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Surface Phase Partitioning in Film Formation of Waterborne Polyurethanes. Monte Carlo Simulations and Internal-Reflectance IR Imaging R. B. Pandey† and Marek W. Urban*,‡ Department of Physics and Astronomy and School of Polymers and High Performance Materials, The University of Southern Mississippi, Hattiesburg, Mississippi 39406 Received August 7, 2003. In Final Form: February 3, 2004
Understanding the film formation mechanisms, in particular for thermosetting polymeric systems, has attracted considerable interests of experimentalists1-3 as well as theoreticians4-7 in recent years. While laboratory measurements provide the opportunity to examine the effect of external and internal stimuli (temperature, molecular weight, reactivity of individual components, solubility, and others) on the film formation,8-10 computer simulations offer other advantages in understanding the macroscopic properties evolving from the microscopic details in response to such stimuli.11 For example, the effects of molecular weight, driving field, and temperature on the film formation can be studied effectively.12,13 This is particularly important when multicomponent systems are considered; even though there are difficulties associated with computational analysis because of the increased number of parameters and chemical reactivity of the system, computer simulations remain the useful theoretic tool to probe such a complex system. However, when theoretical and experimental studies are carried out concurrently, a wealth of complementary information can be obtained regarding the highly complex multicomponent systems. One example of such complexity is represented by the two-component waterborne polyurethane (2K WB PUR) polymers,14 which appear to be quite sensitive to numerous external and internal stimuli, such as relative humidity, miscibility of individual components, reactivity, evaporation rates, temperature, as well as rheological characteristics. In essence, in addition to chemical reac-
tions, hydrophobic and polar interactions, which are not easily measurable, may play an important role. Further complications arise when such systems are constrained by the surface of the substrate on which the film formation occurs. Thus, a number of physical and chemical processes come into play simultaneously, which may be manifested by stratification, miscibility, or phase separation during the film formation, to name just a few. In this paper, we combined computer simulations13,15,16 and compared them with the experimental findings from the recently developed internal-reflection IR imaging (IRIRI)17 measurements in an effort to correlate the morphological evolution of the film formation in 2K WB PUR. Before we focus on these results, let us first identify the macroscopic morphological changes resulting from the changes of the cross-linking conditions. As shown in Figure 1, the optical images of the same PUR films cross-linked at different temperatures indicate significant morphological changes. Thus, the main questions are as follows: (1) What is the origin of the morphological features in addition to the chemical reactions leading to the formation of polyurethane/polyurea (PUR/PUA)? (2) What is the observed surface heterogeneity/roughness, the interface/ surface phenomenon, the reflection of the bulk behavior at the film surface, or both? To address these issues, polyurethane films were prepared using polyester resin dispersion (Bayhydrol XP-7093; Bayer Corp.; 62.1 wt %, approximately 30% solids), which was further diluted in deionized water to obtain 11.4 wt % final concentration with an overhead agitation at 1800 rpm for 10 min. The polyol dispersion was supplied preneutralized with ammonia to a pH of 7-8, and in a typical experiment, hydrophilized polyisocyante based on hexamethylene diisocyanate trimers (Bayhydur 302; Bayer Corp.; 26.4 wt %) was subsequently added under the same shearing conditions. While the figure below illustrates the general reactions leading to the PUR/PUA formation with polar and hydrophobic entities, further details concerning the experimental details were described elsewhere.14
* Author to whom correspondence should be addressed. E-mail:
