Kinetics of the Adsorption of a PDMS-g-PEO Copolymer at the PDMS

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Kinetics of the Adsorption of a PDMS-g-PEO Copolymer at the PDMS/PEO Interface Gabriel Schreyeck and Pascal Marie* Institut Charles Sadron (CNRS, UPR 022), 6 rue Boussingault, 67083 Strasbourg Cedex, France Received February 26, 1999. In Final Form: July 1, 1999

The kinetics of interface formation between poly(dimethylsiloxane) (PDMS) and poly(ethylene oxide) (PEO) with and without low molecular weight copolymer PDMS-g-PEO has been studied by interfacial tensiometry. For the PDMS/PEO interface, interfacial tension is constant with time and the interface is immediately formed. For the PDMS/PEO interface with copolymer, interfacial tension decreases slowly or goes to a minimum (unexpected) with time before reaching its equilibrium value, depending on copolymer concentration in the PEO. This kinetics of interface formation with an overshoot has been explained with two processes: adsorption of the copolymer at the interface by transfer over an energy barrier and relaxation of the interfacial layer.

1. Introduction Polymer interfaces play an important role in polymer technology through the processes of wetting, adsorption, and coating, and through their effects on the kinetics of phase separation and mechanical mixing of molten polymers. An accurate description of polymer interfaces is important because phase separation and immiscibility are the rule rather than the exception for polymer mixtures.1 This is especially true for multicomponent polymeric materials (polymer blends or microphaseseparated copolymers), where nonhomogeneous structures can form.2 Considerable interest has been shown recently in studies of the nonhomogeneous interfacial region,3,4 where a certain limited amount of mutual penetration of the different chain macromolecules occurs. An important parameter in these systems is the interfacial tension which determines the thermodynamic stability of the interface and also can be utilized to regulate the particle size in a phase-separated polymer blend.5 The interfacial tension changes with the temperature, pressure, and molecular weight.3 To increase the compatibility of different homopolymers, one solution is to add a block or graft copolymer containing the same monomeric units as the homopolymer pair. An approach proposed by Leibler6 provides a basic understanding of the copolymer segregation at polymerpolymer interfaces. The adsorption of amphiphilic A-B copolymer at the interface between two incompatible homopolymers A and B has been studied both theoretically 6-9 and experimentally.10-12 It is widely recognized that * To whom correspondence should be addressed. E-mail: [email protected]. (1) Olabisi, O.; Roberson, L. M.; Shaw, M. T. Polymer-Polymer Miscibility; Academic Press: New York, 1979. (2) Wu, S. Polymer Interface and Adhesion; Marcel Dekker: New York, 1982. (3) Koberstein, J. T. Encyclopedia of Polymer Science and Engineering; Wiley: New York, 1987, Vol. 8, p 237. (4) Stamm, M.; Schubert, D. W. Annu. Rev. Mater. Sci. 1995, 25, 325. (5) Fayt, R.; Jerome, R.; Teyssie´, Ph. Polym. Eng. Sci. 1987, 27, 328. (6) Leibler, L. Makromol. Chem., Macromol. Symp. 1988, 16, 1. (7) Shull, K. R.; Kramer, E. J. Macromolecules 1990, 23, 4769. (8) Noolandi, J.; Hong, K. M. Macromolecules 1982, 15, 482; Macromolecules 1984, 17, 1531. (9) Semenov, A. N. Macromolecules 1992, 25, 4967. (10) Green, P. F.; Russell, T. P. Macromolecules 1991, 24, 2931.

