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Adhesion force between particles and substrate in a humid atmosphere studied by atomic force microscopy
Advanced Powder Technol., Vol. 17, No. 5, pp. 567– 580 (2006) © VSP and Society of Powder Technology, Japan 2006. Also available online - www.brill.nl/apt
Translated paper SPTJ Best Paper Award ’05 ∗ Adhesion force between particles and substrate in a humid atmosphere studied by atomic force microscopy AKIO FUKUNISHI and YASUSHIGE MORI † Department of Chemical Engineering and Materials Science, Doshisha University, 1-3 Miyakodani, Tatara, Kyotanabe 610-0321, Japan Japanese version published in JSPTJ Vol. 41, No. 3 (2004); English version for APT received 6 May 2006
Abstract—Using an atomic force microscope (AFM), adhesion forces between glass particles or AFM tips and hydrophilic or hydrophobic substrates were measured as a function of relative humidity (RH). The observed adhesion force between the glass particles and the hydrophilic substrate increased with RH due to strong capillary condensation. In contrast, the adhesion force between the glass particles and the hydrophobic substrate was found to be almost constant for all RHs, due to weak capillary condensation. The adhesion force between an AFM tip and a mica plate had a maximum value at a certain RH. This can be evaluated by calculating with consideration for the tip shape. On the other hand, the adhesion force for a silica plate increased drastically over a certain RH and could be explained due to the surface roughness of the silica plate. The presence of nanometer-scale roughness can play a critical role in the absolute value of the adhesion force between an AFM tip and the substrate in a humid atmosphere. Keywords: Adhesion force; atomic force microscope; relative humidity; hydrophilic surface; hydrophobic surface; contact angle; surface roughness.
NOMENCLATURE
A a D Fad Fc
Hamaker constant (J) radius of a sphere (m) diffusion coefficient of a water molecule in air (m2 /s) adhesion force (N) capillary pressure force (N)
∗ The † To
title of the Jotaki Award has been changed to the SPTJ Best Paper Award in 2006. whom correspondence should be addressed. E-mail: [email protected]
568
Fs Fw h M p/ps p R r1 r2 T Vm
A. Fukunishi and Y. Mori
surface tension force (N) van der Waals force (N) separation distance between surfaces (m) molecular weight (kg/mol) relative humidity (—) calippary pressure (Pa) gas constant (J/(K mol)) horizontal distance of meniscus intersection on particle (m) curvature radius of meniscus (m) temperature (K) volume of bridging water (m3 )
Greek α γ θ1 θ2 ρ
filling angle (rad) surface tension of liquid (N/m) contact angle of liquid for particle (rad) contact angle of liquid for substrate (rad) density (kg/m3 )
1. INTRODUCTION
The adhesion phenomena between particles and a wall surface or among particles causes various problems in many powder operations. The adhesion force consists of physical interactions such as van der Waals, electrostatic and capillary forces, and of chemical bonding such as hydrogen bonding. Many researchers have presented experimental and theoretical views to clarify the contribution of those forces and the adhesion mechanism. The experimental approaches for the adhesion force can be divided into the methods for the powder [1, 2] and for a single particle [3]. Recently, a surface force apparatus [4] and an atomic force microscope (AFM) [5 –9] have been used for the direct measurement of the adhesion force (which are classified as belonging to the latter method). The adhesion force under a humid atmosphere is controlled by the capillary force which is generated by condensing water vapor in the gap, so that it becomes a function of the relative humidity (RH). It is reported that the effect of the RH on the adhesion force differs by particle shape [3], size [5], chemical property of the surface [5 –8] or geometric condition of the particle [8, 9]. Xudong et al. [6] reported that the adhesion force between an AFM tip and a smooth silica plate can be predicted by their theory. However, the measurement results of the adhesion force did not always agree with theoretical calculations and this discrepancy was often explained as being due to the surface roughness. Rabinovich et al. [9] proposed
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569
a theoretical formula considering the surface roughness and compared it with the measurement results. In this paper, AFM measurement of the adhesion force with a smooth surface was carried out by changing the contact angle of the plate and the experimental results were compared with the theory of Xudong et al. [6]. The effect of the particle size on the adhesion force was also examined by using a colloid probe instead of a AFM tip.
2. ADHESION FORCE IN A HUMID ATMOSPHERE
The capillary condensation of water vapor in the air occurs in the gap of the spherical particle and the flat plate. As a result, a water bridge is formed between both surfaces as shown in Fig. 1. The adhesion force, F ad , between the particle and the plate under the presence of the water bridge can be expressed by van der Waals force, F W , capillary force, F P , which originates from the internal and external pressure difference in the liquid film, and the force due to surface tension, F S , of a liquid film: Fad = FW + FP + FS .
(1)
The contact radii of the liquid film at the particle, r1 , and the radius of curvature for the liquid surface, r2 , are given by the following equations: r1 = a sin α,
r2 =
h + a(1 − cos α) , cos(θ1 + α) + cos θ2
(2)
where a is the particle radius, α is the filling angle, h is the distance between a particle and substrate, and θ1 and θ2 are contact angles of the liquid with the particle and substrate, respectively.
Figure 1. Schematic illustration of liquid formed between a spherical particle and a flat substrate.
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A. Fukunishi and Y. Mori
The capillary pressure of the liquid, p, as a function of surface tension, γ , is obtained from the Laplace equation: 1 1 p = γ . (3) − r1 r2 The capillary force can be expressed by the cross-section area, π r12 , of the contact zone of the particle, (2) and (3): cos (θ1 + α) + cos θ2 2 FP = −π r12 p = π γ a − sin α + (4) sin α . h/a + 1 − cos α The force due to the surface tension is expressed in the product of the perpendicular component to the substrate of surface tension, γ cos{π/2−(θ1 +α)} = γ sin(θ1 +α) and the contact length of the liquid film at the particle, 2π r1 : FS = 2π γ r1 sin(θ1 + α) = 2π γ a sin α sin(θ1 + α).
