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Effect of Surface Confinement on Chain Relaxation of Entangled cis-Polyisoprene Qiang Zhang and Lynden A. Archer* School of Chemical and Biomolecular Engineering, Cornell University, Ithaca, New York 14853 Received April 17, 2003. In Final Form: June 17, 2003
Normal-mode relaxation of entangled cis-polyisoprene (PI) confined in porous glass was studied using broadband dielectric spectroscopy. In our designed model systems, geometric confinement effects are much weaker than surface adsorption effects, allowing relaxation dynamics of polymer chains at the surface to be determined from the dielectric response. PI confined in glass pores exhibits two relaxation processes: one fast mode and one slow mode. The fast dynamics are almost independent of polymer molecular weight and appear to be controlled by dynamic adsorption/desorption of chain segments at the surface. The slow dynamics correspond to the global chain relaxation, which is broadened and shifted to lower frequencies compared with the bulk process. The characteristic relaxation time of the slow mode τs shows much stronger molecular weight M dependence (e.g., τs ∼ M5.7(0.15 at 30 °C) than the bulk relaxation time τb (τb ∼ M3.5). Another noteworthy finding is that the activation energy of the slow mode increases with M. These results indicate an increase of surface confinement effects as M increases. It is also found that surface confinement effects decrease with increasing temperature and can be largely eliminated by coating the pore walls with a monolayer of oligomers to prevent surface adsorption. The structure of PI at surfaces and molecular mechanisms available for relaxation of adsorbed chains are discussed.
Introduction Polymer chains under confinement are generally expected to exhibit properties that are quite different from molecules in bulk melts and solutions.1,2 These differences are important for both scientific research and applications. For example, diffusion of polymer liquids into clay galleries many times smaller than the average size of polymer molecules controls the intercalation dynamics in polymer/ clay nanocomposites.3 Likewise, relaxation dynamics of polymer liquids tethered to solid substrates are an important determinant of boundary lubrication properties of thin polymer films.4 Relaxation dynamics of polymers under confinement share many features with confined glass-forming liquids. For example, the glass transition temperature Tg and the R process have been found to depend strongly on the confining geometries.5,6 However, the long backbones of polymer molecules add an additional source of dynamic complexity, the global chain relaxation. (Here, the global chain means the entire single molecule.) If topological constraints due to entanglements with neighboring molecules are absent, bulk polymer molecules generally follow Rouse dynamics. On the other hand, reptation dynamics dominate in the entangled state.7 When polymer chains are subjected to confinement, additional constraints besides topological entanglements will influence their orientational relaxation. The end effect is that the global chain relaxation is prolonged, and the characteristic (1) de Gennes, P. G. Macromolecules 1980, 13, 1069. (2) Hu, H. W.; Granick, S. Science 1992, 258, 1339. (3) Vaia, R. A.; Giannelis, E. P. Macromolecules 1997, 30, 8000. (4) Klein, J.; Kamiyama, Y.; Yoshizawa, H.; Israelachvili, J. N.; Fredrickson, G. H.; Pincus, P.; Fetters, L. J. Macromolecules 1993, 26, 5552. (5) Jackson, C. L.; McKenna, G. B. J. Non-Cryst. Solids 1991, 131, 221. (6) Keddie, J. L.; Jones, R. A. L.; Cory, R. A. Europhys. Lett. 1994, 27, 59. (7) Doi, M.; Edwards, S. F. The Theory of Polymer Dynamics; Clarendon: Oxford, 1986.
time required for long-range translational diffusion of the center of mass (the characteristic relaxation time) is enhanced. The lowered mobility of polymers constrained by solid surfaces is usually attributed to two mechanisms: geometric confinement and surface confinement. In the bulk state, polymer chains are usually modeled as Gaussian coils. If they are restricted in areas even smaller than polymer random coils, they cannot maintain their random configurations and are therefore geometrically confined. When polymer chains are adsorbed at solid surfaces, their reorientation dynamics slow down. This type of confinement is due to surface adsorption. In this study, we will focus on the latter by successfully removing the geometric confinement. How surface confinement effects influence relaxation dynamics of entangled polymers is not well understood, though several possible mechanisms have been proposed. For instance, it has been argued that physical attachments of polymer chains to the surface efficiently arrest the reptational diffusion, and these chains have to relax via slower molecular processes such as “constraint release” and “arm retraction”.8,9 Some other authors argue that chain confinement increases the cooperativity of chain motions,10,11 causing the relaxation process to be dominated by many collective glasslike motions.12 This may lead to much longer characteristic relaxation times than possible in bulk. Various characterization tools such as dielectric relaxation spectroscopy (DRS),13-15 microscopic force measure(8) Ajdari, A.; Brochard-Wyart, F.; de Gennes, P. G.; Leibler, L.; Viovy, J. L.; Rubinstein, M. Physica A 1994, 204, 17. (9) Watanabe, H. Prog. Polym. Sci. 1999, 24, 1253. (10) Montfort, J. P.; Hadziioannou, G. J. Chem. Phys. 1988, 88, 7187. (11) Kajiyama, T.; Tanaka, K.; Takahara, A. Macromolecules 1995, 28, 3482. (12) Matsuoka, S. Relaxation Phenomena in Polymers; Hanser: New York, 1992. (13) Schonhals, A.; Stauga, R. J. Chem. Phys. 1998, 108, 5130. (14) Schonhals, A.; Goering, H.; Schick, C. J. Non-Cryst. Solids 2002, 305, 140.
