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Wetting kinetics of modified polyimide surfaces: interactions with polar solvents
Journal of Colloid and Interface Science 279 (2004) 515–522 www.elsevier.com/locate/jcis
Wetting kinetics of modified polyimide surfaces: interactions with polar solvents Richard R. Thomas ∗ OMNOVA Solutions, 2990 Gilchrist Road, Akron, OH 44305, USA Received 23 January 2004; accepted 30 June 2004 Available online 28 July 2004
Abstract Contact angle relaxation studies were performed on a base hydrolyzed PMDA-ODA polyimide surface using methanol, pyridine and 1-methyl-2-pyrrolidinone (NMP) as probe liquids. The results were fitted parametrically to the molecular-kinetic theory to obtain the relevant molecular parameters that govern wetting rates. The probe liquid NMP appeared to have the greatest interaction of the three solvents studied with the modified polyimide surface. The differences in wetting rates are explained to result from the hydrogen bonding capability of the probe liquids with the modified polyimide surface and due to the difference between bulk and surface pKa of the modified polyimide. 2004 Elsevier Inc. All rights reserved. Keywords: Polyimide; Wetting; Kinetics; Contact angle relaxation
1. Introduction Polyimides are used widely in the electronics industry as interlayer dielectric materials. They are often the materials of choice in such applications due to excellent chemical, thermal and mechanical properties. The use of polyimides as interlayer materials implies their role as a component of a composite material. As such, it is often necessary to bind adhesively other materials to its surface. One of the most popular methods of attaching another material to a polyimide surface is through the use of spin coating. Typically, a polymeric precursor is dissolved in a suitable solvent that is then used to spin coat the polyimide surface. After a curing step, the composite material is formed. A necessary prerequisite of a coating is that it wet the surface to which it will be adhered. This factor introduces a temporal component to the wetting process and, therefore, to the successful application of a coating. The temporal component is manifested to a great extent in shear at the coating/substrate interface. Shear is induced by rapid creation of incipient coating sur* Fax: +1-330-794-6375.
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face either by motion of the coating relative to the substrate or motion of the substrate relative to the coating. The process of wetting is described often by a contact angle of a liquid on a solid surface. After a liquid is applied to a surface, there is a finite amount of time required for the liquid to assume its equilibrium contact angle, θ . The equilibrium contact angle follows the well known Young equation [1] γsl cos θ = γsv − γsl ,
(1)
where the variable γ refers to interfacial tension of the solid– liquid (sl), solid–vapor (sv) and solid–liquid interfaces (sl). Even for low viscosity fluids, the relaxation of contact angle from its initial (high) value to an equilibrium (low) value can take seconds. Spin coating represents a particularly high shear process that includes a radial spatial component. If the contact angle relaxation of the newly deposited coating to equilibrium predicted by (1) is slow compared to the speed at which the coating is forced to spread over the substrate surface, then defects in the coating can occur. These can take the form of air entrainment [2], dewetted or nonwetted areas and/or result in a nonconformal coating. In either case, these defects can be catastrophic. Therefore, it is important
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to understand contact angle relaxation and its effect on the coating process under a given set of conditions. The property robustness displayed by polyimides translates into coating and adhesion problems at the film surface. For example, spin coating of the PMDA precursor poly(amic acid) on a fully cured PMDA-ODA film does not result in a good adhesive bond without some surface modification. A number of methodologies have been demonstrated to modify the surface of a polyimide film to accept a coating. One of the more popular and easiest to execute is base hydrolysis [3,4]. In essence, base hydrolysis is the reverse of the poly(amic acid) to polyimide cure cycle used, with the exception that the modification is confined largely to just the outermost surface of the film. Base hydrolysis aids wetting and adhesion due to at least one of the following: (i) creation of more wettable carboxylic acid groups and/or (ii) introduction of more reactive functional groups capable of transfacial reaction with components of the coating to be applied. Based hydrolysis of polyimide has been studied by a number of researchers and reversion of polyimide to poly(amic acid) has indeed been confirmed by a number of techniques [3,4]. The creation of carboxylic groups on the polyimide surface creates a higher free energy surface that is more wettable by liquids such as water. Furthermore, the pKa of the carboxylic acid groups is evidenced in a large change in wettability as the pH of a wetting probe is increased beyond the surface pKa [4]. In addition, a free energy calculation can be used to quantify the number of incipient carboxylic acid groups on the modified surface [5]. Using this methodology, the kinetics of base hydrolysis of a polyimide surface have been proposed [6]. In earlier work, a contact angle relaxation study was performed on a modified polyimide surface as a function of base hydrolysis conditions [7]. This prior study used pH 2 and 11 buffered water as a probe. Very substantial differences were noted between the two liquids and attributable to the presence of ionizable carboxylic acid groups. The present work is an extension using polar organic liquids including 1-methyl-2-pyrrolidinone (NMP) as a probe. 1-methyl-2-pyrrolidinone is a major constituent of the solvents used for poly(amic acid) solutions. Moreover, NMP is known to interact very strongly with the precursor poly(amic acid) [8].
2.2. Instrumentation Contact angle relaxation data were acquired using an FTÅ200 contact angle goniometer equipped with a CCD camera, frame grabber and image analysis software from First Ten Ångstroms. Drop volumes in the range of 3–5 µL were used for measurements. In this volume range, dynamic contact angle data were reproducible.
3. Results and discussion In a previous study, contact angle relaxation kinetics were examined on a polyimide surface modified by base hydrolysis followed by neutralization using acetic acid [7]. This scheme is shown in Fig. 1. The polyimide (PMDA-ODA) studied was the condensation product of pyromellitic dianhydride and 4,4 -oxydianiline. Details regarding the experimental and data analysis methodology have been published earlier [7]. Contact angle relaxation data were collected on a native polyimide surface and ones that had been base hydrolyzed for periods of time followed by neutralization. Comparing theory and experimental contact angles as a function of pH, the surface density of incipient carboxylic acid groups, Ns , was determined. The pH of the probe liquid was chosen to be 2 and 11 as these values were below and above the estimated surface pKa (≈ 7) of the hydrolyzed polyimide [4], respectively (Fig. 1C). Methodology for the determination of Ns has been given earlier [5]. Contact angle relaxation data were analyzed according to the molecular-kinetic of wetting [9–11]. For molecularkinetic wetting, the main dissipation mechanism is the result of molecular displacements between substrate and wetting fluid at the three-phase boundary. Another valid theory is
2. Experimental 2.1. Materials Complete details of the poly(amic acid) precursor and preparation of polyimide samples are given in an earlier report [7]. Methanol (Fisher Scientific, HPLC grade), NMP (Fisher Scientific, ACS grade) and pyridine (Aldrich, 99.8%, anhydrous) were used as received.
Fig. 1. Modification scheme for native (A) PMDA-ODA polyimide by base hydrolysis (B) and subsequent ionization as pH of probe liquid is changed through the pKa (C). Shown only are the para isomers.
