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Double Layer Capacitance Measurements to Characterize the Water Intrusion into Porous Materials Pradeep Kumar Sow, Zhaowei Lu, Hoda Talebian, Luke Damron, and Walter Merida J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b07861 • Publication Date (Web): 10 Oct 2016 Downloaded from http://pubs.acs.org on October 11, 2016

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The Journal of Physical Chemistry

Double Layer Capacitance Measurements to Characterize the Water Intrusion into Porous Materials Pradeep Kumar Sow, Zhaowei Lu, Hoda Talebian, Luke Damron, Walter Mérida* Clean Energy Research Centre, The University of British Columbia, 6250 Applied Science Lane, Vancouver, BC Canada V6T 1Z4 *Corresponding author: Tel: +1.604.822.4189 Fax: +1.604.822.2403 E-mail: [email protected] Abstract: In this work, we have proposed and substantiated a novel approach to study the dynamic wetting behavior during water intrusion, demonstrated for a porous carbon fiber substrate. The proposed methodology quantifies the evolution of the wetted interfacial area during intrusion by electrochemically measuring the double layer capacitance, which is proportional to the solid-liquid interfacial area. We investigated the intrusion behavior for three commercially available substrates with distinct thicknesses and internal microstructures, using a combination of capacitance and pressure measurements. For the same imbibed volume of water, the pressure increase was comparable, while the capacitance increase was distinct for the substrates with dissimilar internal microstructure. The hydraulic radius and the cross section of the intruding meniscus of water reduced during the course of intrusion. A correlation between the capacitance and the pressure-volume work has been proposed as a measure for quantifying the favorability of wetting the fiber surface, during the liquid intrusion into the porous structure. The pressure-volume work done in wetting the fiber surface showed dependence on the internal microstructure and remains constant during the course of water intrusion. The approach presented here can facilitate quantitative characterization of the wetting behavior and the new parameter (wetted interfacial area) could be used as the basis of analytical models for the water transport behavior through these porous structures. 1 ACS Paragon Plus Environment


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1. Introduction The porous carbon fiber substrate finds application in a wide range of electrochemical devices as an electrode, such as in metal-air batteries1,2, electrolysers 3, carbon-dioxide electrolysis4, fuel cells5,6, redox flow batteries7 and supercapacitors8. For these applications, the solid-liquid interfacial interactions occurring inside the porous structure can either hinder or enhance the overall device performance. To understand these interfacial interactions, liquid intrusion studies are conventionally used, where the liquid phase is forced into the porous structure and the effects of the intrusion are studied parametrically. Approaches commonly employed to study the intrusion behavior include the measurement of the differential pressure

9–13

or the

visualization of the two-phase intrusion (Nuclear Magnetic Resonance (NMR), X-ray tomography, Neutron imaging, optical imaging, fluorescence microscopy)14,15. Among these methods, the pressure measurement is most widely used, because of the experimental simplicity and it also provides a quantifiable metric dependent on the interfacial interaction. The underlying concept for using the pressure measurement follows that the liquid intrudes a pore when the applied pressure is higher than the capillary pressure of a pore. The capillary pressure (PC) relates to the interfacial surface tension (γ), effective pore radius (Reff) and the contact angle between the liquid-air interfaces (θ), given by the Young-Laplace equation (also referred as the Washburn equation) 13,16 as:

PC = −

2γ cos(θ ) Reff

(1)

In this article, we present a novel approach and a parameter to study the water intrusion behavior into the porous structure of the carbon fiber substrates. Here, the relative change in the wetted area associated with the liquid intrusion has been presented as the quantitative metric, which can provide a new perspective in understanding the two-phase intrusion behavior. During intrusion, an increase in the volume of water forced into the porous structure 3 ACS Paragon Plus Environment


