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Decomposing Bridging Adhesion between Polyelectrolyte Layers into Single Molecule Contributions Georg Papastavrou,* Luke J. Kirwan, and Michal Borkovec Laboratory of Colloid and Interface Chemistry, Department of Inorganic, Analytical, and Applied Chemistry, UniVersity of GeneVa, Sciences II, 30 Quai Ernest Ansermet, 1211 GeneVa 4, Switzerland ReceiVed July 14, 2006. In Final Form: October 4, 2006 A novel approach to analyze the force response of multiple polymer strands, which are bridged between two surfaces, is proposed. The response of single polymer strands is experimentally accessible by measuring the force upon separation of two polymer-coated surfaces with the atomic force microscope. Our approach is based on the decomposition of the stretching and desorption sequence into contributions of independently bridged chains and of the elimination of loops formed on the opposite surface during contact. This approach was applied to investigate the bridging adhesion of surfaces coated with poly(vinylamine) (PVA). The force response of single PVA molecules was described on the basis of a recently proposed model, which accounts for the discrete chain character of the polymer at higher extension forces. As exemplary results, we determined the length distributions of the individual chains and the loop number distribution of these bridging chains on the polyelectrolyte-coated surfaces. The former were compared with scaling theories of polymer adsorption.
Probing the stretching response of individual polymer chains with the atomic force microscope (AFM) received major attention recently.1,2 This technique, which is often referred to as singlemolecule force spectroscopy, measures the force response of a polymer chain bridged between a substrate and the AFM tip and has been used to study nucleic acids,3 polysaccharides,4 and synthetic polymers.5-8 To determine the force response of an individual polymer, just a single polymer chain has to bridge the tip and the sample. Therefore, substantial effort has been devoted to design experiments to favor bridging of single molecules9 or to identify the response of single molecules by scaling arguments (i.e., master plot).4 In this fashion, one can study conformational transitions within the chain4 or determine its physical properties, such as its persistence length, by applying the wormlike chain (WLC) model.10 Bridging of multiple polymer chains is relevant for the understanding of adhesive properties of polymer-coated surfaces, particularly in the context of surface functionalization or development of polymer-based glues.11,12 The bridging of a single chain represents an exception in these situations, and the adhesive properties will be dictated by the stretching response of an ensemble of polymer chains. While major experimental and theoretical efforts have been devoted to single chain force response, little information is available on the force response of an ensemble of bridging chains.6,13 * To whom correspondence
[email protected].
should
be
addressed.
E-mail:
(1) Janshoff, A.; Neitzert, M.; Oberdorfer, Y.; Fuchs, H. Angew. Chem., Int. Ed. 2000, 39, 3213-3237. (2) Hugel, T.; Seitz, M. Macromol. Rapid Commun. 2001, 22, 989-1016. (3) Rief, M.; Clausen-Schaumann, H.; Gaub, H. E. Nat. Struct. Biol. 1999, 6, 346-349. (4) Rief, M.; Oesterhelt, F.; Heymann, B.; Gaub, H. E. Science 1997, 275, 1295-1297. (5) Ortiz, C.; Hadziioannou, G. Macromolecules 1999, 32, 780-787. (6) Bemis, J. E.; Akhremitchev, B. B.; Walker, G. C. Langmuir 1999, 15, 2799-2805. (7) Hugel, T.; Grosholz, M.; Clausen-Schaumann, H.; Pfau, A.; Gaub, H.; Seitz, M. Macromolecules 2001, 34, 1039-1047. (8) Hugel, T.; Rief, M.; Seitz, M.; Gaub, H. E.; Netz, R. R. Phys. ReV. Lett. 2005, 94, 048301. (9) Cui, S.; Liu, C.; Zhang, X. Nano Lett. 2003, 3, 245-248. (10) Marko, J. F.; Siggia, E. D. Macromolecules 1995, 28, 8759-8770. (11) Creton, C. MRS Bull. 2003, 28, 434-439. (12) Granick, S. Eur. Phys. J. E 2002, 9, 421-424. (13) Sun, G. X.; Butt, H. J. Macromolecules 2004, 37, 6086-6089.
