A comparative analysis of surface structure and surface tension of hybrid silica films

Journal of Non-Crystalline Solids 209 Ž1997. 51–60

A comparative analysis of surface structure and surface tension of hybrid silica films C. Della Volpe ) , S. Dire, ` E. Pagani Department of Materials Engineering, UniÕersity of Trento, Õia Mesiano 77, I-38050 Trento, Italy Received 25 September 1995; revised 8 May 1996

Abstract Unsupported SiO 2-based films have been prepared by cohydrolysis of methyltriethoxysilane ŽMTES. and tetraethoxysilane ŽTEOS. in different molar ratios. Analysis of surface structure and surface tension have been performed; FTIR-ATR Žattenuated total reflectance. results were compared with results obtained from atomic force microscopy ŽAFM. and dynamic contact angle ŽDCA. techniques. The chemical nature of the exposed surface is discussed on the basis of calculations of surface tension components using different theoretical models. Due to the different sampling depth of the techniques used, a complete and original description of the surface structure of SiO 2-based films is proposed. The relative ratio between the exposed groups Si–OH, Si–Oy and Si–CH 3 depends on the TEOSrMTES ratio. Increasing %MTES produces a decrease of Si–OH and Si–Oy surface content. The surface of pure MTES derived film appears to be a flat and dense arrangement of Si–Me groups pointing outward.

1. Introduction Sol–gel process was originally developed to produce inorganic oxides from precursor solutions and has been more recently extended to the production of a new class of amorphous solids characterized by the organic modification of oxide structures w1,2x. Since the silicon–carbon bond present in compounds like RX x SiŽOR.4yx is preserved during hydrolysis–condensation, these reagents have been extensively used to produce organic modified ceramics Žormocers. w3,4x. RX groups bonded to silicon reduce the degree of crosslinking, acting as modifiers of SiO 2 network,

)

Corresponding author. Tel.: q39-461 882 409; fax: q39-461 881 977; e-mail: [email protected].

leading to final materials with features between glass and organic polymers w5x. Among the unique properties consequent to the introduction of organic groups in the silica network is the formation of unsupported thick films w6,7x. Ordinary gelling solutions of SiŽOR.4 give thick films only by multistep processes w8x because of restricted aging and drying conditions w9x. The presence of hydrophobic groups and the lower degree of crosslinking characteristic of sols prepared from organic modified silicon alkoxides permit marked increase in silica films thickness thereby avoiding the use of supports. The synthesis and applications of ormocers have been widely investigated, however less attention was devoted to the structural characterization and the surface features of these materials. The characterization methods usually employed to study surfaces are

0022-3093r97r$17.00 Copyright q 1997 Elsevier Science B.V. All rights reserved. PII S 0 0 2 2 - 3 0 9 3 Ž 9 6 . 0 0 5 4 7 - 9

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C. Della Volpe et al.r Journal of Non-Crystalline Solids 209 (1997) 51–60

spectroscopic techniques like infrared spectroscopy w10,11x, X-ray photoelectron spectroscopy w12,13x, and Rutherford backscattering spectrometry w14x. Ormocers are useful for low temperature applications such as the production of membranes for gas separation where the interaction between gases and surface may represent a key point for the separation capability. Thus, the knowledge of surface properties constitutes an important pre-qualification required in planning steps. This fact spurred us to undertake this work devoted to the physical–chemical characterization of SiO 2 gel films obtained with various concentrations of organic modifiers by the sol–gel method. To this aim, we determined the contact angle values which give definite information on the chemical arrangement of the exposed surface, according to the work of Zisman w15x and subsequent theories based on polar and dispersive contribution of surface tension w16–20x or on Lewis acid–base theory w21–24x. This analysis, developed and widely used in the field of polymer materials w25x, may be applied to all surfaces. Results are compared with data gained by other techniques, i.e. FTIR-ATR Žattenuated total reflectance. spectroscopy and atomic force microscopy ŽAFM.. This latter technique, complementary to SEM or optical microscopy, offers the advantage to obtain accurate information on the vertical dimension by enhancing the image contrast. The integration between dynamic contact angle ŽDCA. and AFM data, relevant to few angstroms depth, and FTIR-ATR results probing a deeper surface layer, appears essential to propose a tenable chemical surface structure.

