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An alternative method to evaluate the surface free energy of mineral fillers based on the generalized Washburn equation
Construction and Building Materials 231 (2020) 117164
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An alternative method to evaluate the surface free energy of mineral fillers based on the generalized Washburn equation Derun Zhang a,⇑, Rong Luo b a b
Zachry Department of Civil Engineering, Texas A&M University, 3136 TAMU, College Station, TX 77843, USA School of Transportation, Wuhan University of Technology, 1178 Heping Avenue, Wuhan, Hubei Province 430063, China
h i g h l i g h t s Model liquid wicking into capillaries of mineral fillers using generalized Washburn equation. Condition mineral fillers by saturated reference liquid vapors to form a duplex liquid film. Determine resultant effective capillary radius by conducting column wicking test on conditioned mineral fillers. Calculate surface free energy components of mineral fillers based on GvOC model. Evaluate accuracy of measured filler surface free energy by two reference methods.
a r t i c l e
i n f o
Article history: Received 5 May 2019 Received in revised form 26 September 2019 Accepted 4 October 2019
Keywords: Mineral fillers Surface free energy Spreading pressure Generalized Washburn equation Column wicking method
a b s t r a c t This paper presents a new method to measure surface free energy of the mineral fillers. This method takes the generalized Washburn equation as theoretical basis. First, the mineral fillers are conditioned to form a duplex liquid film by saturated reference liquid vapors. The resultant effective capillary radius of the mineral fillers is then measured through the column wicking test of the conditioned mineral fillers using the reference liquid as test probe. After that, three independent liquids are selected to measure their spreading pressures on the mineral fillers based on their column wicking test results along with the measured resultant effective capillary radius. Finally, an equation set based on the Good-van OssChaudhury model is established to compute the surface free energy of the mineral fillers. The newly developed method has been successfully applied to measure the surface free energy for four different types of mineral fillers. Distribution of the three surface energy components and range of the total surface free energy of the selected mineral fillers have been found to be consistent with those reported in literature for the particle aggregates with similar mineralogical composition. Besides, insignificant variation has been identified in each surface energy component of the mineral fillers measured from the new method and from the two references methods. In these regards, this new method can be used as an alternative for accurately measuring the surface free energy of the mineral fillers with simple test technique and high efficiency. Published by Elsevier Ltd.
1. Introduction Mineral fillers are essential components in asphalt mixtures. Their adhesion with asphalt binders has a noticeable impact on the performance of asphalt pavements [1–4]. Such adhesion property is usually quantified through the surface free energy of the mineral fillers and of the asphalt binder [5–10]. For mineral fillers, their surface free energy is in general measured with the column
wicking method [9–11]. The key idea of this method is to correlate the surface free energy of the mineral fillers to the column wicking rate of the test liquid in terms of the imbibition mass m or the penetration height h through a suitable variable. In the traditional column wicking method [12,13], contact angle serves as such a variable to characterize the penetration of the test liquid into the capillary of the tightly packed mineral fillers based on the classical Washburn equation [14]:
h r c cosh ¼ L 2gL t 2
⇑ Corresponding author. E-mail addresses: [email protected] (D. Zhang), [email protected] (R. Luo). https://doi.org/10.1016/j.conbuildmat.2019.117164 0950-0618/Published by Elsevier Ltd.
ð1Þ
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D. Zhang, R. Luo / Construction and Building Materials 231 (2020) 117164
where r is the effective capillary radius of a single capillary of the mineral fillers; cL is the surface tension of the probe liquid; h is the contact angle between the probe liquid and the mineral fillers; and gL is the viscosity of the probe liquid. Obviously, the classical Washburn equation used in the traditional method is applicable to the low surface energy materials for which a stable contact angle of the liquid should be formed. However, it does not hold for the high-energy mineral fillers because the spreading pressure has been identified as the driving force for the liquid rising through the dry filler capillary rather than the capillary pressure induced by the liquid surface tension [15–17], as shown in Fig. 1. Based on this identification, a generalized Washburn equation has been derived by the authors to address any potential wetting behavior of the liquid rising into the capillary of the high-energy powders in the form of imbibition mass m, as expressed in Eq. (2). Note that a linear relationship exists between m2 and t. The detailed derivation can be referred to elsewhere [18,19].
m2 p2 R5e q2L DGSL ¼ t 2gL
ð2Þ
where qL is the liquid density; Re is the resultant effective capillary 2
radius of the high-energy powders, ¼ n5 r; n is the number of parallel capillaries in the cross section of the packed powders; and DGSL is the change of the Gibbs free energy, which serve as the driving force for the liquid penetrating into the capillary of the powders. The change of the Gibbs free energy shown in Eq. (2) depends on the thermodynamic state of both the powders and the test liquid [20]. Thus, the generalized Washburn equation is capable of addressing various wetting cases, such as the spreading wetting, partial wetting and immersional wetting, etc. According to this equation, two methods with different principles have been further put forward by the authors in previous studies to measure the surface free energy of the high-energy mineral fillers, which are termed as the reference method 1 and the reference method 2, respectively. In reference method 1 [19], a liquid is selected as the reference liquid to conduct the vapor adsorption test so as to directly measure its spreading pressure on the mineral fillers. This reference liquid is also used to conduct the column wicking test to measure the slope of m2 =t. With combination of the measured spreading pressure and the slope of m2 =t, the resultant effective capillary radius (Re ) of the mineral fillers can be determined through Eq. (2). In reference method 2 [21], a series of eight aploar liquids are selected to conduct the column wicking test and a parabolic function is then employed to fit the column wicking test results against the square root of the liquid surface tension to determine the resultant effective capillary radius (Re ). Once the resultant effective capillary radius is obtained from either of these two methods, the spreading pressure values of other independent
Powder Wall
2r
ΔGSL
ΔGSL Spreading wetting
Liquid Fig. 1. Test liquid spreading over the capillary wall of high-energy powders.
liquids can be determined from Eq. (2) based on their column wicking test results with respect to the same mineral fillers. With the measured spreading pressure values of at least three test liquids, the surface free energy components of the mineral fillers can be finally computed using the Good-van Oss-Chaudhury (GvOC) model [22,23]:
2cL þ pe ¼ 2
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
LW cLW S cL þ
qffiffiffiffiffiffiffiffiffiffiffiffiffiffi
cSþ cL þ
qffiffiffiffiffiffiffiffiffiffiffiffiffiffi
cS cLþ
ð3Þ
pffiffiffiffiffiffiffiffiffiffiffiffiffiffi AB LW in which cS ¼ cLW cSþ cL . S þ cS ¼ cS þ 2 where c is the total surface free energy; cLW ; cAB ; cLW þ ; c are the apolar, polar, polar acid, and polar base surface free energy component, respectively; and subscripts ‘‘S” and ‘‘L” denote solid and liquid, respectively. The above-mentioned two methods have been demonstrated to be capable of accurately measuring the surface free energy of the mineral fillers, and very little variation has been identified in the same surface free energy component obtained from these two methods [19,21]. However, method 1 consists of a complicated test protocol for both the column wicking test and the vapor adsorption test. Also, this method requires an expense vapor adsorption equipment and high level of expertise. In method 2, a total of at least 10 test liquids are needed to conduct the column wicking test, which involves significant cost of labors and time. All these drawbacks are in fact the obstacles for these two methods being used widely. For the purpose of measuring the surface free energy of mineral fillers in a more effective and easier way with simpler test techniques, this paper focuses on developing a new method as an alternative. The newly developed approach will make full use of the generalized Washburn equation as the theoretical basis to determine the resultant effective capillary radius as well as the spreading pressure of liquid-filler. First, the development of the new method is detailed. Then the paper describes the test materials used and the test procedures related to the newly devised method. This is followed by a section that presents the results measured from the new method on typical types of the highenergy mineral fillers as well as the validation of the new method with the two reference methods. The final section summarizes the major findings of this study. 2. Development of the new approach As stated previously [19,21], for the case of a test liquid rising into the capillaries of the dry mineral fillers, the Gibbs free energy change included in Eq. (2) is essentially identical to the spreading pressure, i.e. DGSL ¼ pe . Accordingly, the generalized Washburn equation becomes:
m2 p2 R5e q2L pe ¼ t 2gL
ð4Þ
where pe is the spreading pressure of the mineral fillers with respect to the test liquid. It can be observed that Eq. (4) captures the driving force (i.e. spreading pressure) that contributes to the spreading wetting of the probe liquid on high-energy mineral fillers. Once the spreading pressure is obtained from this equation, the surface free energy of the high-energy mineral fillers can be calculated using Eq. (3) along with the known surface free energy of the test liquid. However, in Eq. (4) besides pe also Re is unknown and has to be determined. Physically, for a given type of powder, its resultant effective capillary radius Re is only related to the porosity of the packing in the powder column and independent of the liquid selected [24,25]. Thus, it is reasonable to select a reference liquid to measure Re and then select three independent liquids to determine the spreading pressure pe and the surface free energy of the mineral fillers.
