Film Formation from Aqueous Polyurethane ... - ACS Publications

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Film Formation from Aqueous Polyurethane Dispersions of Reactive Hydrophobic and Hydrophilic Components; Spectroscopic Studies and Monte Carlo Simulations Daniel B. Otts,† Luis A. Cueva-Parra,†,‡ Ras B. Pandey,‡ and Marek W. Urban*,† School of Polymers and High Performance Materials, Shelby F. Thames Polymer Science Research Center, and Department of Physics and Astronomy, The University of Southern Mississippi, Hattiesburg, Mississippi 39406 Received October 1, 2004. In Final Form: February 23, 2005 Film formation of waterborne two-component polyurethanes is exceedingly complex due to the heterogeneous nature along with simultaneous progression of several parallel physicochemical processes which include water evaporation, cross-linking reactions, phase separation, and droplet coalescence, to name a few. While internal reflection infrared imaging (IRIRI) spectroscopy clearly facilitates analysis of chemical changes resulting from film formation, the complexity of processes leading to formation of specific surface/interfacial entities is a major experimental challenge. For this reason, we combined a spectrum of surface/interfacial analytical approaches including IRIRI, atomic force microscopy, and attenuated total reflectance Fourier transform infrared spectroscopy with Monte Carlo computer simulations to advance the limited knowledge of how temperature, stoichiometry, concentration levels, and reactivities of individual components affect the development of surface morphologies and compositional gradients across the film thickness. These studies show that in heterogeneous systems having both hydrophobic and hydrophilic components stratification of individual components to the film-air (F-A) interface is ultimately responsible for formation of rough surface topographies. These studies show that simultaneous stratification of hydrophobic components along with water evaporation to the F-A interface results in metastable interfacial layers, leading to surface dewetting. Subsequently, surface roughness is enhanced by higher concentrations of water in the cross-linking film.

Introduction Understanding film formation and the development of film chemical and physical morphologies, such as phase separation and surface roughness, has been the focus of previous research efforts. While numerous experimental approaches focused on development of film surface roughness as a function of temperature,1 polymer chain architecture,2 solvent evaporation,3-5 and molecular weight,6 theoretical studies have dealt with morphological evolution during film formation.7,8 Since both experimental and theoretical approaches have benefits and drawbacks, the challenge is to combine both to enhance our limited knowledge of film formation. These studies attempt to combine experimental and theoretical findings to enhance limited knowledge of aqueous dispersions containing reactive hydrophilic and hydrophobic polyurethane (PUR) precursors. Specifically, due to the significance and limited knowledge of waterborne two-component polyurethanes (WB 2K-PURs), which consist of a hydrophobic polyiso* To whom all correspondence should be addressed. † School of Polymers and High Performance Materials, The University of Southern Mississippi. ‡ Department of Physics and Astronomy, The University of Southern Mississippi. (1) Benz, M.; Euler, W. B.; Gregory, O. J. Langmuir 2001, 17, 239243. (2) Budhlall, B. M.; Shaffer, O. L.; Sudol, E. D.; Dimonie, V. L.; ElAasser, M. S. Langmuir 2003, 19, 9968-9972. (3) Ho, C. C.; Khew, M. C. Langmuir 2000, 16, 2436-2449. (4) Strawhecker, K. E.; Kumar, S. K.; Douglas, J. F.; Karim, A. Macromolecules 2001, 34, 4669. (5) Mu¨ller-Buschbaum, P.; Gutmann, J. S.; Wolkenhauer, M.; Kraus, J.; Stamm, M.; Smilgies, D.; Petry, W. Macromolecules 2001, 34, 13691375. (6) Wool, R. P., Ed. Polymer Interfaces Structure and Strength; Hanser Publishers: Munich, 1995. (7) Urban, M. W.; Pandey, R. B. Langmuir 2003, 20, 2970-2974. (8) Tsige, M.; Grest, G. S. Macromolecules 2004, 37, 4333.

