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Molecular Weight Dependence of Interdiffusion and Adhesion of Polymers at Short Contact Times Robert Gurney, Anastase Henry, Regis Schach, Anke Lindner, and Costantino Creton Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.6b03972 • Publication Date (Web): 18 Jan 2017 Downloaded from http://pubs.acs.org on January 23, 2017

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Molecular Weight Dependence of Interdiffusion and Adhesion of Polymers at Short Contact Times Robert Gurney1,3, Anastase Henry4, Regis Schach4, Anke Lindner2,3, Costantino Creton1,2* 1. Laboratoire de Sciences et Ingénierie de la Matière Molle, CNRS, ESPCI Paris, PSL Research University, 10 Rue Vauquelin, 75005 Paris, France 2. Global Station for Soft Matter, Global Institution for Collaborative Research and Education, Hokkaido University, Sapporo, Japan 3. Laboratoire de Physique et Mécanique des Milieux Hétérogènes, ESPCI Paris, Paris, France 4. Centre de Technologies Michelin, Ladoux, France [email protected], [email protected], [email protected] *Corresponding author

Abstract The autohesion and subsequent debonding of thin layers of three linear and monodisperse random copolymers of styrene-butadiene (SBR) with molecular weights varying between 30 and 75 times the average molecular weight between entanglements Me was investigated using a carefully controlled tack adhesion testing device in conjunction with a fast camera setup over a range of contact times tc (10 ms to 10 s) much shorter in comparison to the terminal relaxation times of the polymers. The evolution of the stress-strain curves and debonding mechanisms with increasing contact time was examined, and the work required to debond the layers was found to be strongly dependent on molecular weight at long contact times, but not at short contact times. We propose a cut-off contact time of 300 ms, corresponding to 104 times the entanglement time τe after which molecular weight becomes important in controlling the interdiffusion process and the debonding mechanisms of the tack test. For contact times over 300 ms the debonding energy plotted as a function of tc normalized by the reptation time τrep, collapses onto a master curve. Below this threshold tc, by comparing the adhesion of SBR on itself with the adhesion of SBR on glass, we also show that interdiffusion plays a part in adhesion of two identical polymer layers even at the shortest contact times, where the interdiffusion is controlled by the number of entanglements formed which scales with 1⁄√ .

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1. Introduction In industrial manufacturing applications of rubbers, adhesive contact between two uncrosslinked polymeric materials well above their glass transition must often occur after very short contact times during the assembly process. A very well-known example is found in tire manufacturing, where several layers of uncrosslinked or “green” filled rubber are rapidly laminated together for tire assembly1,2. For obvious reasons, delamination of the layers before final crosslinking is extremely undesirable and a good control of the adhesion between these elastomeric materials at short dwell times is essential. From a fundamental point of view, contact between two uncrosslinked polymers above their bulk glass transition temperature is particularly interesting due to the possibility of chain mobility across the interface. For several decades, scientists have understood that, in general terms, adhesion strength increases as a function of the amount of time that two polymer surfaces are left in contact3–6. This increase is typically attributed to changes in contact area3,7,8, polymer chain relaxation9,10, and chain interpenetration across the interface creating entanglements4,11–13. While polymer chain relaxation always occurs as short portions of the polymer network rearrange and relax to conform to the opposing surface, chain interdiffusion across the interface can only occur between two surfaces composed of mobile polymers which are at least partially miscible14,15. Many experimental investigations have been conducted for contact times ranging from hundreds of milliseconds to 105 seconds and have focused on the relationship between contact time and debonding energy1,11,16–18. While the behavior at long contact times depends clearly on the diffusion kinetics, at short contact times the picture is less clear since the creation of a new interface occurs simultaneously with the molecular interdiffusion. Historically, the first notable experimental setup used to probe short dwell times was the swinging pendulum experiment developed by Gent and coworkers1,17 that allows the application of short contacts (dwell time, tc ranging from 3 to 100 ms). This test has been employed primarily to study adhesion between elastomer and glass and between elastomer and elastomer for both crosslinked and uncrosslinked materials. The difference between the approach and retraction velocities of the pendulum is used to calculate the total energy dissipated during the contact event, and by subtracting the energy dissipated by compression of the material, the adhesion energy can be estimated. While the swinging pendulum test is an ingenious way to measure polymer adhesion at short dwell times, parameters such as contact time and pressure and debonding velocity are closely coupled and cannot be varied independently. To overcome these key experimental design challenges, Davis et al.19 developed a new setup with an independent control of the contact time tc, the approach and retraction velocities and with the added ability to monitor normal force, displacement, and contact area during each test. Using this new instrument, they studied the relationships between tc and the debonding energy, wdeb for two different soft materials, a crosslinked (PDMS) material representative of a very elastic rubber, and an uncrosslinked (SBR) material with a broad distribution of molecular weights. The autohesion and adhesion between these materials and a rigid glass substrate was measured for a range of tc varying between 40 ms and 10 s. For the crosslinked and very elastic PDMS, no dependence of adhesive strength or separation mechanism on tc was observed (PDMS-Glass). However the debonding mechanisms observed for SBR interfaces (SBR-Glass and SBR-SBR) were shown to differ strongly with increasing tc. Specific attention was paid to the establishment of molecular contact between the surfaces and Davis et al. showed that this contact formation could be heterogeneous even for very smooth contacting surfaces. Note that interdiffusion below the bulk Tg can also occur by segmental interdiffusion across the interfaces as the healing temperature remains above the surface Tg.20–22 Because only the autohesive properties of one polydisperse SBR was investigated, it was not possible to establish a relation between the molecular structure of the adhering polymers and the measured adhesion energy for short contact times.

