Liquid Interface of Two Immiscible Polymer Films

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Friction at the Liquid/Liquid Interface of Two Immiscible Polymer Films Hongbo Zeng,†, Yu Tian,†,‡, Boxin Zhao,†,§ Matthew Tirrell,† and Jacob Israelachvili†,* †

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Department of Chemical Engineering, Materials Research Laboratory, California NanoSystems Institute, University of California, Santa Barbara, California 93106, ‡State Key Laboratory of Tribology, Tsinghua University, Beijing 100084, People’s Republic of China and §Department of Chemical Engineering, University of Waterloo, Canada. H.Z. and Y.T. contributed equally to this work. Received July 31, 2007. Revised Manuscript Received January 27, 2009 We studied the friction between two immiscible polymer melts of polybutadiene (PBD) and polydimethylsiloxane (PDMS). Polymer films (100-300 nm thick) were coated onto smooth mica substrates, and then were brought into contact and sheared (slid) to and fro in a surface forces apparatus (SFA). Stop-wait-start experiments were also carried out at different sliding velocities to investigate the characteristic relaxation times of the interdigitation and disinterdigitation processes at both the static and shearing interfaces. By virtue of their limited interdigitation/interpenetration across the contact interface, immiscible polymers never fully coalesce into a continuous homogeneous material. This affects both their dynamic adhesion and friction forces. The immiscible interface exhibits various “characteristic” parameters such as its static and dynamic widths and at least two relaxation times: the static interpenetration time and the velocity adaptation time. The interfacial width saturates at some small but finite value, resulting in Stribeck-like behavior for the friction force as a function of the sliding velocity, characterized by F having a minimum value at some characteristic sliding velocity V. The presence of solvents at the immiscible interface can have a dramatic effect on the friction or lubrication forces. The implications of the results regarding the depth and dynamics of interdigitation and interpenetration of immiscible chains across an interface are discussed in relation to the adhesion, friction, and strength of polymer composites and the coalescence of immiscible droplets.

Introduction For the three states of matter, there are five kinds of two-phase interfaces: solid/solid, solid/liquid, solid/gas, liquid/liquid, and liquid/gas. In the area of friction (tribology), the solid/solid interface is the one that is most widely studied.1-7 For solid/solid friction, Amontons’ law is usually obeyed. This law states that the lateral friction force F is linearly proportional to the normal load L through the friction coefficient μ (i.e., μ = F/L = constant).8 Bowden and Tabor9 found that the real area of contact between two surfaces is proportional to L, which leads to Amontons’ linear relationship, and Berman et al.10 found that it also applied to (nonadhering) Hertzian contacts. Amontons’ law *Corresponding author. E-mail: [email protected]. (1) Autumn, K. Am. Sci. 2006, 94, 124–132. (2) Bhushan, B.North Atlantic Treaty Organization. Scientific Affairs Division. Micro/Nanotribology and Its Applications; Kluwer Academic: Dordrecht, The Netherlands, 1997. (3) Gao, J. P.; Luedtke, W. D.; Landman, U. J. Phys. Chem. B 1998, 102, 5033–5037. (4) Tian, Y.; Pesika, N.; Zeng, H. B.; Rosenberg, K.; Zhao, B. X.; McGuiggan, P.; Autumn, K.; Israelachvili, J. Proc. Natl. Acad. Sci. U.S.A. 2006, 103, 19320–19325. (5) Urbakh, M.; Klafter, J.; Gourdon, D.; Israelachvili, J. Nature 2004, 430, 525–528. (6) Persson, B. N. J. Sliding Friction: Physical Principles and Applications, 2nd ed.; Springer: Berlin, 2000. (7) Bhushan, B. Modern Tribology Handbook; CRC Press: Boca Raton, FL, 2001. (8) Gao, J. P.; Luedtke, W. D.; Gourdon, D.; Ruths, M.; Israelachvili, J. N.; Landman, U. J. Phys. Chem. B 2004, 108, 3410–3425. (9) Bowden, F. P.; Tabor, D. Friction: An Introduction to Tribology; Heinemann Educational: London, 1973. (10) Berman, A.; Drummond, C.; Israelachvili, J. Tribol. Lett. 1998, 4 95–101.

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is applicable only to nonadhering junctions. For adhering surfaces, the adhesion acts as an additional “internal” load.11 Other theories or models on friction and the relationship between adhesion and friction have also been developed recently.12 For solid/liquid interfaces, at the macroscopic level, it is usually accepted that there is no slip at the boundary when a viscous fluid flows past a solid wall. Thus, at the boundary the velocity of the fluid relative to the solid wall is zero. The noslip boundary condition has proven to be accurate and useful for understanding macroscopic flows. However, recent experimental and theoretical research has suggested that for certain fluids flowing past certain hydrophilic or hydrophobic surfaces, full or partial wall slip may occur at the submicroscopic level,13-21 resulting in higher flow rates or, effectively, reduced viscous drag forces.

(11) Homola, A. M.; Israelachvili, J. N.; Mcguiggan, P. M.; Gee, M. L. Wear 1990, 136, 65–83. (12) Johnson, K. L. Proc. R. Soc. London, Ser. A 1997, 453, 163–179. (13) McGuiggan, P. M.; Gee, M. L.; Yoshizawa, H.; Hirz, S. J.; Israelachvili, J. N. Macromolecules 2007, 40, 2126–2133. (14) Tretheway, D. C.; Meinhart, C. D. Phys. Fluids 2002, 14, L9–L12. (15) Watanabe, K.; Yanuar; Udagawa, H. J. Fluid Mech. 1999, 381 225–238. (16) Watanabe, K.; Yanuar; Mizunuma, H. JSME Int. J., Ser. B 1998, 41, 525–529. (17) Campbell, S. E.; Luengo, G.; Srdanov, V. I.; Wudl, F.; Israelachvili, J. N. Nature 1996, 382, 520–522. (18) Barrat, J. L.; Bocquet, L. Phys. Rev. Lett. 1999, 82, 4671–4674. (19) Bocquet, L.; Barrat, J. L. Soft Matter 2007, 3, 685–693. (20) Robbins, M. O.; Thompson, P. A. Science 1991, 253, 916–916. (21) Thompson, P. A.; Robbins, M. O. Phys. Rev. Lett. 1989, 63 766–769.