R.R. Thomas / Journal of Colloid and Interface Science 279 (2004) 515–522
Table 1 Properties of probe liquids Liquid
Surface tension (mN/m)
Viscosity (mPa s)
pKa
Methanol Pyridine NMP
22.6 38.0 40.0
0.55 0.59 1.65
15.3 5.23 –
based on hydrodynamic wetting theory [12]. In this case, viscous dissipation is rate-determining in contact angle relaxation. Molecular-kinetic theory was chosen for data analysis simply as it provided greater details in regards to the solid– liquid interface for the relatively nonviscous fluids chosen such as methanol, pyridine and NMP. In that regard, the viscosities of the probe liquids chosen were relatively small and did not differ significantly. Properties of the probe liquids studied are given in Table 1. The main difference between properties lies in their pKa values and surface tensions. These effects on contact angle relaxation are the subjects of the current study. Details regarding the molecular-kinetic theory of contact angle relaxation and previous work on PMDA-ODA polyimide are given in a prior publication [7]. A short summary will be given here for the sake of completeness. The basis for molecular-kinetic theory is the Eyring activated-rate theory for liquid transport proposed first by Blake and Haynes [9], γlv 0 (cos θf − cos θ ) ν = 2K λ sinh 2nkB T = (K + − K − )λ = Knet λ, (2) where ν is the wetting line velocity, K 0 is the quasiequilibrium frequency of molecular displacements, λ is the distance between two neighboring adsorption sites, n is the number of adsorption sites/unit area, kB is the Boltzmann constant, T is absolute temperature, θ is the contact angle at time t, θf is the contact angle at equilibrium, K + is the molecular displacement frequency in the wetting direction while K − is the molecular displacement frequency in the opposite direction and Knet is the net molecular displacement frequency (= 0 at equilibrium). Using the spherical cap approximation that is valid for the small (∼5 µL) volumes used in the current study, the droplet radius r can be described analytically, 1/3 3V sin3 θ , r= (3) π(2 − 3 cos θ + cos3 θ ) where V is the volume. Since the droplet volume is constant, ∂θ 3V ∂r (1 − cos θ )2 =ν =− (4) . ∂t ∂t π (2 − 3 cos θ + cos3 θ )4/3 The combination of Eqs. (2) and (4) leads finally to the relevant differential equation for contact angle relaxation, θf −cos θ) 2K 0 λ sinh γlv (cos ∂θ 2nkB T =− 3V 2 ∂t π (1 − cos θ ) × (2 − 3 cos θ + cos3 θ )4/3 .
(5)
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The numerical approach taken in the current study is that given by de Ruijter et al. [11]. The raw contact angle data versus time were subjected to linear interpolation between experimental time limits to discretize the data in the time domain necessary for solution of Eq. (5) by a fourth-order, time-adaptive Runge–Kutta algorithm [13]. The difference between theoretical and experimental data was performed by minimizing χ 2 using a downhill simplex algorithm [14,15]. Errors were estimated on the basis of a Monte Carlo simulation (100 cycles). Simulated contact angle relaxation data values were obtained by replacing 1/e of experimental data by normally distributed random numbers generated using experimental data as mean and a standard deviation of 1◦ . The experimental data to be replaced were chosen at random and varied between simulations. Values of χ 2 obtained in this fashion were acceptable given the experimental errors (±0.5◦ ). Earlier contact angle relaxation work on base hydrolyzed and neutralized PMDA-ODA polyimide surface showed some intriguing results when pH 2 and 11 liquids were used as probes [7]. K 0 and λ values were nearly invariant for different hydrolysis times using a pH 2 liquid while dramatic increases were observed with increasing hydrolysis time (increasing extent of modification) when the probe liquid was changed to pH 11. This was reflected also in activation free energies of wetting on a molar (G) or surface area basis (g). In summary, it does not appear that a pH 2 probe liquid can distinguish between an interaction with an imide, carboxylic acid or carboxylate anion. In contrast, the response of a pH 11 probe liquid is quite sensitive to the nature of the functional group at the interface. To extend the study of the interaction of different probe liquids with native and modified polyimide surface, the polar liquids methanol, pyridine and NMP were chosen. These liquids have nearly the same viscosities but differ in surface tensions and pKa values above (methanol) and below (pyridine) the surface pKa of the modified polyimide. Furthermore, NMP is a major constituent in the solvent system used for the poly(amic acid) precursors. In addition, the interaction of NMP with poly(amic acid) has been studied in detail in the bulk during curing studies [8]. A strong interaction was found that was claimed to be due to the formation of a complex between NMP and poly(amic acid). Contact angle relaxation data were gathered on native and polyimide surfaces that were modified for 10, 20, 30 and 60 min using 0.20 M NaOH followed by neutralization. Results of parametric fitting using Eq. (5) are given in Tables 2–4 for methanol, pyridine and NMP, respectively. Contact angle relaxation data for NMP on native and surfaces hydrolyzed for 10, 20 and 30 min are shown in Fig. 2. Shown in Fig. 3 are the K 0 values versus hydrolysis times for the liquid examined. Values of K 0 for all solvents studied are 3–4 orders of magnitude larger than when using pH-buffered water as a probe [7]. This is indicative of the much weaker molecular interaction between methanol, pyridine or NMP than with water. This fact could be anticipated
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Table 2 Contact angle relaxation data using methanol Hydrolysis time (min)
Ns (× 10−17 m−2 )
K0 (× 10−6 s−1 )
n (× 10−17 m−2 )
λ (Å)
G (kJ/mol)
g (mJ/m2 )
χ2 (mN2 /m2 )
0 10 20 30 60
0 3.48 ± 1 3.96 ± 0.8 3.83 ± 0.5 4.40 ± 0.3
11.20 ± 0.6 6.99 ± 0.02 6.00 ± 0.07 10.50 ± 0.01 13.70 ± 0.01
4.88 ± 0.5 3.06 ± 0.02 3.00 ± 0.07 5.17 ± 0.08 4.94 ± 0.1
14.3 ± 7 18.1 ± 9 18.2 ± 9 13.9 ± 7 14.2 ± 7
32.8 ± 0.1 33.9 ± 0.01 34.3 ± 0.03 32.9 ± 0.02 32.3 ± 0.01
26.5 ± 3 17.2 ± 0.1 17.1 ± 0.4 28.3 ± 0.5 26.5 ± 0.01
0.27 0.26 0.80 1.0 0.30
Table 3 Contact angle relaxation data using pyridine Hydrolysis time (min)
Ns (× 10−17 m−2 )
K0 (× 10−6 s−1 )
n (× 10−17 m−2 )
λ (Å)
G (kJ/mol)
g (mJ/m2 )
χ2 (mN2 /m2 )
0 10 20 30 60
0 3.48 ± 1 3.96 ± 0.8 3.83 ± 0.5 4.40 ± 0.3
9.47 ± 0.1 9.17 ± 0.2 9.06 ± 0.08 10.00 ± 0.001 23.3 ± 0.05
7.13 ± 0.2 7.42 ± 0.3 7.41 ± 0.1 7.25 ± 0.1 7.28 ± 0.3
11.8 ± 6 11.6 ± 6 11.6 ± 6 11.8 ± 6 11.7 ± 6
33.2 ± 0.04 33.3 ± 0.05 33.3 ± 0.02 33.0 ± 0.02 31.0 ± 0.02
39.3 ± 1 41.0 ± 2 40.9 ± 0.8 39.8 ± 0.6 37.4 ± 2
0.13 0.37 0.26 0.29 0.86
Table 4 Contact angle relaxation data using NMP Hydrolysis time (min)
Ns (× 10−17 m−2 )
K0 (× 10−6 s−1 )
n (× 10−17 m−2 )
λ (Å)
G (kJ/mol)
g (mJ/m2 )
χ2 (mN2 /m2 )
0 10 20 30 60
0 3.48 ± 1 3.96 ± 0.8 3.83 ± 0.5 4.40 ± 0.3
