Stress Fluctuations in Drying Polymer Dispersions

Transcription

1 pubs.acs.org/langmuir 2010 American Chemical Society Stress Fluctuations in Drying Polymer Dispersions Alexander M. K onig and Diethelm Johannsmann* Institute of Physical Chemistry, Clausthal University of Technology, Arnold-Sommerfeld-Str. 4, D Clausthal-Zellerfeld, Germany Received January 30, Revised Manuscript Received March 10, 2010 Drying polymer dispersions usually experience tensile stress, induced by the reduction in volume and by the rigid substrate. Due to edge-in drying, the stress is usually heterogeneous over the film. Stress peaks play a decisive role in the formation of cracks. This work relies on membrane bending, a technique that provides spatially resolved stress maps. In the experiments reported here, stress fluctuations on the order of 10% on the time scale of a few seconds were found. The stress fluctuations occur coherently over the entire drying front. Fluctuations go back to slight fluctuations in humidity of the environment (as opposed to local stress relaxations due to reorganizations of the particle network). The stress fluctuations disappear when covering the sample with a lid. They can be enhanced by blowing humid or dry air across the sample surface. Modeling builds on the assumption that all stresses go back to capillary pressure created at the menisci in between different spheres at the film-air interface. The local radius of curvature changes in response to slight variations in ambient humidity according to the Kelvin equation. The fluctuations are observed under a wide variety of drying conditions and should be included in film formation models. Introduction Film formation from aqueous polymer dispersions is of outstanding relevance for the coatings industry. 1-5 Current environmental regulations pose strict limits on the release of volatile organic compounds (VOC). The market volume of waterborne coatings is constantly growing. Despite the fact that latexes contain almost only water as solvent, they have the benefit that the material properties can be tuned over a broad range. Examples for nanostructured composites are manifold, i.e., latex blends 6,7 or core-shell particles. 8 Of course, the film formation process also is challenging in a few ways. The drying film undergoes a series of transformations, which are water evaporation, particle deformation, interparticle boundary break-up, and polymer interdiffusion. A number of film defects are related to specific steps in the drying process. For example, skin formation happens *Author for correspondence. johannsmann@pc.tu-clausthal.de. (1) Keddie, J. L. Film formation of latex. Mater. Sci. Eng. R 1997, 21, (3), (2) Steward, P. A.; Hearn, J.; Wilkinson, M. C. An overview of polymer latex film formation and properties. Adv. Colloid Interface Sci. 2000, 86, (3), (3) Winnik, M. A. Latex film formation. Curr. Opin. Colloid Interface Sci. 1997, 2, (2), (4) Dobler, F.; Holl, Y. Mechanisms of latex film formation. Trends Polym. Sci. 1996, 4, (5), (5) Keddie, J.; Routh, A. F. Latex Film Formation: with Applications in Nanomaterials, 1st ed.; Springer: Heidelberg, (6) Tzitzinou, A.; Keddie, J. L.; Geurts, J. M.; Peters, A.; Satguru, R. Film formation of latex blends with bimodal particle size distributions: Consideration of particle deformability and continuity of the dispersed phase. Macromolecules 2000, 33, (7), (7) Colombini, D.; Hassander, H.; Karlsson, O. J.; Maurer, F. H. J. Influence of the particle size and particle size ratio on the morphology and viscoelastic properties of bimodal hard/soft latex blends. Macromolecules 2004, 37, (18), (8) Juhue, D.; Lang, J. Film formation from dispersion of core-shell latexparticles. Macromolecules 1995, 28, (4), (9) Eckersley, S. T.; Rudin, A. Drying behavior of acrylic latexes. Prog. Org. Coat. 1994, 23, (4), (10) Routh, A. F.; Russel, W. B. Deformation mechanisms during latex film formation: Experimental evidence. Ind. Eng. Chem. Res. 2001, 40, (20), (11) Erkselius, S.; Wadso, L.; Karlsson, O. J. Drying rate variations of latex dispersions due to salt induced skin formation. J. Colloid Interface Sci. 2008, 317, (1), if water evaporation is so fast that particles accumulate at the air-water interface Cracking usually is initiated in the particle deformation stage, where there is a volume shrinkage on an elastically coupled network of particles Due to the rigid substrate, the film cannot shrink in all three dimensions. Tensile stress-and possibly even cracks-results. Tensile stress is usually monitored by applying the film to a flexible substrate. Upon drying, the substrate bends upward as first reported by Stoney in Today, the beam bending technique is wellestablished A complication in the beam bending technique is the fact that the drying of dispersions usually proceeds heterogeneously. In the experiments reported below, the films experienced edge-in drying. The particles consolidate at the edges first. Later, a drying front propagates from the edge toward the center. The stress is largest at the drying front. Importantly, such heterogeneities are not easily captured by the beam bending technique because the latter only detects an average stress. We have previously reported on a technique that allows for spatially resolved stress measurements, termed membrane bending. 