0912f50c5d35935c99000000

Advances in Colloid and Interface Science .98 2002 245264

Problems of contact angle and solid surfacefree energy determination

Emil Chibowski ,1, Rafael Perea-Carpio

Department of Physics, Faculty of Science, Uniersity of Jaen, 23071 Jaen, Spain

Abstract

The current general problems of formulation and determination of surface free energyare discussed. So far several theories and approaches have been proposed, but formulationof surface and interfacial free energy, as regards its components, is still a very debatableissue. However, as long as no method for determination of real surface free energyquantities is known, even relative values charged with many simplified assumptions areuseful for better understanding of the wetting processes. In this paper special focus isconcentrated on powdered solids for which direct measurement of the contact angles is notpossible. For such solids the porous layer imbibition techniques are most frequently applied.Then, using the wicking results the contact angle is calculated from Washburns equation.However, such a procedure leads to overestimated contact angle values in comparison tothose measured directly on smooth surfaces of the same solid, if such surface can beobtained at all. As a consequence, the solid surface free energy components calculated viasuch overestimated contact angles are significantly lower than those obtained from contactangles measured directly. Methodologies to avoid this problem are also described. 2002Elsevier Science B.V. All rights reserved.

Keywords: Contact angles; Powdered solids; Washburn equation

Corresponding author. Department of Physical Chemistry, Maria Curie-Sklodowska University,20-031 Lublin, Poland. Tel.: 48-81-537-56.

.E-mail address: [email protected] E. Chibowski .1 On leave from the Department of Physical Chemistry, Faculty of Chemistry, Maria Curie-Sklo-

dowska University, 20-031 Lublin, Poland.

0001-868602$ - see front matter 2002 Elsevier Science B.V. All rights reserved. .PII: S 0 0 0 1 - 8 6 8 6 0 1 0 0 0 9 7 - 5

( )E. Chibowski, R. Perea-Carpio Adances in Colloid and Interface Science 98 2002 245264246

Contents

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2462. General problems of surface free energy formulation and determination . . . . . . . . 2463. Problems of the contact angle and surface free energy determination for powdered

solids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262

1. Introduction

Knowledge about interfacial free energy interactions is necessary for understand-ing and modeling many surface and interface processes which involve such wettingphenomena as preparation of suspensions and emulsions, flotation of minerals,detergency, adhesive joints, painting, drug preparation, and others. Despite severaldecades of struggle, actual formulation of the surface free energy and its determi-nation are still problems. Although several theories and approaches have beenadvanced so far, there are still serious doubts about them, and none of theapproaches allows unambiguous interpretation of the experimental data, particu-larly those depending on temperature. The methods used most frequently for thesolid surface free energy determination rely on wetting contact angle measure-ments. However, interpretation of the measured values in terms of the surface freeenergy components is still debatable, especially for powdered solids. The aim ofthis paper is to depict problems dealing with contact angle determination, espe-cially for powdered solids. To view the current situation, at first some problemsdealing with surface free energy determination in general will be discussed.

2. General problems of surface free energy formulation and determination

Although the method of expressing surface free energy as a sum of components was formulated by Fowkes 13 almost 40 years ago, at present it is still a

debatable issue. Recently Lyklema 4 revisited fundamental aspects of pheno-menological thermodynamics for the surface excess energy and entropy in relationto surface and interfacial tensions of liquids and arrived at some importantconclusions. For the sake of clarity and because the conclusions involve fundamen-tal questions of the surface and interface free energy formulation, it is worthy torecall some of them in extenso. As it is well known for pure liquids over a broadrange of temperatures their surface tension decreases linearly with temperature

. .growth and because S T , and U T T , therefore, thea p a psurface entropy S and energy U can be evaluated from the relationshipsa adetermined experimentally. The linear decrease means that the entropy and energymust be constant in the considered range of temperatures. Based on literature

data, Lyklema 4 found that for many liquids, including molten salts and metals,

( )E. Chibowski, R. Perea-Carpio Adances in Colloid and Interface Science 98 2002 245264 247

the surface entropy remains practically the same within the range of experimentalerrors. While there is no systematic variation in the entropy S, the energy U a avaries over three orders of magnitude. Thus he concluded that the energy is aliquid-specific property, and the entropy a generic one. This has an important

impact on the validity of Fowkes equation 13 , which describes interfacial free . .energy between phase 1 and 2 , say, between two immiscible liquids or liquid and

solid. For the phases interacting by dispersion forces the equation reads:

12d d . . 2 112 1 2 1 2

where the work of adhesion W for the phases is expresses by the geometric meana .12 .of the dispersion interactions. Here Berthelots rule u u u for the11 22 12

interfacial dispersion interactions between two phases was applied. According to Lyklema 4 , this equation has a weak thermodynamic background just because the

work of adhesion is formulated by the geometric mean, like the energy u . His12argument is that thermodynamic quantities, here the surface tensions, are mixedup with mechanical ones, i.e. internal energy. The description of thermodynamic

parameters involves temperature, while the mechanical quantity does not 4 . In . d d.12Eq. 1 the term is formulated as temperature independent, because the1 2

. .Helmholtz energy U TS is actually considered as the energy U , which is .obviously not true. However, for many systems Eq. 1 well describes wetting and

adhesion processes in conjunction with contact angles. Lyklema 4 considers two .reasons for such behavior: i the same type of approximation made for two

coupled phenomena, i.e. surface tension and contact angle, which may lead to .compensations of the errors and thus pointing to the consistency; ii for most

liquids the surface entropy is a generic property and the combination of differentpairs of liquids gives the same error. The final statement of Lyklema is that there

.is a reason to continue using equations like Eq. 1 , although one has to .reconsider the data. However, there is no reason to over-interpret this equation

.by empirically adding extra terms like acidbase interactions , let alone combining values with contact angle data, using an additional empirical expression to obtainsolidliquid interfacial tensions.... A correct equation describing the interfacial

tension should be the following 4 :12

12 ,d ,d . . 2 U U T S 212 1 2 1,a 2,a adh a

.From Eq. 2 it would result that for water the dispersion component of surfaced .tension, 21.8 mNm as determined by Fowkes 1,2 is probably underesti-w

mated by approximately 8% 4 . However, before Lyklemas paper was published 4 , van Oss et al. 57 in the

late 1980s put forward a concept for experimental determination of the Lewisacidbase surface free energy interactions, which is now receiving increasing

attention. In most cases the acidbase interactions the electron donor and.electron acceptor are due to hydrogen bonding between hydrogen and oxygen, as


well as other electron donating atoms they have expressed, the interfacial free . .energy between phase 1 and 2 :12