copolymers preferentially segregate to the polymerpolymer interface, improve the adhesion between immiscible polymers, and reduce the interfacial tension.13-15 Moreover, it was shown that the reduction in interfacial tension between incompatible homopolymers with increasing block copolymer concentration and molecular weight arises mainly from the energetically preferred orientation of the blocks at the interface into their respective compatible homopolymers, and that the main counterbalance which limits the accumulation of the copolymer of the interface is the loss of entropy. Despite this activity, most studies have been devoted to the equilibrium aspects of polymer adsorption16 and little work to date has focused on the kinetics of the adsorption process owing to the difficulty in measuring dynamic processes at an interface.17 Moreover, most studies concern polymer adsorption on a solid surface. In many cases, it has been shown that the kinetic parameters control the final conformation of the adsorbed polymer and that large kinetic barriers exist because of the slow entanglement of adsorbed polymer chains. As pointed out by Granick,17 “these complex kinetics events cannot be described by a single time constant”. With amphiphilic copolymers, the effects of bulk solution phase behavior such as micellization, aggregation, and microphase separation complicate the adsorption process. It has been shown both experimentally18,19 and theoretically20 that the copolymer adsorption kinetics clearly displays several regimes and (11) Dai, K. H.; Kramer, E. J.; Shull, K. R. Macromolecules 1992, 25, 220. (12) Brown, H. R.; Char, K.; Deline, V. R. Macromolecules 1993, 26, 4155. (13) Anastasiadis, S. H.; Gancarz, I.; Koberstein, J. T. Macromolecules 1989, 22, 1449. (14) Schreyeck, G.; Marie, P. C. R. Acad. Sci. Paris 1995, 320, Se´r. II, 653. (15) Hu, W.; Koberstein, J. T.; Lingelser, J. P.; Gallot, Y. Macromolecules 1995, 28, 5209. (16) Halperin, A.; Tirrell, M.; Lodge, T. P. Adv. Polym. Sci. 1992, 100, 31. (17) Granick, S. In Physics of Polymer Surfaces and Interfaces; Sanchez, I. C., Ed.; Butterworth-Heinemann: Stoneham, MA, 1992; Chapter 10. (18) Tassin, J. F.; Siemens, R. L.; Tang, W. T.; Hadziioannou, G.; Swalen, J. D.; Smith, B. A. J. Phys. Chem. 1989, 93, 2106. (19) Munch, M. R.; Gast, A. P. Macromolecules 1990, 23, 2313. (20) Johner, A.; Joanny, J. F. Macromolecules 1990, 23, 5299.

10.1021/la990229w CCC: $18.00 © 1999 American Chemical Society Published on Web 09/23/1999

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Table 1. Molecular Characteristics of the PDMS and PEO Polymersa-c sample PDMS 50000 PDMS 28000 PDMS 5970 PEO 10000 PEO 1000

Mw (g‚mol-1) 000a

50 38 000a 9 800a 11 400b

Mn (g‚mol-1)

Mw/Mn

producer

22 400a 15 700a 6 100a 9 500c 990c

2.23 2.42 1.60 1.20

Petrach Petrach Petrach Hoechst Hoechst

a Measured by size exclusion chromatography or osmometry. Measured by light scattering. c Measured by chemical dosage or osmometry.

b

strongly differs from the usual homopolymer adsorption kinetics. In particular, equilibrium is approached through an unusually slow process. However, there is no study, to our knowledge, about the kinetics of interface formation in the case of incompatible homopolymers in the presence of copolymer and without solvent. The present experimental study deals with the kinetics of interface formation between poly(dimethylsiloxane) (PDMS) and mixtures of poly(ethylene oxide) (PEO) with a PDMS-g-PEO copolymer. The two homopolymers used are strongly incompatible and very different as PDMS is hydrophobic and amorphous, whereas PEO is hydrophilic and semicrystalline. The interface formation is investigated through interfacial tension (γ) measurements. Several authors have studied such systems with respect to the influences of concentration, chain length, molecular architecture and chemical composition.21-23 An outline of this paper is as follows: section 2 describes briefly the materials and the pendant-drop technique used for measuring interfacial tensions. Section 3 details the experimental relaxation γ-time curves of a ternary system, PDMS, PEO, and PDMS-g-PEO, in which an overshoot is observed. These experimental data are compared with theoretical models so as to better understand the adsorption kinetics of copolymer at a polymerpolymer interface. The paper ends with a conclusion section. 2. Experimental Section Materials. The molecular characteristics of trimethylsiloxy-terminated poly(dimethylsiloxane) and R,ω dihydropoly(ethylene oxide) are given in Table 1. PDMS was used as received. PEO was purified by vacuum-drying at 80 °C for a minimum of 3 days to reduce the water content to less than 0.1 wt %. We used a graft copolymer PDMS-g-PEO of molecular weight 1200 g‚mol-1 with 67 wt % of ethylene oxide. From 1H NMR measurement we have determined that the copolymer has a backbone of four dimethylsiloxane monomers on which are grafted two chains of nine ethylene oxide monomers (Figure 1). The copolymer was exclusively preblended with PEO, the denser compound forming the drop, since it is insoluble in the matrix phase consisting of PDMS. The mixtures of PEO and copolymer were prepared by weighting an amount (mC) of copolymer and an amount (mPEO) of PEO homopolymer. These mixtures are stirred and dried in the same way as the PEO samples. The copolymer concentrations (Ccop) are expressed as weight percent of the copolymer blended into the drop. (21) Wagner, M.; Wolf, B. A. Polymer 1993, 34, 1460. (22) Jorzik, U.; Wolf, B. A. Macromolecules 1997, 30, 4713. (23) Patterson, H. T.; Hu, K. H.; Grindstaff, T. H. J. Polym. Sci., Part C 1971, 34, 31.