cyanate cross-linker, a hydrophilic polyester polyol, and water, this system is of particular interest. While traditional solventborne two-component systems exist as clear, homogeneous mixtures in the solution state in which the polyol and cross-linker are both hydrophobic and are solvated on a molecular level with all components existing in the same phase, substituting water for organic solvents creates a significantly more complex solution morphology. Although one would anticipate the development of phaseseparated morphologies, in which a predominantly aqueous phase surrounds nano-dispersed reactant droplets, the intermixing of components as well as the extent of side reactions in the solution state are critical parameters. Furthermore, reaction kinetics, product distributions of postreaction components, and extents of phase separation become equally important features during the film formation. These studies focus on physical and chemical morphological features of WB 2K-PUR films prepared using welldefined experimental conditions as well as computational simulations of their respective film forming processes. The ultimate goal is to correlate specific physical surface morphological features obtained in experimental studies with the mechanisms of film formation. The latter will be achieved by Monte Carlo simulations, which correlated with experimental chemical and morphological imaging, will allow us to develop a model of film formation in WB 2K-PURs. Experimental Section PUR/urea films were prepared by mixing Bayhydrol XP-7093 (Bayer Corp.) polyester polyol resin dispersion [approximately 30% (w/w) solids in water] with neat Bayhydur 302 (Bayer Corp.) water-dispersible polyisocyanate cross-linker based on poly(ethylene glycol) (PEG)-modified polyisocyanate of HDI using

10.1021/la047564r CCC: $30.25 © 2005 American Chemical Society Published on Web 03/26/2005

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Figure 1. AFM height images of PUR films illustrating surface morphological changes resulting from environmental stimuli. (A) Before exposure to water; (B) after 1 h of exposure to water. Images are shown at the same scale. overhead agitation at 1800 rpm with a small four-blade polytetrafluoroethylene impeller in a 20-mL glass vial at 25 °C for 10 min. The relative amounts of all components were adjusted to yield isocyanate to hydroxyl (NCO/OH) molar equivalent ratios of 2.0, while maintaining 45% (w/w) solids. Following the mixing process, resulting reactive dispersions were held without agitation for 15 min to allow for viscosity reduction. Such mixture was applied to obtain approximately 40 µm (( 3 µm) thick films (dry) on glass after cross-linking for 3 days in controlled environments at 30 °C and 11, 32, 52, 75, 82, and 97% relative humidities (% RH). Contact mode atomic force microscopic (AFM) images were obtained using a TA Instruments micro thermal analyzer 2990 which incorporates a Thermo Microscopes Explorer model AFM. Topographic images were acquired using scan rates ranging from 50 to 200 µm/s using a silicon nitride contact AFM probe. Specular gloss measurements were performed using a BYK Gardner micro TRI gloss meter at a 20° angle of inicidence. Internal reflection infrared (IRIR)9 images were obtained using a Digilab FTS 6000 Stingray system with a Ge internal reflection element (IRE). This system consists of a Digilab FTS 6000 spectrometer, a UMA 500 microscope, an ImagIR focal plane array image detector, and a semi-spherical Ge IRE. IRIR images were collected using the following spectral acquisition parameters: undersampling ratio of 4, step-scan speed of 2.5 Hz, 1777 spectrometer steps, 64 images per step, and 8 cm-1 spectral resolution. In a typical experiment, a spectral data set acquisition time was approximately 20 min. Image processing was performed using the Environment for Visualizing Images software (Research Systems, Inc., version 3.5). When appropriate, baseline correction algorithms were applied to compensate for baseline deviations. Single internal reflection Fourier transform infrared (FTIR) spectra representing average chemical information over a 2-mm diameter circular area were obtained using a MIRacle accessory (Pike Technologies) with a Ge crystal at a 45° angle of incidence, providing an approximate penetration depth of approximately 0.65 µm.

Results While WB 2K-PUR films offer a number of advantages, these PURs exhibit inherent sensitivity to moisture.10 Figure 1, image A, illustrates a contact-mode AFM height image of a PUR film prepared at 30 °C and 82% RH. As seen, such conditions result in topographical features that appear as “hills” and “valleys” and have been examined previously.11,12 These features were attributed to subtle compositional variations in PUR/polyurea (PUA) distri(9) Otts, D. B.; Zhang, P.; Urban, M. W. Langmuir 2002, 18, 64736477. (10) Wicks, Z. W.; Wicks, D. A.; Rosthauser, J. W. Prog. Org. Coat. 2002, 44, 161-183. (11) Otts, D. B.; Urban, M. W. Polym. Prepr. 2003, 44, 105-106. (12) Otts, D. B.; Urban, M. W. Proc. Int. Waterborne, High-Solids, Powder Coat. Symp. 2003, th, 365-374.

