contact angle 69326_18

Part 4

Surface Free Energy and Relevanceof Wettability in Adhesion

Comparison of Apparent Surface Free Energy of SomeSolids Determined by Different Approaches

Emil Chibowski ∗ and Konrad Terpilowski

Department of Physical Chemistry-Interfacial Phenomena, Faculty of Chemistry,Maria Curie Sklodowska University, 20-031 Lublin, Poland

AbstractFour different approaches to determination of solid surface free energy (van Oss et al.’s (LWAB), Owensand Wendt’s (O–W), Chibowski’s contact angle hysteresis (CAH) and Neumann’s equation of state (EQS))were examined on glass, silicon, mica and poly(methyl methacrylate) (PMMA) surfaces via measurementsof advancing and receding contact angles. Sessile drop and tilted plate methods were employed to measurethe contact angles of probe liquids water, formamide and diiodomethane. The results obtained show thaton a given solid the advancing contact angle is slightly larger and the receding one smaller if measured bytilted plate method. Hence, the resulting hysteresis is larger than that from the contact angles measured bysessile drop. The calculated (apparent) surface free energy is the greatest if determined from O–W equation.Unexpectedly, EQS fails for weakly polar polymer PMMA surface, giving significantly lower value of thecalculated energy. In rest of the tested systems LWAB, CAH and EQS approaches give comparable resultsfor the apparent surface free energy of the tested solids. A hypothesis is put forward that using a probeliquid only apparent surface free energy of a solid can be determined because the strength of interactionsoriginating from the solid surface depends on the strength of interactions coming from the probe liquidsurface.

KeywordsSolids, surface free energy, different approaches

1. Introduction

Despite numerous papers published dealing with solid surface free energy determi-nation, it is still an open problem. Not only regarding the theoretical approach, butalso regarding which measured contact angle on a real solid surface is appropriatefor use in the Young equation [1–4]. A critical evaluation of the approaches andthe resulting equations used for calculations of surface tension components and/orsolid surface free energy was published by Lyklema [5], who pointed out a weakthermodynamic basis underlying the derivations and concluded: “So there is a rea-

* To whom correspondence should be addressed. Tel.: +48-81-537 56 51; Fax: +48-81-533 33 48; e-mail:[email protected]

Contact Angle, Wettability and Adhesion, Vol. 6

Koninklijke Brill NV, Leiden, 2009

284 E. Chibowski and K. Terpilowski

son to continue using equations like equation (16). However, there is no reasonto over-interpret equation (16) by empirically adding extra terms (like acid–baseinteractions), let alone combining γ values with contact angle data, using an ad-ditional empirical expression to obtain solid–liquid interfacial tensions. . .”. Theequation mentioned above is that used for the first time by Fowkes [6, 7], in whichfor the dispersion interactions Berthelot’s rule was applied:

γ12 = γ1 + γ2 − 2(γ d1 γ d

2 )1/2, (1)

where subscripts 1 and 2 denote two phases, for example solid and liquid, andsuperscript d means dispersion interactions. Using this equation and measuring n-alkane/water interfacial tensions Fowkes determined the dispersion interaction forwater to be 21.8 mN/m, and hence the resulting polar (now interpreted as acid–basehydrogen bonding [8–10]) interaction to be 72.8−21.8 = 51.0 mN/m. These valuesare still commonly accepted.

Keeping in mind Lyklema’s [5] criticism, one would ask whether there is anysense in calculating surface free energy of a solid using known approaches, and theinterpretation of measured (apparent) contact angles is even more problematic. Onthe other hand, knowledge of solid surface free energy is a valuable quantity forprediction of many interfacial processes, especially those depending on wetting. Inour opinion, such calculations can still be useful, but one should be aware that thecalculated values are apparent ones, similarly like the measured contact angles onreal surfaces, both the advancing and receding, are also mostly apparent. It is alsoworth mentioning a review article published recently by Etzler [11], in which thetheoretical approaches and experimental determination of solid surface free energyare reviewed together with some other ‘supporting’ methods that “can shed consid-erable insight into the nature of the surfaces”, with 137 references.

