Ind. Eng. Chem. Res. 2009, 48, 2387–2394
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Competitive Coadsorption Dynamics in Surfactant-Copolymer Formulations Pazit Bar-Yosef Ofir, Bogdan Zdyrko, and Maria M. Santore* Department of Polymer Science and Engineering, UniVeristy of Massachusetts, 120 GoVernors DriVe, Amherst, Massachusetts 01003
The adsorption of surfactant copolymer mixtures can be complicated by interfacial competition between different components. Using a commercial formulation, Silwet L-720, based on a silicone-poly(ethylene oxide)-poly(propylene oxide) graft copolymer, this work demonstrates how one can determine the adsorption of different populations within a sample by comparing their behaviors on different surfaces. We discovered that on hydrophilic silica, the L-720 formulation appeared to adsorb strongly and quickly in a transportlimited fashion, which is the maximum possible. Surprisingly, however, adsorption was more rapid still on a model hydrophobic surface (C16 self-assembled monolayer), suggesting that only one or two populations within the formulation were actually able to adsorb onto silica. A quantitative analysis revealed the fraction able to adsorb on silica to be quite low, less than 50% of the overall formulation. Furthermore, adsorption of the same material on the hydrophobic surface produced stepwise kinetic traces, a signature of a sample in which distinctly different components adsorbed cocompetitively: Once the surface appeared saturated to a particular constituent, it stopped adsorbing and was displaced by other compounds within the formulation that continued to adsorb, up to surface saturation. Introduction While fundamental studies of adsorbed polymer layers employ samples of relatively high purity that are well-characterized, a large body of applications that exploit polymer adsorption rely on commercial-grade materials which, for reasons of practicality or economy, may be highly polydisperse or contain multiple polymer fractions. As a result, both equilibrium and dynamic layer properties are complicated by competition between different species within a sample. This competition can produce qualitatively different adsorption behavior compared with that of samples of high purity and low polydispersity. In the case of classical polydispersity of adsorbing homopolymers, long chains are thermodynamically preferred on the surface compared to shorter ones.1,2 As a result, samples that contain a range of chain lengths exhibit the well-known signature of rounded adsorption isotherms, as short and long fractions compete for surface area. With polydisperse homopolymers adsorbing onto an attractive surface, the adsorption kinetics also tend to be rounded compared with narrow molecular weight samples of the same polymer.3,4 It has been shown with bimodal mixed samples containing well-defined populations of short and long chains5-7 that, when the adsorbing surface is relatively empty, all fractions within a polydisperse sample tend to adsorb. When the surface becomes crowded, a dynamic competition, in which long chains replace short ones as the interfacial mass continues to accumulate, causes the adsorption to slow, producing unusually shaped kinetic traces. If one extrapolates the bimodal kinetics to a polydisperse continuum, the result is rounded kinetic traces. In addition to competition driven by differences in molecular weight, there are other possible bases for diversity in a polymer sample.8,9 For instance, random A-B copolymers potentially present a compositional spectrum that could drive competitive adsorption. This type of competition would be entirely separate from chain length polydispersity, which might also be present. Further, for block copolymers, compositional variations, that * To whom correspondence should be addressed. E-mail: Santore@ mail.pse.umass.edu.
is, differences in the lengths of the individual blocks, may be as important as variations in the overall chain length.10,11 Then, depending on the particular surface, solvent, polymer chemistry, and polymer architecture, some population within the sample may be thermodynamically preferred on the surface: At equilibrium, the surface composition would differ from that in the solution. An understanding of this effect and the time scales on which it occurs are important to successful application. Surface domination by the less desired species within a mixture can cause applications to fail via “interfacial malfunction”, including, but not limited to, colloidal destabilization. To illustrate the complexities that can arise during the adsorption of multicomponent copolymer formulations, the current paper examines the adsorption behavior of a commercial graft copolymer formulation, Silwet L-720, from GE Polymers. The advertised component of the formation is a graft copolymer with a polydimethyl (PDMS) backbone, which is highly hydrophobic. The side chains are water-soluble random copolymers of poly(ethylene oxide) (PEO) and poly(propylene oxide) (PPO). The formulation also contains substantial amounts of the sidearm chains that have not been attached to the PDMS backbone. In general, this class of polymers (PDMS-PEO/PPO graft copolymers) are employed as wetting agents, antifoaming or foam-control compounds, and surface modifiers. L-720 appears as an ingredient in diverse situations: foam-manufacturing processes (e.g., cushions),12 ink-jet printing ink formulations,13 hair conditioner,14 coatings for medical diagnostic elements,15,16 and biological assays.17 Of note, copolymers containing PDMS hydrophobic blocks distinguish themselves from a host of other copolymers because of the low glass transition temperature of the PDMS, which imparts unusually high mobility to the backbone, in terms of its segmental motions. With PEO also having a low Tg, PDMS-PEO copolymers find a market as “superspreaders”,18-21 whose character as wetting aids goes beyond that of more conventional surfactant formulations. As scientific attention to these copolymers has focused on wetting and spreading18-21 rather than adsorption fundamentals, there are limited reports of PDMS-PEO copolymer adsorption in the
