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Effects of Contact Time and Polarity Level on Adhesion between Interacting Surfaces Emmanuel Girard-Reydet,†,‡ Robert Oslanec,† Philip Whitten,† and Hugh R. Brown*,† BHP Steel Institute, University of Wollongong, Wollongong, New South Wales 2522, Australia, and Laboratoire Mate´ riaux Macromole´ culaires, INSA Lyon, 20 avenue Albert Einstein, 69621 Villeurbanne Cedex, France Received June 3, 2003. In Final Form: October 9, 2003 We have measured the rate at which adhesion develops between two surfaces that interact by hydrogen bonding. A poly(dimethylsiloxane) elastomer lens with a slightly oxidized surface was pushed against a polystyrene-based copolymer substrate that contained acid groups. The interaction was measured on both forming and breaking the contact using the JKR technique. The toughness of the joint, Gc, increased considerably with increasing acid content in the substrate while the apparent work of adhesion, W, measured while making the contact, decreased with increasing acid content. This decrease in W implies that the acid groups caused repulsion between the surfaces when they were not in contact, but the increase in Gc shows that they formed bonds after contact was made. The rate of increase of Gc with time was found to depend on the acid content in the substrate, but for moderate acid levels, Gc was found to saturate at values that varied approximately linearly with acid content. For 8% acid and 47% acid substrates, the rate of adhesion development over a period of 24 h could be fitted by a model assuming (i) the toughness increased linearly with areal density of bonds between the substrate and the elastomer and (ii) the rate of reaction between the substrate and the elastomer varied as the cube of the density of unreacted acid groups. This cube law may possibly be explained by the kinetics of motion of the elastomer chains on the substrate.
Introduction The JKR theory provides the analytical framework for measurement of interfacial energy and is well-suited to analyzing the contact at interfaces where at least one of the materials is relatively soft.1-4 For the contact between an elastic hemisphere and a flat surface, the JKR model1 predicts the radius of the contact patch, a, resulting from effects of both the surface forces and external forces to be given by
a3 )
R {P + 3πWR + (6πWRP + (3πWR)2)1/2} (1) K
where K ) 4E/3(1 - ν2), with E being the Young modulus and ν the Poisson ratio of the elastomer, R is the radius of the undeformed lens, P is the external load, and W is the thermodynamic work of adhesion. Two consequences follow from eq 1: first in the absence of an external load, the contact radius takes a nonzero value; second, a remains positive even if a small negative load is applied. An analysis of eq 1 also shows that, by recording the experimental variation of the contact radius with applied load, one can independently determine W and K by a two-parameter fit. Although this approach yields satisfactory agreement with contact experiments in which the load on the sample is increased with time, very often a substantial hysteresis * To whom correspondence should be addressed. † BHP Steel Institute, University of Wollongong. ‡ Laboratoire Mate ´ riaux Macromole´culaires, INSA Lyon. (1) Johnson, K. L.; Kendall, K.; Roberts, A. D. Proc. R. Soc. London, Ser. A 1971, 324, 301-313. (2) Maugis, D.; Barquins, M. J. Phys. D: Appl. Phys. 1978, 11, 19892023. (3) Chaudhury, M. K.; Whitesides, G. M. Langmuir 1991, 7, 10131025. (4) Chaudhury, M. K.; Whitesides, G. M. Science 1992, 255, 12301232.