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For this purpose, a new method is proposed, which is composed of the following three major steps.
Duplex Liquid Film
The critical step of measuring Re of the mineral fillers is to condition the dry high-energy mineral fillers with vapors of a reference liquid. As presented in Fig. 2, the mineral fillers are conditioned in a vacuum desiccator through saturation by the reference fluid vapor molecules. Due to the surface free energy interaction, the vapor molecules are continuously adsorbed by the high-energy mineral fillers until the mass of the mineral fillers remains unchanged. Up to that point, the adsorption equilibrium is considered to reach and a duplex liquid film is assumed to be formed on the surface of high-energy mineral fillers. After saturation conditioning, the total surface free energy of the mineral fillers changes from cS to cSV due to the presence of duplex liquid film [26,27]. These conditioned mineral fillers are then used to conduct the column wicking test with the reference liquid as the test probe to measure the slope of m2 =t. As illustrated in Fig. 3, when the reference liquid wicks such conditioned mineral fillers, the spreading wetting behavior can still be observed at
Powder Wall
2.1. Measure Re of the mineral fillers with a reference liquid
ΔGSL= γL
γL Spreading wetting
Liquid Fig. 3. Wicking of reference liquid into conditioned mineral fillers.
pe ¼
m2 2gL t p2 R5e q2L
ð8Þ
2.3. Determine the surface free energy of the mineral fillers
h ¼ 0 . However, the Gibbs free energy of the system alters from the spreading pressure to the liquid surface tension due to the thermodynamic state change of the mineral fillers [28,29], as given by:
DGSL ¼ cSV cSL ¼ cL
ð5Þ
where cSV is the total surface energy of mineral fillers in equilibrium with reference liquid vapor; and cSL is the interfacial free energy of the liquid-filler. By substituting Eq. (5) into Eq. (2) yields:
m2 p2 R5e q2L cL ¼ t 2gL
ð6Þ
Eq. (6) is the constitutive equation for the liquid wicking the mineral fillers covered by a duplex liquid film. By rearranging this equation, Re can be then calculated through:
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2gL 5 m Re ¼ t p2 q2L cL 2.2. Calculate liquids
Subsequent to the completion of measuring Re , three independent liquids are selected to perform the column wicking test on the same dry mineral fillers to measure the slope of m2 =t. Then the spreading pressure pe of each liquid with respect to the same mineral fillers can be calculated through:
Duplex Liquid Film
3. Experimental 3.1. Test materials
ð7Þ
pe of the mineral fillers with three independent probe
Desiccator
Substituting the three calculated values of the spreading pressure pe into Eq. (3), the surface free energy components of the mineral fillers can be finally determined. In summary, the method proposed in this section fully captures the mechanism of the spreading wetting behavior of the probe liquid on the mineral fillers so that it has capability to accurately measure the surface free energy for the mineral fillers. As compared to the traditional methods, it has an advantage of determining the resultant effective capillary radius by changing the thermodynamic state of the mineral fillers with a single selected reference liquid. A flowchart illustrating the application of this method is summarized in Fig. 4.
Saturated Vapor Molecules Mineral Fillers
Reference Liquid Fig. 2. Conditioning mineral fillers with saturated reference liquid vapors.
Four types of mineral fillers are selected as the test samples, including limestone, diabase, gravel and amphibolite. All these mineral fillers are crushed from the stones, which have distinct mineralogical compositions as well as an average particle size of 69 ± 6 mm. It is worth to note that all the selected mineral fillers have been used in the reference methods and have been identified as the high-energy powders [19,21]. In addition, four liquids (i.e. toluene, n-hexane, methyl propyl ketone (MPK), and formamide) with distinct surface energy components are used as the probe liquids. Table 1 lists the physical properties of these liquids at 20 °C [30,31]. Among them, toluene is designated as the reference liquid to measure Re of the mineral fillers in the proposed method due to the following two reasons. First, this liquid can easily form a duplex liquid film on the mineral fillers due to its relatively high volatility and low surface tension. Second, toluene has been commonly used as one of the probe vapors in the vapor adsorption test for directly measuring the spreading pressure of the solid [22,23,32], which will facilitate the comparison between the new method and the reference method 1. 3.2. Test procedures and raw test data Prior to the column wicking test, test samples are dried at 150 °C for at least 8 h and then pre-treated through the following two ways:
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Selection of a reference liquid Generalized Washburn equation (Eq. 2) Measurement of m2/t of mineral fillers
Mineral fillers conditioned with reference liquid
Column wicking test on conditioned mineral fillers
Computation of Re of mineral fillers (Eq. 7) Selection of three independent probe liquids
Measurement of m2/t of mineral fillers
Column wicking test on dry mineral fillers
Calculation of πe of mineral fillers (Eq. 8) Determination of surface free energy of mineral fillers (Eq. 3) Fig. 4. Flowchart of determining surface free energy of mineral fillers.
Table 1 Properties of four probe liquids 20 °C [30] Probe Liquid
Toluene n-Hexane MPK Formamide
Surface free energy (103 J/m2)
cLW L
cLþ
cL
cAB L
cL
28.3 18.4 21.7 39.0
0 0 0 2.28
2.7 0 19.2 39.6
0 0 0 19.0
28.3 18.4 21.7 58.0
Drying: As shown in Fig. 5(a), Mineral fillers are stored in a sealed desiccator with phosphorus pentoxide (P2O5) at 20 °C for at least 12 h; and Conditioning: Mineral fillers are cured in a sealed desiccator with saturated toluene vapors at 20 °C (Fig. 5(b)) until the filler mass remains constant. The mass of mineral fillers that are conditioned with the saturated toluene vapors is continuously monitored to judge whether the conditioning equilibrium is achieved. Fig. 6 illustrates the change of the filler mass m with the time t. It is observed that the mass of the conditioned mineral fillers remains constant after 60 h, indicating that adsorption of toluene vapors on mineral fillers
Viscosity gL (103 Pas)
Density qL (g/cm3)
0.590 0.326 0.500 3.607
0.867 0.661 0.809 1.133
has reached steady state and the surface of the mineral fillers has been covered by a duplex liquid film of toluene. After the pre-treatment, the dry and well-conditioned filler samples are used to perform the column wicking test with the aid of a tensiometer (K100, KRÜSS GmbH, Hamburg, Germany). The configuration of this equipment is presented in Fig. 7. As shown in Fig. 8, before each measurement, 5 g of the samples are packed properly into a stainless-steel tube. The tube is then hung vertically onto the electrical balance, while the probe liquid stored in the container is placed inside the thermostat to maintain the liquid temperature at 20 ± 0.5 °C. Once the test starts, the lift is automatically elevated until the base of the tube is dipped 1 mm below the liquid surface. The liquid subsequently penetrates
Desiccator
Desiccator Mineral Fillers P2O5
Mineral Fillers Toluene (a) Drying
(b) Conditioning
Fig. 5. Pre-treatment of mineral fillers in two different ways.
