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The effect of surface polarity on the adsorption of nonionic surfactants. I. Thermodynamic considerations
The Effect of Surface Polarity on the Adsorption of Nonionic Surfactants I. Thermodynamic Considerations B E N G T K R O N B E R G AND PER STENIUS Institute for Surface Chemistry, Box 5607, S-114 86 Stockholm, Sweden Received March 14, 1984; accepted May 24, 1984 A thermodynamic model is used to predict the adsorption of nonionic surfactants on latexes with different polarity. The model, which is based upon the Flory-Huggins theory of polymer solutions, predicts that the adsorption decreases as the polarity o f the latex increases. It is predicted that adsorption should occur even when it is unfavorable to replace a surface-water contact with a surfacesurfactant contact. This is due to a lower n u m b e r of unfavorable hydrocarbon-water contacts when the surfactant is adsorbed, compared to when it is free in solution. It is also predicted that it is in principle possible to determine the latex polarity or solubility parameter, from adsorption measurements, provided that a similar experiment is carded out on a latex with known polarity, or solubility parameter. © 1984AcademicPress,Inc. INTRODUCTION
In a previous publication (1) a thermodynamic model for the adsorption of nonionic surfactants was presented. The model uses the Flory-Huggins expression to calculate the chemical potential in the bulk solution as well as in the surface phase. In the model both the solute-solvent molecular size difference and solute-solvent interaction are taken into account. Using the model it can be shown that the adsorption free energy can be split up into two contributions according to Aaadsorption
= qm(x],s - X2,s) +
r(x],2 -
X~,2).
[1]
Here the index 1 = solvent (water), 2 = solute (surfactant), and S = surface. The net interaction between components i and j is represented by x i j . It is regarded as an excess free energy of mixing over the combinatorial entropy as expected by the Flory-Huggins equation. The r is the molecular size ratio of solute to solvent, m is the number of segment-surface nearest neighbors divided by the lattice coordination number and q is the
number of solute segments in contact with the surface. The first term in Eq. [1] represents the exchange of surface-solvent contacts for surface-solute contacts. The second term represents the difference in solute-solvent interaction strength in the bulk solution and in the surface phase. In the lattice theory of equal-sized molecules such a difference is due to a lower number of solute-solvent nearest neighbors of an adsorbed solute. The model was applied to experimental results of adsorption of nonionic surfactants (nonylphenol-polyethylene oxide, NP-EO,) on polystyrene latex. It was shown that approximately 20% of the adsorption free energy is due to the exchange of surface-water contacts for surface-surfactant contacts, i.e., the first term in Eq. [1]. The remaining 80% of the adsorption free energy was found to be due to the orientation of the surfactant molecules at the surface, expressed in the second term in Eq. [ 1]. The surfactant molecules orient with their hydrophobic part directed toward the surface and their hydrophilic part directed toward the aqueous solution. This results in the
410 0021-9797/84 $3.00 Copyright© 1984by AcademicPress,Inc. All fightsof reproduction in any form reserved.
Journal of Colloidand InterfaceScience, Vol. 102, No. 2, December1984
ADSORPTION OF NONIONICS, I replacement of unfavorable contacts between water and hydrophobic moieties of the surfactant with hydrophobic moiety-hydrophobic moiety contacts and water-water contacts; i.e., this driving force for adsorption is to a large extent very similar to the driving force for micellization. Although the surface polarity thus only affects a minor fraction o f the total energy of adsorption, it will be very important in explaining differences between adsorption on different latexes. The contribution from the lower probability of water-surfactant hydrocarbon contacts should be fairly independent of the latex. We note that a strong influence of the surface polarity has been observed for the adsorption of the anionic surfactant sodium dodecyl sulfate (SDS) (2). It is the purpose of this article to discuss further the effect of surface polarity on the adsorption of nonionic surfactants. In the accompanying paper (3) the principles discussed here will be applied to the adsorption of NP-EO, on a polymethyl methacrylate latex. In order to compare different surfaces we need a way to measure the "polarity" of a surface. Our approach will be to express it in terms of the free energy involved in the substitution of surface-solvent contacts for surface-surfactant contacts. Other approaches are possible. For example Vijayendran has introduced (2) the "polarity," X v, which is defined as XP = 3`P/3',
411
packing of the surfactant molecules compared with a latex polymer with a lower polarity. We will discuss in this article the reasons for this effect. THE ADSORPTION MODEL In our model (1) the nonionic surfactant is assumed to consist o f r segments, each with a size equal to a solvent (water) molecule (see Fig. 1). The surface and the bulk solution are considered as separate phases in equilibrium with each other. I n t h e surface phase the surfactant is adsorbed with q segments in contact with the surface. Since the latex surface is mainly hydrophobic it is assumed that these q segments belong to the hydrocarbon chain of the surfactant. The standard states are taken as the pure components. Figure 1 illustrates that the thickness of the surface phase in the standard state, which is the pure surfactant phase, is r/q lattice layers on the surface (1). In the model the thickness o f the surface phase is kept constant at all surface concentrations. This is because the number of surfactant segments in contact with the surface, q, is kept constant irrespective o f surface concentration. a
[2]
where 3' and 3'P are, respectively, the surface tension and the polar part of the surface tension. They are related through 3"p + 3"d = % [3] where 3"d is the dispersion part of the surface tension. Experimentally, the influence of the latex polymer polarity on the adsorption is most commonly presented in terms of the crosssectional area occupied per surfactant molecule at close packing on the surface. The c o m m o n interpretation is that a polymer latex with a high polarity gives a less-dense
J
f
J
J
J
J
J
J
b
0-0 0 e~ll 0 0-0 0 ~
~
FIG. 1. In the model the surfactant molecule consists of r segments. (a) The surfacephase in the standard state (pure surfactant) and (b) with solvent. Here r = 12, q = 2, the filled circles represents hydrocarbon and the open circlesrepresentsethyleneoxideor water molecules. cules. Journal of Colloid and Interface Science, Vol. 102, No. 2, December 1984
412
KRONBERG AND STENIUS
In a more realistical model one would assume q to depend on the surface coverage. This, however, would increase the complexity of the model and introduce one more adjustable parameter. In the interpretation o f t h e predictions of the model one should, however, r e m e m b e r such simplifying assumptions.