(5)
The van der Waals force can be expressed in the following equation considering the liquid geometry in the gap between the particle and the substrate when the liquid partially fills in the gap [6]: Ag a 1 1 Aw a FW = 1− + 2 , (6) 2 2 6h [1 + a(1 − cos α)/ h] 6h [1 + a(1 − cos α)/ h]2 where Aw and Ag are the Hamaker constants with water and air as medium. The Hamaker constants used in this paper are listed on Table 1, which are constant between the same materials with air medium, Aii . The Hamaker constant between different materials, 1 and 2, with air medium, Ag , can be approximated by: Ag = A11 A22 . (7) On the other hand, the Hamaker constant between different materials with water medium, Aw , can be approximated by: (8) A11 − A33 A22 − A33 , Aw = where A33 is the Hamaker constant of water with air as medium. Table 1. Hamaker constant of materials Aii in air Material
Hamaker constant (10−20 J)
Reference
Mica SiO2 Glass Si Water
9.5 18.0 50.0 25.6 5.45
[10] [10] [11] [10] [11]
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The relationship between the filling angle and RH can be obtained by the Kelvin equation, (2) and (3): p ρRT = ln γM ps
1 1 − r1 r2
=
cos(θ1 + α) + cos(θ2 ) 1 − . a sin α h + a(1 − cos α)
(9)
When the distance between the particle and the substrate, h, is decided, the filling angle can be calculated from (9) with the RH, p/ps , and the contact angles. The adhesion force can be obtained using the filling angle calculated by (9).
3. EXPERIMENTAL METHODS
A Nanoscope II E AFM (Digital Instruments) was used in the contact mode. The cantilever mount was replaced with a commercial fluid-phase cell (Digital Instruments) in order to examine the effect of the humidity on the adhesion force and the gas which controlled the humidity was run in it at a flow rate of 50 ml/min. The cantilever (spring constant k = 2 N/m) was used for the observation of the surface shape. The colloid probe was used for the measurement of the adhesion force, which was prepared by attaching a glass bead (MBP 1-10; The Association of Powder Processes Industry and Engineering) to a cantilever (k = 2 or 42 N/m) by epoxy adhesive (Araldite, two-liquid mixing type; Nichiban). The glass beads used in this study were about 8 μm in radius and were cleaned by the following method referring to Ref. [12]. The glass beads were dipped in the mixed solution at 80◦ C for 10 min, which was mixed 28% aqueous ammonia, 30% hydrogen peroxide water and ultrapure water (Millipore Milli-Q grade) in a volume ratio of 0.1:1:5. They were rinsed using a large amount of ultrapure water and then dried under a vacuum. Mica and silica flat plates were used as a substrate. A mica plate was freshly cleaved prior to use. A silicon wafer with an oxide film of 200 nm thickness was washed in the same manner as the glass particles in the mixed solution, which is hereafter called Silica A. Silica A was immersed further in the mixed solution with surplus ammonium (volume ratio in the mixed solution of 1:1:5) to create the nano-scale roughness on a silicon wafer. The silicon wafer after etching is hereafter called Silica B. The hydrophobic substrate was made from Silica A using octadecyltrichlorosilane (OTS; Shin-Etsu Chemical) and is hereafter called OTS/Silica. Table 2 shows the root mean square (r.m.s.) of the surface roughness of the substrate measured by AFM, and the contact angle of water with the substrate measured by the contact angle meter (CA-D; Kyowa Interface Science). The contact angle of a glass bead was assumed to be equal to the contact angle of a glass plate.
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A. Fukunishi and Y. Mori Table 2. The r.m.s. of roughness of substrate and contact angle of water Substrate
r.m.s. of roughness (nm)
Contact angle (deg)
Mica Silica A Silica B OTS/Silica Glass
0.05 0.10 0.18 0.09 0.13
5 45 51 110 35
4. RESULTS AND DISCUSSION
4.1. Adhesion force between a particle and a plate with a hydrophilic surface In the following, the experiment using the colloid probe is described with the experiment using the particle. Figure 2 shows the effect of the humidity on the adhesion force between a particle and a substrate. The calculation result of adhesion the force using (1) is also indicated by the solid line. The distance, h, between the particle and substrate is estimated as 0.2–0.4 nm in the literature [6, 9], so that we took 0.3 nm in this paper and assumed it does not depend on the RH. Using mica plate as a substrate, the adhesion force increased with RH as shown in Fig. 2a. The experimental results agreed well with the calculated values. Equation (9) did not have a solution in the RH region of less than 5%, because h is the finite value of 0.3 nm. This means a liquid film having a curvature radius which satisfies the Kelvin equation cannot cross-link both surfaces. The range where this calculation is impossible becomes large to the high humidity region when the contact angle increases. The adhesion force at this region, where the liquid film could not be formed, is equal to the van der Waals force in air medium and is indicated as the solid triangle at 0% RH. The adhesion force measured between a particle and Silica A increased with RH as shown in Fig. 2b, and agreed well with the calculated value. As the Hamaker constant between silica and glass is larger than that between mica and glass, the adhesion force using Silica A becomes strong compared to the case of mica at low RH. In the meantime, the strong capillary force works on the mica plate, because the contact angle of the mica plate is smaller than for Silica A. Therefore, the adhesion forces of both flat plates became almost equal in the case of high RH. 4.2. Adhesion force between a cantilever tip of the AFM and a plate with a hydrophilic surface The curvature radius of the cantilever tip was estimated at 90 nm from the SEM micro-graph, so that the adhesion force measurements using a cantilever tip will give useful information about the adhesion of the nanoparticle. Figure 3 shows the measured adhesion force values and the calculation line. The solid triangle key at 0% RH in Fig. 3 indicates the van der Waals force in air (as in Fig. 2). In the
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Figure 2. Adhesion force between a glass particle and a hydrophilic substrate as a function of RH. (a) Mica surface. (b) Silica A surface.