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causes the water to come in contact with the fiber surface resulting in an increase in the solidliquid (S-L) interfacial area. The interfacial area change characterizes the geometric configuration of the pore space involved in the two phase flow and can also serve as a parameter for simulating the two phase intrusion. The quantification of the S-L interfacial area change presented here employs an electrochemical approach by using the properties of the carbon fiber substrates. These carbonaceous materials are conductive and can also support an electric double layer, which can be measured electrochemically as the capacitance17,18. The electric double layer capacitance is an interfacial phenomenon and the resulting capacitance is proportional to the solid-liquid (S-L) interfacial area, and can be approximated as

C = ε rε 0

Asl d

. In the representation, C is the capacitance, ε r is the relative permittivity of

19,20

the solvent, ε 0 is the permittivity of the vacuum, Asl is the solid-liquid interfacial area and d −1

is the double layer thickness. The double layer thickness “d” is approximated as 1.5 κ , −1 where κ is the Debye-Hückel length21, mathematically given as κ −1 =

ε r ε 0 k BT 2C 0 z i2 e 2

. In the

above relation, k B is the Boltzmann constant, T is the temperature, C 0 is the bulk concentration of electrolyte, z is the ion charge and e is the elementary charge. Based on the above expression, the double layer thickness is a property of the electrolyte medium and the temperature of the system and therefore can be considered constant. As the parameters ε r , ε 0 and d are constants, any change in the S-L interfacial area during intrusion will result in a proportional change in the measured capacitance. Applying the above concept, we designed an experimental setup and measurement methodology to quantify the relative change in the wetted area under forced water intrusion by utilizing the electric double layer capacitance as a characterization metric.


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Recently, we reported the use of double layer capacitance for investigating the wetted area under a sessile drop and its correlation to the optically measured contact angles18,22. Using the double layer capacitance, we found that the contact angle can show deviation from the predictions based on the Cassie-Baxter and Wenzel equations. For the fibrous materials, we deduced the possible reason being the instability of the Cassie-Baxter wetting state, causing the liquid meniscus under the droplet to sag into the porous structure18. Although, the degree of instability showed dependence on the breakthrough pressure, the surface wetting behaviour itself cannot explain the interactions inside the porous structure, which is the focus for this work. Compared to surface wetting, the contact angle inside the porous structure cannot be quantified directly due to the limited optical accessibility. Here, the experimental procedure targets the simultaneous measurement of the pressure, volume and the capacitance during the course of intrusion to obtain the quantifiable metrics. In contrast to the droplet placed on the surface where the liquid interacts only with the surface structures, the internal microstructure and the sample thickness dictate the intrusion process. Therefore, the studies were conducted on three commercially available materials with distinct thicknesses and internal microstructures. Here, we show that the capacitance has a stronger dependence on the internal microstructure of the porous substrate as compared to the pressure during the course of intrusion. The capacitance provides a quantitative representation of the intrusion process and therefore, it can be linked to other metrics such as pressure and volume. We used the capacitance data to evaluate the evolution of the hydraulic radius, which represents how the cross section of the intruding liquid phase changes during the course of intrusion. We developed a correlation between the pressure-volume work and the capacitance as a measure for the favorability of wetting the fiber surface during intrusion. We also show that the pressure-volume work required for wetting the internal structure remains constant for all the substrates during the course of intrusion and is a function of the internal microstructure of the substrate. 5 ACS Paragon Plus Environment


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2. Experimental 2.1. Materials In this work, three commercially available materials were studied: two carbon fiber papers (Toray paper: TGP-60, TGP-120) and a carbon fiber felt (10AA). These materials have been studied extensively, due to their application in electrochemical devices25,26. Toray papers (TGP-60 and TGP-120) were purchased from the Fuel Cell Store and 10AA SGL, Sigracet was purchased from Ion-Power. The materials were used without any Teflon (PTFE) treatment. The two Toray papers (TGP-60 and TGP-120) consist of randomly oriented straight fibers stacked in layers and are classified as carbon papers. The TGP-120 (363 µm) is thicker than the TGP-60 (193µm), but they have similar fiber diameters (approximately 7.5µm) and bulk porosity (78%). Therefore, the two carbon papers have a similar microstructure arising from the fiber distributions, which can be seen in the SEM images (Figure 1).

