Surface Polarizability

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J. Adhesion Sci. Technol., Vol. 21, No. 10, pp. 961981 (2007) VSP 2007.Also available online - www.brill.nl/jast

Polar interactions at liquid/polymer interfaces

ALAIN CARR

Corning SAS, Corning European Technology Center, 7 bis, Avenue de Valvins, 77210 Avon, France

Received in final form 28 May 2007

AbstractNumerous relationships have been proposed in the literature to interpret wettability interms of solid and liquid surface free energies. In the classical approach based on surface free energycomponents, the energy of interactions between the liquid and the solid is obtained from the geometricmean of the dispersion and polar contributions of the liquid and solid surface free energies. In thiswork, it is shown that the surface polarity of polar liquids can be modeled by the interaction of alignedpermanent dipoles. A good agreement is found between the surface polarity characterized by polarcomponent of the surface free energy of polar liquids (water, formamide and ethylene glycol) and thedipolar energy of interactions calculated from their dipole moment. At the liquid/polymer interfaces,polar interactions are better described by a simple relationship of proportionality with the polarcomponent of the liquid surface free energy. This observation leads us to evaluate the hypothesis ofinduced polar interactions at liquid/polymer interfaces, the surface polarity of the solid being inducedby the polar liquid in contact with the solid surface. Thus, the variation of the contact angle of a seriesof polar and non-polar liquids on various polymer substrates appears to be in better agreement whencompared to the classical description of permanent polar interactions, so that a surface polarizabilityis defined for polymers. Using the surface polarizability approach rather than the polar componentfor the solid surface, we find also that the dispersion (non-polar) component of the polymer surfacefree energy is obtained with a better confidence, especially by taking into account the contact anglesof both non-polar and polar liquid probes, or even by considering only polar liquid probes.

Keywords: Wetting; wettability; contact angle; surface free energy; surface tension; polar forces;dispersion forces; interfaces.

1. INTRODUCTION

There are various approaches in the literature to evaluate the surface free energyof solid materials from wetting experiments. Contact angle measurements withdifferent liquid probes with known surface tension form the basis for the calculationof the surface free energy of solids. However, the solid surface free energy, or

parameters related to the surface free energy, can be different depending on the

Tel.: (33-1) 6469-7371; Fax: (33-1) 6469-7455; e-mail: [email protected]


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962 A. Carr

model chosen. One basic problem is that the Young equation (SV = L cos +SL)describing the equilibrium of a liquid drop, L, having a contact angle on asolid surface, S, involves two unknowns: the solid surface free energy, SV, andthe interface free energy between the liquid and the solid, SL (L is the liquidsurface free energy). As one equation having two unknowns cannot be solved,several theories taking the Young equation as the starting point have been proposed.Depending on the theoretical basis, three major approaches are still under debate:the Fowkes type approach [13], involving the geometric mean of the liquid andsolid polar and non-polar components of the surface free energy, the Equation-of-State of Neumann [4, 5] and the Lifshitzvan der Waals/acidbase approachproposed by van Oss, Chaudhury and Good [6, 7]. In a comprehensive paper,Sharma and Hanumantha Rao [8] exposed the arguments and the objections for eachof these different approaches. Etzler [9] also published a review on both theoreticalapproaches and experimental methods for determining the surface free energy ofsolids. Recently, Chibowski [10, 11] has developed another theory based on contact-angle hysteresis and on the supposed existence of a liquid film left behind a recedingliquid front to deduce the value of the solid surface free energy.

Interestingly, it was mentioned by Fowkes [12], on the basis of data publishedby Dann [13], that the polar energy of interaction between polar liquids (theclassical series of liquid probes used in wetting studies) and polymers includingpolystyrene, polyamides, polyesters and poly(vinyl chloride) was proportional tothe liquid polarity quantified by the polar component of the liquid surface freeenergy. However, this result which apparently did not fit with the geometric meanapproach was never deeply analyzed. We made similar observations, and proposehere an alternative to describe polar interactions between polar liquids and polarpolymers.

After presenting the theoretical background of intermolecular interactions, wewill show that a better coherence between theory and experiments is obtained whenthe polar interaction at a liquid/polymer interface is considered to be proportionalto the liquid polarity. One possible explanation is that the polar liquid/polymer

interactions result from polar forces induced by the liquid at the solid surface.

2. THEORETICAL

With the surface energy component approaches, there is a general agreementwith the description of the non-polar solid/liquid interactions from the dispersioncontributions of the surface free energies of the solid and liquid. The calculation ofthe dispersion interactions with the geometric mean relationship was successfullyestablished by Fowkes [14, 15]. The description of non-dispersion or polarinteractions raises more difficulties, and there is no unanimously recognized model.


