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-38678 Clausthal-Zellerfeld, Germany Received January 30, 2010. 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 blends6,7 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.
[email protected]. (1) Keddie, J. L. Film formation of latex. Mater. Sci. Eng. R 1997, 21, (3), 101-170. (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), 195-267. (3) Winnik, M. A. Latex film formation. Curr. Opin. Colloid Interface Sci. 1997, 2, (2), 192-199. (4) Dobler, F.; Holl, Y. Mechanisms of latex film formation. Trends Polym. Sci. 1996, 4, (5), 145-151. (5) Keddie, J.; Routh, A. F. Latex Film Formation: with Applications in Nanomaterials, 1st ed.; Springer: Heidelberg, 2009. (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), 2695-2708. (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), 6865-6873. (8) Juhue, D.; Lang, J. Film formation from dispersion of core-shell latexparticles. Macromolecules 1995, 28, (4), 1306-1308. (9) Eckersley, S. T.; Rudin, A. Drying behavior of acrylic latexes. Prog. Org. Coat. 1994, 23, (4), 387-402. (10) Routh, A. F.; Russel, W. B. Deformation mechanisms during latex film formation: Experimental evidence. Ind. Eng. Chem. Res. 2001, 40, (20), 4302-4308. (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), 83-95.
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if water evaporation is so fast that particles accumulate at the air-water interface.9-12 Cracking usually is initiated in the particle deformation stage, where there is a volume shrinkage on an elastically coupled network of particles.13-16 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 1909.17 Today, the beam bending technique is wellestablished.18-20 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), 7580-7589. (13) Lee, W. P.; Routh, A. F. Why do drying films crack? Langmuir 2004, 20, (23), 9885-9888. (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), 1721-1730. (15) Singh, K. B.; Bhosale, L. R.; Tirumkudulu, M. S. Cracking in drying colloidal films of flocculated dispersions. Langmuir 2009, 25, (8), 4284-4287. (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), 172-175. (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), 4717-4731. (19) Martinez, C. J.; Lewis, J. A. Shape evolution and stress development during latex-silica film formation. Langmuir 2002, 18, (12), 4689-4698. (20) Petersen, C.; Heldmann, C.; Johannsmann, D. Internal stresses during film formation of polymer latices. Langmuir 1999, 15, (22), 7745-7751. (21) von der Ehe, K.; Johannsmann, D. Maps of the stress distributions in drying latex films. Rev. Sci. Instrum. 2007, 78, (11), 5.
Published on Web 03/18/2010
DOI: 10.1021/la100454z
9437
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K€ onig and Johannsmann
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.
Figure 1. Sketch of the experimental setup.
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, Tg, 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, lcap = (γ/(Fg))1/2, the film is essentially flat. The curved rim has a width of about lcap ≈ 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, uz(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 uz(x, y) to a surface stress, σf(x, y), (in units of N/m) via the relation21 σf ðx, yÞ ¼
2Γ uz ðx, yÞ dm
ð1Þ
Γ is the lateral tension of the membrane (in units of N/m) and dm 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), 689-757. (24) Asua, J. M. Miniemulsion polymerization. Prog. Polym. Sci. 2002, 27, (7), 1283-1346.
9438 DOI: 10.1021/la100454z
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, σf. 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 dm were around 70 N/m and 12 μm, respectively. In principle, one might convert the surface stress, σf, to an 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. Langmuir 2010, 26(12), 9437–9441
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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 (