I1
_//5,
lo,
2o,
soloo, ,
1.0
X 0.5
The Basic Equation By application of the Flory-Huggins theory to the bulk and surface phases, in equilibrium with one another, the following relation between the volume fraction, ~bz, of the solute in solution and the volume fraction, ¢~, in the surface phase is obtained (1) ln(q~2) = In - (1 -
~9 r
+ rxS(1 - 2~b~)
qa ° -
r x --£-f
(3',
-
3'2),
[4]
where a ° is the surface occupied by one segment or a solvent molecule. Taking this as the cross-sectional area of water, a value of 9.66 A2/molecule was assigned to a ° (1). The X parameter in Eq. [4] represents the average interaction of a surfactant molecule with the water, in the bulk solution phase. It is composed of water-ethylene oxide interaction, XW,EO, water-hydrocarbon interaction, XW,HC, and hydrocarbon-ethylene oxide interaction, XHC,EO. The relation is X = WEOXW,EO + (1 - - WEO)XW,HC
Vw (1 VHc
- --
-
(.0EO)60EOXHC, EO,
[5]
where WEO is the weight fraction of the ethylene oxide chain in the surfactant. Vw and Vnc are the molar volumes of water and the hydrocarbon part of the surfactant, respectively. Figure 2 shows how X depends on the HLB (Hydrophilic Lipophilic Balance) of the surfactant, where HLB is defined as HLB = 20COEO (4). The parameter Xs represents the average surfactant-water interaction in the surface Journal of Colloid and Interface Science, Vol. 102, No. 2, December 1984
O
~[
I
I
I
I
|
10
12
14
16
18
20
HLB FIG. 2. The relation between the X parameter and the HLB value according to Eq. [5] (XW.EO = 0.4, XW.HC = 2.0, and XHC,Eo(Vw/VHc)= 0.4). phase. It differs from X for the following reason. In the very dilute equilibrium solution there are almost exclusively surfactant-water contacts. In the surface phase, however, the surfactant is present at a very high concentration and is oriented with the hydrophobic part toward the surface and the hydrophilic part toward the water. This implies that there is a lower probability for unfavorable hydrocarbon-water contacts in the surface phase compared to the bulk solution. The FloryHuggins treatment takes no account of such n o n r a n d o m mixing effects. Thus, experimentally one will obtain a weaker surfactantwater interaction in the surface phase compared to the solution phase, i.e., x s < x. If one assumes that the n u m b e r of hydrocarb o n - w a t e r contacts is reduced to a fraction ~, of the n u m b e r of contacts in the bulk solution the expression for Xs will be (1) Xs = WEOXW,EO+ )~(1 -- W~o)Xw,nc
Vw
WEO)WEOXHC,EO.
[6]
In Eq. [4] '~1 and 3"2 are the interfacial tensions, or interracial free energies, between the surface and the pure solvent and the pure solute, respectively. The exchange of a surface-water to a surface-hydrocarbon contact is accounted for in the quantity
ADSORPTION
O F NONIONICS,
a° "
~-~ t3/1 - 3/2) --= AE.
[71
Hence it is in this quantity the polarity of the latex surface enters. This will be explored further below. QUANTIFYING
AE
AE can be estimated in several ways. One way is to assume that 72 is equal to the surface free energy of a surface-hydrocarbon contact, where the hydrocarbon has the same chemical composition as that of the hydrophobic moiety of the surfactant. Then 3/1 and "Y2can be estimated by measuring the contact angle of water and the hydrocarbon on the polymer constituting the latex. The relation between the contact angle, 0, and the interfacial tension, 3'1, is 'Y1 = ")IS -- 7 ] ir COS(01) -- 71",
a fraction m of its contact points with the surface, i.e., m is the number of segmentsurface nearest neighbors divided by the lattice coordination number. In a hexagonal lattice m = 1/4. The Xi,s is the interaction parameter of component i with the latex polymer. The X~,s is normalized to the size of a water molecule (1) and hence Vw X~,s = X2,s VHC [12] The interaction parameter, Xi, s, can, in principle be obtained from GLC measurements, although at higher temperatures. However, even without such measurements, an estimate of different contributions to the interaction parameter can be obtained from the solubility parameter concept. The x parameter is related to the solubility parameter, 6, through
[8]
×i,j where 3/]i~ and 3/s are the surface tensions of water and the latex polymer, respectively. Ignoring the difference in surface pressure terms, a-, on this low-energy surface, we have AE kT a0
-
(3/, -
3/~)
____~~/~ir COS(02 ) __ 3/~Jr COS(01).
[9]
Note that Eqs. [8] and [9] can only be used if 0 > 0, i.e., if the liquids do not spread completely on the surface. However, most hydrocarbons will spread on polymer surfaces which necessitates alternative ways to estimate AE. One way to estimate AE is to utilize the interaction parameters between the surface and water or hydrocarbon. Using the lattice model it can be shown that a°,yz kT
- taxi's'
[10]
which through the identity [7] gives
mVl
- -
(61
-
Vl 6 ~__~( i - 6j)2 +
6S)2 +
[I I]
Here it is assumed that a segment, which is in direct contact with the surface, experiences
=
E )(.i,j"
[131
Here, 6 represents the total solubility parameter. The x~Ej parameter is the excess interaction over that which is taken into account through the solubility parameters. In nonaqueous, or nonhydrogen-bonding, polymersolvent systems x ~ j is associated with negative changes in the free volume, upon mixing polymer and solvent, resulting in a positive contribution to X~j. In aqueous hydrocarbonwater systems where structuring of the water occurs in the vicinity of a hydrophobic solute, or for a hydrophobic surface, in contact with water, X~E,j is believed to be an important contribution to x~,j. For a solvent in contact with a solid surface it is possible to estimate X~j from a contact angle measurement, surface tensions, and solubility parameters. Ignoring the surface pressure term in Eq. [8], Eqs. [8], [10], and [13], can be combined to give RT
AE = m(xl,s -- X~,s)-
413
I
E mx~,s
N.a ° -
RT
[%
-
3 , ~ i~ c o s ( 0 , ) ] ,
[141
where N, is the Avogadro number, Journal of Colloid and Interface Science, Vol, 102, No.