Figure 1. SEM images of the three substrates 10AA, TGP-60 and TGP-120. Inset shows the magnifed images of fibres The carbon felt consists of tortuous intertwined fibers and shows a clear difference in the microstructure compared to the Toray papers, which can be observed in Figure 1. The carbon felt 10 AA has a thickness of 382µm, with fiber diameter of approximately 12µm. The fiber dimensions are the average values for 10 measurements, evaluated from the SEM images using open access software ImageJ. SEM images of the materials presented in this study were obtained using a Hitachi SU3500 electron microscope. 6 ACS Paragon Plus Environment

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For the electrochemical measurements, a 0.1M sodium sulphate (Na2SO4) aqueous electrolyte solution was used. The sodium sulphate was procured from Fisher Scientific and the electrolyte solution was prepared in de-ionized (DI) water. Addition of an electrolyte increases the conductivity and provides the ions for the electric double layer formation on the fiber surface. It is to be noted that the addition of an inorganic electrolyte increases the surface tension of water. However, the increase in the surface tension due to the addition of 0.1 M Na2SO4 is low with the surface tension for a 0.1 M Na2SO4 electrolyte solution being 72.95 mN m−1 as compared to 72.76 mN m−1 obtained for DI water at 20o C 27. Therefore, the intrusion behavior for the electrolyte solution is expected to be similar to that of pure water. It is to be noted that the present experiments have water based electrolyte solution as the intruding liquid. However, different ionic liquids and solvents can also be used for the intrusion studies. 2.2. Experimental Setup Figure 2(a) shows the schematic representation of the experimental design. The system was designed with a liquid injection assembly for forcing water through the bottom of the substrate while simultaneously measuring the pressure using a pressure transducer along with an electrochemical measurement system. This design of the intrusion cell is similar to that of a bottom injection setup used for water intrusion studies with additional components for electrochemical measurements

11,13

. A three electrode arrangement with the porous substrate

as the working electrode was incorporated into the cell, which ensures that any change in electrochemical activity corresponds only to the working electrode. The intrusion cell was fabricated in-house with a liquid injection port and houses the carbon counter electrode (BMA5, Eisenhuth GmbH & Co KG) along with a platinum wire (0.5 mm thickness, Alfa Aesar) as the pseudo reference electrode. With this configuration, the porous substrate acts as the working electrode in the three electrode system. 7 ACS Paragon Plus Environment


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(a)

(b)

(c) Figure 2: a) Schematic representation of the experimental configuration b) and c) shows the conceptual representation of the underlying mechanism involved in the measurement. Experimental procedure involves the measurement of the pressure and the change in the capacitance arising from the water intrusion. Intrusion of a finite volume of water causes an increase in the solid liquid interfacial (Asl) which is proportional to the double layer capacitance (C) and is measured electrochemically.


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The active area through which the intrusion occurs is of 5mm in diameter. Further description of the intrusion cell has been provided in the supporting information section S1. The three electrodes were connected to a Solartron 1470E Cell Test System along with a Solartron SI 1260 Impedance/Gain-Phase analyzer for the electrochemical measurements during the intrusion. The aqueous electrolyte prepared in de-ionized water was forced into the cell using a syringe pump (Harvard apparatus, 11 plus series) while the pressure was measured continuously using an Omega PX409 series pressure transducer. The pressure transducer was connected to a National Instruments (NI) data acquisition system where the data was acquired at a frequency of 100Hz. The assembly was placed on top of an anti-vibration table to reduce the effect of any mechanical vibration towards the intrusion process. All the measurements were conducted at room temperature (20 ± 2oC) and 40-60% relative humidity. 2.3. Experimental methodology 2.3.1. Baseline determination The starting point (referred as baseline) for the intrusion was determined as the point at which the liquid meniscus first comes in contact with the bottom surface of the sample. The evaluation was done by measuring the conductivity between the working electrode and the counter electrode while the water was forced into the intrusion cell using a syringe pump at a flow rate of 0.5 µL s-1. When the advancing meniscus of the liquid comes in contact with the bottom surface of the sample, the ionic circuit becomes complete resulting in a finite conductivity. This was considered as the baseline which is the starting point for the intrusion process. Additionally, a sudden rise in pressure was another detectable sign of liquid intrusion to the pores. However, the sensitivity of the pressure measurement towards identifying the baseline was found to be lower than the conductivity measurements. The pressure increase arises from the resistance offered by the porous structure towards the intruding meniscus based on Eq. 1. Therefore, the change in the pressure is negligible when the water touches the 9 ACS Paragon Plus Environment