Figure 1. Structure of the PDMS-g-PEO copolymer with two PEO chains grafted on the PDMS backbone.

The determination of interfacial tension requires the knowledge of the densities (F). The following expressions for pure polymers were used:

PDMS 50000:

F ) 0.9919-8.925 × 10-4T + 2.65 × 10-7T2 - 3 × 10-11T3

PDMS 28000:

F ) 0.99358-9.0303 × 10-4T

PDMS 5970:

F ) 0.98846-8.9838 × 10-4T

PEO 10000 and PEO 1000: F ) 1.1426-8.0768 × 10-4T with F in g‚cm-3 and T in °C. The densities of the PDMS 5970 and PDMS 28000 are given by the producer and the others are taken from the literature.24,25 The density of the copolymer was measured with a digital density meter (Kratky DM 60) capable of measuring density as a function of temperature. The following result was found:

F ) 1.0233-8.5394 × 10-4T

PDMS-g-PEO 1200:

For the mixtures of PEO plus copolymer, the densities were calculated with the following formula:

1 Fmix

)

φ C 1 - φC + Fc FPEO

(1)

where φC ) mC/(mC + mPEO) is the weight fraction of copolymer in the mixture of density Fmix. Surfactant Behavior of the Copolymer at the Air/ Water Interface. To establish the surfactant nature of the copolymer and to estimate the conformation and the dimensions of the copolymer at the polymer (PDMS)polymer (PEO) interface, we have drawn a parallel between three interfaces: air/copolymer PDMS-g-PEO/ water (or PEO), PDMS/copolymer/PEO, and hydrophobic medium/copolymer/hydrophilic medium. In a previous study,14 we have shown that the variation of the surface tension versus log copolymer concentration in water or in PEO was linear.The application of Gibb’s law had made it possible to find the quantity of copolymer adsorbed at the surface (Γ) and the specific area occupied per copolymer molecule (A ) 1/NΓ ≈ 0.62 nm2, where N is Avogadro’s number). Moreover, we have also deduced the thickness of the adsorbed copolymer layer (L ≈ 3 nm) from the simple equation L ) MΓ/df ) M/dANf, where M is the molecular weight of copolymer, d is the density of the adorbed layer (24) Shih, J.; Flory, P. J. Macromolecules 1972, 5, 758. (25) Arlie, J. P. Thesis, University Strasbourg, 1965.

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Figure 2. Schematic conformation of the copolymer molecule at the air/water interface.

Figure 3. Schematic setup of the pendant-drop apparatus for interfacial tension measurement.

(d ≈ 1), and f is the density fraction of the copolymer in the layer (packing factor) (f ≈ 1). From these data, we can give a schematic conformation of the copolymer molecule at this kind of interfaces which should not be very different from that of the PDMS/PEO interface (Figure 2). Interfacial Tension Measurements. The interfacial tensions were measured with a pendant-drop apparatus which uses a video digital image processing technique. A schematic representation of the tensiometer is given in Figure 3. The drop-forming system consists of glass capillary tube (internal diameter 1.1 mm) which is connected to an SMI Micro/Pettor positive displacement syringe. The pendant drop of the more dense constituent (PEO or blends of PEO and copolymer) is formed at the tip of the tube inside a Hellma quartz cell (10 × 10 × 45 mm) containing the second polymer (PDMS). The capillary tube and the cell are placed in a oil-circulating thermostated chamber. The temperature stability is better than (0.02 °C. For experiments with high content of copolymer, wetting of the outside of the capillary tube was minimized by treating the glass capillaries with a Teflon spray. The drop is illuminated with a white-light source (Dolan-Jenner FiberLite system) through an iris diaphragm and a heavily frosted diffuser for minimizing the heat input to the drop and producing a uniform and collimated beam. The image-forming and recording system consists of a Nachet M4 macro-zoom microscope coupled to a Panasonic WV-CD50 CCD video camera with 500(H) × 582(V) pixels sensor, a Panasonic WV80 digital timer, a video recorder, and a Matrox video frame grabber board resident a microcomputer for performing the image digitization. The chamber and optical system are mounted on an optical bench seated on a vibration isolation table. To focus the optics and to correct optical distortions, we use a cross-scale reticle on an optical glass that is placed at the drop location. The calibration of the instrument has been considered and performed carefully, since it is potientially the greatest source of error (the interfacial tension measured by drop shape analysis is proportional to the square of magnification). The vertical and horizontal