10.1021/la0346649 CCC: $25.00 © 2003 American Chemical Society Published on Web 08/16/2003
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ments,16 optical techniques,17 and nuclear magnetic resonance18 have been employed to study the global chain dynamics of confined polymer liquids. Cho et al.,16 for example, measured dielectric and mechanical responses of polyisoprene films (the film thickness was of the order of nanometers) sandwiched between mica surfaces with a surface force apparatus (SFA). They found that the dielectric normal-mode relaxation (or the global chain relaxation) of PI in thin-film geometries was moderately slower than that of the bulk and the mode distribution was broader. However, independent dynamic mechanical analysis of these PI films showed that the terminal viscoelastic relaxation time was much longer than the dielectric relaxation time. The origin of this difference was not very clear according to these authors. Dao and Archer17 recently used an evanescent wave laser polarimetry technique to investigate the relaxation of entangled 1,4-polybutadiene (PBD) melts and polystyrene/ diethyl phthalate solutions near rigid glass substrates following application of small-amplitude step shear deformations. For both systems, the terminal relaxation time of polymers near the surface τs was found to be larger than the bulk relaxation time τb. In the case of PBD, τs had much stronger molecular weight dependence (τs ∼ M4.2) than the corresponding bulk properties (τb ∼ M3.4). Dao and Archer interpreted their findings in terms of constraint release models and the equilibrium structure of adsorbed polymer chains. Polymer relaxation dynamics in bulk liquids are most often characterized using mechanical viscoelastic measurements. These measurements have convincingly shown that bulk polymer responses are viscoelastic and can be influenced by polymer molecular weight, architecture, temperature, polydispersity, solution concentration, and structure and chemistry of polymer segments. However, it is difficult to probe the mechanical response of polymer liquids constrained on nanometer length scales. An alternative approach is to use dielectric spectroscopy to explore dynamics of polymers with type A dipoles in porous media. For these materials the dielectric spectra contain accessible information about the normal-mode relaxation (or the global chain relaxation) that occurs at lower frequencies than the R process.19 A typical polymer having type A dipoles is cis-polyisoprene. This polymer is commercially available in a wide range of molecular weights with well-defined architecture and low polydispersity, making it ideal for fundamental studies of dielectric normal-mode relaxations. Dielectric responses of type A polymers in porous media have been investigated in several studies. Schonhals et al.13,14 performed DRS measurements on unentangled poly(propylene glycol) (PPG) in controlled porous glass (CPG) with pore diameters ranging from 2.5 to 20 nm. They found that the global chain relaxation of PPG was retarded because of confinement effects, which they argued were mainly due to surface confinement. The adsorption mechanism of PPG at glass surfaces is strong hydrogen bonding, which may explain the strong influence of surface adsorption on dynamics. Similar studies using unentangled to marginally entangled cis-PI in CPG (the mean pore diameter is 10.2 nm) identified a relaxation process much faster than the bulk relaxation.15 This process was (15) Petychakis, L.; Floudas, G.; Fleischer, G. Europhys. Lett. 1997, 40, 685. (16) Cho, Y. K.; Watanabe, H.; Granick, S. J. Chem. Phys. 1999, 110, 9688. (17) Dao, T. T.; Archer, L. A. Langmuir 2001, 17, 4042. (18) Chornaya, V.; Todosijchuk, T.; Lipatov, Y. J. Colloid Interface Sci. 1998, 198, 201. (19) Adachi, K.; Kotaka, T. Prog. Polym. Sci. 1993, 18, 585.
Langmuir, Vol. 19, No. 19, 2003 8095 Table 1. Nomenclature and Characteristics of Polyisoprene name
M h w (g/mol)
M h w/M hn
Rga (nm)
PI12 PI26 PI35 PI81
12 500 26 000 35 000 81 100
1.04 1.04 1.04 1.04
3.8 5.4 6.3 9.5
a The radius of gyration R is estimated by R 2 ) 1/ Nb2. N is g g 6 the degree of polymerization, and b is the statistical step length (b ∼ 0.68 nm for polyisoprene).