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Polar interactions at liquid/polymer interfaces 963

2.1. Non-polar (dispersion) interactions

The intermolecular attractions, which cause surface tension, arise from a variety of

well-known intermolecular forces. London dispersion forces exist in all types ofmaterials and always produce an attractive force. Fowkes [15] demonstrated thatthe dispersion interaction, ID12, between two phases, 1 and 2, was given by:

ID12 = 2D1

D2 , (1)

where Dj (j= 1 or 2) is the dispersion component of the surface free energy. Theusefulness of the geometric mean approach for calculating dispersion interactionswas demonstrated for both liquid/liquid and liquid/solid interfaces. As an example,

its validity is easily verified by measuring the interfacial tension between water andsaturated hydrocarbons where only dispersion forces are operative.

2.2. Permanent dipole/dipole interactions

The energy of interaction between two aligned dipoles, of dipole moments 1 and2, is given by [16, 17]:

i12 =212

40r312, (2)

where 0 is the permittivity of free space (0 = 8.854 1012 C2 J1 m1) and r12the interacting, center to center, distance of dipoles. Equation (2) applies in a polarmedium when i12 is higher than the thermal energy kT, k being the Boltzmannsconstant (1.381 1023 J/K) and T the temperature in K.

Therefore, in a polar liquid the interaction for a pair of aligned dipoles is writtenas:

iLL =22L

40r3LL. (3)

First, we propose to test the validity of equation (3) with pure polar liquids. We canestimate the polar interaction energy per unit area at the surface of a polar liquid,IPLL, by considering that:

IPLL =nS

2iLL, (4)

where nS is the number of molecules per unit area (the number of dipoles perunit area is half ofnS). This number can be obtained from the density d and themolecular weight M of the liquid, and considering that nS n2/3V , nV being thenumber of molecules per unit volume. Therefore, nS can be deduced from:

nS d

MN

2/3, (5)


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where N is the Avogadro number (6.021023). The average molecular distance canalso be estimated by considering that rLL a1/2 = (1/nS)1/2 = v1/3 = (1/nV)1/3,a and v being the molecular area and volume, respectively.

The polar interaction energy per unit area obtained from equations (4) and (5)can be compared with the experimental polar interaction obtained from the polarcomponent, PL , of the surface free energy, L(= DL + PL ), i.e.:

IPLL = 2PL . (6)

The comparison of these two calculations is presented in Table 1 with water(PL = 51 mJ/m2), formamide (PL = 18.7 mJ/m2) and ethylene glycol (PL =19 mJ/m2) [13]. Their permanent dipole moments L are 1.85, 3.73 and 2.28 Debye,

respectively [18] (1 Debye (D) = 3.336 1030

C m). The polar interactions inwater, formamide and ethylene glycol include hydrogen bonds which are no morethan a particularly strong type of directional dipole/dipole interactions [16]. Thevalues of polar interactions obtained from the components of liquid surface freeenergies (equation (6)) are relatively close to the energy of interactions deducedfrom the dipole moments (equations (3) and (4)), especially for water and ethyleneglycol. The agreement is not as good for formamide. A small adjustment of theinteraction distance (rLL fit in Table 1) is necessary to get the correct agreement(rLL fit = 6.1 1010 m versus rLL v1/3 = 4.04 1010 m for formamide).

This simple analysis shows that we can consider the polar interactions at the surfaceof polar liquids simply as resulting from the interaction between aligned dipoles.The description of polar interactions at the interface between two phases having

permanent dipoles is compatible with the geometric mean of polar contributions ofsurface free energies because as IP12 12 and IPjj 2j , it is easily concludedthat [17]:

IP12 =IP11I

P22 = 2

P1

P2 . (7)

However, equation (7) assumes implicitly that:

r12 = r11r22. (8)

Equations (1) and (7) constitute the basis of the Owens and Wendt theory ofsolid/liquid interactions [19]. However, it is usually recognized that the use of thegeometric mean is not really satisfactory to describe polar liquid/solid interactions.As noted by Fowkes [12], a direct proportionality between IPSL and

PL seems to be

more accurate. The following section would explain this experimental result.

2.3. Dipole/induced dipole interactions

The interaction, ii12, between a polar molecule of permanent dipole moment 1(of a polar liquid, for example) and a polarizable molecule of polarizability 2


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Table1.