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magnification factors are obtained from a calibration procedure using the reticle. The digitized image was analyzed with Visilog software (Noesis-France) by using a morphological gradient method, adaptative thresholding, and mathematical morphology function (skeleton and thinning)26 to locate the interface contour and to extract the arbitrary coordinate points of the drop profile. The experimental profile was analyzed with a robust shape-comparison algorithm developed by Neumann and co-workers27 and called the axisymmetric drop shape analysis-profile (ADSA-P). Details of the ADSA-P protocol and data processing have been given by Cheng et al.28 The input parameters are the gravitational acceleration, the density difference of phases across the interface, and the drop profile coordinates. A calculated Laplacian curve is compared with the experimental curve until satisfactory convergence is achieved. The resulting outputs are the interfacial tension, the drop volume, and the drop surface area. The prediction interval for the interfacial tension measurements at 95% confidence is (0.05 mN/m. To determine the interfacial tension, five experiments were performed at atmospheric pressure and each temperature. Each experiment was performed on one pendant drop, recording the profiles as a function of time. Interfacial tension measurements were carried out from 80 to 180 °C. The interfacial tension is the mean value of five measures or experiments. The standard deviation for the interfacial tension values can be estimated at 0.01 mN‚m-1. 3. Results and Discussion PDMS/PEO Interface without Copolymer. Whatever the molecular weight of the polymers, variations of γ with time are negligible compared to the measurement accuracy. Since the interfacial tension is constant with time, we have inferred that the interface forms immediately. This is not surprising as PDMS and PEO are strongly incompatible polymers. Interaction parameter (χ), estimated from solubility parameter29,30 at 80 °C is 0.62. Interfacial tension decreases almost linearly with temperature in the range 80-180 °C. The temperature coefficients (-∂γ/∂t), obtained from a least-squares fit of the data, are found to be ≈0.008 mN‚m-1/°C. The values are consistent with those published earlier.2 Equilibrium interfacial tension has been found to increase with molecular weight according to a power law: γ ) γ∞[1 - C(χ(Mn)PEO)-x - C(χ(Mn)PDMS)-x], where γ∞ is the interfacial tension at infinite molecular weight, χ is the Flory-Huggins interaction parameter between polymers PEO and PDMS, and (Mn)PEO and (Mn)PDMS are the number-average molecular weights of PEO and PDMS, respectively. In the strong segregation limit (typical incompatibility degree wi ) χ(Mn)i > 5), the coefficient C in front of 2/χM in the power law is very close to the coefficient π2/12 ≈ 0.82.35 Helfand et al.36 have found C ) ln 2 ≈ 0.69 because of a slightly different treatment of the entropy of mixing (effect of chain ends). Values for the scaling exponent, x, ranging from 0.5 to 1.0 have been (26) Coster, M.; Chermant, J. L. Pre´ cis d'Analyse d'Images; Presses du CNRS: Paris, 1989. (27) Rotenberg, Y.; Boruska, L.; Neumann, A. W. J. Colloid Interface Sci. 1983, 93, 169. (28) Cheng, P.; Li, D.; Boruska, L.; Rotenberg, Y.; Neumann, A. W. Colloids Surf. 1990, 43, 151. (29) Galin, M. Polymer 1983, 24, 865. (30) Roth, M. J. Polym. Sci., Polym. Phys. Ed. 1990, 28, 2715.