Table 2. Nomenclature and Characteristics of CPG
name
mean pore diam (Å)
pore diam distribution (%)
specific pore vol (mL/g)
surface functional group
CPG82 CPG128 CPG166 CPG236 CPG128AP CPG112GL
82 128 166 236 128 112
7.95 5.1 5.8 4.3 5.1 5.1
0.37 0.80 0.81 0.95 0.80 0.51
none none none none aminopropyl glyceryl
argued to originate from dynamic adsorption/desorption processes of chain segments at pore walls. Furthermore, because the low-frequency dielectric loss was dominated by ionic conductivity effects, the slower global chain relaxation process was not detected. Most polymers that were used in the studies reviewed in the previous paragraph were either unentangled or weakly entangled. In this article, entangled cis-PI in CPG was used as our model system to study the dielectric normal-mode relaxation of entangled polymers at solid surfaces. Our objective is twofold. First, it will broaden the probed molecular weight range to capture the dependence of relaxation dynamics of confined polymers upon polymer molecular weight. At the same time, experimental and theoretical investigations of entangled polymers at surfaces will be very useful for further understanding of the influences of surface confinement on their molecular relaxation processes. Experiment 1,4-Polyisoprenes with different molecular weights were purchased from Polymer Source, Inc. Their molecular characteristics are summarized in Table 1. According to the manufacturer, these materials have the following isomer contents: ∼81% cis-1,4 addition, ∼15% trans-1,4 addition, and ∼4% 3,4 addition. Since cis-1,4 addition and trans-1,4 addition produce type A dipoles, 96% of the chain segments have type A dipoles and contribute to the dielectric normal-mode relaxation. The glass transition temperature of bulk PI is approximately -70 °C. The host material was dielectrically inert CPG purchased from CPG, Inc. Porous glass particles (37-74 µm) with various pore sizes and surface properties (Table 2) were used. It is also evident from Table 2 that the pore size distribution is quite narrow. The following procedures were adopted to fill the pores of CPG with PI chains. First, the polymer was dissolved in toluene, producing a 5 wt % solution. CPG powders were heated to 250 °C for 3 h to remove water and organic solvents, cooled to room temperature, and then added into the PI/toluene solution. This mixture was continuously stirred with the solvent evaporating slowly. After the weight no longer changed, the sample was further dried in a vacuum (∼20 mTorr) for 24 h to thoroughly remove the residual solvent. This step was very important as even a small amount of residual solvent would dramatically influence the dielectric response of the sample. The mass of PI used was computed so that the amount of PI was just enough to fill the CPG pores. These calculations assumed that the density of PI in glass pores is the same as that in the bulk state. This assumption was tested and validated in the following way. For samples with more PI than the calculated amount, it was observed
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that CPG particles adhered strongly with each other, confirming the existence of a bulk liquid phase outside CPG particles. This behavior was also accompanied by the presence of an extra relaxation process in the dielectric relaxation spectra, similar to that expected from bulk PI. On the other hand, for samples with PI loadings equal to or less than the calculated amount, CPG particles had very weak adhesion with each other, and dielectric studies did not manifest a signature of bulk polymers surrounding CPG particles. Samples for DRS experiments were packed into pellet shapes and sandwiched between two gold-plated copper disks. The upper disk had a diameter of 20 mm, and the diameter of the lower one was 40 mm. All DRS experiments were performed using a commercial Novocontrol BDS-80 broadband dielectric spectrometer that runs in a wide frequency range (10-5-107 Hz) and at temperatures between -170 and 400 °C. By use of the Novocontrol Quatro Cryosystem, the sample temperature was controlled with a nitrogen gas stream, which also provided a protective environment to avoid oxidative degradation of polymers. In these experiments, the complex dielectric function *(f) ) ′(f) - i′′(f) was measured. Here, f is the frequency of the electric field, ′(f) is the dynamic dielectric constant, and ′′(f) is the dielectric loss. The dielectric loss contributed by CPG was found to be around 6 × 10-4 at all frequencies, which is negligible in comparison to the polymer contribution for the materials studied here. The measured dielectric loss ′′(f) mainly contains two components:20
′′ (f) ) ′′d (f) + ′′c (f)
(1)
where the effective dielectric loss ′′d(f) arises from molecular dipole relaxation and ′′c(f) is produced by ionic conductivity. The conductivity term can be described empirically by
′′c (f) )
( ) σ 2πf0
n
(2)
where σ is the dc conductivity, 0 is the permittivity of vacuum, and n is a fitting parameter ranging from 0 to 1, which quantifies the effect of electrode polarization due to ionic conduction.21 Because the ionic conductivity effect is dominant at low frequencies, σ and n can be determined by fitting eq 2 to the low-frequency experimental data. The effective dielectric loss due to molecular dipole relaxation ′′d(f) can be obtained by subtracting the conductivity contribution from the measured data. ′′d(f)/φ is the effective dielectric loss divided by the volume fraction of PI chains in the sample. This rescaled dielectric loss is widely used in this article since it best compares dielectric properties of bulk PI and PI in glass pores. For simplicity, the subscript “d” is omitted in the following discussion. ′′ and ′′/φ therefore refer to the effective dielectric loss and the rescaled effective dielectric loss unless stated otherwise.
