Practical use of concentration-dependent contact angles as a measure of solid-liquid adsorption. 1. Theoretical aspects

Langmuir 1992,8, 2005-2012 2005

Practical Use of Concentration-Dependent Contact 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-dependent contact 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 simultaneously measures 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 techniques are described and applied to an experimental system 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 cationic surfactant cetyl bromide (in water) were applied as test surfactants. A relatively smooth decrease in [I'(al) - with increasing solid surface wettability was observed for the Tween/saline system. These observations were 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 surface wettability which were attributed toa rapid transition from a "Tween-like" hydrophobic adsorption mechanism to an ion-pairing adsorption mechanism 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, under- standing 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 methods falling 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 surface energetics of 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

( 2 ) Neumann, A. W. Adu. Colloid Interface Sci. 1974, 4 , 105. Press: New York, 1989; Vol. 1, p 244.

material scientists studying protein adsorption since biological macromolecules are easily denatured and the hydrated state is most relevant to the biological environ- ment 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-dependent contact 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 excess quantities at solid- liquid (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 (polyoxyethylene sorbitan 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 Cl , 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

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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):

(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 somewhere within 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 f 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

r(lV) = -(l/Rn[dT(lv)/d In Cl

(3) Johnson, R. E.; Dettre, R. H. In Surface and Colloid Science; Mat- ijevic, 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)l cannot 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 examine potential relative magnitudes of 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 simul- taneous 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 I 8 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 magnitudes of qSv), I'(,l), and r(lv) cos 8. Three subordinate conditions of eq 3 can be resolved

(3a)

(3b)

( 3 ~ )

d8/d In C < 0 r(sl) > r(av) - r(lv) COS 8

d8/d In c = o I-(,,) = qSv) - qlV) COS e doid ~n c > o qSl) < qSv) - qlV) COS e

Furthermore, Oo I 8 I 180° establishes boundary values for the r(lv) cos 8 term in eqs 3a-c, corresponding to -r(lv) I I'(lv) cos 8 I rclv). 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 re- sultant magnitude of I'(,l) with the stipulation that 1. 0. Of course, < 0 is of no particular interest since negative exceas quantities must be relatively small. 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~)I 1 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.

Concentration-Dependent Contact Angles

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 special deviation 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 circumstances under which these conditions were observed for Tween and cetyl bromide (see Results and Discussion). Agenerality that can be drawn from this discussion is that the r(sv) = 0 condition can be realistically expected only for nonwettable surfaces exhibiting 8 > 0' and d8/d In C I 0. As a consequence, [I'(al) - I'(sv)l cannot 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 nonionic surfactant solutions such as Tween-80. Surfactant can adsorb with nonpolar residues directed toward nonpolar surfaces and polar residues extending into solution. Under this adsorption regime, surfaces become more wettable with increased surfactant adsorption and the contact angle decreases con- comitantly. From Table I, it is apparent that r(sl) can exceed r(lv) for r(sv) I 0 on poorly wettable surfaces exhibiting 90° I 8 I 180' (rows 1 and 2 of column 3). The only physical constraint (row 1 of column 4) is that + I'(lv)l 1 0 so that r(sl) I 0, in accordance with the expectation that r values not take on large negative values. 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 a t 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' I 8 I 90' in Table I, it is apparent that d8/d In C < 0 imposes highly restrictive physical circumstances (identified in the footnotes) requiring r(sv) I 0 (row 1 of 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 rule3 states 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 impossible for 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 I 180' (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

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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 I 8 I 90' (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 energetically preferred instead, as described previously for the d8/d In C < 0 condition. Consequently, increasing contact angle with added surfactant can be observed on nonwettable surfaces exhibiting 90' < 8 I 180° only in the circumstance that r(sl) < [r(sv) + I'(lv)1 (row 5 of column 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 necessarily equivalent 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 characteristic of 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 TO 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,

(11) Martin, D. A,; Vogler, E . A. Langmuir 1991, 7, 422. 355.