12 12 12LW LW . . . W 2 12 1 2 a 1 2 1 2 1 2 1 2 .3

where LW is the apolar, called the Lifshitz van der Waals component, is theelectron acceptor component, and is the electron donor component for phase . . .1 and 2 , respectively. Eq. 3 results from the surface free energy formulated bythem for a phase i as the sum of apolar LW and polar acidbase AB componentsi i 57 :

12LW AB LW . . 2 4i i i i i i

.As it is seen in Eq. 4 , the acidbase component is expressed by a geometricmean of the electron donor and electron acceptor parameters of the phase i

surface free energy 57 . But, in the light of Lyklemas 4 conclusions, the .expression for the work of adhesion in Eq. 3 is not justified. Nevertheless, in the

meantime numerous papers have been published in which this approach was usedfor determination of the solid or liquid surface free energy components. For solid

.surface s the components can be determined from measured contact angles for .at least three probe liquids l , whose surface tension components are known. Such

components for several liquids were given by van Oss et al. 810 , but the valuesare relative because they refer to water acidbase components, arbitrary assumed

2 2to be equal to each other, 25.5 mJm 510 . The value 25.5 mJmw wresults from LW AB 21.8 51 72.8 mJm2.w w w

. . .Then using Youngs equation Eq. 5 and combining it with Eqs. 3 and 6results:

. cos 5s l sl

12 12 12LW LW . . . . .W 1 cos 2 6a l a 1 2 1 2 1 2

It contains three unknowns: apolar, electron donor and electron acceptor de-scribing the solid surface free energy components. Having the contact angles

.measured for three liquids, Eq. 6 containing three unknowns can be solved simultaneously. However, among others, Kwok et al. 11,12 have shown that for

the tested solid surfaces the method 510 did not give comprehensive values ofthe free energy components. The components varied from triad to triad of the

probe liquids used for contact angle measurements. Berg 13 also criticized the approach 57 because it always gives a high value of the electron donor compo-

nent , and a low one of the electron acceptor , even for polyvinyl chloride,2 1which so far was considered as a monopolar acidic solid or in other words, the

. electron acceptor . Later, van Oss et al. 14 tried to justify such occurrences as


resulting from the residual polar property of the surface and not of the cohesion.interactions in the bulk phase . This residual polarity is determined by sessile drop

experiments, and it turns out to be an electron donor one. Another reason for theelectron donating properties of solid surfaces may be that in typical experimental

conditions we always deal with adsorbed water hydrating the surface 14 . Della Volpe et al. 1517 have proposed using a matrix of the measured contact

angles for many probe liquids to determine averaged apolar and polar componentsfor the tested solids. They also used other components than proposed by van Oss et

al. 810 for the probe liquids 16 to achieve better consistency of the calculatedvalues. The appropriate choice of liquid may render the components more consis-

tent 17,18 , although formally there should be no limitation in probe liquid selection. Lee 19 , based on solvatochromic parameters, earlier suggested a

different set of components for probe liquids. It should be stated that, although theuse for calculations of different sets of surface tension components of probe liquidsaffects the calculated acidic and basic parameters, the acidbase component ABs

. .remains the same because the and are interrelated Eqs. 4 and 6 . Theres sis also a problem of the film pressure behind the drop, which must be neglected to

.solve Eq. 6 . The presence of a film behind the drop changes the solid surface freeenergy. It seems, however, that for carefully measured advancing contact angles,

under well-ventilated conditions the film effect may be neglected 20,21 see also, .for example, 22 . Another question is whether the solid surface free energy

components remain constant independently of the liquid used, and it seems that this is not always the case 23 , as was postulated by Fowkes 1,2 .

The so-called equation of state theory about the surface free energy determination should also be mentioned 2430 . This approach entirely disqualifies the

component approach, stating that the interfacial free energy is completely de-termined by the liquid surface tension and the solid surface free energy, sl .f , , and in conjunction with Youngs equation the current proposed form oflv sv

the equation of state is as follows 3032 :

2sv .l s .cos1 2 e 7( lv 2 .2where is the constant equal to 0.000115 mJm , which was fitted from

experimental contact angles measured on polymeric solids mostly 31,32 . This equation can be solved numerically 30 . However, derivation of the equation of

state was criticized 33,34 , but the authors of the equation of state published several papers to show that it is correct 2628 . This equation rather fails for

higher energy polar solids 35 . Spelt et al. 30 tried to show that Fowkes approach .was wrong Eq. 1 while the equation of state gives true values of solid surface

.free energy. Using contact angles of various liquids apolar and polar measured on . . .a fluorocarbon FC-721 , Teflon FEP , and polyethylene tetraphthalate PET ,

they plotted cos vs. , thus obtaining smooth curves. Hence they concludedl lthat cos depends only on and , and not on the surface tensionl l scomponents, which vary randomly from liquid to liquid. However, this conclusion


is not justified. To illustrate it, exact data of the contact angles and the liquid surface tensions quoted by the authors 30 were used, and in Fig. 1 their curve for

.fluorocarbon FC-721 is re-plotted curve 1 . The closed squares in Fig. 1 present d.12 the results of cos vs. , which are also calculated from the authorsl l l

data 30 . Fluorocarbon F-721 may be assumed as a completely apolar solid ford .which . Then taking Fowkes equation Eq. 1 combined with Youngss s

.equation Eq. 5 we obtain:

12d . . cos 2 8'l s sl s 1 1Next, taking the literature data for the dispersive component of the polar liquids

d.12 discussed 810 and plotting cos vs. , a straight-line relationshipl l l .should result. The linear fit straight line 2 in Fig. 1 obtained can be considered as

quite a good approximation with the regression coefficient R 0.993, more so thatthe low energy apolar liquid n-hexane which film could be present behind the

. drop on FC-721 surface and highly polar water which could induce some polar .interactions 1,2,23 were also taken into account. To show that no smooth