[email protected]. † Department of Physics and Astronomy. ‡ School of Polymers and High Performance Materials. (1) Urban, M. W. In Film Formation in Waterborne Coatings; Provder, T., Winnik, M., Urban, M. W., Eds.; ACS Symposium Series 648; American Chemical Society: Washington, DC, 1996. (2) Fu, B. X.; Hsiao, B. S.; Pagola, S.; Stevens, P.; White, H.; Rafailovich, M.; Sokolov, J.; Mather, P. T.; Jeon, H.; Phillips, S.; Lichtenhen, J. D.; Schwab, J. Polymer 2001, 42 (2), 599-611. (3) Dreher, W. R.; Zhang, P.; Urban, M. W. Macromolecules 2003, 36 (4), 1228. (4) Barabasi, A.-L.; Stanley, H. E. Fractal Concepts in Surface Growth; Cambridge University Press: Cambridge, U.K., 1995. (5) Dynamic of Fractal Surfaces; Family, F., Vicsek, T., Eds.; World Scientific: Singapore, 1991. (6) Foo, G. M.; Pandey, R. B. Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top. 2000, 61, 1793. (7) Thompson, R. B.; Ginzburg, V. V.; Matsen, M. W.; Balazs, A. C. Science 2001, 292, 2469-2472. (8) Yacoub, A.; Urban, M. W. Biomacromolecules 2003, 4, 52-56. (9) Zhao, Y.; Urban, M. W. Macromolecules 2000, 33, 8426. (10) Han, Q.; Urban, M. W. J. Appl. Polym. Sci. 2001, 81, 2045. (11) Peng, G.; Qiu, F.; Ginzburg, V. V.; Jasnow, D.; Balazs, A. C. Science 2000, 228, 1802-1804A. (12) Pandey, R. B. Bull. Am. Phys. Soc. 2003, 48, 939. (13) Pandey, R. B. Struct. Chem. 2002, 13, 161. (14) Otts, D. B.; Zhang, P.; Urban, M. W. Langmuir 2002, 18 (17), 6473.
For computational experiments, the following model was developed: A discrete lattice of size Lx × Ly × Lz was placed on the bottom layer of the substrate (z ) 1) and
10.1021/la035450u CCC: $27.50 © 2004 American Chemical Society Published on Web 03/03/2004
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Figure 1. Optical images of the WB 2K PUR films cross-linked at 82% RH. A ) 20 °C; B ) 30 °C; C ) 40 °C.
designed by placing the appropriate substrate components (S) at each site. As shown in Figure 2, water, the solvent (A ) blue), and the polar group (B ) red) along with the hydrophobic component (C ) white) were distributed randomly in the lattice at concentrations pA, pB, and pC, respectively, with only one component at a lattice site. Thus, the fraction of the occupied sites (concentration) for each component is given by
pD ) p A + p B + p C
(1)
and the empty sites (E ) blue) with the fraction
pE ) 1 - pD
(2)
can be considered as an effective medium representing, for example, the effect of other solvent components. The molecular weight of the solvent (MA) is much smaller than that of the components B and C, i.e., MA , MB ()MC). Apart from the gravitational energy and the surface interaction (tension) of the substrate, which may pull down individual components (for higher molecular weights, the larger the sedimentation, or for higher surface tension differences between the substrate and the film, the stronger the driving forces for stratification). The nearest neighbor interactions between the components at each lattice site are described as
E)
∑i ∑k J(i,k)
(3)
where the index i runs over the components at each lattice site and k runs over all of the nearest neighbor sites of i with UAA ) AA, UAB ) AB, etc. For simplicity, the interaction energy matrix in an arbitrary unit is selected as
AA ) 1, AB ) -2, AC ) 2, AE ) -1
(4a)
BB ) -2, BC ) 0, CC ) -2, BE ) -1 (4b) AS ) 1, BS ) -2, CS ) -1, CE ) -1
(4c)
Using these parameters, the metropolis algorithm was used to move each component to their neighboring sites, which were randomly selected. The gravitational energy change (∆PEg)(∆PEg/kBT ) -Mi∆Z) with MA ) 0.01, MB ) MC ) 1.0 was used along with the change in the interaction energy ∆E in evaluating the Boltzmann weight factor to move the constituent particles. kB is the Boltzmann constant, and T is the temperature. While the periodic boundary condition was used along the transverse (15) Otts, D.; Urban, M. W. Proceedings of the 30th International Symposium on Waterborne, High Solids, and Powder Coatings; New Orleans, LA, 2003. (16) Bentrem, F. W.; Pandey, R. B.; Family, F. Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top. 2000, 62, 914. (17) Family, F.; Pandey, R. B. J. Phys. A: Math. Gen. 1992, 25, L745.
