Wettability of a Single Carbon Fiber - Langmuir (ACS Publications)

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Wettability of a single carbon fiber Si Qiu, Carlos Anibal Fuentes Rojas, Dongxing Zhang, Aart Willem van Vuure, and David Seveno Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.6b02072 • Publication Date (Web): 22 Aug 2016 Downloaded from http://pubs.acs.org on August 24, 2016

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Wettability of a single carbon fiber Si Qiu,†,‡ Carlos A. Fuentes,‡ Dongxing Zhang,*,† Aart Willem Van Vuure,‡ David Seveno,‡ † School of Material Science and Engineering, Harbin Institute of Technology, Harbin 150001. China ‡ Department of Materials Engineering, KU Leuven, Leuven 3001, Belgium, ABSTRACT Wettability, i.e. contact angle measurement, is a suitable method to characterize the physical bonding of a polymer matrix and reinforcing fibers, but it is highly challenging to measure the capillary force exerted by a probe liquid on a fiber accurately for very fine fibers like single carbon fibers. Herein, we propose an innovative method for measuring dynamic contact angles with a tensiometer, considering both the intrinsic variability of the carbon fiber diameter and the extremely small amplitude of the capillary forces, allowing the measurement of reliable dynamic contact angles over a large range of contact line velocities. The analysis of the contact angle dynamics by the molecular-kinetic theory permits to check the relevancy of the measured contact angles and to obtain the static contact angle value, improving the prospect of employing tensiometry to better understand the wetting behavior of carbon fibers.

1. INTRODUCTION Carbon-fiber-reinforced polymer (CFRP) composites have received considerable attention due to outstanding characteristics and wide application in many fields such as aircraft and marine industries.1-5 The strength of the adhesion between the reinforcing carbon fibers and the matrix plays a decisive role in determining the final mechanical properties of the composite material and

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therefore its potential application.6-7 Adhesion in general can be attributed to mechanisms including physical interactions, mechanical entanglement, and chemical bonding.8 The wettability of carbon fibers exercises great influence on the physical adhesion and can be obtained by measuring the contact angles between liquids and fibers. Compatibility between the fibers and the matrices is either estimated directly by measuring the contact angles made by the liquid polymer around the fibers or by deriving the surface free energy components 8 of each material. Both methods require accurately measuring contact angles. The direct optical method and the Wilhelmy balance method are currently the two principal methods used to estimate the wettability of fibers. The latter one is favored owing to its higher accuracy when testing the contact angle of fine fibers with known diameter.9 The Wilhelmy balance method is a frequently used method which consists of measuring the capillary force exerted by a liquid on a solid substrate.9-10 This method was for example applied to reveal the effects of the modification of carbon fiber surfaces.11-15 However, testing the wettability of single carbon fibers with micron scale diameters is highly challenging as slight variations of the fiber diameter and the measured capillary forces can greatly influence the finally determined contact angles. To minimize errors, a typical approach consists in immersing several aligned carbon fibers simultaneously which leads to a larger wetting force to be detected.16-18 Compared with a single fiber measurement, it is difficult to guarantee that every tested fiber is entering the liquid perpendicular to the liquid surface without bending.19 In both cases, it is equally necessary to obtain high precision wetted length to evaluate the contact angle correctly. It is a common practice to assume that the tested carbon fibers share nearly the same diameter 20-22 even if experiments showed that they have a given variability, determined from either capillary force experiments or Scanning Electron Microscopy (SEM).This significantly influences the