10.1021/ie800791h CCC: $40.75 2009 American Chemical Society Published on Web 09/18/2008
2388 Ind. Eng. Chem. Res., Vol. 48, No. 5, 2009 Table 1. L-720 and Its Components DLS molecular weight L-720 50-HB-260 50-HB-2000 50-HB-5100
graft copolymer with PEO-PPO random copolymers 50-50 PEO/PPO random copolymer 50-50 PEO/PPO random copolymer 50-50 PEO/PPO random copolymer
graft component: 20000 260 g/mol 2000 g/mol 5100 g/mol
literature.22-24 More recently, with a series of commercial PEO-PDMS copolymers, we reported that beyond micelle formation and adsorption, large dense aggregates exist in solution and dominate adsorption in ways that are highly substrate-dependent.25 In some instances, competitive adsorption between aggregates and smaller species in solution was reported; however, this competition represented a dynamic behavior rather than one of compositional variations: The aggregates potentially contained the same species that were also present in the form of micelles in some of the samples. The current contribution focuses on the competitive adsorption between chemically distinct components within L-720: The main graft copolymer with its extremely hydrophobic backbone and excess unattached sidearm chains. The work will show how, for adsorption on model hydrophilic and hydrophobic surfaces, the surface composition evolves in time with continued surface exposure to this polymer/surfactant mixture. The results suggest that some species within the formulation can be readily displaced from the surface, while others simply do not adsorb. In applications, it therefore can become a challenge to ensure that the desired component goes to the interface in the right amount and that any nonadsorbing species do not cause problems in the bulk phase or at other surfaces that are later encountered. This paper demonstrates how, without sophisticated labeling methods, one can infer the competitive adsorption behavior of different components by comparison of the adsorption on surfaces of two chemistries. Experimental Details Silwet L720 and three PEO-PPO random copolymers were provided by Bectin Dickinson (Table 1). The “primary” component of L-720 (as suggested by its classification as a silicone surfactant) is a graft copolymer with an average molecular weight of 20 000. Its backbone is PDMS and its side arms are random copolymers of PEO and PPO, with 50 mol % proportions. As we argue below, the side arms likely are comprised of three distinct molecular weight fractions which, according to the MSDS, are also present as free linear chains in the formulation. Indeed, the amount of free PEO-PPO copolymer is disclosed as being between 30 and 60% of the formulation. In this work, we consider the possibility that the average molecular weights of the three copolymer fractions are 260, 2000, and 5100 (corresponding, on average, to three degrees of polymerization: 5, 30, and 100). Our study focused on the three random PEO-PPO polymer surfactants in Table 1, in addition to the L-720 formulation itself. The graft copolymer in pure form was not available for study. The L-720 and polymer surfactants in Table 1 were used without further purification. These were dissolved in pH 7.4 phosphate buffer, 0.008 M Na2HPO4, and 0.002 M KH2PO4, from Fisher. The model substrates, acid-washed silica and C16 selfassembled monolayers on glass, were chosen to represent extremes in hydrophobicity. Silica surfaces were produced by soaking microscope slides (Fisher Finest) overnight in concen-
D, cm2/s 1.1 3.3 3.3 3.3 2.8
× × × × ×
10-7 10-6 10-6 10-6 10-6
calcd Rh, nm
D, cm2/s
Rh, nm
22 (and 0.74) 0.75 0.75 0.89
4.5 × 10-6 1.6 × 10-6 1.0 × 10-6
0.55 1.52 2.43
trated sulfuric acid. Exposure to concentrated sulfuric acid has been shown to leach sodium and other metal ions from the surface, leaving a surface region of pure silica, on the order of 10 nm thick.26 C16 monolayers were formed on microscope slides that had been immersed in piranha solution (30% of 30% hydrogen peroxide and 70% of concentrated sulfuric acid 98%, both from Fisher Scientific) for 30 min. Following the piranha treatment, slides were rinsed repeatedly with DI water and dried under nitrogen. Slides were then immediately immersed in 0.4% (v/ v) trichlorohexadecylsilane (Gelest) in dry toluene (Fisher, water content less than 0.03%) for 4 h at room temperature. Slides were then rinsed three times with toluene and sonicated for 5 min in toluene. The slides were next heated for 10 min at 120 °C. Contact angle was employed to assess the surface quality. Samples having advancing contact angles of 105°-110°, measured on a Kruss DSA10 goniometer (analyzed via pendant drop shape analysis), were used for adsorption studies. Adsorption was measured in real time using a home-built near-Brewster reflectometer, operating in back-reflection mode.26 A parallel-polarized 633 nm HeNe laser was brought to the test interface through the back of the substrate microscope slide, guided by a triangular prism. The intensity of the back-reflected beam, which vanishes at the Brewster angle for a perfect interface, increases with the adsorbed amount. The interfacial mass for each point in time was determined from a two-layer optical