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bottom surface of the substrate and increases as the water penetrates into the pore. This highlights the reason for the low sensitivity of the pressure measurements towards baseline determination. In light of the above discussion, the conductivity measurements were used for the identification of the baseline for all the studies. 2.3.2. Water intrusion experiments After the baseline was determined, the electrolyte solution was injected in discrete 20 µL volumetric steps, at a constant flow rate of 0.5 µL s-1 until the first breakthrough. The water breakthrough is associated with the complete penetration of the liquid and the liquid emerged on the other side of the sample forming a droplet, accompanied by a reduction in the pressure. The pressure was monitored and recorded continuously during the experiment. After each volumetric

intrusion

step

of

20

µL,

the

syringe

pump

was stopped (flowrate zero) and the cyclic voltammetry (CV) experiments were done. CV was done in a potential window of 0.4 V (-0.2 V to +0.2 V vs. Pt pseudo-reference electrode) at a scan rate of 200mV/s. As Figure 3(b) shows, the CV curves are fairly rectangular, which is typically observed for double layer capacitance22. The capacitance was calculated from the CV data using the following equation28:

C =

1

Vf

2υ (V f − V0 ) V∫0

I (V )dV

(2)

Where, the integral term was evaluated based on the area enclosed by the CV curve, ʋ represents the scan rate and (Vf-V0) represents the potential window for the measurement. The CV and the pressure data was processed using Origin 9.1. Studies were done for five samples of each material and the average values are reported with the corresponding standard deviation as the error bars.


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3. Results and Discussion Figure 3(a) shows the typical raw data obtained for the pressure during the course of intrusion along with the CV curves obtained at different stages of intrusion. The figure shows the CV curves obtained during the time interval A, B and C respectively, during which the flowrate was zero. It is to be noted that during this period of zero flowrate, the pressure remained constant. As it can be observed the area enclosed by the CV curve increases due to the increase in S-L interfacial area (Figure 2(b) and (c)). Additionally, the steady state pressure measured after each intrusion step was also found to increase till the breakthrough. The experimentally evaluated pressure and the capacitance (using Eq. 2) as a function of volume of water imbibed into the structure is shown in Figure 4(a) and (b). As it can be observed from the plots, the measured values of pressure and capacitance for the five samples are fairly consistent and the results are fairly reproducible. The capacitance and the pressure increased after each intrusion step until the water breakthrough for all the samples. In Figure 4(a) and (b), the pressure and capacitance measured at the baseline have been subtracted from the data set to isolate the changes corresponding to water transport inside the porous structure. Also, the values corresponding to the breakthrough have been excluded from the representation due to the uncertainty in the measured capacitance at the breakthrough point.