5
110
1.5
100
1.2 Steady state
Limestone Diabase Gravel Amphibolite
90
80
m (g)
m (g)
D. Zhang, R. Luo / Construction and Building Materials 231 (2020) 117164
0.9 0.6 Gravel: Conditioning Amphibilite: Conditioning Gravel: Drying Amphibilite: Drying
0.3
70 0
20
40
60
80 100 120 140 160
t (h)
0 0
Fig. 6. Change of the mass of conditioned mineral fillers with time.
through the filter and the mass gain m of the liquid with time t is constantly recorded by the electric balance and stored through the LabDesk-Software. More detailed procedures of this test can be found in [18]. The column wicking test is repeated three times on each fillerliquid combination. The corresponding raw test data of m versus t for each measurement can be acquired by the data acquisition system of the tensiometer. Fig. 9 presents the raw test data of both dry and conditioned mineral fillers using the reference liquid of toluene as the test probe. It is obvious that the imbibition of the liquid by the conditioned mineral fillers is significantly lower than that by the dry mineral fillers. This is explainable by the fact that
100
200 t (s)
the conditioned mineral fillers have a relatively lower surface free energy due to the adsorption of the reference liquid vapors, thus their interactions with the test liquid are weaker as compared to those between the dry mineral fillers and the same test liquid. 4. Results and discussion The column wicking test is conducted on each type of dry mineral fillers with three probe liquids (i.e. n-hexane, MPK, and
Powder Sample Data Acquisition Probe Liquid Lift
Fig. 7. Configuration of the tensiometer.
(a) Test sample preparation
400
Fig. 9. Adsorbed mass of toluene on two selected mineral fillers.
Electrical Balance Temperature Sensor
300
(b) Samle tube hung on balance
Fig. 8. Test procedures of the column wicking measurement.
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D. Zhang, R. Luo / Construction and Building Materials 231 (2020) 117164
formamide) and on the conditioned mineral fillers with the reference liquid (i.e. toluene). Once obtaining the raw test data of m ~ t, the corresponding slope of m2 =t can be determined by adopting a liner fit. Fig. 10 presents examples of the linearly fitting results of dry mineral filler-toluene. It is clear that values of R2 are all above 0.99, demonstrating an excellent linear relationship between m2 and t. Table 2 summarizes the average slope of m2 =t of each liquid-mineral filler from the three replicates. In order to evaluate the repeatability of this test, the coefficient of variation (CV) is also calculated and included in this table. It can be observed the CV value is very low (less than 5%) for all the measurements which indicates the good repeatability of the test procedure. These measured average slopes will be further utilized to evaluate Re and pe of the mineral fillers. Based on the measured slope of m2 =t of conditioned mineral fillers-toluene, Re of each type of mineral fillers can be computed using Eq. (7). Then the spreading pressure pe of the remaining three probe liquids on the mineral fillers is calculated through Eq. (8). The calculation results are listed in Table 3. It is obvious that with respect to the same type of mineral fillers, the pe value varies with the selected probe liquid and a liquid with larger surface free energy products a higher spreading pressure, which is mainly due to the stronger interaction provide by the higher surface energy liquid with the mineral fillers. 1
y = 0.005326397x - 0.085874823 R² = 0.9999
m2 (g2)
0.8 Limestone Diabase Gravel Amphibolite Linear (Limestone) Linear (Diabase) Linear (Gravel) Linear (Amphibolite)
0.6 y = 0.003406024x - 0.100594470 R² = 0.9987 y = 0.002498313x - 0.091685770 R² = 0.9983
0.4 0.2
y = 0.002795595x - 0.050514849 R² = 0.9996
0 0
100
200
300
400
500
t (s) Fig. 10. Linear fit of m2 versus t of conditioned mineral fillers-toluene.
After determination of spreading pressure pe of the three probe liquids on the selected mineral fillers, the three surface energy þ components (i.e. cLW S ; cS ; cS ) of each type of mineral fillers can be determined in the following order: using the measured pe of the apolar liquid (i.e. n Calculate cLW S hexane) on the mineral fillers through Eq. (9); Compute cSþ based on the measured pe of the unipolar liquid (i.e. MPK) on the mineral fillers via Eq. (10); and Determine c S according to the measured pe of the bipolar liquid (i.e. formamide) on the mineral fillers using Eq. (11).
cLW ¼ S
ðpe þ 2cLa Þ2 4cLa qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2
cSþ
ð9Þ
LW pe þ 2cLu 2 cLW S cLu ¼ 4cLu
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ð10Þ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2
LW pe þ 2cLb 2 cLW cSþ cLb S cLb 2 cS ¼ 4cLb
ð11Þ
where subscripts ‘‘La”, ‘‘Lu”, and ‘‘Lb” stand for apolar, unipolar, and bipolar liquid, respectively. Table 4 summarizes the computed surface free energy of the four selected types of mineral fillers. It is interesting to note all the mineral fillers are identified as having a consistent order in terms of the magnitude of the three surface energy components: the polar-base component (c S ) is predominant, followed by the þ apolar component (cLW S ), and then the polar-acid component (cS ). Also, the measured total surface free energy (cS ) is always above 0.100 J/m2 for all the selected mineral fillers. All these observations are consistent with those reported in literature for the particle aggregates with similar mineralogical composition [33–36]. In order to evaluate the accuracy of the determined surface free energy, the surface free energy of the selected mineral fillers determined from the method developed in this study (terms as the development method) is compared with that measured from the two reference methods. The variation of each surface energy component between the different methods are summarized in Table 5.
Table 2 Measured slope of m2/t from the column wicking test. Probe Liquid
Toluene1 n-Hexane2 MPK2 Formamide2
Parameter
m2/t CV m2/t CV m2/t CV m2/t CV
Unit
103 g2/s % 103 g2/s % 103 g2/s % 103 g2/s %
Mineral Fillers Limestone
Diabase
Gravel
Amphibolite
2.438711 2.51 2.542782 0.97 3.188373 4.28 1.746721 1.80
5.336057 2.28 4.676490 3.16 6.350839 4.44 4.440579 3.64
2.841882 1.63 2.345215 2.95 4.154028 3.21 2.155991 2.88
3.518764 2.78 3.145511 1.26 5.216201 2.29 3.371031 2.74
1 Column wicking test is conducted on the mineral fillers conditioned by the saturated vapor of reference liquid using reference liquid as probe liquid. 2 Column wicking test is conducted on the dry mineral fillers using the corresponding liquid as probe liquid.
Table 3 Calculated Re and
pe from the developed method.