8.42 ± 0.1 3.33 ± 0.005 3.25 ± 0.02 3.25 ± 0.02 3.21 ± 0.01
6.51 ± 0.2 7.43 ± 0.02 7.49 ± 0.1 7.49 ± 0.1 7.28 ± 0.05
12.4 ± 6 11.6 ± 6 11.6 ± 6 11.6 ± 6 11.7 ± 6
33.5 ± 0.03 35.8 ± 0.003 35.8 ± 0.02 35.8 ± 0.02 35.9 ± 0.009
36.2 ± 1 44.1 ± 0.1 44.6 ± 0.6 44.6 ± 0.6 43.3 ± 0.3
0.71 0.32 0.52 0.49 0.15
based simply on a hydrogen bonding capability argument. The magnitude and trends of K 0 with modification extent for methanol or pyridine are similar and differ only slightly in magnitude. There is an initial decrease in K 0 follow by a large increase. The initial decrease in K 0 is easy to rationalize as it indicates a greater interaction of these solvents with the increasing number of hydrogen bonding capable carboxylic acids. This results in a lessened displacement frequency that is seen, vide infra, in activation free energy of wetting analyses. The increase in K 0 beyond the initial decrease is more difficult to explain. An even greater number of carboxylic acid groups have been created with the concomitant ability to hydrogen bond to methanol and pyridine, yet K 0 increases indicating a weaker interaction. The trends in K 0 with extent of modification require further comment. Fortunately, parametric fitting of the contact angle relaxation data according to (5) affords additional molecular detail. Fitting results in the calculation of an adsorption site distance, λ, and density, n. These values are related inversely and quadratically (λ = n−1/2 ). Shown in Fig. 4 are plots of λ as a function of surface modification extent. The values of λ are higher than expected based on close-packing of small solvent molecules on a polyimide surface. This is, again, not indicative of a strong interaction between probe liquid and polymer surface. Values for pH-buffered water exhibited a similarly high value [7]. In
an independent study, it was found that values of λ were comparable to calculated radii of gyration of solvent molecules during a contact angle relaxation study of hydrocarbons on PET and glass indicating rather close-packing of probe molecules on the surface [11]. Within experimental error, values of λ were comparable for the different probe liquids evaluated. A more informative representation is by plotting Ns against n. This is shown in Fig. 5. The data plotted in this fashion a more revealing. As expected Ns increases with hydrolysis time. Surprisingly, the adsorption site density, n, calculated from parametric fitting of contact angle relaxation data using Eq. (5) with methanol as a probe is a mirror image of Ns values. Using pyridine and NMP as probes results in higher calculated values for n that are nearly constant against extent of modification. The explanation postulated is due to the greater hydrogen bonding capabilities of pyridine and NMP with the polyimide surface compared to methanol. It is important to note that n represents the total adsorption site density. The implicit assumption of molecularkinetic theory is that the adsorption sites are distributed homogeneously. It does not account for any differences in interaction strength based on functional group identity. The value of Ns reflects only the number density of carboxylic acids created through base hydrolysis. Mathematically, n = λ−2 and, accounting for the contribution of Ns , n can be
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Fig. 2. Contact angle relaxation data on PMDA-ODA polyimide surfaces based hydrolyzed for 0 (A), 10 (B), 20 (C) and 30 (D) min followed by neutralization using NMP as the probe liquid. The solid line is a theoretical fit of the data using Eq. (5).
Fig. 3. Variation of K 0 with hydrolysis time for PMDA-ODA polyimide. Shown are data for methanol (2), pyridine (") and NMP (Q).
Fig. 5. Variation of Ns and n with hydrolysis time for PMDA-ODA polyimide. Shown are values of Ns (2), and n for methanol ("), pyridine (Q) and NMP (a).
approximated as −2 Ns + m i λi n≈ m+1
Fig. 4. Variation of λ with hydrolysis time for PMDA-ODA polyimide. Shown are data for methanol (2), pyridine (") and NMP (Q).
(6)
using simple averaging, where i is summation index over all adsorption sites, m. This implies a linear shift of the ordinate in Fig. 5 to higher site densities if interactions between functional groups present on the modified surface and probe liquid are identical or comparable. Such a shift is observed for pyridine and NMP but not for methanol. One point regarding the use of Eq. (5) needs to be discussed. The value of sinh(x) approximates x for small values of x and, as a result, K 0 and λ may not be fully independent. Not given in the current manuscript but stated in a study pub-
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Fig. 6. Values of λ as a function of K 0 using as probe liquid methanol (A), pyridine (B) and NMP (C).
lished previously [7], fitting of (5) was done using two adjustable parameters: a = 2K 0 λ and b = γlv /(2nkB T ) with λ being given as n−1/2 and allowing for derivation of the value of K 0 . The downhill simplex algorithm used to determine a and b allowed the variables to adjust freely until a minimum χ 2 was found between experimental and theoretical data. Ultimately, the variables a and b are a simple product at small values of x such that sinh(x) ≈ x. That being the case, there is no way to “decouple” the values and a correlation (approaching −1 logically) should be observable. Plots of λ as a function of K 0 are shown in Fig. 6. Within experimental error and for all probe liquids used, λ was invariant as a function of K 0 implying a very low correlation between the two values. Note that the different points correspond to different hydrolysis times for each probe liquid; however, the hydrolysis times used for each probe liquid were identical. The invariance of λ with K 0 suggests that the distance between adsorption sites remains the same as a function of extent of hydrolysis while the molecular displacement frequency only is affected. The results of parametric fitting of contact angle relaxation data using (5) can be used subsequently to evaluate activation free energies of wetting on a molar, G, and surface area, g, basis [11], hK 0 , G = −NA kB T ln kB T nG g = (7) , NA where NA is Avogadro’s number, h is Planck’s constant and the other variables defined previously. The results of the calculation for each probe liquid are shown textually in Tables 2–4 and graphically in Figs. 7 and 8 for G and g, respectively. For both methanol and pyridine, G values increase with increasing extent of hydrolysis and then decline. Clearly, this is indicative of a lessened interaction with increasing number of carboxylic acid groups or, conversely, with decreasing number of imide groups. The molar activation free energy of wetting for NMP exhibits an initial increase with increasing hydrolysis time and then remains
Fig. 7. Molar activation free energy of wetting for methanol (2), pyridine (") and NMP (Q) as a function of hydrolysis time for PMDA-ODA polyimide.