2. Experimental 2.1. Preparation of Si(OEt)4 r MeSi(OEt)3 films Methyltriethoxysilane ŽMTES. and tetraethoxysilane ŽTEOS. were mixed together without solvent in different molar ratios and hydrolyzed with acidic water ŽpH 1.5.. The different compositions are labelled T x M y, x and y indicating the molar ratio of TEOS ŽT. and MTES ŽM., respectively Ž x q y s 100, 0 - x - 100.. In the case of pure TEOS ŽT100. ethanol was used as solvent Žmolar ratio: TEOS:EtOHs 1:0.5.. The amount of water used for

the hydrolysis was calculated for each composition so that the ratio Ž0.5 mol of water.rŽmol of alkoxide group. was maintained in all cases. Solutions were poured in clean polystyrene dishes Ždiameter 8 cm. and gelation was observed in 10 days. Transparent gel films with thickness from 10 to 40 mm were allowed to dry in air at 258C and cut to obtain regular samples for the characterization. Samples were stored at constant humidity at 258C. AFM, FTIR and DCA data were collected for each composition on the same sample after four months to assure a steady state of aging. 2.2. Characterization techniques FT-IR spectra were recorded in the reflectance mode on a Nicolet 5DXC instrument equipped with a horizontal attenuated total reflectance ŽHATR. accessory. In ATR, internal reflectance of the infrared radiation in a high refractive index crystal creates an evanescent wave which extends beyond the surface of the crystal into the sample held in contact with it. The sampling depth is determined by the refractive indexes of the crystal and the sample and the incident angle and wavelength of infrared radiation. T x M y samples were cut in order to expose to IR radiation the same area and 64 scans were collected for each spectrum. A profile fitting program w26x was employed to calculate the peaks area. Advancing and receding contact angles were measured by Wilhelmy technique w27x, using a Cahn micro balance, model 322 at a speed of 20 mmrs at 25 " 28C. HPLC water, RPE glycerol and synthesis grade methylene iodide ŽMerck Bracco., were used as received; their surface tension values were determined at the experiment temperature. The dynamic method was used after the control of equivalence between the two faces of films by measuring the static values of contact angles in water at 25 " 28C, with a home-built equipment. All measurements were performed at constant temperature. The system was thermostated with a time lag variable from 5 to 10 min which was also judged sufficient to obtain saturation of the microbalance-chamber with the vapor of the test liquid. Saturation of the microbalance chamber was assured by continuous presence of a beaker containing the solvent used inside the chamber.

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53

The dynamic contact angle ŽDCA. technique was used for determination of contact angles. Advancing and receding values of contact angle were obtained by immersion of a sample of constant section, suspended to a Wilhelmy microbalance, in the test liquid ŽFig. 1.. The forces acting on the sample are sample weight, buoyancy and surface tension along the immersion perimeter: F 1 s F y mg s Pg cos u y r gV

Ž 1.

1

where F is the total force measured on the sample, m and P the mass and the perimeter of the sample, V is the volume of sample immersed in the liquid of density r and surface tension g , u is the contact angle at the ternary interface of the studied system Žtest liquid, film or plate sample, and air. and g is the acceleration due to gravity. Extrapolating the trend of the total force to the zero depth of immersion ŽZDOI. ŽFig. 2., where the buoyancy is zero, and considering a constant sample weight, we obtain: F 1 s F y mg s Pg cos u .

Ž 2.

The total surface tension and the surface tension components were obtained using a program for performing calculations described in the Appendix. Due to the brittleness of materials tested, it was difficult to obtain samples of correct shape which may be the cause of high values of contact angles standard deviations.

Fig. 2. An ideal Wilhelmy experiment. The results are expressed in terms of measured force versus the immersion depth. The ZDOI represents the point at which sample touches the liquid surface; immersion depth is measured assuming this point as zero.

Atomic force microscopy ŽAFM. w28x probes the surface of a sample with a sharp pyramidal Si or silicon nitride tip, located at the end of a cantilever. Cantilever deflections, due to tip–surface interaction, are amplified to obtain a map of surface topography or other surface characteristics such as the tribological properties. AFM analyses were performed in contact and lateral force modes in air using a Topometrix TMX 2000 model with a scan rate of 75 mm Žmaximum resolution 2 nm. at a speed of 6 lines per second.