.Fig. 1. Dependence between cos and surface tension of liquids curve 1 and between cos l l 12 .and for the same liquids, from contact angles of the liquids measured on fluoropolymerl l

.FC-721 from 29 .


d AB .changes in the dispersion and polar acidbase components of the liquidl 1surface tension occur, which would cause linearity of the function cos vs. ,l lthese components vs. the liquid surface tensions are shown in Fig. 2. As can beseen, there is no smooth relationship between the parameters. From the resultspresented in Figs. 1 and 2 it can be concluded that Fowkes equation works quite

.well for this fluorocarbon. It is worth noting that, apart from water Fig. 1 , thedata were also applied to other highly polar liquids like ethylene glycol, formamide,glycerol, as well as for other apolar n-alkanes; hexane, decane, dodecane, tetrade-

.cane. On the other hand, results of Spelt et al. Fig. 1, curve 1 can be very wellfitted to a parabola type equation: cos a b c2, for which thel l l

.regression coefficient is R 0.9998 Fig. 1 . But, this equation has nothing in .common with the equation of state Eq. 7 . Therefore, the above results clearly

show that the conclusion of Spelt et al. 30 that Fowkes model is wrong, whichdoes not result from the results presented by them. A rather more serious problem

connected with Fowkes equation is that shown by Lyklema 4 , which was discussedabove.

The authors of this paper recently proposed 23,36 an approach by which thetotal surface free energy of solids can be evaluated from the contact anglehysteresis, which is the difference between the advancing and receding a r

contact angles 37 . The equation proposed for free energy calculation is as follows:

2 .1 cosa . . cos cos 9s l r a 2 2 . .1 cos 1 cosr a

The obtained values of the surface free energy depend to some extent on thekind of liquid used, like the calculated components of the energy depend on the

probe liquid triad 11,12,1517,23,26 . But surprisingly, the average value de-termined from the contact angle hysteresis of several probe liquids agreed very well

with the average value calculated from van Oss et al.s 810 approach using the advancing contact angles for various combinations of these liquids 23,26 . It can be

due to the same type of approximation applied in both approaches, as was concluded by Lyklema 4 .

More references on the issues discussed above, and others dealing with adhesion, can be found in a brief review by Clint 38 . However, he made a misstate-

ment saying that Della Volpe and Siboni 16 were the first to propose alternativevalues of the probe liquid surface tension components to those given by van Oss et

al. 810 , while Lees paper 19 was published earlier. It would also be advanta- geous to look at Vol. 61 of Current Opinion in Colloids & Interface Science 39 ,

which is devoted to wetting problems.From the above considerations it can be concluded that the current problems of

experimental determination of solid surface free energy are not likely to be solvedsoon. On the other hand, to better understand the interfacial phenomena involvingspreading, immersional and adhesional wetting processes some knowledge aboutinterfacial interactions is required. Therefore, as long as we do not possess direct


Fig. 2. The dispersion d and acidbase AB components of the liquids, given in Table 1, against theirl lsurface tensions .l

and unambiguous methods for determination of the real magnitudes of the surfacefree energy interactions, even these relative values are useful, which at present canbe evaluated experimentally.

3. Problems of the contact angle and surface free energy determination forpowdered solids

Many naturally occurring or artificially obtained solids which are of greatpractical interest, like soils, clays, pigments, polymers, pharmaceutics, and others,can be obtained only as powders and no flat and smooth surface of them can beprepared. For such solids the contact angle cannot be measured directly. Measure-ments of contact angles on compressed pellets of the solids are charged with someerror. The pellets are usually rough and porous, which usually causes a smallercontact angle to be measured on the pellet than would be obtained on a smooth


specimen of this solid. Hunter 40 commented on the method of contact angledetermination on compressed discs as At best, useless. At worst, positively mis-leading. However, in the case of finely ground powders compressed at a suffi-

.ciently high pressure on a support e.g. a low energy foil , it is sometimes possible to obtain reasonable results 4145 . The Wilhelmy plate method was also applied

for this purpose 4648 , and yet such results may be positively misleading.Other methods applied for determination of powdered solid surface free energy

are inverse gas chromatography 4952 , adsorption gas chromatography 5357 ,and methods based on dissolution or crystallization parameters, which were re-

cently overviewed by Wu and Nancollas 58 . At present, however, the methodsbased on imbibition of solid porous layer by a liquid, are seemingly gettingincreasing interest, therefore, more attention will be focused on these methods.

The methods employ Washburns equation, which was published in 1921 59 , and then Burtell and Whitney 60 , and Eley and Pepper 61 were among the first to

use the equation for contact angle determinations in porous columns. A new impact on usage of Washburns equation was made by van Oss et al. 62,63 about a

decade ago, who initiated a method called thin layer wicking 62 . In this method athin layer of the studied solid powder is deposited on glass slides. It facilitatespenetration of the liquid into the layer, and a sharp visible progressing contact linecan usually be seen. Later, besides the thin layer, porous columns were applied for

this purpose, but of a smaller diameter than those used previously 6366 .Moreover, instead of measurement of the wicked distances vs. time, also the weightgained by the porous layer vs. time can be recorded and then a modified Wash-

burns equation applied 6570 .Having measured for a probing liquid the wicked distance x in the porous layer

as a function of time t, one can formally calculate the wetting contact angle fromWashburns equation:

t R coseff l2 .x 102

where R is the effective radius of the interparticle capillaries in the porous layer,eff is the surface tension of the probe liquid, and is the liquid viscosity. The Rl effvalue can be estimated from wicking experiments by using a low energy liquid, like