Fig. 8. Surface activation free energy of wetting for methanol (2), pyridine (") and NMP (Q) as a function of hydrolysis time for PMDA-ODA polyimide.
constant after. The free energy difference between NMP and the other solvents employed ≈ 2–4 kJ/mol when each is at its maximum to 4–5 kJ/mol as an absolute greatest difference under the current experimental conditions. On a unit area basis, the activation free energy trends are a little different. The free energy for methanol drops initially with increasing hydrolysis time, then returns and remains constant. Pyridine and NMP are comparable with the exception that NMP increases initially with increasing hydrolysis extent while pyridine does the opposite. In previous work with pH 2- and pH 11-buffered probes, G and g were found to be constant for pH 2 and found to decrease substantially with increasing hydrolysis times for pH 11. According to (7), the main difference between G and g lies in the values of the adsorption site density, n. A discussion of the combined results is now warranted. If the adsorption site density, n, is constant between experiments as in the present case and the interactions are equal in strength, then the rate of contact angle relaxation, ∂θ/∂t can be approximated as ∂θ ≈ γlv (cos θf − cos θ ) (8) ∂t according to (5). Since the differences in contact angle and the change over the experimental lifetime is small, cos θf − cos θ can be approximated linearly. The largest factor governing the relaxation rate is γlv . Given in Table 1 are γlv values for the liquids used. The probe liquid NMP has the
R.R. Thomas / Journal of Colloid and Interface Science 279 (2004) 515–522
largest γlv ; therefore, it would be expected to exhibit the largest ∂θ/∂t if everything else (specifically, interactions) is equal. Experimentally, the relaxation rate for NMP is slower than both pyridine and methanol reflecting substantial differences in interaction potentials. The molecular-kinetic theory contains two terms relevant to the adsorption site density; namely, n and λ, that are, vide supra, related. This theory assumes a homogeneous distribution of the number and identity of adsorption sites. This may not be valid entirely in the present case. The chemical modification scheme involves a substantial change in the identity of chemical species; for example, imide, amide and carboxylic acid. Each species will have a particular interaction energy with another functional group. Consider, for example, the capacity for hydrogen bonding. The result of only a small interaction of methanol compared to pyridine and NMP with the modified polyimide surface appears a little unusual a first glance. Since carboxylic acids and alcohols are reactive in reactions such as esterification, one would assume a substantial interaction between the two. In unpublished results, a number of attempts were made to further modify the initial hydrolyzed polyimide surface by esterification with alcohols under standard organic chemistry conditions. This included attempting esterifications in pure alcohol as both reagent and solvent at reflux temperatures. All attempts were unsuccessful with no conversion to the ester noted. This result was perplexing also. Consider for example, the pKa of a “model” PMDA-ODA polyimide unit, N -phenylphthalamic acid was measured to be 3.80 [16]. From the contact angle titration method (contact angle versus pH) [17], the pKa of the hydrolyzed PMDA-ODA polyimide (in essence, poly(amic acid)) was estimated to be ≈7 [5]. The difference between bulk and surface lies in the difference in free energy between bulk and surface ionization of functional groups (G = RT[pKa (bulk) − pKa (surface)]) [18] that amounts to a free energy loss ≈ 7.9 kJ/mol at room temperature to ionize a carboxylic acid at a surface compared to the bulk. Stated simply, this free energy loss can account for the lack of reaction between methanol and the modified polyimide surface as well as a lessened interaction during contact angle relaxation studies compared to the other fluids studied. Note also, that the relatively large pKa of bulk methanol (15.3) versus the surface pKa of the modified polyimide does not favor an interaction. The data do appear to show more favorable interactions with pyridine and NMP with NMP showing a slightly larger interaction depending on whether G or g is more indicative. It is important that the differences do not even amount to the free energy of a single hydrogen bond estimated at ∼12–44 kJ/mol [19,20]. Here also, it is important to note the differences observed between bulk and interfacial chemistry. During curing studies of poly(amic acid)s to polyimides [21], it was observed that the addition of amines accelerated the rate of reaction; presumably, by the formation of a quaternary amine salt through the reaction of amic acid with amine. The bulk pKa values of poly(amic acid)
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would predict the formation of this salt in a typical acid– base reaction. Consider this same reaction in light of the estimated surface pKa of the modified polyimide as ≈ 7. In this case, the carboxylic acid is actually a better base than pyridine with a bulk pKa estimated to be ≈ 5.23 [16]. Thermodynamics would not predict a strong of an interaction as that observed during the bulk reaction of an amine with an amic acid. The results of another curing study of polyimides from poly(amic acid)s lends some insight into the nature of the interaction between NMP and the poly(amic acid). It was found that two distinct NMP–poly(amic acid) complexes were formed during the curing process with decomplexation enthalpies of ∼20 and 55 kJ/mol for the first and second complexes. This is a clear reflection of the hydrogen bonding interaction between NMP and the poly(amic acid) and may well account for the differences seen with this probe liquid compared to methanol and pyridine.
4. Conclusions Contact angle relaxation of base hydrolyzed PMDAODA polyimide surfaces was examined using polar liquids such as methanol, pyridine and NMP. The data were fitted parametrically according to the molecular-kinetic theory of wetting. Parameters such as quasi-equilibrium wetting frequencies, K 0 , and adsorption site densities, λ, were calculated as a function of extent (base hydrolysis time) of modification of the polyimide surface. Somewhat surprisingly, the interaction with methanol appeared to be relatively weak when compared to pyridine and NMP. This can be explained by a comparison of the bulk pKa of poly(amic acid) estimated to be ≈ 5 compared to the measured surface pKa ≈ 7. This would explain also that lack of reactivity in attempts to esterify the modified polyimide surface with a variety of alcohols. Pyridine and NMP showed stronger interactions with the modified polyimide surface. Typically, the interaction of pyridine with an organic acid should be relatively strong unlike that measured here. Again, this may be due to the elevated pKa of the modified polyimide surface compared to bulk. The probe NMP showed what appeared to be the strongest interaction with the modified polyimide surface and is reminiscent of the observation of complex formation between NMP and poly(amic acid) in the bulk. Molecularkinetic wetting theory was derived based on the assumption of homogeneity in the identity and surface density of adsorption sites. This assumption is likely not to be valid entirely in the present case. A version of this theory modified to account for heterogeneity would be valuable. References [1] A.W. Adamson, Physical Chemistry of Surfaces, fifth ed., Wiley, New York, 1990, p. 385. [2] T.D. Blake, K.J. Ruschak, Nature 282 (1979) 489. [3] K.-W. Lee, S.P. Kowalczyk, J.M. Shaw, Macromolecules 23 (1990) 2097.