In the present letter, we address the bridging adhesion between adsorbed polymer layers and show that the force profile upon separation can be decomposed into stretching events of individual polymer chains and events resulting from elimination of loops formed on the opposite surface. This decomposition will be exemplified by analyzing interactions between preadsorbed poly(vinylamine) (PVA) layers on silica. While the stretching response of single chains of this cationic polyelectrolyte has been previously studied with an AFM tip,7,8 the present study uses a colloidal probe, which leads to a larger contact area, and facilitates the bridging of multiple polymer chains. The polyelectrolyte films were prepared by adsorption of PVA to silica colloidal probes and fused silica wafers (SchottGuinchard, Switzerland). The PVA, which was synthesized by BASF (Ludwigshafen, Germany), had a molecular mass of 520 kDa, and 95% of its functional groups were in the form of primary amines. Colloidal probes were prepared by attaching colloidal silica particles (Bangs Laboratories) with a diameter of 5-7 µm to tipless AFM cantilevers (NTSC12, µ-masch, Estonia) by means of UV-curable glue (NO 68, Norland Adhesives). The solid substrates and the colloidal probes were cleaned for 5 min in air-plasma (35 W, PDC-32G Harrick Instruments). Afterward, they were incubated for at least 12 h in a solution of 50 mg/L PVA, which was of adjusted to pH 4 with HCl, and quickly rinsed with pure electrolyte solution in order to remove any loosely adsorbed PVA. The force measurements by AFM (MFP3D, Asylum Research) were preformed in 10 mM KCl solutions at pH 4. Figure 1a shows the force acting on the cantilever as a function of the separation distance between the two PVA-coated surfaces. In this experiment, the colloidal probe is first approached toward the substrate, then both surfaces are pressed together with a maximum force in the range of 2-12 nN (∼1-5mN/m when normalized by the radius of the colloidal particle). Finally, both surfaces are separated by retracting the probe. Upon approach, repulsive forces are observed. While PVA is a weak polyelectrolyte, at pH 4, it is fully charged and therefore adsorbs primarily in a flat conformation.14 The long-range interaction is thus dominated by electrostatic forces due to overlap of diffuse layers (14) Kirwan, L. J.; Papastavrou, G.; Borkovec, M.; Behrens, S. H. Nano Lett. 2004, 4, 149-152.
10.1021/la062046x CCC: $33.50 © 2006 American Chemical Society Published on Web 11/03/2006
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segments L1and L2 are sufficiently different, the total force response of the loop is practically indistinguishable from the one of its shorter segment L1and we can summarize true tails and these loops as pseudo-tails. The force response of single polymer chains was interpreted with the WLC-DC model.16 This model includes discrete chain (DC) effects at higher extension forces, while at lower extension forces, it reduces to the standard WLC model. The crossover between these two regimes is located at 50-100 pN for synthetic polyelectrolytes with saturated carbon chains, such as PVA.16 The force response, F ) Fˆ (D,L), as a function of the extension, D, of a polymer with a contour length L is given by16
D/L ) 1 - {(fWLC-1[Fleff/kBT])β + (cFb/kBT)β}-1/β + F/γ˜ (1) where leff is the effective persistence length, γ˜ the stretching modulus, and fWLC-1 is the inverse function of the normalized force response of the WLC model
3 1 x2 fWLC[x] ) - + 4 x 4
Figure 1. Force-distance curve between two surfaces precoated by poly(vinylamine) (PVA) measured in 10 mM KCl and pH 4. The solid gray circles indicate the approach and the open circles the retraction part of the box-averaged force profile. The retraction of the probe is dominated by stretching and subsequent rupture of PVA segments involving (a) multiple chains and (b) few chains. (c) Detail of the last stretching event shown in (b) where finally only one PVA segment is pulled. The solid line represents the WLC-DC model with a persistence length of 0.25 nm. The inset illustrates the definition of pseudo-tails as bridged polymer chains, which are either true tails (heavy, solid line) or loops with highly diverse segment lengths (broken line).
