistent with the x-ray scattering data, but the accuracy of these models is limited due to the lack of experimental data on the relevant length scale. The simplest structural model is the cluster model in which charge can percolate from different sites.8 Although the percolation model supports conductivity measurements,9 this model ignores large scattering lengths (i.e. small Q) and is limited to low water content.3 The parallel water cylinders model proposed by Schmidt-Rohr and Chen argues that the low angle scattering features are due to aqueous domains arranged as cylinders.7 This model, however, relies on numerical Fourier transform methods and an assumed image of real space is required. Furthermore, this model also does not account for structural reorganization with increased hydration. The bicontinuous network model derived from Maximum Entropy reconstructions of the scattering data, which suggests a random network of hydrophobic and hydrophilic components, does not require a priori assumptions of the morphology.10 This model, however, does not predict the existence of fluorocarbon crystallites; a primary scattering feature in the parallel cylinder model. In order to achieve a more detailed understanding of how membrane morphology influences proton conductance more experimental data is required. In-situ conductive probe AFM (cp-AFM) is one of the few techniques that provides direct insight into channel connectivity.11,12 While the current image is acquired in contact mode and the phase image is acquired in tapping mode, correlations between the images indicate which of the hydrophilic channels results in electrochemical current.11 These experiments show relative conductance of individual channels consistent with the model of Scmidt-Rohr and Chen, but also


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shows the existence of hydrophilic surface domains that do not support proton conductance or produce electrochemical current. We have denoted these hydrophilic domains as dead-end channels that do not connect one side of the membrane to the other. Since these dead-end channels do not produce electrochemical current, cp-AFM does not report on the structure of these domains. In addition, cp-AFM usually requires imaging under hydrated conditions and becomes challenging under dry conditions.13,14 Finally, cp-AFM is a contact-mode technique while attractive mode phase imaging is a non-contact tapping mode technique, which means that the two images must be acquired sequentially under different scanning conditions.15 Thus, exact comparisons between tapping mode and current images are challenging. Electrostatic Force Microscopy (EFM) is a tapping mode technique that offers improved resolution over cp-AFM.28 EFM has been established for decades and have been used to investigate the surface charge characteristics of both isolated nanostructures21,22,29,30 and structures imbedded in an insulating thin film.31 EFM has been used for acquiring local impedance spectra of Nafion.16,17 EFM is influenced by tip-sample geometry, surface charge, and dielectric properties. Hence we can infer how differences in the surface charge and dielectric properties are influenced by differences in channel size and shape. An additional advantage of EFM is that a phase image can be acquired in the 1st pass while a capacitive force image can be acquired over the exact same image area in an inter-leaved scanning fashion. By varying the DC bias between the tip and sample, charge migration can be observed and directly correlated in XY with the attractive mode phase image. In this article we discuss the use of EFM to map the charge distribution of the Nafion membrane surface on a nanometer scale and to provide insight into the connectivity of individual channels. To our knowledge, no one has used this imaging method to characterize the



connectivity of the hydrophilic channels of Nafion. Our results show a variation in the measured surface charge in the hydrophilic domains which are attributed to differences in channel conductivity. Using our EFM image data we are able to develop a model for the hydrophilic domains based on three categories; connected channels, branched channels and dead-end channels. The morphological domains we propose are consistent with the parallel water cylinders model proposed by Schmidt-Rohr and Chen.7

Methods and Materials: Sample preparation Conductive substrates consisted of single sided copper tape on a glass coverslip. The copper was cleaned by rinsing with deionized (DI) water for 1 minute followed by rinsing in isopropyl alcohol (IPA) for 1 minute. Thin films of Nafion were deposited on the copper by dipping the coverslip halfway into a 50 mL beaker of 5% Nafion: IPA solution. The films were left to dry in a sealed container at ambient conditions (30-50% RH) for 3 days. The thickness of the films was measured to be 100-300 nm using AFM topography across the edge of the film. A fluorine-doped tin oxide (FTO) substrate was also used for EFM experiments to determine if the membrane-electrode interface was influencing the measurements. We found no measureable differences in surface charge variation between FTO and copper substrates.