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Figure 4. Time dependence of the interfacial tension at 80 °C for the system PDMS 50000/copolymer/PEO 1000 at different concentrations of the copolymer in the PEO phase. 4, 1%; O, 2.5%; 3, 5%; 0, 7.5%; ], 10%.

observed experimentally14,31-34 or predicted from recent theories.35-37 In our measurements, the molar mass of PDMS was kept constant and the molar mass of PEO varied between 200 and 10 000 g‚mol-1. By performing linear regression of the data, we have obtained a slightly better correlation coefficient when the exponent x ) 1. Naturally this is not sufficient to prove the dependence of γ on the -1 power law mass as underlined by Koberstein et al.34 Kinetics of PDMS/(PEO + Copolymer) Interface Formation. The time dependence of the interfacial tension at 80 °C for PDMS 50000/(PEO 1000 + PDMSg-PEO 1200) system, at different concentrations of the copolymer in the PEO phase, is shown in Figure 4. We can observe a fast decrease of γ with time to a minimum value, followed by a slow increase toward an equilibrium interfacial tension. At 140 °C, we observe similar behaviors with a shift to the shorter times (Figure 5). We have three kinds of kinetics depending on the copolymer concentration in the PEO phase: For Ccop j 2 wt %, we observe as expected a weak decrease of γ as a function of time toward an equilibrium value. For Ccop J 40 wt %, initial values of γ are very small (about 2 mN‚m-1) and γ decreases as a function of time. Equilibrium is obtained after a loss of 1.2 mN‚m-1 corresponding to approximately 3 h. For 2 wt % j Ccop j 40 wt %, experimental data γ ) f(t) show a decrease to a minimum value (for tmin ≈ 30 min) (31) LeGrand, D. G.; Gaines, G. L., Jr. J. Colloid Interface Sci. 1973, 42, 181; J. Colloid Interface Sci. 1975, 50, 272. (32) Gaines, G. L., Jr.; Gaines, G. L., III. J. Colloid Interface Sci. 1978, 63, 394. (33) Anastasiadis, S. H.; Gancarz, I.; Koberstein, J. T. Macromolecules 1988, 21, 2980. (34) Fleischer, C. A.; Koberstein, J. T.; Krukonis, V.; Wetmore, R. A. Macromolecules 1993, 26, 4172. (35) Broseta, D.; Fredrickson, G. H.; Helfand, E.; Leibler, L. Macromolecules 1990, 23, 132. (36) Helfand, E.; Bhattacharjee, S. M.; Fredrickson, G. H. J. Chem. Phys. 1989, 91, 7200. (37) Tang, H.; Freed, K. F. J. Chem. Phys. 1991, 94, 6307.

Figure 5. Time dependence of the interfacial tension at 140 °C for the system PDMS 50000/copolymer/PEO 1000 at different concentrations of the copolymer in the PEO phase. (a) 4, 1%; O, 2.5%; 3, 5%; 0, 7.5%; ], 10%; (b) 2, 20%; b, 30%; 1, 50%; 9, 70%.

followed by an increase toward an equilibrium interfacial tension obtained after about 6 h. This last kind of kinetics of interface formation for which interfacial tension passes through a minimum is very surprising and has never been observed before. The problem is how to interpret the measured interfacial tensions in terms of copolymer adsorption. Adsorption Kinetics and Overshoot. When polymers are adsorbed at an initially uncovered interface, it usually takes a long time before the steady state is reached. Adsorption increases monotonically with time, with an asymptotic approach toward the equilibrium level.17,38 Several models for the dynamic adsorption process have (38) Fleer, G. J.; Stuart, M. A. C.; Scheutjens, J. M. H. M.; Cosgrove, T.; Vincent, B. Polymers at Interfaces; Chapman and Hall: London, 1993.