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values of the calculated contact angles.23 Furthermore, some reports 19, 24 outlined that the inexact wetting force caused by adsorption of probe liquids or inaccurate experiments, like the bending of the fiber when contacting the liquid surface, could also lead to incorrect extrapolations and wrong estimations of the wettability of carbon fibers. Moreover, the Wilhelmy method is a dynamic process with advancing (the fiber is dipped in the liquid) and receding (the fiber is withdrawn from the liquid) phases at a constant velocity. Meanwhile, the static advancing and receding contact angles are more relevant when calculating the components of the surface energy based on the Owens-Wendt 25 or Van Oss-Chaudhury methods 26. Accordingly, much attention has been paid to the dynamic advancing contact angle at extremely low velocity, assuming it has a value close to or even equal to the value of the static advancing contact angle.17, 27-29 Receding contact angles have rarely been reported 30-31 whereas contact angle measurements at contact line velocities above 10mm/min have never been studied. This lack of clarity leads to controversial contact angle values ranging from 62º to 79º 16, 29, 32-33 for desized T300 carbon fibers wetted by de-ionized water. From a theoretical point of view, dynamic contact angles can be analyzed using various approaches 34 even if it is widely accepted that the Molecular-kinetic theory (MKT) proposed by Blake 35 is able to describe eclectic liquid/solid systems. Bamboo,10 glass,36 PET 37 and nylon fibers 38 were analyzed via the MKT to deepen the understanding of the dynamic wetting properties of these large fibers (compared to carbon fibers). So far, studies dedicated to the dynamic wetting of carbon fibers are not available even if it is a key to the manufacturing of carbon fiber composites.39-40 In the present study, reliable and accurate water contact angles around single carbon fibers are reported. We propose a methodology which permits to measure dynamic contact angles taking into consideration both the intrinsic variability of the carbon fiber diameter and the extremely small amplitude of the capillary forces. The effectiveness of the method was strengthened by


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fitting the experimental contact angle values by the MKT which permitted to assess the static advancing contact angle as well as the dynamic wetting parameters of the carbon fibers considered in this work. 2. MATERIALS AND METHODS 2.1. Materials. FT300-3000-40A polyacrylonitrile-based carbon fibers manufactured by Toray Carbon Fibers Europe S.A. were used in this study. To obtain clean surfaces, the fibers were washed in ethyl alcohol and dried at 80ºC for 1h. This gentle cleaning procedure removes dust and grease without altering the sizing that is typically present on commercial carbon fiber. The main properties of the test liquids (n-Hexane: Acros; Deionized water: Millipore Direct Q-3 UV) are listed in Table 1. Table 1. Liquid/vapor surface tension and density of the probe liquids 3 Test liquid γ (mN/m) ρ (g/cm ) LV

n-Hexane Deionized water

18.4 72.8

0.659 0.98

2.2. Sensitivity of the contact angle measurements. Advancing and receding contact angles were measured with a high-precision Force Tensiometer – Krüss K100SF (Krüss GmbH, Hamburg, Germany). The instrument was designed to characterize the wettability of single fibers according to the Wilhelmy method.41-42 The K100SF tensiometer has a claimed weight resolution of 0.1µg with testing velocities ranging from 0.1mm/min to 500mm/min. During the experiments, a single carbon fiber was attached to the sample holder and set perpendicular to the surface of the test liquid. If standard procedures are followed,24 forces when the fiber is dipped in and then withdrawn from the liquid bath are detected by the microbalance. The fiber is actually not displaced, but the vessel holder moves up (advancing cycle) and down (receding cycle) during the experiments. A sketch of this apparatus is shown in Figure 1.


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Figure 1.Schematic drawing of the K100 SF tensiometer.

Contact angles at constant advancing and receding velocities can be calculated from:9

Fmeasured = Pγ LV cos θ + mg − Fbuoyancy

(1)

where Fmeasured is the force detected by the microbalance, P the perimeter of the fiber, θ the dynamic contact angle, m the mass of the fiber, and Fbuoyancy the buoyancy force. All tests were conducted in monitored and controlled environment (25ºC, 65% relative humidity and soundproof cabinet), so that γ LV is a constant value depending on the test liquid. The calculation of the buoyancy force is based on the density of the test liquid and of the immersed volume of the fiber, Vimmersed.