In this paper we would like to compare the surface free energy results for severalsolid surfaces evaluated from the known approaches, being aware of the problemsassociated with their use. In one of the approaches both advancing and recedingcontact angles are utilized. The contact angles were measured on glass, silicon,mica and PMMA by sessile drop and tilted plate methods using three probe liquidswater, formamide and diiodomethane. The surfaces investigated were molecularlyflat. We were interested in finding whether these two methods of the advancingand receding contact angle measurements gave compatible results. In the publishedliterature there are not many papers in which comparison of the energy values hasbeen done for the same solids and using the contact angles measured by differentmethods. The results should answer the question whether all known approaches aresuitable to satisfactorily evaluate the apparent surface free energy of an investigatedsolid.

Comparison of Apparent Surface Free Energy 285

2. Brief Descriptions of the Approaches Used

2.1. Owens and Wendt Approach

One of the approaches for solid surface free energy determination which is stillfound in the published papers is that of Owens and Wendt [12]. It is based onextended Fowkes’ equation (1) and Young–Dupré equation (2):

WA = γl(1 + cos θ), (2)

where WA is the work of adhesion of probe liquid (l) to solid surface (s) and θ isthe liquid advancing contact angle. Hence:

γl(1 + cos θ) = 2(γ ds γ d

l )1/2 + 2(γps γ

pl )1/2, (3)

where the superscript d means dispersion interactions and p means polar interac-tions, which can be considered as dipole–dipole or hydrogen bonding. To determinethe components γ d

s and γps of solid surface free energy, contact angles of apolar

(diiodomethane) and polar (water or formamide) liquids have to be measured andthen the two equation (3) obtained can be solved simultaneously, thus obtaining thecomponents and the total surface free energy as the sum of the two components.

2.2. Neumann’s Equation of State Approach

It is a well known equation, which has been criticized in the literature [13, 14], butit is also used for solid surface free energy determination, especially of polymericmaterials [15, 16]. This equation is expressed as follows:

cos θ = −1 + 2√

γs

γle−β(γl−γs)2

, (4)

where β = 0.000125 (m2/mJ)2 is an experimental constant. In this approach nosurface free energy components are considered.

2.3. Lifshitz–van der Waals Acid–Base (LWAB) Approach of van Oss, Chaudhurryand Good

These authors [8–10] in the late eighties of the past century offered a new theoreticalapproach to describe to surface and interface free energy, where free energy of a sur-face i is expressed as a sum of two components, apolar Lifshitz–van der Waals γ LW

iand polar Lewis acid–base γ AB

i , which is determined by two parameters electrondonor γ −

i and electron acceptor γ +i . In most cases the acid–base interaction is due

to hydrogen bonding. They assumed that γ ABi could be expressed as the geometric

mean of γ −i and γ +

i parameters and included the dipole–dipole, and dipole–inducedipole (if present) into the γ LW

i component in which the principal interaction isLondon dispersion. In fact, experimentally only this latter interaction is determinedfrom the contact angle of an apolar liquid, mostly diiodomethane. Thus for a solidsurface its total surface free energy can be written as:

γ tots = γ LW

s + γ ABs = γ LW

s + 2(γ −s γ +

s )1/2 (5)


and for solid/liquid interfacial free energy the equation reads:

γsl = γs + γl − 2(γ LWs γ LW

l )1/2 − 2(γ +s γ −

l )1/2 − 2(γ −s γ +

l )1/2. (6)

Next, taking into account equation (2), and the definition of work of adhesion WA:

WA = γs + γl − γsl (7)

and the advancing contact angles θa one obtains:

γl(1 + cos θa) = 2(γ LWs γ LW

l )1/2 + 2(γ +s γ −

l )1/2 + 2(γ −s γ +

l )1/2. (8)