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Shearing liquid/liquid interfaces abound in two phase flows22-27 and biological systems28,29 and include such phenomena or systems as polymer blends, immiscible flows, and cell rolling and spreading. Understanding such flows is also important for making new composite materials and colloidal formulations, emulsions, gels, liquid soaps, cosmetics, and processed food and for understanding many biological flow processes. In such systems, the liquid/liquid interface is usually modeled by its interfacial tension or energy, γ12. Through direct optical observation of deforming shapes (e.g., of a pendant or spinning drop), the equilibrium interfacial energy of two immiscible liquids can be measured under static or quasi-static conditions.30-33 For the miscible liquid/liquid interface, the friction of surface-anchored polymer chains sliding against a polymer melt or a cross-linked bulk polymer surface of the same material has been studied in detail both experimentally and theoretically.34-38 At the interface of two miscible polymers or segments, the interfacial tension is zero (γ12 = 0), whereas it is finite at the immiscible interface; this completely changes the adhesion and friction behavior. Under dynamic (flow) conditions, time-dependent deformations of the liquid/liquid interface are much more complex than can be described just by the interfacial energy of the interface. The viscosities of the two fluids also play important roles, and even the simplest systems are often still not fully understood. Thus, the bulk viscosity of polymer blends is usually much lower than theoretical predictions,39-43 and slip at immiscible polymer melt interfaces has been observed during the dewetting of one polymer film on another immiscible polymer film by Brochard et al.44 and also in rheological tests and using confocal microscopy.45-48 The static (equilibrium) immiscible polymer interface has been theoretically modeled in terms √ of parameters such as the interfacial width aI ≈ 2b/ (6χ), where b is the (22) Barsky, S.; Robbins, M. O. Physical Review E 2001, 6302. (23) Lee, H. M.; Park, O. O. J. Rheol. 1994, 38, 1405–1425. (24) Gunstensen, A. K.; Rothman, D. H. J. Geophys. Res. 1993, 98 6431–6441. (25) Utracki, L. A. J. Rheol. 1991, 35, 1615–1637. (26) Gunstensen, A. K.; Rothman, D. H.; Zaleski, S.; Zanetti, G. Phys. Rev. A 1991, 43, 4320–4327. (27) Demond, A. H.; Roberts, P. V. Water Resour. Res. 1991, 27, 423–437. (28) Jahn, R.; Sudhof, T. C. Annu. Rev. Biochem. 1999, 68, 863–911. (29) Hernandez, L. D.; Hoffman, L. R.; Wolfsberg, T. G.; White, J. M. Annu. Rev. Cell Dev. Biol. 1996, 12, 627–661. (30) Megias-Alguacil, D.; Fischer, P.; Windhab, E. J. Chem. Eng. Sci. 2006, 61, 1386–1394. (31) Guido, S.; Villone, M. J. Colloid Interface Sci. 1999, 209, 247–250. (32) Milliken, W. J.; Stone, H. A.; Leal, L. G. Phys. Fluids A 1993, 5 69–79. (33) Park, D. W.; Roe, R. J. Macromolecules 1991, 24, 5324–5329. (34) Bureau, L.; Leger, L. Langmuir 2004, 20, 4523–4529. (35) Leger, L.; Raphael, E.; Hervet, H. Polym. Confined Environ. 1999, 138, 185–225. (36) Massey, G.; Hervet, H.; Leger, L. Europhys. Lett. 1998, 43, 83–88. (37) Durliat, E.; Hervet, H.; Leger, L. Europhys. Lett. 1997, 38, 383–388. (38) Ajdari, A.; Brochardwyart, F.; Degennes, P. G.; Leibler, L.; Viovy, J. L.; Rubinstein, M. Physica A 1994, 204, 17–39. (39) Cole, P. J.; Cook, R. F.; Macosko, C. W. Macromolecules 2003, 36, 2808–2815. (40) Han, C. D.; Yu, T. C. J. Appl. Polym. Sci. 1971, 15, 1163. (41) Lyu, S.; Jones, T. D.; Bates, F. S.; Macosko, C. W. Macromolecules 2002, 35, 7845–7855. (42) Tucker, C. L.; Moldenaers, P. Annu. Rev. Fluid Mech. 2002, 34 177–210. (43) Wang, S. Q. Polym. Confined Environ. 1999, 138, 227–275. (44) Wyart, F. B.; Martin, P.; Redon, C. Langmuir 1993, 9, 3682–3690. (45) Goveas, J. L.; Fredrickson, G. H. Eur. Phys. J. B 1998, 2, 79–92. (46) Migler, K. B.; Lavallee, C.; Dillon, M. P.; Woods, S. S.; Gettinger, C. L. J. Rheol. 2001, 45, 565–581. (47) Zhang, J. B.; Lodge, T. P.; Macosko, C. W. J. Rheol. 2006, 50 41–57. (48) Zhao, R.; Macosko, C. W. J. Rheol. 2002, 46, 145–167.

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segment length and χ is the Flory-Huggins interaction parameter.49-58 The interfacial width is√less than the radius of gyration of the polymers, Rg = b/ (6/N), where N is the number of segments. Most of the systems studied so far have involved static or steady-state shearing or sliding. In many real situations, the immiscible interface continually undergoes changes between different dynamic and static states, for example, between transiently static (adhering, sticking) and dynamic (shearing slipping) states or for the changing geometry of the interface. These dynamic processes are important both for scientific understanding and engineering applications. Because the slip at an immiscible polymer melt interface is a commonly observed phenomenon, a systematic study of the dynamic frictional properties of this interface should further our understanding of the dynamic processes at immiscible liquid/liquid interfaces in general.