and can be described by the Poisson-Boltzmann equation.15 Upon retraction, the adhesion is dominated by the bridging adhesion of PVA segments, which detach from the surfaces at large separation distances. Directly upon separation, less pronounced adhesion is observed, which has to be attributed partly to unspecific adhesion and partly to the detachment of very short segments. The force response of single PVA molecules was determined from selected bridging events, which were taken either from curves with just one pulling event or from a curve featuring one well-separated event at the end of an event sequence. The extension distances of the force curves were normalized by their values at a force of F ˜ ) -200 pN and considered only when they superimposed in a resulting master plot.4,7 For a given force profile, F(D), the master was obtained by normalizing the separation distance, D, by a value D ˜ such that F(D ˜) ) F ˜ . The resulting normalized force profiles F(D/D ˜ )in the master plot coincide if all stretched polymers follow the same extension behavior.1 Not only tails, as depicted in Figure 1c by the solid line, but also loops (cf. broken line in Figure 1c) form on the substrates during polyelectrolyte adsorption from solution and thus protrude from the surfaces. When such a loop forms an anchor point on the opposite surface during contact, one observes only one rupture event upon separation. If the lengths of the two (15) Poptoshev, E.; Rutland, M. W.; Claesson, P. M. Langmuir 1999, 15, 7789-7794.
(2)
The transition between the low and high force regime is described by the parameter β. The force response in the later regime is the one of a freely rotating chain (FRC), which differs from the one of a freely jointed chain (FJC) by a different effective bond length. The factor c expresses this difference with respect to the true bond length, b. The force response of a single PVA segment could be fitted with the WLC-DC model very well (see Figure 1c). There are only two adjustable parameters in these fits, namely the effective persistence length, leff, and the contour length, L. All other parameters were fixed to values γ˜ ) 28 nN, b ) 0.154 nm, c ) 2, and β ) 2 determined from simulations of a saturated hydrocarbon chain.16 These parameters have been verified experimentally at large stretching forces for various backbone structures, including the one of PVA.8 The resulting effective persistence length leff ) 0.25 ( 0.12 nm lies well in the range of values determined previously from similar pulling experiments on synthetic polyelectrolytes with the WLC model.5-7 Generally, the effective persistence lengths of synthetic polyelectrolytes obtained from AFM pulling experiments are substantially lower than the persistence lengths measured by light scattering techniques under comparable conditions.17 This apparent discrepancy is related to the scale dependence of the electrostatic persistence length18 and to excluded volume effects, which influence the persistence length obtained from the radius of gyration.19 With increasing applied force, the long wavelength fluctuations of the polymer chain are progressively eliminated, leading to softening of the chain, and a decrease of the effective persistence length, leff. When the applied force is sufficiently high, its value is simply reduced to the bare persistence length, l0, of the polymer. The latter can be estimated from the freely rotating chain model (FRC) from the given bond length, b, and the bond angle of θ ) 70° with the result l0 ) b cos(θ/2)/|ln(cos θ)| ≈ 0.12 nm.16 This value is indeed well comparable to the measured effective persistence length reported above. When torsional potentials are taken into account even a better agreement (16) Livadaru, L.; Netz, R. R.; Kreuzer, H. J. Macromolecules 2003, 36, 37323744. (17) Forster, S.; Schmidt, M. AdV. Polym. Sci. 1995, 120, 51-133. (18) Netz, R. R. Macromolecules 2001, 34, 7522-7529. (19) Ullner, M.; Woodward, C. E. Macromolecules 2002, 35, 1437-1445.
