Compositional Effects on the Adhesion of Acrylic Pressure Sensitive

The contact mechanics-based Johnson-Kendall-Roberts technique has been used to study the adhesion ... centers of spheres have approached after a separ...
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Compositional Effects on the Adhesion of Acrylic Pressure Sensitive Adhesives Afshin Falsafi† and Matthew Tirrell*,‡ Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55455

Alphonsus V. Pocius 3M, St. Paul, Minnesota 55144 Received March 22, 1999. In Final Form: October 25, 1999 The contact mechanics-based Johnson-Kendall-Roberts technique has been used to study the adhesion of cross-linked 2-ethylhexyl acrylate-co-acrylic acid (2EHA-co-AA) elastomers as models of pressure sensitive adhesives (m-PSA). We have addressed the effect of m-PSA composition on intrinsic solid surface energetics and on the mechanical performance of m-PSA. The measured surface energies of the m-PSA were all approximately 30 mJ m-2, indicating surfaces dominated by methylene groups. The extent of adhesion hysteresis for the m-PSA used in our measurements was not a strong function of acrylic acid content implying that the main mechanism contributing to the adhesion of practical un-cross-linked or lightly cross-linked PSA is the viscoelastic dissipation. Several technical and physical issues concerning contact mechanical measurement of adhesion and the observed rate-dependent patterns of adhesion have been addressed.

1. Introduction Pressure sensitive adhesives (PSA) are a class of materials that adhere on contact or application of a slight pressure. Acrylics as model polymers allow the exploration of the relative effects of surface and rheological behavior as a function of composition. Esters of acrylic acid with long alcohols may be used to form soft and tacky polymers of low glass transition temperature (Tg). The suitable monomers commonly reported in patent literature are alkyl acrylates and methacrylates of 4-17 carbon atoms (e.g. 2-ethylhexyl acrylate (2-EHA) which has a polymer Tg of -70 °C). To control the adhesive properties of PSA, the acrylic esters are almost always copolymerized with other monomers with generally higher Tg and/or proper functionality.1 An example of such a secondary monomer is acrylic acid (AA) with a polymer Tg of 106 °C and having carboxyl groups to provide cross-linking sites as well as providing a suspected improvement in adsorption properties. A typical acrylic PSA composition is 50-90% of a major monomer, 10-40% of a modifying monomer, and 2-20% of a monomer with desired functional groups.2 Composition plays an important role in the practical adhesive bonding characteristics of PSA. In addition to the mechanical properties of a PSA, the composition must also provide the desired surface characteristics, one of these being surface energy. Surface energy determination for a PSA is both technologically relevant and practically challenging. It is difficult to determine the surface energies of soft polymers without provoking viscoelastic effects.3 * To whom correspondence should be addressed. † Current address: 3M Dental Products Division, St. Paul, MN 55144. ‡ Current address: College of Engineering, University of California, Santa Barbara, CA 93106. (1) Ulrich, E. W. U.S. Patent 2,884,126, Feb 28, 1955. (2) Satas, D., Ed. Handbook of Pressure Sensitive Adhesive Technology; Van Nostrand Reinhold: New York, 1989.

Figure 1. Cross-cylinder contact geometry used in this study is equivalent to contact between a sphere and a flat. See text for definitions of symbols.

We have used a contact mechanics method based on the Johnson-Kendall-Roberts (JKR) theory of adhesive contact between elastic materials.4 In the JKR theory, the interfacial area is generated or reduced by applying or lowering an imposed compression on curved, contacting surfaces corresponding to “loading” and “unloading” experiments, respectively. The radius of the contact area between two solid spheres with radii of curvature Ri, Young’s modulus Ei, and Poisson’s ratio νi are related to applied force (load) P by

a3 )

R [P + 3πRW + (6πRWP + 9π2R2W2)1/2] (1) K

in which

(

)

2 2 1 3 1 - v1 1 - v2 ) + K 4 E1 E2

1 1 1 ) + R R1 R2

(2)

W, the thermodynamic work of adhesion, is 2γs in the case of self-adhesion or γ1 + γ2 - γ12 in the case of heteroadhesion. The compression, δ, the distance by which the (3) Anastasiadis, S. H.; Gancarz, I.; Koberstein, J. T. Macromolecules 1988, 21, 2980. (4) Johnson, K. L.; Kendall K.; Roberts, A. D. Proc. R. Soc. London, Ser. A 1971, 324, 301.