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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 four- parameter variant of a logistic equation, which is a mathematical description of a sigmoidal curve having the form

Vogler

I'(lv) is available from independently-measured y(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 isomerically pure 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 (<1% w/v), presumably behaving in an ideal way, can be used in most experimental studies. Equilibrium argu- ments, however, are much more complicated. First, equilibrium adsorption is not typically demonstrated with kinetic measurements but rather only inferred from attainment of steady-state contact angle or adhesion tensions. Second, surfaces of common origin such as polymers discussed herein almost always exhibit the phenomenon of contact angle hysteresis3J2 due to surface chemical heterogeneity or roughness-more likely both to some degree. Consequently, advancing and receding angles do not represent equilibrium measurements, even if equilibrium adsorption can be demonstrated.

Clearly, these factors must be borne in mind when making detailed interpretation of adsorption measurements, recognizing that calculation of surface excess for ordinary surfaces and surfactant systems represents an interpretation of laboratory measurements (reality) within the context of a model (reversible thermodynamics) which is founded on principles and assumptions that only approximate the real world. A paradigm that can be adopted for interpreting a1 adsorption treats advancing and receding T measurements as separate equilibrium values representing a pure "advancing phase" or a pure "receding phase", respectively. Thus, in this perspective, r values calculated from advancing and receding B or T

measurements quantify adsorption of a surfactant of some "average" chemical composition to advancing and receding phases. Given that advancing and receding measurements bound observable angle and tension measurements, it can be anticipated that corresponding r values will bracket maximum and minimum adsorption.

Materials and Methods Substrates. Wettable glass cover slips (Clay Adams Gold

Seal, 24 X 30 X 0.1 mm) used in Wilhelmy balance measurements of y(lv) were prepared by sequential rinses in distilled water, 2- propanol, and Freon to remove putative surface contaminants followed by 15-min exposure to an oxygen plasma (100 W of 13.56-MHz radiofrequency power, -50 mTorr of 02). Hydro- phobic surfaces were prepared from cleaned cover slips by reaction with 2 % octadecyltrichlorosilane (Petrach) in CHC& for about 2 h at -60 OC in a sealed container. Plates were prepared batch- wise, yielding identically-treated specimens with little batch- to-batch variability (saline contact angles varied about 5 O within and between batches), exhibiting about 20° hysteresis on an advancing contact angle of about llOo. Untreated polystyrene 60" Petri dishes were obtained from the Becton Dickinson Co., Franklin Lakes, NJ. Surfaces were shown to be free of surface contaminante by ESCA and SSIMS. These hydrophobic polystyrene surfaces exhibited advancing saline contact angles around 8 4 O , generally varying no more than loo within the lot of samples used in this work. Polystyrene Petri dishes were cut into test plaques and oxidized at various levels by using a 350-mTorr, 22-W, 13.56-MHz oxygen plasma for between 0 and 30 8. Treated surfaces were held overnight to ensure a stable surface chemistry for adsorption studies.

(12) Johnson, R. E.; Dettre, R. H. Contact Angle, Wettability, and Adheeion; Advances in Chemistry Series 43; American Chemical Society: Washington, DC, 1964; p 112.

Y [ (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 approximation is 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), d o , 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. Slopes of sigmoidal curves 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 thermodynamic meaning 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.

Calculation of 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 original data 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 above for adhesion tension 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

Concentration-Dependent Contact Angles Langmuir, Vol. 8, No. 8, 1992 2009

Table 11. Surfactant Properties of Tween-80 and Cetyl Bromide at the Liquid-Vapor Interface

surface excessc surfactant system Y O W dyn/cm y'(lV), dyn/cm K(lV), h C unitab N(IV) r(lv), pmol/cm2

fitted parameters0

Tween-80 (in saline) 73.5 f 0.2 39.7 f 0.4 15.9 f 0.1 -11.4 f 0.9 215.6 f 9.6 Tween-80 (in water) 72.7 f 0.1 40.7 f 0.3 15.7 i 0.1 -10.4 f 0.3 188.5 f 3.0 cetyl bromide (in water) 72.9 i 0.5 38.3 f 0.7 16.2 f 0.1 -17.3 f 1.8 325.9 f 12.2

