8824
Langmuir 2002, 18, 8824-8828
Logarithmic Adsorption of Charged Polymeric Surfactants at the Air-Water Interface Fre´de´ric Millet,† Patrick Perrin,*,‡ Michael Merlange,† and Jean-Jacques Benattar† CEA/Saclay, Service de Physique de l’Etat Condense´ , F-91191 Gif-sur-Yvette Cedex, France, and ESPCI-CNRS-UPMC, UMR 7615, Laboratoire de Physico-chimie Macromole´ culaire (LPM), 10 rue Vauquelin, 75005 Paris, France Received March 12, 2002. In Final Form: August 5, 2002 We investigated the adsorption of a series of hydrophobically modified poly(acrylic acid) sodium salts (HMPAANa) at the air-water interface by dynamic surface tension measurements. We observed a logarithmic decrease of the surface tension with time over several decades, in good agreement with a reptation-diffusion-based model. The kinetics of adsorption in this logarithmic regime depends on the chain molecular weight and is independent of the polymer concentration and amount of hydrophobic moieties. Moreover, we show that no electrostatics takes place during the adsorption process. Finally, existing theoretical models were used to propose an interpretation of the logarithmic dependence of the adsorption with time.
Introduction Hydrophobically modified poly(acrylic acid) sodium salts (HMPAANa) have been proven to be efficient stabilizers of oil in water macroemulsions.1,2 Recent microscopic investigations of free-standing vertical aqueous films of HMPAANa, viewed as model systems for the interstitial polymer films between oil droplets, have provided some pieces of explanation for this remarkable stabilization.3,4 The steric repulsion between polymer chains adsorbed at both sides of the films at low polymer bulk concentrations and the formation of a physical microgel within the polymer films at higher polymer bulk concentrations (because of the associative properties of the HMPAANa copolymers) are the main reasons for this stabilization. In a previous paper, we had also presented an investigation of the air-water interface by combined surface tension and X-ray reflectivity measurements.5 In particular, we had determined the Gibbs isotherms and the surface excess amounts for HMPAANa copolymers with various amounts of hydrophobes. Moreover, it was observed that the adsorption process is very slow and can last up to 2 days. We now return to the important question of the polymer adsorption kinetics. We present new dynamic surface tension measurements and propose an interpretation for the slowness of this process based on existing theoretical models. It is commonly admitted that the first step of the adsorption process is diffusion-controlled: the polymer molecules migrate from the bulk to the interface and freely adsorb at the bare interface. There is no energy barrier to overcome prior to adsorption, and the phenomenon is thus fast. Both theoretical models and experiments * Corresponding author e-mail:
[email protected]. † CEA/Saclay, Service de Physique de l’Etat Condense ´. ‡ Laboratoire de Physico-chimie Macromole ´ culaire (LPM). (1) Perrin, P.; Lafuma, F. J. Colloid Interface Sci. 1998, 197, 317. (2) Perrin, P.; Lafuma, F.; Audebert, R. Prog. Colloid Polym. Sci. 1997, 105, 22. (3) Millet, F.; Perrin, P.; Benattar, J.-J. Phys. Rev. E 1999, 60, 2045. (4) Millet, F.; Benattar, J.-J.; Perrin, P. Macromolecules 2001, 34, 7076. (5) Millet, F.; Nedyalkov, M.; Renard, B.; Perrin, P.; Lafuma, F.; Benattar, J.-J. Langmuir 1999, 15, 2112.
