Reduction of Liquid Bridge Force for 3D Microstructure Measurements

applied sciences

Article Reduction of Liquid Bridge Force for 3D Microstructure Measurements

Hiroshi Murakami 1,*, Akio Katsuki 2, Takao Sajima 2 and Mitsuyoshi Fukuda 1

1 Department of Mechanical Systems Engineering, Faculty of Environmental Engineering, The University of Kitakyushu, 1-1 Hibikino, Wakamatsu-ku, Kitakyushu, Fukuoka 808-0135, Japan; [email protected] 2 Department of Mechanical Engineering, Faculty of Engineering, Kyushu University, 744, Motooka, Nishi-ku, Fukuoka 819-0395, Japan; [email protected] (A.K.); [email protected] (T.S.) * Correspondence: [email protected]; Tel.: +81-93-695-3201

Academic Editor: Kuang-Cha Fan Received: 14 April 2016; Accepted: 11 May 2016; Published: 16 May 2016

Abstract: Recent years have witnessed an increased demand for a method for precise measurement of the microstructures of mechanical microparts, microelectromechanical systems, micromolds, optical devices, microholes, etc. This paper presents a measurement system for three-dimensional (3D) microstructures that use an optical ﬁber probe. This probe consists of a stylus shaft with a diameter of 2.5 µm and a glass ball with a diameter of 5 µm attached to the stylus tip. In this study, the measurement system, placed in a vacuum vessel, is constructed suitably to prevent adhesion of the stylus tip to the measured surface caused by the surface force resulting from the van der Waals force, electrostatic force, and liquid bridge force. First, these surface forces are analyzed with the aim of investigating the causes of adhesion. Subsequently, the effects of pressure inside the vacuum vessel on surface forces are evaluated. As a result, it is found that the surface force is 0.13 µN when the pressure inside the vacuum vessel is 350 Pa. This effect is equivalent to a 60% reduction in the surface force in the atmosphere.

Keywords: surface force; van der Waals force; electrostatic force; liquid bridge force; microstructure; measurement; optical ﬁber probe; laser diode; coordinate measuring machine (CMM)

1. Introduction Recent years have witnessed an increased demand for a method for precise measurement of the microstructures of mechanical microparts, microelectromechanical systems, micromolds, optical devices, microholes, etc. However, precise measurement of the shape of a microstructure with a large length-to-diameter (L/D) ratio is rather difficult because of the difficulty in probe fabrication and sensing methods where the measuring force is very small. Previous works have reported microstructure measurement techniques that employ a variety of probes such as optical probes, vibroscanning probes, vibrating probes, tunneling effect probes, opto-tactile probes, fiber deflection probes, optical trapping probes, and diaphragm probes [1–9]. In a previous study, we developed a system for the measurement of three-dimensional (3D) microstructures using an optical fiber probe that functions as a kind of displacement measuring probe with a small contact force and wide measurement range [10]. In this system, the shaft of the stylus does not need to be rigid for the detection of the measuring force, because the deflection of the stylus is measured by a non-contact method. In general, when the particle size is less than several tens of micrometers, the effects of surface force generated from the van der Waals force, electrostatic force, and liquid bridge force are strengthened and this surface force becomes greater than the force of gravity [11]. We used a fiber stylus with a 5-µm-diameter sphere on its tip, and as a result, we found

Appl. Sci. 2016, 6, 153; doi:10.3390/app6050153 www.mdpi.com/journal/applsci Appl. Sci. 2016, 6, 153 2 of 11 of gravity [11]. We used a fiber stylus with a 5‐μm‐diameter sphere on its tip, and as a result, we found that the measurement surface draws the stylus tip closer when the tip approaches it and the distance between the stylus tip and the measured surface is less than the regular displacement. When the stylus tip comes into contact with the measured surface, it adheres to the surface and cannot be separated from it. When the measured surface is scanned point by point in the touch‐trigger mode (Figure 1a), the measurement time increases because the stylus tip is required to be separated from the measured surface to overcome the surface force. When the measured surface is scanned continuously in the scanning mode (Figure 1b), the measurement accuracy reduces because of the bending of the stylus shaft due to the adhesion. The observed adhesion, which is influenced by environmental factors (e.g., humidity) and the roughness of the measurement surface, is not reproducible. Therefore, in another previous work, we developed a measurement system for Appl.3D microstructures Sci. 2016, 6, 153 that uses a vibrating fiber probe (Figure 1c) to prevent adhesion of the stylus2 of tip 11 to the surface being measured [12]. In this system, the stylus tip is set to vibrate in a circular motion, where it traces a circle of diameter 0.4 μm in the X‐Y plane. However, the stylus tip actually traces an ellipticalthat the measurement path. The difference surface between draws the the stylus profile tip of closer the perfect when the circle tip and approaches that of the it and actual the elliptical distance pathbetween of the the stylus stylus tip andleads the to measured measurement surface error. is less Moreover, than the the regular surface displacement. roughness cannot When thebe measuredstylus tip comesin the scanning into contact mode with when the using measured the vibrating surface, fiber it adheres probe. to the surface and cannot be separatedIn the from present it. When study, the the measured stylus characteristics surface is scanned are examined. point by pointThen, inthe the effects touch-trigger of the surface mode (Figureforce on1a), the the adhesion measurement are analyzed. time increases The results because confirm the stylus that tip the is primary required cause to be separated of adhesion from is thethe liquidmeasured bridge surface force. to Therefore, overcome thethe surfacemeasurement force. When system, the placed measured in a surface vacuum is scannedvessel, is continuously constructed suitablyin the scanning to prevent mode the (Figure adhesion1b), caused the measurement by the surface accuracy force between reduces the because stylus oftip the and bending the measured of the surface.stylus shaft The due effects to the of adhesion.pressure inside The observed the vacuum adhesion, vessel which on the is influencedsurface force by environmentalare evaluated experimentally.factors (e.g., humidity) The surface and the force roughness is calculated of the by measurement assuming that surface, the optical is not reproducible. fiber probe is Therefore, equal to thein another cantilever previous of the fixed work, support. we developed In other a words, measurement the surface system force for is 3D calculated microstructures by the deflection that uses of a vibratingthe stylus fiber shaft. probe There (Figure are many1c) to techniques prevent adhesion for measuring of the stylus surface tip forces, to the surface such as being those measured involving [ the12]. surfaceIn this system, forces theapparatus stylus tip(SFA), is set atomic to vibrate force in amicroscopy circular motion, (AFM), where micro it tracescantilever a circle (MC), of diameter optical trapping0.4 µm in (OT), the X etc.-Y plane.[13–15]. However, The measuring the stylus method tip actually that uses traces the optical an elliptical fiber probe path. is, The in differenceprinciple, similarbetween to the the profile SFA and of theAFM. perfect As a circle result, and the that surface of the force actual is found elliptical to be path 0.13 of μ theN when stylus the tip pressure leads to insidemeasurement the vacuum error. vessel Moreover, is 350 the Pa. surface This effect roughness is equivalent cannot to be a measured 60% reduction in the in scanning the surface mode force when in theusing atmosphere. the vibrating fiber probe.