Results and Discussion cis-PI chains possess both type A and type B dipoles.19 The normal-mode relaxation (originating from type A dipole relaxation) of cis-PI in the bulk and in glass pores will be our main focus. The lowest molecular weight of cis-PI chosen for this study is around 2.5Me (the entanglement molecular weight Me ∼ 5000 g/mol). As mentioned in the Experiment Section, most PI segments have type A dipoles. Assuming that these type A dipoles are randomly distributed throughout the whole backbone, they can be represented by a single effective molecular dipole in the direction of the end-to-end vector of the chain.19,22 Thus, dielectric relaxation spectroscopy of these polymers provides information about their global chain dynamics. (20) Jonscher, A. K. Dielectric Relaxation in Solids; Chelsea Dielectrics Press: London, 1983. (21) Reiche, A.; Cramer, T.; Fleischer, G.; Sandner, R.; Sandner, B.; Kremer, F.; Karger, J. J. Phys. Chem. B 1998, 102, 1861. (22) Watanabe, H. Macromol. Rapid Commun. 2001, 22, 127.
Figure 1. (a) Frequency-dependent rescaled dielectric loss ′′/φ of PI35 in the bulk state and in glass pores. The solid line is the fit of ionic conductivity. The crossing point of the dashed lines determines fslow. The temperature is 30 °C. (b) Frequencydependent rescaled dielectric loss ′′/φ of PI in glass pores with different molecular weights. The temperature is 30 °C. d h ≈ 2.3Rg for “PI26 in CPG128”, d h ≈ 2.0Rg for “PI35 in CPG128”, and d ≈ 1.7Rg for “PI81 in CPG166”.
The dielectric relaxation behaviors of entangled bulk PIs used in this work are found to be consistent with the generalized tube model.22 For a bulk PI, its dielectric loss spectrum (Figure 1) shows a single relaxation process with a maximum loss frequency fp,bulk. Typical terminal behavior is observed, with ′′ ∝ f, when the frequency f is less than fp,bulk. The characteristic relaxation time τb ≡ (2πfp,bulk)-1 varies with polymer molecular weight approximately as M3.5, in agreement with the molecular weight dependence of terminal relaxation time and zero-shear viscosity deduced from mechanical rheometry measurements for entangled polymer melts and solutions.7 As mentioned in the Introduction, both surface confinement and geometric confinement may exist when PI chains reside in nanopores. The average diameter of polymer random coils is estimated to be around 2Rg, where Rg is the radius of gyration. For a neutral flat substrate adsorbed with monodisperse polymer molecules, experimental and theoretical studies have shown that the interfacial layer thickness is also of the order of 2Rg.23,24 In this study, the average pore diameter of CPG d h was chosen to be around 2Rg so that most polymer molecules are within the interfacial layer. Meanwhile, since the pores are wide enough to accommodate polymer random coils, geometric confinement effects are expected to be weak. This point is supported by experimental data discussed later in this article, which show that dynamic slowing down of PI chains in glass pores can be reversed by (23) Silberberg, A. J. Colloid Interface Sci. 1988, 125, 14. (24) Cohen-Addad, J. P. Polymer 1989, 30, 1820.
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modifying the surface chemistry of the pores alone. Therefore, the systems we used can be approximately modeled as PI chains physically attached to glass substrates without additional geometric constraints. Hence, relaxation dynamics of these “surface” PI molecules can be successfully studied using “bulk” DRS measurements. Dielectric responses of PIs in glass pores are compared with those of their bulk counterparts in Figure 1. ′′/φ data of “PI35 in CPG128” before and after subtracting the conductivity contribution are shown in Figure 1a. Figure 1b illustrates the frequency response of ′′/φ (after subtracting the conductivity) for various PI molecular weights. Bulk PI shows a single sharp relaxation peak at fp,bulk, while PI in glass pores exhibits two relaxation processes: a fast mode and a slow mode. The fast mode has a peak frequency ffast much higher than fp,bulk. The peak frequency and mode distribution of this mode are almost independent of PI molecular weight. The physical origin of these observations will be discussed later. The slow mode should correspond to the orientational relaxation of the end-to-end vector of the entire polymer chain. For PI in glass pores, substantial dielectric loss strength remains even below fp,bulk, where most bulk chains have already relaxed. A perhaps obvious reason for this is that polymer chains in the interfacial layer have lower mobility than bulk PI molecules. The relaxation peak is also significantly broadened, forming a plateaulike zone, which is followed by a terminal zone at frequencies below fslow much lower than the respective fp,bulk. Therefore, fslow is defined to be the characteristic frequency at which most polymer molecules at the surface relax dielectrically. We let τs ≡ (2πfslow)-1 represent the characteristic relaxation time of the slow mode of PI in glass pores and τf ≡ (2πffast)-1 to be the characteristic relaxation time of the fast mode of PI in the glass pores. Another common method to determine the characteristic relaxation time τ is to use the empirical Havriliak-Negami (HN) function to fit the experimental data around a relaxation peak:
*(f) )
∆ + ′ (f f ∞) [1 + (2πf τi)R]β
(3)
where the relaxation strength ∆ equals ′(f f ∞) ′(f f 0), and R and β are parameters that describe respectively the symmetrical and asymmetrical broadening of the relaxation peak. However, the slow mode of PI in glass pores has a broad plateaulike relaxation peak, and locating τs using the HN function method produces large errors. Therefore, the HN function method was not used in this study. Dielectric relaxation dynamics of PI constrained in surface-coated CPG (Figure 2) reveal abundant information. First, they show only one relaxation process, the global chain relaxation, exists in the experimental frequency range. For the system “PI26 in CPG128AP”, the ′′/φ curve is almost flat at high frequencies. For “PI26 in CPG128GL”, there are weak indications of a relaxation process at frequencies above 106 Hz. Despite this difference, both sets of results are consistent with a complete disappearance of the fast relaxation mode observed for the “PI26 in CPG128” system. This phenomenon has already been reported by Petychakis et al.15 and was explained in terms of the importance of PI adsorption/ desorption kinetics at multiple surface sites to dielectric normal-mode relaxation. The alternate adsorption/desorption processes are thought to produce an extra contribution to the dielectric relaxation spectrumsthe fast mode of PI in glass pores. The average number of
Figure 2. Frequency-dependent rescaled dielectric loss ′′/φ of PI26 in the bulk state, in uncoated CPG, and in surface coated CPG. The temperature is 20 °C. d ≈ 2.3Rg for “PI26 in CPG128” and “PI26 in CPG128AP”, and d ≈ 2.1Rg for “PI26 in CPG112GL”.
Figure 3. Effective type A dipole moment between attachment points A and C b pAC before (on the left) and after (on the right) desorption of segment B.
monomers of a subchain between two binding sites is much smaller than the total number of monomers forming a polymer chain. Therefore, this fast mode can be much faster than the bulk relaxation when the adsorption/ desorption kinetics is fast enough. The fact that this process is almost independent of polymer molecular weight is also consistent with its assignment to subchain motions. More careful consideration of the fast mode contribution suggests that type A dipoles alone cannot be responsible for this mode contribution. The molecular dipole moment due to type A polarization b ptypeA represents the end-toend orientation of the polymer backbone. Consider an adsorbed polymer chain, such as that depicted in Figure 3. When one adsorbed segment (segment B) desorbs from the surface, the effective type A dipole moment between A and C b pAC should remain more or less unchanged. Therefore, if one adsorbed segment is detached, b ptypeA will change very little, if at all, unless the desorbed segment is at the chain end. This means that adsorption/desorption processes will make a measurable contribution to type A dipole relaxation only if the segments in question are located at the chain ends. Even then, the intensity of this contribution will be much smaller than the relaxation strength of the whole bulk polymer. This statement is obviously at odds with the relatively large dielectric relaxation intensity of the fast mode observed experimentally. Specifically, from Figures 1-4 the intensity of the fast mode is seen to be comparable to that of the bulk process. Therefore, the fast dynamics observed is not likely to originate from type A dipoles. Instead, it is possibly due to type B dipoles with the following mechanism. Each loop of an adsorbed chain has an effective dipole due to type B polarization. When the attachment points of loops leave the surface, the orientations of these effective dipoles change, resulting in dielectric relaxation. With this mechanism, the relaxation of the effective dipoles is impeded by chain adsorption and hence controlled by surface adsorption/desorption kinetics. It should be noted that this mechanism is different from the R relaxation of bulk polymers. In bulk PI, the R relaxation is related to local chain motions without any influence from surfaces and therefore occurs at much higher frequencies.
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Figure 4. Rescaled dielectric loss ′′/φ as a funciton of frequency of PI12 in the bulk state and in glass pores of different sizes. The temperature is 20 °C.