In this paper, we use three model SBR polymers with identical microstructure and a very narrow polydispersity of molecular weights, in order to understand the molecular weight dependence of the bonding and debonding mechanisms. An improved experimental setup based on that used by Davis et al., with better time and space resolution in the visualization capabilities and values of tc as low as 10 ms is used.

2. Experimental 2.1. Polymer synthesis, characterization and preparation 2


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The polymers used are uncrosslinked and nearly monodisperse random copolymers of styrene and butadiene with 40 wt. % styrene, 15 wt. % 1,4-cis butadiene and 34% wt. % 1,4-trans butadiene and 11% 1,2 cis butadiene synthesized by the Michelin Research Center (Ladoux, France). The polymers were designed to have different number average molecular weights M. Their main molecular characteristics are detailed in Table 1. The materials are henceforth referred to by the codes given in the table. The molecular weight and molecular weight distribution were characterized by Gel Permeation Chromatography (GPC) in THF using light scattering. The samples were further analyzed by DSC (TA Instruments) with a heating ramp of 10°C per minute in order to determine their bulk glass transition temperatures. The samples were heated, cooled and heated again at the same rate, and the Tg was taken as the midpoint of the transition during the heating phase. The samples were found to have narrow molecular weight distributions and nearly identical glass transitions between -31 and -34°C.

Table 1. Sample Properties.

Sample Name

SBR100

SBR170

SBR250

Molecular Weight M [1]

99100

173 023

253 000

Polydispersity Mw/M [1]

1.06

1.09

1.15

Tg (°C) [2]

-31.0

-32.9

-33.9

Measurements by [1] GPC [2] DSC

2.2. Tack Adhesion Instrument The adhesion test geometry can be schematically described as the contact between a 50 µm thick flat and supported polymer film with a hemispherical probe (uncoated, or coated with a 100 nm polymer layer) in a confined Johnson−Kendall−Roberts (JKR) geometry. The glass lens used as a probe has a radius of 16 cm which, when in contact with the flat film at a typical contact force of 1N, results in a circular contact area of radius a = 1-2mm. The adhesion testing device consists of two independent actuators which allow the approach and retraction of the probe to occur in quick succession, controlled by a Labview program. This setup can conveniently be used for contact times varying from 10 ms to 10 s. A calibrated mechanical spring coupled with a capacitance displacement sensor serves as the load cell used to measure the normal force on the probe. A high-speed CMOS camera with a frame rate of 998 frames s−1 is mounted over the setup to allow the acquisition of contact area images over the course of each test. The contact radius a is determined after each test using image analysis software. A schematic of the FastTack device is shown in Figure 1. Further details on the setup can be found in a previous publication using this setup19.