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distance, D, can be summarized as
F(D) )
[
Fˆ (D,L′) D < D* Fˆ (D,L′ + L′′) D > D*
]
(3)
In the second case, two independent pseudo-tails are bridging the surfaces (see Figure 2b). At small separation distances, the overall force is given by the sum of the forces originating from each bridged pseudo-tail of contour lengths L1 and L2 (L1 < L2). With increasing separation, the shorter segment with contour length L1 ruptures at a separation distance D*, and beyond that point, only the longer segment with contour length L2 contributes. Thus, the force reads
F(D) )
Figure 2. Force curves involving two rupture events of bridging polymer chains. (a) A single pseudo-tail with two anchor points on the opposite surface (contact-formed loop) and (b) two independent pseudo-tails with one anchor point each. The continuous, light blue lines are fits to two independent pseudo-tails (cf. eq 4), while the orange lines are fits to one pseudo-tail, which forms a loop on the opposite surface during contact (cf. eq 3). The thicker line gives the best fit, and the corresponding values for χ˜ 2 are given for both models.
can be obtained.20 In this situation, the applied force must be much larger than the crossover force at which the electrostatic contributions to the persistence length are comparable to the intrinsic one. The corresponding crossover force is F ≈ kBTl0κ2 ≈ 50 fN.18 Since such forces are well below the force resolution of our instrument, we conclude that all experiments are in the regime where leff ≈ l0. Frequently, the retraction curves exhibit numerous bridging events between the PVA-coated surfaces (see Figure 1a). The number of bridging events will be enhanced with respect to studies with normal AFM tips since the colloidal probe results in a large contact area. Let us now analyze such a sequence of events in terms of the single molecule force response discussed above. First, consider the situation of two rupture events, which occur at distinct, but not too different, separation distances. Two different configurations for the bridging polymer chains should be considered, namely one pseudo-tail forming a loop and two independent pseudo-tails.6 In the first case, one bridging pseudotail is anchored at two points on the opposite surface, where it formed a loop during contact of the two surfaces (see Figure 2a). Since these loops are formed only during the contact of the two surfaces, we will refer to them as contact-formed loops to distinguish them from the loops formed during the adsorption of the polymer to the bare surfaces. At small separations, only the bridging segment with the contour length L′ contributes to the force. With increasing separation, this segment ruptures from its anchor point at a separation distance, D*, which is typically on the order of its contour length L′. At this point, the contour length increases by the length L′′ of the loop to L′ + L′′. Thus, the force, F, acting on the cantilever as function of the (20) Elias, H. G. An introduction to polymer science; VCH Publishers: Weinheim, 1997.
[
Fˆ (D,L1) + Fˆ (D,L2) D < D* Fˆ (D,L2) D > D*
]
(4)
To determine the adsorption configuration from the force response with two rupture events, the two detachment events are fitted consecutively, starting from the end of the sequence. The force response for each segment is assumed to follow the WLCDC model with the parameters determined above for a single polymer, leaving only the segment contour lengths as free parameters. Figure 2a and b provides examples for the two different elementary configurations. On the basis of the goodness of the fit for the first segment, it is possible to differentiate between them. As a quantitative indicator, we use the reduced χ˜ 2 value (i) 2 (i) (i) 2 defined by χ˜ 2 ) ∑i(F (i) exp - F fit ) /(Nσ ), where F exp and F fit are the experimental and fitted values of the force, respectively. The index i ) 1, ..., N labels the data points, and the standard deviation, σ, was estimated from the cantilever due to thermal noise at large separation distances. For Figure 2a, we obtain χ˜ 2loops ) 1.41 versus χ˜ 2chains ) 2.52 indicating one chain with a loop. For Figure 2b, we have χ˜ 2chains ) 1.46 versus χ˜ 2loops ) 2.44, showing two independent chains. In this type of data analysis, the symmetrical pulling of loops should be also considered. Loops formed during polymer adsorption to the bare surfaces have been considered so far as pseudo-tails assuming very different contour lengths of the two segments (cf. Figure 1c). However, if the lengths of both segments are very similar, both segments are stretched in parallel, and one obtains a force response given by eq 4 with L1 ≈ L2 and D < D*, whereby the subsequent event will be missing. Given the noise in the force measurements, however, such events cannot be distinguished unless the lengths of both segments are the same