Langmuir 1992,8, 2005-2012
2005
Practical Use of Concentration-DependentContact Angles as a Measure of Solid-Liquid Adsorption. 1. Theoretical Aspects Erwin A. Vogler Becton Dickinson Research Center, 21 Davis Drive, P.O.Box 12016, Research Triangle Park, North Carolina 27709 Received January 13, 1992. In Final Form: May 26, 1992
Theoretical aspects of interpreting concentration-dependentcontact angles are discussed. A thermodynamic analysis was applied to deduce relative magnitudes of solid-vapor (sv) and solid-liquid (sl) adsorption for surfaces exhibiting a full range of wettability. It was concluded that the surface excess parameter [rCsl, - I'(sv)l, which simultaneouslymeasures el and sv adsorption, can be interpreted in terms of sl adsorption for nonwettable surfaces under experimental conditions that avoided solute deposition at sv interfaces. Practical computational techniquesare describedand applied to an experimentalsystem consisting of glass cover slips, with and without a hydrophobic silane layer, and polystyrene plaques with different levels of surface wettability imparted by plasma oxidation. The nonionic surfactant Tween-80 (in saline)and the cationicsurfactant cetyl bromide (in water)were applied as test surfactants. A relatively smooth decrease in [I'(al)with increasing solid surface wettabilitywas observed for the Tween/saline system. These observationswere interpreted as a monotonic decrease in sl adsorption with increasing wettability. By contrast, [I'csl) - I'(sv)l values for cetyl bromide/water exhibited sharp changes as a function of surfacewettability whichwere attributed toa rapid transitionfrom a "Tween-like" hydrophobicadsorption mechanism to an ion-pairing adsorptionmechanism involving the cationic head group and putative anionic functionalities on oxidized surfaces.
Introduction Adsorption is undoubtedly one of the most important manifestations of surface and interfacial energetics. The interfacial chemistry created by adsorbed surface-active molecules (surfactants), both biological and synthetic, dominate end-use properties of materials in many different applications. As examples, protein adsorption is known to mediate tissue/cell adhesion to artificial materials and is an important area of research in biomaterials science. Emulsification of adsorbed oils and release of adherent dirt particles is important in the detergent industry, which is critically dependent on the interfacial activity of various surfactants used in detergent formulations. Colloids are frequently stabilized by adsorbed surfactants which serve as steric barriers to flocculation. Consequently, understanding and controlling adsorption are commercially important in various biomedical, biotechnical, detergent, and colloid-related industries. One of the classical methods of quantifying solid-liquid adsorption is by measuring interfacial tensions as a function of surfactant concentration and interpreting results through Gibbs' adsorption isotherm (see, for example, ref 1). Interfacial tensions can be measured by one of the many different methodsfalling under the general umbrella of tensiometry? the most popular and well known of which is probably contact angle goniometry. This approach offers a number of advantages that are unique to wetting measurements. First, contact angles are sensitive to only the outermost atomic layers responsible for surface energetics that drive adsorption. The second advantage is related to the first in that results of contact angle measurements are interpreted directly in terms of the surfaceenergeticsof the adsorbed layer. Third,contact angles provide access to equilibrium or steady-state adsorption since angle measurements do not perturb adsorption dynamics. This is of particular value to bio(1) Hunter, R.J. In Foundations of Colloid Science; Oxford University Press: New York, 1989; Vol. 1, p 244. ( 2 ) Neumann, A. W. Adu. Colloid Interface Sci. 1974, 4 , 105.
material scientists studying protein adsorption since biological macromolecules are easily denatured and the hydrated state is most relevant to the biological environment encountered in end use applications. Finally, under appropriate circumstances, information derived from contact angle measurements can be interpreted in terms of molecular configuration in the adsorbed condition. This paper discusses theoretical aspects of interpreting concentration-dependentcontact angles in terms of Gibbs' surface excess, r, for the purpose of quantifying surfactant adsorption at solid-liquid sl interfaces from aqueous solution. The measurable parameter [I'(sl) - I'(av)l, which is the difference between surface excessquantities at solidliquid (sl) and solid-vapor (sv) interfaces, is discussed for surfaces exhibiting a full range of wettability. Conditions under which [I'(sl) - I'(sv)l r(sl)are identified from this analysis. Computational methods are described including adata-fitting strategy that is useful in the parameterization of adsorption data, allows easy estimation of statistical confidence in these wetting parameters, and has general utility as a computational tool involving contact angle measurements. Theory and practice are illustrated using an experimental system consisting of silane-treated glass slides and polystyrene plaques with a controlled surface oxidation imparted by plasma oxidation. The nonionic detergent Tween-80 (polyoxyethylenesorbitan monooleate) and cationic detergent cetyl bromide (cetyldimethylethylammonium bromide) were applied as test surfactants.