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6000

4000

0.4 0.2

2000

Pressure \ Pa

Breakthrough

0.6

0.0 0

100

200

300

400

2

2

1

1

1

0

Current/ µ A

2

0

-1

-1

-2

500

Time \ s

Current/ µ A

Current/ µ A

-2

-0.2

-0.1

0.0

0.1

0.2

0

-1

-0.2

-0.1

0.0

0.1

0.2

-2

-0.2

Voltage / V

Voltage / V

-0.1

0.0

0.1

0.2

Voltage / V

(a) 3

TGP-120 10AA

2

Current/ µA

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Flow Rate \ µL s-1


TGP-60

1 0 -1 -2 -0.2

-0.1

0.0

0.1

0.2

Voltage/ V (b) Figure 3: a) Raw data showing the pressure measured during the stepwise intrusion through a TGP-60 sample. Cyclic voltammetry data obtained during the time period A, B and C corresponding to the total volumetric intrusion of 0, 40 and 80µL respectively b) CV curves obtained at an intrusion volume of 60µL for the three samples (10AA, TGP-60 and TGP-120) used in the present study


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3.1. Evolution of pressure and capacitance during intrusion A linear correlation between pressure and volume was observed in the pressure-volume (P-V) plot, where the slopes evaluated from the linear correlations are similar for all the samples (Figure 4(a) and Table 1). The linear correlation between the pressure and volume obtained here is in agreement with earlier studies

10,11,13,29

. The breakthrough pressures were found to

be distinct for all the samples, as shown in Table 1. TGP-120 presented with a higher breakthrough pressure (5171 ± 82 Pa) compared to TGP-60 (4291 ± 182) and 10AA (2748 ± 137 Pa). The TGP-120 (363 µm) is thicker than TGP-60 (193 µm), which increases the flow path length for the intruding water, resulting in an increase in the number of pores encountered during the water transport. Various studies reported in literature show that the breakthrough pressure increases linearly with the thickness of the substrate10,13. Breakthrough pressure for 10AA was found to be lower than the Toray Papers which has also been observed in earlier works18. Pressure required to intrude a pore increases with the reduction in the pore size, according to the Washburn equation for the capillary pressure (Eq. 1). 8

5000

3000

Capacitance/ µ F

TGP-120 TGP-60 10AA Fitting

4000

Pressure/ Pa

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


2000

TGP-120 TGP-60 10AA

6

4

2

1000 0

0 0

20

40

60

80

0

100

20

Volume / µL

40

60

80

100

Volume / µL

(a)

(b)

Figure 4: a) Pressure-Volume (P-V) plot and b) Capacitance-Volume (C-V) plot obtained for the forced intrusion of electrolyte solution into the porous materials



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The lower breakthrough pressure for 10AA can be attributed to the higher porosity of the 10AA (90%) as compared to the Toray paper (78%). Although, the breakthrough pressures are different, the slope of the P-V curve is the same for all the samples, which means that the pressure increase for a given volume of water forced into the substrate is indistinguishable for all the samples irrespective of the microstructure. Therefore, the breakthrough pressure identifies the pressence of structural differences (differences in the thickness or porosity), however, the reason behind the difference in the breakthrough pressure, i.e. the thickness or the microstructure cannot be determined conclusively by using only the pressure-volume data. While the pressure showed a linear increase, the capacitance shows a non-linear increase with the volume of liquid intruded into the structure for all the samples. Additionally, the Capacitance-Volume (C-V) profile was found to be distinct for Toray paper (TGP-60 and TGP-120) and 10AA samples as shown in Figure 4(b). As the capacitance is proportional to the S-L interfacial area, the C-V plot represents how the wetted area changes during the course of intrusion. At any volumetric intrusion step before the breakthrough, the wetted area is higher for 10AA as compared to the TGP-60 and TGP-120 for the same amount of water forced into the substrate. Even though the maximum wetted area during the course of intrusion is different for the Toray papers (TGP-60 and TGP-120), the C-V profile is similar for both the materials within the error range for multiple samples. These results demonstrate that the capacitance measurement has a stronger dependence on the microstructure of the fibrous substrates through which the intrusion occurs. 3.2 Evolution of hydraulic radius during intrusion X-ray tomography studies to visualize the water intrusion into the fibrous structure have shown that the pore occupancy is highest near the inlet and reduces with the distance from the inlet during the course of intrusion24. Similar observations were made based on the simulation studies using pore network model, where the cross-sectional averaged liquid water saturation 14 ACS Paragon Plus Environment