Fbuoyancy = ρ gVimmersed

(2)

As low density de-ionized water and hexane were used as test liquids, the buoyancy force is in the order of 10-9mN and can be neglected when compared to the capillary force (the cross section


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of a single carbon fiber is regarded as circular). The contribution of the weight of the fiber is zeroed at every start of an experiment so that contact angles can simply be calculated by: (3)

Fcapillary = π dγ LV cosθ

As γ LV is known in eq 3, θ can be calculated from the capillary force Fcapillary measured by the tensiometer if the fiber diameter, d, is a priori known or measured beforehand. It is common practice to assume that the diameter of regular carbon fibers is about 7µm.16, 20 Considering such diameter, Figure 2 shows the relation between the capillary force and the calculated contact angle in water (using eq 3). When the contact angles are higher than 60º, an approximately linear relation between the force and the contact angle can be observed. For smaller contact angles, or equivalently higher forces, the influence of the force is augmented as for instance a 0.15x10-3mN (from 1.35x10-3mN to 1.5x10-3mN) variation leads to more than 10º difference in the determined contact angle. Considering the force levels in Figure 2, measuring contact angles around a single carbon fiber requires a very accurate measurement of the forces especially if contact angles smaller than 30º, or in between 70º and 110º (small overall capillary force) are obtained.

100 90 80 70

Contact angle(°)

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60 50 40 30 20 10 0 0.0

3.0x10-4

6.0x10-4

9.0x10-4

1.2x10-3

1.5x10-3

1.8x10-3

Force(mN)


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Figure 2.Variation of the contact angle of a single carbon fiber in de-ionized water with a constant diameter of 7µm as a function of the capillary force.

Measuring precise diameters of fibers is also a major prerequisite when calculating contact angles. Yet it is simply overlooked in most studies.22, 43 According to eq 3, when a capillary force is accurately measured by the microbalance, an inaccurate diameter can also lead to erroneous contact angles. Table 2. Capillary force for carbon fiber/Water system calculated (eq 3) using a reference diameter of 7µm. Contact angle (º) 80 70 60 40 30 20 Capillary force (mN) 0.00028 0.00055 0.00080 0.00122 0.00139 0.00150

In Figure 3, variations of the contact angle as a function of diameter are compared based on capillary forces given in Table 2. Figure 3 shows that a small variation of the fiber diameter has a significant influence on the contact angle values (for considered angles between 80º and 20º). This trend is amplified when low contact angles are considered (Figure 3b). 90 85

60

(a)

55

80

50

75

45

70

40

Contact angle(°)

Contact angle(°)

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

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65 60 55 50

80° 70° 60°

45 40

(b)

35 30 25

40° 30° 20°

20 15 10

35

5

30 5

6

7

Diameter(µm)

8

9

0 5

6

7

8

9

Diameter(µm)

Figure 3. Variation of the contact angle as a function of the diameter of a fiber (keeping the measured force constant): (a) high contact angles and (b) low contact angles.

This simple analysis clearly indicates that a high precision in both the capillary force and the diameter of carbon fibers is required, especially for low contact angles. It also explains why receding contact angles around carbon fibers, when reported 24, 44 show large standard deviations


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or are even not reported. These difficulties are often claimed to be circumvented by testing multiple fibers simultaneously. If this technique indeed permits to increase the capillary force, it also suffers from many drawbacks. First, it is more difficult to align several carbon fibers. Second, there is no guarantee that every tested fiber enters the liquid perpendicular to the liquid surface without bending. It is even possible that a fiber bends and does not go through the liquid/vapor interface. Lastly, testing multiple fibers can only provide an effective picture of the wettability of carbon fibers when overlooking the effect of the fiber diameter variations on the final result, neglecting the effect on the force caused by the pinning of the contact lines, resulting in either low receding or large advancing contact angles. For these reasons, in this study, a single fiber was tested with a maximum immersion depth of 5 mm making sure the fiber pierces the liquid/vapor interface without bending.45 2.3. Wetted length measurement. The K100SF tensiometer was also used to measure the diameter of carbon fibers. The measurements were carried out at room temperature. In this case, n-hexane (99.6%) was the test liquid because it is supposed to perfectly wet the fibers, i.e. θ =0º, leading to a simplified version of the Wilhelmy equation: (4)