Figure 2. ATR-FTIR spectra of WB 2K-PUR films prepared at 11, 32, 49, 75, 82, and 97% RH and 30 °C recorded from the F-A (A) and F-S (B) interfaces, respectively. Arrows indicate intensity changes with increasing RH.

butions near the film-air (F-A) interface, as revealed by internal reflection infrared imaging (IRIRI) spectroscopy9 and microthermal analysis. While such surface morphologies affect surface appearance, direct exposure to water (1 h) causes selective swelling of hydrophilic domains at the F-A interface. This is illustrated in Figure 1, image B, where a rougher surface and further reduction in gloss are observed. These findings indicate that water plays an important role not only in the final film properties but also during film formation, since the presence of water during cross-linking ultimately affects the resulting film morphology. The presence of water as well as the rate of water loss also affects the distribution of heterogeneous domains and their interfacial properties. Specifically, the extents of PUR and PUA formation are altered. This is manifested in

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Figure 3. (A) F-S IRIR images of WB 2K-PUR films cross-linked at various conditions. Blue areas correspond to hydrophilic domains; yellow areas correspond to hydrophobic domains. (B) Percent absorbance difference between P and NP areas for 1724, 1681, and 1100 cm-1 bands. RH and T values correspond to part A.

attenuated total reflectance (ATR)-FTIR spectra recorded from WB 2K-PUR films cross-linked at various humidities at F-A (trace A) and film-substrate (F-S; trace B) interfaces, which are shown in Figure 2. Spectral intensity changes are detected at 1724, 1647, 1560, and 1524 cm-1 corresponding to PUR/ester CdO stretching, PUA CdO stretching, PUA NsH bending, and PUR NsH bending vibrations, respectively, and the band intensities due to PUR decrease with a simultaneous increase of the bands responsible for PUA formation. These changes are directly related to the extent of hydrolysis reactions occurring between isocyanate groups and water to ultimately form PUA (by way of an unstable carbamic acid intermediate)13 and reactions between isocyanate groups and hydroxyl groups of polyol to form PUR. In essence, these data

indicate a decrease in the relative ratio of PUR to PUA at higher humidity conditions. As previously mentioned, WB 2K-PUR systems are also capable of undergoing a certain degree of phase separation when film formation occurs at elevated humidities. Such phenomena are clearly demonstrated using IRIRI spectroscopy. As seen in Figure 3, which depicts phaseseparated domains at the F-S interface for WB 2K-PUR films cross-linked at elevated RH for several temperatures, blue areas labeled “P” (for “polar”) correspond to domains with enriched hydrophilic (polyester, polyether) content. Yellow areas labeled “NP” (for “nonpolar”) are attributed to regions with reduced hydrophilic content and may be generally regarded as “hydrophobic” (aliphatic) domains. These images were generated from the intensities of bands

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at 1724 (red), 1681 (green), and 1100 cm-1 (blue) attributed to PUR/polyester CdO stretching, isocyanurate CdO stretching, and PEG CsOsC bending vibrations, respectively. The progression of images in Figure 3 indicates that phase separation is favored with increasing RH and at elevated temperatures. For example, images of films cross-linked at 35 °C only display minor compositional variation; however, the different chemical domains of the specimen cross-linked at 45 °C and 97% RH have an approximately 37% difference in band intensity (and essentially a 37% difference in concentration) for the 1100 cm-1 polyether band attributed to PEG. Consequently, such phase-separated domains form as a result of thermodynamic incompatibility of individual components due to their inherent structural features or due to the reaction products generated during film formation. While spectroscopic analyses shown in Figures 2 and 3 and, in particular, IRIR imaging9,14,15 are extremely useful for monitoring subtle chemical differences, our ultimate objective is to develop a model describing crosslinking reactions and their effects on film formation of WB 2K-PUR films. For this reason, we will utilize Monte Carlo simulations to follow changes in the film evolution over time at each stage of the process while adjusting key parameters that affect film formation. In an effort to be able to correlate theoretical and experimental data, the effects of water concentration, reactant concentrations, stoichiometry, temperature, and interaction energetics on cross-linking processes will be analyzed. For that purpose, let us consider that all reactant and water constituents are placed in a discrete threedimensional lattice of size Lx × Ly × Lz in which all components may adsorb on a substrate that is designed by placing appropriate constituents, S, one at each site, at the bottom layer (z ) 1). Water (A), polar (P), and hydrophobic components (NP) are distributed randomly in the lattice with concentrations pA, pP, and pNP, respectively, with only one constituent at a lattice site. Thus, the fraction (concentration) of occupied sites is given by

pO ) pA + pP + pNP

(1)