.short chain n-alkanes optionally n-heptane to n-nonane . As can easily be seen .from Eq. 10 , at a constant temperature and assuming R to be constant, theeff

squared wicked distances should be a linear function of time, and indeed in many systems such a relationship obeys 7175 . However, in some other cases a

significant deviation from linearity was observed 7577 , which, among otherreasons, was explained by a shift of the visible starting line of the wicking liquid

into the powder, which leads to a parabolic form of Washburns equation 66,76,77 .In some systems this non-linearity problem can be avoided by using an appropri-ate method of liquid transportation from the container to the porous layer, forexample, by using a sandwich chamber, where adsorption of liquid vapors on the

layer can also be avoided to a significant degree 78 . Obviously, this is not the only


reason for the non-linear distance vs. time relationship. Changes in the contact .angles 79 and non-uniform distribution of the pores R changes were amongeff

other things, considered 80 as the reasons for non-linearity. In real poroussystems we never deal with a bunch of parallel capillaries, which in fact are verycomplicated of irregular shapes mutually interconnected with varying cross-sections 66,79,80 . This complicates the liquid penetration and may appear in so-calledHaines jumps, i.e. the meniscus passes rapidly through some shapes of the pores

and the pores with larger radii will fill first 81,82 . Therefore, we deal with someaveraged rates of penetration on the macroscopic level. As mentioned, modifica-tion of the method is weighing the gained liquid in the porous body as a function of

time. Then Washburns equation can be modified to the following form 6670 :

2 t2 .w c cos 11l

where c is the geometric factor, the liquid density, and the rest of the symbols . 2 2 .2have the same meaning as in Eq. 10 . The geometric factor c R r ,eff

where is the porosity of the column and r is the radius of the tube in which thecolumn is packed. The geometric factor c can be obtained from the experimentwith total wetting liquid, like n-alkane. The weight is usually controlled with an

automatic electronic balance 66,69,70 .Static R and hydrodynamic R radii of the porous bed should also beS D

mentioned. The R value can be evaluated from the maximum height of totalSwetting liquid in the porous column being investigated, and the R via R fromD eff

. 2Eq. 10 , where R R R .eff D S Siebold et al. 66 evaluated the radii for a column of silica sand and found

R 43 m and R 16.3 m. They also evaluated theoretically the relationshipS Dbetween the radii and found that this calculated R for equivalent spheres, andDthat from experiments with irregular sand grains were in fact reasonably compara-

. ble, so that no advancing contact angle was considered in Eq. 10 . The authors 66also compared the results obtained by the two techniques, distance vs. time andweight vs. time, and showed how very important standardization of the samplesbefore wicking experiments was to get reproducible results.

However, despite experimental problems there is an important issue dealing withthe theory for porous body imbibition. Namely, in general the contact angles

.calculated from Eq. 10 are not the same as those measured on a smooth surface of this same solid if such a surface could be prepared 21,7174,78,8388 . Thus,

determined contact angles are usually overestimated and some examples will be . .shown later. Nevertheless, many authors apply Eq. 10 or Eq. 11 for direct

calculation of the contact angle from wicking experiments and then for determination of the solid surface free energy components 63,8992 . A somewhat confusing

statement can be found in the review paper by Wu and Nancollas 58 and the paper 92 cited by them that, using, for example n-alkanes, ...with such spreading

liquids, remains exactly equal to zero, so that cos 1, as a result of theformation of a precursor film. It should be stressed that this is only true if the


precursor film has reached the state of duplex film. It implies that the outermostlayer of the film already possesses the properties of the bulk liquid, and the film

pressure is equal to the work of spreading W W W the work of adhesion Ws a c a. minus work of cohesion W 93,94 . Then from Youngs equation,c

. cos 12s l sl

it results that W W W cos W , and hencesf s s s a c l s l a cos .l l

This equality may only occur if cos 1, which happens for 0. Here, issthe solid surface free energy, is the liquid surface tension, and is thel slsolidliquid interfacial free energy. However, if the precursor film exerts any otherfilm pressure than equal to the work of spreading, or no film is present ahead at all .which may happen , this condition is then not fulfilled. For instance, whenn-alkane spreads over a bare solid surface it cannot be assumed that the contactangle is exactly equal to zero in calculations of the surface free energy of a solid .or other immiscible liquids . The alkane will spread over such a surface up to itsmonolayer thickness, of course if the surface area is sufficiently large. If thecontact angle were really exactly equal to zero it could be implied from Youngsequation that the solid surface free energy equals:

. 13s l sl

Zero value of the contact angle is a limiting one for the applicability of Youngsequation for calculations of surface free energy. Then for totally spreading liquidsthe wetting process can be described solely by the work of spreading, W , which forssuch liquids is positive.

. .W 0 14s s l sl

.However, contrary to Youngs equation, Eq. 14 is also valid for contact angleliquids, for which W 0, and at zero contact angles the work of spreading alsos

.equals zero the liquid does not spread spontaneously . Now, if for all spreadingliquids one would like to assume that the contact angle is exactly equal to zero,

.then from Eq. 12 it would result that:

. W 15s l s l a

hence

.W 2 W 16a l c

Considering for simplicity a non-polar solid and n-alkane, i.e. a system in whichacross the interface only dispersive interaction appears and the liquid spreads

.totally, Eq. 15 can be rewritten.

12d d . .W 2 2 17a s l l


d . dBecause for n-alkanes , from Eq. 16 it results that . It wouldl l s lmean that the solid surface dispersive free energy is always equal to surface tensionof the spreading liquid used for the wicking, which is evidently nonsense.

As mentioned above, some authors 58,8992 directly calculated the contactangles from wicking experiments which are significantly overestimated. Lately

Grundke and Augsburg 87 proposed a new methodology to avoid this problem.Using a thin column wicking technique coupled with an electrobalance, they

.plotted K cos vs. determined from Washburns equation Eq. 11 forl lseveral probe liquids on four low energy polymers teflon, polethylene, polypropy-

.lene, and polystyrene . Here K is a geometric factor, whose quantity must notnecessarily be known. Such plots go through a maximum, which, according to the

authors 87 , corresponds to the solid surface free energy. The argument is that tothe left of the maximum and 0 see the above discussed problem ofl s

contact angle exactly equal to zero, as well as the relationship of cos vs. l l.relationship, Figs. 1 and 2 and to the right of the maximum cos . Thus,l l

determined values of the solid surface free energy were then compared with thoseobtained from direct measurements of the contact angles on smooth surfaces of

these polymers, as well as with literature values. The authors 87 have obtainedgood agreement between the values. However, this apparently interesting approach

.should be carefully considered, because for low energy apolar or weakly polarsolids many approaches give reasonable agreement just because the surface energyis low.