PolarinteractionenergyIP LLatpolarliquidsurfacesdeducedfromtheirdipolemoment,L,orfromthepolar

componentoftheirsurfacefreeenergy,

P L

(kT

=

4.0

5

1021Jat293K)

Liquid

P L

L

nS

rLL=

v1

/3

iLLaligned

IP LL

IP LL=

2

P L

rLL

fit

(mJ/m2)

(Debye)

(molecules/m2)

(m)

(J)

(equation(4))

(mJ/m2)

(m)

(mJ/m2)

Water

51

1.8

5

1.0

4

1019

3.1

01010

2.2

9

1020

118.8

102

3.2

7

1010

Formamide

18.7

3.7

3

6.1

1

1018

4.0

41010

4.2

1

1020

128.6

37.4

6.1

0

1010

Ethyleneg

lycol

19

2.2

8

4.8

8

1018

4.5

31010

1.1

2

1020

27.3

38

4.0

6

1010


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corresponds to the following Debye interaction energy [16]:

ii

12 =2

21

(40r312)2 =2

40r312

21

40r312. (9)

As PL 2L (equations (3) and (4)) and assuming that rSL rLL, it can be deducedthat the induced solid/liquid polar interaction has the form:

IPSL = kS PL , (10)where kS will be defined as the surface polarizability of the solid.

Comparing equations (2) and (9), it can also be deduced that the induced dipoleacquires a dipole moment i2 having the following magnitude:

i2 = 240r31212, (11)

such as the induced polar interaction can also be described by:

i i12 =21i2

40r312. (12)

Thus, when a polar liquid is in contact with a polarizable solid surface, the inducedsolid/liquid polar interaction is compatible with the geometric mean as:

IPSL = 2PiS PL . (13)

However, the polar component of the solid surface free energy, PiS , is induced bythe contacting liquid. It is a variable which depends on the liquid polarity, PL .Equations (10) and (13) show that the induced polar contribution to the surface freeenergy of the solid is related to the solid surface polarizability, kS, and to the liquidpolarity by:

PiS =k2S

4PL . (14)

2.4. Consequences with respect to the interpretation of contact-angle

measurements on polymer surfaces

The energy of interactions between a liquid and a solid in a partial wetting situation( = 0) is usually related to the contact angle by combining the Young and Dupreequations as

L(1+ cos ) = IDSL + IPSL, (15)by assuming that the spreading pressure on low surface free energy solids (poly-mers) is negligible (the spreading pressure is the reduction of the solid surface freeenergy resulting from the adsorption of liquid vapor on the solid). The dispersion(non-polar) interaction, IDSL, is described by the geometric mean relationship. As we


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propose to discuss the nature of the polar interaction term, IPSL, as resulting eitherfrom permanent dipole/dipole interactions or possibly from dipoleinduced dipoleinteractions as described above, we will compare the accuracy of equation (15) byconsidering the following two possible expressions, i.e.:

L(1+ cos ) = 2DS

DL + 2

PS

PL (16)

according to the theory of permanent dipole interactions between the liquid and thesolid [19], or

L(1+ cos ) = 2DS

DL + kSPL , (17)

following the hypothesis of the solid surface polarity induced by the liquid in

contact.

3. EXPERIMENTAL

The contact angles of a series of polar and non-polar liquids (water, glycerol, for-mamide, ethylene glycol, diiodomethane, tricresylphosphate (TCP)) were measuredon different substrates of varying hydrophilicity. Water was purified by ionic ex-change followed by organic removal leading to a resistivity of 18 M cm (Elgas-tat, UHP). The organic liquids were of the following grades and origins: glycerol

(99.5%, Prolabo), formamide (99.5%, Sigma), ethylene glycol (99%, Aldrich), Di-iodomethane (99%, Sigma) and tricresylphosphate (98%, Acros Organics).

Our own contact angle measurements were made on polymer surfaces currentlyused as substrates for cell culture. These included non-treated sterile polystyrene(PS) (35 mm culture dish, Nalge Nunc International), PS exposed to gammaradiation (g-PS) (35 mm culture dish, Corning), tissue culture treated (TCT) PS(6-well clear TC-treated microplate, Corning), CellBIND substrate (6-well clearmicroplate, Corning) and Ultra Low Attachment substrates (6-well clear flat bottomUltra Low Attachment microplate, Corning). The CellBIND had received a

proprietary plasma surface treatment to improve cell spreading and attachment. TheUltra Low Attachment (ULA) substrate has a covalently bonded hydrogel layer thatis hydrophilic and neutrally charged so that it inhibits attachment of anchorage-dependent cell lines. The substrates for cell cultures are sterile and ready for useand no special procedures need to be followed to use these surfaces. Therefore,they were used as received.

Contact angle measurements were made using a Ram-Hart contact angle go-niometer at a controlled temperature of 22 1C. The average contact angle wasobtained from measurements on 10 drops of each liquid, measuring the contact an-

gles on both sides of the drop. The liquid drops had a volume of 2 l. The contactangle values correspond to the advancing contact angles at equilibrium measuredat the end of the spreading process. The standard deviation was always lower than1.7, irrespective of the liquid/substrate pair (see Results and Discussion).