calculation, the cantilever tip was assumed as a = 90 nm and 15◦ contact angle [5]. In addition, we took h = 0.25 nm because the radius of the cantilever tip was two orders smaller than the particle radius and, thus, the tip could approach closer to
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A. Fukunishi and Y. Mori
Figure 3. Adhesion force between the AFM tip and hydrophilic substrate as a function of RH. (a) Mica surface. (b) Silica surface.
the substrate. The observed adhesion force increased with RH, became a maximum value at 55% RH and decreased afterwards for the mica plate as shown in Fig. 3. The maximum value appeared even in the calculation as shown by the solid line
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575
in Fig. 3. However, it was at considerably higher value of RH. This discrepancy might be due to assuming that the shape of the cantilever tip was spherical [6]. According to the SEM micrograph, we supposed that the shape of the cantilever tip was parabolic where the horizontal distance from the center of the cantilever tip, x, was less than 20 nm. The surface position of the cantilever tip could be expressed by the height, y, from the top of the cantilever tip and the distance, x, as: y = k1 x 2 .
(10)
At distances larger than 20 nm for x: y = k2 x 3 .
(11)
The constant value, k2 , was determined by the shape of the probe tip of the SEM micrograph, and then the constant value, k1 , was decided as the surface curve was continued at x = 20 nm. In this case, (4)–(6) can be expressed as follows: 1 cos(θ1 + α) + cos θ2 2 2 , (12) FP = −π r1 p = π γ x − + x h+y FS = 2π γ x sin(θ1 + α),
(13)
Ag a 1 1 Aw a 1− + 2 . FW = 2 2 6h (1 + y/ h) 6h (1 + y/ h)2
(14)
Figure 3 shows dotted lines for the calculation results of the adhesion force between a cantilever tip and the substrate using this shape model. When RH is low, the liquid bridge is only formed at the position where the cantilever shape is expressed as (10). Increasing RH, the liquid bridge covers the position described by (11), i.e. the adhesion force can be calculated by (10) for lower RH and by (11) for higher RH. The maximum point of the adhesion force for the calculation (the cross point of two dotted lines) agreed well with experimental value and the decrease of the adhesion force afterwards can be also estimated by the this shape model. For Silica A, on the other hand, the observed adhesion force suddenly increased over 60% RH and there is no phenomenon to decrease the adhesion force in high RH as shown in Fig. 3b. Jones et al. [5] reported similar results to ours, that the adhesion force monotonously increases with RH in the measurement of a glass flat plate. They discussed that this monotonous increase was due to an uncertainty of the measurement by the roughness of the surface. However, we considered that essentially the roughness of the flat plate caused the adhesion force increase phenomenon. Then, the adhesion force measurement was carried out using the Silica B plate having much rougher surface and the results are also shown in Fig. 3b. It was clear that the adhesion force at high RH increased greatly as the surface roughness increased.
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A. Fukunishi and Y. Mori
4.3. Hydrophobic substrate The adhesion forces of a hydrophobic substrate (OTS/Silica) using a particle and a cantilever are shown in Figs 4 and 5, respectively. The van der Waals force in the air
Figure 4. Adhesion force between a glass particle and OTS/Silica as a function of RH.
Figure 5. Adhesion force between the AFM tip and OTS/Silica as a function of RH.
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was indicated as the solid triangle key in 0% RH and the solid line was the calculated value. The adhesion forces were almost constant in the case of the particle as shown in Fig. 4 and the effect of the humidity was almost not observed. On the other hand, the adhesion force decreased when RH increased in case of the cantilever in Fig. 5. Fuji et al. reported that the liquid bridge was not formed between hydrophobic surfaces [7, 8]. We examined whether the liquid bridge on hydrophobic substrate (θ2 = 110◦ ) was formed or not using (9). The liquid bridge was not found to form in the region less than 35% RH in case of θ1 = 0◦ . On the other hand, the liquid bridge was not formed over the whole RH range in the case of θ1 = 70◦ . That is, the liquid bridge is not formed if both surfaces are hydrophobicity, although the liquid bridge is formed at high RH when the other surface is the hydrophilic. For the experiment in Fig. 4, the stepped force curve was observed during the separation period over 70% RH, where the liquid bridge was formed between surfaces. In the calculation result shown in the figures, however, the adhesion forces of both particle and cantilever decreased when RH increased, and the calculated values were below the measured values. There is a report that the hydrophilic surface becomes more and more hydrophilic and the hydrophobic surface becomes more and more hydrophobic when the surface is rough [13]. That is, when using the hydrophobic substrate with a rough surface, the contact angle meter could indicate a large contact angle compared with the flat surface. When the size of the particle decreases to a comparative degree of the size of the surface roughness of the substrate, however, the contact angle could be used for the flat plate without roughness. From this idea, assuming that the contact angles of the flat plates without roughness and with roughness were 98◦ and 110◦ , respectively, the calculated value qualitatively agrees with measured value as shown in Figs 4 and 5, and this idea may be valid. 4.4. Growth of a liquid film In the calculation of the adhesion force we assumed the equilibrium state for the growth of a liquid film. The adhesion force measurements were carried after 5 min from starting the gas running to the liquid-phase cell. We checked whether this period was enough time to reach an equilibrium state of the growth of a liquid film. The time necessary for water condensation was calculated using the assumption that the water which constituted a liquid film was supplied from the water vapor in the atmospheric gas. Assuming a cylinder instead of a sphere for a particle, we used the cylindrical coordinate system shown in Fig. 6. Then the height of a liquid film is approximated to xb2 /(2a), where x b is the axial direction distance of a liquid film from the attached point of both surfaces. The volume of a liquid film, V m , can be calculated as: xb π xb4 x2 π a3 4 Vm = 2π x dx = (15) = sin α. 2a 4a 4 0 The water included in a liquid film formed at a certain RH is regarded as the water vapor in the air space surrounded in a liquid film. Considering the double
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A. Fukunishi and Y. Mori
space including the water vapor for making a liquid film, i.e. the concentration gradient of water vapor in the space between x a and x b in Fig. 6, the steady-state approximation is applied to the calculation of water vapor concentration. The water vapor concentration, C, at x can be expressed by the following equation, using the boundary conditions for C = 0 at x = x b and the equilibrium concentration C s at x = x a which depends on RH: C = CS
xb−2 − x −2 xb−2 − xa−2
.