is observed when the sample is unloaded. Namely, the curves of a versus P recorded during loading do not superimpose with those recorded on unloading. The deformation is not reversible as would be required by the JKR theory. The origin of this hysteresis is not always understood, is sometimes controversial, and may well be different for different situations.5,6 Adhesion hysteresis may be the result of surface reconstruction on forming interfacial contact,7,8 entanglement at the interface,9-12 chemical bond formation in the contact area during the contact time,7,8 or dissipative processes during unloading such as viscoelastic losses.11-13 To investigate the origin of such adhesion hysteresis, the JKR approach can be extended using fracture mechanics.2 The basic insight here is that the crack, as the periphery of the contact area could be viewed, will grow under conditions in which the strain energy released by the failure of the interface more than compensates for the energy required to create two new interfaces. It is the magnitude of this fracture energy, G, that determines whether the crack will grow or not under a given loading. Fracture mechanics allow one to write an expression for G that is the inverted form of eq 1
G)
(
)
a3K 1 -P 3 R 6πKa
2
(2)
Experimentally it is then observed as the signature of adhesion hysteresis that G during loading is approxi(5) Jones, R. A. L.; Richards, R. W. Polymers at surfaces and interfaces, 1st ed.; Cambridge University Press: Cambridge, 1999. (6) Tirrell, M. Langmuir 1996, 12, 4548. (7) Silberzan, P.; Perutz, S.; Kramer, E. J.; Chaudhury, M. K. Langmuir 1994, 10, 2466-2470. (8) Perutz, S.; Kramer, E. J.; Baney, J.; Hui, C. Y. Macromolecules 1997, 30, 7964-7969. (9) Brown, H. R. Macromolecules 1993, 23, 1666-1670. (10) Creton, C.; Brown, H. R.; Shull, K. R. Macromolecules 1994, 27, 3174-3183.
10.1021/la034976b CCC: $27.50 © 2004 American Chemical Society Published on Web 12/23/2003
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mately W, whereas G during unloading, referred to as Gc when it is large enough to propagate the crack, may be much larger and may vary with both the unloading rate10-12 and the contact radius7,8,14 in a way depending on the nature of this hysteresis. The unloading curves have then to be carefully analyzed. In this paper, we have studied in the framework of the JKR methodology the contact between two surfaces that are likely to develop specific interactions with time. Our aim was to investigate the dynamics of the growth of the adhesion and accurately define the source of the adhesion hysteresis that is generated. For that purpose, partially oxidized poly(dimethylsiloxane), PDMSox, lenses were brought into contact with random styrene acid modified styrene copolymers before the load was released. The fracture energy, Gc, was studied as a function of the contact radius, the contact time, and the level of acid of the copolymer. Experimental Section Preparation of Semispherical PDMS Lenses. The PDMS precursor chains obtained from IBM were R,ω-vinyl-terminated with average molecular mass of 9600 g‚mol-1 and polydispersity of approximately 2. The cross-linker was a methylhydrosiloxanedimethylsiloxane copolymer (MHS from Gelest) with average molecular mass of 1050 g‚mol-1 and average functionality in hydride groups of 7.6. The cross-linking reaction was performed via hydrosilation catalyzed by 10 ppm of platinium-divinyl tetramethyldisiloxane complex (PtDS from Gelest) with a ratio of hydride to vinyl groups, r ) 1.5, to ensure maximum crosslinking density. Lenses for the JKR adhesion experiments were prepared by depositing with a microsyringe small droplets of the uncured mixture onto a microscope glass slide that had previously been treated with fluorosilane to prevent complete wetting and reduce adhesion to it. The hydrosilation polymerization reaction was carried out at 60 °C for one night under vacuum. The radii of curvature of these lenses were measured by determining the height and the base of the spherical cap. The prepared lenses had radii of curvature in the range 1-1.5 mm. We have performed experiments on the neat elastomers (as they were obtained after curing) and extracted gels. In the latter case, the lenses were soaked in toluene for 24 h. After this procedure, the fraction of extracted material was around 2 wt %. After extraction, the solvent was removed from the network by drying in a vacuum at 60 °C. Extraction was also observed to have no effect on the adhesion results in both the loading and unloading regimes. Partial Oxidation of PDMS Lenses. To produce polar groups near the surface of the PDMS network, PDMSox, the lenses were partially oxidized in a UV-ozone cleaner for 15 min. That oxidation treatment was concurrently measured on a PDMS flat sheet, prepared from the same materials used in preparing the lenses, and found to induce a decrease of the static contact angle with water from 120 °C (PDMS) to 80 °C (PDMSox). All JKR experiments were performed just after the oxidation treatment to limit surface reconstruction of the lens (polar groups with a higher surface energy than that of the PDMS network would prefer to remain below the surface). Preparation of Polymer Surfaces. The solid surfaces against which the elastomer was compressed were polystyrene and styrene acid modified styrene random copolymers with different levels of acid. The polystyrene, PS, with a narrow molecular mass distribution of Mw equal to 120 000 g‚mol-1 was obtained from Polymer Laboratories. Three random copolymers of molecular mass about 30 000 g‚mol-1 with different levels of (11) Deruelle, M.; Le´ger, L.; Tirrell, M. Macromolecules 1995, 28, 7419-7428. (12) Deruelle, M.; Hervet, H.; Jandeau, G.; Leger, L. J. Adhes. Sci. Technol. 1998, 12, 225-247. (13) Luengo, G.; Pan, J.; Heuberger, M.; Israelachvili, J. N. Langmuir 1998, 14, 3873-3881. (14) Chaudhury, M. J.; Weaver, T.; Hui, C.-Y.; Kramer, E. J. J. Appl. Phys. 1996, 80, 30-37.