10.1021/la990345z CCC: $19.00 © 2000 American Chemical Society Published on Web 12/31/1999

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Table 1. Weight Percentage of Comonomers Used in Synthesis of Cross-Linked Acrylic Pressure Sensitive Adhesivesa comonomer

structure

sample AA2, %

sample AA5, %

sample AA10, %

2-ethylhexyl acrylate acrylic acid 1,6-hexanediol diacrylate

CH2dCHCOOCH2CH(C2H5)C4H9 CH2dCHCOOH CH2dCHCOO(CH2)6OCOCHdCH2

93 2 5

90 5 5

85 10 5

a

Excluding 0.2% AIBN as initiator.

centers of spheres have approached after a separation of R1 + R2 (δ ) 0) is given by

δ)

8πWa a2 R 3K

[

1/2

]

(3)

By setting W to zero, one recovers the Hertz solution which gives a linear relationship between load and the cube of contact radius (a3 ) RP/K).5 As W is increased (at constant P), the JKR contact radius becomes larger compared to the Hertz radius. In the JKR theory, the stress distribution inside the contact area is given by a superposition of the repulsive (Hertzian) stress dominating the central portion, and a tensile stress distribution due to internal loading of the surfaces in the process zone through the action of adhesion. We prepared our samples in the form of cylinders. This choice was made on the basis of the chemistry and composition control required for our samples, as is explained in the synthesis and sample preparation section. The case of contact between two crossed cylinders with equal radii of Rc as illustrated in Figure 1 is identical to the contact between a sphere of Rs ) Rc with a flat of Rf ) ∞; i.e.,6

1 1 1 1 ) + ) R Rs Rf Rc

(4)

In reality, every increase in the surface area of solids or the interfacial area between solids in contact is concomitant with a certain number of nonequilibrium and dissipative processes. Conventional adhesion tests such as the peel and tear tests involve large bulk deformations and generally produce an apparent “adhesion energy” or “peel strength”, sometimes referred to as the strain energy release rate (G), which is much higher than W. Gent and Schultz7 have shown that the adhesion of soft, viscoelastic adherends on glass depends on the peeling rate V and temperature T in a way that can be described by the Williams-Landel-Ferry (WLF) equation.8 Their findings showed that G is related to the thermodynamic work of adhesion W in the following empirical form:

G ) W[1 + Φ(aTV)]

(5)

where aT is the WLF temperature shift factor. Φ is a dimensionless function which in their case represents the contribution of the dissipation of energy by the viscoelastic solid in a region around the crack tip. As V decreases, Φ also decreases. A desirable feature of contact mechanics experiments is the very low contact radius reduction rates or crack growth speeds |da/dt| which are accessible. The rates are in the range of several nanometers per second; thus we can approach a condition in which G ∼ W under near-equilibrium conditions. This condition is typically (5) Hertz, H. In Miscellaneous Papers by H. Hertz 1882; Jones, D. E., Schott, G. A., Eds.; Macmillan: 1896. (6) Johnson, K. L. Contact Mechanics; Cambridge University Press: Cambridge, U.K., 1985. (7) Gent, A. N.; Schultz, J. L. J. Adhes. 1972, 3, 281. (8) Williams, M. L.; Landel, R. F.; Ferry J. D. J. Am. Chem. Soc. 1955, 77, 3701.

