Contact angles, work of adhesion, and interfacial tensions at a dissolving Hydrocarbon surface

Contact Angles, Work of Adhesion, and Interfacial Tensions at a Dissolving Hydrocarbon Surface GC)RAN STROM, MONICA FREDRIKSSON, AND PER STENIUS Institute for Surface Chemistry, Box 5607, S-114 86 Stockholm, Sweden Received March 3, 1986; accepted December 1, 1986 The initial contact angle of a n u m b e r of liquids on solid hydrocarbons and aliphatic alcohols has been measured. Some of these liquids dissolve the substrate. The initial work of adhesion of dissolving liquids is proportional to the square root of the dispersion part of the liquid surface tension (Ta), with slope 4(3",) 1/2 and intercept 2% (% = surface energy of solid). For nondissolving liquids, the slope is 2(%) 1/2 and the intercept is zero. A model in which the finite intercept is associated with solvation of the first molecular layer o f the solid is proposed. It can be used to predict the liquid/solid interfacial tension for the dissolving surfaces and correctly describes the experimental results. The theory is limited to 3' (liquid) > 3' (solid). © 1987AcademicPress,Inc. INTRODUCTION

Equilibrium contact angle measurements are widely used to characterize surface energetical properties such as the wettability, the dispersion part of the surface energy (3<~), the work of adhesion (Is,0, etc. When the solid/ liquid interactions originate from dispersion forces only, the following equation can be used to calculate the work of adhesion, Isa =

Isd,1 = TI(COS 0 + l ) + 71"e

= 2 ~/3'~3'~+ ~re,

[ 1]

while the solid/liquid interfaeial tension is given by 3"s,1 = 3"s -4- 3"1 -- 2 Yl/~aYl d[2] The use of the geometrical mean approximation of the dispersion force interaction that leads to these equations was originally suggested by Fowkes (1, 2). They are widely applied today. Nonequilibrium contact angles have been much less investigated. One should in this case distinguish clearly between two situations: (a) dynamic contact angles which are formed when a liquid moves across an insoluble solid and (b) nonequilibrium contact angles which

are formed while the liquid drop dissolves the solid. The latter types of contact angles have not been studied systematically. However, Fox and Zisman (3) noted that when the critical surface tension is determined using liquids which attack the solid, much higher values than those with nondissolving liquids are obtained. The aim of this investigation is to systematically characterize the behavior of liquids on dissolving polymer surfaces. The initial contact angle (i.e., contact angle extrapolated to zero time after application of the liquid) was measured using solid alkanes, paraffins, and alcohols in combination with a number of liquids, some of which dissolve the solids and others which do not. EXPERIMENTAL

Materials The liquids and solids used were of the highest purity commercially available and were used without further purification. Liquids. Table I shows the supplier, the purity, the surface tension (3"0 and the dispersion part of the surface tension (3"~)of the used liquids. For saturated hydrocarbons 3'1 = 3"~-For 352

0021-9797/87 $3.00 Copyright© 1987by AcademicPress,Inc. All rightsof reproductionin any formreserved.

Journalof Colloidand InterfaceScience, Vol. 119,No. 2, October 1987

WETTING OF A DISSOLVING SOLID

353

TABLE I Supplier Purity and Surface Tension (at 298 K) of the Liquids Used Surface tension (mJ/m2) Liquids

Hydrocarbons Oecane Dodecane Hexadecane Decalin (cis + trans mixture) Methyl naphthalene Halogenated hydrocarbons Sym-tetrachloroethane c~-Bromonaphthalene Sym-Tetrabromoethane Diiodomethane Miscellaneous Water Ethylene glycol Glycerol

Symbol in figures

Supplier

Purity (%)

"Yl

a b c d e

Merck Merck Merck Fluka AG Merck

>99.5 >99.5 >99.5 >98 >98

23.9 a 25.4 ~ 27.6 a 30.6 d 38.6 a

23.9 25.4 27.6 30.6 38.6

f g h i

Merck Merck Merck

>98 >98 >99 >98

36.3 a 44.6 ~ 49.7 ~ 50.8 ~

36.3 e 44.6 e 49.7 e 50.8 e

Merck Merck

>99.5 >99.5

72.8 a 47.7 ~ 63.4 a

21.8 b 30.9 ~ 37.0 ~

k 1 m

~,a

a Ref. (7). b Ref. (6). CRef. (1). a This work. e See text.