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4. RESULTS AND DISCUSSION

The hypothesis of surface polarizability was evaluated with the literature data as

well as with our own contact angle measurements. The current permanent polaritytheory of the solid surface was tested with the linear form of equation (16) writtenas:

LDL

(1 + cos ) = 2DS + 2

PS

PL

DL. (18)

The hypothesis of the induced polarity of polymer surfaces was verified with thelinear form of equation (17) written as:

LDL

(1 + cos ) = 2DS + kS

PLDL

. (19)

We can expect that the best description of polar interactions (permanent polarityversus induced polarity at the polymer surface) is associated to the best fit ofexperimental data with equations (18) and (19).

The first evaluation of the validity of equations (18) and (19) with polar poly-mers was made by considering the wettability data available in the literature[17]. The study is limited to polar polymer surfaces when the water contactangle is lower than 90, but it can be applied to any type of polymer surface.

The series of polar polymers considered comprised poly(ethylene terephthalate)(PET), poly(vinylidene chloride) (PVDC), poly(vinyl chloride) (PVC), poly(methylmethacrylate) (PMMA), poly(vinylidene fluoride) (PVDF), poly(vinyl fluoride)(PVF) and poly(hexamethylene adipamide) (PHMA). The liquid probes and theircorresponding L, DL and

PL values are presented in Table 2 [13].

The contact angle data of Table 3 were used to compare the validity of equations(18) and (19). The surface properties of the series of polar polymers are gatheredin Table 4 in which the surface properties are given either in terms of dispersioncomponent, DS , and polar component,

PS (hypothesis of permanent solid surface

polarity), or in terms of dispersion component, DS

, and surface polarizability, kS(hypothesis of induced surface polarity). The dispersion component DS is deduced

from the ordinate at the origin (2DS ) of the linear regressions of equations (18)

and (19), PS and kS are deduced from the slopes (2PS and kS, respectively). All

Table 2.

Liquid properties (from Ref. [13])

Water Glycerol Formamide Diiodomethane -Bromonaphthalene TCP Hexadecane

L (mJ/m2) 72.8 63.4 58.2 50.8 44.6 40.9 27.6DL (mJ/m

2) 21.8 37 39.5 48.5 44.6 39.2 27.6PL (mJ/m

2) 51 26.4 18.7 2.3 0 1.7 0


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Table 3.

Equilibrium contact angles on polar polymer surfaces (from Ref. [17])

Polimers Contact angle ()Water Glycerol Formamide Diiodomethane -Bromonaphthalene TCP Hexadecane

PET 81 65 61 38 15 * PVDC 80 61 61 29 9 10 PVC 87 67 66 36 11 14 PMMA 80 69 64 41 16 19 PVDF 82 75 59 63 42 28 24PVF 80 66 54 49 33 28 PHMA 70 60 50 41 16

*

, no data reported.

Table 4.

Comparison between geometric mean (equation (18)) and surface polarizability (equation (19)) todescribe polar interactions

Polymer Geometric mean IPSL = 2PS

PL Surface polarizability I

PSL = kSPL

(equation (18)) (equation (19))

DS (mJ/m2) PS (mJ/m

2) R2 DS (mJ/m2) kS R2

PET 38.4 2.7 0.90 41.4 0.46 0.98PVDC 39.7 3.4 0.89 42.9 0.47 0.95PVC 39.7 2.2 0.82 41.6 0.31 0.91PMMA 36.3 3.0 0.83 39.1 0.50 0.95PVDF 28.1 4.8 0.88 31.0 0.61 0.88PVF 33.7 4.8 0.96 37.7 0.57 0.97PHMA 36.2 7.0 0.94 41.1 0.73 0.99Average ofR2 0.89 0.95

the liquids are taken into consideration to calculate the linear regressions. Theparameter R2 is the coefficient of correlation of the linear regression. Except forPVDF where the coefficient of correlation (R2 = 0.88) is the same with bothmodels of polar interactions, the induced polarity at the polymer surface leads toa better correlation, meaning that equation (19) fits the contact angle data betterthan equation (18). For the series of 7 polar polymers, the average coefficient ofcorrelation is 0.89 with the model of permanent solid surface polarity described bythe geometric mean relationship versus 0.95 for the model considering that polarinteractions at liquid/polymer interfaces are induced by the polarity of the liquid.