The fraction of empty sites (E) is

pE ) 1 - pO

(2)

and is considered as a part of the effective medium which imparts sufficient free volume to the system to facilitate motion of A, P, and NP components. The molecular weight of water (MA) is much smaller than that of constituents P and NP, that is, MA , MP () MNP). The gravitational energy which pulls down these constituents according to their molecular weight is given by

PEg/kBT ) MA/P/NPZ

(3)

where kB is the Boltzmann constant, T is the temperature, and Z is the height (distance from the substrate layer). Thus, the higher the molecular weight, the greater the likelihood of adsorption to and subsequent reaction on the substrate. The interaction energy of nearest neighbors (13) March, J. Advanced Organic Chemistery, 4th ed.; WileyInterscience: New York, 1992. (14) Dreher, W. R.; Zhang, P.; Urban, M. W. Langmuir 2003, 19, 10294. (15) Otts, D. B.; Dutta, S.; Zhang, P.; Smith, O. W.; Thames, S. F.; Urban, M. W. Polymer 2004, 45, 6235-6243.

at each lattice site is given as

Ei )

∑i ∑k U(i, k)

(4)

where the index i runs over particles at each lattice site and k over all nearest neighbor sites (6) of i with U(A, A) ) AA, U(A, P) ) AP, and so forth. For computational simplicity, the interaction energy coefficient matrix (in arbitrary units) is selected as

AA ) 1, AP ) -1, ANP ) 1, AE ) -1 (5a) PP ) -1, PNP ) 0, NPNP ) -1, PE ) -1

(5b)

AS) 1, PS ) -1, NPS ) -1, NPE ) -1 (5c) In these studies we used the Metropolis algorithm, which allows movement of each constituent among their neighboring sites. The gravitational energy change (∆PEg; ∆PEg/kBT ) Mi∆Z) with MA ) 0.1 and MP ) MNP ) 1.0 is used along with the change in the interaction energy ∆E in evaluating the Boltzmann weight factor

exp[-∆E/kBT - Mi∆Z]

(6)

to move the constituent particles. Periodic boundary conditions are implemented along the transverse (X, Y) directions for all constituents. Along the longitudinal (Z) direction, an open boundary condition at the top (F-A) and an impenetrable substrate at the bottom (F-S) are implemented. The water constituent (A) may leave the lattice (i.e., evaporate) from the top (z ) Lz), but the number of polar and hydrophobic particles is maintained throughout the simulations of the film formation. Initially, a randomization process is performed to obtain a mixture of P and NP in the water constituent A which is applied to the substrate and each component executes its stochastic motion in its attempt to explore energetically favorable positions. Cross-linking kinetics are implemented by assigning empirical reaction probabilities to active constituents (rPNP ≡ probability associated with reaction of P with NP and so forth). The cross-linking process occurs between active components, which are either in contact with the substrate or are already a part of the forming film. Polar and hydrophobic constituents remain fixed to the substrate with probabilities rSP ) 1.0 and rSNP ) 1.0, respectively. While active components (P and NP) react stochastically to form cross-linked networks, the water constituent (A) evaporates. As the film formation occurs, spatial local densities fluctuate and tend to approach a steady-state value. From the longitudinal density profile, one can monitor the surface roughness by the root-mean-square interface width (W) defined as

W)

x

1

(hij - h h )2 ∑ N ij

(7)

s

in lattice size units (LSUs), where hij is the surface height at location (i, j) on the substrate and h h is the mean surface height averaged over the substrate with Ns ) Lx × Ly sites, expressed as

h h)

∑ij hij/Ns

(8)

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Figure 4. Three-dimensional images of simulated films showing growth at various times, t, as a function of temperature, T.