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been developed. It is well-known that diffusion of surfaceactive molecules through the surrounding bulk medium to the interface, adsorption/desorption controlled by activation barriers, and reconformation of the adsorbed polymer (or configurational rearrangements in the interfacial layer) are the three key steps which are involved in the adsorption process. The adsorption/desorption step is normally represented by a kinetic equation which should of course be consistent with the equilibrium isotherm for the system. In the limiting case, corresponding to a vanishing potential energy barrier and a steady adsorption equilibrium, the diffusion-controlled kinetics can be described by the theory of Ward and Tordai.39 Less well understood are the adsorption processes that present an overshoot of the adsorbed amount (maxima of adsorption). The overshoot phenomenon has been observed by many investigators for different macromolecules in solutions adsorbed onto different surfaces.40-44 The overshoot effect could suggest that the adsorption layer becomes temporarily supersaturated with polymer chains. To explain the general appearance of the overshooting, a theoretical model with a time lag between the adsorption processes was suggested.41 In fact, these experimental data may be explained in the framework of both the kineticconformational-controlled and the kinetic-diffusion-conformational-controlled adsorption.45 In most experimental methods to study adsorption kinetics, the quantity directly measured is the dynamic interfacial tension γ(t) and not the adsorption Γ(t). The γ(t) data must be transformed into adsorption data; to do that, a relationship between Γ and γ coherent with the model assumed for the adsorbed layer must be used. If the ideal mobile layer is assumed, the suitable twodimensional state equation is the two-dimensional perfect gas equation γ° - γ ) ΓkT where k is Boltzmann’s constant, while in the case of interacting adsorbed molecules with finite dimensions the state equation is the two-dimensional van der Waals equation.46 In this framework, we interpret our results in terms of interfacial pressure Π(t) ) γ° - γ(t) defined by the difference between the interfacial tension of the PDMS/ PEO interface without copolymer, γ°, and the interfacial tension with a copolymer concentration (Ccop) in the PEO phase, γ(t). Interfacial pressure can be linked to the quantity of copolymer adsorbed at the interface (Γ) through the state equation Π ) kTΓ. Thus, minima observed in the γ ) f(t) curves correspond to maxima of interfacial pressure and so to maxima of copolymer adsorption at the interface. Kinetics for 2 wt % j Ccop j 40 wt %. The kinetics data reveal a two-stage process on a clearly separated time scale: the first stage corresponds to short times (t < tmin) and the second one to long times (t > tmin). We assume that copolymer micelle formation in PEO, which would cause a particular kinetic adsorption behavior, does not occur. No clear indication of micelle formation was found by Kira`ly et al.47 with the system PEO-b-PDMS/PEO 1000 above room temperature or by us at 140 °C.14 (39) Ward, A. F. H.; Tordai, L. J. Chem. Phys. 1946, 14, 453. (40) Leermakers, F. A. M.; Gast, A. P. Macromolecules 1991, 24, 718. (41) Ohshima, H.; Fujita, N.; Kondo, T. Colloid Polym. Sci. 1992, 270, 707. (42) Dorgan, J. R.; Stamm, M.; Toprakcioglu, C.; Je´roˆme, R.; Fetters, L. J. Macromolecules 1993, 26, 5321. (43) Johnson, C.; Clarson, L.; Granick, S. Polymer 1993, 34, 1960. (44) Dussaud, A.; Han, G. B.; Minassian-Saraga, L. Ter; VignesAdler, M. J. Colloid Interface Sci. 1994, 167, 247. (45) Filippov, L. K.; Filippova, N. L. J. Colloid Interface Sci. 1996, 178, 571. (46) Baret, J. F. J. Colloid Interface Sci. 1969, 30, 1. (47) Kira`ly, Z.; Cosgrove, T.; Vincent, B. Langmuir 1993, 9, 1258.

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Figure 6. Time dependence of the interfacial pressure at 140 °C for the system PDMS 50000/copolymer/PEO 1000 at different concentrations of the copolymer in the PEO phase for t < tmin ≈ 30 min. O, 2.5%; 3, 5%; 0, 7.5%; ], 10%; 2, 20%; b, 30%; s, fit by eq 3.

(a) Decrease of γ (Increase of Π) with Time: t < tmin. The time dependence of the interfacial pressure at 140 °C for the system at different concentrations of the copolymer for t < tmin ≈ 30 min is shown in Figure 6. In the absence of convection and desorption (and no transfer of solute through the interface is considered), we have first tried to understand our results with a kinetic-diffusioncontrolled adsorption model. Neglecting the back-diffusion flux, a rough approximation of the well-known Ward and Tordai equation39 can be obtained that is valid only at the very beginning of an adsorption process.

Π(t) ) 2RTCcop (Dt/π)1/2

(2)

where D is the diffusion coefficient of the copolymer in the “solution” of PEO and Ccop is the uniform bulk concentration of the copolymer in the PEO phase. The diffusion coefficients obtained (D ≈ 10-17 cm2‚s-1) from our experiments with the use of eq 2 are too small compared to the value expected for the diffusion of a copolymer or an aggregate in a melt of PEO (D ≈ 0.95 × 10-7 cm2‚s-1).47 In fact, when the interface is created, copolymer molecules are already present at the interface. Indeed, γ for t ) 0 is much smaller than γ°. The copolymer does not adsorb, as predicted by the model, on a “clean” surface without surfactant. Therefore, this model of pure diffusion cannot be used for our results. In other words, eq 2 is only valid until a certain interfacial coverage of adsorbed molecules is reached, which is immediately the case in our system because of our measurement technique. To get a denser interface coverage, a penetration of a copolymer chain through the existing monolayer has to take place (Figure 7a). This process is much slower than pure diffusion and can be described by an exponential time behavior with a relaxation time τ1 (Langmuir kinetic approach):44,46