As examples, the linear relationships corresponding to the description of perma-nent polar interactions with the geometric mean (equation (18)) are presented inFig. 1A for PHMA and PET. For the same polymers (PHMA, PET), the hypothe-sis of induced polar interactions (equation (19)) corresponds to Fig. 1B. Figure 1A


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(A)

(B)

Figure 1. Comparison of the linear fits of equations (18) (A) and (19) (B) according to the nature ofdipolar solid/liquid interactions (permanent (A) or induced (B) solid polarity) for PHMA and PET.


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and 1B and the R2 coefficients show the improvement of linearity obtained with thesolid polarizability approach (equation (19)).

The model chosen has also an impact on the determination of the dispersioncomponent of the surface free energy of polymer materials. The induced dipolehypothesis leads systematically to a higher value of the dispersion component ofthe surface free energy, DS (Table 4).

When considering liquids of low polarity, such as TCP, diiodomethane and-bromonaphthalene, for which L DL , both equations (18) and (19) can besimplified as

L

D

L

(1 + cos ) 2DS (

DL L), (20)

as the polar interactions, irrespective of their nature, are negligible relatively to dis-persion interactions. In general, this simplified approach to estimate the dispersioncontribution to the surface free energy slightly overestimates the dispersion compo-nent of the solid surface free energy as the liquid/solid work of adhesion is assumedto result only from dispersion interactions, which is not exactly true. The dispersioncomponents, DS , for the same series of polar polymers estimated from the contactangles of low polarity liquids are presented in Table 5. It is obvious that the disper-sion components of the surface free energy of polymers obtained from the contactangles of low polarity liquids and from equation (20) are closer to the values de-

Table 5.

Estimation of the dispersion component, DS (mJ/m2), deduced from the contact angles of low polarity

liquids (TCP, diiodomethane and -bromonaphthalene) and equation (20)

Equation and liquidprobe

PET PVDC PVC PMMA PVDF PVF PHMA (%)

DS from equation (20)and TCP

42.1 41.9 40.4 37.8 37.8

DS from equation (20)and diiodomethane

42.5 46.7 43.5 41.0 28.1 36.5 41.0

DS from equation (20)and -bromonaphthalene

43.1 43.9 43.3 42.9 33.9 37.7 42.9

DS (average) fromequation (20) and non-polar liquids

42.8 44.3 42.9 41.4 33.3 37.3 42.0 0

DS from equation (19)(induced polarity)and all liquids

41.4 42.9 41.6 39.1 31.0 37.7 41.1 3.5

DS from equation (18)(permanent polarity)and all liquids

38.4 39.7 39.7 36.3 28.1 33.7 36.2 11.2

Comparison with the values obtained from the complete series of liquids of Table 2 and equations(19) and (18). is the average difference by taking the mean values obtained from non-polar liquidsand equation (20) as the reference.


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duced from the contact angles of the entire series of non-polar and very polar liquidswith the surface induced polarity hypothesis (equation (19)). In Table 5, is theaverage difference between the following sets of values: D

S

(average) from equa-tion (20) and non-polar liquids, DS from equation (19) (induced polarity) and allliquids, DS from equation (18) (permanent polarity) and all liquids. is expressedin %, by taking the mean values obtained from non-polar liquids and equation (20)as the reference.

Secondly, the concept of surface polarizability was also evaluated with contactangle measurements that we made on the series of polymers described in theExperimental section. The liquid properties and the contact angle data are presentedin Tables 6 and 7. The results are presented in Figs 2 and 3. In Figs 2A and3A, polar interactions are described with the geometric mean of solid and liquid

polar components and the polymer surface polarizability is used in Figs 2B and 3B.Figure 2 relates to PS and ULA substrates. Figure 3 relates to the other substrates,i.e., g-PS, TCT PS and CellBIND. In all cases, except with TCT PS for whichthe coefficient of linear regression is high and of the same level (R2 = 0.96),a better linear correlation is obtained when the polar interactions are consideredas resulting from a solid surface polarity induced by the liquid polarity (Figs 2Band 3B versus Figs 2A and 3A). Following both descriptions of polar interactionsat liquid/polymer interfaces, the surface properties of the polymer substrates aresummarized in Table 8. The dispersion component DS is deduced from the ordinate

at the origin (2DS ) of the linear regressions of equations (18) and (19), PS

and kS are deduced from the slopes (2PS and kS, respectively). For this series

Table 6.

Liquid properties on polymer substrates used in this study

Water Glycerol Formamide Ethylene glycol Diiodomethane TCP

L (mJ/m2) 72.8 63.4 58.2 48.0 50.8 40.9DL (mJ/m

2) 21.8 37.0 39.5 29.0 48.5 39.2PL (mJ/m2) 51 26.4 18.7 19.0 2.3 1.7

Table 7.