(16)
The flow rate N of the water vapor to supply a liquid film is: N=
2π CS D a(xb−2 − xa−2 )
,
(17)
Figure 6. Diffusion through a cylindrical shell.
Figure 7. Effect of contact time on the adhesion force between a glass particle and Silica A surface.
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where D is the diffusion coefficient of the water molecule in air. The necessary period for the supply of water vapor was calculated from (15)–(17). The necessary period that formed a water bridge at RH = 40% was about 11 μs, which was the rapidest time over the whole RH range. When RH increased or decreased from 40%, the necessary period increased, but within 10−4 seconds. Figure 7 shows the effect of the contact time between a particle and Silica A plate on the adhesion force, but this effect was hardly observed. Thus, a liquid film seems to be formed in under 1 ms, as expected by the calculation.
5. CONCLUSION
The following conclusions were drawn from the direct measurement of the adhesion force between solid surfaces using an AFM. (i) The adhesion force between a glass bead and a hydrophilic flat plate with a small contact angle increased with the RH. In case of a hydrophobic flat plate with a large contact angle, the adhesion force was almost constant or slightly decreased when RH increased. The experimental results for the hydrophilic flat plate agreed with the calculation based on the report of Xudong et al. (ii) The adhesion force between the substrate and the cantilever tip of the AFM, whose radius was about 90 nm, was observed to have a maximum at a certain RH, because the filling angle formed a liquid film that was larger than the case of a particle whose radius was the micrometer order. A huge adhesion force was sometimes observed in the high RH region due to the surface roughness. (iii) The equilibrium time for the capillary condensation of water in the gap between a particle and a substrate was calculated as a short time (under 10−4 s). The adhesion force measured at the contact time in 10−2 s was almost equal to the result of a 10-s contact time and this results appears to be valid for the model calculation. Acknowledgements The authors thank Mr. Takashi Minamihounoki (Sharp Manufacturing Systems Co.) for his assistance in obtaining the offer of the silicon wafer from Sharp Co. This work was partially supported by a grant to RCAST at Doshisha University from the Ministry of Education, Japan.
REFERENCES 1. M. Arakawa and M. Nishino, The influence of humidity on the cohesion of powder particle, Zairyo 22, 663–667 (1973). 2. E. Fukuoka, S. Kimura, M. Yamazaki and T. Tanaka, Cohesion of particulate solids. VI. Improvement of application to measurement of cohesiveness at various levels of humidity, Chem. Pharm. Bull. 31, 221–229 (1983).
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3. S. Sano, F. Saito and S. Yashima, Measurement of force of adhesion of powders to glass plate by centrifugal method, J. Chem. Eng., Japan 10, 17–24 (1984). 4. H. K. Christenson, Adhesion between surfaces in undersaturated vapors. A reexamination of the influence of meniscus curvature and surface force, J. Colloid Interface Sci. 121, 170–178 (1988). 5. R. Jones, H. M. Pollock, J. A. S. Cleaver and C. S. Hodges, Adhesion force between glass and silicon surface in air studied by AFM: effects of relative humidity, particle, size, roughness, and surface treatment, Langmuir 18, 8045–8055 (2002). 6. S. Xudong and Q. Linmao, Investigation of humidity-dependent capillary force, Langmuir 16, 8153–8158 (2000) 7. M. Fuji, K. Machida, T. Watanabe and M. Chikazawa, Effect of wettability on adhesion force between silica particles evaluated by atomic force microscopy measurement as a function of relative humidity, Langmuir 15, 4584–4589 (1999). 8. M. Fuji, Influence of moisture on surface properties of particle and adhesional force between particles, J. Soc. Powder Technol., Japan 40, 355–363 (2003). 9. I. Y. Rabinovich, J. J. Adler, M. S. Esayanur, A. Ata, R. Singh and B. M. Moudgil, Capillary forces between surfaces with nanoscale roughness, Adv. Colloid Interface Sci. 96, 213–230 (2002). 10. The Chemical Society of Japan (Eds), in: Kagaku Benran, 4th edn, p. II-99. Maruzewn, Tokyo (1993). 11. K. Okuyama, H. Masuda, K. Higashitani, M. Chikazawa and T. Kanazawa, Interaction between two particles, J. Soc. Powder Technol., Japan 22, 451–475 (1985). 12. W. Kern and D. A. Puotinen, Cleaning solution based on hydrogen for use in silicon semiconductor technology, RCA Rec. 31, 187–206 (1970). 13. M. Tujii and H. Masuda, Wetting of solid surface and its fractal structure, J. Jpn. Soc. Tribol. 44, 941–946 (1999).