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[14] W.H. Press, B.P. Flannery, S.A. Teukolsky, W.T. Vetterling, Numerical Recipes (The Art of Scientific Computing), Cambridge Univ. Press, New York, 1986, chap. 10. [15] J.C. Sprott, Numerical Recipes: Routines and Examples in Basic, Oxford Univ. Press, Oxford, 1998, chap. 10. [16] M.L. Bender, Y.-L. Chow, F. Chloupek, J. Am. Chem. Soc. 80 (1958) 5380. [17] S.R. Holmes-Farley, R.H. Reamey, T.J. McCarthy, J. Deutch, G.M. Whitesides, Langmuir 1 (1985) 725. [18] C.C. Wamser, M.I. Gilbert, Langmuir 8 (1992) 1608. [19] M. Davies, in: D. Hadži (Ed.), Hydrogen Bonding, Pergamon, New York, 1959, p. 393. [20] S. Wu, Polymer Interface and Adhesion, Dekker, New York, 1982, p. 29. [21] J.A. Kreuz, A.L. Endrey, F.P. Gay, C.E. Sroog, J. Polym. Sci. Part A-1 4 (1966) 2607.
Wetting kinetics of modified polyimide surfaces: interactions with polar solvents Richard R. Thomas ∗ OMNOVA Solutions, 2990 Gilchrist Road, Akron, OH 44305, USA Received 23 January 2004; accepted 30 June 2004 Available online 28 July 2004
Abstract Contact angle relaxation studies were performed on a base hydrolyzed PMDA-ODA polyimide surface using methanol, pyridine and 1-methyl-2-pyrrolidinone (NMP) as probe liquids. The results were fitted parametrically to the molecular-kinetic theory to obtain the relevant molecular parameters that govern wetting rates. The probe liquid NMP appeared to have the greatest interaction of the three solvents studied with the modified polyimide surface. The differences in wetting rates are explained to result from the hydrogen bonding capability of the probe liquids with the modified polyimide surface and due to the difference between bulk and surface pKa of the modified polyimide. 2004 Elsevier Inc. All rights reserved. Keywords: Polyimide; Wetting; Kinetics; Contact angle relaxation
1. Introduction Polyimides are used widely in the electronics industry as interlayer dielectric materials. They are often the materials of choice in such applications due to excellent chemical, thermal and mechanical properties. The use of polyimides as interlayer materials implies their role as a component of a composite material. As such, it is often necessary to bind adhesively other materials to its surface. One of the most popular methods of attaching another material to a polyimide surface is through the use of spin coating. Typically, a polymeric precursor is dissolved in a suitable solvent that is then used to spin coat the polyimide surface. After a curing step, the composite material is formed. A necessary prerequisite of a coating is that it wet the surface to which it will be adhered. This factor introduces a temporal component to the wetting process and, therefore, to the successful application of a coating. The temporal component is manifested to a great extent in shear at the coating/substrate interface. Shear is induced by rapid creation of incipient coating sur* Fax: +1-330-794-6375.
E-mail address: [email protected]. 0021-9797/$ – see front matter 2004 Elsevier Inc. All rights reserved. doi:10.1016/j.jcis.2004.06.100
face either by motion of the coating relative to the substrate or motion of the substrate relative to the coating. The process of wetting is described often by a contact angle of a liquid on a solid surface. After a liquid is applied to a surface, there is a finite amount of time required for the liquid to assume its equilibrium contact angle, θ . The equilibrium contact angle follows the well known Young equation [1] γsl cos θ = γsv − γsl ,
(1)
where the variable γ refers to interfacial tension of the solid– liquid (sl), solid–vapor (sv) and solid–liquid interfaces (sl). Even for low viscosity fluids, the relaxation of contact angle from its initial (high) value to an equilibrium (low) value can take seconds. Spin coating represents a particularly high shear process that includes a radial spatial component. If the contact angle relaxation of the newly deposited coating to equilibrium predicted by (1) is slow compared to the speed at which the coating is forced to spread over the substrate surface, then defects in the coating can occur. These can take the form of air entrainment [2], dewetted or nonwetted areas and/or result in a nonconformal coating. In either case, these defects can be catastrophic. Therefore, it is important
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to understand contact angle relaxation and its effect on the coating process under a given set of conditions. The property robustness displayed by polyimides translates into coating and adhesion problems at the film surface. For example, spin coating of the PMDA precursor poly(amic acid) on a fully cured PMDA-ODA film does not result in a good adhesive bond without some surface modification. A number of methodologies have been demonstrated to modify the surface of a polyimide film to accept a coating. One of the more popular and easiest to execute is base hydrolysis [3,4]. In essence, base hydrolysis is the reverse of the poly(amic acid) to polyimide cure cycle used, with the exception that the modification is confined largely to just the outermost surface of the film. Base hydrolysis aids wetting and adhesion due to at least one of the following: (i) creation of more wettable carboxylic acid groups and/or (ii) introduction of more reactive functional groups capable of transfacial reaction with components of the coating to be applied. Based hydrolysis of polyimide has been studied by a number of researchers and reversion of polyimide to poly(amic acid) has indeed been confirmed by a number of techniques [3,4]. The creation of carboxylic groups on the polyimide surface creates a higher free energy surface that is more wettable by liquids such as water. Furthermore, the pKa of the carboxylic acid groups is evidenced in a large change in wettability as the pH of a wetting probe is increased beyond the surface pKa [4]. In addition, a free energy calculation can be used to quantify the number of incipient carboxylic acid groups on the modified surface [5]. Using this methodology, the kinetics of base hydrolysis of a polyimide surface have been proposed [6]. In earlier work, a contact angle relaxation study was performed on a modified polyimide surface as a function of base hydrolysis conditions [7]. This prior study used pH 2 and 11 buffered water as a probe. Very substantial differences were noted between the two liquids and attributable to the presence of ionizable carboxylic acid groups. The present work is an extension using polar organic liquids including 1-methyl-2-pyrrolidinone (NMP) as a probe. 1-methyl-2-pyrrolidinone is a major constituent of the solvents used for poly(amic acid) solutions. Moreover, NMP is known to interact very strongly with the precursor poly(amic acid) [8].
2.2. Instrumentation Contact angle relaxation data were acquired using an FTÅ200 contact angle goniometer equipped with a CCD camera, frame grabber and image analysis software from First Ten Ångstroms. Drop volumes in the range of 3–5 µL were used for measurements. In this volume range, dynamic contact angle data were reproducible.
3. Results and discussion In a previous study, contact angle relaxation kinetics were examined on a polyimide surface modified by base hydrolysis followed by neutralization using acetic acid [7]. This scheme is shown in Fig. 1. The polyimide (PMDA-ODA) studied was the condensation product of pyromellitic dianhydride and 4,4 -oxydianiline. Details regarding the experimental and data analysis methodology have been published earlier [7]. Contact angle relaxation data were collected on a native polyimide surface and ones that had been base hydrolyzed for periods of time followed by neutralization. Comparing theory and experimental contact angles as a function of pH, the surface density of incipient carboxylic acid groups, Ns , was determined. The pH of the probe liquid was chosen to be 2 and 11 as these values were below and above the estimated surface pKa (≈ 7) of the hydrolyzed polyimide [4], respectively (Fig. 1C). Methodology for the determination of Ns has been given earlier [5]. Contact angle relaxation data were analyzed according to the molecular-kinetic of wetting [9–11]. For molecularkinetic wetting, the main dissipation mechanism is the result of molecular displacements between substrate and wetting fluid at the three-phase boundary. Another valid theory is
2. Experimental 2.1. Materials Complete details of the poly(amic acid) precursor and preparation of polyimide samples are given in an earlier report [7]. Methanol (Fisher Scientific, HPLC grade), NMP (Fisher Scientific, ACS grade) and pyridine (Aldrich, 99.8%, anhydrous) were used as received.