2, December 1984
414
KRONBERG AND STENIUS
It has been reported that the contact angle for water on polystyrene is 80 ° (1). For % we use the critical surface tension of polystyrene, 32 m J / m z (5), as was done in Ref. (1). A value of 42 m J / m 2 has been reported for 3's (6). Using 3'c and 3's gives A E = 0.4 and 0.6, respectively. This difference will not alter the qualitative interpretation in Ref. (1) or in this paper. We will find below that it is the difference in A E for two latexes that is of interest. Hence, the choice of 3'c or 3q is not important. For this reason we have chosen to use 3'c in order to be able to use the parameter values obtained in Ref. (1). The solubility parameters of polystyrene and water are 18.6 and 47.9 MPa 1/2, respectively (7). Inserting these values into Eq. [14] we find that XI,S E = --4.4 which is an extremely large negative value. In comparison XE for nonpolar polymer-solvent systems is usually around 0.3-0.5 (7), or, if reduced to the size of a water molecule, x 'E ~ 0.1. Inserting Eq. [13] into Eq. [11] we find mV
/XE = ~
(6~ - 62)(61 + 62 - 263 + m ( x ~,S - x2,s). ,E
[15]
Since 61 >> 62 and X~,s E is large and negative while X2,s ,z is small and positive, Eq. [15] shows that the sign of A E will largely depend on whether or not the solubility parameter of the surface 6s, is larger than the mean of 6t and 62, i.e. (61 .ql- 62)/2. If A E ~< 0 it is not energetically favorable to substitute a surfacewater contact for a surface-hydrocarbon contact. Intuitively one would expect this to be the case for very polar surfaces, i.e., surfaces made up of polymers with a large 6s, as predicted by Eq. [15]. A more polar surface would probably also make the value of (X~,s tE X2,s) less negative, but hardly positive. Note than even though AE is zero, or even negative, adsorption may still be predicted to be favorable. This phenomenon is due to the overwhelmingly large contribution to the adsorption free energy arising from the fewer surfactant hydrocarbon-water contacts in the surface phase compared to the solution phase. -
Journal of Colloid and Interface Science, Vol. 102, No. 2, December 1984
INFLUENCE OF POLYMER POLARITY ON ADSORPTION
To illustrate the effects discussed above, calculations have been performed for the adsorption of a nonionic surfactant, of type nonylphenol-polyethylene oxide with 20 ethylene oxide units in the chain (NP-EO2o), on polymers with different polarity. The adsorption is calculated from Eq. [4], using A E (Eqs. [11] and [15]) as the only variable parameter. It is assumed that X = 0.66 (1) and ~ = 0.5, i.e., half of the hydrocarbonwater contacts are lost upon adsorption and q = 4, i.e., the surfactant adsorbs with 4 hydrocarbon segments in direct contact with the surface. (Justification for this choice is given in Ref. (1).) Further, the following values are taken as constants in Eq. [15]: 61 = 6w = 47.9 MPa 1/2, 6 2 = 6HC ~- 16.0 MPai/2, XE,S = Xw, E s = - 4 . 4 , and X2.s cE ¢E = Xiac,s = 0.1. Figure 3 shows adsorption isotherms for A E = 0.8, 0.4, 0.0, and - 0 . 4 , corresponding to the following solubility parameters of the polymer surface, 6s: 15.3, 18.7, 22.2, and 25.6 MPa 1/2. The ordinate in Fig. 3 is the adsorbed amount, 17 (in ~tmole/ m2), which is related to 4~ through, qP = 17.20 4~ (/~mole/m2). The constant is obtained from the close packing of water molecules at the surface. Figure 3 shows that in all four cases the adsorbed amount reaches a well-defined plateau value. The concentration range within which this plateau remains constant corresponds to those concentration ranges for which we have determined experimental isotherms (3, 8). Experimentally no indications of increasing adsorption beyond a plateau value have been observed. Note that this plateau value corresponds to a constant surface phase composition (i.e., constant surfactant/water ratio) and not to a close-packed surface phase containing only surfactant. (With q = 4, such a pure surfactant layer would correspond to an adsorption of 4.3 umole surfactant/m2). Thus, our model essentially predicts that a Langmuir-type iso-
ADSORPTION OF NONIONICS, I
415
2
0
~
lo
15.3 18.7
b=15.3
22.2
E=,
1/0
18.7
:25,6
s 2
4
6
8
10
x 2 . 10 6
FIG. 3. Calculated adsorption isotherms for NP-EO20 on four latexes with different polarity, as indicated by the solubilityparameter, fis-
I
0
0.5
1.0
1/x2 • 10 4
therm will be observed since a surface phase of (almost) constant composition is formed within a n - - c o m p a r e d to the rising portion of the isotherm--extended range of concentration. As seen in Fig. 3 the plateau values relate to the surface polarity, i.e., the apparent plateau of the adsorption isotherm decreases as the surface polarity, 6s, increases. Note that for b E = - 0 . 4 , i.e., 6s = 25.6 MPa ~/2, AE contributes unfavorably to the adsorption. The surfactant, however, will still adsorb because of the large positive contribution due to the loss of hydrocarbon-water contacts upon adsorption. Note also that the curve for AE = - 0 . 4 is weakly s-shaped, indicating the low tendency toward adsorption at low concentrations. Langmuir plots, i.e., plots of (1/F) versus (1 IX2), give almost straight lines, as is shown in Fig. 4. As was discussed in detail in Ref. (1), the reason for obtaining straight lines is because of a compensation of deviations due to (i) interaction of the surfactant with the water at the surface and (ii) difference in molecular size between the surfactant and the water. The intercept of the lines in Fig. 4 gives the apparent cross-sectional surface area, A2, of the surfactant. Figure 5 shows that A 2 is an increasing function of the surface polarity, ~s. In the following paper, we show that this prediction is confirmed in the adsorption of nonionic surfactants on a poly(methyl methacrylate) latex.