Translated paper SPTJ Best Paper Award ’05 ∗ Adhesion force between particles and substrate in a humid atmosphere studied by atomic force microscopy AKIO FUKUNISHI and YASUSHIGE MORI † Department of Chemical Engineering and Materials Science, Doshisha University, 1-3 Miyakodani, Tatara, Kyotanabe 610-0321, Japan Japanese version published in JSPTJ Vol. 41, No. 3 (2004); English version for APT received 6 May 2006
Abstract—Using an atomic force microscope (AFM), adhesion forces between glass particles or AFM tips and hydrophilic or hydrophobic substrates were measured as a function of relative humidity (RH). The observed adhesion force between the glass particles and the hydrophilic substrate increased with RH due to strong capillary condensation. In contrast, the adhesion force between the glass particles and the hydrophobic substrate was found to be almost constant for all RHs, due to weak capillary condensation. The adhesion force between an AFM tip and a mica plate had a maximum value at a certain RH. This can be evaluated by calculating with consideration for the tip shape. On the other hand, the adhesion force for a silica plate increased drastically over a certain RH and could be explained due to the surface roughness of the silica plate. The presence of nanometer-scale roughness can play a critical role in the absolute value of the adhesion force between an AFM tip and the substrate in a humid atmosphere. Keywords: Adhesion force; atomic force microscope; relative humidity; hydrophilic surface; hydrophobic surface; contact angle; surface roughness.
NOMENCLATURE
A a D Fad Fc
Hamaker constant (J) radius of a sphere (m) diffusion coefficient of a water molecule in air (m2 /s) adhesion force (N) capillary pressure force (N)
∗ The † To
title of the Jotaki Award has been changed to the SPTJ Best Paper Award in 2006. whom correspondence should be addressed. E-mail: [email protected]
568
Fs Fw h M p/ps p R r1 r2 T Vm
A. Fukunishi and Y. Mori
surface tension force (N) van der Waals force (N) separation distance between surfaces (m) molecular weight (kg/mol) relative humidity (—) calippary pressure (Pa) gas constant (J/(K mol)) horizontal distance of meniscus intersection on particle (m) curvature radius of meniscus (m) temperature (K) volume of bridging water (m3 )
Greek α γ θ1 θ2 ρ
filling angle (rad) surface tension of liquid (N/m) contact angle of liquid for particle (rad) contact angle of liquid for substrate (rad) density (kg/m3 )
1. INTRODUCTION
The adhesion phenomena between particles and a wall surface or among particles causes various problems in many powder operations. The adhesion force consists of physical interactions such as van der Waals, electrostatic and capillary forces, and of chemical bonding such as hydrogen bonding. Many researchers have presented experimental and theoretical views to clarify the contribution of those forces and the adhesion mechanism. The experimental approaches for the adhesion force can be divided into the methods for the powder [1, 2] and for a single particle [3]. Recently, a surface force apparatus [4] and an atomic force microscope (AFM) [5 –9] have been used for the direct measurement of the adhesion force (which are classified as belonging to the latter method). The adhesion force under a humid atmosphere is controlled by the capillary force which is generated by condensing water vapor in the gap, so that it becomes a function of the relative humidity (RH). It is reported that the effect of the RH on the adhesion force differs by particle shape [3], size [5], chemical property of the surface [5 –8] or geometric condition of the particle [8, 9]. Xudong et al. [6] reported that the adhesion force between an AFM tip and a smooth silica plate can be predicted by their theory. However, the measurement results of the adhesion force did not always agree with theoretical calculations and this discrepancy was often explained as being due to the surface roughness. Rabinovich et al. [9] proposed
AFM study of adhesion forces
569
a theoretical formula considering the surface roughness and compared it with the measurement results. In this paper, AFM measurement of the adhesion force with a smooth surface was carried out by changing the contact angle of the plate and the experimental results were compared with the theory of Xudong et al. [6]. The effect of the particle size on the adhesion force was also examined by using a colloid probe instead of a AFM tip.
2. ADHESION FORCE IN A HUMID ATMOSPHERE
The capillary condensation of water vapor in the air occurs in the gap of the spherical particle and the flat plate. As a result, a water bridge is formed between both surfaces as shown in Fig. 1. The adhesion force, F ad , between the particle and the plate under the presence of the water bridge can be expressed by van der Waals force, F W , capillary force, F P , which originates from the internal and external pressure difference in the liquid film, and the force due to surface tension, F S , of a liquid film: Fad = FW + FP + FS .
(1)
The contact radii of the liquid film at the particle, r1 , and the radius of curvature for the liquid surface, r2 , are given by the following equations: r1 = a sin α,
r2 =
h + a(1 − cos α) , cos(θ1 + α) + cos θ2
(2)
where a is the particle radius, α is the filling angle, h is the distance between a particle and substrate, and θ1 and θ2 are contact angles of the liquid with the particle and substrate, respectively.
Figure 1. Schematic illustration of liquid formed between a spherical particle and a flat substrate.
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A. Fukunishi and Y. Mori
The capillary pressure of the liquid, p, as a function of surface tension, γ , is obtained from the Laplace equation: 1 1 p = γ . (3) − r1 r2 The capillary force can be expressed by the cross-section area, π r12 , of the contact zone of the particle, (2) and (3): cos (θ1 + α) + cos θ2 2 FP = −π r12 p = π γ a − sin α + (4) sin α . h/a + 1 − cos α The force due to the surface tension is expressed in the product of the perpendicular component to the substrate of surface tension, γ cos{π/2−(θ1 +α)} = γ sin(θ1 +α) and the contact length of the liquid film at the particle, 2π r1 : FS = 2π γ r1 sin(θ1 + α) = 2π γ a sin α sin(θ1 + α).