halogenated and aromatic hydrocarbons the value o f the n o n d i s p e r s i v e p a r t o f 3'1 (i.e., 3'r -- -y~ - 3/2) is quite s m a l l a n d difficult to det e r m i n e accurately. Interracial t e n s i o n m e a s u r e m e n t s against water (4) give values o f 0.4 a n d 0.7 m J / m 2 for d i i o d o m e t h a n e a n d c~-brom o n a p h t h a l e n e , respectively. T h e s e values were c a l c u l a t e d using the g e o m e t r i c m e a n app r o x i m a t i o n to d i v i d e t h e n o n d i s p e r s i v e p a r t o f interfacial t e n s i o n into c o n t r i b u t i o n s f r o m the two liquids, w h i c h is a n a p p r o x i m a t i o n . H o w e v e r , the values i n d i c a t e t h a t 3'P is low. C o n t a c t angle m e a s u r e m e n t s o n solid h y d r o carbon and polytetrafluoroethylene (PTFE) surfaces give higher values (2.3 + 9 m J / m 2 for d i o d o m e t h a n e , - 2 . 4 _+ 7 m J / m 2 for ~ - b r o m o n a p h t h a l e n e (1)) w h i c h also are quite uncertain. F o r h a l o g e n a t e d a n d a r o m a t i c h y d r o c a r b o n s we therefore find it r e a s o n a b l e to m a k e the a p p r o x i m a t i o n 3'~ ~ 0, i.e. 3q = q/~. F o r e t h y l e n e glycol, 3'~ is the m e a n o f three values o b t a i n e d f r o m c o n t a c t angle m e a s u r e -

m e n t s o n h y d r o p h o b i c surfaces: 30.8 m J / m 2 o n P T F E (2), 29.9 m J / m 2 o n p o l y e t h y l e n e (5), a n d 32.0 m J / m z o n n - h e x a t r i c o n t a n e (this work). 3'2 for glycerol was also c a l c u l a t e d f r o m c o n t a c t angle m e a s u r e m e n t s (1). 3'~ for water was c a l c u l a t e d f r o m interfacial t e n s i o n s with h y d r o c a r b o n s (6). T h e w a t e r was d o u b l y distilled. Solids. T h e m e l t i n g b e h a v i o r o f t h e solids was c h a r a c t e r i z e d using a D T A a n d b y visual o b s e r v a t i o n o f the isotropic p o i n t (i.p.), i.e., the t e m p e r a t u r e at w h i c h the solid f o r m s a n isotropic l i q u i d in a test tube. T a b l e II gives the p u r i t y o f the solids, a n d s o m e d a t a characterizing their m e l t i n g behavior.

Preparation of Surfaces P o l y m e r surfaces were allowed to f o r m against air using the following technique. T h e m a t e r i a l was p l a c e d in a b e a k e r o n a water b a t h a n d h e a t e d to ~ 5 ° C a b o v e its i.p. C l e a n e d m i c r o s c o p e p r e p a r a t i o n glass slides Journal of Colloid and Interface Science, Vol. 119, No. 2, October 1987

354

STROM, FREDRIKSSON, AND STENIUS TABLE II Supplier, Purity, and Melting Properties of the Solids Used Solids

Alkanes n-Eicosan n-Docosan n-Tetracosan n-Hexatricontane Paraffins I II III Alcohols 1-Tetradecanol 1-Hexadecanol 1-Octadecanol

Supplier

Purity a (%)

m.p. '~b (°C)

m.r5 (°C)

re.peaka (°C)

i.p. e (°C)

Merck Merck Fluka AG Fluka AG

>98 >98 >99 >98

33-36 42-45 49-51 74-76

43.1-45.1 49.7-51.5

44.5 50.7

36 43 51 77

34-36 58-60 69-73

20-42 46-58 51-79

33 51 59

56 56 78

38.2 50.8 59.5

40 51 59

Chroma Kebo Merck Fluka AG Fluka AG Fluka AG

>98 >99 >99

38-39 49-50 57-58

35.9-39.5 48.5-52.5 56.8-60.5

a Accordingto the supplier. bm.p. = melting point. cm.r. = melting region. d m.peak = peak of the m.r. ei.p. = isotropic point, i.e., lowest temperature for isotropic melt.