Independent parameters in these simulations are concentrations of water (A), polar components (P), and hydrophobic components (NP), their relative interaction strengths (), temperature (T), and reactivity (r). For a given interaction matrix (eq 5a-c), the effect of water concentration, A, on the evolution of interface width is examined for various temperatures (T ) 0.75-2.00 in arbitrary units of Boltzmann constant) and total concentration of water and reactants (combined) of pO ) 0.5, maintaining a constant fraction of empty sites, pE ) 0.5. The attempt to move each particle once defines one unit Monte Carlo step (MCS), which is essentially an arbitrary unit of time for these studies. For each set of parameters chosen, simulations were repeated 10 times to obtain a representative average estimate of the resulting film properties, such as density profiles and interface width. Discussion We begin discussion of the results from simulations by providing a pictorial representation of the film evolution for several temperatures (T ) 1.0, 1.5, and 2.0) at a progression of times during the film formation process, such as is seen in Figure 4. At early times (t )1), the images show the beginning of film formation, with discrete

cross-linked entities randomly distributed on the substrate. However, as time progresses and additional crosslinking occurs, films begin to propagate in an upward fashion as increasing extents of reactants adsorb to the propagation front and subsequently cross-link. The resulting surface topography and specific elevation are represented by differences in color, according to the legend shown beside each image. These images illustrate that the surface of all films exhibits topographic features at each stage of the film formation process similar to those shown in AFM images depicted in Figure 1. Additionally, in these simulations, film growth propagates outwardly from the substrate with increasing time. Although not explicitly shown (for the sake of clarity), additional mobile and/or reactive components are present in significant amounts above the surface of each propagating film; however, the population of these entities diminishes significantly as a steady-state condition is attained (i.e., completion of film formation). It should be pointed out that experimentally observed domains shown in Figure 3 are in the range of 3-10 µm and were detected at the F-S interface. Furthermore, the phase contrast in the IRIR images is due to differences in chemical composition. In the simulations shown in

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Figure 5. Mean square interface width versus time step at T ) 1.0 and pO ) 0.5 with different water concentrations (pA). Sample size is 40 × 40 × 30 with 10 independent runs each. Two regimes with power law evolution of the interface growth are shown. Inset illustrates the power law dependence between the mean square interface width and the water concentration.

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Figure 7. Mean square interface width versus temperature at pO ) 0.5 for different water concentrations (pA). Sample size is 40 × 40 × 30 with 10 independent runs each.

Figure 8. Relative surface roughness (expressed as 100/ [specular gloss value]) plotted as a function of cross-linking temperature for WB 2K-PUR films prepared at elevated humidity (82-97% RH). Specular gloss measurements were performed using a 20° angle of incidence.

Figure 6. Mean square interface width versus time step at T ) 1.5 and pO ) 0.5 with different water concentrations (pA). Sample size is 40 × 40 × 30 with 10 independent runs each. The power law evolution of the interface growth is shown. Also, a power law dependence between the mean square interface width and the water concentration is shown.

Figure 3, the early stages at t ) 1-100 also represent the F-S interfacial features; however, topographical features are represented and their respective sizes are approximately proportional to the IRIRI domains (based on dimensions of the lattice). At the later stages of simulations at t ) 1500-3000 film formation progresses toward the F-A interface, and the topographical features persist based on data in Figures 4-8. Thus, a comparison between the surface topography in Figure 1 and the later stages of computer simulations (Figure 3) appears to show similar features, namely, surface roughness on the order of 0.5

µm. It should be pointed out that the experimental conditions and findings ultimately allowed us to determine significant parameters for computer simulations, resulting in synergistic combination of actual and theoretical experiments. While qualitative assessments allow us to observe subtle differences in each of the images, a quantitative, mathematical treatment of the data utilized in the creation of each image is merited to precisely identify processes occurring during film formation. An ultimate goal of these studies is to vary simulation parameters and to monitor their effects on film formation. Figure 5 shows the variation of the mean square interface width, W2, with time at temperature T ) 1.0 with an initial constant total concentration of all components (pO ) 0.5) while varying the water concentration, pA. Two regimes of interface growth (at the F-A interface) followed by a smooth approach to steady state (constant interface width) is observed for all water concentrations, A. As shown in Figure 5, these two regimes for the water concentration pA ) 0.3, indicated by dashed lines, may be mathematically

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expressed as a power law dependence between the square of interface width and time step such that

W2 ∝ tβ

(9)

The fitted exponents for this set of parameters are β1 ≈ 1.6 and β2 ≈ 1.0 for the first and second regimes, respectively. Furthermore, it should be noted that, for films having reached equilibrium (at long times), the interface width is larger for higher water concentrations; that is, the roughness is enhanced by higher water concentrations, A. The specific dependence, shown in Figure 5 (inset), is given by