The global chain relaxation of PI in surface-coated CPG shows a relaxation peak with a peak frequency almost equal to fp,bulk of its bulk counterpart, except that the relaxation spectrum is moderately broadened. However, this relaxation peak is still sharp in comparison with that of the uncoated CPG system, which does not show an explicit relaxation peak. The surface coating virtually eliminates nonspecific adsorption experienced with uncoated CPG. Surface confinement effects are therefore greatly reduced. Surface chains feel almost no resistance from the pore walls to diffuse away and behave more like PI chains in bulk than like PI chains in uncoated CPG. This finding also confirms our assumption that geometric confinement effects are very weak in our model systems with d h ∼ 2Rg. Dielectric relaxation behavior of PI in glass pores also depend on the pore size. Most PI12 chains in CPG82 (d h ≈ 2.2Rg) are expected to reside in the interfacial layer. For the system “PI12 in CPG128” (d h ≈ 3.4Rg), some polymer chains will be in the bulk state. Finally for “PI12 in CPG236” (d h ≈ 6.2Rg), a large population of PI chains in the pores are therefore expected to be unconstrained by the pore walls. These inferences are supported by data shown in Figure 4. The dielectric loss curve of “PI12 in CPG82” shows the weakest bulk contribution of the three. Its global chain relaxation spectrum is broader than the others, and the fast high-frequency dynamics are most clearly seen. As the average pore size is progressively increased, the global chain relaxation spectrum narrows, and the fast mode is progressively less defined. In the case of “PI12 in CPG236”, signals from surface PI are already fairly weak. The temperature dependences of τb for PI in bulk and τs and τf for PI in glass pores (Figure 5) are compared with expectations from the Vogel-Fulcher-Tammann (VFT) equation
log τ ) log τ0 +
A T - T0
(4)
Here T0 is the Vogel temperature, τ0 is the hightemperature limit of the characteristic relaxation time τ, and A is proportional to the activation energy of dielectric relaxation EA (A ) EA/kB, where kB is Boltzmann’s constant). The parameters used to obtain the fits are summarized in Table 3. The reference temperature T0 for all these relaxation modes shown in Table 3 is approximately 160 ( 5 K, consistent with other studies.15,25 It is apparent that both the slow and fast relaxation modes of PI in glass pores have higher activation
Figure 5. Plot of -log (τ/s) vs 1000/T. τ is the characteristic time of a relaxation process. The data points are fitted with the VFT equation (solid lines). Table 3. VFT Fitting Parameters relaxation mode
-log(τ0/s)
A (K)
T0 (K)
PI35, bulk mode PI35 in CPG128, fast mode PI35 in CPG128, slow mode PI26, bulk mode PI26 in CPG128, fast mode PI26 in CPG128, slow mode
7.2 15.8 8.3 7.6 15.7 8.6
674.5 1450.3 971.2 638.5 1352.9 904.46
160.5 156.7 162.3 162.3 161.8 160.2
energy (larger VFT fitting parameter A) than the bulk relaxation. Although measured τs is always larger than measured τb at a given temperature for both PI26 and PI35 (Figure 5), their difference diminishes at high temperatures. The extrapolated high-temperature intercept -log (τ0/s) of τs via VFT fitting is slightly larger than that of τb, meaning that the extrapolated τs is even smaller than the extrapolated τb at very high temperatures. In reality, τs should never be smaller than τb. It is then reasonable to consider that they are almost equal to each other in the high-temperature limit, and confinement effects are hence negligible. These observations can be explained as follows. The activation energy of bulk PI is primarily due to molecular frictions. The higher activation energy of surface PI (both the slow and fast modes) arises from the combined influences of surface adsorption and intermolecular interactions on molecular relaxation. That the fast mode of PI in glass pores has even higher activation energy than the slow mode suggests that surface adsorption effects play a more important role in the fast mode than in the slow mode. It is consistent with our view that the fast mode is dominantly controlled by dynamic adsorption/ desorption of chain segments. When the thermal energy increases, it becomes easier for chain segments bound to the surface to overcome the energy barrier for desorption. Therefore, surface confinement effects become weaker as the temperature increases. τf of PI26 and PI35 at T > 40 °C is unavailable because the fast process is outside the experimental frequency window at these temperatures. The VFT fit of τf shows that its high-temperature limit is of the order of 10-15 s, which is extremely small. It is because the thermal energy is high enough to dramatically accelerate the adsorption/ (25) Santangelo, P. G.; Roland, C. M. Macromolecules 1998, 31, 3715.
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Figure 6. Comparison of the normalized dielectric loss spectra of the fast mode of “PI26 in CPG128” at different temperatures. ′′peak is the dielectric loss at the maximum loss frequency ffast.
desorption kinetics. Also, because of the exponential dependence of the desorption rate of an adsorbed chain segment kd upon temperature (kd ∼ e-ads/kBT, where ads is the segmental adsorption energy), this mode slows down very quickly with decreasing temperature. At very low temperatures, the fast mode of PI in glass pores can be even slower than the bulk process, though it only corresponds to subchain motions. The relaxation mode distribution of the fast mode is found to vary with the temperature (Figure 6) when the dielectric loss spectrum is plotted in a normalized coordinate. It demonstrates the failure of time-temperature superposition, which usually holds for bulk polymer materials. As discussed, the fast dynamics of surface PI is probably controlled by dynamic surface adsorption/ desorption instead of chain and segmental interactions. Therefore, it is not surprising that time-temperature superposition fails. The molecular weight dependences of τb for PI in bulk and τs and τf for PI in glass pores are also studied. Figure 7a describes the characteristic relaxation times as a function of polymer molecular weight of the following systems: “PI12 in CPG82” (d h ≈ 2.2Rg), “PI26 in CPG128” (d h ≈ 2.3Rg), “PI35 in CPG128” (d h ≈ 2.0Rg), and “PI81 in CPG166” (d h ≈ 1.7Rg). Again, the fast mode of PI in glass pores is found to be insensitive to the chain length. As expected, the bulk polymer approximately obeys the power-law relationship τb ∼ M3.5. For surface PI, the relaxation of the polymer chain is a strong function of molecular weight dependence (τs ∼ M5.7(0.15) obtained by fitting τs data in Figure 7a with a power-law function. Similar behavior has been reported by Dao and Archer for 1,4-polybutadienes adsorbed at silica glass substrates.17 In particular, these authors found a power-law relationship τ ∼ M4.2 between the birefringence relaxation time τ and the polymer molecular weight M. Since the measured birefringence is an average of contributions from polymer chains within 2-3 radii of gyration from the surface, dynamic information recovered using this method includes contributions from surface-adsorbed chains as well as from some bulk chains near the surface. The current study isolates dynamics of polymers adsorbed to glass substrates. It is then perhaps unsurprising that a much stronger relationship between the polymer relaxation time τs and polymer molecular weight is observed. Dao and Archer discussed their observations in the framework of constraint release between surface-adsorbed and bulk polymer chains. In this work, to further explore the relaxation mechanism of surface PI requires knowl-
Figure 7. (a) A log-log plot of the characteristic relaxation time τ vs PI molecular weight. The data points are fitted with the comb model (solid line), the arm retraction model (dashed line), and the power function (dotted lines). The temperature is 30 °C. (b) The τ ∼ M power-law exponent φ of the bulk process and of the slow mode of surface PI as a function of temperature. The dashed line shows the average φ of bulk PI.