21 The principle of detection builds on (12) Konig, A. M.; Weerakkody, T. G.; Keddie, J. L.; Johannsmann, D. Heterogeneous drying of colloidal polymer films: Dependence on added salt. Langmuir 2008, 24, (14), (13) Lee, W. P.; Routh, A. F. Why do drying films crack? Langmuir 2004, 20, (23), (14) Russel, W. B.; Wu, N.; Man, W. Generalized Hertzian model for the deformation and cracking of colloidal packings saturated with liquid. Langmuir 2008, 24, (5), (15) Singh, K. B.; Bhosale, L. R.; Tirumkudulu, M. S. Cracking in drying colloidal films of flocculated dispersions. Langmuir 2009, 25, (8), (16) Singh, K. B.; Tirumkudulu, M. S. Cracking in drying colloidal films. Phys. Rev. Lett. 2007, 98, (21). (17) Stoney, G. G. The tension of metallic films deposited by electrolysis. Proc. R. Soc. London, Ser. A 1909, 82, (553), (18) Francis, L. F.; McCormick, A. V.; Vaessen, D. M.; Payne, J. A. Development and measurement of stress in polymer coatings. J. Mater. Sci. 2002, 37, (22), (19) Martinez, C. J.; Lewis, J. A. Shape evolution and stress development during latex-silica film formation. Langmuir 2002, 18, (12), (20) Petersen, C.; Heldmann, C.; Johannsmann, D. Internal stresses during film formation of polymer latices. Langmuir 1999, 15, (22), (21) von der Ehe, K.; Johannsmann, D. Maps of the stress distributions in drying latex films. Rev. Sci. Instrum. 2007, 78, (11), 5. Langmuir 2010, 26(12), Published on Web 03/18/2010 DOI: /la100454z 9437

2 the deformation of a flexible membrane. The back of the membrane serves as an optical mirror. A regular grid is reflected at the back and imaged by a camera. The distortion of the reflected image can be used to derive the vertical deflection pattern of the membrane and-and in a second step-the stress distribution which causes the deformation. The stress maps acquired with this instrument, generally speaking, confirm the established models of film formation. However, there were also deviations in the details. For example, dilational stress was observed for drying films showing a strong coffee-stain effect. 22 This paper is concerned with stress fluctuations ahead of the drying front. We elaborate on the mechanism driving these fluctuations and their relevance for the film formation process. Experimental Section Material and Experimental. The results reported here were obtained on an acrylic polymer dispersion prepared by miniemulsion polymerization. 23,24 The monomer composition was (49.5:49.5:1) of butyl acrylate (BA):methyl methacrylate (MMA):acrylic acid (AA). Acrylic acid acts as a electrosteric stabilizer. The ratio of BA to MMA was chosen such that the glass transition temperature, T g,as determined by dynamic scanning calorimetry (DSC) was 18 C. Dowfax 2A1, an anionic sulfonate was used as emulsifier (4 wt % with respect to the monomer phase). The solids content was 49 wt %. The particle diameter, as determined by dynamic light scattering (DLS) was 190 nm. The dispersion was kindly provided by Raquel Rodriguez and Maria Barandarian (University of the Basque Country). A volume of 150 μl of the dispersion was spread onto the membrane surface. The wet film was circular in shape with a diameter of 2.5 cm, which corresponds to a wet thickness of 300 μm. Since the diameter of the film greatly exceeds the capillary length, l cap =(γ/(fg)) 1/2, the film is essentially flat. The curved rim has a width of about l cap 2 mm. Unless mentioned otherwise, the film was dried at a temperature of 25 C and a humidity of 45% RH. There was no active control of the environment. However, the experiments were performed in a separate room with no other use. The climate conditions were the same for all experiments. Stress Mapping. The instrument used to acquire the stress maps is described in ref 21. The latex film is deposited on a flexible, partially reflective membrane, which is fixed in a supporting frame and stretched by a tension ring (Figure 1). The membrane material is a PET foil which is coated with an aluminum layer. Under the influence of the drying-induced surface stress, the membrane deforms. The deformation is monitored by imaging a regular object (a grid) across the back of the membrane. The membrane serves as a distorted mirror. A second camera acquires images of the sample from the top simultaneously. Automated image analysis leads to a map of vertical displacement of the membrane, u z (x, y). Assuming that the stress is the same along x and y (in-plane isotropy) and, further, that the bending stiffness of the membrane is negligible, one can convert u z (x, y) to a surface stress, σ f (x, y), (in units of N/m) via the relation 21 σ f ðx, yþ ¼ 2Γ u z ðx, yþ ð1þ d m Γ is