W2 ∝ pAR

(10)

with R ≈ 2.8. As shown in these data, the time required to reach equilibrium varies as a function of water concentration, A. Specifically, films with higher water contents require longer times to equilibrate which is physically justified by the fact that more dilute reactants may have additional translational freedom during the later stages of film formation than in the case of more concentrated reactants. Consequently, more time is necessary for all unreacted entities to find energetically favorable conformations and participate in cross-linking reactions. Having established a general relationship between water concentration and film roughness, it is desirable to examine the effect of temperature, T, for an arrangement similar to the one shown in Figure 5. However, before proceeding, it is necessary to comment on the physical significance of the temperature variable, T, used in these simulations. As shown in eq 6, temperature is a variable used in evaluation of the Boltzmann weighting factor, which determines probability of motion for each entity during film formation. Consequently, by increasing temperature, the entropy and mobility of components in the system are increased. However, in these studies temperature and chemical reactivity are essentially independent of one another (reaction kinetics are empirically determined in a parallel process by chosen values of r). Thus, from this point onward, temperature will be a measure of mobility in the system such that the results of these simulations arising from temperature changes may be justified in the context of measurable experimental quantities such as solution viscosity, glass transition temperature (Tg), phase separation, and surface roughness. As shown in Figure 5, the surface roughness increases with the increasing water content, which is consistent with the experimental observations shown in Figure 1. With these considerations in mind, let us increase the temperature from 1.0 to 1.5 while retaining the remaining parameters. These data are shown in Figure 6, and as seen, increased T results in reduced overall film roughness for all values of pA when compared with the data shown in Figure 5. Similarly, two regimes of interface growth are detected, although the nature of the second regime is significantly different, as there is no power law dependence between W2 and t. Instead, there is a maximum of the F-A interface width at approximately t ) 100-600, followed by relaxation that approaches a steady-state value below the maximum. While this trend is more pronounced at low water concentration (pA ) 0.2), it is almost nonexistent at high concentrations (pA ) 0.3). These results indicate that an initially kinetically controlled second regime of interface growth eventually transitions to a thermodynamically controlled steady state at inter-

mediate times. Analysis of the first regime of interface growth results in an exponent β1 ≈ 1.5, indicating somewhat slower initial surface roughness evolution than for T ) 1.0 and a power law dependence between interface width and water concentration such that R ≈ 3.1 (eq 10). Finally, not only is the relationship between roughness and water concentration, A, preserved at elevated temperatures, but also the change in the magnitude of the difference in all the roughness values is lower. To further explore the effects of temperature changes, additional computations were performed for temperatures ranging from 0.75 to 2.0. Figure 7 establishes the relationship between the square of the interface width and the temperature for different water concentrations, A. As the temperature increases, the square of the interface width decreases somewhat exponentially for all water concentrations. Moreover, an asymptotic value emerges as the temperature increases infinitely. The asymptotic value lies between 3 and 6 approximately. These results indicate that as the entropy (i.e., mobility) of the system is increased, component motion is more facile, and as reactions become less diffusion-limited, smoother surfaces will result. Since this particular PUR system was designed for ambient cross-linking, performing experiments employing a wide range of temperatures is not feasible. Going to lower than ambient temperatures would slow crosslinking reactions infinitely whereas elevated temperature even slightly above ambient cross-linking causes rapid acceleration of the NCO-H2O reaction, consequently increasing film defects due to CO2 production. Taking into account the theoretical results described in Figure 7 which indicate a decrease in surface roughness with increasing temperature, specular gloss measurements were performed on the films prepared at temperatures from 25 to 45 °C. Since surface topography and roughness will strongly affect specular reflection of impinging light, gloss measurements provide an acceptable means by which to quantify the roughness of WB 2K-PUR films prepared at different temperatures. Furthermore, to account for the fact that specular gloss and surface roughness are inversely proportional (i.e., higher gloss values are indicative of smoother surfaces), the relative surface roughness was calculated as 100/(specular gloss value) and the relative surface roughness values are plotted as a function of temperature in Figure 8. As is seen, relative surface roughness decreases with the increasing temperature, thus providing a good correlation between the experimental data and theoretical predicitons discussed in Figure 7. It should be pointed out that under certain experimental conditions, for example, elevated temperatures, the surface roughness may also increase. Up to this point, the reactivities of individual components, and specifically the reaction probabilities, have been kept constant to establish the effects of water concentration and temperature on film formation and interface width development. Let us now consider the effect of increased reactivity of components. Figure 9 illustrates evolution of the F-A interface width as a function of time, t, for reactivities (r ) rPP ) rPNP ) rNPNP) ranging from 0.05 to 0.40. Similarly to the data shown in Figures 5 and 6, for the range of reactivitiy values examined two film growth regimes are observed. The first regime consists of rapid growth of the F-A interface width, followed by a second regime of significantly slowed F-A interface growth that ultimately reaches a steady state where the F-A interface width stays relatively constant. As is seen, enhanced reactivity is observed to result in rougher surfaces. In view of the above theoretical and experimental considerations, previous studies of polymeric coatings and