FIG. 4. "Langmuir plots" of the adsorption isotherms shown in Fig. 3.
Normally a dependency of A2 on the polymer surface polarity, 6s, is interpreted in terms of the " m o d e of adsorption" of the surfactant (2), i.e., it is said that at high ~s the surfactant lies down on the surface while at low 6s it is standing up perpendicular to the surface. In the model calculations resulting in Fig. 5, however, we have kept q constant (=4) for the adsorption on all four polymer surfaces, i.e., the surfactant adsorbs with 4 hydrocarbon segments in direct contact with the surface on each of the four surfaces. (aO/kt)(Y1-y2) -0.4
0
'3° I '
,
140
~)
0.4
0.8
120 110
~,
100 9O 8O I 25
I 20
I 15
solubility parameter of the latex, bs/(MPa l&)
FIG. 5. The molecularcross-sectionalsurface area, A2, at close packing as a function of the surface polarity, obtained from the calculated adsorption isotherms in Fig. 3. Journal of Colloid and Interface Science, Vol. t02, No. 2, December 1984
416
KRONBERG AND STENIUS
One would therefore, at first thought, expect A2 to be independent on the surface polarity. The dependency shown in Fig. 5 is therefore not originating from the adsorption mode, or q, of the surfactant butiS rather a reflection of the fact that the composition of the surface phase depends on the relative adsorption strengths of the water and the hydrocarbon part of the surfactant. Thus, there is a larger water content in the surface layer when the relative adsorption strength of the hydrocarbon part is weakened. DETERMINATION OF LATEX POLARITY FROM ADSORPTION Equation [4] can be rearranged to ln[i [ ~ •
-
]-
q ( a E A -- AEB)
ln(~b2)
~)U
= q A E + r x - rxS[l - 24~].
[16]
For a given value of q, plotting the left-hand side of Eq. [16] versus [1 - 2~b~] gives a straight line with slope = r x ~ and intercept = q A E + r x . Such a plot is shown in Fig. 6. By determination of the adsorption of a nonionic surfactant on a polymer surface, e.g., on a latex, with known AE it is hence possible to obtain both the X a n d x ~ parameters for a given value of q.
80 0
7
@
60
bs=15.3
c
, .2o
-1.0
It will then be possible to determine the polarity of an unknown polymer surface by measuring the adsorption of the same surfactant on that surface. The only necessary assumption is that the surfactant adsorbs in the same way on the known and unknown polymer surfaces, i.e., q is the same in the two cases. Consequently the new adsorption data also give a straight line when plotted as in Fig. 6. The line should have the same slope as the line for adsorption on the known surface, but it should be shifted parallel to the known line giving a different intercept. The shift is caused by a difference in AE for the two adsorption isotherms. From Eqs. [ 15] and [ 16] it is seen that this shift is given by
-0.5
J
I
0
0.5
1.0
FlG. 6. Plots, according to Eq. [16], for the calculated adsorption of NP-EO2o on two latexes with /~s = 15.3 and 22.2 MPa ~/2, respectively. Journal of Colloid and Interface Science. Vol. 102, No. 2, December 1984
q m VI = 2 ~(61--
r2)(rB-- rA)
[17]
for latexes A and B, assuming that the xEs parameters are the same for the two latex polymers. It is recommended that in determining the polarity of a latex surface by adsorption a surfactant with a short ethylene oxide (EO) chain should be used for the following reasons. First, a short EO chain nonionic surfactant packs densely on the surface and hence it is possible to obtain experimental points giving small or even negative values of (1 ~ 2~b~) as shown in Fig. 7. This gives an accurate determination of the intercept. A long EO chain nonionic surfactant packs less densely and hence the experimental points are found at the right-hand corner in Fig. 7, whence a poor accuracy in the intercept is obtained. Second, there might be a possibility for the EO chain to adsorb with the EO chain in direct contact with the polymer surface. This possibility is obviously diminished when short EO chains are used. We suggest that adsorption measurements could perhaps be a method to evaluate the surface composition of a copolymer latex. It
417
ADSORPTION OF NONIONICS, I 8O
~
0
t
1
6O
i
so
NP-EOlo
) i 0
i
-0.1
i
0
i
0.2
=
i
0.4
i
i
0.6
I
I
0.8
i
1.0
(1-2 ~))
FIG. 7. Plots, according to Eq. [16] for the adsorption of NP-EOto and NP-EOso on polystyrene latex (q = 4). (Experimental data obtained from Ref. (8).)
would require an extension of the analysis, presented in this paper, to include the effect of the two different types of surfaces on the mean adsorption of the suffactant. In summary our treatment indicates that the polarity of a polymer latex surface is not dominant in determining whether a nonionic surfactant will be adsorbed on a latex, but it does play an important role in determining the maximum adsorption of the surfactant. The adsorption is predicted to decrease as
the polarity increases. We have also shown that, using the same surfactant on different latexes it is, in principle, possible to obtain a quantitative measure of the surface polarity, ~s, of a polymer latex from adsorption measurements. For such a determination it is required that the adsorption of a given surfactant has previously been measured on a latex with known polarity. The experimental verification of this treatment will be described in the subsequent article (3). REFERENCES 1. Kronberg, B., J. Colloid Interface Sci. 96, 55 (1983). 2. Vijayendran, B. R., J. Appl. Polym. Sci. 23, 733 (1979) and references therein; Piirma, I., and Chen, S-R., J. Colloid Interface Sci. 74, 90 (1980). 3. Kronberg, B., Stenius, P., and Igeborn, G., J. Colloid Interface Sci., 102, 418 (1984). 4. Griffin, W. C., J. Soc. Cosmet. Chem. 5, 249 (1954). 5. Shafin, E. G., in "Polymer Handbook" (J. Brandrup and E. lmmergut, Eds.), pp. 3-221. Wiley, New York, 1975. 6. Owens, D. K., and Wendt, R, C., J. Appl. Polym. Sci. 13, 1741 (1969). 7. Barton, A. F. M., "Handbook of Solubility Parameters and other Cohesion Parameters," Chaps. 7 and 13. CRC Press, Boca Raton, Fla., 1983. 8. Kronberg, B., K~ill, L., and Stenius, P., J. Dispersion Sci. Technol. 2, 215 (1981).