Then three equations of type (8) can be solved simultaneously and the solid totalsurface free energy can be obtained from equation (5) if contact angles of threeprobe liquids are measured and their surface tension components are known. VanOss et al. [8–10] arbitrarily assumed for water at room temperature equal acidic andbasic interactions, i.e., γ −

l = γ +l = 25.5 mN/m, while γ LW

l = 21.8 mN/m. Then thecomponents of surface tension for other probe liquids were determined via contactangle and/or interfacial tension measurements. Using this approach in most casesthe electron donor interaction γ −

s is determined to be much greater than γ +s , which

has caused heated discussion and other values for probe liquids surface tensioncomponents [17–21] have been suggested. Besides other debatable issues, both inOwens and Wendt’s [12] and van Oss et al.’s [8–10] approaches it is assumed thatthe strength of the given kind of interactions from the solid side is the same indepen-dent of the strength of probe liquid interactions, which, it seems, can be questioned.Anyway, at present van Oss et al.’s [8–10] procedure is often used for evaluation ofa solid surface free energy.

2.4. Contact Angle Hysteresis (CAH) Approach

Recently Chibowski [3, 17–19] derived an equation for evaluation of total surfacefree energy of a solid from advancing θa and receding θr contact angles of only oneprobe liquid:

γ tots = γl(1 + cos θa)

2

(2 + cos θr + cos θa). (9)

Thus the evaluated surface free energy of a given solid depends, to some extent,on the kind of probe liquid used. However, if several probe liquids are used theaveraged value (arithmetic mean) of the solid surface free energy agrees perfectlywith the mean value of total surface free energy determined from LWAB approachif several triads of probe liquids are used for the contact angle measurements andthe calculations [18]. If one considers that the equilibrium contact angle θe is thatwhen no hysteresis appears, i.e. θa = θr = θe, then from equation (9) it results that[19]:

γ tots = γl

2(1 + cos θe) = WA

2. (10)


With this assumption, if the equilibrium contact angle of this liquid is known in-deed, the solid surface free energy equals half of the work of adhesion of this probeliquid to the solid surface [19].

2.5. Evaluation of Equilibrium Contact Angle from Tadmor’s Equation

In addition to experimental procedures to determine the equilibrium contact angle[3], it can also be evaluated from the measured advancing and receding contactangles as derived by Tadmor [1, 4].

θo = cos−1(

�a cos θa + �r cos θr

�a + �r

), (11)

where according to the author’s denotations: θo, θa and θr are the equilibrium, ad-vancing and receding contact angles, respectively, and �a and �r are defined asfollows:

�a ≡(

sin3 θa

(2 − 3 cos θa + cos3 θa)

)1/3

, �r ≡(

sin3 θr

(2 − 3 cos θr + cos3 θr)

)1/3

.

Equation (11) has been derived from a combination of Young and Wenzel equationsand recognizing that the equilibrium contact angle results from the global energyminimum in the system [1, 4]. The advancing and receding contact angles resultfrom pinning of the three-phase contact line, resisting motion of the drop. He as-sumed that the resistance to the motion out for advancing drop was just equal tothe resistance to the motion in of the receding drop. This is because both of theseresistances are due to the three-phase contact line pinning to the similar protrusions[1]. In other words, the irregularities on the surface are isotropic with respect totheir nature and distribution [1, 4]. However, this is rather a weak assumption inthe derivations. We will calculate the equilibrium contact angles from equation (11)and then use them in calculations of the solid surface free energy both from LWAB(equation (8)) and CAH (equation (10)) approaches.

3. Experimental

3.1. Materials

Contact angles were measured on 20 mm × 30 mm plates of glass (Comex, Poland),silicon (Semiconductor Co., Czech Republic), mice sheets and PMMA. The glassand silicon plates were washed successively in methanol and acetone in an ultra-sonic bath, then rinsed with Milli-Q water and dried at 100◦C. The mica sheets usedfor the measurements were detached from a larger mineralogical specimen right be-fore the measurements. The PMMA plates after removing the protective foil werewashed for 15 min in 20% aqueous methanol solution in an ultrasonic bath, thenrinsed with Milli-Q water. All the plates before using them for the experiments werekept in a desiccator at room temperature. The AFM images and the histograms ofthe surfaces are shown in Fig. 1.