Fcapillary = π dγ LV

The standard procedure consists of measuring the forces exerted on a fiber while being immersed in N-hexane at a constant speed. The capillary force is constant (zero contact angle) while the buoyancy force increases resulting in a net force linearly decreasing versus the immersion depth. Using a linear regression extrapolated to a zero immersion depth, i.e. no buoyancy, the capillary force is obtained from which the diameter is calculated using eq 4. Normally the dynamic tensiometer has a certain detection sensitivity, so that data recording only starts upon contact with


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the liquid. It was however noted, that with the very small force levels encountered when testing single carbon fibers, various artefacts occurred, causing non-linear and non-steady behavior of the capillary force. Upon doing a static test, the force would e.g. keep drifting upward. This was not noticed before when testing larger fibers, but became noticeable for very small capillary forces. It is hypothesized that this effect is due to either the effect of the air flow induced by the movement of the vessel holder or due to the adsorption caused by the evaporation of n-hexane. Therefore, in this study, the detection sensitivity of the force was set to its minimum value, i.e. 0.1µg, to record forces even before the fiber end is in contact with the liquid surface. Figure 4 shows a typical wetted length measurement curve obtained with n-hexane. The first part (from 0 to 1.7mm) represents the measurement before touching the fluid and highlights a drift in the force. The force level, before touching the fluid, will hereafter be called the “pre-force”. The second part of the curve is related to the capillary process. In standard test protocols, only the second part is normally used to calculate the wetted length. During immersion, the measured force should normally go down due to the buoyancy effect, but it is apparent from Figure 4 that this is not the case here. Therefore, we measured the capillary force in this case from the upward jump in the force at the moment of contact. If the normal procedure with extrapolation to zero immersion depth is used in Figure 4, a fiber diameter of 23.7µm is obtained. The new procedure proposed here leads to a diameter of 7.4µm which was proven to be correct by additional SEM analysis. All results in this paper for carbon fiber were measured with this new procedure. The measuring velocity was set to 1mm/min and the maximum rise distance of the stage was 5mm. One fiber was tested 5 times to determine the dispersion of the jump force. Then 20 other


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fibers were selected randomly and measured twice respectively to calculate the average diameter for further comparison with results from SEM. -3

2.0x10

1.8x10-3 -3

1.6x10

1.4x10-3

Force(mN)

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

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1.2x10-3 -3

1.0x10

contact point

-4

8.0x10

-4

6.0x10

pre-force

4.0x10-4 2.0x10-4 0

1

2

3

4

5

Position(mm)

Figure 4.Typical wetted length measurement curve in n-hexane.

2.4. Contact angle measurements. Once accurate and reliable fiber diameters were obtained and the existence of a drift in the force measured by the tensiometer was analysed, contact angle measurements with deionized water (18.2 Ω ⋅ cm resistivity) were implemented. Again, the measurements were carried out at room temperature and the detection sensitivity was set to its minimum value to trigger the tensiometer before the fiber was in contact with the water/air interface. Every fiber was dipped in and withdrawn from the liquid vessel repeatedly for 3 times at a constant velocity to measure respectively a series of dynamic advancing and receding contact angles. The experiments were conducted at 12 velocities ranging from 0.5mm/min to 500mm/min. 10 fibers with known perimeters were tested per velocity for a total of 120 measurements. The rising distance of the stage was set to 5mm for velocities ranging from 0.5mm/min to 50mm/min and to 20mm for velocities ranging from 100mm/min to 500mm/min to obtain sufficient data. For every measurement, fibers were cleaned and fresh water was used to avoid contamination.


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3.0x10-3

3.0x10-3

(a)

original cycle 1 revised cycle 2 revised cycle 3

(b)

-3

2.5x10

2.5x10-3

2.0x10-3

1.5x10-3

Force(mN)

cycle 1 cycle 2 cycle 3

2.0x10-3

Force(mN)

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1.5x10-3

1.0x10-3

1.0x10-3

5.0x10-4

5.0x10-4

0.0

0.0 0

1

2

3

4

5

0

Position(mm)

1

2

3

4

5

Position(mm)

Figure 5. Typical force measurement curves in water: (a) original curves; (b) revised curves.