Journal of Colloid and Interface Science, Vol. t02, No. 2, December1984
In a previous publication (1) a thermodynamic model for the adsorption of nonionic surfactants was presented. The model uses the Flory-Huggins expression to calculate the chemical potential in the bulk solution as well as in the surface phase. In the model both the solute-solvent molecular size difference and solute-solvent interaction are taken into account. Using the model it can be shown that the adsorption free energy can be split up into two contributions according to Aaadsorption
= qm(x],s - X2,s) +
r(x],2 -
X~,2).
[1]
Here the index 1 = solvent (water), 2 = solute (surfactant), and S = surface. The net interaction between components i and j is represented by x i j . It is regarded as an excess free energy of mixing over the combinatorial entropy as expected by the Flory-Huggins equation. The r is the molecular size ratio of solute to solvent, m is the number of segment-surface nearest neighbors divided by the lattice coordination number and q is the
number of solute segments in contact with the surface. The first term in Eq. [1] represents the exchange of surface-solvent contacts for surface-solute contacts. The second term represents the difference in solute-solvent interaction strength in the bulk solution and in the surface phase. In the lattice theory of equal-sized molecules such a difference is due to a lower number of solute-solvent nearest neighbors of an adsorbed solute. The model was applied to experimental results of adsorption of nonionic surfactants (nonylphenol-polyethylene oxide, NP-EO,) on polystyrene latex. It was shown that approximately 20% of the adsorption free energy is due to the exchange of surface-water contacts for surface-surfactant contacts, i.e., the first term in Eq. [1]. The remaining 80% of the adsorption free energy was found to be due to the orientation of the surfactant molecules at the surface, expressed in the second term in Eq. [ 1]. The surfactant molecules orient with their hydrophobic part directed toward the surface and their hydrophilic part directed toward the aqueous solution. This results in the
410 0021-9797/84 $3.00 Copyright© 1984by AcademicPress,Inc. All fightsof reproduction in any form reserved.
Journal of Colloidand InterfaceScience, Vol. 102, No. 2, December1984
ADSORPTION OF NONIONICS, I replacement of unfavorable contacts between water and hydrophobic moieties of the surfactant with hydrophobic moiety-hydrophobic moiety contacts and water-water contacts; i.e., this driving force for adsorption is to a large extent very similar to the driving force for micellization. Although the surface polarity thus only affects a minor fraction o f the total energy of adsorption, it will be very important in explaining differences between adsorption on different latexes. The contribution from the lower probability of water-surfactant hydrocarbon contacts should be fairly independent of the latex. We note that a strong influence of the surface polarity has been observed for the adsorption of the anionic surfactant sodium dodecyl sulfate (SDS) (2). It is the purpose of this article to discuss further the effect of surface polarity on the adsorption of nonionic surfactants. In the accompanying paper (3) the principles discussed here will be applied to the adsorption of NP-EO, on a polymethyl methacrylate latex. In order to compare different surfaces we need a way to measure the "polarity" of a surface. Our approach will be to express it in terms of the free energy involved in the substitution of surface-solvent contacts for surface-surfactant contacts. Other approaches are possible. For example Vijayendran has introduced (2) the "polarity," X v, which is defined as XP = 3`P/3',
411
packing of the surfactant molecules compared with a latex polymer with a lower polarity. We will discuss in this article the reasons for this effect. THE ADSORPTION MODEL In our model (1) the nonionic surfactant is assumed to consist o f r segments, each with a size equal to a solvent (water) molecule (see Fig. 1). The surface and the bulk solution are considered as separate phases in equilibrium with each other. I n t h e surface phase the surfactant is adsorbed with q segments in contact with the surface. Since the latex surface is mainly hydrophobic it is assumed that these q segments belong to the hydrocarbon chain of the surfactant. The standard states are taken as the pure components. Figure 1 illustrates that the thickness of the surface phase in the standard state, which is the pure surfactant phase, is r/q lattice layers on the surface (1). In the model the thickness o f the surface phase is kept constant at all surface concentrations. This is because the number of surfactant segments in contact with the surface, q, is kept constant irrespective o f surface concentration. a
[2]
where 3' and 3'P are, respectively, the surface tension and the polar part of the surface tension. They are related through 3"p + 3"d = % [3] where 3"d is the dispersion part of the surface tension. Experimentally, the influence of the latex polymer polarity on the adsorption is most commonly presented in terms of the crosssectional area occupied per surfactant molecule at close packing on the surface. The c o m m o n interpretation is that a polymer latex with a high polarity gives a less-dense
J
f
J
J
J
J
J
J
b
0-0 0 e~ll 0 0-0 0 ~
~
FIG. 1. In the model the surfactant molecule consists of r segments. (a) The surfacephase in the standard state (pure surfactant) and (b) with solvent. Here r = 12, q = 2, the filled circles represents hydrocarbon and the open circlesrepresentsethyleneoxideor water molecules. cules. Journal of Colloid and Interface Science, Vol. 102, No. 2, December 1984
412
KRONBERG AND STENIUS
In a more realistical model one would assume q to depend on the surface coverage. This, however, would increase the complexity of the model and introduce one more adjustable parameter. In the interpretation o f t h e predictions of the model one should, however, r e m e m b e r such simplifying assumptions.