model,26 which includes the leached silica layer on the outer surface of the microscope slide along with the C16 layer of the hydrophobic sample. An important feature of the experiment was the use of a laminar slit shear cell through which the adsorbate solution was pumped to give a wall shear rate of 5 s-1: The microscope slide carrying the test surface, comprising one wall of the test chamber, was clamped against a black Teflon block containing a rectangular trough, to make the flow chamber. Dynamic light scattering (DLS) was conducted on an instrument that employed a 514.4 nm Lexel 95 8 W argon ion laser. A Brookhaven Instruments photomultiplier detector (in photon counting mode) was aligned, through a 200 µm pinhole aperture, at 90° to the incident beam. Time-dependent intensity fluctuation data were correlated with a BI 9000AT digital correlator (Brookhaven Instruments) over a delay range from 25 ns to 100 ms (using 342 channels plus four extended channels). The autocorrelation function was analyzed using a non-negatively constrained least-squares method (regularized CONTIN) over a particle size range from 1 nm to 10 µm. Results In addition to nominal information about molecular weights of the four copolymer surfactants, Table 1 contains measurements (via DLS) and calculated estimates of sizes and diffusivities for the different species. The calculated estimates of Rh, the hydrodynamic radius, for the three 50-HB copolymers followed a few key assumptions: (A) Though the three copolymer surfactants actually contained two segment types, we treated each backbone as containing a single type of segment whose molecular weight
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Figure 1. Adsorption of L-720 formulation on (A) silica and (B) a C16 self-assembled monolayers. Concentrations are indicated in ppm.
was the averaged of that of PEO and PPO (51 g/mol) and whose length, l, was 0.3 nm, slightly larger than the value of 0.29 nm reported for PEO. (B) Rg, the radius of gyration, was calculated from N1/2l/6, neglecting excluded volume. Here N is the number of statistical segments. Then, Rh was estimated from the relation Rh ) 0.676Rg for a nondraining coil.27 The calculated diffusivity followed from the Stokes-Einstein relationship. Dynamic light scattering measurements of the three copolymer surfactants were difficult because these solutions did not scatter much light. Quantifiable scattering signal from the 50HB series could not be obtained for concentrations below 3000 ppm, the range of experimental interest. At higher concentrations, unimolecular species were dominant in all three samples with sizes in the range of 1-2 nm, pushing the limit of instrumental resolution and motivating the calculated estimates as a check. We conclude that these copolymers do not form micelles or aggregates in aqueous solution and are present as individual molecules of low molecular weight. (Hence, the adsorption study at concentrations from 10 to 2000 ppm would see the same single molecular species that were present at the higher concentrations of 3000 ppm via DLS.) The lack of scattering micelles in the 50-HB series is consistent with the lack of surface activity of these compounds: They failed to reduce the surface tension of water by more than 5 D/cm, even for concentrations as high as 2000 ppm. The L-720 formulation itself did scatter light and was seen to contain a polydisperse species ∼22 nm in size over a broad range of concentrations, signaling the presence of micelles and aggregates. Additionally, when the sample concentration was 3000 ppm, we could resolve a second peak between 1 and 2 nm, consistent with the presence of 50-HB-200, 50-HB-2000, and/or 50-HB-5100. The aggregates and micelles in this formulation are consistent with the strongly hydrophobic nature of the PDMS backbone.25 Adsorption Data. Figure 1 shows a series of kinetic adsorption traces for the L-720 formulation at different concentrations. Part A shows the adsorption traces on silica while
part B shows the kinetics on C16 SAMs. On the silica surfaces, the adsorption appears unremarkable. The adsorbed amounts are nearly linear in time up to the point of surface saturation for each concentration, and the shoulders that occur as the surface saturates are relatively sharp. The subsequent plateaus in coverage are also relatively flat with only a very small gradual increase as a result of extremely slow incorporation of the final molecules into the adsorbed layer. Indeed, one might expect more rounded kinetic traces for polydisperse or multicomponent samples, were there dynamic exchange between molecular weight fractions or between chemically different constituents. The dynamic traces on silica therefore suggest that either (1) only one component of the multicomponent formulation actually adsorbs or (2) if multiple species adsorb, they both adsorb simultaneously to the point of surface saturation and they do not exhibit a competitive exchange process, in which the preferred species displaces the more weakly adsorbing component as the surface saturates. This latter situation can only occur if multiple adsorbing species are sufficiently strongly bound that they are kinetically trapped. At equilibrium, even a modest surface preference for one component of a mixture tends to produce surfaces whose adsorbed layers are dominated by the most strongly binding species. (This is the case even when the strongly binding species is not dominant in solution.) Though the layers resist rinsing in buffer (whose injection is indicated by the arrows), the binding is still reversible. Therefore, we consider scenario 2 highly unlikely. The adsorption traces on the C16 