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Adhesive Transfer of Thin Viscoelastic Films Kenneth R. Shull,* Elizabeth F. Martin, Peter L. Drzal, Mark C. Hersam, Alison R. Markowitz, and Rachel L. McSwain Department of Materials Science and Engineering, Northwestern University, 2220 North Campus Drive, Evanston, Illinois 60208-3108 Received July 26, 2004. In Final Form: September 17, 2004
Micellar suspensions of acrylic diblock copolymers are excellent model materials for studying the adhesive transfer of viscoelastic solids. The micellar structure is maintained in films with a variety of thicknesses, giving films with a well-defined structure and viscoelastic character. Thin films were cast onto elastomeric silicone substrates from micellar suspensions in butanol, and the adhesive interactions between these coated elastomeric substrates and a rigid indenter were quantified. By controlling the adhesive properties of the film/indenter and film/substrate interfaces we were able to obtain very clean transfer of the film from the substrate to the portion of the glass indenter with which the film was in contact. Adhesive failure at the film/substrate interface occurs when the film/indenter interface is able to support an applied energy release rate that is sufficient to result in cavity nucleation at the film/substrate interface. Cavity formation is rapidly followed by delamination of the entire region under the indenter. The final stage in the transfer process involves the failure of the film that bridges the indenter and the elastomeric substrate. This film is remarkably robust and is extended to three times its original width prior to failure. Failure of this film occurs at the periphery of the indenter, giving a transferred film that conforms to the original contact area between the indenter and the coated substrate.
1. Introduction A variety of patterning techniques have been developed for transferring a thin film from one surface to another. Examples include thermal transfer printing and the various adaptations of “soft lithography”.1 Soft lithography involves the contact of a flexible material, typically poly(dimethylsiloxane) (PDMS) with a second surface onto which a pattern is to be transferred. Microcontact printing is perhaps the most common version of this technique, where transfer of a liquid forms a selfassembled monolayer that acts as a barrier to subsequent etching steps.2 In some more recent examples, including nanoscale transfer printing3 and decal transfer microlithography,4 a patterned solid is transferred directly during the contact process, eliminating the need for an etching step. In all of these cases control of the relative wetting or adhesion of a thin film to two different surfaces is required. Figure 1 illustrates the physical processes taking place when a portion of a continuous thin film is transferred between two surfaces. In this case, the film to be transferred exists on top of a compliant substrate and is pressed into contact with a second surface. For the specific case of the experiments described in this paper, the compliant substrate is a PDMS elastomer, and the film is transferred to a glass hemispherical indenter. If the adhesion between the film and the indenter is sufficiently high in comparison to adhesion characterizing the film/ substrate interface, the film will ultimately be transferred to the indenter as illustrated in Figure 1c. The distinguishing feature of the use of a continuous film, as opposed to a preexisting pattern used in the lithographic techniques mentioned above, is that initiation of failure at the film/substrate interface is required. No (1) Xia, Y.; Whitesides, G. M. Annu. Rev. Mater. Sci. 1998, 28, 153. (2) Kumar, A.; Whitesides, G. M. Appl. Phys. Lett. 1993, 63, 2002. (3) Loo, Y.-L.; Willett, R. L.; Baldwin, K. W.; Rogers, J. A. Appl. Phys. Lett. 2002, 81, 562. (4) Childs, W. R.; Nuzzo, R. G. J. Am. Chem. Soc. 2002, 124, 13583.
Figure 1. Mechanism of adhesive transfer: (a) failure initiation at the film/substrate interface; (b) cavity propagation; and (c) film fracture and transfer to the indenter. Prior to film fracture, the film is stretched between the indenter and the substrate, as illustrated in Figure 2.
preexisting crack exists at the film/substrate interface, so the adhesion at the film/indenter interface must be comparatively large for crack initiation and eventual adhesive transfer to occur. Crack initiation at the film/substrate interface begins with nucleation and growth of a cavity, which grows laterally and eventually leads to delamination of the film inside the circular contact area. After subsequent strain of the film due to further extension of the indenter, as illustrated in Figure 2, failure occurs by tearing of the film around the contact perimeter. Adhesive transfer requires that the film/indenter interface be sufficiently strong. The adhesive properties of the film/indenter interface can be quantified in terms of an expression between the applied energy release rate, G, and the resultant crack velocity, v. For elastomeric
10.1021/la048120y CCC: $30.25 © 2005 American Chemical Society Published on Web 12/08/2004
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where adhesive forces can be neglected,
P′ )
Figure 2. Illustration of the extension of the continuous diblock copolymer membrane at the periphery of the contact with the glass indenter.