agree on a t1/2 dependence of the adsorbed amount with time.6-14 Rapidly, a layer is formed creating a steric hindrance to further adsorption. Different models propose a diffusion of polymer molecules through the adsorbed layer with a diffusion coefficient derived from those in dilute solution and calculate a t1/2 dependence of the adsorbed amount.9,10,15,16 These models do not propose any physical mechanism for the diffusion of the polymer chains through the adsorbed layer. Other models suggest a reconformation of the adsorbed layer7,8,11-13,17 that could eventually lead to the formation of a surface mesophase7 or even to a collapse of the layer.17 For instance, a theory for the adsorption of protein molecules suggests that a new molecule adsorbs at the interface only when a surface area has been cleared at the interface by compression of the adsorbed molecules.12,14,18 Consequently, the energy barrier to overcome is given by the Boltzmann factor associated to the surface free energy of the surface to be cleared. In general, two difficulties arise in the application of these models and in the description of the dynamic surface tension measurements. First, the relationship between the surface tension and the surface excess amount is nontrivial. Second, the equilibrium surface tension value, which is experimentally difficult to determine, intervenes in many models. The equilibrium value can (6) Ward, A. F. H.; Tordai, L. J. Chem. Phys. 1946, 14, 453. (7) Chang, S. A.; Gray, D. G. J. Colloid Interface Sci. 1978, 67, 255. (8) Nahringbauer, I. J. Colloid Interface Sci. 1995, 176, 318. (9) Rosen, M. J.; Song, L. D. J. Colloid Interface Sci. 1996, 179, 268. (10) Filippov, L. K.; Silebi, C. A.; El-Aasser, M. S. Langmuir 1995, 11, 872. (11) Graham, D. E.; Phillips, M. C. J. Colloid Interface Sci. 1979, 70, 403. (12) Damodaran, S.; Song, K. B. Biochim. Biophys. Acta 1988, 954, 253. (13) Lankveld, J. M. G.; Lyklema, J. J. Colloid Interface Sci. 1972, 41, 454. (14) McRitchie, F.; Alexander, A. E. J. Colloid Interface Sci. 1963, 18, 453. (15) Miller, R.; Lunkenheimer, K. Colloid Polym. Sci. 1983, 261, 585. (16) Fainerman, V. B.; Zholob, S. A.; Miler, R. Langmuir 1997, 13, 283. (17) Beverung, C. J.; Radke, C. J.; Blanch, H. W. Biophys. Chem. 1998, 70, 121. (18) Ward, A. F. H.; Tordai, L. Rev. Trav. Chim. 1952, 71, 572.
10.1021/la020249p CCC: $22.00 © 2002 American Chemical Society Published on Web 10/16/2002
Adsorption of Charged Polymeric Surfactants
Langmuir, Vol. 18, No. 23, 2002 8825
then be viewed as an adjustable parameter so that the models cannot always be tested rigorously. We analyze here our dynamic surface tension measurements in light of a model based on a reptation-diffusion model.19,20 We observe a logarithmic decrease of the surface tension γ over three decades of time, in good agreement with the theoretical predictions. We show that the kinetics of adsorption of HMPAANa copolymers in the long range of times is independent of the copolymer concentration, the hydrophobicity of the copolymers, and the presence of an excess of salt. These observations result in a remarkable feature since all the curves representing the variation with time of -(dγ/dt) regroup on a single general curve in the long range of times. Experimental Section Materials. A series of hydrophobically grafted polymers were synthesized from various poly(acrylic acid) precursor polymers supplied by Polysciences. They were obtained under their neutralized sodium salt form
with τ being the degree of grafting (τ ranging from 1 to 10 mol %). Details of the synthesis were previously reported.21 The chemically grafted hydrophobic moieties along the polymer backbone are randomly distributed. Three different backbone molecular weights appear in this work: Mw ) 18 000, 120 000, and 525 000 g/mol. A recent capillary electrophoresis experiment22 has achieved the differentiation of the electrophoretic mobilities of HMPAANa copolymers with regard to their degree of grafting (unmodified PAANa precursor homopolymers and HMPAANa copolymers with τ ) 3, 7, and 10 mol %). The degree of grafting is then well-characterized, and the polydispersity of grafting is negligible. For the sake of clarity, the modified polymers are referred to as (Mw × 10-3) τC12. C12 reminds us that the number of carbons composing the grafted moiety is 12 (n-dodecyl chain). The polymer concentrations are expressed in weight per weight percent (w/w %). Methods and Equipment. Surface tensions (γ) were measured by the Wilhelmy method using a Cahn 1000 electrobalance and a paper filter plate with a length of 2 cm. The paper filter ensures a zero contact angle. The electrobalance is sensitive to a variation of weight as small as 0.5 µg corresponding to a variation of surface tension of 0.1 mN/m. Measurements were carried out in a Teflon trough (4 cm diameter) housed in a Plexiglas box. Prior to each run, the surface tension of pure water was measured. After each run with polymer solution, the surface tension of pure water was measured with the same plate. The surface tension was always within 2% of that of pure water, indicating that a negligible adsorption of the polymer on the plate occurs. A rate of loss of the surface tension as small as 10-3 mN/(m‚min) was determined by measuring a surface tension variation of 0.1 mN/m over a period of 100 min. The experimental uncertainty was estimated to 10% (which corresponds to the size of the data points reported in the figures of this paper) until -(dγ/dt) remained higher than 10-2 mN/(m‚min) and to a fixed value of 10-3 mN/(m‚min) when it was lower than 10-2 mN/(m‚ min). The temperature was kept constant (20 ( 0.5 °C) during all experiments. The solutions were prepared by dissolving a known quantity of synthesized polymer in double-distilled deionized water (Milli-Q system from Millipore). The complete dissolution was obtained by gently stirring the mixture for 24 h. The dynamic (19) Ligoure, C.; Leibler, L. J. Phys. 1990, 51, 1313. (20) Johner, A.; Joanny, J.-F. Macromolecules 1990, 23, 5299. (21) Wang, K. T.; Iliopoulos, I. Polym. Bull. 1989, 20, 577. (22) Collet, J.; Tribet, C.; Gareil, P. Electrophoresis 1996, 17, 1202.