surfaces in Figure 1B are more interesting and would even perhaps appear puzzling without our preamble concerning dynamic competitive coadsorption. Both the adsorption rates and adsorbed amounts increase with bulk solution concentration, as was the case with silica. Here, however, the adsorption kinetics exhibit fast and slow steps: The adsorption is initially quite rapid. Then, following a relatively sharp shoulder that appears at coverages near 0.3 mg/m2, the adsorption slows dramatically. Most remarkably, however, the adsorption rate later increases again (spontaneously!), establishing a second linear adsorption regime, albeit slower than the initial adsorption rate. A second relatively sharp shoulder is followed by a gradual continued increase that persists for some time. The plots in Figure 1B truncate this slow increase with the injection of flowing buffer. Much like the situation on silica, the adsorbed layers are retained in flowing buffer, indicating strong adsorption. The unusual kinetic signature is most pronounced in dilute solutions, but scrutinization of the adsorption traces in the inset suggest that the signature persists at high bulk solution concentrations. It is worth emphasizing that the apparent spontaneous acceleration in adsorption, following the slow kinetics but before the second shoulder, is unusual and potentially challenging to explain. We have, however, reported similar signatures for competitive adsorption of homopolymers.5,6 To decipher the L-720 adsorption, we measured adsorption kinetics for all three samples of the 50-HB series on both surfaces over a full range of bulk solution concentrations from 10 to 2000 ppm. Figure 2 presents a typical example for 50HB-2000 adsorbing on silica. The shapes of these adsorption traces resemble those of all three surfactants adsorbing on both surfaces (not included here). Features common to all the 50HB series adsorption runs were (1) a low ultimate coverage, 0.3 mg/m2 or less; (2) adsorption kinetics that were fast relative to those of the L-720, consistent with the lower molecular weight and faster diffusivities of the 50-HB series; and (3) a substantial
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Figure 2. Adsorption of 50-HB-2000 on silica.
Figure 4. Direct comparison of L-720 adsorption kinetics on silica and C16 surfaces.
Figure 3. Adsorbed amounts (“isotherms”) on (A) silica and (B) C16 SAM.
rinsing effect, with up to 50% of the adsorbed mass washing quickly from the surface. Certain features specific to particular polymer-surfactant/ substrate pairs are worth mentioning: First, there was no adsorption of the 50-HB-260 copolymer surfactant on silica for bulk solution concentrations of 2000 ppm or less. The 50-HB2000 surfactant adsorbing on silica in Figure 2 shows the most dramatic concentration dependence of the six combinations of surfactant/substrate pairs studied. At 50 ppm, the 50-HB-2000 adsorbs negligibly, but the adsorbed amount increases with free solution concentrations between 100 and 1000 ppm. This concentration dependence suggests binding is only of modest strength. By contrast, the 50-HB-5100 surfactant adsorbing on silica exhibited coverages near 0.25-0.3 mg/m2 for the full range of concentrations studied from 20 to 2000 ppm. Also, for all three copolymers adsorbing on the C16 surface, the coverage levels were generally between 0.2 and 0.3 mg/m2. These features are summarized in Figure 3 (which we hesitantly refer to as containing “adsorption isotherms,” as we do not necessarily mean to imply thermodynamic equilibrium). From
these data it is clear that the random copolymer surfactants bind more strongly to C16 surfaces than to silica. The weaker binding on silica is borne out by the lack of 50-HB-260 adsorption and the rounded “isotherm” for 50-HB-2000. Only once the molecular weight is reasonably high (5100) are there enough segment-surface contacts to produce enough binding energy per chain to produce substantial chain retention on the surface. Figure 3 also contains the ultimate adsorbed amounts of the full L-720 formulation on both surfaces: L-720 exhibits an order of magnitude higher coverage than the copolymer surfactants. From this we conclude that the graft copolymer, with its hydrophobic PDMS backbone, is responsible for the higher coverages seen with the L-720 formulation compared with the behavior of the copolymer surfactants comprising the side arms. The graft copolymer seems to dominate both surfaces, at least in terms of the adsorbed amount at long times. Consistent with this observation, we previously reported substantial adsorption of lower molecular weight PDMS-PEO graft copolymers on a silica and C16 surfaces.25 Figure 4 plots kinetic L-720 adsorption data from Figure 1 in a manner that allows more direct comparison of adsorption kinetics on silica and C16 surfaces. The concentrations of 20 and 100 ppm have been chosen because they most clearly illustrate the initial adsorption rates (slopes, especially of the linear regions of the traces) and, as we will show below, the slopes of these traces tend to be dominated by diffusion in a pseudo-steady-state manner (that is, with a well-defined masstransport coefficient). In Figure 4 it is clear initially that the adsorption on the C16 surface (slope 1) is faster than that on the silica. When adsorption on the C16 surface slows (slope 2), it becomes slower than on silica. Then, when the adsorption spontaneously accelerates, its rate (slope 3) again becomes faster than that on silica, but not as fast as the initial rate. Then, following the second shoulder for the data on the C16 surface, the adsorption approaches its final state at a slower rate.