Some time ago, Chibowski et al. 7175 proposed an approach and wickingprocedure which gives the results of the solid surface free energy similar to thoseobtained from contact angles measured on a smooth solid surface. However,

recently Wu and Nancollas 58 stated without any argument that in our approachthere are errors in the treatment of capillary rise. When these are corrected, theexpression for the reduction in the free energy, when a liquid advances by adistance dx into a horizontal capillary can be written . . . as follows:

. .dG 2 dx 18s sl

Although the authors 58 have not referred to it, this equation was published by Good in 1973 99 . In our papers 7175 the validity of using this equation was

questioned for a thin porous layer of a powdered solid deposited on a solid .substratum e.g. a glass slide . As mentioned above, such a layer consists of

complicated three-dimensional systems of irregular and interconnected capillaries 66,7981,88 . Hence, it may be expected that the penetrating liquid will rather fillthe capillaries first by a spreading process than instantly by an immersional one.

The obtained results confirmed the validity of our approach 7175,78,9698 . Good 99 assumed in his derivation that during the liquid movement by a distance

.dx into the capillary having radius r, the work of immersion Eq. 18 is responsi- ble for free energy reduction dG. Using the results of Wu and others 100 it will


.be shown later that contact angle calculation directly from Eq. 10 leads to muchlower values of the solid surface free energy components. It is due to much highercontact angles obtained from such calculations than those measured directly on a

smooth surface of the same solid. Yang and Zografi 88 showed in 1986 thatcontact angles calculated from Washburns equation were much higher thanmeasured directly on smooth surfaces of the same solids. They used siliconizedglass and PMMA coated glass and measured contact angles of water, ethanol and

.aqueous solutions of ethanol at different concentrations 590% . The differencesin the contact angles ranged from 11 to 20 on siliconized glass and from 15 to 55on PMMA coated glass. Moreover, they found that penetration of the liquids intothe coated glass beads had not occurred at the advancing contact angles higher

.than 7476 and not exceeding 90, predicted in the Washburn equation Eq. 10 ,where a cylindrical capillary model is assumed. They concluded that calculation ofcontact angles from the penetration data and the Washburn equation resulted inincorrect values, even if a linear relationship x 2 vs. t was observed. However, if

instead of the work of immersion 99 that of spreading is taken into considerationthe free energy changes dG vs. dx reads:

. .dG 2 dx 19s l sl

In the case where the duplex film is present ahead of the penetrating front of theliquid, the solid surface free energy is modified to the work of spreading W by thes

. film pressure 93,94 . Inserting it into Eq. 19 , dG 0 is obtained 75 . Neverthe-less, the liquid will still enter the capillaries. This is because of a concave meniscusformed there. The meniscus will be spherical if the capillary is cylindrical and theliquid duplex film is present. A detailed discussion on this issue can be found, for

example, in Adamson and Gasts book 94 . It is worth mentioning that thepresence of such a duplex film is a necessary condition to be fulfilled in order to

determine the liquid surface tension by the capillary rise method 94 . The effectiveradius R of porous layer can be determined by using a completely wetting liquideff .n-alkane . The porous layer has to be precontacted with saturated vapors of theliquid, for example, by being closed in a vessel for a sufficiently long time to attainthe adsorption equilibrium and the state of duplex film. As is well known, acrossthe curved surface of the meniscus the Laplace pressure appears, which for a

spherical meniscus equals 94 :

2 l .P 20r

Replacing the capillary radius r by the effective radius R , a spherical shape ofeffthe appearing meniscus must be assumed for this complicated system of theinterparticle irregular capillaries. Therefore, this R is rather a fitting parametereffwhich for better or worse includes geometry of the porous system. The appearing


pressure difference P must obey Poiseuilles law for the liquid motion in acapillary:

dx r 2P . 21

dt 8x

. .Inserting Eq. 20 into Eq. 21 and integrating it one obtains for the porous solidlayer.

R teff2 .x 22l2

While the detailed derivation of this equation is given in Chibowski and Gonzalez-Caballero 75 , Wu and Nancollas 58 have arrived at the same equation

in its differential form by an acclamation, saying that, if the solid surface iscovered by the duplex film of liquids prior to wicking, actually equals , ands l

2 . hence d x d t r2 is obtained. Then the authors 58 argue that thelspreading of liquids in a capillary is different from that over flat solid surfacesbecause in the case of a capillary no liquidvapor interface is formed during thespreading process and the change in the free energy is then given by G s s S . Here, S is the so-called spreading coefficient, which is the same assl l

.the work of spreading W the definition recommended by the IUPAC 101 , andaS is the work of immersion. However, this relationship is true only if a columnlof liquid enters the capillary at an angle of 90 and no duplex film is present on thecapillary walls ahead of the entering liquid column, i.e. when the immersionalwetting process occurs, for which the work of immersion W equals:i

.W 23i s sl

The immersional wetting process corresponds to the situation where W i s . cos 90 , and the case of duplex film was discussed above, wheresl l

W . However, if the liquid does not completely wet the capillarys s sl lsurface andor no duplex film is present, then at the liquid contact line a definitecontact angle is formed and the energy change is not equal to the work ofimmersion. In fact, when the liquid front progresses into a capillary by distance dx,

.the solidvapor interface is continuously replaced by the solidliquid inter-sv . .face . However, it is accompanied by the foregoing liquidvapor interface ,sl lv

which is renewing whose size is determined by the capillary dimension, especiallyin a porous thin layer. The latter interface contributes to the total free energy

.change by cos see above .lv As the experiments have shown 7175,9598 , imbibition of the porous layer by

a liquid is realized rather by a spreading wetting than immersional wetting process.This is because of a very complicated three-dimensional capillary system wheremany short and open capillaries of irregular shapes are present. Hence, the liquid


probably spreads first over the surface and then the capillaries are filled 7984 . Therefore, a general form of Washburns equation was proposed 7175,78 :

t Reff2 .h G 242

where G stands for the specific total free energy changes during the imbibitionprocess at the progressing liquidsolid contact line. Details of the theoreticalbackground, experimental procedure and the results can be found in the literature 7175,78,9598,102 published earlier. Here, the only description of the resultingG and the relationships between some of them are given for four possible cases.

.1. For a completely spreading liquid e.g. n-alkane , whose duplex film wasformed ahead of the penetrating line the porous layer precontacted with the.liquid saturated vapor, the subscript p , then G . It allows determina-p l

.tion of R from the Washburn equation Eq. 10 and this case was discussedeffabove.