I1
_//5,
lo,
2o,
soloo, ,
1.0
X 0.5
The Basic Equation By application of the Flory-Huggins theory to the bulk and surface phases, in equilibrium with one another, the following relation between the volume fraction, ~bz, of the solute in solution and the volume fraction, ¢~, in the surface phase is obtained (1) ln(q~2) = In - (1 -
~9 r
+ rxS(1 - 2~b~)
qa ° -
r x --£-f
(3',
-
3'2),
[4]
where a ° is the surface occupied by one segment or a solvent molecule. Taking this as the cross-sectional area of water, a value of 9.66 A2/molecule was assigned to a ° (1). The X parameter in Eq. [4] represents the average interaction of a surfactant molecule with the water, in the bulk solution phase. It is composed of water-ethylene oxide interaction, XW,EO, water-hydrocarbon interaction, XW,HC, and hydrocarbon-ethylene oxide interaction, XHC,EO. The relation is X = WEOXW,EO + (1 - - WEO)XW,HC
Vw (1 VHc
- --
-
(.0EO)60EOXHC, EO,
[5]
where WEO is the weight fraction of the ethylene oxide chain in the surfactant. Vw and Vnc are the molar volumes of water and the hydrocarbon part of the surfactant, respectively. Figure 2 shows how X depends on the HLB (Hydrophilic Lipophilic Balance) of the surfactant, where HLB is defined as HLB = 20COEO (4). The parameter Xs represents the average surfactant-water interaction in the surface Journal of Colloid and Interface Science, Vol. 102, No. 2, December 1984
O
~[
I
I
I
I
|
10
12
14
16
18
20
HLB FIG. 2. The relation between the X parameter and the HLB value according to Eq. [5] (XW.EO = 0.4, XW.HC = 2.0, and XHC,Eo(Vw/VHc)= 0.4). phase. It differs from X for the following reason. In the very dilute equilibrium solution there are almost exclusively surfactant-water contacts. In the surface phase, however, the surfactant is present at a very high concentration and is oriented with the hydrophobic part toward the surface and the hydrophilic part toward the water. This implies that there is a lower probability for unfavorable hydrocarbon-water contacts in the surface phase compared to the bulk solution. The FloryHuggins treatment takes no account of such n o n r a n d o m mixing effects. Thus, experimentally one will obtain a weaker surfactantwater interaction in the surface phase compared to the solution phase, i.e., x s < x. If one assumes that the n u m b e r of hydrocarb o n - w a t e r contacts is reduced to a fraction ~, of the n u m b e r of contacts in the bulk solution the expression for Xs will be (1) Xs = WEOXW,EO+ )~(1 -- W~o)Xw,nc
Vw
WEO)WEOXHC,EO.
[6]
In Eq. [4] '~1 and 3"2 are the interfacial tensions, or interracial free energies, between the surface and the pure solvent and the pure solute, respectively. The exchange of a surface-water to a surface-hydrocarbon contact is accounted for in the quantity
ADSORPTION
O F NONIONICS,
a° "
~-~ t3/1 - 3/2) --= AE.
[71
Hence it is in this quantity the polarity of the latex surface enters. This will be explored further below. QUANTIFYING
AE
AE can be estimated in several ways. One way is to assume that 72 is equal to the surface free energy of a surface-hydrocarbon contact, where the hydrocarbon has the same chemical composition as that of the hydrophobic moiety of the surfactant. Then 3/1 and "Y2can be estimated by measuring the contact angle of water and the hydrocarbon on the polymer constituting the latex. The relation between the contact angle, 0, and the interfacial tension, 3'1, is 'Y1 = ")IS -- 7 ] ir COS(01) -- 71",
a fraction m of its contact points with the surface, i.e., m is the number of segmentsurface nearest neighbors divided by the lattice coordination number. In a hexagonal lattice m = 1/4. The Xi,s is the interaction parameter of component i with the latex polymer. The X~,s is normalized to the size of a water molecule (1) and hence Vw X~,s = X2,s VHC [12] The interaction parameter, Xi, s, can, in principle be obtained from GLC measurements, although at higher temperatures. However, even without such measurements, an estimate of different contributions to the interaction parameter can be obtained from the solubility parameter concept. The x parameter is related to the solubility parameter, 6, through
[8]
×i,j where 3/]i~ and 3/s are the surface tensions of water and the latex polymer, respectively. Ignoring the difference in surface pressure terms, a-, on this low-energy surface, we have AE kT a0
-
(3/, -
3/~)
____~~/~ir COS(02 ) __ 3/~Jr COS(01).
[9]
Note that Eqs. [8] and [9] can only be used if 0 > 0, i.e., if the liquids do not spread completely on the surface. However, most hydrocarbons will spread on polymer surfaces which necessitates alternative ways to estimate AE. One way to estimate AE is to utilize the interaction parameters between the surface and water or hydrocarbon. Using the lattice model it can be shown that a°,yz kT
- taxi's'
[10]
which through the identity [7] gives
mVl
- -
(61
-
Vl 6 ~__~( i - 6j)2 +
6S)2 +
[I I]
Here it is assumed that a segment, which is in direct contact with the surface, experiences
=
E )(.i,j"
[131
Here, 6 represents the total solubility parameter. The x~Ej parameter is the excess interaction over that which is taken into account through the solubility parameters. In nonaqueous, or nonhydrogen-bonding, polymersolvent systems x ~ j is associated with negative changes in the free volume, upon mixing polymer and solvent, resulting in a positive contribution to X~j. In aqueous hydrocarbonwater systems where structuring of the water occurs in the vicinity of a hydrophobic solute, or for a hydrophobic surface, in contact with water, X~E,j is believed to be an important contribution to x~,j. For a solvent in contact with a solid surface it is possible to estimate X~j from a contact angle measurement, surface tensions, and solubility parameters. Ignoring the surface pressure term in Eq. [8], Eqs. [8], [10], and [13], can be combined to give RT
AE = m(xl,s -- X~,s)-
413
I
E mx~,s
N.a ° -
RT
[%
-
3 , ~ i~ c o s ( 0 , ) ] ,
[141
where N, is the Avogadro number, Journal of Colloid and Interface Science, Vol, 102, No.