(75 × 26 mm) were dipped into the melt which immediately solidified onto the cool glass surface. The slide was carefully drawn out of the melt and placed in a horizontal position. Final solidification was allowed to take place in contact with air. This procedure gave very smooth surfaces of the solid paraffins, the alcohols, and n-eicosan. Due to their high crystallinity, the surfaces of higher alkanes became less smooth. However, they were deemed acceptable for contact angle studies since the measurements of contact angle were well reproducible (usually within 2-3 ° ) and the calculated values of'r~ agreed within experimental accuracy with those expected from the literature.

Solubilities and Contact Angles The solubility of the solids in the different liquids was roughly characterized in test tubes at 22 _+ 2°C by adding a few milligrams of the solid to a few milliliters of the liquid and observing whether the solid was soluble in the liquid or not. The solubility was also characJournal of Colloid and Interface Science, Vol. 119, No. 2, October 1987

terized by the appearance of the surface after the contact angle measurements. About 2 h after application of the drop it was sucked off and the solubility was classified according to the appearance of the residual spot. For each solid the liquids were classified as nondissolving (n), partly dissolving (p), and totally dissolving (d). Partly dissolving liquids gave a mark on the solid, usually a shallow pit, but the solubility in the test tube experiment was low. Totally dissolving liquids gave a mark on the surface and dissolved the solid completely in the test tube. Nondissolving liquids had no effect in either experiment. All contact angles were measured as advancing angles. For nondissolving liquids the angle was recorded after the volume of the droplet had been successively increased by the addition of small amounts of liquid to the initial drop, until the contact angle reached a constant value, The angle was measured on both sides of at least three drops. The values reported are mean values of such measurements with a standard deviation of about 3 o. When a drop of a dissolving or partly dis-

WETTING

355

OF A DISSOLVING SOLID

solving liquid is applied it spreads steadily out over the substrate to form a drop with a finite contact angle and a shape that does not change for at least 10 min. The measurements of the initial contact angle was done within 30 s after the application. It was assumed that changes of the surface tension of the dissolving liquid due to the dissolution of the solid during this time was negligibly small. The contact angles were measured at 22 + 2°C using a R a m t - H a r t Model A100 contact angle goniometer. The surface tensions were measured at the same temperature using a Wilhelmy glass plate connected to a microbalance. Differential thermal analysis was done with a Mettler TA 2000 thermal analysis system. Conventional corrections for errors due to the temperature scan rate (2°C/rain) were made. RESULTS

The liquids and solids investigated, the equilibrium contact angles formed by nondissolving liquids, the initial contact angles formed by dissolving liquids, and the observed solubilities of the solids are given in Table III.

Eicosane, docosane, and tetracosane dissolved totally within 15 min in the liquid hydrocarbons sym-tetrachloroethane and a-bromonaphthalene in the test tubes. Hexatriacontane was soluble in decalin only. The solid fatty alcohols dissolved within 15 rain in the hydrocarbons, tetrachloroethane, a-bromonaphthalene, and tetrabromoethane, but they were insoluble in diiodomethane. The paraffins are a mixture of different alkanes. The mean molecular weight increases with the paraffin melting point. Paraffin III has a broad melting region (see Table II) with a lower limit close to that of tetracosane, which is soluble in most of the liquids used. It is thus likely that this paraffin contains a considerable amount of both soluble and insoluble alkanes. Indeed, the test tube experiments showed that paraffins I and II are totally dissolved in the hydrocarbons, tetrachloroethane, and abromonaphthalene, while paraffin III appeared insoluble. The liquids did, however, produce a shallow pit after resting 2 h on this paraffin. Tetrabromoethane or diiodomethane did not dissolve the paraffins. Dissolution of the paraffins was much slower than that for the alkanes and the alcohols.