edge of the structure of PI chains adsorbed to the pore walls and of the entangled state of chain segments in the pores. The adsorption mechanism of polyisoprene on glass surface is believed to be physisorption.26 A scaling theory of polymer adsorption has been developed by de Gennes.1 This theory assumes a loop-tail-train model and uniform adsorption, where tails can be considered as half-loops. For an adsorbed N-mer chain in thermodynamic equilibrium at the surface, the average number of loops per chain scales as xN. Since there are much less segments in trains than in loops, the total number of monomers in loops is approximately N. Therefore, the average number of monomers per loop is proportional to N/xN ) xN. If PI chains at glass surfaces adopt this equilibrium structure and the loops are assumed to be evenly distributed along the chain, their reorientation dynamics may be similar to those of a comb polymer; although the PI chains studied here do not have a comb architechture. In this case the “backbone” of the imaginary “comb” is the whole PI chain. Each loop is attached to the surface at both ends and can be roughly regarded as a “comb branch”, which in this case also forms the comb backbone when the loop retracts and the anchor points desorb. In this picture the adsorbed segments therefore serve as dynamic “branching points” because they may frequently reach and leave the surface during the relaxation of “comb branches”. The “comb backbone” is therefore comprised of the entire N monomers, and each “comb branch” has CxN monomers, where C is a constant. One model of comb polymers27 assumes that the whole backbone relaxes via constraint (26) Ono, S.; Kiuchi, Y.; Sawanobori, J.; Ito, M. Polym. Int. 1999, 48, 1035. (27) Roovers, J.; Toporowski, P. M. Macromolecules 1987, 20, 2300.
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Zhang and Archer
release while each comb branch relaxes via arm retraction. The terminal relaxation time is therefore
τcomb ∼ N 2 τbranch
(5)
The relaxation time of each “comb branch” via arm retraction is9
[
τbranch ∼ xN 1.5 exp
Cν′ xN Ne
]
(6)
which can be substituted into eq 5 to give
[
τcomb ∼ N 2.75 exp
Cν′ xN Ne
]
(7)
Usually, ν′ ) 15/8 for Gaussian chains.7 In this case, we also assume that Ne (number of monomers between entanglements) is equal to that of bulk entangled chains. The predictions provided by eq 7 with the fitting parameter C ) 10.1 are compared with the τs data in Figure 7a. If the adsorption energy ads between polymer segments and the substrate is higher than kBT, but not so high as to produce a flattened configuration of adsorbed PI chains, the extra mobility at the chain ends favors formation of long tails. In this case, the chain structure may be described as two long tails and short loops and trains,17 and the global chain relaxation is dominated by tail dynamics. The number of monomers of per tail is estimated to be 0.5N if we neglect the short loops and trains. A Gaussian coil configuration of the tails is expected with one end attached to the surface. If the tail is surrounded by a sufficient number of mobile bulk chains, it will most easily relax via a constraint release process. Constraint release models for linear polymers8 yield a power-law exponent of 4.4. If the contour length fluctuation of the matrix chains is taken into account,9 this index can be as high as 5.0, still lower than the 5.7 found in Figure 7a. If surrounding chains are trapped at the surface, a simple arm retraction process may be more plausible than constraint release. According to the general arm retraction model,9 the terminal relaxation time of adsorbed chains scales as
τAR ∼ τtail ∼
[
(0.5N)1.5 exp
]
[
]
ν′ ν′ 0.5N ∼ N 1.5 exp N (8) Ne 2Ne
Here, ν′ becomes a fitting parameter. In the Doi-Kuzuu (DK) model,9 ν′ is an adjustable parameter close to unity. Again, Ne is chosen to be equal to that of bulk entangled chains. Predictions of τs obtained using eq 8 with ν′ ) 1 are also represented in Figure 7a. It is clear from the figure that the quality of the comb model fit is better than that provided by eq 8. Nonetheless, in evaluating these predictions, it should be kept in mind that the entanglement structure of adsorbed polymer chain segments is likely quite different from in bulk and that some polymer segments in the CPG pores will be well removed from adsorption sites. The analogy between relaxation dynamics of entangled, physisorbed polymer chains and those of entangled comb or star polymers in a bulk liquid is, therefore, perhaps overly simplistic. The temperature dependence of the τ - M power-law exponent is investigated in Figure 7b. Here, a simple power function τ ∼ Mφ is used to fit the relaxation modes, and the power-law exponent φ is plotted as a function of the temperature. For bulk PI, φ is around 3.5 at all temper-
Figure 8. VFT fitting parameter A of the bulk process and of the slow mode of surface PI as a function of polymer molecular weight. The dashed line shows the average A of bulk PI.