Langmuir, Vol. 20, No. 3, 2004 709 acid (8%, 47%, and 81% molar units which are COOH terminated, respectively) were synthesized and kindly given by Petr Vlcˇek. In the following, for example, PS-8%acid will denote the random copolymer whose 8% molar units are COOH terminated. Films were spin coated from either a 2% polymer solution in toluene (PS and PS-8%acid) or a 2% solution in THF (PS-47%acid and PS-81%acid) onto silicon wafers and then annealed under vacuum at 145 °C for 2 h. Film thicknesses measured by ellipsometry were in the range 80-110 nm. Adhesion Experiments. The JKR apparatus is similar to those already described in the literature. It is designed to measure the adhesion between two bodies, typically a hemisphere and a flat surface, where at least one of the bodies is elastic. The top sample, the PDMSox hemisphere, is placed on a transparent microscope glass slide, which slides into the upper part of the sample holder assembly where it is held firmly. The PS or copolymer film is placed onto a sample platform, which is mounted on a load cell. The load cell is a precision gram range load cell, model GSO-25 from Transducer Techniques, which can be loaded to a maximum of 25 g with an approximate sensitivity of about 1 mg. The load cell is attached to the moving shaft of a Burleigh inchworm motor, IW-710, controlled by a 6000ULN controller. The load and displacement are thus imposed by the motor, which controls the movement of the PS or copolymer film. The radius of the contact area, a, is measured by recording images of the contact area using a video imaging system. The contact area is viewed in reflection mode by a high-resolution video camera, and the images can be stored in a digital form through a frame grabber card. The measurement was first performed by pressing the two surfaces against each other at a fixed motor movement speed (0.1 µm/s) until a maximum load (typically 0.2 g) was reached and measuring the load, P, the imposed displacement of the bodies, δ, and the radius of the circular contact area, a (loading regime). The time delay between two consecutive measurements was 2 s. The load was then released (unloading regime) in the same way as the loading regime, either directly after loading or after the system was held in contact for a given time. The basic data of the JKR experiments will be presented in the form of the strain energy release rate, G, as a function of a. For that purpose, the elastic constant, K, was first calculated from the best fit between the experimental loading data and eq 1. This calculated value was then used to determine G during the loading and unloading regimes according to eq 2. A preliminary basic JKR experiment (no specific contact time before unloading) was performed on PDMS before oxidation in contact with pure PS, as their adhesion energy has already been measured by the method of contact mechanics.15 This experiment showed first, from the concurrence of the loading and unloading data, that there is no adhesion hysteresis for this system. Second, the fit between the experimental data and eq 1 yielded values of elastic constant of the elastomer, K ) 2.15 MPa, and work of adhesion, WPDMS/PS ) 45 mJ‚m-2, in excellent agreement with the literature.15
Results Two sets of experiments were carried out. In the first set involving all polymer surfaces from pure PS to PS81%acid, the unloading was performed just after the maximum load was reached at the end of the loading regime. In the second set of experiments limited to PS8%acid and PS-47%acid, the system substrate/PDMSox lens was held in contact for different times, tc, under that maximum load before the load was released. Figures 1-4 show the results obtained from the first set of experiments, where the strain energy release rate, G, is plotted during loading and unloading as a function of the contact radius, a, between the PDMSox lens and the PS, PS-8%acid, PS-47%acid, and PS-81%acid, respectively. For the PS film, the data obtained from both the loading and unloading experiments fall on the same curve (15) Li, L. H.; Macosko, C.; Korba, G. L.; Pocius, A. V.; Tirrell, M. T. J. Adhes. 2001, 77, 95-123.