-16Esa3 9R
(3)
In these expressions a is the radius of the circular contact between the indenter and the adhesive film and R is the radius of curvature of the indenter itself. Also, we have defined tensile loads and displacements in the positive sense for reasons of convenience, which is contrary to the standard contact mechanics convention. The elastic modulus can be determined from simultaneous measurements of P, δ, and a, utilizing the following expression for the displacement:9,10
δ)-
a2 3(P - P′) + R 8Esa
(4)
Equations 2-4 are valid for incompressible materials with a Poisson’s ratio of 0.5, in cases where the contact radius is much less than the thickness of the elastomeric substrate. These conditions are met in our experiments, although the extension of this approach to compressible materials and thin elastic layers is relatively straightforward.10 The displacement that is directly controlled in our experiments is not the sample displacement, δ, but the motor displacement δmotor. This displacement includes an extension of the spring in the load cell, which must also be taken into account in the measurements:
δ ) δmotor -
P k
(5)
where P′ is the Hertzian load, corresponding to the case
where k is the spring constant of the load cell. Solution of eqs 1-5 for a given loading history, specified by the value of the motor velocity, enable predicted “tack” curves to be obtained as the indenter is separated from the adhesive film.11 The parameters needed for the analysis are the indenter geometry (R), the stiffness of the load measuring device (k), the elastic properties of the base elastomer (Es), and the adhesive properties of the film/ indenter interface (G0, v*, n). The analysis assumes that the adhesive film remains bonded to the elastomeric substrate. In fact, delamination of the adhesive film occurs for values of the energy release rate that are sufficiently large in comparison to the strength of the film/substrate interface. The aim of this paper is to develop an understanding of the criterion for adhesive transfer of a model viscoelastic film and to characterize the film transfer mechanism. The basic structural unit of the viscoelastic films used in our experiments is a micelle formed from a poly(methyl methacrylate)/poly(n-butyl acrylate) (PMMA/ PnBA) diblock copolymer. When dissolved in warm butanol and subsequently cooled, the diblock copolymer solution goes through a micellar transition followed by a subsequent glass transition of the micelle core. Unlike triblock copolymer gels, which are formed from similar solvent systems with the same polymer chemistry,12 a micellar solution can be spun cast directly onto the substrate to give either continuous adhesive films or films consisting of isolated micelles. By casting the micellar solution directly onto the elastomeric substrate, an intimate and
(5) Maugis, D.; Barquins, M. J. Phys. D: Appl. Phys. 1978, 11, 1989. (6) Ahn, D.; Shull, K. R. Langmuir 1998, 14, 3646. (7) Ahn, D.; Shull, K. R. Langmuir 1998, 14, 3637. (8) Johnson, K. L.; Kendall, K.; Roberts, A. D. Proc. R. Soc. London, Ser. A 1971, 324, 301.
(9) Johnson, K. L. Contact Mechanics; Cambridge University Press: Cambridge, 1985. (10) Shull, K. R. Mater. Sci. Eng., R 2002, 36, 1. (11) Barquins, M.; Maugis, D. J. Adhes. 1981, 13, 53. (12) Drzal, P. L.; Shull, K. R. Macromolecules 2003, 36, 2000.
Figure 3. Schematic representation of the axisymmetric contact apparatus.
materials with some viscoelastic character, this expression is often expressed in the following form:5-7
[ (v*v ) ]
G ) G0 1 +
n
(1)
where G0 is the critical amount of energy required to initiate the debonding process, v* is a characteristic crack velocity for the interface of interest, and n is a fitting parameter that describes the nature of the relationship between G and v.6,7 Use of eq 1 in our case can be explained in the context of our experimental geometry, shown in Figure 3. Because the adhesive transfer film is very thin (less than 3 µm in all of our experiments), the relevant elastic modulus that determines the overall compliance of the system and, hence, the energy release rate, is the elastic modulus, Es, of the PDMS substrate. For our geometry, the relationship between G and the applied load is the following familiar expression, derived in a different form by Johnson et al.8 and in this form by Maugis and Barquins:5
G)
3(P - P′)2 32πEsa3
(2)
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reproducible contact between the micellar film and the elastomeric substrate is produced. A variety of experimental methods were used to fully characterize the structural and viscoelastic properties of the adhesive film used in our experiments. Dynamic light scattering was used to determine the hydrodynamic diameters of the block copolymer micelles in solution, and atomic force microscopy (AFM) was used to study the structural features of isolated micelles and of micellar films deposited onto rigid surfaces. The viscoelastic response of relatively thick micellar films was measured directly to establish the solidlike character of these films on experimentally relevant time scales. A series of contact experiments were then performed to study the transfer of these materials from a silicone elastomer to a hemispherical glass indenter and to quantify adhesion of the film to these surfaces. Oxidation of the elastomeric silicone substrate prior to deposition of the micelles along with a polystyrene (PS) coating on the indenter enhanced the film/substrate adhesive interactions while reducing film/ indenter adhesion, suppressing transfer to the glass indenter and enabling us to study adhesion at the film/ indenter interface. Film transfer occurred when uncoated glass indenters were brought into contact with coated PDMS elastomers that had not been oxidized. The experimental methods are described in more detail in the following section, followed by a description of the results that have been obtained. 