atures. However, for the slow mode of PI in glass pores, φ decreases continuously with increasing temperature. These results again demonstrate that surface confinement effects diminish as the temperature increases. We guess that φ for surface PI might gradually approach that of the bulk at very high temperatures. These results also suggest that the exchange kinetics of attachment points, which is a function of temperature, cannot be ignored in analyzing the terminal relaxation process. The real relaxation mechanism of surface PI should include the influence of adsorption/desorption exchange of chain segments. Figure 8 shows the molecular weight dependence of the VFT fitting parameter A, which is proportional to the activation energy of dielectric relaxation. The parameter A of entangled bulk PI is nearly independent of polymer molecular weight. (A is around 650 ( 50 K when the reference temperature T0 is fixed to be 160.0 K, very close to previously reported data,25 A ∼ 630 K.) However, the independence of the activation energy upon polymer molecular weight is no longer valid when polymers are in the interfacial layer. Dielectric relaxation of higher molecular weight chains requires higher activation energy than that of lower molecular weight chains, suggesting that higher molecular weight PI in glass pores experiences much stronger surface immobilization. Desorption of physisorbed polymer chains is known to be controlled by energetics of surface detachment.28 Compared with short chains, long chains have more attachment points. It takes more energy to detach long polymer chains from the surface. Then it is not surprising that surface confinement effects increase with increasing polymer molecular weight. Conclusion We used cis-PI in CPG to investigate dielectric relaxation dynamics of entangled polymer liquids at a solid/ liquid interface. The pore size of CPG was chosen to be almost equal to the polymer random coil size, so that polymer confinement effects are mostly due to surface adsorption. Compared with the bulk, PI in glass pores exhibits a much broadened global chain relaxation maxima and terminal behavior at much lower frequencies. An additional high-frequency relaxation process is also found for PI in CPG glass pores. Several characteristics of this process indicate that it is probably due to dynamic adsorption/desorption processes of chain segments. When the glass surface is coated with a monolayer of oligomers, surface confinement effects almost disappear, and dielectric relaxation behavior of PI in glass pores becomes (28) Douglas, J. F.; Frantz, P.; Johnson, H. E.; Schneider, H. M.; Granick, S. Colloids Surf. A 1994, 86, 251.
Entangled cis-Polyisoprene
similar to relaxation behavior in bulk liquids. This finding confirms that both the slowing down of global chain relaxation and the existence of the fast mode arise from surface adsorption. Fitting the experimental data using the VFT equation indicates that both the fast and the slow modes of surface PI are characterized by much higher activation energy than the bulk relaxation process. The enhanced activation energy is believed to arise from surface adsorption effects in addition to intermolecular interactions. For surface PI, the characteristic relaxation time of the slow mode τs posesses a much stronger molecular weight dependence than the bulk relaxation time τb, while the characteristic relaxation time and mode distributions of the fast mode are almost independent of PI molecular weight. Molecular structures and possible relaxation mechanisms of surface PI are presented and discussed in terms of classical, if simplistic, models of entangled polymer systems. Surface confinement effects were also found to diminish at high temperature. In the high-temperature limit, τs approaches the bulk relaxation time τb, and the fast mode
Langmuir, Vol. 19, No. 19, 2003 8101
of surface PI becomes extremely fast. Second, as the temperature increases, τs has a weaker and weaker molecular weight dependence, getting close to the bulk behavior. These results indicate that surface adsorption/ desorption kinetics is also important in relaxation dynamics of PI at surfaces. At the same time, the activation energy of the global chain relaxation of surface PI is found to monotonically increase with polymer molecular weight. This result, plus the strong molecular weight dependence of τs, indicates that surface confinement effects are also influenced by the chain length. Acknowledgment. We are grateful to the Cornell Center for Materials Research (CCMR), a Materials Research Science and Engineering Center of the National Science Foundation (DMR-0079992), and to the National Science Foundation Tribology Program (Grant CMS0004525) for supporting this study. LA0346649