not attainable in normal adhesive bond tests such as peel tests. In peel tests, the additional shearing and bending during crack growth could amount to higher values of G.9 One frequent, complicating feature of contact mechanics is a difference in G measured for loading versus unloading. This difference is commonly known as adhesion hysteresis and has been interpreted as the enhancement of zero rate adhesion arising from the change of the state of the interface after adhesive contact. This might be due to specific chemical interactions or interfacial rearrangements developing upon interface formation.10-16 Our objective is to use very low rate contact mechanics to measure the surface energies of model PSA (m-PSA) by measurement of G at near-zero-rate crack extension as a function of its chemical composition. 2. Materials and Experimental Procedures 2.1. System. We synthesized a series of varying acrylic acid content as described in Table 1. To provide the elasticity necessary for simple contact mechanics analysis, 5% 1,6-hexanediol diacrylate (HDDA) difunctional monomer was used to cross-link the material. 2.2. Synthesis and Sample Preparation. The monomers were purchased from Aldrich. Inhibitors were removed using molecular-sieve packed columns. Monomers were then purged with high-purity argon and transferred to an argon-purged glovebox to avoid any oxygen poisoning of the free radical polymerization reaction. The monomers were added in appropriate amounts to a flask containing azobisisobutyronitrile (AIBN) and mixed well at room temperature. AIBN concentrations were maintained at 0.2%. To avoid compositional changes due to selective volatility of a monomer in the course of the reaction, the samples had to be confined in sealed tubes during polymerization. Samples were conveniently prepared in 1 mm radius quartz capillary tubes. The capillary tubes were cleaned and dried before being used. Filled tubes were capped with extreme care not to exert extra force on the fragile tubes. Similarly, flat disks of these materials (2 mm thick and 20 mm wide; made for contact angle measurements) were prepared by confining the mixture by a stainless steel ring and sandwiched between two high-quality release surfaces supported on glass disks. The samples were then taken out of the glovebox and placed in a convection oven. The polymerization reaction was carried out at 80 °C for 24 h. The half-life of AIBN at this temperature is around 1 h. Hydrogen bonding between acrylic acid carboxyl groups is expected to dissociate above 60 °C. The choice of HDDA as cross-linker was based on minimization of blockiness. We were aiming for the most random possible copolymers. The reactivity ratios for copolymerization of AA (1) and 2-EHA (2) are r1 ) k11/k12 ) 1.08 and r2 ) k22/k21 ) 0.98 at 138 °C, where kij is the rate constant of the propagation reaction in which comonomer i enters a copolymer already ended with comonomer j.17 The copolymers were not characterized for their (9) Deruelle, M.; Tirrell, M.; Marciano, Y.; Hervet, H.; Leger, L. Faraday Discuss. 1994, 98, 55. (10) Chaudhury, M. K.; Whitesides, G. M. Langmuir 1991, 7, 1013. (11) Brown, H. R. Macromolecules 1993, 26, 1666. (12) Silberzan, P.; Perutz, S.; Kramer, E. J. Langmuir 1994, 10, 2466. (13) Mangipudi, V. S.; Tirrell, M.; Pocius, A. V. J. Adhes. Sci. Technol. 1994, 8, 1251. (14) Deruelle, M.; Leger, L.; Tirrell, M. Macromolecules 1995, 28, 7419. (15) Tirrell, M. Langmuir 1996, 12, 4548. (16) Choi, G. Y.; Kim, S.; Ulman, A. Langmuir 1997, 13, 6338. (17) Polymer HandBook, 2nd ed.; Brandrup, J., Immergutt, E. H., Eds.; John Wiley: New York, 1975.

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Figure 2. Schematic of the JKR apparatus used in contact mechanics measurements.18 blockiness, but we expect to have random copolymers for this system since r1r2 ≈ 1. The PSA-like samples were released by gently touching and breaking the capillary tubes and immersing them in ethyl acetate. Shrinkage due to a decrease in molar volume in acrylate systems is substantial, and this provided a means for easy removal of the cross-linked cylinder from the quartz. There was no obvious adhesion between the quartz tube and the m-PSA cylinder. Ethyl acetate is a good solvent for acrylic PSA. Therefore, the cylinders swell and free themselves from the shattered quartz tubes. The swollen cylinders of PSA were soaked in fresh ethyl acetate for a few days and/or subjected to Soxhlet extraction. The extracted sol part was not measured; however, there was no obvious cloudiness of the solvent in the course of extraction. The cylinders were stored in the soaked state and were cut in pieces of around 1 cm long (giving an aspect ratio L/R of around 10). Half-cylinder samples were made by cutting the swollen full cylinders using a guillotine-like tool. This was done to improve the optics by providing a minimum number of curved surfaces in the reflected light path. Cylinders act as a symmetric lens only if they are aligned perfectly perpendicular and have the same radii. The (half) cylinders were transferred onto a glass slide in a clean glass Petri dish which was partially filled with ethyl acetate. This provides a saturated environment for slow drying of the samples that would break and crack on rapid drying. For X-ray photoelectron spectroscopy (XPS), PSAs were made by free radical solution polymerization in 50% ethyl acetate. The 2-EHA and AA monomers and AIBN initiator were added to an equal amount of ethyl acetate as solvent. The polymerization was carried out in an agitating temperature bath at 60 °C. No cross-linker was used for these PSAs. The samples for this analysis were made by spin-coating the dilute solution (3%) polymers onto a silicon wafer. The coating thickness was around 0.3 µm after complete drying. 2.3. Contact Mechanical Measurements. 2.3.a. JKR Apparatus. Our JKR apparatus18 is illustrated in Figure 2. The upper (half-cylindrical) sample is placed on a transparent piece of glass which is firmly attached to a rigid frame. The frame is clamped on the carriage of a precision translation stage. The stage, Newport PM500, is a motion device capable of interfacing with a host computer for receiving commands and sending information. This stage has a built-in optical encoder to read the (18) Falsafi, A. Ph.D. Thesis, University of Minnesota, 1998.