Figure 1. Top-down schematic of FastTack experimental setup

During a typical adhesion test, the curved probe is brought into contact with the flat film at a constant velocity of 500 µms−1 until a maximum compressive load, Fm = 1 N, is reached. The position of the probe is held fixed at this compressive displacement for the specified contact time, tc, and then the probe is retracted with the same velocity until 3


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complete separation occurs between the probe and the film. The contact times tested were logarithmically spaced at 10, 30, 100, 300 ms and 1, 3 and 10 s. Force F and relative displacement δ are recorded for the duration of the test. Tests were performed in a temperature controlled room at 21 - 23°C which is significantly (approximately 50°C) above the bulk glass transition temperatures of the materials. The relatively fast approach velocity was required to minimize the time taken for the probe to reach the desired contact force and to allow the shortest possible contact time while still controlling the contact pressure. In addition the retraction velocity was chosen to allow short contact times and to deform the layer at an average strain rate where the material behaves as an elastic rubber. Wdeb is defined as the work required to debond the interface, and is given by:

= ℎ

(1)

where ε is the displacement normalized by h the initial thickness of the sample, and Amax is the maximum contact area between the two materials. We also use the nominal stress σ = F/Amax. Adhesive films were prepared by drop casting the polymer from a 10 wt. % solution in toluene onto silanized glass slides (reference procedure), which were allowed to dry at room temperature in air for 2 days before a final drying step at 50°C under vacuum for 1 hour. Film thicknesses were measured as 55 ± 10 µm by stylus and optical profilometry (Dektak IIA SP, and OP Veeco Wyko NT3300). For the probe, glass lenses of radius 16 cm were used as-is, and also spin-coated with a thin polymer layer from a 1 wt. % solution in toluene. The thicknesses of the films spin-coated on the lenses were measured as 100 ± 10 nm by optical profilometry.

2.3. Rheological Characterization The rheological properties of the materials were measured using a RDAII parallel plate rheometer (Rheometrics). Disks of 8 mm in diameter and 1mm thickness were tested using a parallel plate geometry applying a strain between 0.1% and 0.5%, in order to be within the linear regime. Frequency sweeps were performed from 0.01 to 100 rad s -1 at a range of temperature varying from -40°C and 80°C. Master curves were constructed by horizontally shifting tan δ (ω) curves and G’ (ω) and G’’ (ω) curves were then constructed wityh the same horizontal shifts and using additional vertical shifts. The fitted vertical shifts were in line with predictions from density and temperature variations.

3. Results and Discussion 3.1. Rheological properties and relaxation times To obtain time temperature superposition of the rheological data, the tanδ data was first horizontally shifted across the range of temperature and frequency range, and then vertically shifted with G’. This was done using a matlab script which uses the G' and G'' data acquired across the range of temperatures and frequencies to compute the aT and bT shift coefficients. The resulting constructed curves for G’ and G” as a function of reduced frequency, and tan δ, are shown in Figures 2a and b respectively.

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(a)

(b)

1/τe

1/τ0

1/τrep

Figure 2. Curves from shear rheology as a function of shifted angular frequency (a) Storage (G’, solid lines) and Loss (G”, dashed lines) moduli, and (b) tan δ. Green = SBR100; Blue = SBR170; Red = SBR250. The vertical dashed line represents a frequency equivalent to the initial strain rate applied in a probe-tack experiment when debonding. Where tanδ crosses the horizontal dashed line at tanδ = 1 shows the relaxation times for each sample.