Stylus tip

Measured surface Z Z

X X (a) (b)

Stylus tip

Z X Circular motion X

(c)

Figure 1.1. VariousVarious types types of of probes. probes. (a )(a Touch-trigger) Touch‐trigger probe; probe, (b) scanning(b) scanning probe; probe, and ( cand) vibrating (c) vibrating probe (touch-triggerprobe (touch‐trigger mode). mode).

In the present study, the stylus characteristics are examined. Then, the effects of the surface force on the adhesion are analyzed. The results confirm that the primary cause of adhesion is the liquid bridge force. Therefore, the measurement system, placed in a vacuum vessel, is constructed suitably to prevent the adhesion caused by the surface force between the stylus tip and the measured surface. The effects of pressure inside the vacuum vessel on the surface force are evaluated experimentally. The surface force is calculated by assuming that the optical fiber probe is equal to the cantilever of the fixed support. In other words, the surface force is calculated by the deflection of the stylus shaft. There are many techniques for measuring surface forces, such as those involving the surface forces apparatus (SFA), atomic force microscopy (AFM), micro cantilever (MC), optical trapping (OT), etc. [13–15]. The measuring method that uses the optical fiber probe is, in principle, similar to the SFA Appl. Sci. 2016, 6, 153 3 of 11 and AFM. As a result, the surface force is found to be 0.13 µN when the pressure inside the vacuum vessel is 350 Pa. This effect is equivalent to a 60% reduction in the surface force in the atmosphere.

2. Measurement Principle Figure2 shows a diagram of the developed optical measurement system. The stylus consists of a 2.5-µm-diameter optical fiber to which a 5-µm-diameter glass stylus tip is attached. The total length of the stylus is 0.38 mm. The probing system consists of the fiber stylus, two laser diodes with a 650 nm wavelength (LDX and LDY in the X- and Y-directions, respectively), and two dual-element photodiodes (PX and PY in the X- and Y-directions, respectively). The stylus shaft is fixed to a tube-type piezo driver element in order to perform attitude adjustment of the stylus shaft; the stylus shaft is installed between the laser diodes and the dual-element photodiodes, which are oriented orthogonally. The laser diodes are mounted above the stylus tip, and the focused laser beams irradiate along the X- and Y-directions onto the stylus shaft. The two dual-element photodiodes are located opposite the laser diodes beyond the stylus. The laser beams that pass through the stylus shaft are received by these dual-element photodiodes. The beam intensities detected by the photodiodes are converted into voltages; hereafter, these intensities are denoted as IPX1, IPX2, IPY1, and IPY2 (V). The output signal IX in the X-direction obtained using IPY1 and IPY2 and the output signal IY in the Y-direction obtained using IPX1 and IPX2 are defined as given in Equations (1) and (2), respectively. A charge-coupled device is employed to monitor the positions of the stylus and test piece during the setting up of the equipment and the measurement. IX “ IPY1 ´ IPY2 (1)

Appl. Sci. 2016, 6, 153 IY “ IPX1 ´ IPX2 4 of(2) 11

Figure 2. Measurement system using optical fiber ﬁber probe.

IPY2＝ IPY1 To illustrate the measurement principle of theIRY2 optical< IRY1 ﬁber probe, Figure3 showsIRY2 ＝ IRY1 a cross-sectional diagram of the X-Y plane of the optical system shown in Figure2. Before the stylus tip comes into contact with the measured surface, the light intensities measured by each element of the dual-element Y photodiode are equal (i.e., IPX1 = IPX2 and IPY1 = IPY2), as shown in Figure3a. When the stylus tip comes X Movement direction into contact with the measuredFiber stylus surface in the X-direction, the laser-irradiated part of the stylus shaft is

IPX2 IRX2 displaced, and theD light intensities measured by each element of the IRX2 dual-element photodiode are no ＝ <

PX1 ＝ I IRX1 longer equal to each other (i.e., IPX1 = IPX2 and IPY1 > IPY2), as shown IRX1 in Figure3b. When the stylus shaft is displaced in theDual-element +X-direction, photodiode the angle of refraction Movement direction of the laser beam passing through the stylus shaft in the Y-directionCondenser lens changes owing to a shift in the part of the stylus shaft being irradiated. Additionally, when the stylus tip comes into contact with the measured surface in the Y-direction, the light intensities measured by each element of the dual-element photodiode are no longer equal to each (a) (b) (c) other (i.e., IPX1 < IPX2 and IPY1 = IPY2), as shown in Figure3c. As a result, the contact direction and

Figure 3. Principle of measurement. (a) initial stage, (b) displacement in X‐direction, and (c) displacement in Y‐direction.