Ind. Eng. Chem. Res., Vol. 48, No. 5, 2009 2391
Figure 5. Adsorption rates used in analysis (A) as a function of L-720 concentration, (B) close-up at low concentrations, and (C) as a function of wall shear rate to the 1/3 power on silica.
Interpretation. The shapes of the kinetic adsorption traces on C16 surface suggest that there exist distinct “fractions” within the L-720 sample, rather than a continuum of chain lengths, architectures, or chemical compositions. There still may be much polydispersity within each fraction, but the fractions themselves are qualitatively different in their adsorption behavior, producing stepwise adsorption traces rather than a single rounded trace with a monotonically decaying slope. By process of elimination, we can deduce (as explained below), that the L-720 sample contains, in addition to its primary graft-architecture constituent, three fractions of more weakly adsorbing polymer of substantially lower molecular weight than the graft polymer, and also not having the tendency for aggregation and micellization exhibited by the PDMS-containing graft chains. In order to make this interpretation quantitative, we establish, in Figure 5, that the adsorption rate on silica, and portions of the adsorption traces on C16 surfaces (in the concentration range 20-100 ppm) follow pseudo-steady-state transport limited kinetics (the fastest possible in this particular flow geometry): 1 γ dΓ ) dt Γ(4/3)91/3 DL
1⁄3
( )
DC
(1)
Here dΓ/dt represents the rate (slope) of the adsorption traces or portions thereof, C represents the bulk solution concentration,
γ is the wall shear rate, L is the distance from the entrance of the flow cell to the point of the observation, and on the righthand side (here and only here), Γ represents the gamma function evaluated at an argument of 4/3. D is a bulk solution diffusion coefficient, and for polydisperse or bimodal systems, it can be a weighted average. Likewise, for situations where multiple species adsorb at the transport-limited rate, eq 1 can be applied to each species independently. Equation 1 was derived by Leveque28 for mass transfer-limited adsorption in a laminar slit flow chamber such as that in the current study: Flow in a channel of rectangular cross section is parallel to the adsorbing surface and the only relevant diffusion term is normal to the surface. Additionally, eq 1 applies only at pseudo-steady state, when the concentration profile near the interface does not change with time, thus producing a constant adsorption rate. This occurs when the surface capacity is sufficiently large and the bulk solution concentration sufficiently small that the concentration profile has time to be established, as described quantitatively by Lok et al.29 Adsorption on Silica. Figure 5A,B shows the initial slopes of the kinetic traces as a function of bulk solution concentration, while Figure 5C considers the effects of flow rate on the adsorption rate of L-720 on silica. In Figure 5A, the L-720 adsorption rate on silica is linear in concentration over nearly the full range of concentrations studied, suggesting that adsorption is indeed pseudo-steady-state transport-limited, per eq 1. Further in Figure 5C, the adsorption kinetics of L-720 on silica conform to the wall shear rate to the 1/3 power scaling of eq 1, further supporting that pseudo-steady-state transport-limited kinetics hold. As the transport-limited adsorption rate (as seen on silica) is the maximum possible, it seems contradictory that the same solution adsorbs more rapidly on C16 surfaces than on silica in the dilute limit, in Figures 4 and 5B. The explanation, taking into account the multicomponent nature of the L-720 formation, becomes obvious: Some components within L-720 adsorb on silica at the transport-limited rate, while the rest do not adsorb at all. The isotherms of Figure 3 established that low molecular weight compounds such as the 50-HB-260 surfactant do not adsorb on silica. Indeed, with an overall L-720 concentration of 20 ppm, the intermediate molecular weight surfactant, 50HB-2000, will not adsorb either. At an overall concentration of 100 ppm, 50-HB-2000 will adsorb on silica only if it comprises more that 50 ppm of the overall concentration. On silica, then, the graft copolymer is the only component sure to adsorb. In addition, the highest molecular weight random copolymer, 50HB-5100, might adsorb. The other components are sure not to adsorb. (Indeed examination of the adsorption behavior on the C16 surface further leads to the conclusion that the 50-HB5100 adsorbs negligibly on silica in the dilute regime.) It is interesting to consider what mass fraction of the L-720 is actually capable of adsorbing on silica. This is presumably the PDMS-containing graft copolymer along with any HB-5100: The material safety data sheet (MSDS) states the graft copolymer comprises anywhere from 30-60% of the total formulation. We applied eq 1 to the initial slopes of the adsorption traces of L720 on silica, now letting the concentration, C, be the actual concentration of the graft copolymer in the mixture, rather than the total concentration that was weighed out when the solutions were made. We found that graft copolymer weight fractions from 0.25 to 0.40 closed eq 1 when the bulk solution diffusivity was set to be within a factor of 2 for that measured by dynamic light scattering [(0.5-1) × 10-7 cm2/s, for the 22 nm species attributed to the graft species aggregates]. (We note, for example,