The characteristic relaxation times of entangled polymers are inherently related to the polymer’s mechanical and diffusive behavior and are presented in Table 2 below. The first value calculated from the rheology curves is the plateau modulus, GN0, taken as the value of G’ at the minimum of G” along the plateau region of G’ shown in Figure 2a. At 10 Hz (the frequency of probe-tack debonding) values of G’ are quite similar for all samples, but the values of G” are slightly different. Within the context of adhesion tests, it is interesting to note that this difference suggests a difference on the dissipation properties of the materials, which will influence the debonding mechanisms. Three characteristic relaxation times are associated with changes in flow behavior at the macroscopic scale, i.e. a large shift in elastic and dissipative properties such as at Tg, and are intrinsically linked to dynamic molecular properties. These times are determined by the frequency at which values of G’ and G” cross, of which 3 are observable within the 14 decades of frequency reported in Figure 2. These crossover points are also given by the frequencies at which tan δ = 1, marked on Figure 2b. The terminal relaxation, or reptation time, τrep is the low-frequency crossover point of G’ and G” and is seen for the samples studied here between 1 and 1000 s. It represents the time taken for a chain to diffuse a distance of the order of its radius of gyration, or in other words to forget its original position. It has been shown theoretically to scale with M3 and experimentally with M3.4. The second crossover, just after the G’ plateau, is the entanglement relaxation time, τe. This corresponds to the time taken for an entanglement strand to move a distance equal to its radius of gyration, where Ne is the number of segments between entanglements in a chain of length N monomers, and is related to the entanglement molecular weight by

= . The entanglement relaxation time is obviously much shorter than the terminal relaxation time and is related to

the reptation time by the cube of the number of entanglements23

~ 6

(2)

Furthermore, the relaxation time of an individual segment τ0 is seen as a third and highest frequency crossover on the rheology curve and is related to the entanglement relaxation time by ! ~ "

(3)

The relationship between the three relaxation times is as follows: % #$ ~ 6 ~ 6 !

(4)

In addition, values of the entanglement molecular weight (or entanglement molar mass) Me can be derived from the plateau modulus23: 5


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& =

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'() *+

(5)

These characteristic times are also controlling the diffusion dynamics of individual molecules inside the material. For an entangled polymer the chain diffuses along its confining tube and the diffusion distance along the tube is related to the diffusion time t by:

< - > = /012

(6)

The curvilinear diffusion coefficient along the tube Dc is the Rouse diffusion coefficient and is inversely proportional to the chain length and related to the segmental relaxation time τ0 by:

12 ~

3)

4

~

"

(7)

Therefore for a given value of diffusion time, a chain has diffused along a tube length of:

< - > ~5

6 "

(8)

An entanglement length along the tube is given by 7 / so that a chain diffusing for a time t has moved along its tube by: 6

9

< 8 > ~ 5 5

(9)

entanglement lengths. These characteristic times are shown for each material in Table 2, and represented in Figure 3, taking the experimental value of τrep for the calculations of the other theoretical relaxation times. It should be noted that these are approximate values since the actual chain size and flexibility (the Kuhn segment or the constant C∞) are not known for these copolymers. They are nevertheless a very useful approximation. Table 2. Rheological Characteristics and relaxation times of the materials at 22 °C.

Sample Name GN0 (MPa) Me (g/mol) τrep (s) τe (s) τe (s) τ0 (s) τ0 (s)

†

†

†

SBR100 0.70 ± 0.09 3050 ± 350 2.0 ± 0.5 2.2 ± 0.4 x 10-5 1.0 ± 0.2 x 10-5 4.3 ± 0.5 x 10-8 3.2 ± 0.8 x 10-8

SBR170 0.78 ± 0.06 2800 ± 200 25 ± 3 1.5 ± 0.3 x 10-5 2.2 ± 0.3 x 10-5 4.3 ± 0.6 x 10-8 6.2 ± 0.8 x 10-8

SBR250 0.74 ± 0.11 3300 ± 500 180 ± 25 1.7 ± 0.3 x 10-5 5.0 ± 0.6 x 10-5 3.4 ± 0.5 x 10-8 1.4 ± 0.3 x 10-7

† denotes value calculated from the formulas above. Other values taken directly from shear rheometry data.

The reptation time is strongly dependent on M and covers two decades for the three different molecular weights. However, as expected from theory, the shorter relaxation times (τe, τ0) and the plateau modulus GN0 are, within experimental error, independent of molecular weight. That is to say that movement or diffusion on the entanglement length scale or the monomer length scale is independent of molecular weight24–26.