A typical dynamic contact angle measurement at a speed of 10mm/min is shown in Figure 5a. At the beginning of the first cycle, the force curve initially shows the same kind of upward trend already observed with hexane. After elevating the stage for about 1.5mm, the fiber contacts the water/air interface. The detected force jumps to a higher steady value from which a dynamic advancing contact angle can be measured until a displacement distance of 5mm. The reverse process then takes place (the vessel holder goes down) and a steady receding force can be measured. A stable force is also detected when the fiber moves out of the water. This force, which is higher than the pre-force, is hereafter named “post-force”. The initial force of the next cycle (i.e. the pre-force of the 2nd cycle) appears to have exactly the same value as the post-force of the first cycle, as shown in Figure 5a. The pre- and post-force values were large enough compared to the real capillary forces that they can significantly impact the contact angle values. Therefore, also here a correction was made to the force measured by the tensiometer. For the first cycle, the pre-force goes up for the whole advancing contact angle test process whether the fiber contacts the liquid or not. Due to this, the actual capillary force cannot be evaluated. For the second and third cycle, the amplitude of the


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pre-force was stable and then subtracted from the force during immersion, see Figure 5b. This way reliable steady advancing contact angles were obtained for carbon fiber in water. 2.5. Scanning electron microscopy (SEM). After the contact angle measurements, every tested fiber was observed in a FEI XL30 FEG scanning electron microscope to double check the values of the diameters obtained with the K100SF tensiometer. The fibers were dried to remove the water on the surface and then attached by double-sided adhesive tape on the SEM stage. The immersed sections were imaged at a magnification of 5000x under a voltage of 12kV. Three pictures were taken over the length of the immersed sections of the carbon fibers and diameters were measured at 3 different locations for each picture. 2.6. Molecular-kinetic theory (MKT). To model the contact line motion during wetting, the MKT,35, 46 considers a dissipation process occurring close to the contact line where liquid atoms jump on the solid surface from one adsorption site to another. This dissipation is caused by the

(

)

0 wetting driving force, i.e. the out-of-balance Young’s force γ LV cos θ − cos θ where θ 0 is the

static contact angle.47 In its general form, the MKT predicts the following relationship between the static and dynamic wetting properties: γ λ 2  V = 2κ 0 λ sinh  LV ( cos θ 0 − cos θ )   2 k BT  where λ is the atomistic jump length, κ0 is the atomistic jump frequency, V is the contact line velocity, k B is the Boltzmann’s constant, and T is the temperature (K). The MKT is not the only available theoretical description; the hydrodynamic approach, the combined models of De Ruijter and Petrov, and the Shikhmurzaev’s formula also describe the


(5)

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dynamic wetting properties.34 However for low viscosity liquids like water, the MKT demonstrated its ability to accurately describe the motion of the contact line around a fiber.37 The purpose is here to check if the experimental dynamic wetting data can be modelled by such standard approach.8 If successful, this fitting procedure would support the experimental methodology and give access to θ 0 .34 However, it will neither validate the measurements nor the theory as λ and κ0 are molecular parameters which cannot be measured experimentally. Typical values of around one nanometer for λ and one megahertz for κ0 are however expected.48

3. RESULTS AND DISCUSSION 3.1. Wetted length measurements. Figure 6 shows the force curves for a single fiber immersed in a vessel filled with n-hexane five times consecutively. For each immersion, a jump in the force is observed. Furthermore, drift forces significantly decrease when repeating the wetting experiment. It is attributed to the saturation of adsorption of n-hexane onto the fiber. The average result of diameter measurements for this fiber is 7.24±0.22µm (Table 3).The result shows that the average diameter is close to the expected value of 7µm and the standard deviation is small. Moreover, it indicates that the measured fiber diameters do not depend on the level of adsorption.