within 25%. Such events are expected to be infrequent. Therefore, the force response of all pulling events was approximated as originating from single polymer chains. The stretching response of the elementary configurations described by eqs 3 and 4 can be extended to a larger number of rupture events. With an increasing number of rupture events, various combinations of these configurations have to be considered. Figure 3 illustrates four different possibilities for three successive events. In detail, Figure 3a shows the case of a single pseudo-tail with two contact-formed loops, Figure 3b one long pseudo-tail with one contact-formed loop and another independent, shorter pseudo-tail without contact-formed loops, Figure 3c one independent long pseudo-tail and another shorter pseudo-tail with one contact-formed loop, and Figure 3d three independent pseudo-tails without loops. Each of these cases has been identified on the basis of the lowest χ˜ 2 value from all possible configurations. A further possible configuration is a pseudo-tail, which is desorbing between the two desorption events of a contact-
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Figure 4. (a) Distribution of the contour lengths as obtained after decomposing the complex bridging events into contact-formed loops (open circles) and independently bridged pseudo-tails (filled circles). For comparison, the distribution for the chain rupture distances (stars) is also given. The solid lines indicate a power law with a negative exponent a ) 3/2. (b) Probability for an independent pseudo-tail of forming n loops on the opposite surface during contact of the surfaces.
Figure 3. Force curves involving three (a-d) or more (e) rupture events of bridging polymer chains. (a) A single pseudo-tail with two contact-formed loops, (b) one long pseudo-tail with a contact-formed loop and a shorter independent pseudo-tail, (c) one long pseudo-tail and an independent shorter pseudo-tail with a contact-formed loop, and (d) three independent pseudo-tails. (e) More than three rupture events, which have been decomposed into independently bridged pseudo-tails (I-IV) and contact-formed loops. The thin lines are fits to independent pseudo-tails solely (cf. eq 4) and to one pseudo-tail with contact-formed loops (cf. eq 3), respectively. The heavy lines indicate the best fit, and the corresponding values for χ˜ 2 are given for both aforementioned models.
formed loop of another pseudo-tail. One expects that such intermixing of pulling events must be rather infrequent, and for three events, it could not be found in the available dataset. Another difficulty in the analysis is the occasional occurrence of plateaulike force responses, which result from the desorption or sliding of polymer segments on the substrate (arrow in Figure 3d).7,21 These problems can be greatly reduced by restricting the data analysis to events occurring at separation distances >50 nm. The analysis scheme can be generalized to arbitrary numbers of rupture events. Depending on the quality of the data, we are
usually able to differentiate the chain conformations for up to five to seven detachment events. In favorable situations, a substantially larger number of events can be resolved. Such an example is shown in Figure 3e, which shows 13 rupture events. The retraction force profile can be decomposed into four independently bridged pseudo-tails with one having three contactformed loops and other three having two contact-formed loops each. This model leads to an excellent fit of the data. When the resulting fit is compared with conventional models of completely independent chains or only one chain forming loops on the opposite surface, taking into account exclusively either one of these configurations fails to describe the observed pattern of polymer stretching and rupture events. Even for such complex retraction profiles, the intermixing of rupture events occurring between the independent chains seems to have a low probability. We have analyzed the force curves with up to eight events by allowing for this possibility, but less than 10% of all events could be eventually interpreted as intermixed pulling events. Therefore, this process seems to be rather unlikely. The presented decomposition scheme has substantial potential to characterize the bridging mechanisms between two adsorbed polymer layers. To illustrate this point, we have analyzed the statistical distributions for the segment lengths as obtained from the decomposition of retraction curve profiles between adsorbed PVA layers. This analysis is based on about 150 force profiles obtained from two independent experiments. The segment length distributions were obtained from histograms with bin sizes of 10 nm, except 5 nm for loops. Figure 4a compares the number (21) Al-Maawali, S.; Bemis, J. E.; Akhremitchev, B. B.; Leecharoen, R.; Janesko, B. G.; Walker, G. C. J. Phys. Chem. B 2001, 105, 3965-3971.