0 Indicated uncertainties are standard errors of the statistical, least-squares fitting procedure. In all cases, the R2 goodness of fit parameter was 95 % or better. b Concentration units expressed as picomoles per liter. Indicated uncertaintywas estimated from error in fitted coefficienta (see Appendix). Cetyl bromide exhibits an autophobic effect at high concentration (>1 X ), possibly causing a systematic low estimate of y'(lv) and r(lv). Measurements based on static contact angles indicate an upper error limit of 5% on y'(lv) and 20% on r(lv).

cetyl bromide (in saline) 71.8 f 0.5 36.8 f 0.6 15.4 i 0.1 -27.8 f 3.3 555.4 f 20.2

Wetting Measurements. Wilhelmy balance measurements of yov) were carriedout as described in ref 11. All Tween solutions were observed (by contact angle goniometry) to completely wet oxidized glass cover slips used as plates in the Wilhelmy experiment, verifying the assumption that y(lv) cos 0 = ~ ( 1 ~ ) . The 6 = 0 condition for higher cetyl bromide concentrations was experimentally unattainable as shown in Figure 4 due to autophobic adsorption behavior noted for this cationic surfactant on clean anionic glass surfaces. This potentially introduced a systematic underestimation of y(lv) values. Error analysis indicates that the upper limit of error on y(lv) is 5% which, in turn, translates into a maximal 20% potential error on r(lv) values listed in Table 11. These error estimates represent conservative upper bounds since it is observed that concentration-dependent receding contact angles measured by the Wilhelmy balance technique are smaller than those observed in goniometry at high surfactant concentrations (see the companion paper in this issue), and y(lv) curves show no evidence of a significant autophobic effect (see Figure 1).

Advancing and receding contact angle measurements were made with a goniometer fitted with a tilting stage (Rame' Hart). A humidified environmental chamber was employed to minimize evaporation and a vibration-isolation table (Newport) used to dampen apparatusvibrations. Contact angle measurements were made after a 15-30-min equilibration of a 10-pL droplet containing the surfactant concentration of interest on test surfaces. Equil- ibration was carried out with test surfaces held in the horizontal mode, and readings were made when angles were observed to be stable with time. The stage was then slowly tilted to 30-35O for advancing/receding angle readings. All contact angles were read by a single experimentalist. Multiple readings of the same angle suggest that precision in separate contact angle observations was about 2 . 5 O with agreement between three different experimen- talists within 5 O . This variation was smaller than plate-to-plate variations.

Solutions. Tween40 (polyoxyethylene sorbitan monooleate, nominal MW = 1309.68, d = 1.064, used as received from Ald- rich) solutions were prepared in physiologic saline (0.9%, Ab- bott). Cetyldimethylethylammonium bromide (nominal MW = 378.49, used as received from Aldrich) was prepared in deionized and distilled water.

Results and Discussion Theoretical and computational aspects of using con-

centration-dependent contact angles as a measure of adsorption discussed in the preceding sections were applied to polystyrene plaques and glass cover slips. Polystyrene was rendered increasingly wettable by plasma oxidation, producing surfaces with Oo I O0 I 90°. Glass cover slips were cleaned and silane treated as required, yielding surfaces exhibitingadvancingOO = 0' or Bo = 110'. Tween- 80 in saline and cetyl bromide in water served as surfactant systems for adsorption measurements. Tween was prepared in high-ionic-strength saline solution to mask any possible ionic interactions between ionic impurities of unknown origin in this nonionic detergent and oxidized surfaces. Thus, Tween/saline served as a surfactant system for which it is anticipated that there is only a single predominant adsorption mechanism involving partition of hydrophobic residues from aqueous solution to hydrophobic interfaces, with reduction of interfacial energetics

I 0

0 4 8 12 16 20 24 3 0 ' ' I ' ' ' ' I I ' ~

In C (picomoles/liter) Figure 1. Liquid-vapor interfacial curves for Tween-80/saline (filled circles) and cetyl bromide/water (open circles), plotting interfacial tension y(lv) against surfactant concentration on a logarithmic scale. Smooth curves through the data represent the best fit to the logistic equation. Vertical lines bounding the linear-like portions of the curves represent the range through which surface excess r(lv) was calculated.

providing the sole driving force. Cetyl bromide/water, by contrast, served as a surfactant system with the potential of exhibiting two alternative adsorption mechanisms: one exactly analogous to that of Tween and the other involving ion-pairing of cationic head groups with putative anionic or polar moieties on surfaces. The partitioning mechanism can be expected to predominate on hydrophobic surfaces with little or no oxidized surface functionalities whereas ionic interactions can be expected to predominate on highly oxidized, wettable surfaces.