Fig. 1. Modification scheme for native (A) PMDA-ODA polyimide by base hydrolysis (B) and subsequent ionization as pH of probe liquid is changed through the pKa (C). Shown only are the para isomers.
R.R. Thomas / Journal of Colloid and Interface Science 279 (2004) 515–522
Table 1 Properties of probe liquids Liquid
Surface tension (mN/m)
Viscosity (mPa s)
pKa
Methanol Pyridine NMP
22.6 38.0 40.0
0.55 0.59 1.65
15.3 5.23 –
based on hydrodynamic wetting theory [12]. In this case, viscous dissipation is rate-determining in contact angle relaxation. Molecular-kinetic theory was chosen for data analysis simply as it provided greater details in regards to the solid– liquid interface for the relatively nonviscous fluids chosen such as methanol, pyridine and NMP. In that regard, the viscosities of the probe liquids chosen were relatively small and did not differ significantly. Properties of the probe liquids studied are given in Table 1. The main difference between properties lies in their pKa values and surface tensions. These effects on contact angle relaxation are the subjects of the current study. Details regarding the molecular-kinetic theory of contact angle relaxation and previous work on PMDA-ODA polyimide are given in a prior publication [7]. A short summary will be given here for the sake of completeness. The basis for molecular-kinetic theory is the Eyring activated-rate theory for liquid transport proposed first by Blake and Haynes [9], γlv 0 (cos θf − cos θ ) ν = 2K λ sinh 2nkB T = (K + − K − )λ = Knet λ, (2) where ν is the wetting line velocity, K 0 is the quasiequilibrium frequency of molecular displacements, λ is the distance between two neighboring adsorption sites, n is the number of adsorption sites/unit area, kB is the Boltzmann constant, T is absolute temperature, θ is the contact angle at time t, θf is the contact angle at equilibrium, K + is the molecular displacement frequency in the wetting direction while K − is the molecular displacement frequency in the opposite direction and Knet is the net molecular displacement frequency (= 0 at equilibrium). Using the spherical cap approximation that is valid for the small (∼5 µL) volumes used in the current study, the droplet radius r can be described analytically, 1/3 3V sin3 θ , r= (3) π(2 − 3 cos θ + cos3 θ ) where V is the volume. Since the droplet volume is constant, ∂θ 3V ∂r (1 − cos θ )2 =ν =− (4) . ∂t ∂t π (2 − 3 cos θ + cos3 θ )4/3 The combination of Eqs. (2) and (4) leads finally to the relevant differential equation for contact angle relaxation, θf −cos θ) 2K 0 λ sinh γlv (cos ∂θ 2nkB T =− 3V 2 ∂t π (1 − cos θ ) × (2 − 3 cos θ + cos3 θ )4/3 .
(5)
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The numerical approach taken in the current study is that given by de Ruijter et al. [11]. The raw contact angle data versus time were subjected to linear interpolation between experimental time limits to discretize the data in the time domain necessary for solution of Eq. (5) by a fourth-order, time-adaptive Runge–Kutta algorithm [13]. The difference between theoretical and experimental data was performed by minimizing χ 2 using a downhill simplex algorithm [14,15]. Errors were estimated on the basis of a Monte Carlo simulation (100 cycles). Simulated contact angle relaxation data values were obtained by replacing 1/e of experimental data by normally distributed random numbers generated using experimental data as mean and a standard deviation of 1◦ . The experimental data to be replaced were chosen at random and varied between simulations. Values of χ 2 obtained in this fashion were acceptable given the experimental errors (±0.5◦ ). Earlier contact angle relaxation work on base hydrolyzed and neutralized PMDA-ODA polyimide surface showed some intriguing results when pH 2 and 11 liquids were used as probes [7]. K 0 and λ values were nearly invariant for different hydrolysis times using a pH 2 liquid while dramatic increases were observed with increasing hydrolysis time (increasing extent of modification) when the probe liquid was changed to pH 11. This was reflected also in activation free energies of wetting on a molar (G) or surface area basis (g). In summary, it does not appear that a pH 2 probe liquid can distinguish between an interaction with an imide, carboxylic acid or carboxylate anion. In contrast, the response of a pH 11 probe liquid is quite sensitive to the nature of the functional group at the interface. To extend the study of the interaction of different probe liquids with native and modified polyimide surface, the polar liquids methanol, pyridine and NMP were chosen. These liquids have nearly the same viscosities but differ in surface tensions and pKa values above (methanol) and below (pyridine) the surface pKa of the modified polyimide. Furthermore, NMP is a major constituent in the solvent system used for the poly(amic acid) precursors. In addition, the interaction of NMP with poly(amic acid) has been studied in detail in the bulk during curing studies [8]. A strong interaction was found that was claimed to be due to the formation of a complex between NMP and poly(amic acid). Contact angle relaxation data were gathered on native and polyimide surfaces that were modified for 10, 20, 30 and 60 min using 0.20 M NaOH followed by neutralization. Results of parametric fitting using Eq. (5) are given in Tables 2–4 for methanol, pyridine and NMP, respectively. Contact angle relaxation data for NMP on native and surfaces hydrolyzed for 10, 20 and 30 min are shown in Fig. 2. Shown in Fig. 3 are the K 0 values versus hydrolysis times for the liquid examined. Values of K 0 for all solvents studied are 3–4 orders of magnitude larger than when using pH-buffered water as a probe [7]. This is indicative of the much weaker molecular interaction between methanol, pyridine or NMP than with water. This fact could be anticipated
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Table 2 Contact angle relaxation data using methanol Hydrolysis time (min)
Ns (× 10−17 m−2 )
K0 (× 10−6 s−1 )
n (× 10−17 m−2 )
λ (Å)
G (kJ/mol)
g (mJ/m2 )
χ2 (mN2 /m2 )
0 10 20 30 60
0 3.48 ± 1 3.96 ± 0.8 3.83 ± 0.5 4.40 ± 0.3
11.20 ± 0.6 6.99 ± 0.02 6.00 ± 0.07 10.50 ± 0.01 13.70 ± 0.01
4.88 ± 0.5 3.06 ± 0.02 3.00 ± 0.07 5.17 ± 0.08 4.94 ± 0.1
14.3 ± 7 18.1 ± 9 18.2 ± 9 13.9 ± 7 14.2 ± 7
32.8 ± 0.1 33.9 ± 0.01 34.3 ± 0.03 32.9 ± 0.02 32.3 ± 0.01
26.5 ± 3 17.2 ± 0.1 17.1 ± 0.4 28.3 ± 0.5 26.5 ± 0.01
0.27 0.26 0.80 1.0 0.30
Table 3 Contact angle relaxation data using pyridine Hydrolysis time (min)
Ns (× 10−17 m−2 )
K0 (× 10−6 s−1 )
n (× 10−17 m−2 )
λ (Å)
G (kJ/mol)
g (mJ/m2 )
χ2 (mN2 /m2 )
0 10 20 30 60
0 3.48 ± 1 3.96 ± 0.8 3.83 ± 0.5 4.40 ± 0.3
9.47 ± 0.1 9.17 ± 0.2 9.06 ± 0.08 10.00 ± 0.001 23.3 ± 0.05
7.13 ± 0.2 7.42 ± 0.3 7.41 ± 0.1 7.25 ± 0.1 7.28 ± 0.3
11.8 ± 6 11.6 ± 6 11.6 ± 6 11.8 ± 6 11.7 ± 6
33.2 ± 0.04 33.3 ± 0.05 33.3 ± 0.02 33.0 ± 0.02 31.0 ± 0.02
39.3 ± 1 41.0 ± 2 40.9 ± 0.8 39.8 ± 0.6 37.4 ± 2
0.13 0.37 0.26 0.29 0.86
Table 4 Contact angle relaxation data using NMP Hydrolysis time (min)
Ns (× 10−17 m−2 )
K0 (× 10−6 s−1 )