Experimental Methods The relevant bulk properties of the polymers used are tabulated in Table 1, and the molecular weights of both the PBD and PDMS used in our study are higher than their entanglement molecular weights. For the PBD used, there was about 9% vinyl branching and a random distribution of cis (34%) and trans (57%) CdC bonds. Note the much higher viscosity of PDMS compared to that of PBD. Thin films of the polymers were prepared from solutions of ∼2 wt % PBD in THF and ∼2 wt % PDMS in hexane. The films were spin coated onto mica surfaces that were glued onto cylindrical glass disks of radius 20 mm and then either fully dried (vaccuum dried for >10 h) or only air dried and installed into an SFA59,60 so that they were positioned as shown in Figure 2a. The film thicknesses, T1 and T2, were estimated by comparing the interference fringe positions of the uncoated mica-mica contact with the coated film-film contact and ranged from 100 to 300 nm. The upper (PBD) surface was connected to a friction (shear or lateral) force sensor. The lower (PDMS) surface was driven by a piezoelectric bimorph translation stage.59 The two surfaces were brought together slowly, at a speed of less than 10 nm/s, until they jumped into adhesive contact as a result of the medium-ranged van der Waals force. Immediately after the jump, the contact area increased rapidly (,1 s), as shown in Figure 2b, and then grew much more slowly.61-63 Sliding was commenced several minutes after contact, by which time the spreading of the less viscous PBD film on the PDMS surface had slowed down to a rate such that the contact radius did not change much during the time of the friction experiment. Typical experimental protocols and conditions were (49) Degennes, P. G. C. R. Seances Acad. Sci., Ser. B 1979, 219–220. (50) Degennes, P. G.1992, 55-71. (51) Kausch, H. H.; Tirrell, M. Annu. Rev. Mater. Sci. 1989, 19, 341–377. (52) Kramer, E. J.; Green, P.; Palmstrom, C. J. Polymer 1984, 25 473–480. (53) Brochard, F.; Jouffroy, J.; Levinson, P. Macromolecules 1984, 17, 2925–2927. (54) Brochard, F.; Jouffroy, J.; Levinson, P. Macromolecules 1983, 16, 1638–1641. (55) Binder, K. J. Chem. Phys. 1983, 79, 6387–6409. (56) Helfand, E.; Tagami, Y. J. Chem. Phys. 1972, 56, 3592. (57) Helfand, E.; Tagami, Y. J. Chem. Phys. 1972, 57, 1812. (58) Helfand, E.; Tagami, Y. J. Polym. Sci., Part B 1971, 9, 741. (59) Homola, A. M.; Israelachvili, J. N.; Gee, M. L.; Mcguiggan, P. M. J. Tribol. 1989, 111, 675–682. (60) Israelachvili, J. N. Intermolecular and Surface Forces; 2nd ed.; Academic Press: London, 1991. (61) Cazabat, A. M.; Fraysse, N.; Heslot, F.; Carles, P. J. Phys. Chem. 1990, 94, 7581–7585. (62) Leger, L.; Joanny, J. F. Rep. Prog. Phys. 1992, 55, 431–486. (63) Zeng, H. B.; Tian, Y.; Zhao, B. X.; Tirrell, M.; Israelachvili, J. Langmuir 2007, 23, 6126–6135.

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Zeng et al. Table 1. Bulk Properties of the Polymers Used to Prepare the Immiscible Films polymer property (at 20 C)

polybutadiene (PBD) (Sigma-Aldrich)

polydimethylsiloxane (PDMS) (United Chemical Technologies)

7000, Mw/Mn e 1.1 164 400, Mw/Mn≈1.42 d molecular weight, Mw (Da), and polydispersity index entanglement molecular weight, Me 1850 47 000 3 9 radius of gyration, Rg (nm) viscosity, η (Pa s) 6 350 γ1 = 32.5 γ2 = 21.3 surface tension, γi (mJ/m2 or mN/m) γ12 ≈ 1.2a interfacial tension, γ12 (mJ/m2 or mN/m) b c c c contact angle (PBD on PDMS) Θ √ √ 2 b = 52, Θ = 42 ( 3, ΘA = 65 ( 3, c ΘR = 31 ( 2 a 41 Estimated from the combining relation: γ12 ≈ ( γ1 - γ2) . Estimated using the Young equation. Measured values shown in Figure 1. d Measured by light scattering using a Wyatt QELS (quasi-elastic light scattering) instrument.

Figure 1. Contact angle of PBD on PDMS: (a) advancing, ΘA = 65 ( 3, (b) receding, ΘR = 31 ( 2, and (c) static Θ=42 ( 3. as follows: Spin-coated or solution-cast films of PBD and PDMS were deposited on mica substrates with (original) thicknesses of 200-300 and ∼100 nm, respectively. After drying, the surfaces were installed into the SFA. On bringing the surfaces into contact, the low-viscosity PBD film thinned so that its thickness during the shearing runs was 15-20 nm, which translates to a small value of Rg (Rg ≈ 3 nm). The thickness of the much higher viscosity PDMS film remained essentially unchanged from its original value of ∼100 nm. A friction experiment consisted of to-and-fro sliding at a constant amplitude (strain) of ∼60 μm at speeds V ranging from 0.12 to 120 μm/s. Stop-start experiments were also carried out by suddenly stopping the sliding for a certain time ts and then restarting at the same sliding speed. The stopping (resting) times ts ranged from 2 to 1000 s. Figure 2 shows and describes typical microscopic images of the surfaces as viewed by FECO optical interferometry, Newton’s rings, and normal optical microscopy under different experimental conditions: (1) before the surfaces are brought into contact, (2) immediately after the surfaces jumped into adhesive contact, (3) after some relaxation time with the surfaces in contact under no external load, as well as during sliding at low velocities, and (4) during sliding at high velocities. The optical techniques used to image the surfaces allowed us to obtain very detailed information about the surface deformations and PBD film thickness in different regions of the roughly circular contact circle (meniscus or neck), the displacement of the center of the contact circle relative to the point of closest approach of the two surfaces (the central axis of the surfaces), and the mean diameter and shape of the contact region (which included minute fingers at the advancing and trailing edges for sliding at high speeds). We observed no changes in the junction geometry (curvature) or the surface separation (duplex film thickness) at the junction during shearing. Had there been flow anywhere other than at the polymer/polymer interface, say, at the polymer/mica interfaces or within the films themselves, given the geometry of the surfaces and films, especially the less-viscous film, we would have seen dilatency and pile up at the front end and a depression at the back/trailing end of the junction, as previously seen in other systems.64 It is (64) Chen, Y. L.; Kuhl, T.; Israelachvili, J. Wear 1992, 153, 31–51.