(5)
The van der Waals force can be expressed in the following equation considering the liquid geometry in the gap between the particle and the substrate when the liquid partially fills in the gap [6]: Ag a 1 1 Aw a FW = 1− + 2 , (6) 2 2 6h [1 + a(1 − cos α)/ h] 6h [1 + a(1 − cos α)/ h]2 where Aw and Ag are the Hamaker constants with water and air as medium. The Hamaker constants used in this paper are listed on Table 1, which are constant between the same materials with air medium, Aii . The Hamaker constant between different materials, 1 and 2, with air medium, Ag , can be approximated by: Ag = A11 A22 . (7) On the other hand, the Hamaker constant between different materials with water medium, Aw , can be approximated by: (8) A11 − A33 A22 − A33 , Aw = where A33 is the Hamaker constant of water with air as medium. Table 1. Hamaker constant of materials Aii in air Material
Hamaker constant (10−20 J)
Reference
Mica SiO2 Glass Si Water
9.5 18.0 50.0 25.6 5.45
[10] [10] [11] [10] [11]
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571
The relationship between the filling angle and RH can be obtained by the Kelvin equation, (2) and (3): p ρRT = ln γM ps
1 1 − r1 r2
=
cos(θ1 + α) + cos(θ2 ) 1 − . a sin α h + a(1 − cos α)
(9)
When the distance between the particle and the substrate, h, is decided, the filling angle can be calculated from (9) with the RH, p/ps , and the contact angles. The adhesion force can be obtained using the filling angle calculated by (9).
3. EXPERIMENTAL METHODS
A Nanoscope II E AFM (Digital Instruments) was used in the contact mode. The cantilever mount was replaced with a commercial fluid-phase cell (Digital Instruments) in order to examine the effect of the humidity on the adhesion force and the gas which controlled the humidity was run in it at a flow rate of 50 ml/min. The cantilever (spring constant k = 2 N/m) was used for the observation of the surface shape. The colloid probe was used for the measurement of the adhesion force, which was prepared by attaching a glass bead (MBP 1-10; The Association of Powder Processes Industry and Engineering) to a cantilever (k = 2 or 42 N/m) by epoxy adhesive (Araldite, two-liquid mixing type; Nichiban). The glass beads used in this study were about 8 μm in radius and were cleaned by the following method referring to Ref. [12]. The glass beads were dipped in the mixed solution at 80◦ C for 10 min, which was mixed 28% aqueous ammonia, 30% hydrogen peroxide water and ultrapure water (Millipore Milli-Q grade) in a volume ratio of 0.1:1:5. They were rinsed using a large amount of ultrapure water and then dried under a vacuum. Mica and silica flat plates were used as a substrate. A mica plate was freshly cleaved prior to use. A silicon wafer with an oxide film of 200 nm thickness was washed in the same manner as the glass particles in the mixed solution, which is hereafter called Silica A. Silica A was immersed further in the mixed solution with surplus ammonium (volume ratio in the mixed solution of 1:1:5) to create the nano-scale roughness on a silicon wafer. The silicon wafer after etching is hereafter called Silica B. The hydrophobic substrate was made from Silica A using octadecyltrichlorosilane (OTS; Shin-Etsu Chemical) and is hereafter called OTS/Silica. Table 2 shows the root mean square (r.m.s.) of the surface roughness of the substrate measured by AFM, and the contact angle of water with the substrate measured by the contact angle meter (CA-D; Kyowa Interface Science). The contact angle of a glass bead was assumed to be equal to the contact angle of a glass plate.
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r.m.s. of roughness (nm)
Contact angle (deg)
Mica Silica A Silica B OTS/Silica Glass
0.05 0.10 0.18 0.09 0.13
5 45 51 110 35
4. RESULTS AND DISCUSSION
4.1. Adhesion force between a particle and a plate with a hydrophilic surface In the following, the experiment using the colloid probe is described with the experiment using the particle. Figure 2 shows the effect of the humidity on the adhesion force between a particle and a substrate. The calculation result of adhesion the force using (1) is also indicated by the solid line. The distance, h, between the particle and substrate is estimated as 0.2–0.4 nm in the literature [6, 9], so that we took 0.3 nm in this paper and assumed it does not depend on the RH. Using mica plate as a substrate, the adhesion force increased with RH as shown in Fig. 2a. The experimental results agreed well with the calculated values. Equation (9) did not have a solution in the RH region of less than 5%, because h is the finite value of 0.3 nm. This means a liquid film having a curvature radius which satisfies the Kelvin equation cannot cross-link both surfaces. The range where this calculation is impossible becomes large to the high humidity region when the contact angle increases. The adhesion force at this region, where the liquid film could not be formed, is equal to the van der Waals force in air medium and is indicated as the solid triangle at 0% RH. The adhesion force measured between a particle and Silica A increased with RH as shown in Fig. 2b, and agreed well with the calculated value. As the Hamaker constant between silica and glass is larger than that between mica and glass, the adhesion force using Silica A becomes strong compared to the case of mica at low RH. In the meantime, the strong capillary force works on the mica plate, because the contact angle of the mica plate is smaller than for Silica A. Therefore, the adhesion forces of both flat plates became almost equal in the case of high RH. 4.2. Adhesion force between a cantilever tip of the AFM and a plate with a hydrophilic surface The curvature radius of the cantilever tip was estimated at 90 nm from the SEM micro-graph, so that the adhesion force measurements using a cantilever tip will give useful information about the adhesion of the nanoparticle. Figure 3 shows the measured adhesion force values and the calculation line. The solid triangle key at 0% RH in Fig. 3 indicates the van der Waals force in air (as in Fig. 2). In the
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Figure 2. Adhesion force between a glass particle and a hydrophilic substrate as a function of RH. (a) Mica surface. (b) Silica A surface.