2. Experimental Methods 2.1. Diblock Copolymer Synthesis. Diblock copolymers were formed by modification of an anionically polymerized poly(methyl methacrylate)/poly(tert-butyl acrylate) diblock copolymer following procedures similar to those utilized by Varshney et al.13,14 Sequential polymerization of tert-butyl acrylate and methyl methacrylate was carried out in tetrahydrofuran, using secondary butyllithium/1,1-diphenylethylene as the initiator. An excess of lithium chloride was added to control the reactivity of the propagating species. Conversion of the tert-butyl groups to n-butyl groups was performed by acid-catalyzed transalcoholysis in butanol to give the resultant PMMA/PnBA diblock copolymers. The respective molecular weights of the PnBA and PMMA blocks were 120 000 g/mol and 20 000 g/mol, as verified by gel permeation chromatography and NMR. On the basis of the analysis of polymers produced by similar methods, the n-butyl acrylate blocks are expected to contain about 4 mol % acrylic acid groups that are introduced during the conversion reaction.7 2.2. Dynamic Light Scattering. Diblock copolymers were added to butanol at a concentration of 4.6 wt % and heated to 70 °C to completely dissolve the polymer. The solution was gradually cooled below the critical micelle temperature of approximately 55 °C. This micellar solution was then diluted to 0.46 wt % at room temperature. Dynamic light scattering was performed using a Coulter N4 multi-angle scanner, with a light source wavelength of 633 nm. The decay of the autocorrelation function was measured at increasing temperatures between 25 and 45 °C. The autocorrelation functions followed a nearly pure exponential decay, indicative of a narrow distribution of micelle sizes. The temperature of the solution was then increased to 70 °C to redissolve the micelles. This solution was cooled to room temperature for additional measurements to compare the hydrodynamic diameters of micelles formed with solution concentrations of 0.46 wt % to the original micelles, which were formed with a solution concentration of 4.6 wt %. In all cases measurements were made with scattering angles of 30, 60, and 90°, and the results were in good agreement with one another. Published values of the viscosity of butanol15 were used to obtain (13) Hautekeer, J.-P.; Varshney, S. K.; Fayt, R.; Jacobs, C.; Je´roˆme, R.; Teyssie´, P. Macromolecules 1990, 23, 3893. (14) Varshney, S. K.; Jacobs, C.; Hautekeer, J.-P.; Bayard, P.; Je´roˆme, R.; Fayt, R.; Teyssie´, P. Macromolecules 1991, 24, 4997.
Shull et al. hydrodynamic diameters for the micelles from the StokesEinstein equation. 2.3. AFM. The 4.6 wt % micellar solutions utilized for the light scattering experiments were diluted to 0.046 wt % at room temperature. Diluted and undiluted solutions were used to spin cast micellar films directly onto silicon substrates. AFM was performed under ambient conditions in intermittent contact mode using a Thermomicroscopes CP Research atomic force microscope. All imaging was accomplished with a triangular silicon nitride cantilever with a spring constant of 3.2 N/m. To reference the same micelles before and after a 1-h ex situ annealing treatment, a 4 µm × 4 µm marker was generated by rastering the tip across an adjacent region of the sample in contact mode, using a relatively large contact force. Imaging with a fresh tip reveals an area in which the polymer micelles have been scratched away, leaving a clear region with a slightly elevated border around the edges where the majority of the displaced material has been deposited. This region can be relocated throughout the experiment, enabling us to quantify the thermally induced spreading of individual micelles by using a second fresh silicon tip. 2.4. Bulk Mechanical Characterization. A 5 wt % solution of the diblock copolymer was made in 2-ethyl hexanol and heated to approximately 80 °C. A micellar solution was produced as the film was allowed to cool to room temperature. This solution was cast on a glass microscope slide, and the solvent was allowed to evaporate at room temperature over a period of about 2 weeks. Previous work with similar acrylic triblock copolymers has shown that the micellization processes in butanol and 2-ethyl hexanol are quite similar.12 We used 2-ethyl hexanol to form the thick films because it was easier to obtain an appropriately slow drying rate. The resultant dry film, with a thickness of 58 µm, was sufficient for bulk rheological measurement, utilizing a recently developed methodology for the determination of the dynamic mechanical properties of adhesive films with thicknesses in this range.16 The technique utilizes the experimental device shown in Figure 3, but with the silicone elastomer replaced by a rigid glass slide so that the sample compliance is entirely dominated by the adhesive film. Oscillation of the indenter in the direction normal to the film surface enables the frequency-dependent elastic modulus to be obtained, provided that adhesive forces are sufficient to maintain a constant adhesive/indenter contact area during an oscillation, as was the case here. 2.5. Contact Experiments. All samples were tested using the axisymmetric adhesion apparatus illustrated in Figure 3. An inchworm stepping motor is coupled to a 50g load cell (k ) 1000 N/m) and drives a hemispherical glass indenter with a 6-mm radius of curvature into the coated PDMS