2. For the same completely spreading liquid, but penetrating into the bare surfaceof the porous layer G W W W because the spreading wettingb s a c

.process was assumed to occur in the porous layer, the subscript b .3. For a contact angle liquid and bare surface of the porous layer, the free energy

change equals G .b1 .4. For the same liquid, but penetrating into the layer precontacted with its vapors

prior to wicking, the energy change amounts G .p1.

From experiments, theoretical consideration and by analogy to static systems, it was deduced 7175,78,9498,102 that the following relationship holds:

. G G W W . This relationship has been proved lately by an experimentb p a c using single glass capillaries 103 . All G values described above can be de-

. .termined from Eq. 24 using at least one completely spreading liquid n-alkaneand two polar liquids, e.g. water and formamide. Then the solid surface compo-

.nents can be determined by simultaneously solving three equations Eq. 6 .Obviously, the proposed procedure is time consuming, and it leads to results of

solid surface free energy and its components comparable to those obtained from contact angles measured directly on smooth surfaces of the same solid 74 . In

.contrast, direct calculation of the contact angles from Eq. 10 , as suggested by Wu and Nancollas 58 and others 62,63,92,100 , gives much lower energy values than

those obtained from direct contact angle measurement. In one of Wus papers 100 there are listed surface free energy components for various solids, asdetermined from direct measurement of the contact angles and also from thin layer

. .wicking via first calculated contact angles Eq. 10 and then Eq. 6 . These valuesare shown in Table 1 for three different solids, where the solid surface freeenergies and the components are given. It is clearly seen that the thin layer wicking


Table 1 .Solid surface free energy as determined from direct contact angle measurements CA and from thin

2 . layer wicking TW , in mJm , and measured or calculated contact angles of water, respectively from .100

LW tot a .Solid Method s s s s

Calcite CA 40.2 1.3 54.4 57.0 6.2Ground calcite TW 29.1 0.5 31.6 37.0 55.9Glass slide CA 33.7 1.3 62.2 51.7 9.0Ground glass TW 31.7 0.4 37.1 39.4 49.4Dolomite CA 37.6 0.2 30.5 42.5 51.7Ground dolomite TW 27.1 0.2 13.6 30.4 76.5

a From Constanzo et al. 92 .

method gives the surface free energy components, and the calculated total valuesof the energy are significantly lower than those from direct measurements of thecontact angles. Despite changes in the surface free energy upon grinding of the

solids that might be expected but rather an increase of the energy because fresh.crystalline surfaces are formed , the calculated energy for the particular solids

presented in Table 1 decreased by 2535%. This obviously results from tremen-dously overestimated contact angles by the TW method, which is also shown inTable 1.

In another paper 92 , the authors tried to prove that on a monosized synthetichematite the contact angles calculated via thin layer wicking and measured directlyon the hematite layer deposited on glass slides coincided within a few degrees.

However, as it was already shown in another paper 74 , serious doubts can beraised because there are some errors in the calculations. Taking the wicking data

from that paper 92 one can calculate for water contact angle 84.8, while theauthors calculated 25.85 and measured 22.5 directly on the hematite layer for

. details see 74,92 . The contact angles were calculated 92 basing on only approxi-mately 1 cm penetrated distances over a long time. The wicked distances weretaken for 2-mm intervals, which indicates that the time vs. distance readingaccuracy was low.

On the other hand, the results of surface free energy obtained from ourapproach, for example on silica plates used in thin-layer chromatography silica gel

.60, Merck , agree well with those for various silica originating materials as determined from direct measurements of contact angles 74 . Thus, determined

Lifshitzvan der Waals components are listed in Table 2. From this table it is again .seen that the contact angles calculated from Washburns equation Eq. 10 are

much higher than those measured directly, thus giving significantly lower values ofthe solid surface free energy. However, by applying the procedure described abovethe determined values fit well the values calculated from the contact anglesmeasured on flat surfaces. It is also worth noting the free energy value obtained

.from contact angles measured on compressed pellets Table 2 . It is remarkably


Table 2LWContact angle , and Lifshitzvan der Waals component , for various SiO originating materialss 2

LWMaterial Liquid Ref.s2 .mJm

Fused silica, plates, DI 31 43.8 104200 C

Quartz plate, DI 36.6 41.3 105105 C, 1 h

Glass, Thermisil DI 40 39.4 65 200 C, 2 h -BR 25 40.3 65 Glass, microscope plate, DI 31 43.8 45 110 C, 2 h -BR 14 43.1 45 Glass, microscope plate, DI 36 41.6 45 200 C, 2 h -BR 21 41.5 45

. SiO Merck from TLC, DI 17.5 48.5 7422pellets, 100 kgcm

a . SiO Merck TLC plates Alkanes, TLW 41.1 742DI, -BR

b . SiO Merck TLC plates DI 60 28.5 742b

-BR 47 36.8

DI, diiodomethane; -BR, -bromonaphthalene; TLW, thin layer wicking.a .Average value from n-alkanes hexane to hexadecane , diiodomethane and -bromonaphthalene

TLW and applying this authors theoretical approach.b .Contact angles calculated from Eq. 1 .

2 . higher 48.5 mJm than that obtained on flat surfaces where the average is2 .approx. 40 Jm . This is a result of porosity of such pellets and roughness of its

surface, which causes the liquid to be sucked in to the pellet and the appearingcontact angle is smaller than in the case of smooth solid surface. As a consequence,the calculated dispersion component of the free energy is higher. Finally, havingdetermined the free energy components for a solid surface it is possible tocalculate the dynamic advancing contact angle appearing in the Washburn equa-

.tion Eq. 10 . Such calculations were conducted for the silica discussed above, for a series of n-alkanes from pentane to hexadecane 78 . The angles were from 20

for pentane, 31 for heptane, 49 for octane, and then the appearing anglesfluctuated between 53 and 57 for the rest of the n-alkanes. These values seem tobe reasonable.

In conclusion, it has clearly been shown again, as was done earlier in numerouspapers, that direct calculation of the contact angles from Washburns equation,which are then applied in Youngs equation, leads to erroneous results of thusdetermined solid surface free energy components. However, it should be kept inmind that independently of the applied method, the obtained values for surfacefree energy and its components are relative ones and at least debatable. Therefore,studies on new approaches and experimental procedures to solve the problems arestill needed.