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Force(mN)

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-3

2.5x10

-3

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1st Measurement 2nd Measurement 3rd Measurement 4th Measurement 5th Measurement

0.0 0

1

2

3

4

5

Position(mm)

Figure 6.Multiple wetted length measurements for one carbon fiber in n-hexane. Table 3. Carbon fiber diameters obtained from Figure 6. Testing sequence Average Standard deviation 1 2 3 4 5 Diameter (µm)

7.43

7.4

6.94

7.36

7.07

7.24

0.22

Figure 7a shows a SEM picture of a fiber, exhibiting a rough, ditch-like structured surface with particles of dried sizing agents (marked by an arrow). These defects not only locally change the fiber diameter, but could serve as anchor points pinning the contact line and affecting the capillary force measurements. More importantly, the macroscopic morphology of the sample shows some variation in diameter (Figure 7b). Differences in two measured diameters (D1:6.59µm and D2: 6.10µm), though quite small, could be sufficient to induce different locally determined contact angles, especially when receding contact angle measurements are considered (see Section 2.2).


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(a)

(b)

Figure 7. SEM image of surface of a single carbon fiber: image (a) showing defects marked by an arrow; image (b) showing the variation of the diameter for one fiber.

The wetted diameters of 20 carbon fibers obtained from both the tensiometer and SEM are shown in Figure 8. There is a good agreement between the average results obtained from the SEM method (6.83 ± 0.44 µm) and the tensiometer method (7.13 ± 0.44 µm). However, most results of the image analysis are lower than those obtained with the tensiometer. A possible explanation for this variation is that the roughness of the fiber observed in Figure 7 leads to slightly higher perimeters detected by the tensiometer but not reflected by the projected diameters obtained in the SEM. In addition, for the implemented tensiometer method, we only can get local perimeters or diameters. Hence, we selected the diameters obtained from the image analysis technique to calculate the contact angles with water.


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10

SEM Tensiometer

9 8 7

Diameter(µm)

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6 5 4 3 2 1 0 0

5

10

15

20

mean value

Sample number

Figure 8.Comparison of carbon fiber diameters obtained from the tensiometer and by SEM.

3.2. Contact angle measurements. As discussed in Section 2.4, quantifying stable force values when the fiber is not yet (advancing phase, pre-force) or not anymore (receding phase, post-force) in contact with water is needed to correct the capillary forces as illustrated in Figure 5. The same phenomenon can be observed for each test velocity. Average stable pre- and postforce values as a function of contact line velocity for 10 tested fibers are shown in Figure 9. The results indicate that the values of these forces are not randomly distributed, but are speeddependent for both advancing and receding phases. As the contact line velocity increases, the preand post- forces show a linear increasing trend towards respectively negative and positive values. They are explainable as the effect of air flow when the stage moves up and down. At low velocities, pre- and post-forces are distributed around 5x10-4mN which is likely to be overlooked but remains important when single fibers are tested.


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2.0x10-3

Pre-force (advancing) Post-force (receding)

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1.0x10-3 5.0x10-4

Force(mN)

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0.0 -5.0x10-4 -1.0x10-3 -1.5x10-3 -2.0x10-3 0

100

200

300

400

500

Velocity(mm/min)

Figure 9. Pre- (Advancing) and post-force (Receding) values as a function of the contact line velocity.

To have a better overview of the wettability of a single fiber, the distribution of contact angles of every tested fiber is then calculated taking into consideration the measurement of the precise wetted perimeter and corrections to the capillary forces obtained from the tensiometer. Dynamic advancing contact angles show finite values, the receding ones have basically values fluctuating between 20º and 0º regardless of the contact line velocity. A typical curve of receding contact angles versus position at 0.5mm/min is shown in Figure 10. Even though forces were very carefully measured, the sensitivity of the tensiometer is not good enough as very high accuracy is required to obtain reliable small contact angles (see Section 2.2). That is why only advancing contact angles are shown in this research. Figure 11 shows the typical advancing contact angle distributions at the lowest and highest velocities (0.5mm/min and 500mm/min), which were fitted by a Gaussian distribution (eq 6) with the values of the fitted parameters given in Table 4.