Π(t) ) Πmax + (Πo - Πmax)e-t/τ1

(3)

where Πo ) γ° - γo is the film pressure of the first

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Figure 8. Time dependence of the interfacial pressure at 140 °C for the system PDMS 50000/copolymer/PEO 1000 at different concentrations of the copolymer in the PEO phase for t > tmin ≈ 30 min. O, 2.5%; 3, 5%; 0, 7.5%; ], 10%; 2, 20%; b, 30%; s, fit by eq 4.

Figure 7. Schematic interpretation of the formation kinetics of the PDMS/PDMS-g-PEO copolymer/PEO interface: (a) adsorption of the copolymer to the interface through the existing layer; (b) inhomogeneous layer of surface micelles; (c) oversaturated subphase; (d) equilibrium state obtained by relaxation of the metastable (b) and (c) states.

measurement and Πmax ) γ° - γmin is the interfacial pressure of an metastable equilibrium obtained for t ) tmin. This equation implies that adsorption is governed by the slow penetration process of chains through the activation barrier formed by the already adsorbed chains and characterized by the relaxation time τ1. The curves corresponding to the fits to eq 3 of the experimental data at 140 °C for t < tmin are shown in Figure 6. The relaxation time τ1 is about 6 min and does not depend on copolymer concentration. (b) Increase of γ (Decrease of Π) with Time: t > tmin. For a given copolymer concentration, the minimum of γ is associated with a maximum of interfacial pressure and therefore with a maximum of copolymer adsorption at the interface. The value of this maximum depends on the copolymer concentration, but the corresponding time tmin is constant for a given temperature. The decrease of interfacial pressure with time for t > tmin implies a slow modification of the interfacial layer. To explain this, we can consider either a desorption of the copolymer from the interface or a conformational change of the copolymer molecules adsorbed at the interface. Rearrangements in the adsorbed layer by a conformational modification of the adsorbed segments (surfacephase transition) can be an explanation to the overshoot phenomenon.40 However, this assumption is unlikely in our case because of the small size of the copolymer. Desorption of the copolymer from the interface can be understood as a desorption in the PEO phase or a transfer through the PDMS. We do not believe that copolymer desorption in the PDMS can occur because the copolymer

is immiscible with the PDMS. Moreover, the transport across the interface is hindered by an activation barrier.15 For desorption in the PEO phase, we have considered two processes. The first one is the formation of an inhomogeneous and metastable layer consisting of surface micelles48 and individual molecules. This system may slowly relax toward a homogeneous layer with the expulsion of copolymer molecules from the interface to the PEO phase14 (Figure 7b). The second possibility considered is an equilibrium between the interface saturated with the copolymer molecules and an oversaturated subphase. This subphase may act as a mirror for the arriving molecules which bounce back into the bulk. After that, this system may also relax toward a less dense layer44 (Figure 7c). In other words, for t > tmin, the observed kinetics (interfacial layer relaxation) correspond either to a desorption or to a repulsion of the copolymer in the PEO phase. By analogy to studies of adsorption from polymer solutions onto solid surfaces, we have fitted our experimental results of Π as a function time for t > tmin with the equation

Π(t) ) Π∞ + (Πmax - Π∞) e-(t-tmin)/τ2

(4)

where τ2 is the characteristic relaxation time and Π∞ ) γ° - γ∞ the equilibrium interfacial film pressure. Fitting curves corresponding to eq 4 are shown in Figure 8. The relaxation time τ2 at 140 °C does not depend on the copolymer concentration and is about 150 min. To summarize, the maximum of interfacial pressure (overshoot) has been explained by the combination of two kinetic mechanisms and the model proposed considers two relaxation times corresponding to each mechanism. Consequently, each experimental curve Π ) f(t) over the entire measurement time can be considered as the sum of three contributions (Figure 9). (48) Ligoure, C. Macromolecules 1991, 24, 2968.

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Figure 9. Model of interfacial pressure-time evolution. Decomposition of the experimental data (b) (overshoot effect) as the sum of three types of processes: (1) initial interfacial pressure (Π0); (2) adsorption (eq 3); (3) interfacial layer relaxation.