Acknowledgements

.One of the authors E.Ch. very much appreciates the financial support from theauthorities of the University of Jaen, Spain, for his stay at the Department ofPhysics of this university.

References

.1 F.M. Fowkes, J. Phys. Chem. 66 1962 382. .2 F.M. Fowkes, Ind. Eng. Chem. 56 1964 40. 3 F.M. Fowkes, Wetting, Soc. Chem. Ind. Monograph 25, London, 1967, p. 3. .4 J. Lyklema, Colloids Surf. A 156 1999 413. .5 C.J. van Oss, R.J Good, M.K. Chaudhurry, J. Colloid Interface Sci. 111 1986 378. .6 C.J. van Oss, R.J. Good, M.K. Chaudhurry, Langmuir 4 1988 884. .7 C.J. van Oss, M.K. Chaudhurry, R.J. Good, J. Chem. Rev. 88 1988 927. .8 C.J. van Oss, R.J. Good, M.K. Chaudhurry, J. Chromatogr. 391 1987 53. .9 C.J. van Oss, R.J. Good, J. Macromol. Sci.-Chem. A 26 1989 1183. .10 R.J. Good, C.J. Van Oss, in: G. Loeb Ed. , Modern Approaches to Wettability: Theory and

Application, Plenum, New York, 1992. .11 D.Y. Kwok, D. Li, A.W. Neumann, Langmuir 10 1994 1323. .12 D.Y. Kwok, Colloids Surf. A 156 1999 191. .13 J.C. Berg, in: J.C. Berg Ed. , Wettability, Marcel Dekker, New York, 1993, p. 75. .14 C.J. van Oss, R.F. Giese, W. Wu, J. Adhesion 63 1997 71. .15 C. Della Volpe, A. Deimichel, T. Ricco, J. Adhesion Sci. Technol. 12 1998 1141. .16 C. Della Volpe, S. Siboni, J. Colloid Interface Sci. 195 1997 121. .17 C. Della Volpe, S. Siboni, J. Adhesion Sci. Technol. 14 2000 235. .18 A. Hollander, J. Colloid Interface Sci. 169 1995 493. .19 L.-H. Lee, Langmuir 12 1996 1681. .20 C.J. van Oss, R.F. Giese, W. Wu, J. Dispersion Sci. Technol. 19 1998 1221. .21 T.D. Blake, in: J.C. Berg Ed. , Wettability, Marcel Dekker, New York, 1969, p. 251. .22 J.J. Moura Ramos, Langmuir 13 1997 6607. .23 E. Chibowski, R. Perea-Carpio, A. Antiveros-Ortega, J. Ahesion Sci. Technol. submitted . .24 C.A. Ward, A.W. Neumann, J. Colloid Interface Sci. 49 1974 286. . .25 A.W. Neumann, P. Sell, Z. Phys. Chem. Leipzig 187 1964 227. .26 J. Gaydos, E. Moy, A.W. Neumann, Langmuir 6 1990 888. .27 D. Li, A.W. Neumann, Langmuir 9 1993 3728. .28 J. Gaydos, A.W. Neuman, Langmuir 9 1993 3327. .29 J.K. Spelt, E. Moy, D.Y. Kwok, in: A.W. Neumann, J.K. Spelt Eds. , Applied Surface Thermody-

namics, Marcel Dekker, New York, 1996, p. 293. .30 J.K. Spelt, D. Li, in: A.W. Neumann, J.K. Spelt Eds. , Applied Surface Thermodynamics, Marcel

Dekker, New York, 1996, p. 239. .31 D. Li, A.W. Neumann, J. Colloid Interface Sci. 137 1990 304. .32 D. Li, A.W. Neumann, J. Colloid Interface Sci. 148 1992 190. .33 I.D. Morrison, Langmuir 5 1989 540. .34 I.D. Morrison, Langmuir 7 1991 1883. 35 B. Janczuk, J.M. Bruque, M.L. Gonzalez-Martin, J. Moreno del Pozo, A. Zdziennicka, F.

.Quintana-Gragera, J. Colloid Interface Sci. 181 1996 108. 36 E. Chibowski, Proceedings, Second International Symposium on Contact Angle, Wettability and

Adhesion, Newark, N.J., USA, June 2123, 2000. .37 R.J. Good, in: R.J. Good, R.R. Stromberg Eds. , Surfaces and Colloid Science, 11, Plenum

Press, New York, 1979.


.38 J.H. Clint, Curr. Opin. Colloid Interface Sci. 6 2000 28. .39 Curr. Opin. Colloid Interface Sci. 61 2001 . 40 R.J. Hunter, Clarendon Press, Oxford, Foundations of Colloid Science, vol. 1, 1995. .41 P. Chassin, C. Jouang, H. Quiquampoix, Clay Miner. 21 1986 899. .42 C. Jouanny, P. Chassin, Colloid Surf. 27 1987 289. .43 E. Chibowski, P. Staszczuk, Clays Clay Miner. 36 1988 455. .44 B. Janczuk, T. Bialopiotrowicz, Clays Clay Miner. 36 1988 243. 45 E. Chibowski, L. Holysz, A. Zdziennicka, F. Gonzalez-caballero, in: A.K. Chattopadhyay, L.

.Mittal Eds. , Surfactants in Solution, 64, Marcel Dekker, New York, 1996, p. 31. .46 G. Buckton, J. Adhesion Sci. Technol. 7 1993 219. .47 G. Bucton, J.M. Newton, Powder Technol. 46 1986 201. 48 A. Chawla, G. Buckton, K.M.G. Taylor, J.M. Newton, M.C.R. Johnson, Eur. J. Pharm. Sci. 2