Imaging EFM is an amplitude modulation - AFM technique based on two-pass interleave scan. In the first pass, the tip is maintained in attractive mode, in which tip-surface interactions are influenced by both van der Waal’s and electrostatic forces. At this regime, the distance of the


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cantilever z position is ~ 5nm away from the point of contact position of the Nafion surface. We define the point of contact position as the point in which the lower turning point of the tip apex makes contact with the surface. This is measured by taking force deflection curves, shown in figure S10. We map the topography and spatial variation of the hydrophilic domains surrounded by the hydrophobic matrix using the first pass phase images. Scan regions of interest are located by finding flat areas (roughness of 4 nm peak-to-peak) to ensure the attractive interactions of the probe are not corrupted by topography. In the second pass, the tip is lifted from the attractive mode, corresponding to ~105 nm from the surface. In EFM, a constant DC sample bias is applied to the electrode substrate while the tip is held at ground. We scanned the same region for different voltage biases applied to the substrate from the microscope controller. We applied 1.5V to +1.5V in 0.5V increments. Before background subtraction, we observed parabolic dependence of the phase shift with bias voltage. Images were collected using an Asylum Research MFP3D AFM with a conductive Ptcoated tip provided by Micromasch (model HQ:XSC11/Pt) with a resonant frequency of ~325 kHz, spring constant k = 40 N/m, nominal quality factor Q = 424, and tip radius of curvature (< 27 nm). We found higher resonant frequency tips are optimal for attractive-mode phase imaging. We have also shown that while imaging in attractive-mode, the sizes of the domains are not limited by the radius of curvature of the probe.13 The measurements were done under ambient conditions (30-50% RH) and at room temperature such that the pore morphology would be observed. All the images were acquired using the retrace image scanning top to bottom.

Analysis



The images were analyzed in Igor Pro with an MFP3D image analysis plugin. Hydrophilic domains were manually chosen for analysis by inspecting the consistency between the trace and retrace phase images. Throughout analysis the (x,y) position of the domains in the phase image were marked by a cursor which highlights the (x,y) position in the EFM images. Domains that appeared to be influenced by roughness in the height image were neglected. Domains that were influenced by scan direction were also neglected. A more detailed description on our method of discriminating against image artifacts can be found in the supporting information. The sizes of the domains in first pass phase images were analyzed by applying an iterative method image threshold. The EFM phase data was averaged over the spatial location of the domain in the first pass and an uncertainty was also computed. The EFM phase as a function of VEFM (Vtip - Vsubstrate) was plotted for each domain and was fit to a 3rd order polynomial.


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Results and Discussion: The chemical structure of Nafion, shown in Figure 1A, consists of a Teflon-like backbone and acidic side chain. These components phase separate to form a network of nanoscale hydrophilic channels imbedded in a hydrophobic fluorocarbon matrix, as represented in the cartoon of Fig. 1B.

Figure 1: (A) Chemical structure of Nafion. (B) Schematic of EFM-Nafion system. In our EFM experiment, a two pass scanning method is used; topography is acquired via tapping-mode phase in the 1st pass and EFM phase shift is acquired in the 2nd pass. In the 1st pass, the Nafion is imaged under attractive mode conditions. The results of EFM applied to a Nafion film are presented in Figure 2. The topography and phase images are shown in Figs. 2A and 2B, respectively. Contrast in the 1st pass tapping-mode phase is related to the power dissipated by tip-sample interactions.18 Phase greater than 90° signify attractive mode and deviations toward 90°, or dark contrast in Fig. 2B, signify maximum power dissipation and are assigned as the hydrophilic domains. As we have discussed in our previous work, the phase



Figure 2: AFM images that include the first pass (A) height and (B) attractive mode phase and the second pass EFM phase shifts. The lift height above the surface is 100 nm. Ci-iii shows EFM phase images at different Vbias. Di shows phase shift as a function of VEFM for the average background. Dii shows the background subtracted phase shift as a function of Vbias for three different highlighted domains in B and C. All of the domains were fit to a quadratic function.