y = y0 + Ae

−

( x − xc )2

(6)

2ω 2


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where x is the advancing contact angle (º), y is the count, y0 is the offset, xc is the central position of the peak (º), ω is the width of the distribution, and A is the amplitude of the distribution. It can be seen that the width of the curves becomes narrower with increasing contact line velocities. This implicates that the distribution of dynamic contact angles is more concentrated at high velocity. An explanation for higher spread at lower velocity is that typically lower contact angles are presented at lower velocities (see e.g. the MKT analysis), which are more easily to be influenced by slight variations of the measured forces or/and wetted length (see section 2.2). Also, all the contact values follow Gaussian distributions which indicate the correctness of the measurements. 60

Dynamic receding contact angle(°)

50

0.5 mm/min 40 30 20 10 0 -10 0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

Position(mm)

Figure 10. Typical dynamic receding contact angles versus position at 0.5mm/min. 35% 30%

35%

(a)

30%

(b)

Velocity=0.5mm/min 25%

25%

Relative Frequency

Relative Frequency

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

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20% 15% 10% 5%

20%

Velocity=500mm/min

15% 10% 5%

0% 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110

Dynamic advancing contact angle(°)

0% 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110

Dynamic avancing contact angle(°)

Figure 11.Typical dynamic advancing contact angle distributions: (a) at 0.5mm/min; (b) at 500mm/min.


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Table 4. Parameters of distribution fitting for dynamic advancing contact angles. Velocity(mm/min) 0.5 1 2 5 10 20 50 100 200 300 Data points** 4740 10038 6804 6768 4381 1890 1114 1065 569 473 xc(º) 69.0 68.5 71.4 70.7 71.2 73.9 81.2 85.6 88.9 90.4 ω 5.6 5.9 4.1 7.3 8.5 7.4 2.6 2.8 3.2 3.5 0.97 0.96 0.97 0.92 0.80 0.71 0.95 0.93 0.98 0.95 Adj. R-Square* * Adjusted coefficient of determination which indicates how well data fit a statistical model **

400 348 90.8 3.6 0.96

500 291 91.6 4.7 0.85

Number of individual contact angle measurements obtained from the tensiometer

After averaging the tested values for each velocity, the dynamic advancing contact angles as a function of the contact line velocity are shown in Figure 12. The contact angles vary from 65.7±10.0º to 92.0±4.8º in water with increasing wetting velocity. The same relation between the advancing contact angles and the contact line velocity has already been observed for other types of fibers.10, 38 100 95 90 85 80

85

75

80

70

75

Advancing contact angle(°)


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

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65 60 55

70

65

60

50

55

45

50 0

5

10

15

20

25

Velocity(mm/min)

40 0

50

100

150

200

250

300

350

400

450

500

550

Velocity(mm/min)

Figure 12.Dynamic advancing contact angle at various measurement velocities. The inset zooms in on the low velocities.

3.3. Dynamic contact angle modelling. The modelling of the contact angle dynamics was carried out with the G-Dyna software 49 so that the quality of the fit and the distributions of the free parameters, i.e. κ0, λ and θ 0 , can be obtained and their consistency evaluated.10 Figure 13a


Langmuir

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

shows that the experimental data can be modelled by the MKT quite well. The distributions for

λ and θ 0 are narrow whereas the κ0 values shows a wider distribution (see Figure 13). However, the calculation of a simple average and its associated standard deviation remains meaningful and is presented in Table 5. There is no known previous report about the MKT parameters for carbon fibers. However, these results are consistent with those published for Nylon 38 and PET 48 fibers. More interestingly, this fitting procedure also provides a value for θ 0 of 65.8±2.9º. This is a key parameter to determine the surface energy components 34 of the fiber and will be further developed in a forthcoming article. The model also indicates that the dynamic contact angles measured at low velocities, from 0.5mm/min to 20mm/min, are not dissimilar to the static value. It means that dynamic contact angles measured within this range of velocity can be used to calculate the surface energy components of the carbon fibers investigated in this research. A similar behavior was obtained in previous publications for bamboo fibers.10, 50 For the higher velocities, the contact angles are too far from the static value. Low velocities were also used to measure static contact angles between T300 carbon fiber and water in other studies (62.5º,16 71.70±3.06º 17 and 75.1±2.4º 20).