3. Results 3.1. DCA measurements and surface tensions calculations

Fig. 1. The Wilhelmy experiment. The forces acting on the sample are indicated together with the contact angle, u and the immersion depth, x.

The equivalence of the two surfaces of our films, a fundamental qualification to perform DCA analysis, was ascertained by static contact angle measurements. DCA results are reported in Table 1 where advancing and receding contact angles obtained in three different liquids are compared. For all solvents Q values decrease as the percentage of TEOS increases corresponding to an increase of the total surface tension. Data were averaged over 5 independent measurements with a standard deviation of "38.

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54

Table 1 Advancing and receding contact angles Ž8. versus %TEOS %TEOS

uadv H 2 O

urec H 2 O

uadv Glycerol

urec Glycerol

uadv CH 2 I 2

urec CH 2 I 2

0 30 50 70 100

94 96 78 67 66

65 72 32 46 35

94 92 79 82 70

61 70 37 40 29

70 75 63 62 54

60 62 47 47 32

It is noteworthy that the values of contact angles in glycerol for samples with high TEOS are greater than in water, without an observable absorption of liquid, contrary to previous findings w23x. The hysteresis values, i.e. the difference between advancing and receding values of contact angles, are reported in Table 2. Hysteresis values are commonly related to the surface roughness and to surface chemical heterogeneity due to domains with lateral size greater than 0.1 % 0.5 mm w29,30x. Although data are affected by a considerable standard deviation, a significant increase of DQ is observed between 0% and 100% TEOS, maximum DQ corresponding to intermediate compositions, for water and glycerol solvents. Contact angles allow calculation of surface tension components using equations described in the Appendix. Our calculations are based on the Owens, Wendt and Kaelble’s theory w17,18x for determining g d and g p , i.e. the dispersive and polar components of gs , with both geometrical and harmonic means; from Good w22x and van Oss w24x theory, gq, gy, g AB and g LW components of gs were also determined. Calculated values, obtained by advancing contact angles, are reported in Table 3. Data are affected by "3 mJrm2 uncertainty. gq values are at least one order of magnitude lower than gy ones, preventing any reliable comparison of gq among different samples. In general terms, gs values obtained by differ-

ent approaches, appear in substantial agreement although gs obtained by the Good–van Oss approach should be calculated assuming a positive value of gsq . This assumption is justified by the high standard deviation values which affect also their sign. The general gs trend corresponds to a net increase as the %TEOS increases. It is noteworthy that surface tension parameters of liquids are tabulated at 208C w24x, while our measurements were performed at 258C. For water it is possible to interpolate the value of components at 258C w24x. For CH 2 I 2 we assumed that also at 258C the acid–base components of methylene iodide remained zero, as at 208C w24x whereas for glycerol the values at 208C were used, any variation being within the experimental error.

(

3.2. FTIR-ATR Spectra were collected in the reflectance mode to increase the resolution of the technique for the surface layer. In our case, tested depth was about 0.3 mm and the incident angle was 458 on a ZnSe crystal.

Table 2 Contact-angle hysteresis Ž8. versus %TEOS %TEOS

Du H 2O

D u Glycerol

D u CH 2 I 2

0 30 50 70 100

29 24 46 21 31

33 22 42 42 41

10 13 16 15 22 Fig. 3. FTIR-ATR spectrum of T50M50 sample.

C. Della Volpe et al.r Journal of Non-Crystalline Solids 209 (1997) 51–60

55

Table 3 Surface tension components ŽmJrm2 . versus %TEOS; geometrical mean, harmonic mean and acid–base components Geometrical mean

Harmonic mean

Acid–base

%TEOS

gd

gp

gs

gd

gp

gs

g LW

gy

gs

0 30 50 70 100

21 18 22 22 26

3 3 9 16 15

24 21 32 38 41

19 17 20 20 23

8 8 15 21 20

27 25 35 41 43

23 20 27 27 32

7 5 15 36 24

25 a 20 27 36 a 32

a

gs values were calculated assigning a positive sign to

'g

q

.