Theory Surface Excess as a Measure of Adsorption. Gibbs' adsorption isotherm in its simplest form for an ideal dilute solution of an isomerically pure, nonionizing surfactant states that I' is proportional to the rate of change of interfacial tension with logarithmic surfactant dilution: r = -RT[dy/d In C l , where RT is the product of the gas constant and Kelvin temperature with combined dyn/ (cmmol) units, y is interfacial tension (dyn/cm),and C is the dimensionless surfactant dilution expressed in terms 0 1992 American Chemical Society
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Table I. Relative Maanitude of Surface Excess Values ~~~~
~
conditional values
a
Probable r(Bv) = 0. * Essential l'(nv)> 0. Not possible for ordinary surfactants.
of chemical potential, activity, or mole fraction. The isotherm can be directly applied when y values are experimentally available as in, for example, measurement of concentration-dependent liquid-vapor interfacial tension y(lv):
r(lV) = -(l/Rn[dT(lv)/dIn Cl
(1)
The physical interpretation of surface excess for this case is that I'(lv)is the amount of surfactant collected within the interphase separating bulk liquid and vapor phases, in excess of that attributable to bulk liquid concentration. The dimensions of I' are moles per unit area of Gibbs' interface. The interface is an infinitely thin plane located somewherewithin the interphase, drawn parallel to similar planes bounding the interphase. There are a number of texts on surface physical chemistry including ref 1 that the interested reader can refer to for a detailed mathematical discussion of Gibbs' approach. For the present purposes, however, it is sufficient to consider the isotherm as a method of measuring the number of moles of surfactant adsorbed at the junction between two insoluble phases in mutual contact. Results of this measure of adsorption are reported as a ratio to the area of junction. Technically speaking, I' can be either a positive or negative number, representing conditions of interfacial excess or depletion, respectively. However, for the case of dilute aqueous solute solutions considered herein, it is important that interfacial depletions (I' < 0) cannot be large negative numbers because the population of molecules at an interface is already overwhelmingly solvent; there are few solute molecules to "lose" relative to bulk concentration. Consequently, I' = 0 can be considered as a lower bound for surface excess without incurring significant error. By contrast, I' can take on relatively large positive values because the interface can become saturated with adsorbate relative to bulk concentration. As an example that will be discussed in more detail in the Results and Discussion, I'(lv)for Tween-80 was 216 pmol/ cm2, meaning that there were 216 pmol of Tween-80 collected within the lv interphase over and above that attributable to bulk concentration,per unit area of contact. The interpretation of Gibbs' isotherm for sl adsorption is not so straightforward because contact angles 8 do not directly sense energetics at sl interfaces through ~ ( ~ 1 ) . Instead, contact angles actually measure the difference in surface energetics at sv and sl interfaces as given by the Young equation; T y(lv)cos 8 = y(av)- Y(,I), where T is the adhesion tension (dyn/cm) (see, for example, refs 2 and 3). Gibbs' isotherm can be applied to sl adsorption through a differentiated form of the Young equation:4*6 f
(3) Johnson, R.E.; Dettre, R. H. In Surface and Colloid Science; Matijevic, E.; Ed.; Wiley-Interscience: New York, 1969; Vol. 1, p 85. (4) Smolders,C. A. In Chen.Phys. Appl. Surface Actiue Subst., h o c . Int. congr., 4th Int. cong. on Surf.Actiue Agta., Bruseela,Sept 2-7,1964; Overbeek, J. Th., Ed.; Gordon and Breach New York, 1967; p 343. (5) Gau, C.-S.; Zograf, G. J. Colloid Interface Sci. 1990, 140, 1.