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important to note that our tribological geometry involves a top surface (of finite area) shearing across a bottom surface of effectively infinite area, which requires new material to come in at one end and out at the other end of the contact junction during the motion. This is quite unlike the situation in standard rheological measurements (rotating disk, cone on plate or concentric cylinders) where the same material remains between the surfaces at all times (i.e., where there is no continuous inflow and outflow of material from and to the outside bulk reservoir or surface film). Typical friction traces are shown in Figures 3 and 4, with the former being shown more to define the various parameters that were varied and/or measured during the experiments. Sliding of the surfaces usually required a certain so-called stiction or static friction force, Fs, to be overcome, after which the friction force decreased (by ΔF = Fs - Fk) to the steady-state dynamic or kinetic friction force, Fk (Figure 3). (Sliding of surfaces means that the surfaces move relative to each other. At low velocities, a creep regime generally precedes the onset of rapid sliding at the static friction force Fs so that the actual point where sliding commences is strictly at a force of 1 μm/s in the case of Figure 6a, the friction forces increased with increasing V, closely obeying the relation FV n

ð2Þ

(65) Berman, A. D.; Ducker, W. A.; Israelachvili, J. N. Langmuir 1996, 12, 4559–4563. (66) Israelachvili, J.; Maeda, N.; Rosenberg, K. J.; Akbulut, M. J. Mater. Res. 2005, 20, 1952–1972. (67) Luengo, G.; Heuberger, M.; Israelachvili, J. J. Phys. Chem. B 2000, 104, 7944–7950.

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considered below) from solidlike to liquidlike. Such transitions are usually characterized by the Deborah number69,70 : De ¼ τ0 a I =aI ¼ τ0 V0 =l

ð3Þ

where τ0 is the relaxation time (here for molecules at the interface), aI is the interfacial width or the characteristic length of the interfacial molecules (which is shown in eq 1to : be 1) and more liquidlike at De < 1, which is the opposite from what is observed here. However, the present system is complex and composite, most likely exhibiting more than one relaxation mechanism, with different characteristic lengths l and times τ0 in eq 3. These will manifest themselves at much higher or lower rates and, therefore, more than one Deborah number. The friction occurring at the PBD/PDMS interface is different from that for the duplex film as a whole, which will have different characteristic values; for example, we should expect the viscous, liquidlike behavior observed at Vc > 1 μm/s eventually to transition to solidlike behavior of the whole film, followed by decreasing friction force F with V. The turning point in F will now be a maximum and will resemble the more conventional manifestation of the Deborah number.69,70 (69) Zeng, H. B.; Maeda, N.; Chen, N. H.; Tirrell, M.; Israelachvili, J. Macromolecules 2006, 39, 2350–2363. (70) Zeng, H. B.; Tirrell, M.; Israelachvili, J. J. Adhes. 2006, 82, 933–943. (71) Brochard, F.; Degennes, P. G. Langmuir 1992, 8, 3033–3037.

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Stop-Start Experiments and Saturation in the Interdigitations, Interpenetrations, and Friction Forces. Figures 3 and 4b show typical stop-start and to-and-fro friction traces at an intermediate sliding velocity of V = 1.2 μm/s. When the friction is restarted after a stopping time ts, the static friction force Fs is more of a smooth overshoot than a sharply discontinuous stiction spike as in Figure 4a,66,67 although the distinction is more of a quantitative one.65 Stiction spikes are very common in solid/solid friction as well as in solid/ liquid interactions,65,66,70 and two similar (and clean) solid surfaces can even become welded together if the stopping time (i.e., static contact time) is long enough. In the case of two polymer melt surfaces, the stiction comes from the interdigitations (diffusive interpenetration) of the polymer chains across the interface, which does not continue indefinitely but must reach saturation for two immiscible polymers. Perhaps surprisingly, the magnitudes of Fs, Fk, and stiction spikes ΔF = Fs - Fk vary with the sliding velocity V, even for the same stopping time ts as shown in Figure 6a, suggesting that the rate of interdigitation does not depend only on the time that the surfaces are in static contact, ts. 65,66,70 The reason for the higher ΔF, especially at lower V, is likely due to the enhanced ability of the polymers to interpenetrate and interdigitate rapidly after stopping because at low V they have time to interdigitate partially even during sliding, as also manifested by the small increase in Fk at low V. There have been many papers (and theories) describing how the shear force at a polymer interface or across a confined polymer film can increase dramatically with decreasing shear rate or sliding velocity.2,13,72-77 Note that this is a shear-thinning effect in a confined geometry where the effective viscosity is higher at low shear rates, falling to the bulk value at high rates, which is qualitatively similar but quantitatively different from bulk shear thinning. This effect is believed to be related to the upturn in the Stribeck curve at low sliding velocities.72,74 At high V, both Fs and Fk increase as expected for any viscous fluid. The result is a minimum in Fs and Fk at some sliding velocity and a steady decrease in the stiction spike height ΔF with increasing V. Figure 6b shows the effect of varying the stopping time at constant sliding velocity. The graph shows the stiction force normalized by the kinetic friction force, which is very close to the static force at very short stopping times (i.e., as ts f 0, Fs/ Fk f 1 and ΔF f 0, as expected). The Figure shows that the static or stiction friction force increased with stopping time by a factor of ∼6 before saturating. Thus, the chains do not totally or continually interpenetrate into each other: limited mixing occurs over a finite time and only over a thin interfacial layer. The stiction force is determined by the number of interdigitated van der Waals bonds between the PBD and PDMS chains or segments at the interface that need to be ‘broken’ (at least partially) in order for the surfaces to shear past each other. On the basis of this simple semiquantitative picture, the interdigitation number at the interface (72) Ruths, M.; Israelachvili, J. In Nanotribology and Nanomechanics: An Introduction, 2nd ed.; Bhushan, B., Ed.; Springer: Berlin, 2008. (73) Luengo, G.; Schmitt, F. J.; Hill, R.; Israelachvili, J. Macromolecules 1997, 30, 2482–2494. (74) Luengo, G.; Israelachvili, J.; Granick, S. Wear 1996, 200, 328–335. (75) Vanalsten, J.; Granick, S. Macromolecules 1990, 23, 4856–4862. (76) Thompson, P. A.; Grest, G. S.; Robbins, M. O. Phys. Rev. Lett. 1992, 68, 3448–3451. (77) Thompson, P. A.; Robbins, M. O.; Grest, G. S. Isr. J. Chem. 1995, 35, 93–106.