(a)

(b)

(c)

Figure 1. 3D AFM images (left) of glass (a), silicon (b), mica (c), and PMMA (d) surfaces andtopography of the surfaces. Rrms roughness and the average heights of the surfaces are given in thefigures (right).

As the probe liquids we used: water from Milli-Q system, formamide (Fluka,>99%) and diiodomethane (POCh Co., Poland, p.a.). Their surface tension and itscomponents, as well as the molecule’s volume and its diameter (calculated from


(d)

Figure 1. (Continued.)

Table 1.Surface tension and its components in mN/m of the probe liquids used and volume (Å3) and diameter(Å) of the molecules

Liquid γL γ LWL γ +

L γ −L γ AB

L Vmolec., Å3 d, Å

Water 72.8 21.8 25.5 25.5 51.0 29.9 3.8Formamide 58.0 39.0 2.28 39.6 19.0 66.1 5.0Diiodomethane 50.8 50.8 0 0 0.0 133.9 6.3

molecular volume of the liquid and Avogadro’s number and assuming sphericalshape of the molecule) are presented in Table 1.

3.2. Methods

3.2.1. Contact Angle MeasurementsContact angles were measured using a contact angle meter (GBX France) equippedwith a video camera with sessile drop and tilted plate methods. In the sessile dropmethod 6 µl droplet of the probe liquid was gently deposited on the surface by anautomated deposition system and advancing contact angle was measured. Then 1 µlof the liquid was withdrawn into the syringe and the receding contact angle wasmeasured.

3.2.2. AFM Images10 mm × 10 mm size plates were investigated using a Nanoscope (Veeco, USA)atomic force microscope (AFM) with standard silicon tip and contact mode. Theimages were obtained at room temperature and in open atmosphere. Then the rough-ness of the surfaces were analyzed using WSxM 4.0, Develop 8.0 software [20].


4. Results and Discussion

4.1. Topography of the Surfaces

Figure 1a–d shows 3D (top view, zero angle inclination) AFM images (left) andhistograms (right) of the investigated surfaces. As can be seen the most flat surfaceis that of silicon (Fig. 1b) whose average roughness height is 0.43 nm and the Rrms(root mean square roughness) roughness amounts to 0.12 nm. The silicon surfaceroughness distribution is quite symmetrical around 0.43 nm and it ranges between0–0.8 nm. The greatest height, 4.91 nm (Rrms = 0.88 nm) is found for the PMMAsurface, and it is distributed between 2 to 8 nm (Fig. 1d). One would expect micasurface to be a very flat one. But, as seen in Fig. 1c in the 3D image there aresmall patches on the smooth large mica sheet surface. Hence, the average height is2.35 nm (Rrms = 0.72) and the protrusion height ranges from 0 up to 5 nm, but 80%of them lie between 1.2 and 3.5 nm. As for the glass plate surface (Fig. 1a), theaverage height of the protrusions is 2.59 nm (Rrms = 0.95 nm) and higher protru-sions than their average height are seen in the histogram in significant amounts. Theprotrusions can affect contact angle hysteresis of the probe liquids, i.e. the biggerthe height and less dense their distribution the larger the contact angle hysteresis[21–23]. But, this may only occur if the contact angle is measured for the same liq-uid on the same solid surface but possessing different roughnesses. However, Önerand McCarthy [24] show that the contact angle of water on silane-modified siliconsurface (dimethyldichlorosilane (DMDCS) possessing 2–32 µm2 square posts, witha height of 40 µm, the contact angle hysteresis is almost similar 26–35◦, while it isonly 5◦ on the flat surface. But, the hysteresis increases sharply to 58◦ if the postsize is 64 µm2 and again drops down to 36◦ if the posts are 128 µm2. Moreover,the same authors [24] found that on the surface with 16 × 16 µm or 32 × 32 µmsquare posts, with heights between 20 and 120 µm, water contact angle hysteresiswas similar. These contact angles were well above 100◦ and even up to 176◦. Theprotrusions of the surfaces studied here by us are of only few nanometers scale,therefore the surfaces can be regarded as molecularly flat. As can be seen in Table 1the largest molecular volume is for diiodomethane 134 Å3, while that of water isonly 30 Å3, and that of formamide 66 Å3. Therefore, one can expect that water canmuch easily penetrate between the protrusions than diiodomethane or formamide.On the other hand, the differences in the diameter of the molecules, if consideredas spheres, are not as great (Table 1). However, it should be kept in mind that theliquid molecule penetration depends on its surface tension as well as on whetherany polar interactions (e.g. acid–base) occur from the solid side.