2, December 1984
414
KRONBERG AND STENIUS
It has been reported that the contact angle for water on polystyrene is 80 ° (1). For % we use the critical surface tension of polystyrene, 32 m J / m z (5), as was done in Ref. (1). A value of 42 m J / m 2 has been reported for 3's (6). Using 3'c and 3's gives A E = 0.4 and 0.6, respectively. This difference will not alter the qualitative interpretation in Ref. (1) or in this paper. We will find below that it is the difference in A E for two latexes that is of interest. Hence, the choice of 3'c or 3q is not important. For this reason we have chosen to use 3'c in order to be able to use the parameter values obtained in Ref. (1). The solubility parameters of polystyrene and water are 18.6 and 47.9 MPa 1/2, respectively (7). Inserting these values into Eq. [14] we find that XI,S E = --4.4 which is an extremely large negative value. In comparison XE for nonpolar polymer-solvent systems is usually around 0.3-0.5 (7), or, if reduced to the size of a water molecule, x 'E ~ 0.1. Inserting Eq. [13] into Eq. [11] we find mV
/XE = ~
(6~ - 62)(61 + 62 - 263 + m ( x ~,S - x2,s). ,E
[15]
Since 61 >> 62 and X~,s E is large and negative while X2,s ,z is small and positive, Eq. [15] shows that the sign of A E will largely depend on whether or not the solubility parameter of the surface 6s, is larger than the mean of 6t and 62, i.e. (61 .ql- 62)/2. If A E ~< 0 it is not energetically favorable to substitute a surfacewater contact for a surface-hydrocarbon contact. Intuitively one would expect this to be the case for very polar surfaces, i.e., surfaces made up of polymers with a large 6s, as predicted by Eq. [15]. A more polar surface would probably also make the value of (X~,s tE X2,s) less negative, but hardly positive. Note than even though AE is zero, or even negative, adsorption may still be predicted to be favorable. This phenomenon is due to the overwhelmingly large contribution to the adsorption free energy arising from the fewer surfactant hydrocarbon-water contacts in the surface phase compared to the solution phase. -
Journal of Colloid and Interface Science, Vol. 102, No. 2, December 1984
INFLUENCE OF POLYMER POLARITY ON ADSORPTION
To illustrate the effects discussed above, calculations have been performed for the adsorption of a nonionic surfactant, of type nonylphenol-polyethylene oxide with 20 ethylene oxide units in the chain (NP-EO2o), on polymers with different polarity. The adsorption is calculated from Eq. [4], using A E (Eqs. [11] and [15]) as the only variable parameter. It is assumed that X = 0.66 (1) and ~ = 0.5, i.e., half of the hydrocarbonwater contacts are lost upon adsorption and q = 4, i.e., the surfactant adsorbs with 4 hydrocarbon segments in direct contact with the surface. (Justification for this choice is given in Ref. (1).) Further, the following values are taken as constants in Eq. [15]: 61 = 6w = 47.9 MPa 1/2, 6 2 = 6HC ~- 16.0 MPai/2, XE,S = Xw, E s = - 4 . 4 , and X2.s cE ¢E = Xiac,s = 0.1. Figure 3 shows adsorption isotherms for A E = 0.8, 0.4, 0.0, and - 0 . 4 , corresponding to the following solubility parameters of the polymer surface, 6s: 15.3, 18.7, 22.2, and 25.6 MPa 1/2. The ordinate in Fig. 3 is the adsorbed amount, 17 (in ~tmole/ m2), which is related to 4~ through, qP = 17.20 4~ (/~mole/m2). The constant is obtained from the close packing of water molecules at the surface. Figure 3 shows that in all four cases the adsorbed amount reaches a well-defined plateau value. The concentration range within which this plateau remains constant corresponds to those concentration ranges for which we have determined experimental isotherms (3, 8). Experimentally no indications of increasing adsorption beyond a plateau value have been observed. Note that this plateau value corresponds to a constant surface phase composition (i.e., constant surfactant/water ratio) and not to a close-packed surface phase containing only surfactant. (With q = 4, such a pure surfactant layer would correspond to an adsorption of 4.3 umole surfactant/m2). Thus, our model essentially predicts that a Langmuir-type iso-
ADSORPTION OF NONIONICS, I
415
2
0
~
lo
15.3 18.7
b=15.3
22.2
E=,
1/0
18.7
:25,6
s 2
4
6
8
10
x 2 . 10 6
FIG. 3. Calculated adsorption isotherms for NP-EO20 on four latexes with different polarity, as indicated by the solubilityparameter, fis-
I
0
0.5
1.0
1/x2 • 10 4
therm will be observed since a surface phase of (almost) constant composition is formed within a n - - c o m p a r e d to the rising portion of the isotherm--extended range of concentration. As seen in Fig. 3 the plateau values relate to the surface polarity, i.e., the apparent plateau of the adsorption isotherm decreases as the surface polarity, 6s, increases. Note that for b E = - 0 . 4 , i.e., 6s = 25.6 MPa ~/2, AE contributes unfavorably to the adsorption. The surfactant, however, will still adsorb because of the large positive contribution due to the loss of hydrocarbon-water contacts upon adsorption. Note also that the curve for AE = - 0 . 4 is weakly s-shaped, indicating the low tendency toward adsorption at low concentrations. Langmuir plots, i.e., plots of (1/F) versus (1 IX2), give almost straight lines, as is shown in Fig. 4. As was discussed in detail in Ref. (1), the reason for obtaining straight lines is because of a compensation of deviations due to (i) interaction of the surfactant with the water at the surface and (ii) difference in molecular size between the surfactant and the water. The intercept of the lines in Fig. 4 gives the apparent cross-sectional surface area, A2, of the surfactant. Figure 5 shows that A 2 is an increasing function of the surface polarity, ~s. In the following paper, we show that this prediction is confirmed in the adsorption of nonionic surfactants on a poly(methyl methacrylate) latex.
FIG. 4. "Langmuir plots" of the adsorption isotherms shown in Fig. 3.