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increased about 6-fold when the stopping time was increased from zero (or several seconds) to 1000 s, as shown in Figure 6b, from which we also obtain a characteristic time of τs ≈ 140 s for the interdigitations to saturate. Note that one does not expect a velocity effect on Fs (or Fs/Fk) versus ts unless the velocities are very different. Previous work has shown that the static friction force of hexadecane films in the liquid state (21 C) changes little as the sliding velocity is changed: FS changed by ∼25% over a 5-fold change in V.78 Because during high-speed kinetic sliding the number of bonds at any instant across the interface is typically 3 per segment (assuming them to be spheres moving across a closepacked surface of similarly sized spheres), a 6-fold increase implies 18 bonds, or a penetration depth of ∼3 segments (because each penetrated segment will have 6 nearest neighbors surrounding it) or ∼1.5 nm per polymer chain. This thickness is about half of the value of ∼2.7 nm estimated for the equilibrium penetration depth (cf. eq 1) and is similar to results from previous work with short-chained surfactant monolayers where the adhesion hysteresis and similarly large friction forces could be explained in terms of the interdigitations or interpenetration of only a few methylene groups.51 Note that the above estimation is a simple semiquantitative model rather than a sophisticated theory where we assume that the energy of the van der Waals bonds that are broken each time a molecule is moved to the next ‘site’ is dissipated as heat and therefore can be equated to the energy per unit length and hence the friction force. The close-packed lattice is used as the model structure, and the polymers are assumed to be identical spherical beads (segments) on a string (backbone). In this case, when there is no penetration, each sphere at the surface of polymer A is in contact with three spheres on the surface of polymer B. The rest follows geometrically. The point that we are trying to make is to show how only a very small degree of interpenetration can significantly increase the friction force. Also, if the surface layer is assumed to be l = 2 nm thick and it took t = τs = 140 s to saturate fully, then the effective diffusion coefficient, given by l2 = 2Dt, would be D ≈ 10-16 cm2/s. This is much smaller than the bulk self-diffusion coefficients estimated from79 D≈kT=6πησ

ð5Þ

where σ is the radius of the diffusing particles or macromolecules. Thus, for PBD 7000, using σ ≈ Rg ≈ 3 nm gives -10 cm2/s, and for PDMS, using σ ≈ Rg ≈ DPBD √ ≈ 10 0.56 (NPDMS/6) ≈ 9 nm gives DPDMS ≈ 10-13 cm2/s at room temperature. Both of these bulk self-diffusion coefficients are significantly smaller than estimated for the polymers to interdiffuse across the PBD/PDMS interface. This difference may be a reflection of the retarded diffusion rate of the polymers when diffusing against an increasingly unfavorable energy gradient. Also note that eq 5 is not valid for entangled melts.39,41,43,47,48 (A more quantitative discussion is given in the Theoretical Analysis section.) Relaxation Processes in the Friction Forces. The abovementioned results suggest that at room temperature there are at least two relaxation times associated with the immiscible (78) Yoshizawa, H.; Israelachvili, J. J. Phys. Chem. 1993, 97, 11300– 11313. (79) Larson, R. G. The Structure and Rheology of Complex Fluids; Oxford University Press: New York, 1999.

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PBD/PDMS interface: one in the millisecond regime associated with the dynamics of the surface molecular groups between liquid- and solidlike behavior during shear (Figure 6a) and one in the ∼100 s time regime associated with the diffusion across the interface to saturation when the surfaces are at rest (Figure 6b). Here we describe other relaxation processes at the immiscible polymer/polymer interface. When sliding at high velocities, the difference between the static and kinetic friction forces disappears. However, both forces exhibit (different) transient decays after the initiation of cyclic (to-and-fro) sliding, as shown in Figure 7a. Plots of Fk(t)/Fk(¥) versus the sliding time t are shown in Figure 7b, in which Fk(t) is normalized by the final, steady-state friction force Fk(¥). The curves are largely independent of the sliding velocity V in the (somewhat narrow) range investigated, from 12 to 120 μm/s, and closely follow an exponential function Fk ðtÞ=Fk ð¥Þ ¼ 1 þ F0 e -t=τr

ð6Þ

with F0 = 1.6 and a characteristic time constant of τr ≈ 4.5 s. Thus, unlike some previous results on thin lubricating films and boundary lubricant systems,80,81 the liquid/liquid polymer system appears to have a genuine characteristic relaxation time rather than a characteristic sliding distance or strain that defines the transition from static to kinetic sliding. The effect of solvent in the films is shown in Figure 7c, which is for the same PBD/PDMS system except that the films were not completely dried under vacuum but under ambient conditions for 5-10 min after the spin coating. Thus, some of the solvents remained in the films, which significantly lowered their viscosities. (In a previous study on PDMS films63 that were vacuumed for several hours, about 5% of the solvent remained in the film, reducing its viscosity by 90%.) In the present experiments, the lower film viscosities resulted in a much faster spreading of the PBD film (THF solvent) on the PDMS film ( THF solvent (γ = 26.4 mJ/m2) > PDMS (γ = 21-24 mJ/m2) > hexane solvent (γ = 18.4 mJ/m2). Thus, we expect there to be a higher concentration or a thin layer of the low-viscosity THF solvent at the immiscible PBD/PDMS interface. THF replaces the monomer-monomer friction with a much lower monomer-solvent friction and makes it easier for the polymers to interpenetrate each (80) Chen, Y. L.; Helm, C. A.; Israelachvili, J. N. Langmuir 1991, 7, 2694– 2699. (81) Drummond, C.; Israelachvili, J. Physical Review E 2001, 6304.