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Figure 9. Mean square interface width versus time step at T ) 1.0 and pO ) 0.5 (pA ) 0.25, pP ) 0.125, pNP ) 0.125) with different reaction probabilities, r (r ) rPP ) rPNP ) rNPNP). Sample size is 40 × 40 × 30 with 10 independent runs each. Inset shows the relation between interface width and reaction probabilitites.

thin films have indicated that stratification processes may occur, resulting in compositional gradients across the film thickness.16-21 These phenomena have been shown to alter a number of surface/interfacial properties such as appearance, cross-link density, tackiness, and adhesion, to name a few. WB 2K-PUR materials are particularly susceptible to stratification processes, which primarily result from large differences in the polarity of components, incorporation of surface-active moieties, and competing reaction pathways, as well as widely varying diffusivities of components. In an effort to investigate stratification processes occurring during simulated film formation at various water concentrations using T ) 1.0, pO ) 0.5, pA ) x, and pP ) pNP ) (0.5 - x)/2, a series of films that had reached equilibrium (t ) 15 050 MCS) were examined. In this manner, the concentration of water, A, could be adjusted (pA ) 0.20, 0.25, and 0.35) while keeping the stoichiometric ratio of the P and NP components equal. To monitor component distributions across the film thickness for each component, individual longitudinal density profiles were constructed, which are shown for the water, W, polar, P, and hydrophobic, NP, constituents in Figure 10A-C, respectively. The distribution of water, as shown in Figure 10A, indicates a gradient of water concentration, with more water being present near the F-S interface for all values of pA. While one may argue that, at equilibrium, relatively little water should be present in the films, hydrophilic materials such as WB 2K-PUR films have finite water contents, even at equilibrium. The important thing to consider is not the absolute amount of water in the film but the distribution of water across the film thickness. Furthermore, this simulation algorithm facilitates entrapment of water, which is an experimentally observable phenomenon which can occur in conjunction with “surface skinning,” an effect in which a more concentrated layer of reactants forms near the F-A interface and retards diffusion of water from the (16) Dreher, W. R.; Zhang, P.; Urban, M. W. Macromolecules 2003, 36, 1228. (17) Zhao, C. L.; Holl, Y.; Pith, T.; Lambla, M. Colloid Polym. Sci. 1987, 265, 823. (18) Zhao, Y.; Urban, M. W. Macromolecules 2000, 33, 2184. (19) Zhao, Y.; Urban, M. Macromolecules 2000, 33, 7573. (20) Zhao, Y.; Urban, M. Macromolecules 2000, 33, 8426. (21) Zhao, Y.; Urban, M. Langmuir 2001, 17, 6961.

Figure 10. (A) Longitudinal density profile of the water constituent, A, at steady state (t ) 15 050) with T ) 1.0 and pO ) 0.5; (i) pA ) 0.20, pP ) 0.15, and pNP ) 0.15; (ii) pA ) 0.25, pP ) 0.125, and pNP ) 0.125; (iii) pA ) 0.35, pP ) 0.075, and pNP ) 0.075. Sample size is 40 × 40 × 30 with 10 independent runs each. (B) Longitudinal density profile of the polar constituent, B, at steady state (t ) 15 050) with T ) 1.0 and pO ) 0.5; (i) pA ) 0.20, pP ) 0.15, and pNP ) 0.15; (ii) pA ) 0.25, pP ) 0.125, and pNP ) 0.125; (iii) pA ) 0.35, pP ) 0.075, and pNP ) 0.075. Sample size is 40 × 40 × 30 with 10 independent runs each. (C) Longitudinal density profile of the hydrophobic constituent, C, at steady state (t ) 15 050) with T ) 1.0 and pO ) 0.5; (i) pA ) 0.20, pP ) 0.15, and pNP ) 0.15; (ii) pA ) 0.25, pP ) 0.125, and pNP ) 0.125; (iii) pA ) 0.35, pP ) 0.075, and pNP ) 0.075. Sample size is 40 × 40 × 30 with 10 independent runs each.