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τrep

τe τ0

Figure 3. Experimental (filled symbols) and theoretical (open symbols) values of 3 relaxation times for SBR100 (green), SBR170 (blue), and SBR250 (red)

These different relaxation times correspond to chain motions on different length scales and will thus influence contact formation between entangled polymers differently. Mainly the shorter relaxation times correspond to fast movements of chain segments that do not require diffusion of the center of mass, whereas at longer timescales center of mass diffusion takes place. The transition between these two regimes is complex and has been the focus of theoretical predictions and careful interdiffusion experiments15,27. Initially the fast movement of chain ends thus leads to an intermixing of chains, initially separated by a sharp interface rather than to a center of mass diffusion. Such an intermixing process forms new entanglements across the plane of the interface at very short contact times. The latter are expected to increase the interfacial strength and thus to affect adhesion. At longer timescales center of mass diffusion further modifies the interface between the two entangled polymers. Theoretical predictions of the effect of molecular diffusion on fracture energy and comparisons with experiments exist for polymer glasses24,25. However this process remains, to the best of our knowledge, largely unknown for adhesion between polymer melts and is one of the objectives of this study.

3.2. Adhesion Results The level of autohesion between the layers was investigated using a probe tack test as described in the experimental section. Since this is a macroscopic test carried out on deformable layers, the force-displacement response is not uniquely dependent on the molecular structure of the interface between the thin layers but also on the bulk mechanical properties of the layers and on the details of the experimental geometry and conditions28,29, and in particular the degree of confinement a/h and the debonding speed Vdeb. For highly confined soft layers (a/h > 10), the debonding invariably starts with the nucleation and growth of cavities. However, depending on the value of the local elasto-adhesive length Γ/G’(ω), where Γ is the energy per unit area necessary to propagate a crack at the interface and G’(ω), is the elastic modulus at the relevant strain rate, the initial cavities can evolve differently. For Γ/G’(ω) ≲ h (with h being a typical layer height) they evolve toward interfacial cracks and the debonding is then called interfacial, while for Γ/G’(ω) ≳ ℎ the deformation occurs in the bulk and cavities elongate in the tensile direction11,29. For soft viscoelastic materials, Γ is proportional to tan δ and the ratio tan δ/ G’ is shown in the SI for our materials. Since both Γ and G’(ω) depend on the velocity of the probe and on the bulk rheological properties of the adhesive, these failure mechanisms (bulk vs. interfacial) vary also with the same parameters. In this study we kept the probe velocity and the geometry constant and focused therefore on differences only brought by the material (rheology and interdiffusion kinetics). Therefore for a given material an increase in Γ, as caused for example by interdiffusion, leads to a progressive shift from interfacial to bulk debonding leading to an increase in the overall adhesion energy Wdeb. Note also that when the debonding velocity is vanishingly small Γ = Γ0 and is a measure of the intrinsic interfacial strength. Tack tests were performed for each 50 µm film, against a bare glass lens, and again against a lens coated with a 100 nm thick film of the same SBR, which is about 10 times the radius of gyration of the chains. The variables were molecular weight of the SBR (100k, 170k, 250k g/mol) and contact time (between 10 ms and 10 s). Figure 4 shows typical stress strain debonding curves for various contact times and representative images of the debonding process for an intermediate contact time. At short contact times, the debonding curves for each molecular weight sample are of similar shape with a peak stress and a rapid drop signifying a weak adhesion between the layers, and a quick separation of the interface without much deformation of the layers. This trend continues for contact times varying from 10 ms to ~300 ms. For longer contact 7


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times, the debonding response becomes clearly dependent on molecular weight, as seen by the differently shaped curves for each sample with increasing contact time. For SBR100 (Figure 4a) an increasingly broad shoulder is observed, indicating that the polymer in the thick film is deformed to higher strains before failing. This shoulder is a sign of the beginning of cavity growth in the bulk a phenomenon observed only when surfaces are sufficiently strongly bonded.30 Such a cross over between mechanisms with contact time had already been observed by Schach et al.11 for very similar materials, but slightly different conditions. For SBR170 (Figure 4b), as contact time increases from 300 ms to 10 s, a less pronounced shoulder in the stress peak is also observed, and the strain at failure increases. Finally for SBR250 (Figure 4c) no shoulder is observed and only the peak height increases with contact time, meaning that debonding is mainly due to growth of interfacial cracks for this molecular weight.