.1994 253. .49 E. Papirer, J. Schultz, C. Turchi, Eur. Polym. J. 20 1984 1155. .50 M.L. Tate, Y.K. Kamath, S.P. Wesson, S.B. Reutch, J. Colloid Interface Sci. 177 1996 579. .51 F.P. Lin, T.G. Rials, Langmuir 14 1998 536. .52 E. Pisanova, E. Mader, J. Adhesion Sci. Technol. 14 2000 415. .53 B. Bilinski, E. Chibowski, Powder Technol. 35 1983 39. .54 B. Bilinski, Powder Technol. 81 1994 241. .55 B. Bilinski, A.L. Dawidowicz, Appl. Surf. Sci. 74 1994 277. .56 B. Bilinski, J. Colloid Interface Sci. 201 1998 180. .57 B. Bilinski, L. Holysz, Powder Technol. 102 1999 120. .58 W. Wu, G.H. Nancollas, Adv. Colloid Interface Sci. 79 1999 229. .59 E. Washburn, Phys. Rev. 17 1921 2731. .60 F.E. Bartell, C.H. Whitney, J. Phys. Chem. 36 1932 3115. .61 D.D. Eley, D.C. Pepper, Trans. Farad. Soc. 42 1946 697. .62 R.F. Giese, P.M. Constanzo, C.J. van Oss, J. Phys. Chem. Miner. 17 1991 611. .63 C.J. van Oss, R.F. Giese, Z. Li et al., J. Adhesion Sci. Technol. 6 1992 413. .64 L. Holysz, Colloids Surf. A. 134 1998 321. .65 L. Holysz, Adsorpt. Sci. Technol. 14 1996 89. .66 A. Siebold, A. Walliser, M. Nordin, M. Oppliger, J. Schultz, J. Colloid Interface Sci. 186 1997

60. .67 H.W. Kilau, J.E. Pahlman, Colloids Surf. 26 1987 217. .68 R. Varadaraj, J. Bock, N. Brons, S. Zushma, J. Colloid Interface Sci. 167 1994 207. 69 L. Labajos-Broncano, M.L. Gonzalez-Martin, C. Gonzalez-Garcia, J.M. Bruque, J. Colloid

.Interface Sci. 233 2001 233. 70 L. Labajos-Broncano, M.L. Gonzalez-Martin, C. Gonzalez-Garcia, J.M. Bruque, J. Colloid

.Interface Sci. 234 2001 9. .71 E. Chibowski, J. Adhesion Sci. Technol. 6 1992 1069. .72 E. Chibowski, L. Holysz, Langmuir 8 1992 710. .73 L. Holysz, E. Chibowski, Langmuir 8 1992 717. .74 E. Chibowski, L. Holysz, J. Adhesion Sci. Technol. 11 1997 1289. .75 E. Chibowski, F. Gonzalez- Caballero, Langmuir 9 1993 330. 76 L. Lebajos-Broncano, M.L. Gonzalez-Martn, B. Janczuk, J.M. Bruque, C.M. Gonzalez-Garca, J.

.Colloid Interface Sci. 211 1999 175. 77 M.L. Gonzalez-Martn, B. Janczuk, L. Lebajos-Broncano, J.M. Bruque, C.M. Gonzalez-Garca, J.

.Colloid Interface Sci. accepted . .78 E. Chibowski, in: K.L. Mittal Ed. , AcidBase Interactions: Relevance to Adhesion Science and

Technology, 2, VSP, Utrecht, 2000, p. 419. .79 J. Van Brokel, D.M. Heertjes, Powder Technol. 16 1977 91. .80 A. Marmur, Adv. Colloid Interface Sci. 39 1997 13. .81 W.B. Haines, J. Agric. Sci. 20 1930 97. .82 K.S. Sobrie, Y.Z. Wu, S.R. McDougall, J. Colloid Interface Sci. 174 1995 289. .83 L.R. Fisher, P.D. Lark, J. Colloid Interface Sci. 69 1979 486.


.84 Y.-W. Yang, G. Zografi, E.E. Miller, J. Colloid Interface Sci. 122 1988 35. .85 G.E. Parsons, G. Buckton, S.M. Chatham, J. Adhes. Sci. Technol. 7 1993 95. .86 R. Crawford, L.K. Koopal, J. Ralston, Colloids Surf. 27 1987 57. .87 K. Grundke, A. Augsburg, J. Adhes. Sci. Technol. 14 2000 765. .88 Y.-W. Yang, G. Zografi, J. Pharm. Sci. 75 1986 719. .89 Z. Li, R.F. Giese, C.J. van Oss, J. Yvon, J. Ases, J. Colloid Interface Sci. 156 1993 279. .90 Z. Li, R.F. Giese, C.J. van Oss, Langmuir 10 1994 330. .91 C.J. van Oss, W. Wu, R.F. Giese, J.O. Naim, Colloids Surf. B. 4 1995 185. .92 P.M. Constanzo, W. Wu, R.F. Geese Jr., C.J. van Oss, Langmuir 11 1995 1827. .93 A.C. Zettlemoyer, in: F.M. Fowkes Ed. , Hydrophobic Surfaces, Academic Press, New York,

1969, p. 1. 94 A.W. Adamson, A.P. Gast, Physical Chemistry of Surfaces, 6th ed., Wiley, New York, 1997. .95 E. Chibowski, R. Ogonowski, J. Surf. Sci. Technol. 13 1977 77. 96 E. Chibowski, M. Espinosa-Jimenez, A. Ontiveros-Ortega, E. Gimenez-Martn, Langmuir 14

.1998 5237. 97 A. Ontiveros-Ortega, M. Espinosa-Jimenez, E. Chibowski, F. Gonzalez-Caballero, J. Colloid

.Interface Sci. 202 1998 189. 98 E. Chibowski, A. Ontiveros-Ortega, M. Espinosa-Jimenez, R. Perea-Carpio, L. Holysz, J. Colloid

.Interface Sci. 235 2001 283. .99 R.J. Good, J. Colloid Interface Sci. 43 1973 473. .100 R.F. Giese Jr., W. Wu, C.J. van Oss, J. Dispersion Sci. Technol. 17 1996 527. .101 Off. J. Int. Union Pure Appl. Chem. 31 1972 597. .102 E. Chibowski, F. Gonzalez-Caballero, J. Adhes. Sci. Technol. 7 1993 1195. .103 E. Chibowski, R. Perea-Carpio, J. Collloid Interface Sci. 240 2001 473. .104 J. Rayss, A. Gorgol, W. Podkoscielny, J. Widomski, M. Cholyk, J. Adhes. Sci. Technol. 24 1989

15. .105 B. Janczuk, A. Zdziennicka, J. Mater. Sci. 29 1994 3559.

Documents

0912f50c5d35935c99000000