d d d In C = d[yaV,cos 8l/d In C = d[y,,,, - y(,J/d In C = RTD',,,) - r(,,,)I(2) An important aspect of eq 2 is that [I'(,l) - I'(sv)lcannot be unambiguously interpreted in terms of I'(d). This is because I'(sv)is not always negligible, even for nonvolatile surfactants for which no mechanism of solute migration to sv interfaces is readily apparent."7 In fact, trace adsorption or deposition of nonvolatile surfactants at the vapor interface within the microenvironment of the slv line can lead to large since the vapor-phase composition is zero for nonvolatile surfactants. Thus, for the purpose of utilizing [I'(,l) - I'(av)l as a measure of adsorption to sl interfaces,it is of interest to examinepotential relative magnitudesof I'(lv), and I'(sl) under general adsorption conditions that might be observed in the laboratory. Relative Magnitude of Surface Excess Quantities. The fully differentiated form of eq 2 reveals the simultaneous effects of adsorption to lv, sv, and sl interfaces: yOv)sin 8 [d8/d In Cl = RT[r,,,
- qSl) - qlV) COS el
(3) The term dO/d In C is the slope of a 8 vs In C curve for which there are three possible conditions of general interest: (i) decreasing 8 with added surfactant (d8/d In C < 01, (ii) no change in 8 with added surfactant (d8/d In C = 01,and (iii) increasing 8 with added surfactant (dO/d In C > 0). Hypothetically, these conditions might occur for solids exhibiting the full range of wettability Oo I8 I 180°, although it should be noted that 8 for aqueous solutions on smooth surfaces seldom exceeds about 120O. Since the term y(lv)sin 8 is always positive for all 8 in this range, the sign of d8/d In C determines the relative magnitudesof qSv), I'(,l), and r(lv) cos 8. Three subordinate conditions of eq 3 can be resolved d8/d In C < 0
r(sl)> r(av) - r(lv) COS 8
(3a)
d8/d In c = o
I-(,,)= qSv) - qlV) COS e
(3b)
doid ~n c>o
qSl) < qSv) - qlV) COS e
(3~)
Furthermore, Oo I8 I180° establishes boundary values cos 8 term in eqs 3a-c, corresponding to -r(lv) for the r(lv) I I'(lv)cos 8 Irclv). A special case occurs when I'(lV)cos 8 crosses 0 at 8 = No.Table I compiles all combinations of these hypothetical boundary conditions and the resultant magnitude of I'(,l) with the stipulation that 1. 0. Of course, < 0 is of no particular interest since negative exceas quantities must be relativelysmall. Special physical constraints are also noted in Table I related to the conditions that, in general, r 1 0 and r(lv) > 0 for ordinary surfactants in aqueous solution. For examples, [l'(sv) + I'(I~)I1 0 is a physical constraint for r(,l)> [I'(,.,) + I'(lv,1 (row 1 of columns 3 and 4 under d8/d In C < 0 ) (6) Johnson,B. A.; Kreuter, J.; Zogrdi, G. Colloids Surf. 1986,17,326. (7) Pyter, P. A.; Zografi, G.; Mukerjee, P. J. Colloid Interface Sci. 1982, 89, 144.
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because it is essential that r(sl)1 0. The superscript c on r(lv) = 0 (row 2 of column 8 under dO/d In C < 0) denotes a specialdeviation from the expectation that ordinary surfactants adsorb to lv interfaces because positive r(lv) values cause a violation of the r(sl)1 0 constraint. Table I is discussed below for each of the above d8/d In C conditional values with reference to experimental circumstancesunder which these conditionswere observed for Tween and cetyl bromide (seeResults and Discussion). Agenerality that can be drawn from this discussionis that the r(sv) = 0 condition can be realistically expected only 0 and d8/d In C for nonwettable surfaces exhibiting 8 > ' I0. As a consequence, [I'(al) - I'(sv)lcannot be directly interpreted in terms of r(sl)for hydrophilic surfaces exhibiting 8 . ' 0 d8/d In C < 0 Condition. Decreasing contact angles with added surfactant are typical for nonwettable solids in contact with aqueous nonionicsurfactant solutionssuch as Tween-80. Surfactant can adsorb with nonpolar residues directed toward nonpolar surfaces and polar residues extending into solution. Under this adsorption regime, surfacesbecome more wettable with increased surfactant adsorption and the contact angle decreases concomitantly. From Table I, it is apparent that r(sl)can exceed r(lv) for r(sv)I 0 on poorly wettable surfaces exhibiting 90° I8 I180' (rows 1and 2 of column 3). The only physical constraint (row 1of column 4) is that + I'(lv)l 1 0 so that r(sl)I 0, in accordance with the expectationthat r values not take on large negativevalues. Thus, there are no thermodynamic requirements that r(sv) take on large positive values for these relatively hydrophobic surfaces. Under specialized experimental circumstances that avoid inadvertent mechanical deposition of solute at the (sv) interface, as by vibrations or evaporation, for example, it is possible that [I'(sl) - I'(sv)] I'(sl).517 Moving to more wettable surfaces exhibiting ' 0 I8 I 90' in Table I, it is apparent that d8/d In C < 0 imposes highly restrictive physicalcircumstances (identified in the footnotes) requiring r(sv) I 0 (row 1of columns 6 and 8) or, on wettable surfaces with 8 Oo, it is essential that r(sv)> 0 (row 1 of column 8). d0ld In C = 0 Condition. No change in contact angle with added surfactant