(x and y) directions for all components, along the longitudinal (z) direction, the open boundary condition was implemented with the impenetrable substrate at the bottom. During the film formation, an aqueous solvent (A) can leave the lattice (i.e., evaporate) from the top (z ) Lz), but the number of polar and hydrophobic particles is conserved. An attempt to move each particle once defines the unit Monte Carlo (MC) step. The simulation is repeated with a number of independent samples to obtain a reliable estimate of the physical quantities such as the density profiles and the interface width. It is worth pointing out that the phenomenological interaction interactions (eqs 3 and 4) are used to capture the basic characteristics of the constituents (A, B, and C). The relative magnitudes of the molecular weights of these components, energy, temperature, and time steps (in arbitrary units) are not the same quantitatively as those in the experimental systems. The physical quantities measured with the parameters used in the computer simulations on a discrete lattice cannot be compared quantitatively with the corresponding quantities measured in the laboratory. However, the effects of the variation in these parameters on the qualitative behavior of the system, i.e., evolution of the density profiles, segregation, and roughness, can be compared. This is the primary objective of this paper. Further, we would like to point out that even though we are using the Boltzmann distribution to move the constituents, the number of solvent (A) particles is not conserved. The combination of the metropolis algorithm and the implementation of the evaporation mechanism in the presence of gravity lead to a nonequilibrium system. The independent parameters in these simulations are the concentrations of the water (A), polar (B), and hydrophobic (C) groups, their interaction strengths, molecular weights, and temperature. For the set of the interaction matrix, the effect of the water concentration on the growth of the interface was examined at the temperatures T ) 1.0 and 0.5, and the total concentration of the solvent and solute was pD ) 0.5 and 0.7, respectively. While the results of the simulations are presented in the following section, it should be pointed out that in the laboratory experiments, two main parameters were changed: the relative humidity (RH) and temperature. The variations in the RH correspond to different concentration levels of water (A) at a given time of the film formation in the computer simulations. It should be noted that the volume fraction of water in the simulation defines the RH and the concentration (volume fraction) of each component in the lattice differs from the experimental values, but as will be seen, the trends are the same. As soon as the mixture of B and C in A is poured onto the substrate, each component executes their stochastic motion in an attempt to explore their energetically favorable positions; a typical evolution of these components is illustrated by the snapshots presented in Figure 2. As seen, the polar (B) and hydrophobic (C) components progressively phase separate, while the solvent (A) evaporates. As the film formation continues, the spatial local densities fluctuate and tend to approach a steadystate value with the phase-separated B and C components. In an effort to correlate the results of the MC simulations with the actual experimental laboratory data, we utilized IRIRI and determined the chemical as well as morphological features occurring as a result of the film formation. The films utilized for these studies are cross-linked at 30 °C and 82% RH. Figure 3A illustrates the IRIR image of the 1681 cm-1 band, and Figure 3B illustrates two IR spectra obtained from the two circled areas with a radius
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Notes
Figure 2. Snapshots of the film formation on a 30 × 30 × 15 lattice at temperature T ) 1.0, pD ) 0.5 at time steps t ) 1.6, 200, 400, 1000, 2000, and 8000.
Figure 3. (A) Topographic IRIR image of the WB 2K PUR film cross-linked at 30 °C and 82% RH. (B) Corresponding IR spectra from the cross-linker-rich and cross-linker-deficient regions.
of about 10-15 µm spaced about 2-3 µm apart (spatial resolution ) 1 µm). As indicated earlier, the understanding of the morphological features such as those shown in Figure 1 is of interest, and IRIRI allows us to obtain spatially resolved information in the direction parallel to the surface. The IRIR image of 1681 cm-1 (Figure 3A) clearly indicates the chemical heterogeneities on the
surface of the film, where the bluish/brighter area in the IRIR image corresponds to higher absorbances at 1681 cm-1, a characteristic band of the polyisocyanate crosslinker. Consequently, the cross-linker-rich domains exist at the film-air (F-A) interface characterized by higher absorbances at 1681, 1643, 1560, and 1462 cm-1 corresponding to isocyanurate CdO stretching, PUA CdO
Notes
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Figure 4. The width of the interface plotted as a function of the time step for (A) T ) 1.0, pD ) 0.5; (B) T ) 0.5, pD ) 0.5; (C) T ) 0.5, pD ) 0.7, at water (A) concentration levels ranging from 0.2 to 0.6. The simulation sample size is 40 × 40 × 30 with 10 independent runs for each. (D) log-log plot of the data presented in C. (E) log-log plot of the data presented in C in an asymptotic regime for the solvent concentration levels pA ) 0.375-0.550. Corresponding estimate of the power-law exponent β is given in parentheses.