Taken together, these surfaces and surfactants served as a test system exhibiting the three conditional values for d8/d In C listed in Table I. Discussion of the results will focus first on adsorption at lv interfaces. Results of adsorption studies to solid surfaces will be interpreted for each of the three possible outcomes for d8/d In C.

Adsorption to Liquid Interfaces. Figure 1 is a y(lV) curve that compares surfactant properties of Tween/saline and cetyl bromide/water. Smooth curves through the data result from least-squares fitting to the logistic equation (eq4), yielding characteristic parameters yo(lv), y'(lv), &),

and ZV[lv) collected in Table 11. The y0(lv) parameter measures liquid interfacial tension at infinite surfactant dilution and is, therefore, equal to the interfacial tension of saline or pure water used to prepare solutions. Tween and cetyl bromide had similar surfactant properties as measured by y'(lv) and K(lv) values. For further interest, adsorption behavior of each surfactant at lv interfaces was compared in saline and water. Results are listed in Table 11. Tween behavior in saline was similar, but

2010 Langmuir, Vol. 8, No. 8,1992 Vogler

attributed to unequal effects of surface roughness or chemical heterogeneity on concentration-dependent advancing and receding contact angle measurements, which translates into differing effects on calculated [I'(d) - I'(nv)l values through the observed slope of contact angle curves.

Figure 2 is bisected by horizontal lines through [I'(d) - I'(nv)l = 0. Positive values falling above the bisector correspond to I'(sl) > I'(sv) whereas values falling below the bisector correspond to I'(d) < I'(nv) since neither I'w) nor I'(sv) can be large negative numbers. Actual individual magnitudes of I'(al) and cannot be measured experimentally with contact angles alone, but it is of interest to interpret the data in Figure 2 somewhat further with respect to the thermodynamic boundary conditions listed in Table I.

dO/d In C < 0 Condition. All contact angle curves representing data shown in Figure 2 exhibited this condition except those measured for the most wettable surfaces, yielding d8/d In C = 0, as noted in the figure. Qualitative trends in adsorption data can be interpreted in one of three ways: (i) I'(av) = 0 or a constant value for all surfaces, with decreasing [I'(nl) - I'(nv)l, reflecting reduced adsorption to sl interfaces of increasingly wettable surfaces; (ii) l?(nl) = 0 or a constant value for all surfaces, with decreasing [I'(d) - I'(av)l, reflecting increased adsorption to su interfaces of increasingly wettable surfaces; (iii) both I'(sl) and I'(sv) continuously and independently varied over the entire TO range with adsorption to either sl or sv interfaces predominating, depending on the solvent wettability of the surface. Only the third possibility is physically sensible. Options i and ii can be eliminated on thermodynamic grounds because there is no physical rationale that anticipates constant adsorption to sv and sl interfaces for a full range of surface wettability, as outlined in Table I. Only option iii has the intuitive appeal that surface chemistry and energetics control adsorption, and Table I is a statement of the thermodynamic boundary conditions that determine the relative magnitudes of a1 and sv adsorption.