4.2. Advancing and Receding Contact Angles of the Probe Liquids

The advancing and receding contact angles of the probe liquids measured on thetested solid surfaces by sessile drop and tilted plate methods are shown in Figs 2–5.Moreover, the bars representing the advancing contact angles measured by bothmethods are marked with horizontal solid lines which represent the values of


Figure 2. Advancing θa and receding θr contact angles of probe liquids on glass surface measured bysessile drop (open bars) and tilted plate (filled bars) methods. Dashed lines on the advancing contactangle bars show equilibrium contact angles calculated from equation (11). The vertical lines on thebars show standard deviations.

Figure 3. Advancing θa and receding θr contact angles of probe liquids on silicon surface measured bysessile drop (open bars) and tilted plate (filled bars) methods. Dashed lines on the advancing contactangle bars show equilibrium contact angles calculated from equation (11). The vertical lines on thebars show standard deviations.

equilibrium contact angles calculated from Tadmor’s equation (11). As can be seen,generally the standard deviations of the measured contact angles by both methodsare within ±2◦, which is typical. On the same surface, the advancing contact anglemeasured by the tilted plate is in most cases several degrees greater than that mea-sured by the sessile drop. The exception is for water on mica (Fig. 4) and formamide


Figure 4. Advancing θa and receding θr contact angles of probe liquids on mica surface measured bysessile drop (open bars) and tilted plate (filled bars) methods. Dashed lines on the advancing contactangle bars show equilibrium contact angles calculated from equation (11). The vertical lines on thebars show standard deviations.

Figure 5. Advancing θa and receding θr contact angles of probe liquids on PMMA surface measuredby sessile drop (open bars) and tilted plate (filled bars) methods. Dashed lines on the advancing contactangle bars show equilibrium contact angles calculated from equation (11). The vertical lines on thebars show standard deviations.

on silicon (Fig. 3), where the advancing contact angle by the tilted plate is slightlysmaller. The respective receding contact angles measured by tilted plate are gener-ally smaller (except for formamide on mica, Fig. 4) than those measured by sessile


Table 2.Contact angle hysteresis of the probe liquids determined on theinvestigated surfaces by sessile drop and tilted plate methods

Surface Hysteresis, degrees;sessile drop/tilted plate

Liquid

Water Formamide Diiodomethane

Glass 11.2/16.9 7.9/14.4 9.8/17.5Silicon 10.5/17.0 13.1/14.8 7.1/16.7Mica 5.4/7.5 4.2/6.1 5.3/14.3PMMA 13.4/17.4 14.8/19.5 6.5/11.5

drop. This means that the contact angle hysteresis is greater if determined by tiltedplate method. The actual values of the contact angle hysteresis measured by the twomethods are listed in Table 2. Interestingly, irrespective of the kind of investigatedsurface and its roughness, the greatest differences between the extent of hysteresisfound by sessile drop and tilted plate methods appear for diiodomethane. That is,for an apolar probe liquid interacting practically by the dispersion force only, whichamounts to γl ≈ γ d