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Page 21 of 26

(a)

90

80

80

Advancing contact angle(°)


100

70

60

70

60

★data from reference [16] ■ data from reference [17] ▲ data from reference [20]

50 50 0

10

20

30

Velocity(mm/min)

40 0

200

100

500

400

300

Velocity(mm/min)

1.4 1.3 1.2

4 λ (nm)

Frequency count (%)

(c)

(b)

6

2

1.1 1.0 0.9 0.8

0

0.0

0.1

0.2 0.3 0 κ (MHz)

0.4

0.0

0.5

0.1

0.2

0.3

0.4

0.5

0

κ (MHz)

1.4

1.4

(d) 1.3

1.3

1.2

1.2

1.1

1.1

λ (nm)

λ (nm)

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

Langmuir

1.0

1.0

0.9

0.9

0.8

0.8 0

2

4

6

Frequency count (%)

(e)

56 58 60 62 64 66 68 70 72 74 76 78

Static contact angle (°)


Langmuir

(f) 8

Frequency count (%)

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

Page 22 of 26

6

4

2

0

56 58 60 62 64 66 68 70 72 74 76 78

Static contact angle (°)

Figure 13. Dynamic advancing contact angle versus contact line velocity fitted by the MKT. (a): Dynamic advancing contact angle versus contact line velocity. Symbols: Experimental data points (this study and other references). Full line: MKT fit. (b): distribution of κ0. (c): correlation between λ and κ0. (d): distribution of λ . (e): correlation between

λ

and θ 0 . (f): distribution of θ 0 .

Table 5. Average MKT parameters. 0 Liquid κ λ Water

0.15±0.1MHz

1.0±0.08nm

θ0 65.8±2.9º

The MKT fitting is not only a way to model the wetting phenomena but also to show the reliability and accuracy of the presented approach. The MKT provides a good fit to the experimental data, confirming the expected wetting behavior of water on single carbon fiber. The necessary corrections that had to be made to obtain this result, demonstrate that determining wetted length and detected force needs more care when measuring on such fine fibers.

4. CONCLUSION A new method was developed to measure the dynamic contact angles of a single carbon fiber at low and high velocities (0.5mm/min-500mm/min), taking into consideration both the intrinsic variability of the carbon fiber diameter and the extremely small amplitude of the capillary forces. SEM analysis confirmed the accuracy of the wetted length measurement by the modified tensiometer method. The amended capillary force ensures the correct measurement of the calculated contact angles. MKT modelling has been used to closely fit the experimental data,


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Langmuir

demonstrating the effectiveness of the new method and also providing the value of the static contact angle for FT300-3000-40A carbon fiber in de-ionized water (65.8±2.9º). Contact angle values measured at different velocities suggest that dynamic contact angles measured below 20mm/min can be used to calculate the surface energy components of the carbon fibers investigated in this research. In summary, dynamic contact angle tests in water were conducted in a more reliable and accurate way than in previous studies and this will enable better understanding of the wetting behavior of carbon fibers and improve the prospect of employing tensiometry for very fine fibers . The ultimate practical value of this work is to be able to predict and optimize adhesion of a given matrix to carbon fibers, so as to improve the mechanical properties of such composite material.

AUTHOR INFORMATION Corresponding Author *Tel/fax: +86 451 86281403. E-mail: [email protected]

Notes The authors declare no competing ﬁnancial interest.

ACKNOWLEDGMENT This work was supported by the Interuniversity Attraction Poles Programme (IAP 7/38 MicroMAST) initiated by the Belgian Science Policy Office and Si Qiu was also supported by the China Scholarship Council scholarships during his stay in KU Leuven.

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Wettability of a Single Carbon Fiber - Langmuir (ACS Publications)

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