Bearing option iii in mind, the nearly monotonic decrease in [I'u) - I'(nv)l for Tween with increasing T O shown in Figure 2A suggests smoothly decreasing sl adsorption with surface wettability. Starting first with the most hydrophobic surface (Table I1 listing for OTS-glass), it was observed that [I'(sl) - I'(nv)l was larger than I'(lv) (358-317 compared to 216 pmol/cm2). This observation corresponds to the boundaries I'(nl) > + I'(lv)1 or I'(nl) > I'ov) listed in Table I for nonwettable surfaces (see row8 1 and 2 of columns 3 and 4). It seems reasonable to conclude that, under these conditions, sv adsorption must be minimal and [I'(sl) - I'(sv)l = I'(d). To conclude otherwise, unreal- istically high levels of sl adsorption, far greater than that measured at the lv interface, would be required. Accordii to this interpretation, then, adsorption to an organized and presumably closely-packed silane layer at the el interface of OTS-glass surfaces is more structured than at the lv interface, leading to a somewhat higher packing density. This is in agreement with the general expectation from dispersion theory which anticipates a slightly greater level of interaction between solute and a dense solid phase compared to the interaction with a relatively less-dense vapor phase.

Moving to the other test surfaces which were more wettable than OTS-glass (Table I11 under PS and PS oxidized), [I'(d) - qsv,1 were smaller positive values, suggesting decreasing sl adsorption. An adsorption mechanism consistent with this observation has water molecules concentrating within the interface as a function of surface wettability through interaction with putative polar groups on these wettable surfaces, effectively reducing the number

N . 5

400

200

0

-200

t -200 \ l [dB/dlnCl = 0 -& 1

l 1 l I I / l I 1 l 30 -10 10 30 50 70

-40?

hydrophobic hydrophilic + -

dyne/cm

Figure 2. Surface excess parameter [I'(s,) - for Tween/ saline (A) and cetyl bromide/water (B) aa a function of solid surface wettability (full circles, advancing contact angles; open circles, receding contact angles). The horizontal lines through [I'w - = 0 represent the rea, = r(sv) circumstance, above which I'(sl) > r(ov) and below which ro) < qSv).

measurablydifferent,%o that in water. By contrast, cetyl bromide/saline was a very different surfactant system than cetyl bromide/water, particularly with respect to the steepness of the y(lV) curve, as measured with the N(lV) parameter.

Interfacial excess values I'(lv) for both surfactanta were calculated from the linear-like slope region of the y(lv) curves (delineated by vertical lines on Figure 1) using eq 1, as described under Computational Aspects. A greater I'(lv) for cetyl bromide (for both water and saline) indicates that the adsorbed molecular area was smaller than that of Tween, leading to a higher packing in a unit area of interface, as might be expected on the basis of relative molecular weight (378.5 v8 1309.7 g/mol, respectively).

Adsorption to Solid Surfaces. Parta A and B of Figure 2 compares results of surface excess calculations made from concentration-dependent contact angle measurements obtained on glass and polystyrene plaques for Tween/saline and cetyl bromide/water, respectively, plotted as a function of pure solvent surface wettability T O .

Data used in construction of the figure are listed in Table 111, with substrates identified in column 2. Figure 3 is an advancingheceding contact angle curve for Tween that is repreaentative of the kind of data from which [I'(nl) - I'(sv)l values plotted in Figure 2 were calculated. Generally speaking, the data in Figure 2 indicate increasing adsorption of both surfactants to surfaces exhibiting decreasing solvent wettability. More definitive conclusions regarding a functional relationship between adsorption and surface wettability must await a much more complete data set. However, it is interesting that advancing excess values were less than receding for both Tween and cetyl bromide on nearly all surfaces. Possibly, this can be

(13) Vogler, E. A. J. Colloid Interface Sci. 1989,133, 228.

Concentration-Dependent Contact Angles Langmuir, Vol. 8, No. 8, 1992 2011

Table 111. Surfactant Properties of Tween-80 and Cetyl Bromide at Solid-Liquid Interfaces. test materials T O , dvn/cm r', dyn/cm

surfactant system solid sample Tween-80 in saline OTS-glass

PS PS oxidized glass

PS PS oxidized PS oxidized PS oxidized glass

cetyl bromide in HzO OTS-glass

advancing

7.4 f 1.3 23.7 f 0.8 72.8 f 0.2 -18.8 f 1.3 7.4 f 1.6 20.7 t 0.5 28.5 f 1.3 73.0 f 0.8 72.9 f 1.0