Normally a dependency of A2 on the polymer surface polarity, 6s, is interpreted in terms of the " m o d e of adsorption" of the surfactant (2), i.e., it is said that at high ~s the surfactant lies down on the surface while at low 6s it is standing up perpendicular to the surface. In the model calculations resulting in Fig. 5, however, we have kept q constant (=4) for the adsorption on all four polymer surfaces, i.e., the surfactant adsorbs with 4 hydrocarbon segments in direct contact with the surface on each of the four surfaces. (aO/kt)(Y1-y2) -0.4
0
'3° I '
,
140
~)
0.4
0.8
120 110
~,
100 9O 8O I 25
I 20
I 15
solubility parameter of the latex, bs/(MPa l&)
FIG. 5. The molecularcross-sectionalsurface area, A2, at close packing as a function of the surface polarity, obtained from the calculated adsorption isotherms in Fig. 3. Journal of Colloid and Interface Science, Vol. t02, No. 2, December 1984
416
KRONBERG AND STENIUS
One would therefore, at first thought, expect A2 to be independent on the surface polarity. The dependency shown in Fig. 5 is therefore not originating from the adsorption mode, or q, of the surfactant butiS rather a reflection of the fact that the composition of the surface phase depends on the relative adsorption strengths of the water and the hydrocarbon part of the surfactant. Thus, there is a larger water content in the surface layer when the relative adsorption strength of the hydrocarbon part is weakened. DETERMINATION OF LATEX POLARITY FROM ADSORPTION Equation [4] can be rearranged to ln[i [ ~ •
-
]-
q ( a E A -- AEB)
ln(~b2)
~)U
= q A E + r x - rxS[l - 24~].
[16]
For a given value of q, plotting the left-hand side of Eq. [16] versus [1 - 2~b~] gives a straight line with slope = r x ~ and intercept = q A E + r x . Such a plot is shown in Fig. 6. By determination of the adsorption of a nonionic surfactant on a polymer surface, e.g., on a latex, with known AE it is hence possible to obtain both the X a n d x ~ parameters for a given value of q.
80 0
7
@
60
bs=15.3
c
, .2o
-1.0
It will then be possible to determine the polarity of an unknown polymer surface by measuring the adsorption of the same surfactant on that surface. The only necessary assumption is that the surfactant adsorbs in the same way on the known and unknown polymer surfaces, i.e., q is the same in the two cases. Consequently the new adsorption data also give a straight line when plotted as in Fig. 6. The line should have the same slope as the line for adsorption on the known surface, but it should be shifted parallel to the known line giving a different intercept. The shift is caused by a difference in AE for the two adsorption isotherms. From Eqs. [ 15] and [ 16] it is seen that this shift is given by
-0.5
J
I
0
0.5
1.0
FlG. 6. Plots, according to Eq. [16], for the calculated adsorption of NP-EO2o on two latexes with /~s = 15.3 and 22.2 MPa ~/2, respectively. Journal of Colloid and Interface Science. Vol. 102, No. 2, December 1984
q m VI = 2 ~(61--
r2)(rB-- rA)
[17]
for latexes A and B, assuming that the xEs parameters are the same for the two latex polymers. It is recommended that in determining the polarity of a latex surface by adsorption a surfactant with a short ethylene oxide (EO) chain should be used for the following reasons. First, a short EO chain nonionic surfactant packs densely on the surface and hence it is possible to obtain experimental points giving small or even negative values of (1 ~ 2~b~) as shown in Fig. 7. This gives an accurate determination of the intercept. A long EO chain nonionic surfactant packs less densely and hence the experimental points are found at the right-hand corner in Fig. 7, whence a poor accuracy in the intercept is obtained. Second, there might be a possibility for the EO chain to adsorb with the EO chain in direct contact with the polymer surface. This possibility is obviously diminished when short EO chains are used. We suggest that adsorption measurements could perhaps be a method to evaluate the surface composition of a copolymer latex. It
417
ADSORPTION OF NONIONICS, I 8O
~
0
t
1
6O
i
so
NP-EOlo
) i 0
i
-0.1
i
0
i
0.2
=
i
0.4
i
i
0.6
I
I
0.8
i
1.0
(1-2 ~))
FIG. 7. Plots, according to Eq. [16] for the adsorption of NP-EOto and NP-EOso on polystyrene latex (q = 4). (Experimental data obtained from Ref. (8).)
would require an extension of the analysis, presented in this paper, to include the effect of the two different types of surfaces on the mean adsorption of the suffactant. In summary our treatment indicates that the polarity of a polymer latex surface is not dominant in determining whether a nonionic surfactant will be adsorbed on a latex, but it does play an important role in determining the maximum adsorption of the surfactant. The adsorption is predicted to decrease as
the polarity increases. We have also shown that, using the same surfactant on different latexes it is, in principle, possible to obtain a quantitative measure of the surface polarity, ~s, of a polymer latex from adsorption measurements. For such a determination it is required that the adsorption of a given surfactant has previously been measured on a latex with known polarity. The experimental verification of this treatment will be described in the subsequent article (3). REFERENCES 1. Kronberg, B., J. Colloid Interface Sci. 96, 55 (1983). 2. Vijayendran, B. R., J. Appl. Polym. Sci. 23, 733 (1979) and references therein; Piirma, I., and Chen, S-R., J. Colloid Interface Sci. 74, 90 (1980). 3. Kronberg, B., Stenius, P., and Igeborn, G., J. Colloid Interface Sci., 102, 418 (1984). 4. Griffin, W. C., J. Soc. Cosmet. Chem. 5, 249 (1954). 5. Shafin, E. G., in "Polymer Handbook" (J. Brandrup and E. lmmergut, Eds.), pp. 3-221. Wiley, New York, 1975. 6. Owens, D. K., and Wendt, R, C., J. Appl. Polym. Sci. 13, 1741 (1969). 7. Barton, A. F. M., "Handbook of Solubility Parameters and other Cohesion Parameters," Chaps. 7 and 13. CRC Press, Boca Raton, Fla., 1983. 8. Kronberg, B., K~ill, L., and Stenius, P., J. Dispersion Sci. Technol. 2, 215 (1981).
Journal of Colloid and Interface Science, Vol. t02, No. 2, December1984