(a)

(b)

(c)

tc=10s

tc=10s 10ms

tc=10s

3s

3s 300ms 1s

1s 10ms

10ms

Figure 4. (i) Stress - Strain tack debonding curves for each material from a polymer lens at a range of contact times from 10 ms to 1 s for (a) SBR100 (b) SBR170 (c) SBR250.

To directly compare the effect of molecular weight, the tack debonding curves for each molecular weight are shown for the shortest contact time of 10 ms in Figure 5a. At that short contact time, the debonding curves are characteristic of the debonding of an elastic material from a weak interface. This weak interface suggests in turn that there was little interdiffusion between the layers. The curves are also relatively symmetric relative to the peak, indicative of a progressive nucleation and growth of a population of preexisting contact defects rather than a nucleation controlled debonding followed by an unstable fast growth. Such preexisting contact defects are observed for all three materials at contact times shorter than 100 ms, where clear evidence of incomplete contact formation is observed and many small bubbles nucleate (presumably from trapped air bubbles) when the probe is separated from the SBR film. Although this mechanism of air entrapment, already observed qualitatively by Davis et al.19, is interesting in its own right, it will not be discussed in detail in the present paper where we will simply note that this defect controlled regime at short contact time appears to be molecular weight independent within the range of M which we explored. The effect of changing the molecular weight of the material on the debonding profile is more pronounced after a longer contact time as seen in Figure 5b. After a contact time of 3 seconds, SBR100 shows a clear shoulder in the stress after the initial cavitation peak. The debonding curve is no longer a symmetric peak as observed at short contact times. The polymer layer is now stretched significantly further before the stress goes to zero dissipating in this way more energy. This is also true for SBR170 but the deformation is less pronounced and the low-stress shoulder does not extend past a strain of 2. Finally, the stress-strain curve of the SBR250 does not show any shoulder at all and retains a symmetric shape, but the stress peak increases.

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(a)

(b)

(c)

Figure 5. Stress vs. Strain tack curves for the each material for SBR100 (green), SBR170 (blue), and SBR250 (red) at (a) tc = 10 ms and (b) tc = 3 s. (c) Work of debonding for contact times shown in (a) and (b).

Figure 5c shows the work of debonding for each of the materials after 10 ms and 3 s contact time. The values of the work of debonding at 10 ms contact times are nearly molecular weight independent, while at longer contact times (3 s) the more deformable low-M materials have larger debonding energies. The measured peak stress and work of debonding for each sample are plotted as a function of contact time in Figure 6a and 6b. Two distinct trends are seen in the values of the work of debonding depending on the interfacial contact time. At contact times below 300 ms, the value of σmax depends strongly on tc but is nearly independent of M, while Wdeb depend weakly on both M and tc . On the other hand for tc > 300 ms, both σmax and Wdeb increase strongly with tc and depend markedly on M.. Interestingly for the longer contact times (tc > 1-3 s) the value of σmax seems to reach a plateau, while the work of debonding keeps increasing. The work of debonding is not only dependent on the strength of molecular interactions but also of the rheological properties of the material in the thick layer. Although a direct and quantitative relation does not yet exist in all generality one can write:29

= ? , A, ℎB

(10)