elastomer. A fiberoptic displacement sensor is used to directly measure the indenter displacement into the sample itself. The elastomers were made from Dow Corning’s Sylgard 184, a PDMS elastomer. Elastomeric substrates were prepared by mixing the polymer with the provided curing agent, 10:1 by weight by the manufacturer’s instructions, and allowing them to cure at 80 °C for 3 h in a cylindrical mold 3-mm deep and 10 mm in diameter. After the PDMS cylinders were cured, un-cross-linked material and excess curing agent was removed by Soxhlet extraction toluene for about 100 h. The substrates were then air-dried for a minimum of 1 week to allow complete solvent evaporation. The dry PDMS substrates were glued to a glass slide to anchor them for spin coating and adhesion testing. Two types of indenters and two types of PDMS elastomers were prepared to control the adhesion at the film/indenter and film/substrate interfaces. For stronger adhesion at the film/glass interface, the indenter was cleaned with acetone and methanol and then exposed to a Jelight UV/ozone source for 15 min. To obtain a weaker film/indenter interface, a thin film of PS with a trimethoxysilyl end group was first spun onto the glass indenter.17 A 50-nm film of PS was then floated onto the coated glass indenter and annealed for 1 h in a vacuum at 150 °C. This process resulted in the grafting of a PS layer to the glass surface, and ensured that the PS film was well-adhered to the indenter. (15) Handbook of Chemistry and Physics; Weast, R. C., Ed.; CRC Press: Boca Raton, FL, 1980. (16) Crosby, A. J.; Shull, K. R.; Lin, Y. Y.; Hui, C.-Y. J. Rheol. 2002, 46, 273. (17) Vitt, E.; Shull, K. R. Macromolecules 1995, 28, 6349.
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Table 1. Hydrodynamic Diameters for the Diblock Copolymer Micelles at a Concentration of 0.46 wt % in Butanola T (°C)
dbefore (nm)
dafter (nm)
T (°C)
dbefore (nm)
dafter (nm)
25 30
60.2 65.0
55.5 58.2
35 40
68.1 55.8
63.6 50.7
a The different sets of values correspond to micelles that were formed from a solution concentration of 4.6 wt %, followed by subsequent dilution to 0.46 wt % at room temperature (dbefore), and the same solution that had been heated to 70 °C and cooled so that the micelles formed at a solution concentration of 0.46 wt % (dafter).
Strong adhesion at the film/substrate interface was obtained by using PDMS elastomers that had been exposed to UV/ozone for 15 min. Weak film/substrate interfaces were obtained by using unmodified PDMS elastomers. In each case micellar layers were cast directly onto the PDMS substrates by spin coating from butanol. Different layer thicknesses were achieved by dilution of the micellar suspension. The resulting film thicknesses for each concentration of micelles in 1-butanol were measured by spin casting under the same conditions onto clean silicon wafers. Film thicknesses on these silicon substrates were measured with a Tencor P-10 surface profiler. Experiments designed to study the adhesion between the indenter and the micellar film were performed by bringing the PS-coated indenter into contact with a film that had been cast onto a UV/ozone-treated PDMS substrate. A fixed motor velocity was used to drive the indenter into the coated elastomer film until a compressive load of 10 mN was reached. The motor was then immediately reversed, and the indenter was retracted from the sample using the same motor velocity. Because the PDMS strengthened the film/elastomer interface while the PS coating on the indenter weakened the film/indenter interface, failure occurred between the film and indenter, enabling us to quantify the adhesive strength of this interface. Velocity effects were studied by using motor velocities of 0.1, 1, and 10 µm/s. Adhesive transfer was studied by using an unmodified PDMS surface that had not been exposed to the UV/ozone treatment and indenters that did not have the PS layer. Adhesive transfer experiments were performed in the same manner as the adhesion experiments, with a single motor velocity of 1 µm/s. Failure was initiated at the film/substrate interface by nucleation of a cavity. Once the cavity grew to a critical size, it was able to propagate along the film/substrate interface causing delamination of the layers inside the contact area, followed by film fracture and transfer. Transferred films were analyzed with scanning electron microscopy. The indenter with a transferred film was sputter coated with 3 nm of gold for inspection in a Hitachi S3500 scanning electron microscope, using an accelerating voltage of 5 kV.
3. Results 3.1. Characterization of the Micellar Film. The fundamental building block of the adhesive films are diblock copolymer micelles formed when the butanol solutions are cooled from an elevated temperature. The hydrodynamic diameters for the micelles as obtained from the light scattering measurements are listed in Table 1. The “before” values correspond to micelles that were formed from a 4.6 wt % solution that was subsequently diluted to 0.46 wt % at room temperature. The stability of the micelles in solution is a function of the glass transition temperature of the PMMA cores, which are substantially swollen with butanol. This glass transition temperature is 36 °C, as obtained from triblock copolymer analogues of the diblock copolymers used here.12 Below this temperature individual molecules are not able to exchange in and out of the micelles, and the aggregation number of the micelles is not affected by dilution of the micellar solution. The increase in hydrodynamic diameter with increasing temperature up to 40 °C corresponds to the swelling of the micelles at a fixed aggregation number.