Figure 3. Typical contact area between crossed cylinders viewed in loading and unloading contact mechanics experiments. The diameter of the contact area is approximately 200 µm. position of the carriage plate with a resolution of 50 nm and an accuracy better than 1.4 µm over the whole travel. This reading is fed back to a driving DC motor through the motion controller to maintain the set point position. The contact area is viewed in reflection mode by a video zoom-CCD camera assembly on a dedicated monitor and/or computer screen through a frame grabber board. The range of field of view corresponding to optical and digital components of the imaging system is 200 µm to several millimeters with a few micrometers resolution. The illumination source is automatically turned on and off, by a computercommanded relay switch, a few seconds before and after a picture corresponding to a data point is recorded, respectively. This system, along with the use of several IR mirror and filters avoids excessive heating of the samples and minimizes possible light sensitive phenomena. The image is stamped with real experimental time by a time code generator (TCG) and can be recorded by a VCR. However, the main mode of image acquisition is through a computercommanded frame grabber which captures and saves picture files which are named by the computer according to the user-

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Figure 4. Displacement variation prescribed and load change measured in the course of loading and unloading contact mechanics experiments for the 2% AA system: (b) load and (+) ) displacement.

Figure 5. Cube of contact radius as a function of load for the 2% AA system (the JKR plot): (( and 0) are loading and unloading data, respectively; (s) is the JKR fit (eq 1) for loading data with K ) 1.9 MPa and W ) 60 mJ m-2. defined times of acquisition (computer generated time stamp). The software image processing and analysis are implemented using GLOBAL LAB Image application. The lower sample is firmly adhered to the silicon wafer attached on a temperature compensation stage (TCS). The TCS eliminates any change in the compression due to unaccounted expansion and/or contraction of the supporting fixtures, brackets, etc. The TCS lies on the pan of an analytical balance SCIENTECH SA 310 which reads the load P with a precision of 0.1 dyn (1 µN). The operating principle of the balance is based on electromagnetic load generation in order to restore the position of the pan that is internally probed by a capacitive sensor and fed back to the load generating mechanism. The apparent zero compliance of the balance and the rigidity of other components of the system, aside from the samples, characterizes our JKR apparatus as displacement-controlled. The balance is interfaced with the host computer to collect load variation with time. Another feature of the apparatus is the independent measurement of compression using a Fotonic sensor. The Fotonic sensor has two probes which are targeted on the upper and lower sample holders. The differential reading of the sensor from the probes is δ, which is

Figure 6. Variation of strain energy release rate G in the course of loading (() and unloading (×) contact mechanics experiments on the 2% AA system. W ) 2γs is the thermodynamic work of adhesion. The decompression rate is 1 nm s-1. sent to a host computer to be recorded. The entire experiment is commanded by the host computer under user-defined conditions through MEASURE software. 2.3.b. Experimental Procedure. The two cylindrical samples are glued by applying small amounts of thoroughly mixed fast setting epoxy to the supporting surfaces. After reaching thermal equilibrium and complete curing of the epoxy in the apparatus enclosure (3 h), the samples are crossed through close examination at lower magnification. A slight contact is made in order to align the vide zoom with the center of contact. The cylinders are then separated, and the system is allowed, for at least 3 h, to equilibrate mechanically and thermally. When a predetermined start time is reached, the motion controller starts to approach the upper cylinder to the lower one in steps of 0.1 µm. When the separation between the tip lines of the cylinders becomes comparable to the range of intermolecular forces, the surfaces jump into contact. At this point, corresponding to a negative value for load P and a finite value for radius of contact a, the motion is temporarily ceased and the computer and time code generator times are set to zero. From this point on, 12 steps of 1.5 µm compressions are imposed every 30 min. Load, compression, and contact area picture files are saved every 1, 5, 10, 20, and 30 min after each

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Figure 7. Strain energy release rate, G, in terms of crack growth rate V ≡ |da/dt| for the 2% AA system (unloading experiment). G0 is the threshold value of the strain energy release rate. The decompression rate is 1 nm s-1.