T A B L E III C o n t a c t Angles o f Dissolving a n d N o n d i s s o l v i n g L i q u i d / S o l i d C o m b i n a t i o n s Alkanes Liquids

C2o

Cz~

Paratfins C24

C36

I

I1

Alcohols III

Hydrocarbons Decane

- - 5a

8.8 d

Dodecane

~8 a

t4.2 d

9.7 d

19.3 p

C14

C16

Cta

25.1 a

20.5 d

10 d

12.5 d

Hexadecane Decalin

~10 d

13.0 d

13.0 d 20.5 d

35.8 n 44.2 d

15.7 d 13.3 d

17.7 d 13.0 d

27.5 p 28.3 p

9.8 d 7.0 d

34.8 d 37.4 d

30.0 d 35.3 d

Methyl naphthalene

~12 d

22.8 d

29.6 d

54.8 ~

14.2 d

19.8 a

41.6 p

8.3 d

27.3 d

40.5 d

~10 d 17.2 a 37.0 n 54.7"

19.0 d 27.5 d 41.2 n 57.3"

29.5 d 32.4 d 55.7" 66.2 n

45.2 n 61.0" 67.8" 62.5 ~

15.3 d 16.8 d 31.8" 41.3 p

17.0 d 25.7 d 40.8 n 61.5 ~

42.3 p 48.6 p 57.7 n 64.6 ~

<5 d 13.6 d 18.5 d 60.8 n

19.1 d 29.8 d 31.8 a 64.3 n

21.8 d 42.0 d 42.2 d 61.1"

103.2 n

H a l o g e n a t e d h.c. Sym-tetrachloroethane a-Bromonaphthalene Sym-tetrabromoethane Diiodomethane Miscellaneous Water

112.5 n

105.5"

106.0 n

103.0 n

108.8 n

108.5 n

E t h y l e n e glycol

76.8"

82.5 ~

84.5"

81.0 n

77.2"

80.3"

82.2 n

Glycerol

90.8"

92.8"

99.0"

92.2"

88.3"

92.2"

89.3"

Note. d T o t a l l y dissolving liquid, n n o n d i s s o l v i n g liquid, p p a r t l y dissolving liquid.

Journal of Colloid and Interface Science, Vol. 119, No. 2, October 1987

356

STROM, FREDRIKSSON, A N D STENIUS

When the solid dissolves in the liquid during contact between the solid and a liquid drop, the topography of the solid changes, and the surface tension of the liquid decreases and so does the interaction energy between the solid and the liquid. These effects are believed to be very small and not to affect the significance of the contact angle measurements for dissolving systems; since the dissolution was very slow, the contact angle could be easily and reproducibly measured and the shape of the drop and the contact angle stayed constant for at least 10 min after the first rapid spreading when the drop was applied. DISCUSSION

Nondissolving Systems The only substrate that did not dissolve in the hydrocarbons (except decalin) and the ha-

°t 80-

E 70-

4" 60

0 0 ,J

50

40

3O

20-

10-

1

i

i

i

i

i

1

2

3

4

5

6

/

7

V~LI'(mJ/m2)½"1 FIG. 1. Work o f adhesion between n-hexatriacontane and different liquids that do not attack the surface as a function of ~ . (A) This work, ( e ) data from Fox and

Zisman (3). Journal of Colloid and Interface Science, Vol. 119,No. 2, October 1987

logenated hydrocarbons was hexatriacontane. Figure 1 shows the work of adhesion, i.e., "rl(COS 0 + 1) calculated from Eq. [1] plotted versus ~ using our data and the data published by Fox and Zisman (3). The two sets of results fall on separate straight lines. Both lines extrapolate to the origin. The plot shows that the energy of interaction between hexatriacontane and these liquids can be satisfactorily estimated using the geometrical mean approximation proposed by Fowkes. It also indicates that the spreading pressure re is either negligible or a linear function of ~ . The surface energy of hexatriacontane can be calculated from the slope of the line or Eq. [1]. Our measurements give a surface energy of 24.1 _+ 2 m J / m 2 while the Fox and Zisman data give a value of 20.2 + 2 m J / m 2. The difference is somewhat larger than experimental accuracy. However, it is not unreasonable that a systematic difference occurs between the two sets of results, since Fox and Zisman used extremely pure crystalline hexatriacontane platelets, while our material was commercial hexatriacontane and certainly not as carefully crystallized. The dispersion part of the surface energy of the other solids was estimated using Eq. [ 1]. It was assumed that 7re is negligible and the measured contact angles and surface tensions of those liquids that did not dissolve the surfaces were used. The only available liquid that could be used for measurements on solid al, cohols is diiodomethane. Strongly polar liquids such as water and alcohols may change the orientation of the solid molecules at the surface (8). Also, their interaction with the surfaces may not be due solely to dispersion forces. For the solid alkanes and paraffins II and III the ~ is the mean value of the values calculated from the contact angles of the nondissolving liquids (see Table III). These values are collected in Table IV. The standard deviation of the surface energies is 4-5 m J / m 2. This relatively high value is due to the uncertainty in the measurement of the contact angles (2-3°). For high surface tension liquids an error in the contact angle