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Figure 10. Time dependence of the interfacial pressure at 140 °C for the system PDMS/copolymer/PEO 1000 for 5 wt % of copolymer in the PEO phase and various PDMS molar masses: 3, PDMS 50000; 9, PDMS 28000; O, PDMS 5970; s, fit by the model described in the text.

The first one (1) is the value of the interfacial pressure at t ) 0; it is a constant equal to

Π1 ) Πo ) γ° - γo The second one (2) is a slow adsorption kinetics which leads to a plateau value Πmax - Πo:

Π2(t) ) (Πmax - Πo) (1 - e-t/τ1) The third process (3) is the interfacial relaxation phenomenon which starts at tmin and leads to a value Π∞ - Πmax:

Π3(t) ) (Π∞ - Πmax) (1 - e-(t-tmin)/τ2) Kinetics for Ccop j 2%. In the case of a low copolymer concentration in the PEO phase, the density of copolymer molecules near the interface is weak and the relaxation process does not have to be considered. Interfacial pressure increases as expected to an equilibrium value. Kinetics for Ccop J 40%. For these high copolymer concentrations, the copolymer forms a micellar solution in the PEO14 and the previous behavior is no longer valid. Kinetics is slowed and the times τ1 (due to the energetic barrier) increase with copolymer concentration. We believe that there is a preferential segregation of the volume micelles to the interface.49 As micelles cannot adsorb, we can imagine that they relax very slowly by expulsion of individual copolymer molecules which can adsorb at the interface.20 Influence of Molar Masses of PDMS. Figure 10 shows the results of kinetics of interface formation between PDMS of various molar masses and melts at 5% copolymer with PEO 1000. The different curves look similar. The kinetics described in the previous section seems to be well adapted and allows the fit of experimental data points for short times (t < tmin) and long times (t > tmin). (49) Shull, K. R.; Winey, K. I.; Thomas, E. L.; Kramer, E. J. Macromolecules 1991, 24, 2748.

Figure 11. Time dependence of the interfacial pressure at 140 °C for the system PDMS 50000/copolymer/PEO for 5 wt % of copolymer in the PEO phase and two different PEO molar masses: 3, PEO 1000; 9, PEO 10000.

The relaxation time τ1 does not change with the molar mass of PDMS. That is not surprising because the first part of the kinetics process only involves the PEO phase. When the PDMS mass decreases, the relaxation time τ2 decreases (from 150 min for PDMS 50000 to 60 min for PDMS 5970). This means that the approach to equilibrium is faster with lower molecular weights of PDMS. Influence of Molar Masses of PEO. We have measured variations of γ as a function of time for the system PDMS 50000/mixtures of PEO 10000 with copolymer. The kinetics of interfacial formation are similar to those obtained with the PEO of lower molar mass; the only difference is a less pronounced magnitude. Figure 11 shows

Adsorption of PDMS-g-PEO Copolymer

as an example the variations of Π as a function of time for the interface between PDMS 50000 and melts at 5% of copolymer with PEO 1000 and PEO 10000. The relaxation time τ1 increases with the molar mass of PEO. This is consistent with the fact that high molecular weights of PEO are entangled and thus the copolymer moves slowly in this medium. Therefore, there will be less copolymer at the interface and the second kinetics process will be less developed. Indeed, we observe a decrease of the relaxation time τ2 when the PEO mass increases. 4. Conclusion In this paper, we have shown that the pendant-drop interfacial tension measurement could be successfully used to study the kinetics of adsorption of a low molecular weight PDMS-g-PEO copolymer at the PDMS-PEO interface. The most important result we have found is an unexpected kinetics of interface formation. Interfacial tension first decreases with time to a minimum value before an increase takes place toward an equilibrium value. In other words, the adsorption process presents an

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overshoot of the adsorbed amount. Another surprising feature of our experiments is the observation of extremely long lived nonequilibrium states for such short copolymers. To explain these results, the kinetics of copolymer adsorption can be described by two consecutive processes on a clearly separated time scale: the adsorption of the copolymer chains at the interface by transfer over an energy barrier formed by the already adsorbed chains and the relaxation of the interfacial layer corresponding either to a desorption or to a repulsion of the copolymer in the PEO phase. This model is not capable of providing a detailed nature of this overshoot effect nor a molecular mechanism. Moreover, reliable molecular interpretation cannot be based on results obtained with interfacial tension only. Additional characterization of the adsorbed layer itself is needed. We are currently investigating this by X-ray or neutron reflectivity. LA990229W