Figure 1. Example for the decrease with time of the surface tension of a HMPAANa copolymer solution on a semilog plot (3% (w/w) concentrated 120 1C12 copolymer solution). After 1 h, the surface tension varies like log(t). The deviation from the logarithmic dependence after 10 h could announce the approach of a thermodynamic equilibrium. measurements of the surface start as soon as the solution is poured into the Teflon trough. The paper filter is then brought in such a way that it comes into contact with the surface of water. This latter operation takes a few seconds, and the fact that we first measure the surface tension of water proves that negligible adsorption occurred during the placement of the paper filter.
Results and Discussion We first present the general behavior of the decrease of the surface tension with time of a 3% concentrated 120 1C12 copolymer solution (Figure 1). This curve is sigmoidal-shaped on this semilog plot, as it is often reported for the adsorption kinetics of macromolecules.7-9 In particular, between t ) 1 h and t ) 10 h, the decrease of γ with t is logarithmic. After 10 h, an inflection of the slope of the curve indicates the approach of a situation of thermodynamic equilibrium between the adsorbed layer and the bulk solution. This deviation from the logarithmic dependence has often been considered in theoretical models and in the interpretation of experimental observations as a criterion for the appearance of an adsorptiondesorption equilibrium.17,19 We are essentially interested in the rate of loss of the surface tension because it reveals some physical information on the adsorption process, as will be pointed out further. It is thus more relevant to plot the derivative of the surface tension versus time. Figure 2a presents the time dependence of -(dγ/dt) for the 120 1C12 copolymer for bulk concentrations ranging from 0.75 to 12 w/w %. First, we observe that -(dγ/dt) is constant during the first step of the adsorption process: the surface tension decreases linearly with time during a time t0 varying like 1/c (Figure 2b), c being the bulk concentration. We deduce that t0(-dγ/dt)0 is independent of the bulk concentration. If π(t0) is the pressure of the surface at the end of the first adsorption step, we can write that t0(-dγ/dt)0 ) π(t0). This observation means that the first step lasts until the surface pressure reaches the value of 3 mN/m, irrespective of bulk polymer concentration. We now discuss this point. Clearly, t0 is much too long (up to 80 min at low concentration) to be interpreted as a characteristic time of diffusion of the polymer chains from the bulk as described in the theory of ref 18. The duration of the first adsorption regime (t < t0) is long and rather tends to reveal that the adsorption of molecules is
8826
Langmuir, Vol. 18, No. 23, 2002
Millet et. al
kinetics is only controlled by surface phenomena. Moreover, we have here evidenced a logarithmic decrease of the surface tension that we discuss now. First, let us briefly describe a theoretical model19 for the kinetics of adsorption of neutral diblock copolymers from selective solvents. One block is in bad solvent conditions and adsorbs at the interface while the other block dangles on the subphase and forms a neutral brush. According to the model, no diffusion effect from the bulk is here considered, and the polymer molecules are supposed to arrive instantaneously at the interface. Once the brush has formed, additional chains coming from the bulk in the vicinity of the interface have to stretch out to penetrate the brush, adopting a reptation-diffusion mechanism. These chains have to cross a stretching energy barrier equal to NΓ2/3 (in kT units), Γ being the adimensioned adsorbed amount at time t (0 e Γ e 1 and Γ ) 1 when there is not any solvent molecule at the interface but only adsorbed moieties), and N being the polymerization index of the nonadsorbing blocks that form the brush and increase the brush density after adsorption of the macromolecule. The authors obtain the following expression for the rate of adsorption: 2/3 2/3 dΓ 1 ) (Γeqe-NΓ - Γe-NΓeq ) dt τ
Figure 2. (a) Variation of -(dγ/dt) with time for 120 1C12 copolymer solutions at various bulk concentrations indicated above (w/w %). After a time (t0) that depends on the bulk concentration (c), all the data points regroup on a unique curve. It indicates that the surface evolution is not correlated with the solution properties. A logarithmic decrease of γ is then observed over several decades of time, in good agreement with theoretical models.19,20 (b) t0 varies such as 1/c: the first step of the adsorption process is faster at high concentration.