the lateral tension of the membrane (in units of N/m) and d m is the membrane thickness. Since the bending stiffness of a (22) Konig, A. M.; Bourgeat-Lami, E.; Mellon, V.; Von der Ehe, K.; Routh, A. F.; Johannsmann, D. Dilational stress in drying latex films. Langmuir 2010, accepted. (23) Antonietti, M.; Landfester, K. Polyreactions in miniemulsions. Prog. Polym. Sci. 2002, 27, (4), (24) Asua, J. M. Miniemulsion polymerization. Prog. Polym. Sci. 2002, 27, (7), Figure 1. Sketch of the experimental setup. Figure 2. (A,B) Photographs of the setup. (C) Distorted image of a grid. The lateral displacement of the dots is proportional to a local stress gradient. Integration provides the stress map (panel D). membrane scales with the cube of its thickness, the membrane should be as thin as possible. A membrane s extensibility scales linearly with the inverse thickness. The membrane must be strong enough to support a tension Γ larger than the film stress, σ f.for that reason, a practical lower limit for the membrane thickness is around 10 μm. Γ was calibrated by placing known weights onto the membrane. Γ and d m werearound70n/mand12μm, respectively. In principle, one might convert the surface stress, σ f,toan average bulk stress, Æσæ, by dividing by the film thickness. However, since the stress distribution along the vertical may very well be heterogeneous, such a conversion is potentially misleading. We therefore discuss the surface stress only. Results and Discussion A typical stress map is shown in Figure 2D. Usually, the stress front originates at the rim and later propagates toward the center (Figure 3). The stress front coincides with the drying front, where the latter is identified as the border between the white and the transparent portions of the sample. At the drying front, the stress is at a maximum. Stress fluctuations reported below occur only close to the drying front. Neither the wet center nor the dry areas fluctuate in stress. Figure 4 shows subsections of the raw images separated by time intervals of 2 s. The location of the stress front is indicated by a vertical line. The lateral displacements of the dots correspond to changes in the stress gradients. Clearly, the encircled dots move back and forth. Note that the apparent position of a dot reflects the local deflection of the membrane, it therefore is proportional to the stress gradient at the respective position. The absolute stress (cf. Equation 1) results from integration over the vector field of local deflections DOI: /la100454z Langmuir 2010, 26(12),

3 Figure 3. Stress profiles along a cut through the image at different times. Clearly, tensile stress evolves at the rim and later propagates toward the center. Figure 5. Lateral displacement of dots at the stress front versus time. The lateral displacement is proportional to the stress gradient. (A) Ambient conditions (45% RH, 25 C). (B) Humid air (>95% RH) blown across the sample surface at the times indicated by arrows. (C) Dry air (<10% RH) blown across the sample surface at the time indicated by an arrow. Figure 4. Raw images of the grid at the stress front. The lateral displacement reflects the stress gradient. Vertical lines indicate the location of the stress front. Panel A shows a sequence of three images (time interval 2 s) for a film drying under ambient conditions (45% RH, 25 C). The dots move horizontally. The sequence shown in panel B shows the same experiment, a few seconds later. At the time corresponding to image II, a stream of humid air was blown across the sample surface. Clearly, the magnitude of the movement is greatly increased compared to panel A. Roman numbers in panel B correspond to the same numbers in Figures 5 and 6. Figure 4A shows images taken under typical drying conditions (nominally stagnant air), whereas Figure 4B shows a case where humid air was blown across the sample surface. Image II corresponds to the time of high local humidity. The movement of the dot is much stronger in Figure 4B. However, in Figure 4A the movement of the dot exceeds the signal-to-noise ratio by a factor of 1000, as well. After covering the sample with a lid, the stress fluctuations are below the accuracy of the image analysis software, which is 10-4 pixels. Figure 5 displays the lateral displacement of a single dot vs time. Figure 6 shows the same data converted to surface stress. Panel A in both Figures 5 and 6 correspond to Figure 4A (typical drying conditions). Panels B and C show experiments where humid air (B) and dry air (C) were blown across the sample surface. Roman numbers in Figure 5B and Figure 6B correspond to the same numbers in Figure 4B. Arrows indicate the time when humid or dry air was blown across the sample surface. While these findings suggest that a variable ambient humidity is the cause of the stress fluctuations, one might also consider local rearrangements of the particle network (void collapse) as a possible origin. Such void collapses might, for instance, be caused (25) Holmes, D. M.; Kumar, R. V.; Clegg, W. J. Cracking during lateral drying of alumina suspensions. J. Am. Ceram. Soc. 2006, 89, (6), (26) Holmes, D. M.; Tegeler, F.; Clegg, W. J. Stresses and strains in colloidal films during lateral drying. J. Eur. Ceram. Soc. 2008, 28, (7), Langmuir 2010, 26(12), Figure 6. Surface stress at the stress front versus time for the same experiment as in Figure 5. by the mechanism described in refs 25 and 26, where Holmes et al. dried electrostatically stabilized silica dispersions. They measured the height of drying dispersions versus time and conclude that charged particles may form an elastically coupled (metastable) network without actually touching each other. Later, the increasing pressure forces the particles into direct (van der Waals) contact, they overcome the electrostatic DLVO barrier. One can argue that such collapse events should lead to sudden drops of local stress in consequence to stress fluctuations. This scenario can be excluded as a driving mechanism for the fluctuations reported here. Figure 7 shows differences between successive stress maps. Gray scales are the differences in stress between successive images. The time interval was 0.5 s. The sign of the difference is reversed between panels A and B. Figure 7 reflects a transient peak in stress. Importantly, the stress peak occurs coherently over the entire stress front. This finding is incompatible with void collapse as the driving factor. Fluctuations of humidity, on the contrary, are expected to affect the entire film synchronously. A second argument against void collapse as the source of stress fluctuation is derived from the details of the fluctuation pattern. Local void collapse should cause a sudden drop in stress and a slow, subsequent increase, as the sample keeps drying. DOI: /la100454z 9439

4 Figure 7. Differences between three stress maps such as shown in Figure 2B at a time interval of 0.5 s. (A) second - first; (B) third - second. The sign of the difference is reversed between panels A and B. Importantly, the fluctuations occur coherently over the entire stress front. Plotting the local stress versus time, we find no such sudden drops (Figure 6A). We applied statistical analysis to Figure 6A (and a larger data set of that type) to search for sudden drops. We produced a histogram of stress differences between successive data points and calculated the skewness of this distribution. Sudden collapse should make this histogram asymmetric (skewed). However, the skewness was always compatible with zero. Note that the sudden drops visible in Figure 6B are not caused by void collapse. At the times indicated by vertical arrows, humid air was blown across the sample. The local humidity abruptly increases and the stress decreases accordingly. It takes a few seconds to recover to the previous state. Therefore, the peaks have an asymmetric shape. The asymmetry is caused by an abrupt increase of humidity rather than void collapse. Figure 6C shows the analogous experiment with dry air. In the following, we argue that even slight changes of humidity can easily cause stress fluctuations of the magnitude observed in experiment. A related phenomenon is known from the field of moist granular media. 23 The forces of capillary adhesion are difficult to predict, partly because small fluctuations in humidity lead to large fluctuations in capillary pressure. The model builds on a combination of the Kelvin and the Laplace equation. 27 It assumes that the stress is governed by capillary pressure. The analysis below shows that capillary pressure-rather than dry or wet sintering-is the mechanism for particle deformation. Capillary pressure, Δp,isgivenby Figure 8. Sketch of the postulated mechanism leading to stress fluctuations. Interstitial volumes of the particles at the top of the film are filled with serum. The curved surface exerts a capillary force onto the particles. The local curvature responds to small variations in ambient humidity which, in turn, causes fluctuations in capillary pressure and film stress. fast equilibration, the relative humidity, RH = p vap /p sat,planar,is therefore close to p sat,curved /p sat,planar, at any time. Combination of eq 2 and eq 3 leads to the relation Δp ¼ RT V ln p sat, curved RT p sat, planar V ln RH ð4þ Δp ¼ 2γ ð2þ r K where γ is the air-water interfacial tension and r K is the radius of curvature at the meniscus; see Figure 8. The radius of curvature, in turn, is governed by the Kelvin equation Pressure fluctuations, δ(δp), can be expressed as δðδpþ ¼ dðδpþ drh δrh According to eq 4, the derivative is ð5þ ln p sat, curved p sat, planar ¼ 2γV r K RT where V is the molar volume of the solvent (18 cm 3 /mol), p sat,curved and p sat,planar are the equilibrium vapor pressures above a curved and a planar surface, respectively, R is the gas constant, and T is the temperature. As shown below, the vapor pressure above a curved interface, p sat,curved, is almost equal to the instant local vapor pressure, p vap. While