Table 4 Position and intensity of SiOy and SiOH IR peak versus composition of T x M y films Sample label %MTES Frequency Žcmy1 . Area of the peak T100 T70M30 T50M50 T30M70 M100

0 30 50 70 100

953 945 935 917 not present

0.045 0.040 0.025 0.015 —

Fig. 3 presents the FTIR-ATR spectrum recorded on a T50M50 film in the range 4000–650 cmy1 . The wide band in the 3700–3000 cmy1 interval corresponds to overlapping of water O–H and Si–OH stretchings. In the low-frequency field a sharp peak at 1270 cmy1 , assigned to the stretching of Si–CH 3 bond w31x, is present together with two main peaks at 1131 and 1056 cmy1 and a signal at 775 cmy1 attributed to the antisymmetric and symmetric stretchings of the Si–O bond w32x, respectively.

Complex signals due to the stretching Ž3000–2850 cmy1 . and bending Ž1480–1330 cmy1 . of C–H bonds are observable suggesting the presence of unreacted alkoxy groups, as well as CH 3 groups directly bonded to Si. The peak at 935 cmy1 is attributed to the stretching vibrations of Si–OH and Si–Oy groups w33x. The position and intensity of this peak is affected by gel composition. Table 4 reports the frequencies and calculated intensities of this peak. They increase as MTES decreases. In case of M100 film this signal is absent suggesting an amount of Si–OH and Si–Oy bonds undetectable for our instrument. 3.3. AFM AFM analysis were performed in contact mode Žor topographic imaging. to obtain roughness data and in lateral force mode. Fig. 4 shows the surface of M100 sample. Images represent the same part of the sample and have been

Fig. 4. AFM images of M100 in lateral force mode; images represent the same part of the sample with a 908 rotation. The waviness has the geometrical characteristics of capillary waves, whose length, in fact, increase with surface tension.

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C. Della Volpe et al.r Journal of Non-Crystalline Solids 209 (1997) 51–60

Fig. 5. A pictorial representation of waviness on M100 and T100 as obtained from AFM analysis.

collected with a 908 rotation of collecting cantilever, in order to eliminate artifacts. The film surface appears flat, with roughness of 1 nm and roughness spacing of few nanometers. T100 sample displays a waviness of 10–15 nm and a waviness spacing of 6–8 mm, M100 film shows a waviness of 20–30 nm and a waviness spacing of 2–3 mm ŽFig. 5.. The films roughnesses are similar, while waviness is different with the greater spacing being associated with a lower amplitude. These surface features were not detected by standard scanning microscopy ŽSEM..

4. Discussion Suitable reaction conditions allow us to obtain SiO 2-based disks 8 cm in diameter and 10–40 mm in thickness. For all T x M y compositions, the disks are crack-free, transparent and macroscopically homogeneous. The compliance of samples increases with MTES demonstrating a progressive modification of the silica network. The nearly identical static contact angles suggest a symmetric development of the network, which is in accord with the results of Klein and Giszpenc w34x. Although T100 sample is obtained from ethanol solution and other samples are prepared by mixing the pure components, we disregard this parameter because ethanol is produced upon hydrolysis and condensation. The equilibrium reached between samples and environment during preparation and storage may remove any difference due to this aspect of the preparation procedure. FTIR spectroscopy, recorded in ATR mode ŽFig. 3., shows that the surface of the T50M50 film is composed of Si–CH 3 Ž1270 cmy1 ., Si–Oy and SiOH terminal groups Ž935 cmy1 .. In the high frequency region, the wide band Ž3700–3100 cmy1 ., associated with O–H stretching vibrations, suggests the presence of adsorbed water and mainly hydrogen bonded silanols w30x. The surface seems to be charac-

terized by a small amount of free surface silanols which should display a definite signal at 3740 cmy1 w35x. FTIR-ATR spectra of all T x M y samples indicate the evolution of the Si–Oy and Si–OH signals, as reported in Table 4. The intensity decrease is attributed to a lower content of surface Si–Oy and Si–OH groups as MTES content increases and the corresponding shift to lower frequencies may be related to the increased load of Si–CH 3 affecting Si–O bond polarity and local geometry. The lowering of Q values as the %TEOS increases is consistent with the total surface tension which increases from about 24 to about 40 mJrm2 as %TEOS increases from 0 to 100. The surface tension of M100 is similar to reported values w15x in case of surfaces covered by –CH 3 groups. M100 surface may be described as a flat and dense arrangement of –CH 3 groups pointing outward, as shown in Fig. 6A. Consequently, the basic component due to the lone pairs of bridging oxygen atoms is reduced or removed in agreement with low gy value Žandror with low g p data. found for this sample. Ultimately, M100 surfaces behave like completely hydrophobic surfaces obtained by reaction of hydroxylated silica with hydrophobing reagents w36x. This borderline situation is not surprising since the development of the surface structure from the MTES gelling solution allows flexible oligomeric units to reach the mini-