357

W E T T I N G OF A DISSOLVING SOLID TABLE IV

Surface Energies of Solids Obtained from Contact Angles Using Nondissolving, Partly Dissolving, and Totally Dissolving Liquids, and the Regression Analysis Correlation Coefficient (RAC) for the Experimental Data to Fit Eq. [8] Dissolvingliquids

Substrate Alkanes n-Eicosane n-Docosane n-Tetracosane n-Hexatricontane Paraffins I II III Alcohols 1-Tetradecanol 1-Hexadecanol 1-Octadecanol

Nondissolving liquids'y~ (mJ/m2)

-),~(mJ/m2) from slope

'y, (mJ/m2) from intersect

RAC coetfieient

5 5 4 2

33.4 27.0 25.5 --

33.4 27.4 26.4 --

0,9999 0,9999 0,9986 --

32 ± 5 29 ± 4 29 ± 4

34.2 28.3 (14.1)

34.6 28.8 (13.0)

0.9997 1.0000 0.996

28 26 28

33.9 36.0 30.2

34.0 38.4 34.3

0.9999 0.9994 0.9992

30 ± 30 ± 26 ± 24 ±

of a few degrees produces a large error in the value of 3'~, in particular when 0 ~ 90 °. In this case an error of 2 ° in the water contact angle gives an error of 3 m J / m 2 in 3'~. However, in view of the inherent uncertainty involved in the geometric mean approximation, conclusions based on very small changes in surface tensions determined with high precision are in any case not warranted. There is no doubt that despite the high values of the standard deviation a significant decrease in q,~ is observed when the molecular weight of the solid alkanes or the melting point of the paraffins is increased. Obviously, an increased solidification slightly reduces the surface energy. The dispersion energy of the solid alcohols is about the same as that for alkanes and paraffins. This indicates, as is indeed well known (8) that the alcohol molecules at the surface are oriented with their hydrocarbon chain toward the air.

Paraffin III, which is a partly dissolving system, will be discussed in the next section. For all systems the dependence on ~ is very closely linear. Small deviations are observed for low surface tension liquids on some of the solids. The deviation takes the form o f a change in the slope of the lines and it is most pronounced for hexadecanol and octadecanol. Smaller, but still significant deviations are observed for paraffin I, paraffin II, and tetracosane. For the slopes at liquid surface tensions above those giving deviations, the interesting observations are made that they are almost exactly twice as large as those found for the nondissolving surface (Fig. 1) and that they do not intercept the ordinate at origo. A simple model to explain these observations can be formulated in the following way. The interfacial tension can be pictured as the work required to increase the interface by bringing molecules from the interior of the two bulk phases to meet at the new interface. For a solid/liquid interface this work is given by

Dissolving Systems Figures 2, 3, and 4 show "rl(COS0 + 1) versus for the dissolving liquids on solid alkanes, solid paraffins, and solid alcohols, respectively.

"rs,1 = 3's + ~1 - Is,l,

[3]

where Is,l is the interaction energy between the two phases. Journal of Colloid and Interface Science, Vol. 119,No. 2, October 1987

358

STROM, FREDRIKSSON, AND STENIUS requiring the work of cohesion I~,s, and solvated them, gaining the work of solvation between the molecules of the solid and the liquid. This we assume is approximately given by Is,~. Thus, neglecting any entropy contributions and assuming that the surface tension of the liquid is not changed during this initial solvation process, the work involved in forming the solid/liquid interface for a liquid spreading on a slowly dissolving surface is

r--n 9 0 .