At temperatures above about 40 °C, the PMMA core is no longer glassy, and the micelles are able to equilibrate, resulting in exchange of block copolymers out of the micelles and a decrease in the aggregation number and hydrodynamic diameter. When the solution is heated above the critical micelle temperature of about 55 °C and subsequently cooled, micelles rapidly reform. These micelles, formed from a solution concentration of 0.46 wt %, have hydrodynamic diameters that are about 10% less than the hydrodynamic diameters of micelles formed from the original solution concentration of 4.6 wt %. The AFM results are consistent with our expectation that the thickness of a spun-cast micellar film can be controlled by appropriate dilutions of a parent micellar solution, without affecting the structure of the individual micelles themselves. Figure 4 is a comparison of AFM images obtained from spun-cast films obtained from the solution concentrations of 4.6 and 0.046 wt %. Isolated micelles with dimensions comparable to the hydrodynamic diameters obtained from the light scattering measurements are clearly observed in the more dilute case. The concentrated case results in a continuous film with a thickness of 380 nm, as determined by profilometry. The AFM images of these thicker films show features with a size comparable to isolated micelles and are consistent with the view that the underlying micellar structure of the film is maintained in these thicker films. The stability of the micellar structure is also verified by the spreading behavior of individual micelles on silicon substrates, which is driven by favorable interactions between the PMMA blocks and the oxidized silicon surface. Figure 5 is a comparison of a line scan taken across the center of two individual micelles before and after an annealing treatment at 80 °C. While not all micelles have the same original height, the relative change in this height during the annealing treatment is quite reproducible. As illustrated in Figure 6, the micelles do not completely spread over the silicon substrate until the annealing temperature reaches 120 °C, which in the absence of solvent is the glass transition temperature for the isotactic PMMA that forms the micelle cores. Note that this glass transition temperature corresponds to “dry” PMMA and is substantially higher than the glass transition temperature of 36 °C for the solvent-swollen PMMA mentioned earlier. Because the micellar nature of the adhesive films is not expected to change simply by changing the film thickness, we can use much thicker films to quantify the mechanical properties of continuous micellar films. The rheological response of a film with a thickness of 58 µm is shown in Figure 7. The dynamic moduli exhibit a power law frequency dependence but with a relatively low exponent, Λ, of 0.2 that confirms the largely elastic character of these films over time scales that are relevant to our experiments. The power law response implies a constant phase angle, δ, of Λ × 90° ) 18° (tan δ ) 0.32) for these materials over the frequency range investigated.16 3.2. Adhesive FailuresOxidized PDMS Substrates. Oxidation of the silicone elastomer via the UV/ozone treatment gives sufficient film/substrate adhesion so that failure occurs at the film/indenter interface. The indenter/ substrate adhesion in this case is well described by a relationship between the energy release rate and crack velocity given by eq 1, with G0 ) 0.1 J/m2, n ) 0.5, and v* ) 2.5 nm/s. The loading portion of the tack curve is fit with a constant value of G (defined here as Gload) that is very close to 0 (Gload ) 0.001 J/m2). In fracture mechanics terminology, the loading portion of the experiment corresponds to a receding crack. Energy dissipation in the
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Figure 4. Topography (a) and phase (b) images indicating the presence of individual diblock copolymer micelles as cast from 0.046 wt % solution in butanol. Topography (c) and phase (d) images for a continuous micellar film with a thickness of 380 nm, obtained by spin casting from a micellar solution with a concentration of 4.6 wt %.
Figure 5. Line scans across individual micelles, illustrating the change in micellar height after annealing at 80 °C for 1 h.
Figure 6. Micelle heights obtained by AFM after 1 h of annealing treatments at the indicated temperatures. The heights are normalized by the heights of the same micelles prior to the annealing treatment.
vicinity of the crack tip gives a value of G during loading that is less than the thermodynamic work of adhesion, so in qualitative terms one expects a value that is quite low.10
Figure 7. Frequency-dependent dynamic moduli for a micellar diblock copolymer layer with a thickness of 58 µm.
Our experiments are not particularly sensitive to the specific value of the Gload that is used. Here we merely point out that the low value used in our analysis is consistent with the relatively high loading rates used in our experiments. Inclusion of the elastic modulus of the silicone elastomer (Es ) 1.7 × 106 Pa) and the spring constant of the load cell (k ) 1000 N/m) enables us to quantitatively reproduce the time dependence of the displacement, load, and contact radius during the tack test, by numerical solution of the equations in section 1. This point is illustrated in Figure 8, where measured and predicted values of the contact radius are plotted as a function of the displacement, for tests conducted with a motor velocity of 1 µm/s. Assurance that a single parameter set accurately describes the adhesive behavior requires that a large range of motor velocities be used. Figure 9a
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Figure 8. Contact radius as a function of displacement for a PS-coated spherical indenter in contact with a micellar diblock copolymer layer with a thickness of 380 nm. The elastomeric substrate had been oxidized by a 15 min UV ozone treatment prior to deposition of the micellar layer. Measured values are compared to predictions from the tack model of section 1, with k ) 1000 N/m, vmotor ) 1 µm/s, Es ) 1.7 × 106 Pa, n ) 0.5, v* ) 2.5 nm/s, G0 ) 0.1 J/m2, and Gload ) 0.001 J/m2.