images show a surface morphology consistent with both the parallel water cylinders7 and bicontinuous network models10 predicted from bulk small angle scattering, but quantitatively distinct in size and density of aqueous domains on the surface.13


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In the 2nd pass, the EFM image is acquired. In EFM the conductive tip is placed at a height of 100 nm above the surface and is mechanically driven at its resonant frequency while a DC bias is applied between the tip and substrate. The topography image acquired in the 1st pass is used to maintain the 100 nm separation during the 2nd pass. During both passes, a bias is applied to the tip and FTO sample electrode. The bias voltage between the tip and the FTO sample is defined conventionally as VEFM = (Vtip - Vsample).

In all of our experiments the

voltage at the tip is held at ground, which implies the bias voltage VEFM = - Vsample. Protons migrate according to the sign of the bias. 16,20 A bias voltage VEFM = - 0.5V for example, implies a positive sample voltage, which forces protons toward the surface. The presence of protons within the hydrophilic channels results in an electrostatic force on the tip. Difference in phase between the drive signal and the response of the cantilever caused by this electrostatic force is measured as the EFM phase shift, which is imaged in EFM.19 Figs. 2Ci, 2Cii, and 2Ciii show EFM phase images of Nafion at three different applied voltages VEFM = -0.5V, 0V, and +0.5V, respectively. Some topographically-induced image artifacts can be seen in the EFM image. It is important to note that we have neglected these regions from analysis. Structural information can be gleaned from the EFM phase images by considering the voltage dependence of the EFM phase signal for individual aqueous domains. The blue square, green oval and magenta circle in 2B are used to mark the locations of three individual hydrophilic domains. These same markers are used in the EFM phase images of Fig. 2Ci, 2Cii and 2Ciii to illustrate the change in EFM phase contrast of these three individual domains as a function of applied voltage. Fig. 2D shows a plot of EFM phase shift vs. VEFM for each of these three domains. The data points are labeled by blue squares, green ovals and magenta circles; the same colors as in the corresponding EFM



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images in Figs. 2Ci, 2Cii and 2Ciii. The line traces in Fig. 2D represents a fit to the data points using a quadratic function as described below. EFM phase shifts as a function of applied bias and can be described mathematically via Equation 1.26

∆Φ = −

( − )

(1)

where Q is the quality factor of the cantilever, k is the spring constant of the cantilever, and Vs is the surface potential. It is important to note that Vs differs from Vsample due to the dielectric constant of Nafion. EFM has been used to quantitatively measure the surface charge and permittivity of isolated nanostructures,21,22 as well as nanostructures imbedded in thin insulating films.23,24, 48 For these relatively simple systems the EFM signal can be readily interpreted. Melin et al. has presented a plane capacitor model for an arbitrarily shaped tip and nanoparticle system to estimate the amount of stored charges of the nanoparticle.19 Based on their model, an analytical expression for the stored charge was derived and compared with numerical calculations of a cone-shaped tip and cylindrical nanoparticle. This model is illustrated in Figure 3A, which depicts an isolated dielectric cylinder with nonzero charge density attached to an electrode surface. The cylinder has height h, relative permittivity, , and surface charge density . A cone shaped tip is positioned at a distance z from the electrode surface. The plane capacitor approximation is valid for ≫ ℎ/. For this model system the EFM phase shift (ΔΦ) can be written as the sum of two components; the charge force gradient (∆Φ ), and the capacitive force gradient (∆Φ ), which allows Eqn. 1 to be written in the form


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∆Φ = ∆Φ ∆Φ = !

(2)

where A and B are fitting parameters to the linear and quadratic terms, respectively.

Figure 3: (A) Schematic of EFM plane capacitor influenced by a cylindrical nanostructure described by Melin et. al. (B) Similar description of cylindrical nano-channels embedded in a fluorocarbon matrix.