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that a diffusivity of 2 × 10-7 cm2/s corresponds to only 10 wt % graft copolymer in the formulation, which contradicts the MSDS, so our estimates included some possible error in the diffusivity that went in the other direction, to be consistent with the constraints on the MSDS.) While this calculation is intended only as an estimate of the L-720 composition, the error bars are sufficiently tight for us to be sure that the graft copolymer (along with any HB-5100 that also adsorbs) comprises less than half (by weight) of the overall formulation, consistent with the MSDS. The adsorption and light scattering data suggest the actual concentration of the graft copolymer lies at the lower limit of that reported on the MSDS. Adsorption on C16. Figure 4 clearly shows that two regimes of L-720 adsorption on the C16 surface proceed more rapidly than on silica. This means that there are two distinct fractions, in addition to the graft copolymer, that adsorb on the C16 surface. The first linear regime in Figure 4 has the greatest slope because the bare surface receives each adsorbing species at its own diffusion-limited rate, a concept established for competitive homopolymer adsorption.5,6,8 Once the surface appears full to one of the adsorbing fractions (here near 0.25-0.3 mg/m2), that fraction stops adsorbing. The reduced slope beyond this point results from the continued adsorption of the remaining species. In the case of L-720, the reduced slope is dramatically slow: less than transport-limited adsorption of the graft component on silica. This large reduction in net adsorption rate can only be explained by a scenario in which the species that stopped adsorbing near a total coverage of 0.3 mg/m2 is now displaced as other fractions continue to adsorb. This is the dynamic exchange portion of the competitive coadsorption process. Once the less favored species has completely been displaced from the surface, the remaining species continue their adsorption at the same rate. This produces the appearance of accelerated adsorption, now without desorption to detract from the magnitude of the total signal. The second linear adsorption regime (slope 3 on C16) also has a slope greater than the transportlimited rate on silica. This indicates multicomponent adsorption on C16 at coverages from 0.3 to 1.4 mg/m2, up to another shoulder. The second shoulder occurs when the surface appears saturated to the next species, and so on. This process is illustrated schematically in Figure 6. Our ability to estimate the bulk solution concentrations of the species adsorbing on the C16 surface depends on the extent to which the adsorption of each is mass transport-limited and described by the pseudo-steady-state physics in eq 1. That the graft-containing aggregates adsorb on C16 via eq 1, as they did on silica, is a near certainty. The argument is slightly more difficult to make for the lower molecular weight components, because their pure-solution surface saturation levels are so low. Figure 5A indicates break down of pseudosteady state conditions above 100 ppm L720 for the first and third slopes on the C16 surface. We therefore present the quantitative analysis for the 20 ppm data and for two additional runs at 5 ppm (not shown) on a C16 SAM. The breakdown of pseudo-steady-state conditions29 at the higher concentrations leads to quantitative deviation from our calculations, though the same mechanism qualitatively applies at higher bulk solution concentrations. The calculations that employ eq 1 to estimate the L720 composition may, however, have a slightly reduced value for dΓ/dt (by no more than 2 times), which would underestimate the amount of the component of interest (by no more than 2 times). First, by application of eq 1 to the differences between the initial slope (slope 1) on C16 and on silica, we can calculate
Figure 6. Competitive coadsorption dynamics: The C16 trace represents the evolution of the total adsorbed amount. The behaviors of the 50-HB2000 and 50-HB-5100 are drawn in. The adsorption on silica represents the transport-limited behavior of the graft component only. At short times on the C16 surface (1), three species adsorb independently. Then in the first exchange region (region 2), still on the C216 surface, the 50HB-2000 is displaced as the graft component and the 50-HB-5100 continues to adsorb. The exchange time (region 2) ends when all the 50-HB-2000 has been displaced. In region 3, the graft copolymer and the 50-HB-5100 continue to adsorb at the same rate as they did in region 2. The slope in region 3 is greater than in region 2, because region 2 reflects both adsorption and desorption. The slope in region 3 is greater than that on silica because 50HB-5100 apparently does not adsorb significantly onto silica at these concentrations, a conclusion that is not apparent from the silica data alone. A second exchange region near the end of the run occurs as the graft copolymer slowly displaces the 50-HB-5100.