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Figure 1. Loading (O) and unloading (0) G as a function of the radius of contact, a, between PDMSox and PS.
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Figure 5. Unloading G as a function of the radius of contact, a, between PDMSox and PS-8%acid for different contact times, tc: (4) no contact time; (b) tc ) 1 h; (0) tc ) 4 h; ([) tc ) 9 h; (×) tc ) 24 h.
Figure 2. Loading (O) and unloading ([) G as a function of the radius of contact, a, between PDMSox and PS-8%acid. Figure 6. Unloading G as a function of the radius of contact, a, between PDMSox and PS-47%acid for different contact times, tc: (4) no contact time; (b) tc ) 3 min; (s) tc ) 15 min; (0) tc ) 1 h; (×) tc ) 24 h.
Figure 3. Loading (O) and unloading ([) G as a function of the radius of contact, a, between PDMSox and PS-47%acid.
Figure 4. Loading (O) and unloading ([) G as a function of the radius of contact, a, between PDMSox and PS-81%acid.
indicating no adhesion hysteresis. On the other hand, all the other systems based on acid-modified PS showed considerable hysteresis. While the loading G remains independent of a, the unloading G actually increases as a decreases from the maximum contact radius (corresponding to the maximum load) to the center of contact. Clearly, the level of acid has a profound effect on the magnitude of the adhesion hysteresis and the fracture energy in the unloading regime that can become greater than 1 J‚m-2 in the case of the PS-81%acid film. For PS47%acid and PS-81%acid, we notice that the unloading G initially increases without any variation of a (that remains equal to the maximum contact area) before a critical
fracture energy, Gci, is reached from which a shrinks while Gc keeps on monotonically increasing. (We use Gc to refer to a value of G obtained while the crack is propagating so the contact patch is shrinking and Gci to refer to the initial value of G where the propagation starts.) Such a behavior has already been reported in the literature8 without much discussion of the criteria required to observe it. However, Gc can be seen to increase with the level of acid. The results of unloading G as a function of a after different contact times, tc, obtained in the second set of experiments, are presented in Figures 5 and 6 for PS8%acid and PS-47%acid, respectively. In each plot, the initial difference of maximum contact radius before the load was released arises from the difference of radius of curvature between the different lenses used for these experiments. For both substrates, a big effect of contact time on Gci is observed. We will come back with details to this point in the Discussion. Nevertheless, the hysteresis can be seen to evolve differently with contact time depending on the level of acid in the substrate. When the level of acid remains low, the unloading Gc becomes independent of a (and equal to Gci) for long contact times. Alternatively, when the level of acid is much higher, Gc invariably increases above Gci while a decreases giving evidence for some differences in the origin of the adhesion hysteresis. Discussion First, it is worth emphasizing that all the JKR experiments performed with various substrates and different contact times consistently gave, from the best fit between the experimental loading data and eq 1, the same value of elastic constant, K ) 2.15 ( 0.15 MPa (i.e., elastic modulus, E ) 1.2 ( 0.1 MPa) for the elastomer, PDMSox. This value is also the same as the one calculated for PDMS
Adhesion between Surfaces
Figure 7. Work of adhesion, W, of PDMSox on acid-modified PS as a function of the level of acid.