likely to be controlled by a barrier of energy. According to the theory presented in ref 20, the polymer chains forming micelles in diblock copolymer micellar solutions have to be expelled from the micellar aggregates before they can adsorb at the interface. This process actually leads to a linear increase of the surface coverage with time on a time scale of a few minutes. The same linear variation holds for the surface tension because the surface pressure, which remains low at adsorption times lower than t0, varies linearly with the coverage. Our observations are hence in qualitative agreement with this theory. However, this interpretation (although possible) presents limitations. First, the polymer concentration regime studied in Figure 2a is large since it extends from 0.75 to 12%. Consequently, the presence of hydrophobic aggregates in all the investigated 120 1C12 solutions is not straightforward, particularly at low concentrations as discussed in refs 1 and 2. Second, the expulsion of HMPAANa chains from intra- and/or intermolecular hydrophobic aggregates probably does not occur in the same manner as that of diblock copolymer chains. We now turn to the second step of the adsorption process. At t ) t0 (i.e., when the surface pressure reaches the value of 3 mN/m), the adsorbed chains form a brush that is dense enough to create a steric hindrance to further adsorption, and a second much slower adsorption process is observed. At times larger than t0, all the data points regroup on one single curve. It is an important result as it shows that the second step of the adsorption process is not correlated to the bulk properties. Hence, adsorption
(1)
where Γeq is the equilibrium value of Γ and τ is a time of the order of the microsecond that is model-dependent. The first term of the right member of eq 1 corresponds to the adsorption phenomenon, while the second one corresponds to desorption. Both phenomena follow first-order kinetics, and the rates of adsorption and desorption are proportional to the Boltzmann factor associated with the stretching energy. As long as the system is out of equilibrium, the desorption term can be neglected, and the integration of eq 1 leads to 2/3
Γ1/3eNΓ )
2N t Γ 3 eq τ
(2)
By taking the logarithms of both members of eq 2 and by neglecting the terms ln(N) and ln(Γ):
Γ∝
ln3/2(t/τ) N3/2
(3)
A logarithmic variation of the surface excess amount with time is obtained as long as no desorption takes place. The deviation from the logarithmic behavior here indicates that the desorption progressively appears and that the equilibrium is about to be reached. To compare our results to this model, the relationship between the surface pressure π and the surface excess Γ has now to be established. In the framework of the ideal gas theory, the surface pressure is π ) γ0 - γ ) ΓRT, and in the case of a more concentrated adsorbed layer the two-body interactions are predominant and π ) A2RTΓ2. Here R and T have their usual meaning, γ0 is the surface tension at the bare air-water interface, and A2 is the second virial coefficient. Although combined surface radioactivity and surface tension measurements on other systems showed that a linear growth of π with Γ can be observed up to high surface excess amounts,11,23 the quadratic form is probably much more relevant for the expression of π. We can even consider the case where the three-body interactions are dominant, which is interesting (23) MacRitchie, F. Colloids Surf. 1989, 41, 25.