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Figure 7. Relaxation of friction forces at high velocities. (a) Reproduction of a real friction trace. The dashed curves Fk(t) indicate the decay of the friction force toward steady-state sliding. The sharp stiction spikes Fs are due to the inertia of the substrates and forcemeasuring springs and are not considered to be part of the intrinsic decay kinetics of the friction forces. (b) Normalized kinetic friction force Fk by the final stable kinetic friction force Fks of PBD/PDMS surfaces where the films were vacuum dried for over 10 h. (c) Friction of PBD/PDMS surfaces for films that were not vacuum dried. other across the interface. This is likely the reason for the large reduction in the friction forces, which could be brought about by only a few molecular layers of THF (for example, a monolayer or two of water between two mica surfaces is enough to lower the friction coefficient by more than 2 orders of magnitude59,82). It is well established that a surface may be saturated with a monolayer of solute molecules even when the bulk has very little of it (i.e., that very low concentrations (82) Ohnishi, S.; Stewart, A. M. Langmuir 2002, 18, 6140–6146.

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of solutes (in the bulk) can accumulate at surfaces and interfaces). What matters is the concentration, not the amount, of THF at the interface and in the bulk. In the case of spin-coated polymer layers, a number of researchers have found that solvent evaporation (e.g., toluene from poly (methyl methacrylate) (PMMA)) occurs much more slowly than expected from the diffusion coefficient.83,84 It has also been observed85 that at the interface of PMMA and PS some of the solvent lost from the PMMA film appears to be adsorbed into the PS film, where it “then acts as a plasticizer in the PS, with the potential of creating a rubbery interface”. It is also well established that a monolayer can be sufficient to reduce friction forces dramatically. This is the basis of boundary lubrication,72 where at the cmc, which can be as low as 10-11 M, there is already a full monolayer at the surface. Another good example of this effect, which involves a liquid rather than a surfactant, is the very low friction of ice in the presence of only a monolayer or two of liquid water at the interface.72 Theoretical Analysis of Penetration and Pull-Out Processes at the Immiscible Polymer/Polymer Interface. The results of this research show that both the kinetic and static friction forces change with the sliding velocity and solvent content, that the static friction force increases with stopping time until it finally saturates, and that various relaxation times (e.g., τs and τr) have different sensitivities to changes in the samples and experimental conditions. The friction forces and relaxation dynamics depend mainly on the density, extent (depth), and rate of interpenetration across the immiscible polymer/polymer interface.86-88 Ajdari et al.38 and Bureau et al.34 studied the friction of two miscible polymers (i.e., having zero interfacial tension γ12). However, one cannot really model the energetics of the immiscible system (with finite γ12) using the miscible model. The relaxation times obtained in our experiments were much longer than the typical Rouse time of a single polymer segment. For example, for PDMS, the monomer-monomer friction coefficient from self-diffusion measurements is ξ ≈ 1.5  10-11 N s/m, which gives a characteristic time for the diffusion of one monomer over its size, τ1 = ςa2/3(π2kT) ≈ 3  10-11 s (using a ≈ 0.5 nm). Then the Rouse time for a chain with 10 monomers is τR ≈ τ1N2e = 3  10-9 s.34,35 However, this short Rouse time is different from what we are measuring, which is the collective relaxation of both single and interconnected segments across the immiscible (twocomponent) interface as shown in Figure 5. This time is bound to increase the relaxation time. The long relaxation times obtained in our experiments can be supported by both independent previous experimental and theoretical studies: (1) Previous neutron reflection and ellipsometric measurements89-91 suggested that the time required to reach the equilibrium interpenetration depth at (83) Kelley, F. N.; Bueche, F. J. Polym. Sci. 1961, 50, 549. (84) Wang, B. G.; Yamaguchi, T.; Nakao, S. I. J. Polym. Sci., Part B-: Polym. Phys. 2000, 38, 846–856. (85) Richardson, H.; Carelli, C.; Keddie, J. L.; Sferrazza, M. Eur. Phys. J. E 2003, 12, 437–440. (86) Dudko, O. K.; Filippov, A. E.; Klafter, J.; Urbakh, M. Proc. Natl. Acad. Sci. U.S.A. 2003, 100, 11378–11381. (87) Evans, E. Annu. Rev. Biophys. Biomol. Struct. 2001, 30, 105–128. (88) Galligan, E.; Williams, P. M.; Roberts, C.; Davies, M.; Tendler, S. J. B. Biophys. J. 2001, 80, 324a–324a. (89) Yukioka, S.; Inoue, T. Polymer 1993, 34, 1256–1259. (90) Yukioka, S.; Inoue, T. Polym. Commun. 1991, 32, 17–19. (91) Fernandez, M. L.; Higgins, J. S.; Penfold, J.; Ward, R. C.; Shackleton, C.; Walsh, D. J. Polymer 1988, 29, 1923–1928.

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the immiscible polymer/polymer interface can range from seconds to hours depending on the properties of the immiscible polymer pair, such as their Flory-Huggins interaction parameters χ and mutual diffusion coefficient. (2) Classic polymer theories51-58,92-94 also suggest that the time to attain thermodynamic equilibrium at an immiscible polymer/polymer interface can range from seconds to hours, which is definitely very much longer than the Rouse time. The following is a simple calculation, based on the mutual diffusion theory,51-58,92-94 for obtaining an order of magnitude estimate of the equilibration time at the immiscible PDMS/PBD interface. In our study, NPBD ≈ 118, Ne,PBD ≈ 34, NPDMS = 1567, and Ne,PDMS ≈ 634, where Ni is the degree of polymerization and Ne,i is the number of monomers per entanglement length of component i. The mutual diffusion coefficient D is given by  D ¼

 1 1 þ -2χ φPBD φPDMS DT φPBD NPBD φPDMS NPDMS ð7Þ

where φi is the volume fraction of component i and φPBDφPDMSDT is an Onsager transport coefficient. There are two theoretical approaches to predicting DT: (i) The slow theory developed separately by Brochard et al.53,54 and by Binder,55 who proposed  DT ¼

φPBD φPDMS þ NPDMS DPDMS NPBD DPBD

 -1

ð8Þ

. (ii) The fast theory proposed separately by Kramer et al.52 and by Sillescu,94 who proposed DT ¼ φPBD NPDMS DPDMS þ φPDMS NPBD DPBD