Figure 8. The comparison between the imposed displacement by stage and the calculated compression of the cylinders from JKR theory: (b and ×) loading and unloading data, respectively.

Figure 9. Elastic moduli of the studied m-PSA measured in frequency sweep experiments on RSA-II solid analyzer at room temperature: (O) AA2, (4) AA5, and (0) AA10. The imposed strain is 2%.

Figure 10. Comparison between Young’s moduli of the studied m-PSA based on RSA-II and JKR experiments.

Table 2. Summary of Contact Mechanical Characterization of Cross-Linked Acrylic Pressure Sensitive Adhesives W, mJ m-2 G0, mJ m-2 K, MPa

sample AA2

sample AA5

sample AA10

60 ( 3 110 ( 15 1.9 ( 0.2

61 ( 3 130 ( 15 1.7 ( 0.2

60 ( 3 140 ( 20 1.4 ( 0.2

Table 3. X-ray Photoelectron Spectroscopy Results for Acrylic Pressure Sensitive Adhesives for given analyzer angle, deg atomic concn or ratio

sample AA2 20° 90°

sample AA5 20° 90°

sample AA10 20° 90°

C1s, % O1s, % C1s/O1s C1s/O1s, bulka

86.3 13.7 6.2

85.5 14.5 5.9

84.7 15.3 5.5

84.6 15.4 5.5 5.4

83.9 16.1 5.2 5.3

83.2 16.8 5.0 5.1

a Calculated from stoichiometry as (1 - AA/100 × 11/3) + (AA/ 100) × (3/5).

step compression (static loading). For each compression 10 min of contact was shown to be enough to capture all time-dependent phenomena. At the end of the loading experiment, the samples are not touched for a contact time of 60 min after which the surfaces are separated continuously at a constant rate of 1-10 nm s-1 (dynamic unloading). (It was observed that performing the unloading experiment in step fashion provided similar information but required longer experimental time.) The decompression progresses until the surfaces are completely separated.

Figure 11. Advancing and receding contact angle measurements on flat samples of the m-PSA. There was no clear distinction between advancing angles for a given testing liquid on the m-PSA: advancing, (/) for all; receding, (9) AA2, (×) AA5, and (b) AA10. The apparatus enclosure temperature and relative humidity were generally 23 ( 1 °C and 1 ( 1%. The contact area, in general, was slightly elliptic with a a1/a2 ratio (1 and 2 are the principal axes) of less than 1.1. The geometric mean a ) (a1a2)1/2 was used as the appropriate value.6 The radii of the (half) cylinders were calculated from their side view images by taking measurements of the height and base of the arcs obtained at different crosssections close to the tip line. The radii of the cylinders were on average 10% smaller than the radius of the capillary tubes. This is due to the density increase of acrylics upon polymerization

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Figure 12. Illustration of surface and interfacial rearrangements in the cross-linked PSA. and possible extraction of free chains. In the case of two different values of radius for the two contacting cylinders, the harmonic mean was taken as the equivalent radius.6 2.4. Mechanical Testing Procedure. Rheology of the cylinders, the same as that used for the contact mechanics experiment, was studied in a parallel plate geometry in a Rheometrics Solid Analyzer RSA-II. This analyzer measures the Young’s modulus in a uniaxial tension experiment. The cylinders, approximately 5 mm long (L) and 2 mm in diameter (D), are epoxy-bonded between two opposing rods with a diameter of 7 mm. Care was taken to remove the adhesive pile-ups around the sample ends to avoid the edge effects. The relevant L2/D geometry factor and the sample’s Young’s modulus defined a point which was just inside the manufacturer’s recommended window of operation for parallel plate configuration. After pretensioning the system by 5 g and establishing thermal and mechanical equilibrium at laboratory conditions, dynamic strain sweep experiments were performed to test the linear behavior of the m-PSA. The frequency was 1 rad s-1, and the strain range was 0.5-5%. A frequency sweep with a 2% strain was performed in the range from 100 to 0.01 rad s-1. The stress relaxation experiment was also carried out under 2% strain for 1 h. 2.5. XPS Measurements. XPS measurements were performed using a PHI 5400 instrument with Mg anode and 300 W power under ultrahigh vacuum. The escape depth corresponding to the detected photoelectron at angle θ, with respect to the surface, is approximately given by 3λ sin θ, where λ is the inelastic mean free path of the photoelectrons. In this measurement, λ is approximately 30 Å. Therefore, for the analyzer angles of 90 and 20° used in this study the escape depths were 90 and 30 Å, respectively. 2.6. Contact Angle Measurements. Advancing and receding contact angles were measured using a Rame-Hart goniometer.