calculation, the cantilever tip was assumed as a = 90 nm and 15◦ contact angle [5]. In addition, we took h = 0.25 nm because the radius of the cantilever tip was two orders smaller than the particle radius and, thus, the tip could approach closer to
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Figure 3. Adhesion force between the AFM tip and hydrophilic substrate as a function of RH. (a) Mica surface. (b) Silica surface.
the substrate. The observed adhesion force increased with RH, became a maximum value at 55% RH and decreased afterwards for the mica plate as shown in Fig. 3. The maximum value appeared even in the calculation as shown by the solid line
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in Fig. 3. However, it was at considerably higher value of RH. This discrepancy might be due to assuming that the shape of the cantilever tip was spherical [6]. According to the SEM micrograph, we supposed that the shape of the cantilever tip was parabolic where the horizontal distance from the center of the cantilever tip, x, was less than 20 nm. The surface position of the cantilever tip could be expressed by the height, y, from the top of the cantilever tip and the distance, x, as: y = k1 x 2 .
(10)
At distances larger than 20 nm for x: y = k2 x 3 .
(11)
The constant value, k2 , was determined by the shape of the probe tip of the SEM micrograph, and then the constant value, k1 , was decided as the surface curve was continued at x = 20 nm. In this case, (4)–(6) can be expressed as follows: 1 cos(θ1 + α) + cos θ2 2 2 , (12) FP = −π r1 p = π γ x − + x h+y FS = 2π γ x sin(θ1 + α),
(13)
Ag a 1 1 Aw a 1− + 2 . FW = 2 2 6h (1 + y/ h) 6h (1 + y/ h)2
(14)
Figure 3 shows dotted lines for the calculation results of the adhesion force between a cantilever tip and the substrate using this shape model. When RH is low, the liquid bridge is only formed at the position where the cantilever shape is expressed as (10). Increasing RH, the liquid bridge covers the position described by (11), i.e. the adhesion force can be calculated by (10) for lower RH and by (11) for higher RH. The maximum point of the adhesion force for the calculation (the cross point of two dotted lines) agreed well with experimental value and the decrease of the adhesion force afterwards can be also estimated by the this shape model. For Silica A, on the other hand, the observed adhesion force suddenly increased over 60% RH and there is no phenomenon to decrease the adhesion force in high RH as shown in Fig. 3b. Jones et al. [5] reported similar results to ours, that the adhesion force monotonously increases with RH in the measurement of a glass flat plate. They discussed that this monotonous increase was due to an uncertainty of the measurement by the roughness of the surface. However, we considered that essentially the roughness of the flat plate caused the adhesion force increase phenomenon. Then, the adhesion force measurement was carried out using the Silica B plate having much rougher surface and the results are also shown in Fig. 3b. It was clear that the adhesion force at high RH increased greatly as the surface roughness increased.
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4.3. Hydrophobic substrate The adhesion forces of a hydrophobic substrate (OTS/Silica) using a particle and a cantilever are shown in Figs 4 and 5, respectively. The van der Waals force in the air
Figure 4. Adhesion force between a glass particle and OTS/Silica as a function of RH.
Figure 5. Adhesion force between the AFM tip and OTS/Silica as a function of RH.
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was indicated as the solid triangle key in 0% RH and the solid line was the calculated value. The adhesion forces were almost constant in the case of the particle as shown in Fig. 4 and the effect of the humidity was almost not observed. On the other hand, the adhesion force decreased when RH increased in case of the cantilever in Fig. 5. Fuji et al. reported that the liquid bridge was not formed between hydrophobic surfaces [7, 8]. We examined whether the liquid bridge on hydrophobic substrate (θ2 = 110◦ ) was formed or not using (9). The liquid bridge was not found to form in the region less than 35% RH in case of θ1 = 0◦ . On the other hand, the liquid bridge was not formed over the whole RH range in the case of θ1 = 70◦ . That is, the liquid bridge is not formed if both surfaces are hydrophobicity, although the liquid bridge is formed at high RH when the other surface is the hydrophilic. For the experiment in Fig. 4, the stepped force curve was observed during the separation period over 70% RH, where the liquid bridge was formed between surfaces. In the calculation result shown in the figures, however, the adhesion forces of both particle and cantilever decreased when RH increased, and the calculated values were below the measured values. There is a report that the hydrophilic surface becomes more and more hydrophilic and the hydrophobic surface becomes more and more hydrophobic when the surface is rough [13]. That is, when using the hydrophobic substrate with a rough surface, the contact angle meter could indicate a large contact angle compared with the flat surface. When the size of the particle decreases to a comparative degree of the size of the surface roughness of the substrate, however, the contact angle could be used for the flat plate without roughness. From this idea, assuming that the contact angles of the flat plates without roughness and with roughness were 98◦ and 110◦ , respectively, the calculated value qualitatively agrees with measured value as shown in Figs 4 and 5, and this idea may be valid. 4.4. Growth of a liquid film In the calculation of the adhesion force we assumed the equilibrium state for the growth of a liquid film. The adhesion force measurements were carried after 5 min from starting the gas running to the liquid-phase cell. We checked whether this period was enough time to reach an equilibrium state of the growth of a liquid film. The time necessary for water condensation was calculated using the assumption that the water which constituted a liquid film was supplied from the water vapor in the atmospheric gas. Assuming a cylinder instead of a sphere for a particle, we used the cylindrical coordinate system shown in Fig. 6. Then the height of a liquid film is approximated to xb2 /(2a), where x b is the axial direction distance of a liquid film from the attached point of both surfaces. The volume of a liquid film, V m , can be calculated as: xb π xb4 x2 π a3 4 Vm = 2π x dx = (15) = sin α. 2a 4a 4 0 The water included in a liquid film formed at a certain RH is regarded as the water vapor in the air space surrounded in a liquid film. Considering the double
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space including the water vapor for making a liquid film, i.e. the concentration gradient of water vapor in the space between x a and x b in Fig. 6, the steady-state approximation is applied to the calculation of water vapor concentration. The water vapor concentration, C, at x can be expressed by the following equation, using the boundary conditions for C = 0 at x = x b and the equilibrium concentration C s at x = x a which depends on RH: C = CS
xb−2 − x −2 xb−2 − xa−2
.