ð9Þ

where Di is the self-diffusion coefficient of component i, which can be estimated from eq 5. For PBD 7000, using Rg ≈ 3 nm in eq 5 gives DPBD ≈ 1.2  10-11 cm2/s, and for PDMS (Rg ≈ 9 nm), it gives DPDMS ≈ 6.9  10-13 cm2/s at room temperature. Using these values for DPBD and DPDMS and assuming that φPBD ≈ φPDMS ≈ 0.5, the slow theory (eq 8) gives DT ≈ 2.0  10-9 cm2/s and the fast theory (eq 9) gives DT ≈ 7.6  10-9 cm2/s. Returning to eq 7, inserting the above values gives D ≈ 0.5 (0.0091 - χ)DT. Thus, for values of χ that are progressively less than 0.0091, the mutual diffusion coefficient D progressively increases, whereas for values approaching and exceeding 0.0091, D falls to very low values and then becomes negative, which indicates a breakdown of the model and/or is indicative of very slow diffusion.52,55,91 For example, for χ = 0.0090, the slow theory gives D ≈ 10-13 cm2/s, and the fast theory gives D ≈ 3.7  10-13 cm2/s. The time required for thermodynamic equilibrium of the immiscible polymer/polymer interface is given by t = l2/2D ≈ a2I/2D, where l is the penetration depth, here assumed to be the same as the width of the interfacial region √ between the two polymers aI, which is given by aI ≈ 2b/ (6χ), where b is the segment length. For χ = 0.0090, assuming bPBD = bPDMS = 0.5 nm and aI = 4.3 (92) Composto, R. J.; Mayer, J. W.; Kramer, E. J.; White, D. M. Phys. Rev. Lett. 1986, 57, 1312–1315. (93) Anastasiadis, S. H.; Chen, J. K.; Koberstein, J. T.; Sohn, J. E.; Emerson, J. A. Polym. Eng. Sci. 1986, 26, 1410–1418. (94) Sillescu, H. Makromol. Chem., Rapid Commun. 1984, 5, 519–523.

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nm, the time required for the immiscible interface to reach equilibrium is predicted to be t ≈ 1 s by the slow theory and t ≈ 0.3 s by the fast theory. Both of these values are less than the τs ≈ 140 s relaxation time measured in our experiments but much longer than the 10-9 s estimate based on a simple Rouse model analysis. The above calculation almost certainly underestimates the relaxation time for two reasons: (1) As shown below, χ for the PDMS/PBD system in our study is higher than the χ = 0.0090 used above. Thus, previous studies93 on low-molecular-weight PBD and PDMS at room temperature have reported χ ≈ 0.60 for PDMS 3900/PBD 1000 and χ ≈ 0.2 for PDMS 5200/PBD 3000. Even higher χ values are expected for the higher-molecular-weight polymers in our system. Thus, for our system, the mutual diffusion coefficient D is expected to be much less than 10-13 cm2/s, and the characteristic relaxation time is correspondingly much longer than 1 s. (2) As discussed above, in previous studies on the rheology of PBD thin films,73,74 the effective viscosity of a confined 15-20-nm-thick PBD film is much higher than the bulk value, which would predict an even lower value for the self-diffusion coefficients (of both polymers) when calculated using eq 5 (D ≈ kT/6πηRg). Slip at the Polymer-Polymer Interface. At the shearing interface of two polymer melts (Figure 8), if the interfacial strength is strong enough there will be no interfacial slip, and the velocity will be continuous at the interface, as shown schematically in Figure 8b for η1 = η2 and in Figure 8c for η1 6¼ η2, where η1 and η2 are the viscosities of the two fluids. If slip occurs at the interface, as shown in Figure 8d, then a velocity discontinuity will occur at the interface. It is well known that Newtonian flow gives a linear relationship between the shear force and the sliding velocity, viz., F  V (as illustrated in Figure 6a, where the effective viscosity of the 15-20 nm PBD thin layer was assumed to be 120 Pa s). However, this linear relationship was not obtained in our experiments (cf. Figure 6a), although the PBD used in these experiments is Newtonian at shear rates of up to 1000 s-1.73 Thus, as shown in Figure 6a, the exponent n of the kinetic friction force versus the sliding velocity, FVn, increases with V but did not exceed 0.5 at the highest velocity/shear rate attained in these experiments. It therefore appears that the PBD/PDMS interface exhibits frictional slip, as illustrated in Figure 8d, at low sliding velocities and approaches viscous Newtonian bulk flow at higher velocities, a scenario that is analogous to, if not the same as, that described by the Stribeck curve. Figure 2 shows the different geometries of the advancing and receding fronts under static and steady-state sliding conditions; the images show that the circular PBD meniscus moves with the upper surface, that the gap distance does not change during sliding, and that fingers occur at the circular boundary especially at higher velocities, all clearly indicating that all or most of the slip was occurring at the PBD/PDMS interface. (We found no evidence of any slip occurring at the PBD/mica interface, which is further supported by previous results by us and others on the wettability and the no-slip condition of this interface during Couette flow and four-roll mill experiments.13,73,95) The magnitudes and directions of the slip and flow in different regions are shown by the lengths and directions of the thin lines with arrows in Figure 2. At the steady-state speeds studied, inertial effects are negligible (95) Park, C. C.; Baldessari, F.; Leal, L. G. J. Rheol. 2003, 47, 911–942.