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density of contour lengths L for the pseudo-tails (i.e., L1, L2 in Figure 2b or L′ + L′′ in Figure 2a) and of the individual contactformed loops (i.e., L′′ in Figure 2a). The observed length distributions follow the power-law
f(L) ∝ L-a
(5)
where L is the contour length of the chain and can thus be directly compared with scaling theories for polymer adsorption originating from the work of de Gennes and others.22,23 An exponent of a ) 11/5 has been predicted for adsorption in good solvent in the dilute regime,22 while for a so-called Guiselin brush,24 one obtains a ) 3/2. The latter situation corresponds to a polymer layer adsorbed from a dense polymer melt and rinsed with a good solvent afterward. The Guiselin exponent a ) 3/2 is found for the independent chains, as well as for the loops formed during contact, in accordance with the self-similarity of polymer adsorption.25 The same exponent was obtained recently by AFM measurements of rupture distance distributions for polyacrylamine (PAA), either as an adsorbed polymer film26 or for the loop distribution of a single adsorbed chain.27 In the present situation, we can ascertain that the distribution of rupture distances follows closely the distribution of the independent chains. This behavior might seem surprising at first but follows from the low probability of forming a loop on the other surface during contact. The formation of such loops will be enhanced by the large contact area of a colloidal probe with respect to the one of a normal AFM tip. Further details of the loop formation can be extracted from Figure 4b, which shows the probability distribution of the number of loops formed by an (22) De Gennes, P. G. C. R. Acad. Sci., Ser. II 1982, 294, 1317-1320. (23) O’Shaughnessy, B.; Vavylonis, D. J. Phys.-Condes. Matter 2005, 17, R63-R99. (24) Guiselin, O. Europhys. Lett. 1992, 17, 225-230. (25) De Gennes, P. G. Macromolecules 1981, 14, 1637-1644. (26) Senden, T. J.; di Meglio, J. M.; Auroy, P. Eur. Phys. J. B 1998, 3, 211216. (27) Haschke, H.; Miles, M. J.; Koutsos, V. Macromolecules 2004, 37, 37993803.
independent chain during contact. Only 35% of the independent chains form loops on the opposite surface. The loop distribution turns out to be close to exponential, with an average number of loops of nj ≈ 0.77. It is tempting to speculate on the origin of common power-law lengths distributions of contact-formed loops and pseudo-tails for an uncharged polymer film, such as PAA, and for highly charged PVA, as examined here. When both surfaces are pressed into contact, the polymer concentration between the two surfaces increases dramatically and becomes similar to a polymer melt. Therefore, we suspect that the original polyelectrolyte film structure is altered into the one of a Guiselin brush, as proposed by for polymer films recently.28 In conclusion, we present a novel approach to analyze multiple pulling events occurring between adsorbed polymers layers as probed by the colloidal probe technique. The approach is based on the decomposition of the event sequence into contributions of independently bridging pseudo-tails originating from the initial adsorption of the polymer and the elimination of loops formed during the contact of the two surfaces. Both processes occur in parallel, as revealed by a detailed analysis of pulling events occurring between polyelectrolyte-coated surfaces. For example, we have determined the number and length distributions of the contact-formed loops. The number distribution is exponential, while the length distribution follows a power law, which is similar to the length distribution of the individual chains bridging the surfaces. The length distributions are compatible with the exponent 3/2 proposed by Guiselin.24 This exponent was also proposed for neutral polymer chains adsorbed from a melt, suggesting that adsorbed polyelectrolyte layers attain a similar structure under repetitive compression. Acknowledgment. This research was supported by BASF Aktiengesellschaft, Swiss Program TopNano21 and the Swiss National Science Foundation. We thank the BASF laboratories for the synthesis and characterization of the PVA samples and Roland Netz for an illuminating discussion. LA062046X (28) Raviv, U.; Klein, J.; Witten, T. A. Eur. Phys. J. E 2002, 9, 405-412.