-23.9 f 1.5 receding advancing receding -6.6 f 1.1 25.2 f 1.5 40.9 f 0.9 72.8 f 0.2 1.3 f 1.6 22.4 f 1.2 27.6 f 0.3 35.0 f 1.1 70.9 f 2.5 72.9 f 1.0

14.3 f 0.7 29.9 f 1.1 31.4 f 0.6 39.7 f 0.6 13.4 f 1.2 31.4 f 1.2 33.3 f 0.6 36.2 f 1.5 autophobic autophobic

23.0 f 0.5 39.4 f 0.7 38.9 f 0.6 39.7 f 0.6 25.8 f 1.6 34.6 f 0.9 36.0 f 0.6 37.0 f 0.9 37.3 f 1.4 autophobic

[r(d) - r d , pmol/cmZ advancing receding

358.2 f 8.8 157.4 f 17.8 193.3 f 10.9

212.7 f 35.6 367.6 f 45.6 317.3 f 4.1

317.3 f 13.0 173.8 f 22.4 100.2 f 7.4

186.9 f 18.7 118.6 f 40.8 120.5 f 11.3

autophobic -316.8 f 15.9 autophobic autophobic

-212.3 f 5.5 -212.3 f 5.5

-102.7 f 52.6 159.5 f 33.9

a OTS-glass = octadecyltrichlorosilane-treated glass; PS = polystyrene plaque; PS oxidized = plasma-oxidized polystyrene; glass = cleaned and T' and surface excess [r(nl) - r(nv)] was estimated from contact angle glass cover slim (see Materials and Methods). Adhesion tensions

Eurves (see Theory).

80 r

60 - v) Q

Q P

Q F 40 U

6 -

k c, ' \ Q n \

I \ *

0 0 0

o b 1 ! 4 1 1 1 1 " 1 ' 1 8 12 16 20 24

In C (Tween-80 in saline, picomoles/liter) Figure 3. A representative contact angle curve plotting advancing (full circles) and receding (open circles) contact angles as a function of Tween-80 concentration on a logarithmic scale. Smooth curves through the data represent the best fit to the logistic equation. Vertical lines bounding the linear-like portions of the curves represent the range through which surface excess

of adsorption sites for Tween. As discussed previously, ionic interactions with polar surfaces are not expected for this nonionic detergent. Increasing sv adsorption to more wettable surfaces cannot be rigorously eliminated as a possibility accounting for decreasing [I'(sl) - I'(sv)l, but the solvent-concentration mechanism above seems more plausible on chemical grounds, particularly since efforts were made to reduce or eliminate mechanical deposition of solute along the slv line by contact angle droplet vibration or evaporation. Smooth trends in data through the [I'(sl) - l?(ev,l = 0 bisector are also consistent with a single adsorption mechanism. Here, the only alternatives are that rCsl) = r(av) > 0 or r(sl) = r(sv) 0, since I' cannot take on a full range of negative values. The former condition is an unlikely, unique adsorption balance whereas the latter is a plausible result for an adsorption regime where I'(sv) = 0 and I'(sl) smoothly decreases with TO due to solvent displacement.

It is interesting to contrast results for cetyl bromide shown in Figure 2B to those discussed above for Tween. Again, the data set is an inadequate basis on which to draw definitive conclusions, but the general trends are not smooth in appearance as in the Tween case and drop

- I'cnvv,l was calculated.

6o

50 1 I \

II I

, I

0 4 6 12 16 20 24 0-4 ' ' '

In C (cetyl bromide, picomolesiliter) Figure 4. Advancing (full circles) and receding (open circles) contact angles as a function of cetyl bromidetwater solutions on a rigorously cleaned glass surface exhibiting the 'autophobic" or "dewetting" phenomenon of increased angles with added surfactant.