is observed only in a single case of practical interest herein for wettable surfaces exhibiting 8 . ' 0 This is the experimental circumstance purposely imposed on plates used in the Wilhelmy balance method of measuring y(lv),usually by flame or oxygen plasma treatment, so that the measured adhesion tension T = y(lv) cos 8 = y(lv). The fully wetted condition is a very special circumstance because a contact angle droplet fully spreads to a thin film of solution adsorbed to the solid surface. Antonoff s rule3states that ~ ( ~ =1 y(sv) ) - y(lv)for this case. It is of interest that the differentiated form of Antonoff s rule (with respect to In C)leads directly to condition 3b when 8 = 0'. As can be seen in Table I (row 4 of columns 7 and 81, it is physically impossiblefor r(sv) = 0 on wettable surfaces. In fact, sv adsorption follows lv adsorption for the spreading (8 = 0 ' ) condition. A physical interpretation is that surfactant is deposited at the sv interface along the moving slv front as the droplet attempts to spread to a monomolecular film on the surface. It is important to note that any surfactant adsorption at sl interfaces of perfectly wettable surfaces requires that the strongly-adsorbed water layer must be displaced by adsorbate, and this can be energetically prohibitive. Invariant 8 with added surfactant on nonwettable surfaces exhibiting 8 I180' (row 3 of columns 3 and 4) requires a precise adsorption balance at lv, sv, and sl interfaces such that I'(sl) = [I'(sv) + I'(lv)1. This unusual
-
-
-
-
situation would be even more unique in the r(sv) = 0 case, but there are no absolute physical constraints preventing I'(sl) = r(lv).For more wettable surfaces exhibiting 8 90' (row 3 of column 5), it is apparent that d8/d In C = 0 can be met only if r(sl)= r(sv). d0/d In C> 0 Condition. Increasing 8 with added surfactant is descriptive of the "autophobic" or "dewetting" e f f e ~ t ~that @ can ~ ~ be observed when ionic surfactants in aqueous solution are in contact with wettable, high-energy surfaces bearing a countercharge for the surfactant head group, cetyl bromide on clean, oxidized glass bearing anionic groups, for example. The classical explanation of autophobicity is that surfactant adsorbs in the head-down configuration due to charge interactions between surfactant and surface, with hydrophobic residues extending into solution. Thus, the surface becomes less wettable than the original polar surface after adsorption. Contact angle droplets retract to a higher angle,exposing adsorbate to the sv interface. This physical explanation of autophobicity is consistent with the observation from Table I that F(sv)# 0 for surfaces exhibiting Oo I8 I90' (row 6 of columns 4 and 5 ) . Autophobic behavior on low-energy, nonwettable surfaces would be unusual because surfaces are by definition nonpolar. Surfactant adsorption with nonpolar groups directed toward the surface with polar portions extending into aqueous solution would be energeticallypreferred instead, as described previouslyfor the d8/d In C < 0 condition. Consequently, increasingcontact angle with added surfactant can be observed on nonwettable surfaces exhibiting 90' < 8 I 180° only in the + I'(lv)1 (row 5 of column circumstance that r(sl)< [r(sv) 3).
-
Computational Aspects Contact Angle and Adhesion Tension Curves. A plot of contact angles or interfacial tensions against surfactant dilution on a logarithmic scale is an effective way of presenting adsorption data. These graphical constructs are termed contact angle or interfacial tension curves herein. Appropriate interfacial tensions are y(lv)and T for lv and sl interfaces, respectively. There are two different types of T curves. The first is comprised of T data that are directly measured by using a technique such the Wilhelmy balan~e.~,~Jl The second is constructed from synthetic T = y(lv) cos 8 data calculated from separate y(lV)and 8 measurements. These two alternative T curves are not necessarilyequivalent sources of adsorption information, as will be discussed in detail in the second of this two-part series. Adsorption to lv and sl interfaces causes measurable changes in y(lV),8,or T over a concentration range that is characteristicof the surfactant compatibility with solvent and surfactant activity at the interface. It is usually observed that interfacial tensions and contact angles rise or fall as a function of surfactant concentration,from yo(lv), eo, or T O at infinite dilution to a limiting value y'(lv),Of, or T ' that can sometimes be attributed to the critical micelle concentration (cmc) for the surfactant. Parameters yo(lv), eo, and T O are inherent material properties measured with pure solvent that can be used to compare wettability of different materials. Maximal surfactant effect is measured by y'(iV),e', and 7'. Parameterization of Tension and Contact Angle Curves. Tension and contact angle curves are approx(8)Good, R. J. SOC.Chem. 2nd. Monogr. 1967,25, 328. (9) Ruch, R. J.; Bartell, L.S . J. Phys. Chem. 1960, 64, 513. (10) Novotony, V. J.; Marmur, A. J. Colloid Interface Sci. 1991,145, 355. (11) Martin, D.A,; Vogler, E . A. Langmuir 1991, 7 , 422.