l = 50.8 mN/m and this is the highest value among the probe liq-uids used, i.e. γ d

l = 21.8 mN/m for water and γ dl = 39.0 mN/m for formamide

(Table 1). Hence, it can be speculated that this kind of interaction is principallyresponsible for the differences in the contact angle hysteresis values measured bythese two methods. The hysteresis is considered to be due to the pinning and de-pinning energies [1, 4, 24–31]. On the other hand, the diiodomethane molecule isthe largest, its volume is more than four times that of water and two times that offormamide (Table 1). Hence, one would expect Cassie’s wetting mechanism andthe smallest contact angle hysteresis for this liquid. The smallest hysteresis for thethree probe liquids if measured by tilted plate method is found on mica surface, ex-cept for diiodomthane (Table 2). From the above discussion, data in Tables 1 and 2,and Fig. 1a–d, it can be concluded that there is no direct correlation between thesurface roughness, surface tension of the probe liquid and contact angle hysteresis,although some other general features are observed.

4.3. Apparent Surface Free Energy of the Investigated Solids

Taking the measured contact angles (Figs 2–5) and applying the above describedapproaches (equations (3), (4), (8), (9)) the apparent surface free energies of thetested surfaces were calculated. They are shown in Figs 6–9. In the figures are alsomarked arithmetic mean values of the energies calculated from the contact anglesmeasured by sessile drop and tilted plate methods and using the four approaches(the solid lines). As is seen, for a particular surface the surface free energy cal-culated from Owens and Wendt’s equation (equation (3)) is always the highest.


Figure 6. Apparent surface free energy of glass calculated from four different approaches as indicatedin the figure. The horizontal dashed lines show arithmetic mean values from the four approaches andthe solid lines represent the mean values excluding O–W approach.

Figure 7. Apparent surface free energy of silicon calculated from four different approaches as indi-cated in the figure. The horizontal dashed lines show arithmetic mean values from the four approachesand the solid lines represent the mean values excluding O–W approach.

Therefore, in Figs 6–9 are also marked the arithmetic mean values calculated byneglecting the energy values obtained from this equation.

The equation of state (equation (4)) fails for PMMA surface (Fig. 9) giving theenergy lower by ca. 8 mJ/m2 than the mean value from the four approaches (or6.5 mJ/m2 without O–W value). The values of the surface free energy plotted inFigs 6–9 calculated from contact angle hysteresis (CAH) approach are the averaged


Figure 8. Apparent surface free energy of mica calculated from four different approaches as indicatedin the figure. The horizontal dashed lines show arithmetic mean values from the four approaches andthe solid lines represent the mean values excluding O–W approach.

Figure 9. Apparent surface free energy of PMMA calculated from four different approaches as indi-cated in the figure. The horizontal dashed lines show arithmetic mean values from the four approachesand the solid lines represent the mean values excluding O–W approach.

values (arithmetic means) of those determined separately from water, formamideand diiodomethane contact angles hystereses for the given surface. It is worth not-ing that the mean values of the surface free energy calculated from contact angles


measured by sessile drop and tilted plate methods are very close. Only for glass thedifference is 4 mJ/m2 and a higher value is calculated from the contact angles mea-sured by sessile drop. For mica, irrespective of the approach used and contact anglemeasurement method, the determined surface free energy values are the most con-sistent (excluding O–W’s value) (Fig. 8). Taking into account the Rrms and averageheight values for the investigated surfaces (Fig. 1a–d) and the surface free energy, itcan be stated that for mica no direct correlation is observed between these two para-meters and its consistent surface free energy values (Fig. 8). The same is true for thedifference between the mean values of the surface free energy for glass determinedfrom sessile drop and tilted plate methods (Fig. 6). The smoothest surface is that ofsilicon, while roughness of mica surface is comparable to that of glass. On the otherhand, the average height of PMMA surface is the largest, and for this surface thevalues of surface free energy calculated are most scattered (Fig. 9). Similarly, thereis no clearly seen relation between the extent of the contact angle hysteresis and thesurface roughness.