the vapor pressure might, in principle, be different from the saturated vapor pressure, equilibration is fast, and saturation is quickly achieved. Note: this argument applies to vapor pressure immediately above the water surface. This pressure above the water surface is governed by the rate of transfer between the liquid and the vapor. A finite diffusivity in the vapor phase is unessential. Because of (27) Adamson, A. W. Physical Chemistry of Surfaces, 4th ed.; John Wiley & Sons: New York, ð3þ dðδpþ drh ¼ RT V 1 RH Inserting a humidity fluctuation, δrh/rh, of 1% leads to a pressure fluctuation of δ(δp) = N/m 2. In order to convert from pressure (same as bulk stress) to surface stress, one multiplies by the film thickness, h. Usingh 150 μm leadstoδσ f 200 N/m, which is two decades above the values shown in Figure 6A. This estimate shows that even minute fluctuations of humidity cause sizable fluctuations of surface stress. This mechanism is illustrated in Figure 8. Interstitial volumes at the top of the film are partially filled with serum and the curved surface exerts a capillary force onto the particles. The curvature, in turn, responds to variations in ambient humidity above the surface. In the following, we prove that the capillary pressure responds to variations in humidity on the time scale of less than a secondas suggested by the experiments. According to kinetic gas theory, ð6þ 9440 DOI: /la100454z Langmuir 2010, 26(12),

5 where N A is Avogadro s number, p vap is the vapor pressure, and M is the molar mass (18 g/mol for water). Using the values p vap = 31 mbar and T = 298 K leads to collisions per square meter per second. Assuming a size of the water molecule of 0.3 nm leads to a growth rate of 10 7 monolayers (3 mm) per second. Clearly, the recondensation of water equilibrates the vapor pressure and the local curvature of the air-water interface (eq 3) very quickly. When blowing humid air across the sample surface, recondensation is evident from the optical appearance of the film (see Figure 9). The dry region closely behind the drying front (white square in panel B) turns turbid in high humidity. After the cessation of flow, the area quickly becomes transparent again (panels C-E). The fluctuations reported here differ compared to those reported in refs 15 and 16. Singh et al. related the fluctuations to cracking, while we observed stress fluctuations depending on local relative humidity above the drying film. These have no relation to cracking. The current film formation models predict a monotonous increase of stress ahead of the drying front and stress relaxation behind the drying front. Our work shows that the detailed stress evolution is more complex. Even at nominally stagnant air, the residual slight fluctuations in humidity cause stress fluctuations on the order of 10%. Any single sphere does not experience a single peak in stress but rather a series of stress maxima. Such a complex stress history should affect the film formation process. Figure 9. Images acquired from above the sample. ), dry portion;, wet portion; O, drying front. The time interval between the images was 2 s. Humid air was blown across the sample surface shortly before the acquisition of the photograph shown in panel B. Parts of the film which had turned clear already became turbid again, which is a consequence of recondensation. The area indicated by the dotted ellipse stays dark due to an artifact in image acquisition. This portion of the surface is inclined and therefore reflects the light less efficiently than the rest of the sample. For an illustration, see sketch below panel B. The transparency is recovered within a few seconds. the flux of molecules, Z w, colliding with a surface is given by 28 N A p Z w ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2πMRT (28) Somorjai, G. A. Introduction to Surface Chemistry and Catalysis; John Wiley & Sons: New York, ð7þ Conclusions Applying membrane bending, one finds that the local stress at the drying front fluctuates by up to 10%. The stress fluctuations are caused by small variations in the local humidity. Kinetic gas theory in conjunction with the Laplace and the Kelvin equation shows that recondensation of water can explain these findings. The fluctuations have two consequences for the film formation process. On the one hand, a sudden drop in stress can allow for a rearrangement of the packed network of particles which, in turn, would lead to a more homogeneous film. On the other hand, a sudden maximum in stress can lead to the formation of microcracks. Stress fluctuations should be included in the models of film formation. Acknowledgment. This work was funded by the EU under contract IP (Napoleon). We thank Raquel Rodriguez and Maria Barandarian (University of the Basque Country, San Sebastian) for preparing the latex, HVB (Hoch-Vakuum- Beschichtungs GmbH, Berlin) for providing the PET foil, and Alexander F. Routh for helpful discussions. Langmuir 2010, 26(12), DOI: /la100454z 9441