E E ~

80

I:D 0 0 j

70-

d

f

"Y's,1= %,1 + I~,s- I~,1

[4]

with %,1 given by Eq. [3], and Is,~ by 2%, i.e., 60-

3/s,1= 3% + 3'1 - 2Is,1.

50T_

5

6

7

' ~ L I'(mJ/m2) ½]

[5]

Gradually, of course, the solid relaxes in the liquid to form a saturated solution. This changes %,~ and Is,l, but our experiments show that such changes are negligible within the time required for our measurements.

FIG. 2. Initial work of adhesion between solid alkanes and dissolving liquids as a function of f~. (A) C20, (11) C2a, (0) C24, The letters denote liquids as given in Table I.

90-

E

It is generally accepted that the swelling of a large number of polymers, especially glassy polymers, takes place in two stages (9). The first stage is diffusion controlled, leading to a quasi-equilibrium surface concentration that is attained very rapidly in elastomers above their glass temperature and somewhat slower at temperatures below due to lower segmental mobility. The second stage is controlled both by diffusion and by polymer relaxation and is much slower (9). It therefore appears reasonable to assume that at the first stages of the dissolution a solvated layer of molecules is rapidly formed on top of the solid surface. This layer then changes so slowly that during the time required for measurements, the system can be considered to be at a quasi-equilibrium. As before, the work of forming the solid/ liquid interface without dissolution is given by Eq. [3]. In addition, however, we have removed a layer of molecules from the solid, Journal of ColloM and Interface Science, Vol. 119, No. 2, October 1987

80-

fe g 0 0

70-

60-

c d

50 j 4

5

,

6

7

FIG. 3. Initial work of adhesion between solid paraffin and dissolvingliquids as a function of f~~%d.(A) paraffinI, (11)paraffinII, (0) paraffin III. The letters denote liquids as givenin Table I.

WETTING OF A DISSOLVING SOLID

359

If~re is negligible a plot of3q(cos O. + 1) versus should~give a straight line with a slope equal to 4~/3'~ and an intercept at ~ = 0 equal 90to - 2 % . Values for 3'~ and % calculated from Figs. E 2-4 in this way are given in Table IV. All points above the break point in the curves were E 80t._l used and it was assumed that 71"e = 0. This seems reasonable since the plot for the same 4" CD liquids on the nondissolving hexatriacontane 0 70does intercept 3q(cos 0 + 1) = 0 at ~ = 0. 0 The correlation coefficient of the linear regression analysis is >0.999 for all lines corresponding to dissolving solids above the break 60. point. The surface energies ofalkanes and paraffins originate from dispersion forces only and, 5o hence, one expects that 3'~ = %. The values in Table IV corroborate this and also show 4 5 6 7 quite good agreement with the values obtained using nondissolving liquids. The experimental FIG. 4. Initial work of adhesion between solid alcohols accuracies of the % given in Table IV is acand dissolvingliquids as a function of ~ . (A) C 1 4 0 / - I , tually higher than those determined with non(11)C16OH,(O) C18OH.Symbolsfor liquids are given in dissolving liquid, since the surface tension of Table I. the liquids used are lower, the measured contact angle is smaller, and its standard deviation Equation [5] is verified by the results pre- is only 1-2 ° . The surface energy of solid paraffins has sented in Figs. 2, 3, and 4. The liquids used been reported in the literature. Phillips and to obtain these data all are expected to interact Riddiford (10) suggest that the value should with the solid surface mainly by dispersion be close to 33 m J / m 2. Padday (11) found that forces. We then may estimate I~,~from the surface tension of liquid paraffin at 54°C, Is,1 = I~l = 2 ~ . d d [6] just above its melting point, is about 32 mJ/ m 2 while our own measurements on two liquid The Young equation, applied to this situation, paraffins at 22°C give the values 30.8 and 31.2 reads m J / m 2. In good agreement with this, the sur"{ts,1 + ~ I C O S O n = "l/s - - 71"e, [7] face energies of the samples with the lowest melting points (eicosane and paraffin I) are where we once again note that 3/~,~, 0n, and 3q 33-34 m J / m 2 (Table IV). The results indicate are nonequilibrium values. The experiments, that increased solidification decreases the value however, show that true equilibrium is at- of 3's. Fowkes (12) has pointed out that while the tained so slowly that meaningful measurements of contact angles at the initial stage of area occupied by a hydrocarbon chain end dissolution are possible and Eq. [7] can be as- group (-CH3) in a hydrocarbon surface is sumed valid at a state of"quasi-equilibrium." 0.19-0.25 n m 2, the area per methylene group (-CH2-) within the chain is only 0.05-0.17 Equations [5]-[7] give n m 2. Although the dispersion force field from "yl(cos 0, + 1) = 4 ~V~ld-y~-- 2 % - 7re. [8] a methyl group is stronger than from a meth-