before oxidation (see Experimental Section), showing that the oxidation treatment only affects the surface regions of the PDMS network. On the other hand, the loading G, which is independent of a and thought to equal to the work of adhesion, W, drops from 52 mJ‚m-2 on PS to 28 mJ‚m-2 on PS-81%acid as depicted in Figure 7. The value of WPDMSox/PS obtained seems very reasonable compared to the value for WPDMS/PS ) 45 mJ‚m-2 mentioned above. The effect of acid on reducing WA was observed previously15,16 in studies of the contact between a model pressure-sensitive adhesive and itself or two release coatings. For the acrylate-based cross-linked elastomer, copolymerization with 10% acrylic acid was found to significantly reduce the work of adhesion, measured at room temperature, of the elastomer with itself or with two carbamate release coatings. The self-adhesion (W) of the acid-containing polymer was found to increase significantly when the measurement was made at 75 °C, where the hydrogen bonds are expected to break. At 75 °C the W of the acid-containing polymer was slightly greater than that of the acid-free polymer. The authors speculated that this effect had its origin in the enhanced inelastic nature of the acid-containing polymer; however, such an explanation could not apply to the results presented here, as it is the rigid substrate that contains the varying number of acid groups. During the loading process, the contact patch is always larger than that predicted by Hertz theory (W ) 0) because van der Waals and other forces cause an attraction between the two surfaces. Hence the size of the contact patch is controlled by the forces that exist between the two surfaces where they are close but not in contact, not by the energy of the interface when contact is established. The value of WPDMS/PS is very similar to WPDMS/PDMS and probably a measure of the van der Waals forces between the two materials. Weak oxidation of the PDMS increases this value slightly, so why do acid groups in the PS cause such a strong decrease in the attraction? A possible explanation is that the dipoles in the two surfaces are oriented so that they repel each other. Only after contact is established do they reorient to angles where they attract each other. A second possible explanation is based on the idea that water adsorbed on the acidified PS will decrease the attraction. However the work of adhesion between PDMS and water is probably just as large as that between PDMS and PS (a value of 53 mJ‚m-2 can be estimated from the contact angle of 105° of water on PDMS), so it seems unlikely that adsorbed water plays a significant role in this decrease in the measured work of adhesion with acid content. Before detailed consideration of the effects of both the acid level and contact time on the unloading regime and (16) Li, L. H.; Tirrell, M. T.; Korba, G. L.; Pocius, A. V. J. Adhes. 2001, 76, 307-334.
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Figure 8. Displacement, δ, versus load, P, in the initial region of unloading where G increases at a constant radius of contact (a ) 132.6 µm) for the PDMSox/PS-47%acid system after a contact time tc ) 15 min. From the slope, the compliance C ) 2.24 × 10-3 m/N.
discussion of the source of adhesion hysteresis, there is a clear need to address the question of the initial increase of unloading G where the contact area remains fixed (which concerns all the unloading experiments with PS-47%acid or PS-81%acid and the unloading experiments with PS8%acid after the system was held in contact). Figure 8 shows the displacement, δ, as a function of the load, P, in the corresponding region of unloading for one system taken as an example, the PDMSox/PS-47%acid system that has previously experienced a contact time of tc ) 15 min. The fact that δ varies linearly with P in all that region clearly demonstrates that the concurrent increase of G arises from the compliance, C, of the system that is defined by the slope of the plot.17 For an elastic lens on a rigid layer with a radius of contact, a, the compliance is also given by the following equation18
C)
2 3Ka
(3)
that finally leads for our example in Figure 5 to the value of the elastic constant, K ) 2.24 MPa, in very good agreement with K calculated from the fit of the loading curve to the JKR equation. This increase of unloading G at fixed a controlled by the compliance of the system is also the signature that adhesion forces have developed inside the contact area between the materials. The critical unloading fracture energy, Gci, from which a starts to decrease thus becomes the relevant parameter to describe the energy per area necessary to separate the solids. The interactions that are very likely to build up in these systems are hydrogen bonds between the acid groups in the acid-modified PS and polar groups created by oxidation treatment at the surface of PDMSox, and to a lesser extent hydrogen bonding between the acid groups and oxygen in the PDMS chains. Hydrogen bonding between PDMS chains and acid groups has been studied using self-assembled chains.19,20 Hydrogen bonding at the interface as a main source of hysteresis is strongly supported by the absence of adhesion hysteresis with pure PS and the clear tendency of Gci to increase with both the level of acid in the substrate and contact time. It should be noted that the development of these specific interactions during contact certainly occur (17) Shull, K. R.; Ahn, D.; Chen, W.-L.; Flanigan, C. M.; Crosby, A. J. Macromol. Chem. Phys. 1998, 199, 489-511. (18) Johnson, K. L. Contact Mechanics; Cambridge University Press: Cambridge, 1985. (19) She, H.; Malotky, D.; Chaudhury, M. K. Langmuir 1998, 14, 3090-3100. (20) Choi, G. Y.; Kang, J. F.; Ulman, A.; Zurawsky, W.; Fleischer, C. Langmuir 1999, 15, 8783-8786.