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unless there is stick-slip motion or on reversals, and any nonparallel and/or vertical motion (gap distance) was directly monitored by recording the changing shapes and positions (in the wavelength spectrum) of the FECO fringes with a normal resolution of ∼0.5 nm and a lateral resolution of ∼1 μm.60 The normal force was kept at zero at all times, and at low sliding velocities, the gap distance did not change as the surfaces transitioned from rest to steady-state sliding. Implication for Two-Phase Flow and Layered Polymer Blends. For layered polymer composites having various chosen or designed properties in their mechanical strength, viscosity, surface and interfacial tensions, insulation, optical transparency, and permeability, the interfacial strengths of the different interfaces is an important factor in determining the applicability and durability of the composite material. Various investigations have shown that the entanglements and interdigitations at polymer/polymer interfaces are usually not strong enough to eliminate interfacial slip.39,41,47,48,96 Annealing an interface for a time comparable to the reptation time of the polymer chains can substantially enhance the entanglements and interdigitations and increase the adhesion strength/fracture toughness of the interface.47 In a study of a composite material with 20 PS-PMMA interfaces, the critical fracture toughness (or adhesion strength) increased from about 4 to 12 J/m2 with annealing time in an way similar to our results for the PBD/PDMS interface shown in Figure 6b. However, most current studies of the “healing” processes at polymer/polymer interfaces deal with identical (i.e., miscible) polymers,97-99 where both theory and experiment have shown that the fracture strength at short times is proportional to t0.25. For our system, when the stopping time (similar to the annealing or healing time) was shorter than 200 s, the static friction force (cf. Figure 6b) was found to be proportional to t0.3, which is close to the value expected for two identical (miscible) polymers. However, for much longer times, because of the saturation of the chain interdigitations and interpenetrations at the immiscible interface, the static friction force ceased to increase and approached a constant value. Implication for the Drainage in Drop-Drop Coalescence. Research on drop-drop coalescence focuses on the way in which hydrodynamic and molecular interactions and droplet deformations determine whether drops coalesce, pass around one another, or rebound in a flow.95,100-105 Several studies have shown that apparent contact is the key to understanding coalescence but have not yet found a quantitative description of this phenomenon.101 For a head-on collision of two droplets that do not rotate, once the drops are in “apparent contact”, the thin film between them drains away until it reaches a point of rupture (96) Brochard-Wyart, F.; Debregeas, G.; deGennes, P. G. Colloid Polym. Sci. 1996, 274, 70–72. (97) Jordan, E. A.; Ball, R. C.; Donald, A. M.; Fetters, L. J.; Jones, R. A. L.; Klein, J. Macromolecules 1988, 21, 235–239. (98) Jud, K.; Kausch, H. H.; Williams, J. G. J. Mater. Sci. 1981, 16, 204– 210. (99) Prager, S.; Tirrell, M. J. Chem. Phys. 1981, 75, 5194–5198. (100) Baldessari, F.; Leal, L. G. Phys. Fluids 2006, 18. (101) Chesters, A. K. Chem. Eng. Res. Des. 1991, 69, 259–270. (102) Leal, L. G. Phys. Fluids 2004, 16, 1833–1851. (103) Yang, H.; Park, C. C.; Hu, Y. T.; Leal, L. G. Phys. Fluids 2001, 13, 1087–1106. (104) Zeng, H.; Tian, Y.; Zhao, B.; Tirrell, M.; Israelachvili, J. Macromolecules 2007, 40, 8409–8422. (105) Zeng, H. B.; Zhao, B. X.; Tian, Y.; Tirrell, M.; Leal, L. G.; Israelachvili, J. N. Soft Matter 2007, 3, 88–93.

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Figure 8. Slip and nonslip interfaces. (a) Shearing of two fluid films, PBD and PDMS, between two parallel plates; (b) velocity profile across the duplex film when η1 = η2; (c) velocity profile when η1 < η2; (d) velocity profile when η1 < η2 with interfacial slip, where xs is the slip distance. In this study, we assume that there is no wall slip of either fluid at the fluid-solid substrate interfaces. and the drops coalesce. A delay of the drainage time that is much longer than the theoretical predictions based on the van der Waals and hydrodynamic forces and the droplet deformations has recently been found, particularly at low capillary numbers.100 In that study, the drainage time to coalescence increased as the capillary number decreased from about 0.0025 to 0.001 (Figure 17 of ref 100). According to the stribeck curvelike friction behavior of the immiscible polymer melt interface, the static and kinetic friction forces are very high at low sliding velocities, much higher than would be expected from an analysis of the Newtonian viscous drag forces (cf. Figure 6a). As two drops approach each other, the interdigitations between the drops and the suspending liquid (which must be immiscible) are likely to be saturated. To coalesce, the drops have to expel the final layer of the host liquid molecules at different driving velocities, thus the interdigitations between the host liquid and droplet molecules have to be broken. At high capillary numbers (which correspond to high sliding velocities in our experiments), the static friction force is easily overcome by the high shear rate, but at low capillary numbers, corresponding to low sliding velocities, the stiction or high static friction force (Figure 6) at the interface of the host liquid and the drops is high, resulting in the abnormally long drainage times. Such stiction and interdigitation effects at interfaces modify the boundary conditions during thin film drainage and should be incorporated into theoretical models of dropdrop coalescence. Similar situations should occur during liquid/liquid snapoff, drop breakup, and liquid withdrawal through another liquid. When the stiction or shearing velocity effects on the liquid/liquid interfacial friction are significant, these factors should be considered in descriptions of these processes.

Conclusions This article described an experimental study of the dynamics and transient properties of an immiscible polymer

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liquid/liquid (PBD/PDMS) interface undergoing shear. (1) By virtue of their limited interdigitation/interpenetration across the contact interface, immiscible polymers never fully coalesce into a continuous, homogeneous material. This affects both their dynamic adhesion and friction forces. The interface has a lower entanglement density than either of the bulk materials, so this is where the slip is greatest. This interface exhibits various characteristic parameters such as its static and dynamic widths and two relaxation times: the static interpenetration time and velocity adaptation time. (2) The interfacial width saturates at some small but finite value, resulting in Stribeck-like behavior for the friction force as a function of the sliding velocity, characterized by F having a minimum value at some characteristic sliding velocity V. This is typical of surfactant boundary-lubricated solid surfaces where the surfactant chains also interpenetrate across the shearing interface. The tribology of both types of systems appears to be described by a WLF-time-temperature superposition-Deborah number formalism. (3) Perhaps because it is unique to the immiscible polymer interface, it can attract solutes that are present in either of the polymer liquids or materials, even when present in small amounts in the bulk, to the interface, collecting there at high surface coverage as does a surfactant. The presence of such surface-active components can have a dramatic effect on the friction or lubrication forces at the polymer/polymer interface, for example, by increasing the slip distance xS in Figure 8d. The results provide new insights into the factors that determine the strength of polymer composites, the drainage of liquid films, and the coalescence of liquid drops. Acknowledgment. This work was sponsored by the Department of Energy under grant number DE-FG0287ER45331. B.Z. thanks the NSERC (Natural Sciences and Engineering Research Council of Canada) for a postdoctoral fellowship award. Y.T. thanks the Huaxin Distinguished Scientist Scholarship of Tsinghua University.

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