3. Stylus Characteristics

Figure 4 shows the changes in outputs IX and IY when the stylus tip is displaced in the ±X‐direction. Here, the horizontal axis represents the displacement of the stylus tip and the vertical axis represents the changes in IX and IY. It can be seen that when the stylus tip is displaced in the X‐direction, barely any change occurs in the output IY in the Y‐direction and the fiber probe can function as a displacement sensor because the rate of change in IX can approximate a straight line within a ±3 μm range in the X‐direction.

8 Ix 6 Iy 4 2 0 -7-5-3-11357-2 -4 -6 Output voltage Ix, Iy V -8 Displacement X µm

Figure 4. Changes in output voltages IX and IY induced by displacement in ±X‐direction. Appl. Sci. 2016, 6, 153 4 of 11

Appl. Sci. 2016, 6, 153 4 of 11

the magnitude of displacement of the stylus tip can be obtained from the output signals IX and IY. When the stylus tip comes into contact with the measured surface in the Z-direction, the stylus shaft is buckled and deﬂected. This deﬂection is also measured using the above-mentioned method.

IPY2＝ IPY1 IRY2 < IRY1 IRY2 ＝ IRY1

X Fiber stylus Movement direction IPX2 IRX2 D IRX2 ＝＝ IPX1 < Figure 2. Measurement system using opticalIR X1 fiber probe. IRX1 Dual-element photodiode Movement direction

IPY2Condenser＝ IPY1 lens IRY2 < IRY1 IRY2 ＝ IRY1 (a) (b) (c) Y Figure 3.X Principle of measurement. (a) initial stage; (b) displacement in X-direction; Movement direction and Fiber stylus

PX1 ＝ I RX1 IRX1 I

Because the proposedDual-element probe photodiode measures the deflection Movement amplitude direction of the stylus shaft by using a laser-based non-contactCondenser method, lens the stylus shaft does not need to be rigid; this principle also applies to a stylus with a much smaller diameter. This measurement system measures the deflection of the stylus shaft; however, it does not directly measure the displacement of the stylus tip. The noise present in IX (a) (b) (c) and IY is removed via synchronous detection using a lock-in amplifier. The displacement of the stylus is magnified by using it as a rod lens. The surface of the microstructure is measured by recording the displacementFigure 3. ofPrinciple the stylus of shaftmeasurement. as well as (a the) initial coordinates stage, (b at) whichdisplacement the stylus in X comes‐direction, into contactand (c) with the measureddisplacement surface. in Y‐direction.

3. Stylus Stylus Characteristics Characteristics

X Y Figure 44 showsshows thethe changeschanges inin outputsoutputs IX and IY whenwhen the the stylus stylus tip tip is is displaced in the ±˘XX‐direction.-direction. Here, Here, the the horizontal horizontal axis axis represents represents the the displacement displacement of of the the stylus stylus tip tip and and the the vertical X Y axis represents the changes in IX andand IIY. .It It can can be be seen seen that that when when the the stylus stylus tip tip is is displaced in in the Y X‐-direction,direction, barely barely any change occurs in in the output IY inin the the YY‐-directiondirection and and the the fiber ﬁber probe can X functionfunction as a displacement sensor because the the rate of change in IX can approximate a straight line within a ±3˘3 μµmm range range in in the the XX‐-direction.direction.

8 Ix 6 Iy 4 2 0 -7-5-3-11357-2 -4 -6 Output voltage Ix, Iy V -8 Displacement X µm

Figure 4. Changes in output voltages IX and IY induced by displacement in ˘X-direction. Figure 4. Changes in output voltages IX and IY induced by displacement in ±X‐direction.

Appl.Appl. Sci. Sci. 20162016, 6,,6 153, 153 5 5of of 11 11

4. Effects of Surface Force 4. Effects of Surface Force

4.1.4.1. Analyses Analyses of of Liquid Liquid Bridge Bridge Force, Force, Van Van der der Waals Waals force, force, and and Electrostatic Electrostatic Force Force InIn general, general, when when the the particle particle size size is is less less than than several several tens tens of of micrometers, micrometers, the the effects effects of of the the surfacesurface force force generated generated from from the the van van der der Waals Waals force, force, electrostatic electrostatic force, force, and and liquid liquid bridge bridge force force are are strengthenedstrengthened and and this this surface surface force force becomes becomes greater greater than than the the force force of of gravity gravity [11]. [11]. Figure Figure 55 showsshows a a schematicschematic diagram diagram of of the the surface surface force force between between the the stylus stylus tip tip and and the the measurement measurement surface. surface. Because Because thethe fiber ﬁber stylus stylus has has a a 5 5-‐μµmm-diameter‐diameter sphere sphere on on its its tip, tip, the the measurement measurement surface surface draws draws the the stylus stylus tip tip closercloser when when the the stylus stylus tip tip approaches approaches it, it, and and the the distance distance between between the the stylus stylus tip tip and and the the measured measured surfacesurface is is lessless thanthan the the regular regular displacement. displacement. When When the stylusthe stylus tip comes tip comes into contact into withcontact the with measured the measuredsurface, it surface, adheres it to adheres the surface to the and surface cannot and be cannot separated be separated from it. When from it. the When measured the measured surface is surfacescanned is pointscanned by point by in thepoint touch-trigger in the touch mode,‐trigger the mode, measurement the measurement time increases time increases because the because stylus thetip stylus is required tip is torequired be separated to be separated from the measuredfrom the measured surface on surface account on of account the surface of the force. surface When force. the Whenmeasured the measured surface is surface scanned is continuouslyscanned continuously in the scanning in the scanning mode, measurement mode, measurement accuracy accuracy reduced reducedbecause because of the bending of the bending of the stylus of the shaft stylus due shaft to the due adhesion. to the adhesion. The observed The observed adhesion, adhesion, which is whichinﬂuenced is influenced by environmental by environmental factors (e.g.,factors humidity) (e.g., humidity) and the and roughness the roughness of the measuredof the measured surface, surface,is not reproducible. is not reproducible.