Adsorption of Charged Polymeric Surfactants
Langmuir, Vol. 18, No. 23, 2002 8827
from a theoretical viewpoint. Nevertheless, this latter case is unlikely to occur as it corresponds to bad solvent conditions, and the HMPAANa copolymers are in rather good solvent conditions. We will use the general expression π ∝ Γn, where n expresses the type of interaction that is predominant within the adsorbed layer. We show that the value of n does not significantly affect the variation of Γ in the framework of the former model. Equation 3, which remains valid as long as desorption is negligible, then becomes
π∝
ln3n/2(t/τ) N3n/2
(4)
and the derivation of eq 4 leads to (3n/2-1) (t/τ) ln(3n/2-1)(t/τ) ∂π 3n ln ∝ ∝ ∂t 2 t N3n/2t
(5)
The slope of the curve ∂π/∂t as a function of t on a log-log plot is
∂log
(∂π∂t ) ) ∂ln(∂π∂t ) ) 3n2 - 1 - 1
∂log(t)
∂ln(t)
ln(t/τ)
(6)
This slope continuously decreases with time (asymptotically approaching -1 in the limit of infinite time) and is lower than -0.8 as soon as t > 12τ when n ) 1, t > 2 × 104τ when n ) 2, and t > 4 × 107τ when n ) 3, which is rapidly reached because (as was noticed above) τ is of the order of the microsecond. It can then be considered that ∂π/∂t scales such as 1/t. Our results can then reasonably be interpreted within the framework of this theory. Therefore, a steric interaction between the polymer layer first adsorbed at the interface and the polymer chains that aim at adsorbing is likely to be responsible for the slow decrease of the surface tension with time. This logarithmic kinetics is the signature of the so-called “self-inhibited” system. It must be pointed out that we made two important hypotheses. First, we supposed that the electrostatic effects do not affect the adsorption kinetics. Indeed, the HMPAANa polyelectrolytes investigated here are surfaceactive only at concentrations above 0.5%. In this range of concentrations, the Debye screening length is rather short (the concentration of free charges of a 0.5% HMPAANa solution is about 15 mM, which corresponds to a Debye screening length of about 3 nm), and then we do not expect any Coulombian repulsion between the adsorbed layer and the charged chains of the subphase. Second, we supposed that the HMPAANa random copolymers penetrate through the adsorbed layer using a reptationdiffusion mechanism. As a matter of fact, one has to keep in mind that the polymer molecules considered in this paper are different from the block polymer chains considered in the above-described model.19 The experimental results presented below give some pieces of justification to these two hypotheses. We have tested the effect of the electrostatics on the adsorption kinetics of HMPAANa at the air-water interface by investigating the influence of an excess of added electrolytes. Figure 3 compares the variation of -(dγ/dt) with time for the 120 1C12 copolymer for various concentrations in pure water and in the presence of an excess of salt (0.5 M NaCl). As we are here only interested in the second step of the adsorption process when the kinetics does not depend on the bulk polymer concentra-
Figure 3. Comparison of the adsorption kinetics (-(dγ/dt) as a function of time) of the 120 1C12 copolymer in pure water and in an excess of salt (0.5 M NaCl). The various copolymer concentrations are not distinguished here (see Figure 2a for the investigated polymer concentrations). Both curves regroup in the long times, suggesting that electrostatics does not have any influence on the adsorption kinetics. The adsorbed layer seems to be self-screened at polymer concentrations where the modified polyelectrolytes are actually surface-active (>0.5%).
tion, the various concentrations are not distinguished (see Figure 1 for the investigated range of polymer concentrations). Both series of experimental points corresponding to the adsorption in the presence and in the absence of salt regroup on the same curve, and the kinetics is unaffected by the presence of salt. Our first hypothesis about the influence of an addition of salt is then justified: the concentration of charges brought by the polyelectrolyte chains is probably high enough for the charged adsorption layer to be self-screened. These observations at high polyelectrolyte concentrations are different from what is usually predicted and observed for charged polymeric surfactants at lower bulk concentrations.24-27 In the latter case, a strong repulsion between the charged adsorbed layer and the molecules of the subphase has been evidenced, and it causes a noticeable delay in the adsorption process. The influence of the structure of the HMPAANa copolymer on the kinetics has also been investigated. Figure 4a presents the kinetics of adsorption of same molecular weight copolymers (120 000 g/mol) with various degrees of grafting (1, 3, and 10 mol %). Since the concentration does not affect the kinetics of the second step of the adsorption process (Figure 2a), we can compare results obtained at different concentrations. Once again, all the experimental points regroup on a single curve (Figure 4a). The kinetics of adsorption does not depend on the number of grafts along the polyelectrolyte chains. This result is important since it suggests how the HMPAANa random copolymer chains cross the adsorbed layer. As a matter of fact, it seems that the random copolymers do not penetrate grafts-ahead (Figure 4b). In this case, one would expect the kinetics to be a priori highly dependent on the number of grafts. On the contrary, we would rather suggest that the whole chain follows one single graft through the adsorbed layer as shown in Figure (24) Cohen-Stuart, M. A. C.; Hoogendam, C. W.; de Keizer A. J. Phys.: Condens. Matter 1997, 9, 7767. (25) Go¨bel, J. G.; Besseling, N. A. M.; Cohen-Stuart, M. A. C.; Poncet, C. J. Colloid Interface Sci. 1999, 209, 129. (26) Diamant, H.; Andelman, A. J. Phys. Chem. 1996, 100, 13732. (27) Bonfillon, A.; Sicoli, F.; Langevin, D. J. Colloid Interface Sci. 1994, 168, 497.