Figure 9. (a) Measured (solid lines) and predicted (dashed lines) tack curves for the sample characteristics and model parameters listed in Figure 8, for motor velocities of 0.1, 1, and 10 µm/s. (b) Calculated values of the energy release rate corresponding to the predicted tack curves of part a.
shows that the effect of changing the motor velocity is also accounted for in a quantitative manner. The same set of values for v*, G0, n, and Gload can be used to model tack curves obtained with motor velocities of 0.1, 1, and 10 µm/s. The key result of this section is that the classical picture used to describe elastomer adhesion is valid in our case, even though viscoelastic dissipation is confined to a film that has a thickness of only 380 nm. The values for G0, v*, and n are, in fact, quite similar to those obtained for bulk, cross-linked PnBA in contact with a glassy polymer surface.6,7 The degree of adhesion between the film and the indenter is, therefore, well understood and quantifiable, at least at an empirical level. This understanding enables us to calculate the energy release rate, which by the tools of linear elastic fracture mechanics can also be related to the nature of the stress distribution in the vicinity of the edge of contact.10 Calculated values of the energy release rate are plotted in Figure 9b, for the three model tack curves shown in Figure 9a. At this point we are in a position to study the conditions for which the adhesive interactions that sustain these values of the energy release rate are sufficient to transfer the film from the substrate to the indenter. 3.3. Adhesive TransfersUnoxidized PDMS Substrates. 3.3.1. Cavity Nucleation and Growth. Transfer
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Figure 10. Tack curve for transfer of a 170-nm micellar film from an unoxidized PDMS substrate, with contact images illustrating the circumferential propagation of the internal cavity. The region of the tack curve enclosed in the box is shown in detail in Figure 11.
of the adhesive film was studied by utilizing the PDMS films that had not been oxidized, with UV/ozone-treated indenters that did not have the PS coating. In this case, the micellar film is transferred to the indenter because the adhesion between the film and substrate is weaker than the adhesion between the film and the indenter. Elimination of the PS layer from the glass indenter increases the film/indenter adhesion, most likely by specific interactions with functional groups on the glass surface that increase the value of G0.6,7 No discernible crack motion at the glass/indenter interface was seen when these bare glass indenters were used so that the adhesive transfer process could be studied without the complication of simultaneous debonding at the film/indenter interface. A tack curve associated with the transfer process is shown in Figure 10. The load/displacement relationship is linear up to the point of failure, indicating that the contact radius is remaining constant during this part of the test (see eq 4). The measured value of the contact radius can, therefore, be used to obtain the elastic modulus of the PDMS elastomer from the slope of the load/ displacement curve. As a result of the weak adhesion between the film and the PDMS substrate, failure occurred readily at that interface as a cavity nucleated at the perimeter of the contact. Once the cavity grew to a critical size, it propagated over the entire contact area, resulting in a large drop in load. The initial stages of the debonding process at the film/substrate interface are illustrated in Figure 11, which shows the tack curve and corresponding contact images in the vicinity of the load maximum. Film transfer experiments were conducted with micellar film thicknesses ranging between 150 and 1000 nm. The energy release rate characterizing the driving force for failure at the film/indenter interface, at the point in the experiment where cavity nucleation at the film/substrate interface is observed, was independent of the film thickness, with typical values that ranged between 5 and 10 J/m2. Once failure is initiated at the film/substrate interface, crack propagation proceeds much more readily than it does at the film/indenter interface. This difference can be attributed to the high local mobility of molecular segments within the PDMS elastomer, as has been studied in more detail by Amouroux et al.18 3.3.2. Membrane Extension and Failure. As illustrated in Figure 10, a circumferential debonded area between (18) Amouroux, N.; Petit, J.; Leger, L. Langmuir 2001, 17, 6510.
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δa ) δ + R - xR2 - a2
(7)
The specific combination of a, Rm, δ, and R used to plot the membrane profile in Figure 2 corresponds to transfer of a membrane with a thickness of 630 nm, soon after complete detachment of the layer from the region underneath the original contact area with the glass indenter. The corresponding image of the contact is shown in Figure 12a. The region corresponding to the free-standing membrane can be seen in this image as a dark ring with an inner radius of a and an outer radius of Rm. Because a/Rm is relatively close to 1, the curvature of the membrane can be neglected. The strain state of the membrane can be approximated as a linear sheet of original width Rm a that is extended in plane strain by an amount that is determined by the value of δa. The deformation of the membrane is, therefore, described by the extension ratio, λ, which is given by the following simple expression: Figure 11. Detail of the peak of the tack curve in Figure 10, with corresponding contact images showing the early stages of the film/substrate debonding process. The time increment between images is 0.4 s. Debonding is accompanied by a deviation in the slope of the tack curve from the initial slope, represented here by the dashed line.