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reaction constant), the toughness at time t is given by
G ) W + Qx0 -
Figure 9. Comparison of the adhesion kinetics for PS-8%acid and PS-47%acid in contact with PDMSox. The solid curves are a fit to eq 4 with the same reaction rate constant K used for both substrates. The inset shows replots data for the PS-47%acid substrate showing just the first hour of contact.
with the concurrent reconstruction of the acid-modified PS surface that might bury high-energy acid groups in contact with air but rearrange to expose them on contact with polar PDMSox. However this reconstruction is probably sufficiently slow that it has only a small effect on the adhesion development over 24 h. The dynamics of the growth of the adhesion with contact time are compared in Figure 9 for PS-8%acid and PS47%acid. The contact times are not just the time between loading and unloading but also included, where significant, the time during the unloading before the crack started to move. It is interesting to note that Gci for the situation where the direction of motion was reversed with no holding time remains equal to W for PS-8%acid, but it is already nearly 1 order of magnitude larger than W when the level of acid reaches 47%. For that latter substrate, compared with the former, both the rate of development of adhesion is much faster and the plateau value of adhesion energy developed at long contact time much higher, due to the difference in the number of acid groups available at the surface to build up interactions with PDMSox. The plateau value of Gci at long contact time increases about in proportion to the acid content in the PS. This result implies that the acid content in the PS controls the areal density of coupled chains at the interface and that there is an excess of reactive groups on the PDMS surface. Also it seems likely that the toughness varies linearly with the areal density of reacted chains as has been seen in other similar systems.21 Hence it is reasonable to assume that the rate of growth of the adhesion is a reflection of the rate of reaction between the elastomer and the substrate. The difference in the evolution of adhesion hysteresis with contact time between the two substrates shows that the reaction rate is very dependent on the density of acid groups. If the reaction rate varied linearly with the density of unreacted acid groups (first order kinetics), then the growth of adhesion for the two substrates would be described by the same time constant. Clearly this is not the case. If the density of unreacted acid groups is given by x and the initial density by x0, then assuming that the toughness G varies linearly with the areal density of reactions, it is given by G ) W + Q(x0 - x), where Q is a constant. Then, if the reaction order is n (dx/dt ) -Kxn, where K is the (21) Koberstein, J. T.; Duch, D. E.; Hu, W.; Lenk, T. J.; Bhatia, R.; Brown, H. R.; Lingelser, J.-P. J. Adhes. 1998, 66, 229-245.
Qx0 (1 + K(n - 1)x0(n-1)t)1/(n-1)
(4)
First-order reaction kinetics implies the existence of a time constant that would be the same for both the 8% and 47% substrates. Inspection of Figure 9 shows immediately that this is not the case. However both data sets can be fitted by eq 4 assuming either second- or third-order kinetics. However the values obtained for the reaction constant K differed by about a factor of 5 between the two data sets when n was chosen to be 2, whereas the difference between them was insignificant when a value of 3 was chosen for n. The solid lines in Figure 9 are fits to eq 4 where n was chosen to equal 3 and the same value of reaction constant K was used for both data sets. The fit is excellent, and so the time evolution of the adhesion is very well represented by the assumption of the thirdorder reaction kinetics between the acid groups on the substrate and the active groups on the oxidized PDMS lens. It is valuable to consider what kinetics might be expected for the formation of bonds between the PDMS and the acidified PS. If we continue to assume the existence of an excess of reactive groups on the PDMS surface, then it is reasonable to assume that the reaction rate will be controlled by the rate at which these active groups on the PDMS come in contact with the static acid groups on the PS substrate. Hence first-order kinetics might be expected together perhaps with some diffusion effects. Clearly this is not the case, so we need to consider possible reasons for the observed third-order kinetics. As hydrogen bonds are fairly weak, one should really include the rate of dissociation of the bonds, the off-rate, in any consideration of kinetics. This will change the apparent rate of reaction with time, but it is hard to see that it can explain the massive change in apparent time constant between the two substrates. As pointed out by a reviewer, the interaction between the carboxylic groups and the oxidized PMDS is complex, as the Si-OH groups can hydrogen bond with the carbonyl oxygen on the acid groups and thereby decrease the pKA of the acid and hence increase the strength of hydrogen bonding between the terminal H of the acid group and the oxygen in the PDMS. This process again will alter the kinetics but, as a local process, seems unlikely to alter the apparent time constant between the two substrates. It is known from friction experiments that PDMS chains adsorb onto a PS surface and this adsorption must strongly decrease their motion on the surface. The presence of acid groups decreases the work of adhesion, WA, between the PDMS and the substrate. The acid groups must therefore decease the adsorption of the PDMS and so increase the PDMS mobility on the surface. Hence the reaction rate will increase with acid content. Hence second or higher order kinetics might be expected. The reason for specifically third-order kinetics is unclear. As mentioned above, the first set of experiments were done by loading the PDMS lens up to the maximum load and then immediately reversing the motor and starting the unloading. For Gci to be different from W, the rate of growth of Gc with time has to have been greater than the rate of growth of the applied G during the unloading. From the fits shown in Figure 9, it is easy to show that G initially increased with contact time at 0.04 mJ/(m2 s) for the 8% acid substrate but at 5 mJ/(m2 s) for the 47% acid substrate. The unloading increased G initially at 1.5 mJ/(m2 s).