Equilibrium contact angles on polymer substrates used in this study

Polymer Contact angles on polymers ()

Water Glycerol Formamide Ethylene glycol Diiodomethane TCP

PS 85.4 0.7 73.4 1.3 65.3 1.6 59.5 0.7 41.4 1.5 19.3 1.2g-PS 75.9

0.6 70.5

1.7 59.4

1.0 50.2

0.6 32.4

0.5 13.3

1.7

TCT PS 54.3 0.9 48.9 0.8 15.6 1.5 21.3 1.1 32.4 1.2 9.8 0.7CellBIND 37.4 1.0 35.4 0.8 5.0 0.0 11.6 1.1 37.3 0.7 17.2 0.8ULA 18.0 0.7 34.2 1.1 4.2 0.8 6.8 0.9 35.4 0.5 13.0 1.6


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(A)

(B)

Figure 2. Comparison of the linear fits of equations (18) (A) and (19) (B) according to the natureof dipolar solid/liquid interactions (permanent (A) or induced (B) solid polarity) for PS and ULAsubstrates.


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974 A. Carr

(A)

(B)

Figure 3. Comparison of the linear fits of equations (18) (A) and (19) (B) according to the nature ofdipolar solid/liquid interactions (permanent (A) or induced (B) solid polarity) for g-PS, TCT PS andCellBIND substrates.


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Table 8.

Comparison between geometric mean ((equation (18)) and surface polarizability (equation (19)) todescribe polar interactions

Polymer Geometric mean IPSL = 2PS

PL Surface polarizability I

PSL = kSPL

(equation (18)) (equation (19))

DS (mJ/m2) PS (mJ/m

2) R2 DS (mJ/m2) kS R2

PS 33.8 2.1 0.83 37.6 0.39 0.94g-PS 33.3 4.9 0.83 39.3 0.58 0.92TCT PS 31.6 17.9 0.96 44.6 1.06 0.96CellBIND 25.9 31.0 0.97 41.8 1.40 0.98ULA 22.8 40.3 0.95 39.8 1.62 0.99Average ofR2 0.91 0.96

Table 9.

Estimation of the dispersion component, DS (mJ/m2), from the contact angles of TCP and di-

iodomethane and equation (20)

Equation and liquid probe PS g-PS TCT PS CellBIND ULA (%)

DS from equation (20) andTCP

40.3 41.5 42.1 40.8 41.6

D

S from equation (20) anddiiodomethane 40.7 45.2 45.2 42.9 43.8DS (average) from equation(20) and non-polar liquids

40.5 43.4 43.7 41.8 40.3 0

DS from equation (19)(induced polarity) and allliquids

37.6 39.3 44.6 41.8 39.8 4.0

DS from equation (18)(permanent polarity) andall liquids

33.8 33.3 31.6 25.9 22.8 29.7

Comparison with the values obtained from the complete series of liquids of Table 6 and equations

(19) and (18). is the average difference by taking the mean values obtained from non-polar liquidsand equation (20) as the reference.

of polymers, the average coefficient of correlation is 0.91 when permanent polarinteractions are described with the geometric mean (equation (18)) and 0.96 whenpolar interactions are considered as being induced by the liquid (equation (19)).

In Table 9, are given the dispersion components, DS , from the contact angles ofTCP and diiodomethane and from equation (20). It appears also that the dispersioncomponents of the surface free energy of polymers obtained from the contact anglesof these low polarity liquids and from equation (20) are closer to the values deducedfrom the contact angles of the entire series of non-polar and polar liquids byconsidering that the polymer surface polarity is induced (equation (19)). In Table 9,


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976 A. Carr

is the average difference between the two sets of values, expressed in %, by takingthe mean values obtained from non-polar liquids and equation (20) as the reference.

There is no fundamental reason preventing a priori determination of the non-polar component of the surface free energy of a solid from the contact anglesof polar liquid probes, as polar liquids interact also with non-polar interactions.Thus, the description of intermolecular interactions at liquid/polymer interfacesmust allow determining the dispersion (non-polar) components of the surface freeenergy of solids from the contact angles of polar liquids. Thus, it is possible tocompare the dispersion components obtained, on the one hand, from the contactangle of non-polar liquids and equation (20) and, on the other hand, the dispersioncomponents deduced from the contact angles of polar liquids only (water, glycerol,formamide, ethylene glycol). This comparison is made in Tables 10 and 11 with the

Table 10.