n (× 10−17 m−2 )
λ (Å)
G (kJ/mol)
g (mJ/m2 )
χ2 (mN2 /m2 )
0 10 20 30 60
0 3.48 ± 1 3.96 ± 0.8 3.83 ± 0.5 4.40 ± 0.3
8.42 ± 0.1 3.33 ± 0.005 3.25 ± 0.02 3.25 ± 0.02 3.21 ± 0.01
6.51 ± 0.2 7.43 ± 0.02 7.49 ± 0.1 7.49 ± 0.1 7.28 ± 0.05
12.4 ± 6 11.6 ± 6 11.6 ± 6 11.6 ± 6 11.7 ± 6
33.5 ± 0.03 35.8 ± 0.003 35.8 ± 0.02 35.8 ± 0.02 35.9 ± 0.009
36.2 ± 1 44.1 ± 0.1 44.6 ± 0.6 44.6 ± 0.6 43.3 ± 0.3
0.71 0.32 0.52 0.49 0.15
based simply on a hydrogen bonding capability argument. The magnitude and trends of K 0 with modification extent for methanol or pyridine are similar and differ only slightly in magnitude. There is an initial decrease in K 0 follow by a large increase. The initial decrease in K 0 is easy to rationalize as it indicates a greater interaction of these solvents with the increasing number of hydrogen bonding capable carboxylic acids. This results in a lessened displacement frequency that is seen, vide infra, in activation free energy of wetting analyses. The increase in K 0 beyond the initial decrease is more difficult to explain. An even greater number of carboxylic acid groups have been created with the concomitant ability to hydrogen bond to methanol and pyridine, yet K 0 increases indicating a weaker interaction. The trends in K 0 with extent of modification require further comment. Fortunately, parametric fitting of the contact angle relaxation data according to (5) affords additional molecular detail. Fitting results in the calculation of an adsorption site distance, λ, and density, n. These values are related inversely and quadratically (λ = n−1/2 ). Shown in Fig. 4 are plots of λ as a function of surface modification extent. The values of λ are higher than expected based on close-packing of small solvent molecules on a polyimide surface. This is, again, not indicative of a strong interaction between probe liquid and polymer surface. Values for pH-buffered water exhibited a similarly high value [7]. In
an independent study, it was found that values of λ were comparable to calculated radii of gyration of solvent molecules during a contact angle relaxation study of hydrocarbons on PET and glass indicating rather close-packing of probe molecules on the surface [11]. Within experimental error, values of λ were comparable for the different probe liquids evaluated. A more informative representation is by plotting Ns against n. This is shown in Fig. 5. The data plotted in this fashion a more revealing. As expected Ns increases with hydrolysis time. Surprisingly, the adsorption site density, n, calculated from parametric fitting of contact angle relaxation data using Eq. (5) with methanol as a probe is a mirror image of Ns values. Using pyridine and NMP as probes results in higher calculated values for n that are nearly constant against extent of modification. The explanation postulated is due to the greater hydrogen bonding capabilities of pyridine and NMP with the polyimide surface compared to methanol. It is important to note that n represents the total adsorption site density. The implicit assumption of molecularkinetic theory is that the adsorption sites are distributed homogeneously. It does not account for any differences in interaction strength based on functional group identity. The value of Ns reflects only the number density of carboxylic acids created through base hydrolysis. Mathematically, n = λ−2 and, accounting for the contribution of Ns , n can be
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Fig. 2. Contact angle relaxation data on PMDA-ODA polyimide surfaces based hydrolyzed for 0 (A), 10 (B), 20 (C) and 30 (D) min followed by neutralization using NMP as the probe liquid. The solid line is a theoretical fit of the data using Eq. (5).
Fig. 3. Variation of K 0 with hydrolysis time for PMDA-ODA polyimide. Shown are data for methanol (2), pyridine (") and NMP (Q).
Fig. 5. Variation of Ns and n with hydrolysis time for PMDA-ODA polyimide. Shown are values of Ns (2), and n for methanol ("), pyridine (Q) and NMP (a).
approximated as −2 Ns + m i λi n≈ m+1
Fig. 4. Variation of λ with hydrolysis time for PMDA-ODA polyimide. Shown are data for methanol (2), pyridine (") and NMP (Q).
(6)
using simple averaging, where i is summation index over all adsorption sites, m. This implies a linear shift of the ordinate in Fig. 5 to higher site densities if interactions between functional groups present on the modified surface and probe liquid are identical or comparable. Such a shift is observed for pyridine and NMP but not for methanol. One point regarding the use of Eq. (5) needs to be discussed. The value of sinh(x) approximates x for small values of x and, as a result, K 0 and λ may not be fully independent. Not given in the current manuscript but stated in a study pub-
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Fig. 6. Values of λ as a function of K 0 using as probe liquid methanol (A), pyridine (B) and NMP (C).
lished previously [7], fitting of (5) was done using two adjustable parameters: a = 2K 0 λ and b = γlv /(2nkB T ) with λ being given as n−1/2 and allowing for derivation of the value of K 0 . The downhill simplex algorithm used to determine a and b allowed the variables to adjust freely until a minimum χ 2 was found between experimental and theoretical data. Ultimately, the variables a and b are a simple product at small values of x such that sinh(x) ≈ x. That being the case, there is no way to “decouple” the values and a correlation (approaching −1 logically) should be observable. Plots of λ as a function of K 0 are shown in Fig. 6. Within experimental error and for all probe liquids used, λ was invariant as a function of K 0 implying a very low correlation between the two values. Note that the different points correspond to different hydrolysis times for each probe liquid; however, the hydrolysis times used for each probe liquid were identical. The invariance of λ with K 0 suggests that the distance between adsorption sites remains the same as a function of extent of hydrolysis while the molecular displacement frequency only is affected. The results of parametric fitting of contact angle relaxation data using (5) can be used subsequently to evaluate activation free energies of wetting on a molar, G, and surface area, g, basis [11], hK 0 , G = −NA kB T ln kB T nG g = (7) , NA where NA is Avogadro’s number, h is Planck’s constant and the other variables defined previously. The results of the calculation for each probe liquid are shown textually in Tables 2–4 and graphically in Figs. 7 and 8 for G and g, respectively. For both methanol and pyridine, G values increase with increasing extent of hydrolysis and then decline. Clearly, this is indicative of a lessened interaction with increasing number of carboxylic acid groups or, conversely, with decreasing number of imide groups. The molar activation free energy of wetting for NMP exhibits an initial increase with increasing hydrolysis time and then remains
Fig. 7. Molar activation free energy of wetting for methanol (2), pyridine (") and NMP (Q) as a function of hydrolysis time for PMDA-ODA polyimide.