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Figure 10. For PS-8%acid, a comparison between the adhesion data shown in Figure 2 but here plotted as a function of contact time, with the predictions from much longer contact time (eq 4), here shown by the solid line.
Clearly the observation that Gci equals W for the 8% substrate but not for the 47% substrate is entirely consistent with the observed kinetics of the increase of Gc with contact time. For PS-8%acid, the fact that the unloading Gc becomes independent of a when the system was previously held in contact indicates that the hysteresis observed when tc ) 0 (Figure 2) is the direct consequence of the difference of contact time experienced by the material near the maximum contact radius to that experienced by the material near the center of the contact. The loading process actually leads to the development of specific interactions in a spatially nonuniform way inside the contact area, with stronger interactions and thus higher adhesion energy in the center due to longer contact time. Once tc becomes significantly longer than the time scale of the loading experiment (around 2 min), the adhesion energy becomes dominated by the contribution of the new interactions created during the contact and the unloading, G ) Gc, and no longer varies with a. This also means that the experiment in Figure 2 should provide information on the short time adhesion kinetics for the PDMSox/PS8%acid system. The basic idea is to consider each value of unloading G(a) as a distinct measurement of Gc for a given contact time, tc, that can easily be calculated for each a. Figure 10 compares the measured points with the predictions obtained using eq 4 (solid line). It would appear
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that adhesion grows more rapidly than expected in the first two minutes but then tends more to the expected rate. From the lack of dependence of unloading G on the contact radius a, and hence crack speed, it can be inferred that the development of specific interactions at the interface is the only source of adhesion hysteresis in the low acid level substrate which generates relatively low values of adhesion energy. It is interesting to observe that the detachment of these specific interactions does not show enough rate dependence to be observable in these tests. When the level of acid is much higher, typically 47%, the situation becomes different. The variation of unloading Gc (above Gci) with crack speed irrespective of the contact time shows that rate-dependent dissipative processes, probably viscoelastic losses, constitute a source of adhesion hysteresis in addition to energy loss associated with detachment of the hydrogen bonding. Owing to the much higher areal density of hydrogen bonds at the high acid levels, the interface becomes able to sustain a stress greater than the minimum stress required to bring these energy dissipation mechanisms into play. Note that PDMSox is a nearly perfectly elastic material at room temperature (Tg ≈ -120 °C) under small strains and it is therefore very likely that the contribution of any bulk viscoelasticity to the adhesion hysteresis necessitates relatively high adhesion level only afforded by such level of acid modification in the substrate. Conclusion We have demonstrated that, in a hydrogen-bonding system, adhesion can build up with contact time with apparent time constants in the range of hours. The time constant for rearrangement of the acid groups in the substrate surface is much longer, so the adhesion time constant is probably related to the kinetics of attachment of a mobile chain to an interface at many points. The process seems to follow third-order kinetics in unreacted acid, perhaps because the unreacted acid increases the mobility of the PDMS close to the interface. The adhesion increased strongly with the fraction of acid in the substrate while the apparent work of adhesion decreased, demonstrating that there is a huge difference between the thermodynamics of contact formation and actual adhesion. Acknowledgment. The acid-modified polystyrenes were kindly donated by Dr. Petr Vlcˇek. We acknowledge support from the ARC for this work. LA034976B