For the isolated cylinder model in 3A, the coefficients of A and B from Eqn. 2 were determined by first using a plane capacitor approximation for the shape of the tip. In this case one obtains a solution to ΔΦ such that ! = −

=

"

#$% &'

$* +

(

)

ℎ ,

(3)

(4)

q is the total charge enclosed and S is the surface area of the top face of the cylinder. B has no dependence on charge, but only dependent on the cylinder volume. The coefficient A, however, is dependent on the total charge enclosed, the cylinder length, and the relative permittivity. It is important to note that in the isolated cylinder model, comparison between the numerically



computed ratio A/B using a plane capacitor tip versus that of a cone-shaped tip was a simple correction factor (g=1).19 In contrast to the model system of Fig. 3A, a Nafion film is a complex material due to the phase separation, which results in aqueous channels of unknown morphology dispersed randomly in a fluorocarbon matrix. Nevertheless, if we assume that the aqueous domains are roughly cylindrical then we can utilize what we know from the EFM of the isolated cylinder model systems to help interpret our EFM data of Nafion. Furthermore, finite element method calculations qualitatively support this model shown in the Supporting Information. Fig. 3B illustrates a simple cylinder model for aqueous channels imbedded in Nafion. Inspecting the cartoons of Fig. 3A and 3B it is easy to see the similarity between the isolated cylinder model of Fig. 3A and the Nafion film model of 3B. The dielectric cylinders of Fig. 3A are represented in Fig. 3B by the cylindrical aqueous channels surrounded by a fluorocarbon matrix. The main difference between the isolated cylinder model of Fig. 3A and the Nafion model of Fig. 3B is the dielectric constant of the surrounding medium, which is air in the case of Fig. 3A and fluorocarbon in the case of Fig. 3B. Thus, it should be possible to apply what is known from the isolated cylinder model to our Nafion film model. To this end, the EFM phase vs. VEFM data of three individual channels in Nafion shown in Fig.2D were fitted to a quadratic function, which is illustrated in the line traces of Fig. 2D. The data of Fig. 2D are representative of the three categories of EFM phase shifts observed in Nafion films as a function of VEFM: a quadratic (blue), linear (magenta), and null (green) dependence. We have analyzed a total of 19 individual hydrophilic domains with EFM. For each domain the EFM phase (ΔΦ) vs VEFM was fit to Eqn (2), which contains a linear and quadratic term. If A ≅ 0 then the plot of ΔΦ vs VEFM has a


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quadratic dependence. If B ≅ 0 then the plot of ΔΦ vs VEFM has a linear dependence. If both A and B are very small, then the plot of ΔΦ vs VEFM has a null dependence.

Figure 4: (A) Spectrum of quadratic and linear coefficients showing a positive trend from 1

quadratic channels to linear and null channels. The dashed red line shows the 020 = 1 condition. 1

The gray region shows which data points correspond to 020 4 1 . (B) Color-coded histogram of |A/B| values in which blue corresponds to the quadratic channels, purple corresponds to linear, and green corresponds to null. (C) Model proposed illustrating how channel different channel structures give rise to quadratic, linear, and null phase shifts. Figure 4A shows a scatter plot of the fit coefficients: the linear term, A, and the quadratic term, B. Using equations (3) and (4), the ratio A/B provides an expression that is dependent on both the shape and the dielectric properties of the channel:



|1|

'

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∝ " $ ) "7) |2| *

(5)

where ℎ is the channel height, , is the total charge in the channel, 8 is the relative dielectric

constant and = 9 ∙ ℎ is the volume of the channel. The quantity " ) represents the charge 7 density in the channel and is related to the spatial distribution of sulfonate groups that is assumed 1

to be uniform.27 Thus, comparing the ratio 0 0 for different channels results in a comparison of 2

"

'

$*

) for different channels assuming the charge density (i.e. the spatial distribution of the H+ 1

ions within the channel) is roughly constant. The dashed red line shows the 0 0 = 1 condition. 2