the film and the substrate is initially formed at the perimeter of the contact zone with the indenter. The center of this circumferential patch corresponds to a region of the glass indenter that is still bonded to the elastomeric substrate by the micellar film. The radius of this contact region decreases to 0 within a couple seconds. At this point the film is in contact with the indenter itself throughout a circular region with a radius corresponding to the maximum contact radius, a, that was obtained when the indenter was originally brought into contact with the coated elastomeric substrate. As illustrated in Figure 2, the film has peeled away from the PDMS substrate for radial distances less than Rm. Here, Rm is the diameter of the circular region of the film that has completely debonded from the substrate, and a is the diameter of the region that remains in contact with the indenter. Between a and Rm, the micellar layer exists as a free-standing film. The film is nearly continuous but must have at least one hole to admit air into the void space between the indenter and the substrate. This is evident from the drop in the load, because atmospheric pressure of 105 Pa distributed over a circular contact area with a radius of 350 µm corresponds to a load of 38 mN. This represents the load that would need to be supported by the film itself to maintain a vacuum between the indenter and the substrate. This load corresponds to an average stress of P/(2πah) ) 4.5 × 107 Pa in the plane of a film with h ) 380 nm, which can clearly not be supported by a film with an elastic modulus of about 3 × 105 Pa. Detachment of the film from the substrate occurs very rapidly. When the load drops from Pmax to 0, eq 5 indicates that the displacement will increase by an amount equal to Pmax/k. For the data shown in Figure 10, the displacement after the film detaches from the substrate is equal to about 65 µm. If we assume that the membrane between r ) a and r ) Rm has a shape that minimizes the overall surface area, we obtain the following expression for yf, the distance between the membrane and the elastomeric substrate:19
ln(Rm/r) yf ) δa (a < r < Rm) ln(Rm/a) with
(6)
λ ) (1 + ∆2)1/2
(8)
with ∆ ) δa/(Rm - a). As δa is increased, the outer perimeter of the membrane peels away from the silicone substrate, thereby increasing the value of Rm. The value of Rm that is obtained is determined by the value of the applied energy release rate that acts to simultaneously increase Rm and decrease a. Because the strain applied to the membrane is quite large, a large strain theory needs to be used to obtain the appropriate energy release rate for this geometry. The following expression is obtained from the procedure outlined in the appendix, which in turn is an adaptation of the previous result given by Williams:20
G)
|
dUel dRm
δa
)
[
] (
Eh 1 + 3∆2 1 + ∆2 ) 6 (1 + ∆2)2
)
2 Eh 2 3 λ - 2 + 4 (9) 6 λ λ where E is Young’s modulus of the membrane and h is the membrane thickness. If the film is sufficiently tough so that G exceeds Gc, the critical energy release rate for crack propagation at the film/substrate interface, the film will begin to detach from the substrate by growth in Rm. A decrease in a by detachment from the film/indenter interface is prevented by the enhanced strength of this interface. From eq 9 we see that the film strain required for Rm to increase is determined by the quantity Gc/Eh. From the contact images, we find that the extension ratio of the 630-nm membrane is equal to about 3, which from eq 9 gives Gc/Eh ≈ 1.45. The membrane in our case is obviously not perfectly elastic, so we do not expect to be able to use eq 9 in an absolutely quantitative sense. Nevertheless, the relatively weak frequency dependence of the dynamic moduli plotted in Figure 7 suggests that a useful approximation can be obtained by using a value E ≈ 3 × 105 Pa, corresponding to the value of E′ at a frequency of about 0.1 Hz, roughly the inverse of the characteristic time scale of our experiment. With this approximate value of the elastic modulus, we obtain Gc ≈ 0.3 J/m2, which is comparable to the previously measured values for acrylic adhesives in contact with silicone elastomers.18 An interesting consequence of eq 9 is that peeling of the membrane from the substrate only occurs once the (19) Wan, K.-T.; Dillard, D. A. J. Adhes. 2003, 79, 123. (20) Williams, J. G. Int. J. Fract. 1997, 87, 265.
Thin Viscoelastic Film Adhesive Transfer
Figure 12. (a) Contact image of the film stretched between the indenter and the substrate for diblock films with thicknesses of 630 and 170 nm. Values of Rm and a are indicated in the left image to make the connection to the membrane geometry shown in Figure 2. (b) PDMS substrate surface after film tearing is complete. (c) Indenter with transferred film after tearing is complete. The length of the scale bar is 300 µm in each case.