Comparison of the dispersion component, DS (mJ/m2), obtained from non-polar liquids only (TCP,

diiodomethane and -bromonaphthalene) and equation (20), and from polar liquids only (water (w),glycerol (g), formamide (f)) by considering induced polarity (equation (19)) or permanent polarity(equation (18))

Equation and liquid probe PET PVDC PVC PMMA PVDF PVF PHMA (%)

DS (average) from equation(20) and non-polar liquids

42.8 44.3 42.9 41.4 33.3 37.3 42.0 0

DS from equation (19)(induced polarity) and

polar liquids (w, g, f)

38.2 39.9 37.9 32.7 34.0 41.9 40.5 10.3

DS from equation (18)(permanent polarity) andpolar liquids (w, g, f)

27.4 28.7 29.8 21.1 23.6 31.4 25.2 34.0

is the average difference by taking the mean values obtained from equation (20) as the reference.

Table 11.

Comparison of the dispersion component, DS (mJ/m2), obtained from non-polar liquids only (TCP

and diiodomethane) and equation (20), and from polar liquids only (water (w), glycerol (g),formamide (f), ethylene glycol (e-g)) by considering induced (equation (19)) or permanent (equation(18)) polar interactions


DS (average) from equation(20) and non-polar liquids

40.5 43.4 43.7 41.8 40.3 0

DS from equation (19)(induced polarity) and polarliquids only (w, g, f, e-g)

33.8 34.1 50.6 46.9 40.0 13.6

DS from equation (18)

(permanent polarity) and polarliquids only (w, g, f, e-g)

23.7 19.8 28.1 18.9 10.2 52.0



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contact angles taken from the literature (Table 10) and using our own measurements(Table 11). With polar liquids, DS values are deduced from the ordinate at the originof the linear regressions corresponding to equations (18) and (19). In Tables 10and 11, is the average difference for the series of polymers considered by takingthe mean values obtained from non-polar liquids and equation (20) as the reference.The agreement between the two sets of values of the dispersion components ismuch better when the dispersion component is deduced from the contact anglesof polar liquids with the hypothesis of induced polar interactions (equation (19)).The discrepancy reaches more than 50% with the constant polarity and is lowerthan 14% with the hypothesis of induced polarity.

A similar comparison can be made by considering the van Oss, Chaudhury andGood [6, 7] model in which the solid/liquid work of adhesion is expressed as a sum

of three terms:

L(1 + cos ) = 2LWS

LWL + 2

+S

L + 2

S

+L , (21)

where LWi is the Lifshitzvan der Waals (non-polar) component of the surface freeenergy and +i and

i are the Lewis acid parameter and the Lewis base parameter,

respectively. From the contact angles of at least three liquids of known surfacetension parameters (L, LWL ,

+L ,

L ), equation (21) can be used to determine the

van Oss, Chaudhury and Good parameters for the surface free energy of the solid.The van Oss, Chaudhury and Good parameters of liquids are presented in Table 12.Thus, by considering three polar liquids, it is theoretically possible to determine theLifshitzvan der Waals (non-polar) component, LWS , of the surface free energy ofpolymers. This result can be compared to the value obtained with the next equation

L(1+ cos ) = 2LWS

LWL , (22)

established for non-polar liquids (diiodomethane, -bromonaphthalene). Thiscomparison is made in Table 13 with the series of polar polymers considered inthe literature [17]. The results show in most cases a large discrepancy between the

non-polar component LWS of the surface free energy of polymers obtained fromnon-polar or polar liquids. The same conclusion can be drawn with the resultsconcerning the series of polymers used in this study as shown in Table 14. Whatever

Table 12.

Van Oss, Chaudhury and Good surface tension parameters [9] of liquids used in this study and in [17]

Water Glycerol Formamide Ethylene Diiodomethane -Bromonaphthaleneglycol

L (mJ/m2) 72.8 64 58 48 50.8 44.4

LWL (mJ/m2) 21.8 34 39 29 50.8 44.4+L (mJ/m

2) 25.5 3.92 2.28 1.92 0 0L (mJ/m

2) 25.5 57.4 39.6 47.0 0 0


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978 A. Carr

Table 13.

Comparison of the Lifshitzvan der Waals (non-polar) component of the surface free energy ofpolar polymers determined from the contact angles of three polar liquids (water (w), glycerol (g),

formamide (f)) and equation (21), and from the contact angles of non-polar liquids (diiodomethane,-bromonaphthalene) and equation (22), by using the van Oss, Chaudhury and Good approach

Equation and liquid probe PET PVDC PVC PMMA PVDF PVF PHMA (%)

LWS from equation (22)and diiodomethane

40.6 44.6 41.6 39.1 26.8 34.8 39.1

LWS from equation (22)and -bromonaphthalene

43.1 43.9 43.3 42.9 33.9 37.7 42.9

LWS (average) fromequation (22) andnon-polar liquids

41.9 44.3 42.5 41.0 30.4 36.3 41.0 0

LWS from equation (21)and polar liquids (w, g, f)

15.7 7.8 8.4 18.2 59.2 40.6 34.3 57.6


Table 14.