the approximate total concentration of the two additional species adsorbing initially on C16 surface: γ dΓ 1 dΓ ) dt C16-slope1 dt silica Γ(4/3)91/3 L
1/3
()
¯ 2⁄3(Csurf1 + Csurf2) D (2)
j is an average diffusion coefficient, describing the two Here D additional adsorbing species: D ) (xsurf1Dsurf12/3 + (1 - xsurf1)Dsurf22/3)1.5
(3)
In our application of eq 2 to the 20 ppm data of Figure 4, we considered the possibility that both the 50-HB2000 and 50-HB5100 would initially adsorb on the C16 surface (in addition to the graft component). We also considered the full relative range (xsurf 1 ) 0-1) of proportions of these two surfactants in the average weighted free solution diffusion coefficient based on the pure component values in Table 1. (The error in distinguishing the proportions of the two is, at this point, large because their diffusivities in Table 1 are very similar.) Regardless of the wide possible range of relative proportions of the 50-HB2000 and 50-HB-5100, only one fact mattered: The species that adsorb on the C16 surface but are rejected by the silica surface are orders of magnitude smaller than the species adsorbing on silica. As a result, we arrive at the result that the combined concentrations of the two “lesser” species that adsorb initially on the C16 surface (in addition to the graft copolymer) together comprise only 10-15 wt % of the total L-720 formulation. If we further account for the possibility that the values of slope 1 on the C16 surface might be, in the worst case, a factor of 2 smaller than they would be at true pseudo-steady state, we arrive at 30 wt % for the maximum combined amounts of 50-HB2000 and 50-HB-5100 that could be present in solution. With a maximum amount of graft copolymer comprising 40 wt % solution, we conclude that the L-720 contains 30 wt % (a lower bound) of species that do not adsorb appreciably to either silica or hydrophobic C16 SAM. This nonadsorbing fraction might be as large as 50 wt %. It is worth noting that, if the graft copolymer plus the three random copolymers were all to adsorb onto the C16 surface, then closure of the transport equations
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would require a fourth nonadsorbing unknown diluent within the formulation. The final question then is, what is the proportion of the two random copolymer species that do adsorb (reversibly) on the C16 surface (in addition to the graft copolymer)? To determine this, we apply eq 1 to the difference in the two main slopes of the C16 adsorption trace. The quantitative analysis is done only for the 5 and 20 ppm data, because of the likelihood that these data conform mostly closely to pseudo-steady-state adsorption dynamics. Here, employing a diffusivity in the range of (3-4) × 10-6 cm2/s for 50-HB-5100, one concludes that its free concentration is low, on the order of 0.5-3 wt % of the total L-720 formulation. Summary and Implications. This work has demonstrated how the particular formulation, Silwet L-720, contains multiple copolymer surfactant fractions that exhibit distinctly different adsorption behavior on model hydrophobic and hydrophilic surfaces. The lack of adsorption of some components and the competitive dynamic coadsorption of the others leads to adsorption traces that are counterintuitive. On the model hydrophilic surface, silica, only the main PDMS-containing graft copolymer element adsorbs, and its does so at its transportlimited rate over a broad range of concentrations. This PDMS graft copolymer was, however, found to make up only about 25-45 wt % of the L-720 formulation, with the remaining formulation acting as an inert diluent from the perspective of adsorption on hydrophilic surfaces. On the hydrophobic surface, three distinct fractions coadsorbed competitively (the two higher molecular weight random copolymers and the graft copolymer), but still roughly 25-50% of the sample by weight did not adsorb appreciably. Of the adsorbing species, all adsorbed nearly at their diffusion-limited rates up to the point where the surface appeared saturated to the most weakly binding of the three. This most weakly binding species (likely to be similar to the 50-HB-2000) was then displaced as the other two species continued to adsorb. This caused the net adsorption rate to decrease dramatically. Once the surface contained only the two more strongly adsorbing species, there was no more possibility for displacement and adsorption proceeded until the next most weakly binding species was saturated at the mixed interface. The adsorption then slowly approached its final coverage. Using estimates of the sizes of the adsorbing species from dynamic light scattering and calculations, it was found that the small adsorbing species (50HB-2000 and 50-HB-5100) were present in relatively small amounts, not more than 30 wt %. This level might be consistent with a fraction that failed to attach to the PDMS backbone of the graft constituent and