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Figure 11. Schematic illustration of the final stages of simulated film formation which describes the observed maximum in surface roughness at the F-A interface before attaining a steady-state condition. (A) Surface de-wetting due to interfacial phase separation of the nonpolar component and water; (B) maximum in surface roughness immediately after water evaporation; (C) equilibrated film after surface flow and subsequent cross-linking of the nonpolar component, resulting in reduced surface roughness.

film, thereby trapping it within the bulk of the film.22 Figure 10A also indicates that, as the concentration of water decreases, the steepness of the water gradient increases. Additionally, near the F-A interface (Z ≈ 1623), a slightly higher water content is present compared to the minimum value, which occurs around Z ) 13, 16, and 17 for profiles i, ii, and iii, respectively. The profiles of the polar (P) components shown in Figure 10B closely parallel the behavior of the water profiles in Figure 10A. This observation is not surprising if one takes into account the favorable interactions between water, W, and polar, P, components, as specified in the interaction energy matrix shown in eq 5a. Furthermore, Figure 10C, which illustrates the hydrophobic component profiles for the same film formation process, shows enrichment of the hydrophobic component, NP, near the F-A interface, which is likely related to unfavorable energetics between hydrophobic components and the polar and/or water components. Simultaneous analysis of the data presented in Figure 10A-C provides further insights into the film formation process near the F-A interface (Z ≈ 16-23), where a thin layer (approximately 3-4 LSUs) exists in which no polar component is present. Such a thin layer is comprised only of the thermodynamically incompatible, yet reactive, water and hydrophobic components, as a result of which, under sufficient mobility, self-nucleation and growth of phase-separated hydrophobe and water domains occurs, resulting in surface de-wetting behavior. Such behavior is schematically illustrated in Figure 11A, and as is seen, upon complete evaporation of water, only the nonpolar component remains on the surface, which is illustrated in Figure 11B. However, at this point, while a maximum in the surface roughness exists, chemical reactions are still incomplete, and hydrophobic domains that had previously exhibited de-wetting behavior are now able to flow out on the surface and cross-link. Ultimately, surface roughness is somewhat reduced by this process (22) Gutoff, E. B. In Technology for Waterborne Coatings; Glass, J. E., Ed.; American Chemical Society: Washington, DC, 1997; Vol. 663, pp 245-264.

as the film reaches a steady-state equilibrium, which is depicted in Figure 11C. Conclusions These studies combined state-of-the-art experimental evidence with computational analysis using Monte Carlo simulations of film formation in WB 2K-PURs. This approach provided mechanistic insight for a number of processes occurring during film formation. Specifically, we observed that surface roughness scales with water concentration and reactivity of components, but surface roughness decreases with increasing reactant mobilities. While compositional gradients were detected for all conditions, specific compositional profiles were shown to be a function of the simulation parameters. One of the key findings of these studies is that simultaneous stratification of hydrophobic components along with water evaporation to the F-A interface results in a metastable interfacial layer, leading to surface dewetting. It is this specific process that is responsible for the evolution of rough surface features in heterogeneous, multicomponent systems such as WB 2K-PUR. Furthermore, these studies demonstrated that surface roughness is enhanced by higher concentrations of water in the cross-linking film, which from a practical point of view would be expected when cross-linking reactions occur at elevated RH. Consequently, experimental observations of the formation of rough surfaces under high RH conditions are supported by the predictions of the Monte Carlo simulations. Acknowledgment. This work was supported primarily by the MRSEC Program of the National Science Foundation under Award No. DMR 0213883. The authors are also thankful to the National Science Foundation MRI Program under Award No. DMR 0315637 for partial financial support of these studies. Bayer Corporation is acknowledged for providing materials used in these studies. LA047564R