stretching, PUA N-H bending, and -CH2- deformations, respectively. At the same time, the cross-linker-rich region exhibits a significantly lower absorbance of the 1095 cm-1 band, which corresponds to the less content of the CH2O-CH2 groups of the polyether functional molecular segments. Thus, there is a clear chemical phase separation of the system. With this in mind let us go back to the MC simulations and attempt to correlate the results illustrated in Figure 3. From the longitudinal density profile, one can monitor the interface width W4,5,12 defined as
W2 )
∑ij (hij - hh )2
h h)
∑ij hij/Ns
(5)
above. As shown in parts B and C of Figure 4, the increasing polymer and solvent concentration levels enhance the surface roughness, which stabilizes the interface width; thus, it is well-corresponding with the laboratory experiments. It is worth pointing out that the axes in parts A-C of Figure 4 are log-normal scales; thus, significant deviation from the linear relationships exists, suggesting that the approach of the interface width to its asymptotic value is not an exponential decay. Indeed, the log-log plot of the data shown in Figure 4D (the same data as in Figure 4C) illustrates that there is a power-law decay of the interface width
W ∝ t-β
(7)
(6)
where hij is the surface height at the locations i and j on the substrate and h is the mean surface height averaged over the substrate with Ns ) Lx × Ly sites. In other words, the W values represent the density fluctuations of all species from the F-A interface to the substrate. Figure 4A shows the variation of the interface width W with time at temperature T ) 1.0 at concentration pD ) 0.5 of the polymer and solvent mixture as a function of the solvent concentration pA. As seen, a rapid decline of the interface width followed by a very slow approach to the steady-state value is apparent at all solvent concentration levels. It should be noted that the interface width increases with the concentration of the aqueous component, i.e., the roughness increases with the water concentration. This is consistent with the experimental data described
with the β exponent. Close examination of these data in the asymptotic regime shows (Figure 4E) that the exponent β depends on the water concentration levels with β ) 0.270.63 for pA ) 0.550-0.375. The slow decay of the interface width at higher RH levels (concentration of A) is indicative of the depletion rate of water interspersed between the polar and hydrophobic components of the film. Furthermore, the interface width measured as the degree of roughness is higher at higher water concentration levels, which agrees with the experimental data shown in Figure 3. In summary, these studies illustrate that the film formation in 2K WB PUR is driven by two synergistic processes: the chemical reactions between the NCO-OH and NCO-H2O entities leading to the formation of PUR and PUA, respectively, as well as the hydrophobic/ hydrophilic interactions of the individual components.
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While spectroscopic experimental evidence indicates that there are substantial chemical differences at the surface, it is apparent that the surface morphological changes result from the bulk reactions. Interestingly enough, a similar magnitude of the surface roughness is predicted using the MC simulations and again the formation of the separate phases across the entire film thickness. Hydrophobic/hydrophilic interactions play a significant role during the evaporation of water because during this process, hydrophobic polyols become more compatible with hydrophobic isocyanate-based reactive cross-linkers. We plan to include the kinetics of the cross-linking in our future computer simulation studies. This facilitates the interphase mixing and desired cross-linking reactions, thus leading to homogeneous film morphologies. When the concentration levels of water (solvent (A) in MC simulations) are high (high RH), water and water-soluble
Notes
components remain in the film for an extended time and miscibility between the polyol and NCO-based cross-linker becomes less favorable, thus leading to phase partitioning, self-aggregation of similar phases, and greater extents of self-cross-linking. As a result, morphology across the film thickness changes, which is “transmitted” to the surface, which become decorated with the phase-separated domains of PUR and PUA. Acknowledgment. This paper was supported by the National Science Foundation MRSEC program under the award number DMR-0213883 and NSF-EPSCoR award EPS-0132618. Mr. Daniel Otts is acknowledged for supplying the optical and imaging data used for the purpose of these studies.14 LA035450U