FigureFigure 5. 5. SchematicSchematic diagram diagram of of surface surface force force between between stylus stylus tip tip and and measured measured surface. surface.

TheseThese surface surface forces forces are are analyzed analyzed with with the the aim aim of investigating of investigating the thecauses causes of adhesion. of adhesion. First, First, we examinewe examine the liquid the liquid bridge bridge force. force. This This force force has a has large a large effect effect on adhesion on adhesion in a in humid a humid environment; environment; it isit generated is generated by bythe the capillary capillary action action of ofcondensed condensed water water near near the the contact contact zone zone of of the the stylus stylus tip tip and and measured surface. This force increases with increasing relative humidity. The liquid bridge force Fl measured surface. This force increases with increasing relative humidity. The liquid bridge force Fl experiencedexperienced in in the the case case of of a a stylus stylus tip tip of of diameter diameter dd andand under under a a relative relative humidity humidity of of % %RHRH cancan be be calculatedcalculated using using the empiricalempirical formulaformula in in Equation Equation (3) (3) [11 [11].]. This This is the is the empirical empirical formula formula of the of liquid the liquidbridge bridge force betweenforce between a particle a particle and a plateand a with plate a with hard a and hard clean and surface. clean surface. As indicated As indicated by this formula,by this formula,the liquid the bridge liquid force bridge increases force increases with increasing with increasing relative humidity.relative humidity.

Fl = 0.15d{0.5 + 0.0045 × (%RH)} (3) Fl “ 0.15dt0.5 ` 0.0045 ˆ p%RHqu (3) Next, we examine the van der Waals force. This force acts between molecules, and it is a general force Next,of interaction we examine that the acts van between der Waals objects force. at This all force times. acts The between van der molecules, Waals andforce it F isV acan general be calculatedforce of interaction using the thatHamaker acts between constant objects A and at the all distance times. The z between van der the Waals stylus force tipF andV can the be measured calculated surfaceusing theas given Hamaker in Equation constant (4)A [11].and The the distanceHamakerz constantbetween A the is a stylus constant tip andspecific the measuredto materials, surface and itas is givenexpressed in Equation as in Equation (4) [11 ].(5), The where Hamaker n and constantΛ are theA numberis a constant of atoms speciﬁc per unit to volume materials, and and the it constantis expressed of proportionality as in Equation of (5),London where forces,n and respectively.Λ are the number When the of atomsmolecules per of unit the volume stylus tip and and the theconstant measured of proportionality surface come close of London to each forces, other respectively.by the van der When Waals the force, molecules intermolecular of the stylus repulsive tip and force is generated between the molecules of the stylus tip and the measured surface. The molecules Appl. Sci. 2016, 6, 153 6 of 11 are stabilized at the most stable position, which corresponds to the position with the smallest potential energy. At this instant, the separation distance z is about 0.4 nm.

Appl. Sci. 6 2 2016, , 153 FV = Ad/(12z ) 6 of(4) 11

A = n2 π2 Λ (5) the measured surface come close to each other by the van der Waals force, intermolecular repulsive Finally, the electrostatic force generated by an interaction between a charged particle and an force is generated between the molecules of the stylus tip and the measured surface. The molecules are uncharged surface is examined. When a charged particle comes into contact with an uncharged stabilized at the most stable position, which corresponds to the position with the smallest potential surface, the generated electrostatic force Fe can be calculated using Equation (6) in the case that the energy. At this instant, the separation distance z is about 0.4 nm. distance between the stylus tip and the measured surface is negligible because it is remarkably small compared with the diameter of the stylus tip [11]. 2 FV “ Ad{p12z q (4) εε ∙ 2 2 ∙ σ (6) A4ε“ nεεπ Λ (5)