off sharply through the [I'(sl) - I'(sv)l = 0 bisector. Cetyl bromide/water has potential for at least two mechanisms of adsorption, as described previously. These two mechanisms can, in principle, occur simultaneously to a lesser or greater extent, depending on the wettability of the surface. It is reasonable to interpret the data in Figure 2B in terms of a predominately Tween-like adsorption mechanism on OTS-glass and a predominately ion-pairing mechanism on highly oxidized surfaces, with some mixture of mechanisms for surfaces with intermediate wettability. Adsorption in the former regime leads to more wettable surfaces (T' > T O , first four surfaces under cetyl bromide in Table 111) whereas the latter adsorption mechanism leads to less wettable surfaces (T' < P, last two surfaces in Table 111). The sharp transition in the data of Figure 2B is possibly, therefore, associated with an equally sharp transition in the predominance of one adsorption mechanism over another.

d8/d In C = 0 Condition. Tweedsaline exhibits flat 6 = 0 curves for clean, highly wettable glass because contact angle droplets spread completely over these surfaces. As anticipated from Table I, r(ev) = I'(lv) and r(sl) = 0 (row 3 of columns 7 and 8). The physical interpretation is that the interphase is concentrated with water interacting with

2012 Langmuir, Vol. 8, No. 8,1992

polar groups on the solid surface excluding surfactant molecules. For these completely wettable surfaces there is no observable contact angle hysteresis.

Cetyl bromide exhibits d8ld In C = 0 only on the receding mode of the most highly oxidized polystyrene sample listed in Table 111. All other surfaces and, interestingly, the advancing mode on this polystyrene sample exhibit autophobic behavior consistent with an ion-pairing adsorption mechanism.

d6/d In C > 0 Condition. Cetyl bromide was autophobic on wettable glass as shown in the advancing/ receding contact angle curves of Figure 4. The data fitting strategy discussed in the Theory was not applicable to this case, and consequently, f are not listed in Table 111. Increasing contact angles with added surfadant are consistent with I'(sv) 2 I'(lv) (row 5 of columns 7 and 8). The decline in contact angles observed at higher concentrations probably signals formation of adsorbed multilayers by association of nonpolar residues, allowing polar head groups of a forming second adsorbed layer to extend into aqueous solution.9

Vogler

Conclusions

Concentration-dependent contact angles can be interpreted in terms of the Gibbs' adsorption isotherm and applied as a useful, quantitative measure of surfactant adsorption to nonwettable, solid surfaces. In this pursuit, care must be taken to avoid vibration or evaporation of contact angle droplets which can mechanically deposit solute at solid-vapor interfaces and introduce ambiguity in the interpretation of the [I'ca1) - I'(sv)l parameter in terms of sl adsorption.

Acknowledgment. I am indebted to Dr. R. E. Johnson, Professor P. Kilpatrick, and Mr. D. A. Martin for many helpful discussions. Dr. D. B. Montgomery kindly provided the plasma apparatus for surface oxidations. The expert technical assistance of Ms. J. Graper and Mr. H. W. Sugg is gratefully acknowledged.

Appendix

Estimation of Uncertainty. The error in Y values calculated from the logistic equation (eq 4) was estimated by propagating the error in fitted parameters A and D into Y and assuming that the error in Y was uniform over X. Thus, uncertainty in Y could be conveniently evaluated at X = K where eq 4 simplifies to Y = (A + D)/2, yielding

0; = a,2/4 + 4D2/4 (AI)

The error in slope values S 1 (Y2 - Y1)/(X2- XI) = AY/AX was estimated by assuming that the error in A was a good measure of the error in Y2 and that the error in D was a good measure of the error in Y1, so that ab9 U A ~ + U D ~ . It follows that

6: = (b: + no2)/ AX2 (A21

if the error in AX is insignificant. Equations A1 and A2 can be used directly in the estimation of the error in I'(lv) from y(lv) curves and [I'(sl) - from r curves, but propagation of the error through eq 3 leads to a more complicated formulation. Using the notation 8 to sym- bolize the slope of a 8 curve (rad) and Ar [I'(al) - I'(sv)l, propagation of the error into AI' leads to

u ~ : = [[ye/RTJ cos 8 + sin 8I'l2u; + (y sin 8/RZ"12a: + (COS 8)2U,2 + (sin 8e/RT)2a,2 (A3)

where y y(lv), I' r(lv), and the corresponding u terms are calculated from eqs A1 and A2, respectively.