Probe Liquid
Parameter
Unit
Toluene n-Hexane MPK Formamide
Re
104 m 103 J/m2
pe
Mineral Fillers Limestone
Diabase
Gravel
Amphibolite
4.240031 28.05 36.02 72.58
4.958881 23.58 32.79 84.32
4.371863 22.20 40.27 76.87
4.562590 24.05 40.84 97.08
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D. Zhang, R. Luo / Construction and Building Materials 231 (2020) 117164 Table 4 Surface free energy of mineral fillers measured from the developed method. Mineral Fillers
Limestone Diabase Gravel Amphibolite
Surface free energy (103 J/m2)
cLW S
cSþ
cS
cAB S
cS
57.15 49.53 47.30 50.31
1.05 1.47 5.00 4.29
723.99 1035.46 681.53 1062.05
55.19 77.97 116.72 135.03
112.34 127.50 164.02 185.35
Table 5 Comparison of surface free energy between different test methods. Mineral Fillers
Method
Surface free energy (103 J/m2)
cLW S
cSþ
cS
cAB S
cS
Limestone
Developed method Reference method 1 Reference method 2 Variation 1 Variation 2
57.15 57.58 60.61 0.75% 6.05%
1.06 1.06 1.14 0.00% 7.55%
723.99 727.68 753.49 0.51% 4.07%
55.19 55.63 58.70 0.80% 6.36%
112.34 113.21 119.32 0.77% 6.21%
Diabase
Developed method Reference method 1 Reference method 2 Variation 1 Variation 2
49.53 48.35 50.96 2.38% 2.89%
1.47 1.41 1.54 4.08% 4.76%
1035.46 1009.60 1066.61 2.50% 3.01%
77.97 75.38 81.09 3.32% 4.00%
127.50 123.73 132.05 2.96% 3.57%
Gravel
Developed method Reference method 1 Reference method 2 Variation 1 Variation 2
47.30 46.50 48.32 1.69% 2.16%
5.00 4.81 5.24 3.80% 4.80%
681.53 673.23 692.11 1.22% 1.55%
116.72 113.85 120.40 2.46% 3.15%
164.02 160.35 168.72 2.24% 2.87%
Amphibolite
Developed method Reference method 1 Reference method 2 Variation 1 Variation 2
50.31 50.98 53.25 1.33% 5.84%
4.29 4.41 4.81 2.80% 12.12%
1062.05 1076.84 1127.30 1.39% 6.14%
135.03 137.81 147.33 2.06% 9.11%
185.35 188.79 200.58 1.86% 8.22%
It is obvious that with respect to the same type of mineral fillers, the difference of the same surface energy component measured from the three methods that are developed based on different principles is very small and the variation falls within ±10% in most cases (except 12.12% for cSþ of the amphibolite mineral fillers). Considering that the experimental errors may exist in different tests, this level of variable is accepted. Thus, the method developed is validated to be capable of accurately measuring the surface free energy for the mineral fillers.
5. Conclusions This paper focuses on developing a new method for measuring the surface free energy of the mineral fillers in an effective way with simple test technique. This newly developed method takes the generalized Washburn equation as the theoretical basis and consists of the following steps: (1) A reference liquid is first selected to measure the resultant effective capillary radius Re of the mineral fillers. The column wicking test is performed on the conditioned mineral fillers that is covered by a duplex reference liquid film with the reference liquid to measure the slope of m2 =t. Re of the mineral fillers is then calculated using Eq. (7); (2) Three independent liquids are selected as the probe liquids to conduct the column wicking test on the dry mineral fillers to measure the slope of m2 =t. Substituting the calculated Re and the measured slope of m2 =t into Eq. (8), the spreading pressure pe of each liquid on each type of mineral fillers can be then determined; and
(3) With the determined pe of the three independent liquids, the surface free energy of the mineral fillers can be finally solved based on Eqs. (9)–(11). The newly developed method is then used to measure the surface free energy for the four typical types of high-energy mineral fillers. The results show that the distribution of the three surface energy components as well as the range of total surface free energy of the selected mineral fillers are consistent with those reported in literature for the particle aggregates with similar mineralogical composition. The developed method is then validated through comparing its measured surface free energy results with those measured from two reference methods. Insignificant difference of each surface energy component is identified between the different methods. Thus, it is concluded that the method developed in this study can be employed as an alternative to accurately characterize the surface free energy for the high-energy mineral fillers with simple test technique and high efficiency. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgements The authors acknowledge the financial support of the Ministry of Transport of China (Project No. 2014318J22120). Special thanks are to the 1000-Youth Elite Program of China for the start-up funds for purchasing the laboratory equipment that is crucial to this research.
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References [1] P.S. Kandal, C.Y. Lynn, F. Parker, Characterization tests for mineral fillers related to performance of asphalt paving mixtures NCAT Report 98–02, National Center for Asphalt Technology (NCAT)-Auburn University, Auburn, AL, 1998. [2] B. Huang, X. Shu, X. Chen, Effects of mineral fillers on hot-mix asphalt laboratory-measured properties, Int. J. Pavement Eng. 8 (1) (2007) 1–9. [3] C. Villiers, Y. Mehta, M. Tia, R. Roque, B. Dietrich, The importance of mineral filler on construction specifications, Int. J. Pavement Eng. 9 (5) (2008) 343–353. [4] Y. Zhang, T. Ma, M. Ling, et al., Predicting dynamic shear modulus of asphalt mastics using discretized-element simulation and reinforcement mechanisms, J. Mater. Civ. Eng. 31 (8) (2019) 04019163. [5] R. Luo, D. Zhang, Z. Zeng, R.L. Lytton, Effect of surface tension on the measurement of surface energy components of asphalt binders using the Wilhelmy Plate Method, Constr. Build. Mater. 98 (2015) 900–909. [6] D. Zhang, H. Liu, A proposed approach for determining consistent energy parameters based on the surface free energy theory, J. Mater. Civ. Eng. 30 (11) (2018) 04018287. [7] A.E. Alvarez, E. Ovalles, S. Caro, Assessment of the effect of mineral filler on asphalt–aggregate interfaces based on thermodynamic properties, Constr. Build. Mater. 28 (1) (2012) 599–606. [8] A.R. Pasandín, I. Pérez, The influence of the mineral filler on the adhesion between aggregates and bitumen, Int. J. Adhes. Adhes. 58 (2015) 53–58. [9] Y. Tan, M. Guo, Using surface free energy method to study the cohesion and adhesion of asphalt mastic, Constr. Build. Mater. 47 (5) (2013) 254–260. [10] L. Kong, S. Mo, N. Wang, High-temperature performance of asphalt mortar using surface and interface theory, J. Mater. Civ. Eng. 27 (8) (2014). [11] D. Sinkonde, P.W. Hao, Q.Y. Xiao, Evaluate the simple surface energy of aggregates using the capillary rise method, J. Test. Eval. 35 (6) (2007) 618–623. [12] V.C.J. Oss, R.F. Giese, Z. Li, K. Murphy, J. Norris, M.K. Chaudhury, R.J. Good, Determination of contact angles and pore sizes of porous media by column and thin layer wicking, J. Adhes. Sci. Technol. 6 (4) (1992) 413–428. [13] S. Ahadian, M. Mohseni, S. Moradian, Ranking proposed models for attaining surface free energy of mineral fillers using contact angle measurements, Int. J. Adhes. Adhes. 29 (4) (2009) 458–469. [14] E.W. Washburn, The dynamics of capillary flow, Phys. Rev. 17 (3) (1921) 273– 283. [15] L. Holysz, E. Chibowski, Surface free energy components of a-alumina from thin-layer wicking, Langmuir 8 (2) (1992) 717–721. [16] A.O. Ortega, E.J. Jiménez, E. Chibowski, F.G. Caballero, Effect of tannic acid on the surface free energy of polyester dyed with a cationic dye, J. Colloids Interface Sci. 199 (1) (1998) 99–104. [17] L. Ji, B. Shi, A novel method for determining surface free energy of powders using Washburn’s equation without calculating capillary factor and contact angle, Powder Technol. 271 (2015) 88–92.