Fig. 6. ŽA. Proposed structure of M100 surface with Si–CH 3 groups pointing outward. ŽB. Proposed structure of T100 surface with hydrogen-bonded Si–OH groups pointing inward.

C. Della Volpe et al.r Journal of Non-Crystalline Solids 209 (1997) 51–60

mum free energy conformation. According to this hydrophobic surface structure, moisture diffusion into the bulk is prevented, accounting for the absence of Si–OH and Si–Oy vibrational modes at 920–950 cmy1 ŽTable 4.. The effect of TEOS introduction is discussed by considering the data obtained from the Owens, Wendt and Kaelble’s theory and from the data obtained from the Good–van Oss theory ŽTable 3.. As the amount of TEOS increases the g d component increases, within a rather restricted interval, while the g p values increased significantly. This suggests that the increase of g p may be related to the presence of Si–O units derived from TEOS hydrolysis and condensation and to the presence of some unreacted Si–OEt groups. This is also shown by the increase of peak area at 950–920 cmy1 attributed to Si–OH and Si–Oy vibrational modes. The increasing value of the non-polar component with the increasing TEOS content, could be interpreted by invoking an increasing microscopic roughness, so that, for a given geometrical surface, the real exposed surface is greater. The role of Si and O atoms as Lifshitz and van der Waals forces actors may be enhanced by the reduction of methyl groups on the surface as the TEOS content increases. During hydrolysis, due to the different hydrolysis–condensation rates between TEOS and MTES, the tetrafunctionality of TEOS favors the tridimensional growth of oligomers which collapse to the gel network creating SiO 2-microdomains. Discussion of gq and gy contributions to gs offers some additional starting points in the effort to determine the surface nature of organic modified silica gels. As a general behavior, gq values are negligible Ž0.0 % 0.6 mJrm2 . whereas the basic component gy is wide and affected by the TEOS content. This is a common situation in the so-called ‘monopolar’ surfaces. Van Oss describes a monopolar surface as: ‘‘ . . . Its g SAB is equal to zero and then, its total surface tension Ž . . . . is simply equal to its g SLW Ž . . . .. However such substances, which are designated as monopolar Ž . . . . can strongly interact with bipolar materials and with monopolar materials of opposite polarity, notwithstanding the seemingly apolar nature of their surface tension.’’ w24x. Discussing the general magnitudes of acid–base parameters, Good and van Oss w23x analyze the case of some organic substances, which are effective ba-

57

sic monopoles. On the basis of their structure Ži.e. the presence of protons and hydroxyl groups. one might expect that they should be bipolar, showing either acid and basic behaviors. The proposed explanations are: ‘‘Ži. – there are not hydroxyl groups pointing outward to the adjacent phase; Žii. – the adsorbed water is bonded sufficiently tightly to reduce the manifestation of acid character of underlying groups; Žiii. – a general law exists by which the acid character is appreciably smaller than basic one for the same substance, even in absence of self-association.’’ w23x. The reaction conditions employed to produce T x M y films and the aging in contact with moisture, should generate an almost fully hydroxylated SiO 2 surface w37x. Considering the absence of spectroscopic signals corresponding to free surface silanols, the arguments Ži. and Žii. appear tenable to account for our monopolar behavior. Since a significant gq component was found for the surface tension of quartz exposed to air and water vapor w38x, hypothesis Ži. is more conceivable. Thus, according to the picture of Fig. 6B, all silanols in TEOS-derived SiO 2 microdomains should point inward and should be strongly hydrogen bonded whereas CH 3 SiO 1.5 MTES-derived microdomains preserve Fig. 6A conformation, accounting for the increase of gy with %TEOS. In sol–gel process hydroxyl groups are formed since the early stages of the hydrolysis–condensation process. Due to the mobility of the forming network, –OH groups may arrange themselves in order to promote the interactions with the polar medium of the sol rather than with the apolar medium constituted by atmosphere. In this way, the progressive gelling process could freeze –OH groups in their primitive position pointing inward to the gel phase. The case of glass is different: –OH formation by hydration follows the production of the stiff glass surface. Thus, silanols are free to move and can be randomly oriented. This argument could be applied to any SiO 2 surface exposed to atmosphere. The increase of surface tension, passing from pure MTES to pure TEOS, is confirmed from the different waviness between T100 and M100 films. The higher surface tension of T100 corresponds to a more rigid