membrane is stretched to a critical extension ratio that increases with decreasing membrane thickness. If the critical energy release rate for peeling from the substrate is not a strong function of the membrane thickness, sufficiently thin films will always break before peeling can be initiated. This result is consistent with the relative behavior of the 170- and 630-nm films in our experiments that is illustrated in Figure 12b. The 170-nm film breaks very early in the process, with very little peeling from the PDMS substrate. The 630-nm film exhibits substantial peeling from the substrate prior to failure, demonstrating the ability of the diblock copolymer membrane to be extended to three times its original length. Peeling of the film from the PDMS elastomer leaves a film with a jagged appearance on the substrate, as shown in the images in Figure 12b. The final stage in the transfer process is failure of the membrane at the edge of contact with the indenter. In our case film fracture at this contact line occurs very cleanly. The net result is a transferred film that is remarkably free of defects, as illustrated by the optical images in Figure 12c. Two possible explanations exist for the preferential failure of the membrane at the contact line with the indenter. The first is that the rigid indenter introduces local stress concentrations within the membrane that promote membrane fracture at this location, rather than in the central portions of the membrane or at the point of contact with the more flexible elastomeric surface. The second explanation is that the geometry itself plays the dominant role. Equation 9 is valid for a/Rm close to 1. As the displacement is increased, Rm increases but a remains fixed so that a/Rm decreases and the membrane/indenter contact line is more highly curved than the membrane/substrate contact line. In simplistic terms, the membrane stress is concentrated over a smaller length, equal to 2πa, at the indenter interface, which is why tearing of the membrane occurs at this location. 4. Conclusions The important results of this work concern the viscoelastic character of the micellar film and the transfer process resulting from the carefully controlled adhesive
Langmuir, Vol. 21, No. 1, 2005 185
properties of the film/substrate and film/indenter interfaces. Regarding the micellar film itself, we observe the following: (1) The micellar structure of the diblock copolymer film is maintained at room temperature. (2) The micellar films are characterized by a constant value of tan δ ) 0.32 for frequencies between 0.001 and 1 Hz. (3) Submicrometer micellar films can be extended up to three times their original length prior to failure. These thin, highly compliant membranes are excellent model materials for studying the adhesive transfer of viscoelastic solids. Adhesive failure occurs at the interface between the film and the indenter in situations where the PDMS substrate was oxidized and where the indenter was treated with a grafted layer of PS. The velocity dependence of adhesion to the PS-coated glass indenter can be quantified by an empirical relationship between the energy release rate and the rate of crack propagation. The detailed adhesive properties of the film/indenter interface determine the maximum energy release rate that can be applied to the films. Adhesive transfer requires that this energy release rate exceeds some critical value that depends on the detailed nature of the film/substrate interface. For an interface between the film and the unmodified PDMS, this critical value of the energy release rate was between 5 and 10 J/m2 and was not dependent on the film thickness. Adhesive transfer occurs by the following sequence of events: (1) Debonding at the film/substrate interface is initiated at the periphery of the contact zone. (2) The debonded zone grows circumferentially around the perimeter of the contact and then propagates inward until the film underneath the indenter is no longer in contact with the elastomeric substrate. (3) At the perimeter of the contact zone, the film exists as a freely standing membrane linking the perimeter of the contact zone to the portion of the film that is still attached to the substrate. (4) Peeling of the film from the substrate occurs at a film strain that is determined by the quantity Gc/Eh. (5) Failure of the stretched membrane occurs at the perimeter of the contact zone, leaving a high-quality transferred film on the portion of the indenter that was brought into physical contact with the film during the original compressive portion of the experiment. Acknowledgment. This work was supported by the National Science Foundation under Grants DMR-0214146 and DMR-0134706. Appendix: Membrane Adhesion While a detailed quantitative solution requires that curvature effects be accounted for,19 a suitable approximation can be obtained by neglecting these effects and treating the membrane as a strip of width Rm - a that is extended in plane strain conditions. We begin with the Neo-Hookean model for the elastic strain energy density of the deformed membrane. This elastic energy per unit length of the membrane strip is given by the following expression:
Uel )
Eh(Rm - a) 2 (λx + λy2 + λz2 - 3) 6
(10)
where E is the small-strain value of Young’s modulus, h is the thickness of the membrane, and λx, λy, and λz are
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Shull et al.
the principal extension ratios. For plane strain deformation, λx ) 1/λy ) λ and λz ) 1. We also have λ2 ) 1 + ∆2 from eq 8, so the elastic strain energy can be written in the following form:
Uel )
(
Eh(Rm - a) 2 1 -1 ∆ + 2 6 ∆ +1
)
(11)
G)
|
dUel dRm
δa
|
dUel dδa
Rm-a
)
[
]
1 Eh∆ 13 (1 + ∆2)2
]
(
)
For small displacements, these expressions reduce to the following:
Uel )
Eh(Rm - a) 4 ∆ 6
2Eh∆3 3 Eh∆4 G) 2
Fl )
(12)
The energy release rate is given by calculating the change in stored elastic energy associated with a differential increase in the value of Rm:
[
Eh 1 + 3∆2 1 + ∆2 ) 6 (1 + ∆2)2
2 Eh 2 3 λ - 2 + 4 (13) 6 λ λ
The normal force per unit length, Fl, required to maintain this deformation of the strip is obtained as follows:
Fl )
)
(14) (15) (16)
These small strain approximations for Fl and G agree with the large strain values to within 10% when ∆ is less than 0.25 but differ by a factor of order 10 for λ ) 3. LA048120Y