[18] D. Zhang, R. Luo, Development of a method to determine surface energy components of mineral fillers, Constr. Build. Mater. 146 (2017) 370–380. [19] D. Zhang, R. Luo, Characterization of surface free energy of mineral filler by spreading pressure approach, Constr. Build. Mater. 218 (2019) 126–134. [20] M. Lazghab, K. Saleh, I. Pezron, et al., Wettability assessment of finely divided solids, Powder Technol. 157 (2005) 79–91. [21] D. Zhang, R. Luo, A novel method for measuring surface free energy of highly wettable mineral powders, Constr. Build. Mater. 229 (30) (2019) 116915. [22] D. Zhang, R. Luo, Modeling of adsorption isotherms of probe vapors on aggregates for accurate determination of aggregate surface energy components, Constr. Build. Mater. 134 (2017) 374–387. [23] D. Zhang, R. Luo, Modifying the BET model for accurately determining specific surface area and surface energy components of aggregates, Constr. Build. Mater. 175 (2018) 653–663. [24] L. Galet, S. Patry, J. Dodds, Determination of the wettability of powders by the Washburn capillary rise method with bed preparation by a centrifugal packing technique, J. Colloids Interface Sci. 346 (2010) 470–475. [25] S. Kirdponpattara, M. Phisalaphong, B.Z. Newby, Applicability of Washburn capillary rise for determining contact angles of powders/porous materials, J. Colloids Interface Sci. 397 (2013) 169–176. [26] D.H. Bangham, R.I. Razouk, Adsorption and the wettability of solid surfaces, Trans. Faraday Soc. 33 (1937) 1459–1463. [27] E. Chibowski, L. Holysz, Use of the Washburn equation for surface free energy determination, Langmuir 8 (2) (1992) 710–716. [28] A.W. Adamson, A.P. Gast, Physical Chemistry of Surfaces, sixth ed., John Wiley & Sons Inc, New York, USA, 1997. [29] J.M. Douillard, T. Zoungrana, S. Partyka, Surface Gibbs free energy of minerals: some values, J. Petrol. Sci. Eng. 14 (1) (1995) 51–57. [30] C.J.V. Oss, Interfacial Forces in Aqueous Media, second ed., CRC Press, New York, USA, 2006. [31] W. Xu, R. Luo, K. Zhang, et al., Experimental investigation on preparation and performance of clear asphalt, Int. J. Pavement Eng. 19 (5) (2018) 416–421. [32] D. Zhang, R. Luo, Using the surface free energy (SFE) method to investigate the effects of additives on moisture susceptibility of asphalt mixtures, Int. J. Adhes. Adhes. 95 (2019) 102437. [33] J. Howson, E. Masad, A. Bhasin, et al., Comprehensive analysis of surface free energy of asphalts and aggregates and the effects of changes in pH, Constr. Build. Mater. 25 (2011) 2554–2564. [34] M. Arabani, G.H. Hamedi, Using the surface free energy method to evaluate the effects of polymeric aggregate treatment on moisture damage in hot-mix asphalt, J. Mater. Civ. Eng. 23 (2011) 802–811. [35] G.H. Hamedi, F.M. Nejad, Use of aggregate nanocoating to decrease moisture damage of hot mix asphalt, Road Mater. Pavement Des. (2015), https://doi.org/ 10.1080/14680629.2015.1056215. [36] L.G. Cucalon, A. Bhasin, E. Kassem, et al., Physicochemical characterization of binder-aggregate adhesion varying with temperature and moisture, J. Trans. Eng., Part B: Pavements (2017), https://doi.org/10.1061/JPEODX.0000001.
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Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat
An alternative method to evaluate the surface free energy of mineral fillers based on the generalized Washburn equation Derun Zhang a,⇑, Rong Luo b a b
Zachry Department of Civil Engineering, Texas A&M University, 3136 TAMU, College Station, TX 77843, USA School of Transportation, Wuhan University of Technology, 1178 Heping Avenue, Wuhan, Hubei Province 430063, China
h i g h l i g h t s Model liquid wicking into capillaries of mineral fillers using generalized Washburn equation. Condition mineral fillers by saturated reference liquid vapors to form a duplex liquid film. Determine resultant effective capillary radius by conducting column wicking test on conditioned mineral fillers. Calculate surface free energy components of mineral fillers based on GvOC model. Evaluate accuracy of measured filler surface free energy by two reference methods.
a r t i c l e
i n f o
Article history: Received 5 May 2019 Received in revised form 26 September 2019 Accepted 4 October 2019
Keywords: Mineral fillers Surface free energy Spreading pressure Generalized Washburn equation Column wicking method
a b s t r a c t This paper presents a new method to measure surface free energy of the mineral fillers. This method takes the generalized Washburn equation as theoretical basis. First, the mineral fillers are conditioned to form a duplex liquid film by saturated reference liquid vapors. The resultant effective capillary radius of the mineral fillers is then measured through the column wicking test of the conditioned mineral fillers using the reference liquid as test probe. After that, three independent liquids are selected to measure their spreading pressures on the mineral fillers based on their column wicking test results along with the measured resultant effective capillary radius. Finally, an equation set based on the Good-van OssChaudhury model is established to compute the surface free energy of the mineral fillers. The newly developed method has been successfully applied to measure the surface free energy for four different types of mineral fillers. Distribution of the three surface energy components and range of the total surface free energy of the selected mineral fillers have been found to be consistent with those reported in literature for the particle aggregates with similar mineralogical composition. Besides, insignificant variation has been identified in each surface energy component of the mineral fillers measured from the new method and from the two references methods. In these regards, this new method can be used as an alternative for accurately measuring the surface free energy of the mineral fillers with simple test technique and high efficiency. Published by Elsevier Ltd.
1. Introduction Mineral fillers are essential components in asphalt mixtures. Their adhesion with asphalt binders has a noticeable impact on the performance of asphalt pavements [1–4]. Such adhesion property is usually quantified through the surface free energy of the mineral fillers and of the asphalt binder [5–10]. For mineral fillers, their surface free energy is in general measured with the column
wicking method [9–11]. The key idea of this method is to correlate the surface free energy of the mineral fillers to the column wicking rate of the test liquid in terms of the imbibition mass m or the penetration height h through a suitable variable. In the traditional column wicking method [12,13], contact angle serves as such a variable to characterize the penetration of the test liquid into the capillary of the tightly packed mineral fillers based on the classical Washburn equation [14]:
h r c cosh ¼ L 2gL t 2
⇑ Corresponding author. E-mail addresses: [email protected] (D. Zhang), [email protected] (R. Luo). https://doi.org/10.1016/j.conbuildmat.2019.117164 0950-0618/Published by Elsevier Ltd.