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C. Della Volpe et al.r Journal of Non-Crystalline Solids 209 (1997) 51–60

and less deformable surface. This fact can be related to the proposed presence of –OH groups pointing inward and hydrogen bonded, thus forming a quite continuous ‘skin’. On the contrary, the presence of organic modified moieties implies a network modification which affects the mechanical behavior of hybrid materials w7x. Note that T x M y samples with x - 50 are characterized by total surface tension less than 30 mJrm2 . Since polystyrene shows a total surface tension of 33 mJrm2 , T x M y films with x - 50 should adhere to Petri dishes used as sample holders. On the contrary, the lower basic surface tension component of polystyrene w24x, probably, prevents the adhesion in spite of its high total surface tension value.

5. Conclusions Ži. T x M y films surface is characterized by Si– CH 3 , Si–Oy and Si–OH terminal groups, as shown by FTIR-ATR spectra. The relative ratio of these groups on surface depends on film composition. Žii. Total surface tension gs increases from 24 to 40 mJrm2 as the TEOS content increases. This trend is mainly related to the increase of gy Žor g p . values. A monopolar behavior is observed for all surfaces, gq values being negligible. To account for this behavior, it has been proposed that all silanols in TEOS-derived microdomains should be strongly hydrogen bonded and point inward to the gel phase. Žiii. The increase of surface tension with the TEOS content affects the morphology of the surfaces as observed by the AFM technique. Film roughness is similar while waviness and waviness spacing are different.

Acknowledgements

Appendix A The determination of surface free energy and its components can be performed on the basis of contact angle measurements. The calculation methods, developed for organic materials in the last 20 years, use different solvents as probes of surface properties, the choice of the solvents for measuring the contact angles being determined by the different molecular properties of the liquids Žpolarity, polarizability and acid–base behavior.. From contact angles it is possible to calculate the values of surface tension components using the folowing equation systems where all the necessary expressions and definitions for the calculation of the adhesion work between the solid surface s and any liquid i are presented. Different theories use similar concepts, but characterize the surface with two or three components. For a generic material s:

gs s gsd q gsp , gs s gsd q gsp , gs s gsLW q gsAB s gsLW q 2 gsq gsy .

(

For a generic liquid i:

g i s g id q g ip , g i s g id q g ip , y g i s g iLW q g iAB s g iLW q 2 gq i gi .

(

Geometric mean:

( / ž( g Ž 1 q cos u . s 2 ž (g g q (g g / . g 1 Ž 1 q cos u 1 . s 2 g 1dgsd q g 1pgsp , 2

d d 2 s

2

p p 2 s

Harmonic mean: Professor Giovanni Carturan and Professor David Avnir are greatly acknowledged for the helpful discussions. A special thanks to Professor G. Carturan for the critical review of the manuscript. Dr. E. Paganini wishes to thank Provincia Autonoma di Trento for financial support. Mr. Alfredo Casagranda is acknowledged for his skillful technical support.

g 1 Ž 1 q cos u 1 . s 4

g 2 Ž 1 q cos u 2 . s 4

ž ž

g 1dgsd g 1dgsd g 2dgsd g 2dgsd

q

q

g 1pgsp g 1pgsp g 2pgsp g 2pgsp

/ /

,

.

C. Della Volpe et al.r Journal of Non-Crystalline Solids 209 (1997) 51–60

Acid–base components:

w17x or the harmonic means, using the following equations: Geometric mean

g 1 Ž 1 q cos u 3 .