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imately sigmoidal in shape on a logarithmic dilution scale (see Figures 1 and 3 for example). I have found it computationally convenient to fit these curves to a fourparameter variant of a logistic equation, which is a mathematical description of a sigmoidal curve having the form [ ( A-D)/(l + (K/X)N)l+ D (4) where Y is either y(lv),8, or T in this application. The term X = In C = In (surfactant dilution), where surfactant dilution can be conveniently expressed so that X > 0 by using dimensionless concentration scales such as parts per trillion or, if molecular weight is known and the ideal dilute solution approximationis applied, the number equivalent to picomoles per liter (picomolar). The parameter A is the fitted plateau value at infinite surfactant dilution corresponding to yo(lv),do, or T O . Similarly, D is the fitted plateau value at the high-concentration limit corresponding to y'(lv),e', or f . The K parameter measures surfactant concentration (In C units) at half-maximal y(lv),0, or T change, so that surfactants with a low cmc have characteristically low K values. Slopesof sigmoidalcurves are related to the exponential N,which in the formulation of eq 4 is always negative, with higher negative values for steeper curves. Although a logistic equation has no special physical or thermodynamicmeaning in application to surfactant effects, the fitting procedure provides a statistical means of utilizing data gathered over the entire concentration range in the extraction of fitted parameters with error estimates. These parameters can be conveniently tabulated, allowing quick comparison of surfactant properties, and error estimates can be propagated into calculated surface excess to provide a measure of statistical confidence, as described in the Appendix. Calculationof Surface Excess. Practical application of eqs 1 and 2 to tension measurements amounts to calculating slope through linear-like portions of y(lv)or T curves, respectively,where surface excess is nearly directly proportional to the interfacial tension rate of change. A computationally convenient approach employing best-fit logistic equations is to identify transitions in the second derivative which locate low- and high-concentration inflections isolating the linear-like portion on the sigmoid curve (see vertical lines on Figure 1). Denoting concentrations (In C units) corresponding to these inflections as XI and X2 and employing eq 4 to calculate Y2 at X2 and Y1 at XI allow dY/dX to be estimated from (Yz - Yl)/(X2 - XI). This slope can be converted to surface excess units of moles per square centimeter if C is expressed in moles per liter. Error estimates in calculated excess values can be made from fitted logistic parameters as described in the Appendix. A numerical example is also provided. There are two disadvantages in applying the above method of estimating surface excess from adhesion tensions calculated from separate y(lv)and 8 observations. First, it is almost always preferable to perform fitting and calculations on originaldata rather than some transformed quantity such as synthetic T . Second, from a statistical point of view, the error in y(lv) and 8 compounds in calculated T in a nonlinear fashion as a function of surfactant concentration (see eq A4). These problems can be avoided by calculating surface excess using eq 3 which makes direct use of the experimental observable 8. In order to do so, d8/d In C (rad) is determined from 8 curves as described abovefor adhesiontension curves. As a matter of convenience,terms y(lv),sin 8, and cos B can be evaluated a t the half-maximum of the 8 curve because the logistic equation (eq 4) evaluated at X = K simplifies to ( A D ) / 2 and error estimates in each term are very straightforward to calculate (see eqs Al-A3). The final required value
Y
+
I'(lv) is available from independently-measuredy(lv)curves. A numerical example is given in the Appendix. An Adsorption Paradigm. Exact application of Gibbs' adsorption isotherm in eqs 1-3 is critically dependent on a number of factors including solute purity, ideal dilute solution behavior, and attainment of thermodynamic equilibrium. With respect to these criteria, many surfactant systems of interest, including those discussed herein, are not composed of isomericallypure compounds and nominal molecular weights actually represent some sort of an average composition. Surfactant effects of practical interest are usually quite strong so that dilute solutions (