ð1Þ
2
D. Zhang, R. Luo / Construction and Building Materials 231 (2020) 117164
where r is the effective capillary radius of a single capillary of the mineral fillers; cL is the surface tension of the probe liquid; h is the contact angle between the probe liquid and the mineral fillers; and gL is the viscosity of the probe liquid. Obviously, the classical Washburn equation used in the traditional method is applicable to the low surface energy materials for which a stable contact angle of the liquid should be formed. However, it does not hold for the high-energy mineral fillers because the spreading pressure has been identified as the driving force for the liquid rising through the dry filler capillary rather than the capillary pressure induced by the liquid surface tension [15–17], as shown in Fig. 1. Based on this identification, a generalized Washburn equation has been derived by the authors to address any potential wetting behavior of the liquid rising into the capillary of the high-energy powders in the form of imbibition mass m, as expressed in Eq. (2). Note that a linear relationship exists between m2 and t. The detailed derivation can be referred to elsewhere [18,19].
m2 p2 R5e q2L DGSL ¼ t 2gL
ð2Þ
where qL is the liquid density; Re is the resultant effective capillary 2
radius of the high-energy powders, ¼ n5 r; n is the number of parallel capillaries in the cross section of the packed powders; and DGSL is the change of the Gibbs free energy, which serve as the driving force for the liquid penetrating into the capillary of the powders. The change of the Gibbs free energy shown in Eq. (2) depends on the thermodynamic state of both the powders and the test liquid [20]. Thus, the generalized Washburn equation is capable of addressing various wetting cases, such as the spreading wetting, partial wetting and immersional wetting, etc. According to this equation, two methods with different principles have been further put forward by the authors in previous studies to measure the surface free energy of the high-energy mineral fillers, which are termed as the reference method 1 and the reference method 2, respectively. In reference method 1 [19], a liquid is selected as the reference liquid to conduct the vapor adsorption test so as to directly measure its spreading pressure on the mineral fillers. This reference liquid is also used to conduct the column wicking test to measure the slope of m2 =t. With combination of the measured spreading pressure and the slope of m2 =t, the resultant effective capillary radius (Re ) of the mineral fillers can be determined through Eq. (2). In reference method 2 [21], a series of eight aploar liquids are selected to conduct the column wicking test and a parabolic function is then employed to fit the column wicking test results against the square root of the liquid surface tension to determine the resultant effective capillary radius (Re ). Once the resultant effective capillary radius is obtained from either of these two methods, the spreading pressure values of other independent
Powder Wall
2r
ΔGSL
ΔGSL Spreading wetting
Liquid Fig. 1. Test liquid spreading over the capillary wall of high-energy powders.
liquids can be determined from Eq. (2) based on their column wicking test results with respect to the same mineral fillers. With the measured spreading pressure values of at least three test liquids, the surface free energy components of the mineral fillers can be finally computed using the Good-van Oss-Chaudhury (GvOC) model [22,23]:
2cL þ pe ¼ 2
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
LW cLW S cL þ
qffiffiffiffiffiffiffiffiffiffiffiffiffiffi
cSþ cL þ
qffiffiffiffiffiffiffiffiffiffiffiffiffiffi
cS cLþ
ð3Þ
pffiffiffiffiffiffiffiffiffiffiffiffiffiffi AB LW in which cS ¼ cLW cSþ cL . S þ cS ¼ cS þ 2 where c is the total surface free energy; cLW ; cAB ; cLW þ ; c are the apolar, polar, polar acid, and polar base surface free energy component, respectively; and subscripts ‘‘S” and ‘‘L” denote solid and liquid, respectively. The above-mentioned two methods have been demonstrated to be capable of accurately measuring the surface free energy of the mineral fillers, and very little variation has been identified in the same surface free energy component obtained from these two methods [19,21]. However, method 1 consists of a complicated test protocol for both the column wicking test and the vapor adsorption test. Also, this method requires an expense vapor adsorption equipment and high level of expertise. In method 2, a total of at least 10 test liquids are needed to conduct the column wicking test, which involves significant cost of labors and time. All these drawbacks are in fact the obstacles for these two methods being used widely. For the purpose of measuring the surface free energy of mineral fillers in a more effective and easier way with simpler test techniques, this paper focuses on developing a new method as an alternative. The newly developed approach will make full use of the generalized Washburn equation as the theoretical basis to determine the resultant effective capillary radius as well as the spreading pressure of liquid-filler. First, the development of the new method is detailed. Then the paper describes the test materials used and the test procedures related to the newly devised method. This is followed by a section that presents the results measured from the new method on typical types of the highenergy mineral fillers as well as the validation of the new method with the two reference methods. The final section summarizes the major findings of this study. 2. Development of the new approach As stated previously [19,21], for the case of a test liquid rising into the capillaries of the dry mineral fillers, the Gibbs free energy change included in Eq. (2) is essentially identical to the spreading pressure, i.e. DGSL ¼ pe . Accordingly, the generalized Washburn equation becomes:
m2 p2 R5e q2L pe ¼ t 2gL
ð4Þ
where pe is the spreading pressure of the mineral fillers with respect to the test liquid. It can be observed that Eq. (4) captures the driving force (i.e. spreading pressure) that contributes to the spreading wetting of the probe liquid on high-energy mineral fillers. Once the spreading pressure is obtained from this equation, the surface free energy of the high-energy mineral fillers can be calculated using Eq. (3) along with the known surface free energy of the test liquid. However, in Eq. (4) besides pe also Re is unknown and has to be determined. Physically, for a given type of powder, its resultant effective capillary radius Re is only related to the porosity of the packing in the powder column and independent of the liquid selected [24,25]. Thus, it is reasonable to select a reference liquid to measure Re and then select three independent liquids to determine the spreading pressure pe and the surface free energy of the mineral fillers.
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D. Zhang, R. Luo / Construction and Building Materials 231 (2020) 117164
For this purpose, a new method is proposed, which is composed of the following three major steps.
Duplex Liquid Film
The critical step of measuring Re of the mineral fillers is to condition the dry high-energy mineral fillers with vapors of a reference liquid. As presented in Fig. 2, the mineral fillers are conditioned in a vacuum desiccator through saturation by the reference fluid vapor molecules. Due to the surface free energy interaction, the vapor molecules are continuously adsorbed by the high-energy mineral fillers until the mass of the mineral fillers remains unchanged. Up to that point, the adsorption equilibrium is considered to reach and a duplex liquid film is assumed to be formed on the surface of high-energy mineral fillers. After saturation conditioning, the total surface free energy of the mineral fillers changes from cS to cSV due to the presence of duplex liquid film [26,27]. These conditioned mineral fillers are then used to conduct the column wicking test with the reference liquid as the test probe to measure the slope of m2 =t. As illustrated in Fig. 3, when the reference liquid wicks such conditioned mineral fillers, the spreading wetting behavior can still be observed at
Powder Wall
2.1. Measure Re of the mineral fillers with a reference liquid
ΔGSL= γL
γL Spreading wetting
Liquid Fig. 3. Wicking of reference liquid into conditioned mineral fillers.
pe ¼
m2 2gL t p2 R5e q2L
ð8Þ
2.3. Determine the surface free energy of the mineral fillers
h ¼ 0 . However, the Gibbs free energy of the system alters from the spreading pressure to the liquid surface tension due to the thermodynamic state change of the mineral fillers [28,29], as given by:
DGSL ¼ cSV cSL ¼ cL
ð5Þ
where cSV is the total surface energy of mineral fillers in equilibrium with reference liquid vapor; and cSL is the interfacial free energy of the liquid-filler. By substituting Eq. (5) into Eq. (2) yields:
m2 p2 R5e q2L cL ¼ t 2gL
ð6Þ
Eq. (6) is the constitutive equation for the liquid wicking the mineral fillers covered by a duplex liquid film. By rearranging this equation, Re can be then calculated through:
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2gL 5 m Re ¼ t p2 q2L cL 2.2. Calculate liquids
Subsequent to the completion of measuring Re , three independent liquids are selected to perform the column wicking test on the same dry mineral fillers to measure the slope of m2 =t. Then the spreading pressure pe of each liquid with respect to the same mineral fillers can be calculated through:
Duplex Liquid Film
3. Experimental 3.1. Test materials
ð7Þ
pe of the mineral fillers with three independent probe
Desiccator
Substituting the three calculated values of the spreading pressure pe into Eq. (3), the surface free energy components of the mineral fillers can be finally determined. In summary, the method proposed in this section fully captures the mechanism of the spreading wetting behavior of the probe liquid on the mineral fillers so that it has capability to accurately measure the surface free energy for the mineral fillers. As compared to the traditional methods, it has an advantage of determining the resultant effective capillary radius by changing the thermodynamic state of the mineral fillers with a single selected reference liquid. A flowchart illustrating the application of this method is summarized in Fig. 4.