where Γ0 corresponds to the adhesion energy at vanishingly small debonding velocity, as introduced before. Note that Γ0 is not directly measurable for our relaxing materials31. φ(Vdeb,a,h) is the energy dissipated during debonding which is dependent on the geometry of the contact (contact radius a and thickness h), on the viscoelastic properties G’(ω) and G”(ω) of the material and on the probe velocity. Since in our case the probe velocity and the geometry are kept constant, we test essentially the effect of the increase in Γ0 and the differences in viscoelastic properties of the three materials at the chosen debonding velocity of 500 µm/s. For h = 50 µm, the applied average strain rate during debonding (Vdeb/h) is CD =10 s-1. This strain rate can be in principle compared to the rheological measurements recorded at a (shifted) frequency of 10 Hz at the test temperature, as shown by the vertical dashed lines in Figures 2a and b. As discussed before values of G’(ω) at 10 rad/s are comparable for all samples, while the values of G”(ω) differ more. SBR100 is much more dissipative than the others, with SBR250 being the least dissipative. Differences in Wdeb observed between different molecular weights can therefore be mainly attributed to differences in Γ0 and thus to differences in the strength of the interface. Below contact times of 300 ms the energy of adhesion and peak stress are nearly independent of molecular weight for the molecular weights investigated. In this regime contact times are much shorter than the reptation times of the molecules but much larger than the entanglement relaxation time τe, discussed above. This means that entanglements are being created across the interface by polymer interdiffusion. It is interesting to discuss this more quantitatively in view of the available characteristic times. At 10 ms of contact time, and using equation 9 and the data of Tables 1 and 2, the chains of the three polymers have only diffused by a 2-3 entanglements at the most. However at 300 ms, the diffusion has taken place over about 7-12 entanglement lengths depending on the molecular weight of the chain. In this timeframe, the number of entanglements formed remains low and weakly dependent on chain length. At longer contact times, the chain interdiffusion between the layers may shift to a regime controlled no longer by the absolute number of entanglements but by the fraction of the chain that has diffused. For example at 300 ms, SBR100 has diffused a third of its length while SBR250 has diffused less than 10% of its length. At this later stage, adhesion seems to be controlled by the reptation time of the particular material. To demonstrate this, we plot Wdeb above 300 ms for each material as a function of the contact time normalized by τrep, shown in Figure 6c. It is apparent that the normalized data points collapse quite well onto a single curve suggesting that the reptation time is the correct rescaling parameter for the work of debonding of linear entangled chains. 9


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It should be noted that when contact times exceed the reptation time (tc/τrep>1), the interface structure should reach an equilibrium in that the layers have had sufficient time to interdiffuse completely11. In our experiments, SBR100 at contact times of ~τrep and 5xτrep meet this criteria and hence are predicted to have similar debonding curves, and similar σmax and Wdeb. While σmax seems to have stabilized, Wdeb keeps increasing. This may be because the reptation model is intended for tracer diffusion and does not account for collective effects and for the complex nature of the contact and debonding during the experiment, such as the contact pressure and velocity. Hence it is used here as an approximation.

(a)

(b)

(c)

Figure 6. (a) Peak stress and (b) Work of debonding of the SBR-SBR interface as a function of contact time tc. Circled, solid line: M–independent region. Circled, dashed line: M–dependent region. (c) Work of debonding of the samples tested in the M– dependent region plotted against tc normalized by τrep.

3.3. Effects at short contact times Having shown the independence of the debonding energy on molecular weight at short contact times, the role played by molecular interdiffusion is not immediately obvious. In order to show that there is indeed interdiffusion even at 10 ms contact time, we compared the results of the polymer-polymer interface at short contact times with results from the same tests, but using an uncoated glass lens instead of a polymer coated one.

bonded region (light)

Interfacial crack opening (shadow regions indicate crack boundary)

Figure 7. Stress vs. Strain tack curves for the three samples for SBR-Glass interface (solid lines) and SBR-SBR interface (dashed lines) with a contact time tc =10 ms. SBR100 (green), SBR170 (blue), SBR250 (red). Images on the left show contact area during debonding for SBR170 from SBR (top) and glass (bottom). Images on the right show a zoomed region on the centre. Scale bar = 300 µm.

When comparing the debonding curves of the thick SBR layers, there is a clear difference between the values of Wdeb from the bare glass probe and from the polymer-coated probe. A higher peak stress and greater deformation of the thick film are observed when it is debonded from the polymer coated probe, leading to a higher work of debonding 10


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It is interesting to note that this is true even when the surfaces were only in contact for 10 ms, as presented in Figure 7, which indicates that the diffusion over 1-2 entanglement lengths occurring between the polymer layers at such short times of contact is sufficient to significantly increase the adhesion relative to bare glass, although there is little effect of molecular weight, as expected from the similar values of τe for all three materials.