was not removed from the formulation. The striking feature of the adsorption on the C16 surface is the stepwise character of the adsorption traces, which differs markedly from the more rounded signature characteristic of polydisperse samples. The L-720 formulation is therefore fascinating in its distinct adsorbing populations. The success of this formulation in such a broad array of applications may stem from the action of different fractions that are important in the different processes. In any application, however, the presence of excess species that do not go to the interface to perform desired functions there may potentially cause other problems, either in a bulk phase or on other surfaces that may be later encountered. It is worth repeating that the analysis presented here for extremely dilute adsorbing solutions affords a level of quantitation that is not possible at higher concentrations when eq 1 breaks down. The bulk solution compositions deduced from the
dilute limit, however, are more broadly applicable, potentially producing complex adsorption behavior at much higher concentrations. At higher concentrations, one expects to see a more rapid version of the competitive behaviors showcased here, with a surface preference for graft copolymer and a build up of the more weakly adsorbing species in free solution. Also, depending on the proportions of surface area and solution phase in an application, one might expect some kinetic trapping of the 50HB-5100 on hydrophobic surfaces, reducing the coverage of the graft copolymer. In addition to the specific findings on the L-720 formulation, this paper has demonstrated a general approach for understanding the competitive coadsorption behavior of different species in a mixture. While the comparison of adsorption on hydrophobic and hydrophilic surfaces provides surface-related information that is relevant to specific applications, the comparison of adsorption rates between the two surfaces was key in establishing that there were large amounts of species that adsorbed to neither surface. Another important point borne out in this work is how even small amounts of physically small species can, when adsorbing reversibly but persistently, dominate the shape of the adsorption kinetic curves. Acknowledgment This work was supported by a Grant from Bectin Dickinson through UMass CUMIRP. Partial support from the UMassBaystate Cooperative is also gratefully acknowledged. The dynamic light scattering data were obtained on an instrument maintained by S. Bhatia through her award, NSF-CBET0238873, and we thank her for her assistance. Literature Cited (1) Cohen Stuart, M. A.; Scheutjens, J.; Fleer, G. J. Polydispersity effects and the interpretation of polymer adsorption-isotherms. J. Polym. Sci. Part B: Polym. Phys. 1980, 18, 559–573. (2) Koopal, L. K. The effect of polymer polydispersity on the adsorptionisotherm. J. Colloid Interface Sci. 1981, 83, 116–129. (3) Gu, B. H.; Schmitt, J.; Chen, Z.; Liang, L. Y.; McCarthy, J. F. Adsorption and desorption of different organic-matter fractions on ironoxide. Geochim. Cosmochim. Acta 1995, 59, 219–229. (4) Kilduff, J. E.; Karanfil, T.; Chin, Y. P.; Weber, W. J. Adsorption of natural organic polyelectrolytes by activated carbon: A size-exclusion chromatography study. EnViron. Sci. Technol. 1996, 30, 1336–1343. (5) Santore, M.; Fu, Z. L. Direct measurement of molecular-weight driven competition during polymer adsorption. Macromolecules 1997, 30, 8516–8517. (6) Fu, Z. L.; Santore, M. M. Kinetics of competitive adsorption of PEO chains with different molecular weights. Macromolecules 1998, 31, 7014– 7022. (7) Dijt, J. C.; Cohen Stuart, M. A.; Fleer, G. J. Competitive adsorptionkinetics of polymers differing in length only. Macromolecules 1994, 27, 3219–3228. (8) Fu, Z. L.; Santore, M. M. Competitive adsorption of poly(ethylene oxide) chains with and without charged end groups. Langmuir 1998, 14, 4300–4307. (9) Dijt, J. C.; Cohen Stuart, M. A.; Fleer, G. J. Surface exchange kinetics of chemically different polymers. Macromolecules 1994, 27, 3229–3237. (10) Bijsterbosch, H. D.; Cohen Stuart, M. A.; Fleer, G. J. Adsorption of graft copolymers onto silica and titania. Macromolecules 1998, 31, 8981– 8987. (11) Schillen, K.; Claesson, P. M.; Malmsten, M.; Linse, P.; Booth, C. Properties of poly(ethylene oxide)-poly(butylene oxide) diblock copolymers at the interface between hydrophobic surfaces and water. J. Phys. Chem. B 1997, 101, 4238–4252. (12) Strey, R.; Sottmann, T.; Schwan, M. Foamed material and method for production of said foamed material. U.S. Patent 20060127663, 2006. (13) Isobe, K. Inkjet ink and printing method using same. European Patent EP1775326, 2007. (14) Pings, K. D. Hair conditioning compositions. U.S. Patent 5482703, 1996.
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ReceiVed for reView May 16, 2008 ReVised manuscript receiVed August 2, 2008 Accepted August 5, 2008 IE800791H