Saturated Vapor Molecules Mineral Fillers
Reference Liquid Fig. 2. Conditioning mineral fillers with saturated reference liquid vapors.
Four types of mineral fillers are selected as the test samples, including limestone, diabase, gravel and amphibolite. All these mineral fillers are crushed from the stones, which have distinct mineralogical compositions as well as an average particle size of 69 ± 6 mm. It is worth to note that all the selected mineral fillers have been used in the reference methods and have been identified as the high-energy powders [19,21]. In addition, four liquids (i.e. toluene, n-hexane, methyl propyl ketone (MPK), and formamide) with distinct surface energy components are used as the probe liquids. Table 1 lists the physical properties of these liquids at 20 °C [30,31]. Among them, toluene is designated as the reference liquid to measure Re of the mineral fillers in the proposed method due to the following two reasons. First, this liquid can easily form a duplex liquid film on the mineral fillers due to its relatively high volatility and low surface tension. Second, toluene has been commonly used as one of the probe vapors in the vapor adsorption test for directly measuring the spreading pressure of the solid [22,23,32], which will facilitate the comparison between the new method and the reference method 1. 3.2. Test procedures and raw test data Prior to the column wicking test, test samples are dried at 150 °C for at least 8 h and then pre-treated through the following two ways:
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D. Zhang, R. Luo / Construction and Building Materials 231 (2020) 117164
Selection of a reference liquid Generalized Washburn equation (Eq. 2) Measurement of m2/t of mineral fillers
Mineral fillers conditioned with reference liquid
Column wicking test on conditioned mineral fillers
Computation of Re of mineral fillers (Eq. 7) Selection of three independent probe liquids
Measurement of m2/t of mineral fillers
Column wicking test on dry mineral fillers
Calculation of πe of mineral fillers (Eq. 8) Determination of surface free energy of mineral fillers (Eq. 3) Fig. 4. Flowchart of determining surface free energy of mineral fillers.
Table 1 Properties of four probe liquids 20 °C [30] Probe Liquid
Toluene n-Hexane MPK Formamide
Surface free energy (103 J/m2)
cLW L
cLþ
cL
cAB L
cL
28.3 18.4 21.7 39.0
0 0 0 2.28
2.7 0 19.2 39.6
0 0 0 19.0
28.3 18.4 21.7 58.0
Drying: As shown in Fig. 5(a), Mineral fillers are stored in a sealed desiccator with phosphorus pentoxide (P2O5) at 20 °C for at least 12 h; and Conditioning: Mineral fillers are cured in a sealed desiccator with saturated toluene vapors at 20 °C (Fig. 5(b)) until the filler mass remains constant. The mass of mineral fillers that are conditioned with the saturated toluene vapors is continuously monitored to judge whether the conditioning equilibrium is achieved. Fig. 6 illustrates the change of the filler mass m with the time t. It is observed that the mass of the conditioned mineral fillers remains constant after 60 h, indicating that adsorption of toluene vapors on mineral fillers
Viscosity gL (103 Pas)
Density qL (g/cm3)
0.590 0.326 0.500 3.607
0.867 0.661 0.809 1.133
has reached steady state and the surface of the mineral fillers has been covered by a duplex liquid film of toluene. After the pre-treatment, the dry and well-conditioned filler samples are used to perform the column wicking test with the aid of a tensiometer (K100, KRÜSS GmbH, Hamburg, Germany). The configuration of this equipment is presented in Fig. 7. As shown in Fig. 8, before each measurement, 5 g of the samples are packed properly into a stainless-steel tube. The tube is then hung vertically onto the electrical balance, while the probe liquid stored in the container is placed inside the thermostat to maintain the liquid temperature at 20 ± 0.5 °C. Once the test starts, the lift is automatically elevated until the base of the tube is dipped 1 mm below the liquid surface. The liquid subsequently penetrates
Desiccator
Desiccator Mineral Fillers P2O5
Mineral Fillers Toluene (a) Drying
(b) Conditioning
Fig. 5. Pre-treatment of mineral fillers in two different ways.
5
110
1.5
100
1.2 Steady state
Limestone Diabase Gravel Amphibolite
90
80
m (g)
m (g)
D. Zhang, R. Luo / Construction and Building Materials 231 (2020) 117164
0.9 0.6 Gravel: Conditioning Amphibilite: Conditioning Gravel: Drying Amphibilite: Drying
0.3
70 0
20
40
60
80 100 120 140 160
t (h)
0 0
Fig. 6. Change of the mass of conditioned mineral fillers with time.
through the filter and the mass gain m of the liquid with time t is constantly recorded by the electric balance and stored through the LabDesk-Software. More detailed procedures of this test can be found in [18]. The column wicking test is repeated three times on each fillerliquid combination. The corresponding raw test data of m versus t for each measurement can be acquired by the data acquisition system of the tensiometer. Fig. 9 presents the raw test data of both dry and conditioned mineral fillers using the reference liquid of toluene as the test probe. It is obvious that the imbibition of the liquid by the conditioned mineral fillers is significantly lower than that by the dry mineral fillers. This is explainable by the fact that
100
200 t (s)
the conditioned mineral fillers have a relatively lower surface free energy due to the adsorption of the reference liquid vapors, thus their interactions with the test liquid are weaker as compared to those between the dry mineral fillers and the same test liquid. 4. Results and discussion The column wicking test is conducted on each type of dry mineral fillers with three probe liquids (i.e. n-hexane, MPK, and
Powder Sample Data Acquisition Probe Liquid Lift
Fig. 7. Configuration of the tensiometer.
(a) Test sample preparation
400
Fig. 9. Adsorbed mass of toluene on two selected mineral fillers.
Electrical Balance Temperature Sensor
300
(b) Samle tube hung on balance
Fig. 8. Test procedures of the column wicking measurement.
6
D. Zhang, R. Luo / Construction and Building Materials 231 (2020) 117164
formamide) and on the conditioned mineral fillers with the reference liquid (i.e. toluene). Once obtaining the raw test data of m ~ t, the corresponding slope of m2 =t can be determined by adopting a liner fit. Fig. 10 presents examples of the linearly fitting results of dry mineral filler-toluene. It is clear that values of R2 are all above 0.99, demonstrating an excellent linear relationship between m2 and t. Table 2 summarizes the average slope of m2 =t of each liquid-mineral filler from the three replicates. In order to evaluate the repeatability of this test, the coefficient of variation (CV) is also calculated and included in this table. It can be observed the CV value is very low (less than 5%) for all the measurements which indicates the good repeatability of the test procedure. These measured average slopes will be further utilized to evaluate Re and pe of the mineral fillers. Based on the measured slope of m2 =t of conditioned mineral fillers-toluene, Re of each type of mineral fillers can be computed using Eq. (7). Then the spreading pressure pe of the remaining three probe liquids on the mineral fillers is calculated through Eq. (8). The calculation results are listed in Table 3. It is obvious that with respect to the same type of mineral fillers, the pe value varies with the selected probe liquid and a liquid with larger surface free energy products a higher spreading pressure, which is mainly due to the stronger interaction provide by the higher surface energy liquid with the mineral fillers. 1
y = 0.005326397x - 0.085874823 R² = 0.9999
m2 (g2)
0.8 Limestone Diabase Gravel Amphibolite Linear (Limestone) Linear (Diabase) Linear (Gravel) Linear (Amphibolite)
0.6 y = 0.003406024x - 0.100594470 R² = 0.9987 y = 0.002498313x - 0.091685770 R² = 0.9983
0.4 0.2
y = 0.002795595x - 0.050514849 R² = 0.9996
0 0
100
200
300
400
500
t (s) Fig. 10. Linear fit of m2 versus t of conditioned mineral fillers-toluene.