8828
Langmuir, Vol. 18, No. 23, 2002
Millet et. al
Figure 5. Comparison of the kinetics of adsorption for 1C12 copolymers of various weight-average molecular weights: 18 000, 120 000, and 525 000 g/mol. The logarithmic decrease of the surface tension is still observed in the long range of times, and the experimental data points are shifted to longer times for high molecular weights.
characterized by a given value of -(dγ/dt). The first step of the adsorption process (Figure 2a), which is not understood at the present time, is consequently longer for long polymers. Conclusion
Figure 4. (a) Comparison of the kinetics of adsorption of the 120 1C12, 120 3C12, and 120 10C12 copolymers. We are reminded that the kinetics at the long times is independent of the polymer concentration. After about 10 min, all experimental points regroup on a single curve. The adsorption process is then independent of the degree of grafting. These observations suggest that the copolymers do not penetrate grafts-ahead as sketched in panel b. On the contrary, it tends to show that the whole chain follows a unique graft during the diffusion through the adsorbed layer, as sketched in panel c.
4c. This latter model would explain that the kinetics is independent of the copolymer chemical structure. This result justifies our second hypothesis according to which the kinetics of adsorption of the random HMPAANa copolymers resembles that of end-capped polymers such as diblock copolymers in selective solvent. Finally, we investigated the influence of the molecular weight on the adsorption kinetics. Figure 5 compares the kinetics of three copolymers of the same hydrophobicity (1C12) but various weight-average molecular weights (18 000, 120 000, and 525 000 g/mol). Once again, a logarithmic decrease of the surface tension with time is observed in the long range of time irrespective of the molecular weight. The curves are shifted to longer times for high molecular weight polymers. For long polymers, the adsorbed layer is longer to reach a given physical state
We have shown that the adsorption of HMPAANa amphiphilic polyelectrolytes in the long times is a general process since their kinetics is independent of the polymer concentration, polymer structure, or presence of salt in the solution. It solely depends on the polymer molecular weight. For a given molecular weight, all the curves representing -(dγ/dt) as a function of t remarkably regroup on a unique curve. Moreover, we observe a logarithmic decrease of the surface tension over three decades of time. Without any hypothesis about the surface pressuresurface concentration equation of state π(Γ), we have related our results to a reptation-diffusion-based model giving a logarithmic variation of Γ(t) for the adsorption of diblock copolymers from selective solvent. We then conclude that the slowness of the HMPAANa adsorption process at the air-water interface is due to the presence of an energy barrier corresponding to the stretching of the chains before their diffusion through the adsorbed layer. We have also shown that no electrostatics takes place in the adsorption process. This is due to the fact that the HMPAANa polymers are actually surface-active at concentrations that are not too low. Finally, we suggested that the random grafted chains diffuse through the adsorbed layer following a unique hydrophobic graft. However, a theoretical model specifically established for the kinetics of adsorption of randomly modified polyelectrolytes would be very useful. It would also be very interesting to investigate the adsorption properties of poly(acrylic acid) sodium salt end-capped by a dodecyl chain to compare the adsorption kinetics with that of the randomly grafted HMPAANa copolymers in order to test the diffusion mechanism proposed in Figure 4c. Acknowledgment. The authors thank Christian Ligoure for his kind interest in our work and for very fruitful discussions. LA020249P