1

Figure 4B shows the distribution of the ratio 0 0 in which the color of each bin matches the color 2

corresponding to data shown in 4A. EFM phase shifts that have quadratic dependence with VEFM, 1

the ratio of 0 0 is small (< 1.0), which implies a small ℎ and is indicative of a short, dead-end 2

channel. These channels are depicted by the blue data points in the scatter plot of Fig. 4A and 4B. Using the isolated cylinder model19 as a guide we can infer a short cylindrical channel structure as illustrated in Fig. 4C-i. Similarly, for EFM phase shifts that depend linearly with 1

VEFM, 020 is large (> 1.0), which implies large ℎ and is indicative of a long cylindrical channel. These channels are depicted by the purple data points in the scatter plot of Fig. 4A and 4B, and are represented in the structural model of Fig. 4C-ii. In 4A, the gray region shows which data 1

points correspond to 020 4 1. EFM phase shifts that have no dependence on VEFM are referred to by the “null” designation and are represented by the green dots in the scatter plot of Fig. 4A and


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4B. 4A shows 4 green data points. 1 data point falls outside the red dashed lines. 3 other “null” points do not fall directly on the 0,0 origin, but are close given the measurement error of ~0.02°. These channels have | | ≈ 0 and |!| ≈ 0, which was not predicted by the isolated cylinder 1

model of Melin et. al,19 hence why 0 0 ≫ 1 in 4B. We attribute the null dependence to branched 2

channel as depicted in the structural model of Fig. 4C-iii. In the branched channel the charge is not influenced by the voltage bias due to the presence of a path of least resistance for the charge. This path is denoted by the red arrow in the structural model of Fig. 4C-iii. The modulation of charge would be dominated by this larger branch. If the tip is placed over the smaller branch then the observed EFM phase shift would be independent of VEFM, which is consistent with our data. 1

'

It is important to note that the ratio 0 0 is sensitive to " $ ) for each channel. Up to now 2

*

we have assumed that the relative permittivity 8 is the same for each channel.

This

approximation works well for channels with large surface area of the order of 50 nm2. For narrow channels, however, this approximation breaks down. A radial-dependent permittivity has been shown using a Poisson-Boltzmann approach for cylindrical channels. A drop in the permittivity occurs at a distance of 3-6 Å from the sulfonic side chain boundary wall.25 Thus, for 1

very narrow channels both the length of the channel and the permittivity can influence 0 0 . 2

Conclusions: Using EFM we have shown that the pore structure in Nafion can be characterized by long connected channels that conduct protons from one side of the membrane to the other, short deadend channels that are open to one side of the membrane but do not connect to the opposite side of the membrane and branched channels that have multiple paths from one side of the membrane to



the other. The differences in the EFM phase dependence on applied voltage allows each channel to be assigned to a particular structural motif. With these imaging techniques, future comparative studies of thin films under humidity controlled conditions could provide an improved understanding of how channel connectivity is tied to membrane water content.

Author Information: Corresponding Author Steven K. Buratto Department of Chemistry and Biochemistry, University of California, Santa Barbara, CA 931069510, USA; Fax: 1-805-893-4120; Tel: 1-805-893-3393; Email: [email protected]

Notes The authors declare no competing financial interest

Acknowledgments: Our AFM was purchased with funding from the MURI and DURIP programs of the U.S. Army Research Laboratory and U.S. Army Research Office under grant nos. DAAD 19-03-1-0121 and W911NF-09-1-0280. Funding for this work was provided by National Science Foundation grant no. CHE-1213590.

Supporting Information Available:


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Included in the Supporting Information is a description of discriminating against image artifacts in EFM and KPFM. A description of background subtraction of the EFM data is also shown. A computational model of the tip- Nafion system is described and compared with the isolated cylinder model. A description of how lift height is defined is in the Supporting Information. Lastly, Kelvin Probe Force Microscopy was used in our investigation. A description of this technique and images of the phase with the surface potential is shown.

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