whereFinally, ε the, ε, electrostatic and σ are the force dielectric generated constant by an interactionof the vacuum, between the adielectric charged constant particle andof the an measureduncharged surface, surface isand examined. the marginal When surface a charged density particle of the comes charge into of contact the stylus with tip, an unchargedrespectively. surface, the generatedFigure 6 electrostaticshows the forcerelationshipFe can bebetween calculated the using stylus Equation tip diameter (6) in theand case the that surface the distance forces calculatedbetween the using stylus Equations tip and the (3), measured (4), and surface (6). Here, is negligible the horizontal because itaxis is remarkably represents small the stylus compared tip withdiameter the diameter and the vertical of the stylus axis tiprepresents [11]. the van der Waals force, electrostatic force, liquid bridge force, and gravity. It can be seen from this figure that when the stylus tip diameter is less than about π ε ´ ε 1 mm, the effects of surface force generatedF “ from¨ the0 van¨ d2σ der2 Waals force, electrostatic force, and(6) e ε ε ε liquid bridge force are strengthened and the 4surface0 ` force0 becomes greater than the force of gravity. This confirms that the primary cause of adhesion is the liquid bridge force. The van der Waals where ε0, ε, and σ are the dielectric constant of the vacuum, the dielectric constant of the measured forcesurface, and and liquid the marginal bridge force surface are density approximately of the charge equal. of theHowever, stylus tip, the respectively. electrostatic force is much smallerFigure than6 showsthe van the der relationship Waals force between and liquid the stylusbridge tip force. diameter When and the thesurface surface forces forces are calculatedcalculated using Equations (3), (4), and (6).(6) for Here, a stylus the horizontal tip 5 μm axisin diameter, represents the the liquid stylus bridge tip diameter force (50% and RH the), verticalvan der axisWaals represents force, and the electrostatic van der Waals force force,are 0.54 electrostatic μN, 0.36 μ force,N, and liquid 0.0016 bridge μN, respectively. force, and gravity. In this case,It can the be seensum of from the this surface ﬁgure forces that whenis approximately the stylus tip 0.9 diameter μN. Figure is less 7 shows than about the relationship 1 mm, the effectsbetween of thesurface relative force humidity generated and from the the sum van of dersurface Waals forces force, (F electrostaticl + Fv + Fe) calculated force, and using liquid Equations bridge force (3), (4), are andstrengthened (6). It can and be seen the surface from this force figure becomes that the greater liquid than bridge the force force of increases gravity. with increasing relative humidity.

´20 Figure 6. RelationshipRelationship between between stylus stylus tip tip diameter diameter and and surface surface forces: forces: A (SiOA (SiO2) = 21.5) = × 1.510−20ˆ J,10 z = 0.4J, −12 −´1 12 ´1 −2 ´2 nm,z = 0.4 ε nm, = 8.85ε0 =× 8.8510 ˆF∙m10 , ε F=¨ m∞, σ, ε== 26.58, σ μ=C∙ 26.5m . µC¨ m .

This conﬁrms that the primary cause of adhesion is the liquid bridge force. The van der Waals force and liquid bridge force are approximately equal. However, the electrostatic force is much smaller than the van der Waals force and liquid bridge force. When the surface forces are calculated using Equations (3), (4), and (6) for a stylus tip 5 µm in diameter, the liquid bridge force (50% RH), van der Waals force, and electrostatic force are 0.54 µN, 0.36 µN, and 0.0016 µN, respectively. In this case, the sum of the surface forces is approximately 0.9 µN. Figure7 shows the relationship between the relative Appl. Sci. 2016, 6, 153 7 of 11

humidity and the sum of surface forces (Fl + Fv + Fe) calculated using Equations (3), (4), and (6). It can Appl.be Sci. seen 2016 from, 6, 153 this ﬁgure that the liquid bridge force increases with increasing relative humidity. 7 of 11

1.1 1 0.9 0.8

Surface force µN force Surface 0.7 0 20406080100 Relative humidity %

FigureFigure 7. Relationship 7. Relationship between between relative relative humidity and and surface surface force force (stylus (stylus tip diameter:tip diameter: 5 µm). 5 μm).

4.2. Effect4.2. Effect of Relative of Relative Humidity Humidity on on the the Liquid Liquid Bridge ForceForce As Asstated stated in in the the discussion discussion above, above, the the primary primary cause cause of adhesion of adhesion is the liquid is the bridge liquid force, bridge which force, increases with increasing relative humidity. When the measured surface is scanned point by point which increases with increasing relative humidity. When the measured surface is scanned point by in the touch-trigger mode, the measurement time increases because the stylus tip is required to be point in the touch‐trigger mode, the measurement time increases because the stylus tip is required to separated from the measured surface on account of the surface force. When the measured surface is be separatedscanned continuously from the measured in the scanning surface mode, on account the measurement of the surface accuracy force. reduces When owing the tomeasured the bending surface is scannedof the stylus continuously shaft due to in the the adhesion. scanning Therefore, mode, inthe our measurement previous work, accuracy a vibration reduces mechanism owing was to the bendingintroduced of the to stylus prevent shaft the adhesion due to of the the stylusadhesion. tip to Therefore, the measurement in our surface previous caused work, by the surfacea vibration mechanismforce [12 ].was By thisintroduced mechanism, to prevent the stylus the tip adhesion is set to vibrate of the in stylus a circular tip to motion, the measurement where it traces surface a causedcircle by of the diameter surface 0.4 µforcem in the[12].X -ByY plane. this However,mechanism, the stylusthe stylus shaft actuallytip is set traces to vibrate an elliptical in a path. circular motion,The differencewhere it between traces a the circle profile of of diameter the perfect 0.4 circle μm and in that the of X the‐Y actualplane. elliptical However, path ofthe the stylus stylus shaft actuallytip leads traces to measurementan elliptical errors.path. The Moreover, difference the surface between roughness the profile cannot of be the measured perfect in circle the scanning and that of the modeactual when elliptical using thepath vibrating of the fiber stylus probe. tip leads to measurement errors. Moreover, the surface Therefore, the measurement system, placed in a vacuum vessel, is constructed suitably to prevent roughness cannot be measured in the scanning mode when using the vibrating fiber probe. adhesion of the stylus tip to the measured surface caused by the surface force. Figure8 shows a Therefore, the measurement system, placed in a vacuum vessel, is constructed suitably to photograph of the measurement system in the vacuum vessel. The effects of pressure inside the preventvacuum adhesion vessel onof the surfacestylus tip force to are the evaluated measured experimentally. surface caused In theby experiment,the surface theforce. relative Figure 8 showshumidity a photograph is 61% and of thethe temperature measurement is 25.1 system˝C. in the vacuum vessel. The effects of pressure inside the vacuumFirst, vessel the measurement on the surface method force of are the evaluated surface force experimentally. is explained as In follows. the experiment, There are the many relative humiditytechniques is 61% for and measuring the temperature surface forces, is 25.1 such °C. as those involving the surface forces apparatus (SFA), atomic force microscopy (AFM), micro cantilever (MC), optical trapping (OT), etc. [13–15]. The SFA can directly measure the force between two surfaces in controlled vapors or immersed in liquids. The force sensitivity of the SFA is about 10 nN. The SFA contains two curved molecularly smooth surfaces of mica between which the interaction forces are measured using a variety of force-measuring springs. AFM is, in principle, similar to the SFA except that forces are measured not between two macroscopic surfaces but between a fine tip and a surface. The force sensitivity of AFM is 1–10 pN. The measuring method using the optical fiber probe is, in principle, similar to the SFA and AFM. As shown in Figure9, after the stylus tip comes into contact with the measured surface, the stylus tip is displaced in the backward direction by using the piezoelectric stage, due to which it separates from the measured surface. Because the stylus tip is displaced while maintaining its contact with the measured surface, the stylus shaft is deflected and the force required to separate the stylus tip from the measured surface is generated by the deflection of the stylus shaft. With an increase in the displacement of the stylus tip, this required force also increases. Therefore, the stylus tip can be separated from the measured surface when the displacement D of the stylus tip exceeds a certain value.