3.4. Mechanism Map In summary, for contact times over 300 ms the debonding energy plotted as a function of tc normalized by the reptation time τrep, collapses onto a master curve, proving that the relevant timescale in this regime is indeed the reptation time. Below this threshold tc, the energy of adhesion varies only little with contact time and is nearly independent from molecular weight. In this regime interdiffusion is controlled by the entanglement relaxation time τe which is independent of M and significantly smaller than our smallest contact times. By comparing the adhesion of SBR on itself with the adhesion of SBR on glass, we also show that interdiffusion plays a part in adhesion of two identical polymer layers even at the shortest contact times. The detailed observation of the debonding mechanisms provides a more comprehensive picture of the influence of contact time on the mechanisms of debonding. In Figure 8, each point represents a test condition and a material, and the symbol shape gives the type of debonding. For convenience we represent the reptation time in the horizontal axis to separate the materials. Three different debonding mechanisms can be identified.19 Bulk debonding, interfacial crack propagation and defect driven interfacial adhesion. For each type of debonding mechanism Figure 8 shows the conditions and materials where it is observed and a representative debonding image at low and high magnification. Bulk failure, represented by a rectangle in the graph, can be clearly identified in the images by the presence of a large number of small and large cavities scattering light and giving a distinctly dark color. Interfacial crack propagation, represented by a circle, can be identified by the presence of larger cavities with a flat shape and therefore a white region inside the cavity. Finally the defect driven crack propagation (lozenge symbol) is identified by the presence of a uniform population of small cavities present before the stress reaches its peak value. We can see from the figure that the debonding type can be reasonably well predicted based on the polymer reptation time and the contact time between layers. It is clear that bulk debonding is more likely for materials with shorter reptation times (in this case, the materials with lower M) and at longer contact times. The observation of defects is dependent primarily on the contact time and appears to be independent of molecular weight. Perhaps the most interesting sample is the intermediate molecular weight sample SBR170 (blue markers in Figure 8) which, depending on contact time, is seen to debond with three different mechanisms. We do expect SBR100 (green markers) to have the same progression, that is at short contact times interfacial separation with defects would be expected, but we were unable to test short enough contact times with this setup. Likewise bulk separation would be expected from SBR250 (red markers) but given its reptation time of 180 seconds, the contact times tested in this study are too short.

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Mw dependant Interfacial crack propa gation

Bulk debondin g

Mw independent

(b)

(c)

Bulk Failure

(d)

Defect driven interfacial

Interfacial debonding

Figure 8. Phase map of debonding mechanisms for the three materials as a function of contact time and reptation time (see Table 2). Photos of the contact area during debonding for samples circled in the phase map; (a) SBR100, 50 ms after debonding, (b) SBR170, 30 ms after debonding, (c) SBR250, 50 ms after debonding. Scale bar for all images is 300 µm. The phase region boundaries are estimated based on the experimental evidence.

4.

Conclusions

This study investigated the contact time dependence of the autohesion of a series of monodisperse and highly entangled linear SBR polymers of different molecular weights (with reptation times varying between 2 s and 180 s) at contact times varying between 10 ms and 10 s. At contact times longer than 300 ms, SBR layers interdiffuse over a timescale that scales with their reptation time τrep, leading eventually to a strong interface and bulk deformation upon debonding. In this regime the work of adhesion can be plotted as a function of tc/τrep as proposed in an earlier publication.11 However at contact times of less than 300 ms, corresponding to roughly a tenth of the reptation time of the lowest molecular weight, the work of debonding is much less dependent on molecular weight. Since a detailed comparison between debonding of SBR from itself and SBR from glass shows conclusively that even for those short contact times Wdeb on glass is three times lower on glass than on SBR, we infer that in this short contact time regime, interdiffusion clearly occurs at the interface and is controlled by the number of entanglements formed which scales with 1⁄√ . These results may be important to understand the role of interdiffusion in fast or impact contact conditions.

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5. Acknowledgements The authors acknowledge the financial support and provision of polymer samples from the Michelin Research Center at Ladoux in Clermont-Ferrand, France.

6.

Associated Content

Supporting information is available free of charge via the Internet at http://pubs.acs.org/.

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