ž(

y y q s 2 g 1LWgsLW q gq , 1 gs q g 1 gs

(

(

/

gsi y g i y gs s yg i Ž 1 q cos u i .

g 2 Ž 1 q cos u 2 . s2

ž(

g 2LWgsLW

ž(

s y2 g idgsd q g ipgsp . q

(

q

(

y gq 2 gs

q

(

q

(

q gy 2 gs

/,

s2

ž(

(

/

Ž A.6 .

/

Ž A.7 .

Harmonic mean

g 3 Ž 1 q cos u 3 . g 3LWgsLW

59

gsi y g i y gs s yg i Ž 1 q cos u i . y gq 3 gs

q gy 3 gs

/.

s y4

Here is gq – acid or electron acceptor component; gy – basic or electron donor component; g LW – Lifshitz–van-der-Waals component; g AB – total acid–base components 2 gq gy ; g p – polar component; g d – dispersive component; gs or g i – total value of surface tensions g LW q g AB or g p q g d .

'

For the process of adhesion of two different surfaces, i and s, thermodynamics provides us with the Young–Dupre´ equation: DGsia s gsi y g i y gs s g i Ž 1 q cos u i .

Ž A.1 .

which expresses the free energy of adhesion Žor the ‘work of adhesion’. DGsia , by means of surface tension of liquid i, g i , and the contact angle at the interface among liquid, solid and vacuum or vapor, ui. On the other hand, according to Girifalco and Good w39x, Fowkes w40x the surface energy of a solid or a liquid is the sum of different contributions

gs s gsd q gsp q gsh

Ž A.2 .

where the suffixes d, p and h indicate the dispersion, polar and hydrogen-bonding interaction components, respectively. Similar separations into different contributions have been proposed by Gardon w41x for mixing enthalpy D H and by Hansen w42x for solubility parameters d . Owens, Wendt and Kaelble w17,18x and Wu w19x, developed the Fowkes approach, reducing it to two components:

gs s gsd q gsp ,

Ž A.3 .

g i s g id q g ip

Ž A.4 .

and expressing the work of adhesion: DGsia s gsi y g i y gs s DGsiap q DGsiad

Ž A.5 .

by means of two different models, the geometrical

ž

g idgsd g idgsd

q

g i pgs p g i pgs p

where the constants g id , g ip are tabulated for few solvents. The geometric mean rule is commonly known as Berthelot’s geometric combining rule w43,44x. Similarly, following Fowkes w40x, Good w22x and van Oss w24x, we write for phase s and for a liquid i:

gs s gsLW q gsAB ,

Ž A.8 .

g i s g iLW q g iAB

Ž A.9 .

where LW suffix indicates the dipole–dipole, dipole–induced dipole and induced dipole–induced dipole components of total Lifshitz–van der Waals force, while AB suffix indicates the acid–base interaction, in terms of Lewis theory. Assuming the validity of a slightly modified Berthelot geometric mean rule:

gs s gsLW q gsAB s gsLW q 2 gsq gsy

(

Ž A.10 .

where the new parameters Žgq i s acid component and . gy i s basic component have value only in the context of this expression. Thus, the free energy of adhesion can be expressed by:

gsi y g i y gs s yg i Ž 1 q cos u i .

ž(

y q y s y2 g iLWgsLW q gq i gs q gs g i

(

(

/

Ž A.11 . where u i is the contact angle between i and s phases. y The constants g iLW , gq have been tabulated at i , gi y 208C, based on the hypothesis that for water gq i s gi at 208C w24x. Thus, if we know u i for two or three solvents characterized by different polar, dispersive and LW, acid and base components Žusually water, methylene

C. Della Volpe et al.r Journal of Non-Crystalline Solids 209 (1997) 51–60

60

iodide or bromonaphthalene and glycerol, ethylene glycol, DMSO or formamide. we will have, correspondingly, a system of two or three equations in, respectively, two or three unknowns, whose resolution allows to obtain the parameters gsd , gsp or gsLW , gsq, gsy of the solid surface. It is noteworthy that, in the case of acid base theory, the mathematical unknowns are gsLW , gsq , gsy , whose sign can be positive or negative, so that also the total acid–base component gsAB s 2 gsq gsq can be positive or negative.

(

( ( ž( ( /

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