Figure 8. Photograph of measurement system in vacuum vessel.

First, the measurement method of the surface force is explained as follows. There are many techniques for measuring surface forces, such as those involving the surface forces apparatus (SFA), Appl. Sci. 2016, 6, 153 7 of 11

1.1 1 0.9 0.8

Surface force µN force Surface 0.7 0 20406080100 Relative humidity %

Figure 7. Relationship between relative humidity and surface force (stylus tip diameter: 5 μm).

4.2. Effect of Relative Humidity on the Liquid Bridge Force As stated in the discussion above, the primary cause of adhesion is the liquid bridge force, which increases with increasing relative humidity. When the measured surface is scanned point by point in the touch‐trigger mode, the measurement time increases because the stylus tip is required to be separated from the measured surface on account of the surface force. When the measured surface is scanned continuously in the scanning mode, the measurement accuracy reduces owing to the bending of the stylus shaft due to the adhesion. Therefore, in our previous work, a vibration mechanism was introduced to prevent the adhesion of the stylus tip to the measurement surface caused by the surface force [12]. By this mechanism, the stylus tip is set to vibrate in a circular motion, where it traces a circle of diameter 0.4 μm in the X‐Y plane. However, the stylus shaft actually traces an elliptical path. The difference between the profile of the perfect circle and that of the actual elliptical path of the stylus tip leads to measurement errors. Moreover, the surface roughness cannot be measured in the scanning mode when using the vibrating fiber probe. Therefore, the measurement system, placed in a vacuum vessel, is constructed suitably to prevent adhesion of the stylus tip to the measured surface caused by the surface force. Figure 8 shows a photograph of the measurement system in the vacuum vessel. The effects of pressure inside

Appl.the vacuum Sci. 2016, 6vessel, 153 on the surface force are evaluated experimentally. In the experiment, the relative8 of 11 humidity is 61% and the temperature is 25.1 °C.

Appl. Sci. 2016, 6, 153 9 of 11 reduce the liquid bridge force. In order to reduce the van der Waals force, a stylus tip made of a material with a small Hamarker constant may be used. For example, the Hamaker constants of SiO2, Fe, Si, Cu, and Au are 8.55, 21.2, 25.6, 28.4, and 45.5 × 10−20 J, respectively. However, in practice, the use of a material with a small low Hamarker constant can be difficult. In such cases, a stylus tip coated with a material with a small Hamarker constant may be used. The effect of the material of the stylus tip can be made negligible by using a coating that is several nanometers thick. The influence of Figure 8. Photograph of measurement system in vacuum vessel. the electrostatic forceFigure on the 8. surfacePhotograph force of is measurement small; however, system it in is vacuum believed vessel. that various methods of removalFirst, of the electricity measurement or antistatic method agents of thecould surface be useful force in is reducing explained the as electrostatic follows. There force. are many techniques for measuring surface forces, such as those involving the surface forces apparatus (SFA), D

Contact Adhesion Separation

Figure 9. Experimental apparatus for measurement of surface force.

The load acting on the stylus0.4 tip, i.e., the surface force, is calculated by assuming that the optical fiber probe, 2.5 µm in diameter and 0.38 mm in length, is equal to the cantilever of the fixed support. 0.3 In other words, the surface force is calculated by the deflection of the stylus shaft. The surface force F is calculated using Equation (7). 0.2

µN 3EI F “ ¨ D (7) 0.1 L3 where E, I, and L are the Young’s modulus,0 the geometrical moment of inertia, and the length of the stylus shaft, respectively. Figure on stylus tip Load acting 10 shows0 the 1020304050 load acting on the stylus tip under the assumption that the stylus shaft (Young’s modulus E = 72 GPa) is equivalent to the cantilever of the ﬁxed support. In this Displacement of stylus tip D μm ﬁgure, the horizontal axis represents displacement of the stylus tip, and the vertical axis represents the loadFigure acting 10. Load on the acting stylus on tip.the stylus For example, tip (stem whenlength: the 0.38 displacement mm, stem diameter:D required 2.5 μm, to and separate ball the stylusdiameter: tip from 5 μ them). measured surface is about 20 µm, the load acting on the stylus tip is about 0.15 µN immediately before the stylus tip is separated from the measured surface as shown in Figure 10. Therefore, this value of 0.15 µN70 is regarded as the surface force. In this experiment, the spring constant of the stylus shaft is not calibrated.60 However, to accurately measure the surface force, it is necessary to calibrate it [16–19]. 50 40 30 20 10 Relative humidity % 0 0.1 1 10 100 1000 Pressure inside vacuum vessel Pa

Figure 11. Relationship between pressure inside vacuum vessel and relative humidity.