Comparison of the Lifshitzvan der Waals (non-polar) component of the surface free energy ofpolar polymers determined from the contact angles of three polar liquids (water (w), glycerol (g),formamide (f), ethylene glycol (e-g)) and equation (21), and obtained form the contact angles of non-polar liquids (TCP, diiodomethane, -bromonaphthalene) and equation (22), by using the van Oss,Chaudhury and Good approach


LWS from (equation (22)) anddiiodomethane

38.9 43.2 43.2 40.9 41.8 0

LWS from (equation (21)) and3 polar liquids (w, g, f)

26.6 38.9 91.6 55.0 54.1

LWS from (equation (21)) and3 polar liquids (w, g, e-g)

1.6 175.6 16.8 No solution* No solution*

LWS from (equation (21)) and3 polar liquids (w, f, e-g)

32.3 28.0 106.2 98.2 89.2

LWS from (equation (21)) and3 polar liquids (g, f, e-g)

28.5 34.9 96.6 68.7 65.4

LWS (average) from (equation(21)) and polar liquids

22.3 69.4 77.8 74.0 69.6 53.8

is the average difference by taking the mean values obtained from equation (22) as the reference.* No solution; solution of the system of three equations with three unknowns leads to a negative

value ofLWS .

the system of three polar liquids used to calculate the non-polar component LWSof the surface free energy of polymers, the results largely disagree with the

value obtained from equation (22) and the contact angle of the non-polar liquid,diiodomethane.


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Thus, it appears that only the description of liquid/polymer polar interactions aspolar interactions induced by the liquid leads to coherent results when the non-polarcomponent of the surface free energy of polymers is calculated from the contactangles of polar liquids. Both constant polarity and acid/base descriptions failedin allowing to determine the non-polar component of the surface free energy ofpolymers from the contact angles of liquids interacting with the polymer surfacesvia non-polar and polar interactions.

The literature data, as well as our own measurements, show that liquid/polymerpolar interactions are better described when we consider that the surface polymerpolarity is induced by the polarity of the contacting liquids. The first evidenceis a better fit of expressions relating contact angles to the surface properties ofliquids and solids. The second argument in favor of polymer polarizability is the

similarity between the dispersion components, DS , deduced from the contact anglesof the complete series of polar and non-polar liquids or from the contact angles ofonly polar liquids, and the values deduced from contact angles of only low polarityliquids. This approach is in agreement with the remark made in the seventies byFowkes who mentioned the proportionality between polar interaction energy andthe liquid polarity [12].

It may be possible to further improve the description of induced polar interactions,for example by taking into account the actual values of intermolecular interactiondistances between similar and dissimilar molecules. These distances are presently

considered identical (r11 r12).Of course, the idea of induced polar interactions at the interface between apolar liquid and a solid raises numerous fundamental questions. The first oneis to understand why liquids exhibit a permanent polarity at their surface andwhy this would be different at polymer surfaces. The answer may be in themolecular mobility or in the molecular size and structure, obviously quite differentfor molecular liquids and solid polymers. A fixed and random orientation of dipolesin a solid may explain why polymers do not exhibit a significant permanent polarityat their surface.

5. CONCLUSIONS

At liquid surfaces, polar interactions including hydrogen bonds are well describedby the interactions between aligned dipoles. For liquid/polymer interfaces, thehypothesis of induced polar interactions, between a liquid having a permanentdipole and a polarizable polymer surface, appears reasonable when compared toliterature data as well as to our own measurements. Therefore, polar interactionsat liquid/polymer interfaces seem to be essentially induced polar interactions. The

induced polar component of the solid surface free energy is found to be proportionalto the polarity of the liquid in contact with the solid.Twelve different polymer surfaces are considered in this study. In most cases,

the proportionality between the polar interactions and the liquid polarity improves


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15. F. M. Fowkes, in: Surfaces and Interfaces: Chemical and Physical Characteristics, J. J. Burke,N. L. Reed and V. Weiss (Eds), p. 197. Syracuse University Press, Syracuse, NY (1967).

16. J. Israelachvili, Intermolecular and Surface Forces, 2nd edition. Academic Press, San Diego,

CA (1992).17. S. Wu, Polymer Interface and Adhesion. Marcel Dekker, New York, NY (1982).18. R. C. Weast (Ed.), Handbook of Chemistry and Physics, 58th edition. CRC Press, Cleveland, OH

(1977).19. D. K. Owens and R. C. Wendt, J. Appl. Polym. Sci. 13, 1741 (1969).

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Surface Polarizability