.1 Ii

tCr.J/m2½1

Journal of Colloid and Interface Science, Vol. 119, No. 2, October i987

360

STROM, FREDRIKSSON, AND STENIUS

ylene group, the net effect of increasing the fraction of methyl groups in a hydrocarbon surface, must be a decrease in the surface energy. The surface o f a perfect hydrocarbon crystal exposes methyl groups only and has a low surface energy (about 21 m J / m 2, for nhexatriaeontane according to Fox and Zisman (3)). A soft paraffin, on the other hand, has a more disordered structure with some hydrocarbon chains oriented in parallel to the surface. These therefore will contain methylene groups. It is thus quite reasonable that the surface energies that we have calculated for solid hydrocarbons increase with decreasing melting point of the hydrocarbon and reach the value for liquid hydrocarbon just below its melting point. The surface energies of the solid alcohols given in Table IV are not comparable with the energies obtained with nondissolving liquids. This is to be expected, since the crystalline alcohols are oriented with their hydrocarbon tails toward the air. If the surface tensions of liquid alcohols are plotted versus the number of carbon atoms in the alcohol a straight line is obtained which can be extrapolated to chain lengths corresponding to solid alcohols. In this way one obtains the surface energies 34, 36, and 38 m J / m 2 for tetra-, hexa-, and octadecanol, respectively, at 25 nc. These values agree well with the surface energies obtained with the dissolving liquids (34.0, 38.4, and 34.3 mJ/m2). As expected, it is also found that 3"~ is slightly lower than 3"s. Some of the straight lines obtained for the dissolving surfaces (Figs. 2-4) show a break in the lines. The deviation occurs for liquids having a surface tension quite close to or below the surface energy of the solids (as determined using nondissolving liquids). These liquids normally spread on nondissolving surfaces. The deviations are most pronounced for the solid fatty alcohols. These surfaces differ from the other in that I~ > 2% due to the orientation of the molecules in the outermost layer. Therefore, several of the liquids have 3"1< 2 ~,~ and still form finite contact angles. For linear alkanes I~s is also slightly larger than 23"s due Journal of Colloid and Interface Science, Vol. 119,No. 2, October1987

to anisotropic dispersion forces (6). A small break in the lines is indeed observed for solid alkanes and paraffins. Thus, the discussion on the behavior of the dissolving system outlined above is restricted to the system for which 3"i > 3"s.

Partly Dissolving Systems Paraffin III in combination with hydrocarbons or halogenated hydrocarbons can be characterized as a partly dissolving system. The liquids attack the surface but do not completely dissolve the solid in the test tube tests. This system also gives a straight line when %(cos 0n + 1) is plotted against ~ (Fig. 3). There is no break in the line and the values obtained for 3"d and 3'~ from the slope and the intercept are much lower than those for dissolving systems (14.1 and 13.0 m J/m2). A surface which dissolves only partially can be thought of as composed of a dissolving (q~)and a nondissolving (1 - q~) fraction. The initial interfacial tension of such a composite system would be 3"s,l= q~(33q+ 3'1 - 2Is,0 + (1 - ~b)(3"s+ 3"1- Is,l)

[9] which is obtained by using Eq. [3] for the nondissolving and Eq. [5] for the dissolving fraction of the surface. Applying the Young equation and Eq. [6] we obtain 3"l(COS0n + 1) = (1 - ~b)2V3"f3"d - 24~3"~.