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was found to reduce with the distance from the injection point during the intrusion process through these porous layers30. Also, the water intrusion into the porous substrate occurs through multiple inlet points or pores, while the breakthrough occurs from a single pore on the top surface. These observations point towards the fact that the cross section of the advancing liquid front changes along the flow path through the substrate. In order to capture this change in the cross section of advancing liquid front, we correlated the capacitance and the step volume information to evaluate the hydraulic radius of the group of pores imbibed by the water for a given intrusion step. Hydraulic radius (R) of a pore or a group of pores is defined as V/Asl, where V represents the volume of pores and Asl represents the surface area of the pore walls31,32. The hydraulic radius is a measure of the average width of a group of pores and therefore can be used to represent how the cross section of the advancing liquid front evolves during intrusion31. Since the double layer capacitance (C) is proportional to the wetted surface area (Asl), the hydraulic radius for the nth intrusion step (Rn) based on capacitance can be represented as Rn =

V k∆C n

. In this evaluation of Rn, ∆Cn is the change in

capacitance corresponding to each 20µL intrusion volume (V), k is the proportionality constant and the subscript n represents the step number. The ∆Cn for each intrusion step was calculated from the capacitance data obtained during the intrusion experiments represented in Figure 4(b). Here, our focus is to evaluate the relative change in the hydraulic radius for each intrusion step, for which, we evaluated the ratio of hydraulic radius for the nth intrusion step (Rn) and the first intrusion step (R1), representing the relative change in the hydraulic radius with respect to the first intrusion step. Figure 5 shows the plot of ratio Rn/R1, calculated for each intrusion step (n) before the breakthrough. From Figure 5, the hydraulic radius is highest near the inlet and reduces during the course of intrusion with the minimum hydraulic radius corresponding to the step before which the breakthrough is achieved.



TGP-120 TGP-60 10AA

1.0

Rn/R1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

0.5

0.0 1

2

3

4

5

Intrusion Step/ n

Figure 5: Evolution of the hydraulic radius during the course of intrusion. Plot shows the ratio of the hydraulic radius for the nth intrusion step with respect to the first intrusion step as a function of intrusion step number The reduction in the hydraulic radius during the course of intrusion corresponds to a reduction in the cross section of the advancing liquid front intruding through porous network, as observed for the capillary fingering pattern33,23. A higher hydraulic radius at the initial stages of intrusion corresponds to higher pore occupancy near the injection point. Due to capillary fingering, the cross section of the advancing meniscus reduces resulting in the lower hydraulic radius at the latter stages of intrusion before the breakthrough. The reduction in the hydraulic radius due to the capillary fingering can also explain the pressure increase during the course of intrusion. The reduction in the hydraulic radius (Rn) and the cross section of advancing liquid front corresponds to the reduction of the equivalent pore radius (Reff) at the advancing liquid front. According to the Eq. 1, the capillary pressure is inversely proportional to the equivalent pore radius (Reff). Therefore, pressure required for the intrusion is expected to increase along the flow path, which is consistent with the experimentally observed pressure profile.


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3.3. Work done in wetting the fiber surface Intrusion of a finite volume of the water into the porous structure under an applied pressure is accompanied with an increase in the wetted interfacial area leading to an increase in the surface free energy (∆Gs). As the intrusion process is non-spontaneous, we adapted the convention that the forced intrusion increases the surface free energy (+∆Gs). This surface free energy increase is caused by the pressure applied during the intrusion process. By knowing how the pressure (P) evolves with the volume (V) of water forced into the structure, the pressure-volume (P-V) work can be evaluated as: W = ∫ PdV . The effect of the gravitational forces during intrusion can be ignored due to considerably smaller thickness of 1

the substrate (

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