(16)
The flow rate N of the water vapor to supply a liquid film is: N=
2π CS D a(xb−2 − xa−2 )
,
(17)
Figure 6. Diffusion through a cylindrical shell.
Figure 7. Effect of contact time on the adhesion force between a glass particle and Silica A surface.
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where D is the diffusion coefficient of the water molecule in air. The necessary period for the supply of water vapor was calculated from (15)–(17). The necessary period that formed a water bridge at RH = 40% was about 11 μs, which was the rapidest time over the whole RH range. When RH increased or decreased from 40%, the necessary period increased, but within 10−4 seconds. Figure 7 shows the effect of the contact time between a particle and Silica A plate on the adhesion force, but this effect was hardly observed. Thus, a liquid film seems to be formed in under 1 ms, as expected by the calculation.
5. CONCLUSION
The following conclusions were drawn from the direct measurement of the adhesion force between solid surfaces using an AFM. (i) The adhesion force between a glass bead and a hydrophilic flat plate with a small contact angle increased with the RH. In case of a hydrophobic flat plate with a large contact angle, the adhesion force was almost constant or slightly decreased when RH increased. The experimental results for the hydrophilic flat plate agreed with the calculation based on the report of Xudong et al. (ii) The adhesion force between the substrate and the cantilever tip of the AFM, whose radius was about 90 nm, was observed to have a maximum at a certain RH, because the filling angle formed a liquid film that was larger than the case of a particle whose radius was the micrometer order. A huge adhesion force was sometimes observed in the high RH region due to the surface roughness. (iii) The equilibrium time for the capillary condensation of water in the gap between a particle and a substrate was calculated as a short time (under 10−4 s). The adhesion force measured at the contact time in 10−2 s was almost equal to the result of a 10-s contact time and this results appears to be valid for the model calculation. Acknowledgements The authors thank Mr. Takashi Minamihounoki (Sharp Manufacturing Systems Co.) for his assistance in obtaining the offer of the silicon wafer from Sharp Co. This work was partially supported by a grant to RCAST at Doshisha University from the Ministry of Education, Japan.
REFERENCES 1. M. Arakawa and M. Nishino, The influence of humidity on the cohesion of powder particle, Zairyo 22, 663–667 (1973). 2. E. Fukuoka, S. Kimura, M. Yamazaki and T. Tanaka, Cohesion of particulate solids. VI. Improvement of application to measurement of cohesiveness at various levels of humidity, Chem. Pharm. Bull. 31, 221–229 (1983).
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3. S. Sano, F. Saito and S. Yashima, Measurement of force of adhesion of powders to glass plate by centrifugal method, J. Chem. Eng., Japan 10, 17–24 (1984). 4. H. K. Christenson, Adhesion between surfaces in undersaturated vapors. A reexamination of the influence of meniscus curvature and surface force, J. Colloid Interface Sci. 121, 170–178 (1988). 5. R. Jones, H. M. Pollock, J. A. S. Cleaver and C. S. Hodges, Adhesion force between glass and silicon surface in air studied by AFM: effects of relative humidity, particle, size, roughness, and surface treatment, Langmuir 18, 8045–8055 (2002). 6. S. Xudong and Q. Linmao, Investigation of humidity-dependent capillary force, Langmuir 16, 8153–8158 (2000) 7. M. Fuji, K. Machida, T. Watanabe and M. Chikazawa, Effect of wettability on adhesion force between silica particles evaluated by atomic force microscopy measurement as a function of relative humidity, Langmuir 15, 4584–4589 (1999). 8. M. Fuji, Influence of moisture on surface properties of particle and adhesional force between particles, J. Soc. Powder Technol., Japan 40, 355–363 (2003). 9. I. Y. Rabinovich, J. J. Adler, M. S. Esayanur, A. Ata, R. Singh and B. M. Moudgil, Capillary forces between surfaces with nanoscale roughness, Adv. Colloid Interface Sci. 96, 213–230 (2002). 10. The Chemical Society of Japan (Eds), in: Kagaku Benran, 4th edn, p. II-99. Maruzewn, Tokyo (1993). 11. K. Okuyama, H. Masuda, K. Higashitani, M. Chikazawa and T. Kanazawa, Interaction between two particles, J. Soc. Powder Technol., Japan 22, 451–475 (1985). 12. W. Kern and D. A. Puotinen, Cleaning solution based on hydrogen for use in silicon semiconductor technology, RCA Rec. 31, 187–206 (1970). 13. M. Tujii and H. Masuda, Wetting of solid surface and its fractal structure, J. Jpn. Soc. Tribol. 44, 941–946 (1999).