The volume of a sessile drop was increased and decreased over the surface of cross-linked PSA flats until the three-phase boundary moved. The needle of the microsyringe was immersed in the drop during measurements. Usually, the average of three measurements on three different spots was used as a data point. The test liquids were deionized water (γlv ) 72.0 dyn/cm), 1,3butanediol (γlv ) 37.7 dyn/cm), dimethyl sulfoxide (γlv ) 42.9 dyn/cm), formamide (γlv ) 50.8 dyn/cm), and glycerol (γlv ) 63.0 dyn/cm). These liquids were either distilled or purified on the basis of suppliers procedures. A Fisher tensiometer (model 21) was used to measure γlv.

3. Results 3.1. Adhesion Measurements. Figure 3 shows a typical contact area that we observed between crossed m-PSA cylinders. The load variation in the course of an experiment is shown in Figure 4 as a function of the prescribed displacement that is imposed by the precision stage. The loading experiments demonstrate an elastic contact between rubbery materials with small changes in load and contact radius for each step of compression. The JKR plot (Figure 5) expresses the cube of the contact radius as a function of load for loading and unloading experiments. The JKR plots for our studied systems showed persistent hysteresis between loading and unloading curves. The two-parameter curve fitting of loading plots to eq 1 gave a set of values for thermodynamic work of adhesion, W, and elastic constant, K, that best fits the data for each material. For unloading experiments, the strain energy

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release rate G was calculated on the basis of the elastic constant K value obtained from the corresponding loading experiment:

G ) (P - Ka3/R)2/6πKa3

(6)

Figure 6 illustrates typical variations of calculated W and G in the course of loading and unloading experiments. The data for the unloading measurements can be presented alternatively in the form of variations of G as a function of the rate at which the contact radius decreases (V ≡ |da/dt|). Such dynamic information is presented in Figure 7. In the presence of rate effects, it is more appropriate to consider the value of G at some low rate, G0, to be more indicative of interfacial processes. In our experiments, G0’s were based on a 5 nm s-1 value for V. Table 2 summarizes our contact mechanics-based results for the studied PSA-like materials. Figure 8 compares the compression δ calculated from the JKR theory (eq 3) with displacement imposed by the precision stage. The agreement is quite satisfactory for the entire range of loading and unloading experiments. We have observed that in the case of contact between short hemispheres and flats, when the contact diameter becomes larger than the height of the hemisphere, or the flat layer, the calculated compression based on JKR theory exceeds the experimental value. This is known as finite size effects and has also been addressed elsewhere.19 3.2. Mechanical Testing. The Young’s moduli for m-PSA cylinders were measured with the RSA-II solid analyzer as described in the Experimental Section. The dynamic strain sweeps (ω ) 1 rad s-1) for our system of m-PSA confirmed their linear viscoelastic behavior in a range of 0.1-5% of applied strain. The frequency sweep responses are shown in Figure 9. These mechanical responses show the existence of relaxed plateaus for E′ and E at low frequencies and longer times, respectively. The frequency below which, or the reciprocal of time after which, the modulus plateau is observed decreases with an increase in AA content of the system. A possible explanation for this kind of behavior in our cross-linked PSA is discussed in the next section. Figure 10 shows the comparison between the experimentally measured Young’s moduli and Young’s moduli that are calculated from eq 2 using K measured from our contact mechanical measurements. A value of 0.5 was assumed for Poisson’s ratio reducing eq 2 to E ) 18/16 K. 3.3. XPS Measurements. Table 3 gives surface elemental concentrations for the spun cast PSA as a function of analyzer angle. The concentration ratio between carbon and oxygen from the 90° analyzer angle is consistent with the stoichiometry ratio representing the bulk value. The 20° analyzer angle results show carbon enrichment toward the surface. 3.4. Contact Angle Measurements. Contact angle measurements on flat disks of m-PSA were made in order to compare surface energies with those determined from the JKR method. Figure 11 shows the cosine of measured angles as a function of the surface tension of testing liquids. The uncertainty on measured angles was much greater for receding experiments compared to the advancing ones. Advancing angles showed no dependence on PSA chemistry. The estimated values for advancing and receding surface energies of the m-PSA are shown on the basis of the Zisman’s method of analysis. (19) Shull, K. R.; Ahn, D.; Mowery, C. L. Langmuir 1997, 13, 1799.