4.4. Surface Free Energy of the Surfaces Calculated from Equilibrium ContactAngles

Finally, the equilibrium contact angles calculated from Tadmor’s equation (equation(11), Figs 2–5) were employed to determine the apparent surface free energy of theinvestigated solids from CAH approach (equation (9)). The results are shown inFig. 10. The calculated apparent surface free energy for a given solid is practicallythe same irrespective of the ‘origin’ of the equilibrium contact angle of the probeliquid used (sessile drop or tilted plate). Consequently, also the ‘averaged’ values ofthe apparent surface free energy (arithmetic mean of the values calculated from wa-ter, formamide and diiodomethane equilibrium contact angles, marked by dashedhorizontal lines in Fig. 10) are practically the same. From the CAH approach thehighest apparent surface free energy values are those calculated from water and thelowest those calculated from diiodomethane contact angles. A different behavioris observed for PMMA surface, which possesses apolar γ LW

s interaction and onlyrelatively weak electron donor γ −

s interactions. Figure 11 shows the solid surfacefree energy components calculated from LWAB approach (equation (8)) using theequilibrium contact angles calculated from the advancing and receding contact an-gles measured with a sessile drop. In case of PMMA apolar γ LW

s interaction is 48mJ/m2, which is the highest among the four solids studied, but its electron donorparameter γ −

s is the smallest one, 20 mJ/m2, and there is no electron acceptor in-teraction γ +

s [32–34]. These weak acid–base interactions might be the reason thatthe apparent values of PMMA surface free energy calculated from CAH approachand the equilibrium contact angles are similar, irrespective of the probe liquid used,Fig. 10.


Figure 10. Apparent surface free energy of the investigated solids calculated from equilibrium contactangles of water (W), formamide (F) and diiodomethane (D) (CAH approach, equation (10)). Thehorizontal dotted lines show averaged apparent surface free energy values, which are arithmetic meansof the values calculated separately from the three probe liquids. Open bars — the equilibrium contactangles were calculated from the advancing and receding contact angles measured by sessile dropmethod and the filled bars — those measured by tilted plate method.

Figure 11. Surface free energy components of the solids calculated from equilibrium contact anglesobtained from the contact angles measured by sessile drop method and using LWAB approach.

5. Summary and Conclusions

Four different solid surfaces (glass, silicon, mica and PMMA) and two methodsfor the advancing and receding contact angle measurements of three probe liquids


(water, formamide and diiodomethane) were used. Then four different approachesfor the determination of the surface free energy were employed in calculations ofthe apparent surface free energy. The results show that:

– Higher values of the contact angle hysteresis are obtained if tilted plate methodis applied, which is a result of generally slightly higher advancing and lowerreceding contact angles if measured by tilted plate than by sessile drop method.

– The highest values of calculated total surface free energy from the advancingcontact angles are obtained from Owens and Wendt’s equation.

– CAH, LWAB and equation of state (EQS) give comparable values of the totalsurface free energy, except for PMMA surface for which EQS fails, leading tosignificantly lower value.

– Both techniques for the advancing and receding contact angles measurementscan be applied for the apparent surface free energy determination from CAH ap-proach. Comparable values of surface free energy are then obtained. The sameis true if the surface free energy is determined via equilibrium contact anglescalculated from Tadmor’s equation.

– The results obtained lead to the conclusion that only apparent surface freeenergy and its components can be determined from the advancing or advanc-ing/receding contact angles of probe liquids.

– It is hypothesized that the strength of interaction originating from the solidsurface may vary depending on the strength of the same kind of interaction orig-inating from the liquid surface. In other words, surface free energy of a solid asdetermined via contact angle is not an absolute value, but it varies dependingon the kind of probe liquid used.

Acknowledgement

Financial support by the Polish Ministry of Science and Higher Education, projectN204 130435 is gratefully acknowledged.

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