After determination of spreading pressure pe of the three probe liquids on the selected mineral fillers, the three surface energy þ components (i.e. cLW S ; cS ; cS ) of each type of mineral fillers can be determined in the following order: using the measured pe of the apolar liquid (i.e. n Calculate cLW S hexane) on the mineral fillers through Eq. (9); Compute cSþ based on the measured pe of the unipolar liquid (i.e. MPK) on the mineral fillers via Eq. (10); and Determine c S according to the measured pe of the bipolar liquid (i.e. formamide) on the mineral fillers using Eq. (11).
cLW ¼ S
ðpe þ 2cLa Þ2 4cLa qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2
cSþ
ð9Þ
LW pe þ 2cLu 2 cLW S cLu ¼ 4cLu
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ð10Þ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2
LW pe þ 2cLb 2 cLW cSþ cLb S cLb 2 cS ¼ 4cLb
ð11Þ
where subscripts ‘‘La”, ‘‘Lu”, and ‘‘Lb” stand for apolar, unipolar, and bipolar liquid, respectively. Table 4 summarizes the computed surface free energy of the four selected types of mineral fillers. It is interesting to note all the mineral fillers are identified as having a consistent order in terms of the magnitude of the three surface energy components: the polar-base component (c S ) is predominant, followed by the þ apolar component (cLW S ), and then the polar-acid component (cS ). Also, the measured total surface free energy (cS ) is always above 0.100 J/m2 for all the selected mineral fillers. All these observations are consistent with those reported in literature for the particle aggregates with similar mineralogical composition [33–36]. In order to evaluate the accuracy of the determined surface free energy, the surface free energy of the selected mineral fillers determined from the method developed in this study (terms as the development method) is compared with that measured from the two reference methods. The variation of each surface energy component between the different methods are summarized in Table 5.
Table 2 Measured slope of m2/t from the column wicking test. Probe Liquid
Toluene1 n-Hexane2 MPK2 Formamide2
Parameter
m2/t CV m2/t CV m2/t CV m2/t CV
Unit
103 g2/s % 103 g2/s % 103 g2/s % 103 g2/s %
Mineral Fillers Limestone
Diabase
Gravel
Amphibolite
2.438711 2.51 2.542782 0.97 3.188373 4.28 1.746721 1.80
5.336057 2.28 4.676490 3.16 6.350839 4.44 4.440579 3.64
2.841882 1.63 2.345215 2.95 4.154028 3.21 2.155991 2.88
3.518764 2.78 3.145511 1.26 5.216201 2.29 3.371031 2.74
1 Column wicking test is conducted on the mineral fillers conditioned by the saturated vapor of reference liquid using reference liquid as probe liquid. 2 Column wicking test is conducted on the dry mineral fillers using the corresponding liquid as probe liquid.
Table 3 Calculated Re and
pe from the developed method.
Probe Liquid
Parameter
Unit
Toluene n-Hexane MPK Formamide
Re
104 m 103 J/m2
pe
Mineral Fillers Limestone
Diabase
Gravel
Amphibolite
4.240031 28.05 36.02 72.58
4.958881 23.58 32.79 84.32
4.371863 22.20 40.27 76.87
4.562590 24.05 40.84 97.08
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D. Zhang, R. Luo / Construction and Building Materials 231 (2020) 117164 Table 4 Surface free energy of mineral fillers measured from the developed method. Mineral Fillers
Limestone Diabase Gravel Amphibolite
Surface free energy (103 J/m2)
cLW S
cSþ
cS
cAB S
cS
57.15 49.53 47.30 50.31
1.05 1.47 5.00 4.29
723.99 1035.46 681.53 1062.05
55.19 77.97 116.72 135.03
112.34 127.50 164.02 185.35
Table 5 Comparison of surface free energy between different test methods. Mineral Fillers
Method
Surface free energy (103 J/m2)
cLW S
cSþ
cS
cAB S
cS
Limestone
Developed method Reference method 1 Reference method 2 Variation 1 Variation 2
57.15 57.58 60.61 0.75% 6.05%
1.06 1.06 1.14 0.00% 7.55%
723.99 727.68 753.49 0.51% 4.07%
55.19 55.63 58.70 0.80% 6.36%
112.34 113.21 119.32 0.77% 6.21%
Diabase
Developed method Reference method 1 Reference method 2 Variation 1 Variation 2
49.53 48.35 50.96 2.38% 2.89%
1.47 1.41 1.54 4.08% 4.76%
1035.46 1009.60 1066.61 2.50% 3.01%
77.97 75.38 81.09 3.32% 4.00%
127.50 123.73 132.05 2.96% 3.57%
Gravel
Developed method Reference method 1 Reference method 2 Variation 1 Variation 2
47.30 46.50 48.32 1.69% 2.16%
5.00 4.81 5.24 3.80% 4.80%
681.53 673.23 692.11 1.22% 1.55%
116.72 113.85 120.40 2.46% 3.15%
164.02 160.35 168.72 2.24% 2.87%
Amphibolite
Developed method Reference method 1 Reference method 2 Variation 1 Variation 2
50.31 50.98 53.25 1.33% 5.84%
4.29 4.41 4.81 2.80% 12.12%
1062.05 1076.84 1127.30 1.39% 6.14%
135.03 137.81 147.33 2.06% 9.11%
185.35 188.79 200.58 1.86% 8.22%
It is obvious that with respect to the same type of mineral fillers, the difference of the same surface energy component measured from the three methods that are developed based on different principles is very small and the variation falls within ±10% in most cases (except 12.12% for cSþ of the amphibolite mineral fillers). Considering that the experimental errors may exist in different tests, this level of variable is accepted. Thus, the method developed is validated to be capable of accurately measuring the surface free energy for the mineral fillers.
5. Conclusions This paper focuses on developing a new method for measuring the surface free energy of the mineral fillers in an effective way with simple test technique. This newly developed method takes the generalized Washburn equation as the theoretical basis and consists of the following steps: (1) A reference liquid is first selected to measure the resultant effective capillary radius Re of the mineral fillers. The column wicking test is performed on the conditioned mineral fillers that is covered by a duplex reference liquid film with the reference liquid to measure the slope of m2 =t. Re of the mineral fillers is then calculated using Eq. (7); (2) Three independent liquids are selected as the probe liquids to conduct the column wicking test on the dry mineral fillers to measure the slope of m2 =t. Substituting the calculated Re and the measured slope of m2 =t into Eq. (8), the spreading pressure pe of each liquid on each type of mineral fillers can be then determined; and
(3) With the determined pe of the three independent liquids, the surface free energy of the mineral fillers can be finally solved based on Eqs. (9)–(11). The newly developed method is then used to measure the surface free energy for the four typical types of high-energy mineral fillers. The results show that the distribution of the three surface energy components as well as the range of total surface free energy of the selected mineral fillers are consistent with those reported in literature for the particle aggregates with similar mineralogical composition. The developed method is then validated through comparing its measured surface free energy results with those measured from two reference methods. Insignificant difference of each surface energy component is identified between the different methods. Thus, it is concluded that the method developed in this study can be employed as an alternative to accurately characterize the surface free energy for the high-energy mineral fillers with simple test technique and high efficiency. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgements The authors acknowledge the financial support of the Ministry of Transport of China (Project No. 2014318J22120). Special thanks are to the 1000-Youth Elite Program of China for the start-up funds for purchasing the laboratory equipment that is crucial to this research.
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