Fig. 8. Surface activation free energy of wetting for methanol (2), pyridine (") and NMP (Q) as a function of hydrolysis time for PMDA-ODA polyimide.
constant after. The free energy difference between NMP and the other solvents employed ≈ 2–4 kJ/mol when each is at its maximum to 4–5 kJ/mol as an absolute greatest difference under the current experimental conditions. On a unit area basis, the activation free energy trends are a little different. The free energy for methanol drops initially with increasing hydrolysis time, then returns and remains constant. Pyridine and NMP are comparable with the exception that NMP increases initially with increasing hydrolysis extent while pyridine does the opposite. In previous work with pH 2- and pH 11-buffered probes, G and g were found to be constant for pH 2 and found to decrease substantially with increasing hydrolysis times for pH 11. According to (7), the main difference between G and g lies in the values of the adsorption site density, n. A discussion of the combined results is now warranted. If the adsorption site density, n, is constant between experiments as in the present case and the interactions are equal in strength, then the rate of contact angle relaxation, ∂θ/∂t can be approximated as ∂θ ≈ γlv (cos θf − cos θ ) (8) ∂t according to (5). Since the differences in contact angle and the change over the experimental lifetime is small, cos θf − cos θ can be approximated linearly. The largest factor governing the relaxation rate is γlv . Given in Table 1 are γlv values for the liquids used. The probe liquid NMP has the
R.R. Thomas / Journal of Colloid and Interface Science 279 (2004) 515–522
largest γlv ; therefore, it would be expected to exhibit the largest ∂θ/∂t if everything else (specifically, interactions) is equal. Experimentally, the relaxation rate for NMP is slower than both pyridine and methanol reflecting substantial differences in interaction potentials. The molecular-kinetic theory contains two terms relevant to the adsorption site density; namely, n and λ, that are, vide supra, related. This theory assumes a homogeneous distribution of the number and identity of adsorption sites. This may not be valid entirely in the present case. The chemical modification scheme involves a substantial change in the identity of chemical species; for example, imide, amide and carboxylic acid. Each species will have a particular interaction energy with another functional group. Consider, for example, the capacity for hydrogen bonding. The result of only a small interaction of methanol compared to pyridine and NMP with the modified polyimide surface appears a little unusual a first glance. Since carboxylic acids and alcohols are reactive in reactions such as esterification, one would assume a substantial interaction between the two. In unpublished results, a number of attempts were made to further modify the initial hydrolyzed polyimide surface by esterification with alcohols under standard organic chemistry conditions. This included attempting esterifications in pure alcohol as both reagent and solvent at reflux temperatures. All attempts were unsuccessful with no conversion to the ester noted. This result was perplexing also. Consider for example, the pKa of a “model” PMDA-ODA polyimide unit, N -phenylphthalamic acid was measured to be 3.80 [16]. From the contact angle titration method (contact angle versus pH) [17], the pKa of the hydrolyzed PMDA-ODA polyimide (in essence, poly(amic acid)) was estimated to be ≈7 [5]. The difference between bulk and surface lies in the difference in free energy between bulk and surface ionization of functional groups (G = RT[pKa (bulk) − pKa (surface)]) [18] that amounts to a free energy loss ≈ 7.9 kJ/mol at room temperature to ionize a carboxylic acid at a surface compared to the bulk. Stated simply, this free energy loss can account for the lack of reaction between methanol and the modified polyimide surface as well as a lessened interaction during contact angle relaxation studies compared to the other fluids studied. Note also, that the relatively large pKa of bulk methanol (15.3) versus the surface pKa of the modified polyimide does not favor an interaction. The data do appear to show more favorable interactions with pyridine and NMP with NMP showing a slightly larger interaction depending on whether G or g is more indicative. It is important that the differences do not even amount to the free energy of a single hydrogen bond estimated at ∼12–44 kJ/mol [19,20]. Here also, it is important to note the differences observed between bulk and interfacial chemistry. During curing studies of poly(amic acid)s to polyimides [21], it was observed that the addition of amines accelerated the rate of reaction; presumably, by the formation of a quaternary amine salt through the reaction of amic acid with amine. The bulk pKa values of poly(amic acid)
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would predict the formation of this salt in a typical acid– base reaction. Consider this same reaction in light of the estimated surface pKa of the modified polyimide as ≈ 7. In this case, the carboxylic acid is actually a better base than pyridine with a bulk pKa estimated to be ≈ 5.23 [16]. Thermodynamics would not predict a strong of an interaction as that observed during the bulk reaction of an amine with an amic acid. The results of another curing study of polyimides from poly(amic acid)s lends some insight into the nature of the interaction between NMP and the poly(amic acid). It was found that two distinct NMP–poly(amic acid) complexes were formed during the curing process with decomplexation enthalpies of ∼20 and 55 kJ/mol for the first and second complexes. This is a clear reflection of the hydrogen bonding interaction between NMP and the poly(amic acid) and may well account for the differences seen with this probe liquid compared to methanol and pyridine.
4. Conclusions Contact angle relaxation of base hydrolyzed PMDAODA polyimide surfaces was examined using polar liquids such as methanol, pyridine and NMP. The data were fitted parametrically according to the molecular-kinetic theory of wetting. Parameters such as quasi-equilibrium wetting frequencies, K 0 , and adsorption site densities, λ, were calculated as a function of extent (base hydrolysis time) of modification of the polyimide surface. Somewhat surprisingly, the interaction with methanol appeared to be relatively weak when compared to pyridine and NMP. This can be explained by a comparison of the bulk pKa of poly(amic acid) estimated to be ≈ 5 compared to the measured surface pKa ≈ 7. This would explain also that lack of reactivity in attempts to esterify the modified polyimide surface with a variety of alcohols. Pyridine and NMP showed stronger interactions with the modified polyimide surface. Typically, the interaction of pyridine with an organic acid should be relatively strong unlike that measured here. Again, this may be due to the elevated pKa of the modified polyimide surface compared to bulk. The probe NMP showed what appeared to be the strongest interaction with the modified polyimide surface and is reminiscent of the observation of complex formation between NMP and poly(amic acid) in the bulk. Molecularkinetic wetting theory was derived based on the assumption of homogeneity in the identity and surface density of adsorption sites. This assumption is likely not to be valid entirely in the present case. A version of this theory modified to account for heterogeneity would be valuable. References [1] A.W. Adamson, Physical Chemistry of Surfaces, fifth ed., Wiley, New York, 1990, p. 385. [2] T.D. Blake, K.J. Ruschak, Nature 282 (1979) 489. [3] K.-W. Lee, S.P. Kowalczyk, J.M. Shaw, Macromolecules 23 (1990) 2097.
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