Figure 13. Observed patterns of change in G, expressed in terms of crack growth rate V ≡ |da/dt|, for two different rates of decompression dδ/dt: (2) 1 nm s-1; (+) 10 nm s-1.

4. Discussion and Conclusions Our experimental results for the values of thermodynamic work of adhesion, W (Table 2), and advancing contact angles (Figure 11) show that there is no change in surface energetics of the m-PSA with acrylic acid content. The values of 60 mJ m-2 for W from contact mechanics and 28 mJ m-2 for the surface energies from contact angle measurements are more consistent with the surface activity of alkyl chains of 2-EHA when the PSA are in contact with air. Apparently, the system attempts to hide higher energy (carboxyl groups) in the bulk of the material.20,21 The XPS data (Table 3) suggest carbon enrichment in the vicinity of the surface, supporting this hypothesis. A surface free energy penalty for carboxyl groups does not exist in the polymer-polymer interface at the contact area. In the contact region, the carboxyl groups can seek out each other across the interface and form a hydrogen bond. Similar observations of adhesion hysteresis on different systems have been attributed to the formation of hydrogen bonds.12,22,23 The free energy penalty may explain the observed adhesion hysteresis between loading and unloading curves in our contact mechanics experiments and in the advancing and receding contact angles. However, based on our contact mechanics and contact angle measurements, the extent of hysteresis is not a strong function of acrylic acid content. This might be due to the fact that the sizable concentration of crosslinker (5%) has limited the number of hydrogen bonds by decreasing the chain mobility. The above scenario of surface and interfacial rearrangements is depicted in Figure 12. An important observation from Figure 6 is the relative insensitivity of strain energy release rate over the contact area to the position of the crack edge. This is in contrast to the stress dependency of hydrogen bonding suggested from a previous study.12 To study the nature of the observed hystereses, the systems were also decompressed at a rate of dδ/dt ) 10 nm s-1. Figure 13 presents such dynamic information in the form of variations of the strain energy release rate G as a function of crack growth speed V. The patterns of rate dependency are not overlapped over the observed crack growth rate range, though they are similar. This shows that the G of our PSA is not simply a function of (20) Kinning, D. J. J. Adhes. 1997, 60, 249. (21) Elman, J. F.; Johs, B. D.; Long, T. E.; Koberstein, J. T. Macromolecules 1994, 27, 5341. (22) Musto, P.; Karasz, F. E.; MacKnight, W. J. Macromolecules 1991, 24, 4762. (23) Schneider, J. W. Ph.D. Thesis, University of Minnesota, 1998.

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Figure 15. Demonstration of finite size effects in contact mechanics measurements. Figure 14. Contact area viewed in an unloading experiment between two elastic (cross-linked) poly(dimethylsiloxane) (PDMS) caps that were coated with un-cross-linked PSA (several microns thick). The cavitation and fibrillation of the material around the edge of contact is a good piece of evidence for the role of viscoelastic dissipation in adhesion of practical PSA.