The error in y(lv) and 8 does not propagate linearly into "synthetic" r values, but instead leads to eq A4 which is not linear with concentration due to y(lV) and 8 terms. The y(lv) sin 8 term predominates for nonwettable surfaces, and plots of u7 against log concentration have the general shape of y(lV) curves.

~ , 2 = (cos 8)2a,2 + (y sin e)%: (A41

Example Calculations. The following examples il- lustrate parameterization of tension and contact angle curves and calculation of surface excess for Tween-80 solutions in contact with a plasma-treated polystyrene sample (see row 3 of Table 111). Measured interfacial tensions y(lv) of 24 saline solutions of Tween-80 ranging in concentration from 1 to 24 ppt (wt/wt) were plotted against concentration expressed in picomoles per liter on a logarithmic scale, yielding the tension curve shown in Figure 1. Nonlinear least-squares fitting to eq 4 yielded fitted parameters and standard errors of the fit listed in Table I (row 1). Using these coefficients, smoothed values for y(lV) can be calculated from eq 4 at any X, which is useful in calculation of both lv and sl adsorption. The second derivative of the smooth curve identified low- and high-concentration inflections XI = 12.9 and Xz = 16.5 (dimensionless). From the fitted coefficients in Table I, corresponding Y values were calculated from eq 4 to be Y1 = 67.3 and Y2 = 48.30 dyn/cm, respectively, yielding a slope S = (48.30 - 67.31)/(16.5 - 12.9) = -5.28 dyn/cm (equivalently erg/cm2). Dividing S by -RT = -(8.31 X 107 erg/(K-mo1)(298.15 K) yields I'(lv) = 212.3 pmol/cm2. Using the standard error of the fit for yo(lv) and y'(lV) (0.24 and 0.43 dyn/cm from row 1 of columns 1 and 2 of Table 11) as estimates for UA and UD, the error in S from eq A2 us = [(0.242 + 0.432)/(16.5 - 12.9)211/2 = 0.14 dyn/cm or 5.5 pmol/cm2 by division by RT.

Advancing and receding 8 measurements were made for the Tween solutions above and plotted against logarithmic concentration, yielding the contact angle curves shown in Figure 3. Fitting data to eq 4 for the advancing curve gave the following characteristic parameters and error estimates: do = 71.0 f 0.6', 8' = 37.8 f LOo, K = 16.5 f 0.2, and N = -18.3 f 2.8. In a fashion identical to that described above, inflections in the 8 curve were located at X I = 15.2 and XZ = 17.6, yielding a slope and calculated uncertainty of S = -8.08 f 0.24' = -0.141 f 0.004 rad. Equation 3 is implement using the slope S = d8/d In C. Values for 8 and sin 8 were determined from the characteristic parameters in the fitted function [41 evaluated at X = K OK = (8' + 8')/2 = (71.0 + 37.8)/2 = 54.4, sin OK = 0.81, and COS OK = 0.58. The required term y(lv) was calculated from eq 4 with the lv fitted values at X = K = 16.5 by y(lv) = 72.8 - 40.0)/[1+ (14.9/16.5)-10.91 + 40.0 = 48.1 dyn/cm. Using I'(lv) = 212.3 pmol/cm2 determined as described above, eq 3 could be evaluated for [I'(sl) - I'(sv)l = [-[y(lv) sin el/ RTI[dO/d In Cl + r(lv) cos 8 = [-48.1(0.81)/(8.31 x 107)(298.15)l[-0.141 + (212.3 X 10-12)(0.58) = 100.2 pmol/ cm2. This is the value reported in Table I11 (row 3 of column 5). Uncertainty in [rCsl) - I'(sv)l is calculated from eq A3 using these individual values. Registry No. Polystyrene, 9003-53-6; Tween 80,9005-65-6;

cetylethyldimethylammonium bromide, 124-03-8; octadecyltrichlorosilane, 112-04-9.

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Practical use of concentration-dependent contact angles as a measure of solid-liquid adsorption. 1. Theoretical aspects