0.4

0.3

0.2

0.1 Surface forceSurface µN

0 0.1 1 10 100 1000 Pressure inside vacuum vessel kPa Appl. Sci. 2016, 6, 153 9 of 11

reduce the liquid bridge force. In order to reduce the van der Waals force, a stylus tip made of a material with a small Hamarker constant may be used. For example, the Hamaker constants of SiO2, Fe, Si, Cu, and Au are 8.55, 21.2, 25.6, 28.4, and 45.5 × 10−20 J, respectively. However, in practice, the use of a material with a small low Hamarker constant can be difficult. In such cases, a stylus tip coated with a material with a small Hamarker constant may be used. The effect of the material of the stylus tip can be made negligible by using a coating that is several nanometers thick. The influence of the electrostatic force on the surface force is small; however, it is believed that various methods of removal of electricity or antistatic agents could be useful in reducing the electrostatic force.

Contact Adhesion Separation Appl.Appl. Sci. Sci.2016 2016, 6,, 6 153, 153 9 of9 of11 11 Figure 9. Experimental apparatus for measurement of surface force. reduceAppl. Sci. the 2016 liquid, 6, 153 bridge force. In order to reduce the van der Waals force, a stylus tip made9 of of 11 a material with a small Hamarker constant0.4 may be used. For example, the Hamaker constants of SiO2, Fe,reduce Si, Cu, the and liquid Au arebridge 8.55, force. 21.2, In25.6, order 28.4, to andreduce 45.5 the × 10 van−20 J,der respectively. Waals force, However, a stylus tipin practice,made of thea 0.3 usematerial of a material with a small with Hamarker a small low constant Hamarker may be constant used. For can example, be difficult. the Hamaker In such constantscases, a stylus of SiO 2tip, −20 coatedFe, Si, with Cu, anda material Au are with 8.55, a 21.2, small 0.225.6, Hamarker 28.4, and constant 45.5 × 10 may J, be respectively. used. The effectHowever, of the in material practice, of the the

stylususe of tip a canmaterial be made with negligible a small µN low by using Hamarker a coating constant that iscan several be difficult. nanometers In such thick. cases, The a influence stylus tip of 0.1 thecoated electrostatic with a material force on with the a surface small Hamarker force is small; constant however, may be it used. is believed The effect that of variousthe material methods of the of stylus tip can be made negligible by using a coating that is several nanometers thick. The influence of removal of electricity or antistatic agents0 could be useful in reducing the electrostatic force. the electrostatic force on the on stylus tip Load acting surface 0force is 1020304050 small; however, it is believed that various methods of removal of electricity or antistatic agents could be useful in reducing the electrostatic force. Displacement of stylus tip D μmD

FigureFigure 10. 10.Load Load acting acting on on the the stylus stylus tip tip (stem(stem length:length: 0.38 0.38 mm, mm, stemD stem diameter: diameter: 2.5 2.5 μm,µ m,and and ball ball diameter:diameter: 5 µ 5m). μm). Contact Adhesion Separation Figure 11 shows the relationshipContact70 betweenAdhesion the pressure insideSeparation the vacuum vessel and the relative Figure 9. Experimental apparatus for measurement of surface force. humidity. Further, Figure 12 shows60 the relationship between the pressure inside the vacuum vessel 50 and the surface forces.Figure Finally, 9. Experimental Figure 13 showsapparatus the for relationship measurement betweenof surface force. the relative humidity and 400.4 the surface force. From Figure 13, it is conﬁrmed that surface force decreases with decreasing relative 300.4 0.3 µ humidity. It is found that the surface20 force is 0.13 N when pressure inside the vacuum vessel and relative humidity are 350 Pa and 7%100.3RH, respectively. This effect is equivalent to a 60% reduction in the Relative humidity % 0.2 surface force in the atmosphere. However,µN a large residual surface force still acts between the stylus tip 00.2 0.10.1 1 10 100 1000 and the measured surface. This isµN because the amount of van der Waals force is almost the same as that of the liquid bridge force. Therefore,0.1 thePressure surface inside force vacuum is thought vessel to Pa reduce by slightly a little more than 0 60%. When the stylus tip diameter on stylus tip Load acting is 5 µm as shown in Figure6, the theoretical van der Waals force in 0 0 1020304050 a vacuum environmentFigure 11. Relationship is about on stylus tip Load acting 0.36 betweenµN. However, pressure inside according vacuum to vessel the obtained and relative experimental humidity. results, the 0Displacement 1020304050 of stylus tip D μm van der Waals force in a vacuum environment is about 0.13 µN. Thus, the theoretical and experimental Displacement of stylus tip D μm resultsFigure are different. 10. Load Because acting on the the amount 0.4stylus tip of van(stem der length: Waals 0.38 force mm, is stem affected diameter: by the 2.5 surface μm, and roughness ball of diameter:Figure 10. 5 μ Loadm). acting on the stylus tip (stem length: 0.38 mm, stem diameter: 2.5 μm, and ball the stylus tip and that of the measurement0.3 surface [11], the surface roughness of the stylus tip and that of the measurementdiameter: 5 μm). surface are, in turn, thought to be affected by the amount of van der Waals force. 700.2 70 600.1 5060forceSurface µN 4050 0 0.1 1 10 100 1000 3040 2030 Pressure inside vacuum vessel kPa 1020 Relative humidity % 10 Relative humidity % 0 00.1 1 10 100 1000 0.1Pressure 1 inside vacuum 10 vessel 100 Pa 1000 Pressure inside vacuum vessel Pa