crack growth speed. The slight increase in the slope of G at higher V region for the higher decompression rate suggests the importance of bulk related phenomena at higher V regions. On the other hand, the weak dependency of G on V for lower values of V implies that the dynamics of adhesion is not dominated by interfacial rate processes. This observation is consistent with our findings concerning self-adhesion dynamics for “bulk” samples and layered samples of some block copolymers.18 Bulk nonequilibrium processes could include viscoelastic effects,24 as well as possible inertial effects, corresponding to accelerating cracks at the onset of instability which occurs prior to complete detachment of the surfaces. The results for these highly cross-linked PSA imply that the main mechanism contributing to the adhesion of practical un-cross-linked or lightly cross-linked PSA must be the viscoelastic dissipation,25-33 which has been shown to be composition dependent.34 Figure 14 shows the contact area in an unloading experiment between two elastic (cross-linked) poly(dimethylsiloxane) (PDMS) caps that were coated with un-cross-linked PSA (several micrometers thick). The observed cavitation and fibrillation of the material around the edge of the contact area is additional evidence for the crucial role of viscoelastic dissipation in adhesion of PSA.35,36 (24) Falsafi, A.; Deprez, P.; Bates, F. S.; Tirrell, M. J. Rheol. 1997, 41 (6), 1349. (25) de Gennes, P. G. Langmuir 1996, 12, 4497. (26) Piau, J.-M.; Verdier, C.; Benyahia, L. Rheol. Acta 1997, 36, 449. (27) Kamyab, I.; Andrews, E. H. J. Adhes. 1996, 56, 121. (28) Benyahia, L.; Verdier, C.; Piau, J.-M. J. Adhes. 1997, 62, 45. (29) Chang, E. P. J. Adhes. 1997, 60, 233. (30) Ahn, D.; Shull, K. R. Macromolecules 1996, 29, 4381. (31) Shanahan, M. E. R. J. Phys. D: Appl. Phys. 1990, 23, 703. (32) Shanahan, M. E. R.; Michel, F. Int. J. Adhes. Adhes. 1991, 11 (3), 170. (33) Carre, A.; Shanahan, M. E. R. J. Colloid Interface Sci. 1997, 191, 141. (34) Cho, C. K.; Cho, K.; Park, C. E. J. Adhes. Sci. Technol. 1997, 11, 443. (35) Baljon, A. R. C.; Robbins, M. O. Science 1996, 271, 482.

As mentioned earlier in this section, the relatively large amount of cross-linker (5%) used in this study might have limited the mobility of chains, thus minimizing the number of hydrogen bonds that would have been formed between carboxyl groups in an un-cross-linked situation. Equivalently, this lack of mobility suggests that the number of effective cross-links should not be a strong increasing function of acrylic acid concentration but be more dependent on cross-linker density. The observation of a decrease in modulus with an increase in acrylic acid concentration (Figure 9) can be explained by a possible tendency of cross-linker to homopolymerize, competing with acrylic acid for copolymerization with 2-EHA, a process in which the effective number of cross-links is decreased. It would be interesting to compare the selfand cross-propagation rate constants of HDDA with AA and 2-EHA. Efforts to address this issue by testing samples with lower amounts of cross-linker are underway. Our results have several implications pertinent to the JKR methodology. The plateau values of load and contact radius seem to fit the JKR theory well with reproducible values for the K modulus and thermodynamic work of adhesion W. The good agreement, shown in Figure 10, between the Young’s moduli obtained from our contact mechanical measurements and the independent mechanical tests confirms the validity of JKR theory for modulus measurements in the presence of adhesion. Figure 8 shows that, in the absence of finite size effects, the JKR theory predicts the correct compliance of the system such that calculated compression is in agreement with experimental values. To the best of our knowledge, such a direct comparison has not been made before. Figure 15 illustrates the finite size effect for contact between a cross-linked PDMS sheet and a polyurethane cap. The change in slope of a3 as a function of load is clear in this figure. The contact diameter corresponding to this critical load is equal to the PDMS sheet thickness. Deformations larger than this critical value are influenced by the glass substrate supporting the sheet. In conclusion, we have been able to prepare samples of PSA that are elastic enough for JKR-type adhesion (36) Creton, C. In Material Science and Technology; Cahn, R. W., Haasen, P., Kramer, E. J., Eds.; VCH: Weinheim, Germany, 1997.

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measurements. The load-deformation data in our experiments follow the JKR predictions. The JKR and contact angle measurements both give consistent surface energies and adhesion hysteresis. The extent of adhesion hysteresis increases with the acrylic acid content, but the surface energy does not. Acknowledgment. The authors would like to thank Franky Yip, David P. Smith, Lihua Li, and Peggy Sheridan

Falsafi et al.

(3M) for their help and useful conversations. We also thank 3M and the Center for Interfacial Engineering, an National Science Foundation sponsored Engineering Research Center at the University of Minnesota, for financial support.

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