[ 10]

For a paraffin, % = 3"dand we may therefore calculate 3"~ and 4~ from the slope and the intercept of the plot in Fig. 3. We obtain 2(1 - q~)f%%= 15.0 and -24~3"s = - 2 6 which gives $ = 0.57 and 3"~ = 22.8 m J / m 2. This value is a mean value for 3"~ of all the hydrocarbons in the paraffin and it lies, as expected, between the values for paraffin II and pure hexatriacontane.

Negative Interfacial Tension The work involved in forming the "solvated interface," 3"s,b becomes negative if Is,j > Is,~

WETTING OF A DISSOLVING SOLID + %,~ (see Eq. [4]). Figure 5 shows "y's,1calculated f r o m Eq. [5] as a function o f 3'1 for 3q >~ % and systems for which % = "yd. It is seen that this work is never positive and it b e c o m e s m o r e negative as the surface tension o f the liquid increases or the surface tension o f the solid decreases. CONCLUSIONS T h e contact angles between n o n p o l a r liquids and macromolecular organic solids which are n o t very rapidly dissolved by the liquids can be measured. For the series o f solids investigated, (advancing) contact angles that are stable for several minutes after initial application o f the liquids are observed. The experimental results show that the w o r k involved in forming the solid/liquid interface in such systems can be expressed as

~,'s,~ = 3'~,~ + A%,~,

[1 1 ]

where %,1 is the standard expression for the calculation o f interfacial tension f r o m surface tensions and contact angles as proposed by

361

Fowkes (2) and A%,~ is the difference between the work of cohesion o f the solid and the solid/ liquid w o r k o f adhesion. F o r dissolving systems, with 3'1 > %, 3"sa b e c o m e s negative. The surface energy o f solid alkanes increases with the decreasing melting point o f the alkanes and approaches the value for liquid alkanes at temperatures just below the melting point. APPENDIX: LIST OF SYMBOLS 0n = nonequilibrium contact angle 3'1 -- surface tension o f liquid % =- surface energy o f solid %,~ = solid/liquid interfacial tension ~/'s,~= energy o f forming interface between liquid and solvated solid I~,~--- solid/liquid work o f adhesion I~,s = work of cohesion o f solid fraction o f surface that is dissolved by ~ = liquid U p p e r index a denotes dispersive part o f interfacial energy. ACKNOWLEDGMENTS

YL 20 .

30

[mJ/m2] 40

50 t

This work was supported by the Jacob Wallenberg Research Foundation. Drs. Bengt Kronberg and Lars Odberg are thanked for enlightening discussions. REFERENCES

¢N

E

~-5.

E -/ -10-

-15-

-20-

FIG. 5. Work of forming the solvated interface between a solid surface and a dissolving liquid at the initial stages of dissolution when 3'1= ~/~ >/% = %d.

1. Fowkes, F. M., Ind. Eng. Chem. 56, 40 (1964). 2. Fowkes, F. M., J. Phys. Chem. 66, 382 (1962). 3. Fox, H. W., and Zisman, W. A.,J. ColloidSei. 7, 428 (1952). 4. Girifalco, L. A., and Good, R. J., J. Phys. Chem. 61, 904 (1957). 5. Dann, J. R., J. Colloid Interfaee Sci. 32, 302 (1970). 6. Fowkes, F. M., J. Phys. Chem. 84, 510 (1980). 7. Fox, H. W., and Zisman, W. A., ,L Colloid Sci. 17, 334 (1950). 8. Yiannos, P. N., J. ColloidlnterfaceSei. 17, 334 (1962). 9. Rogers, C. E., in "Physics and Chemistry of the Organic Solid State" (D. Fox, M. M. Labes, and A. Weissberger, Eds.), p. 619. Interscience, New York, 1965. 10. Phillips, M. C., and Riddiford, A. C., Y. Colloid Interface Sci. 22, 149 (1966). 11. Padday, J. F., "Proceedings, Int. Congr. Surface Activity, 2nd, London, 1957," Vol. 3, p. 136. 12. Fowkes, F. M., J. Colloid Interface Sci. 28, 493 (1968). Journal of Colloid and Interface Science, Vol. 119, No. 2, October 1987