FigureFigure 11. 11.Relationship Relationship betweenbetween pressure inside vacuum vacuum vessel vessel and and relative relative humidity. humidity. Figure 11. Relationship between pressure inside vacuum vessel and relative humidity.

0.4 0.4 0.3 0.3 0.2 0.2 0.1

Surface forceSurface µN 0.1 Surface forceSurface µN

00 0.10.1 1 10 100 100 1000 1000 Pressure inside vacuum vessel kPa Pressure inside vacuum vessel kPa Figure 12. Relationship between pressure inside vacuum vessel and surface forces. Appl. Sci. 2016, 6, 153 10 of 11

Appl. Sci. 2016, 6Figure, 153 12. Relationship between pressure inside vacuum vessel and surface forces. 10 of 11

0.4

0.3

0.2

0.1 Surfaceforce µN

0 0 20406080 Relative humidity %

Figure 13. Relationship between relative humidity and surface forces. Figure 13. Relationship between relative humidity and surface forces. 4.3. Alternative Reduction Method for Surface Force 5. Conclusions According to the above-mentioned experimental results, it is possible to reduce the liquid bridge In this study, the stylus characteristics are examined, and then, surface forces are analyzed in force considerably by using a vacuum vessel. However, in scenarios where the use of a vacuum vessel order to investigate the causes of adhesion, which reduces the measurement accuracy. The analysis is difficult, the stylus tip coated with a water-repellent coating has the potential to reduce the liquid results of surface forces reveal the liquid bridge force to be the primary cause of adhesion. Therefore, bridge force. In order to reduce the van der Waals force, a stylus tip made of a material with a small the measurement system placed in the vacuum vessel is constructed suitably to prevent adhesion of Hamarker constant may be used. For example, the Hamaker constants of SiO , Fe, Si, Cu, and Au the stylus tip to the measured surface because of the surface forces, mainly by2 reducing the liquid are 8.55, 21.2, 25.6, 28.4, and 45.5 ˆ 10´20 J, respectively. However, in practice, the use of a material bridge force. As a result, it is found that the surface force is 0.13 μN when the pressure inside the with a small low Hamarker constant can be difficult. In such cases, a stylus tip coated with a material vacuum vessel is 350 Pa. This effect is equivalent to a 60% reduction in the surface force in the with a small Hamarker constant may be used. The effect of the material of the stylus tip can be made atmosphere. negligible by using a coating that is several nanometers thick. The influence of the electrostatic force onAcknowledgments: the surface force This is small; study however,was partly it supported is believed by that a research various grant methods from the of removal Mitutoyo of Association electricity for or antistaticScience and agents Technology could and be usefulby JSPS in KAKENHI reducing Grant the electrostatic Number 26420392. force. Author Contributions: Hiroshi Murakami conceived and wrote the paper; Akio Katsuki and Takao Sajima 5.manufactured Conclusions the vacuum vessel and analyzed the data; Hiroshi Murakami and Mitsuyoshi Fukuda performed the experimentsIn this study, and theanalyzed stylus the characteristics surface forces. are examined, and then, surface forces are analyzed in orderConflicts to investigateof Interest: The the authors causes declare of adhesion, no conflict which of interest. reduces the measurement accuracy. The analysis results of surface forces reveal the liquid bridge force to be the primary cause of adhesion. Therefore, theReferences measurement system placed in the vacuum vessel is constructed suitably to prevent adhesion of the stylus1. Masuzawa, tip to the T.; measured Hamasaki, surface Y.; Fujino, because M. Vibroscanning of the surface method forces, for mainly nondestructive by reducing measurement the liquid of bridge small force.holes. As a CIRP result, Annals it is 1993 found, 42 that, 589–592. the surface force is 0.13 µN when the pressure inside the vacuum vessel2. Hidaka, is 350 K.; Pa. Saito, This A.; effect Koga, is equivalentS.; Study of a to micro a 60%‐roughness reduction probe in the with surface ultrasonic force sensor. in the CIRP atmosphere. Annals 2008, 57, 489–492. Acknowledgments: This study was partly supported by a research grant from the Mitutoyo Association for Science3. Bauza, and TechnologyM.B.; Hocken, and R.J.; by JSPSSmith, KAKENHI S.T.; Woody, Grant S.C. Number Development 26420392. of a virtual probe tip with an application to high aspect ratio microscale features. Rev. Sci. Instrum. 2005, 76, doi:10.1063/1.2052027. Author Contributions: Hiroshi Murakami conceived and wrote the paper; Akio Katsuki and Takao Sajima manufactured4. Claverley, the J.D.; vacuum Leach, vessel R.K. and A analyzedvibrating the micro data;‐scale Hiroshi CMM Murakami probe andfor Mitsuyoshimeasuring Fukudahigh aspect performed ratio the experimentsstructures. Microsyst. and analyzed Technol. the surface 2010, 16 forces., 1507–1512.

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