DOI: 10.1021/la100454z 9437Langmuir 2010, 26(12), 9437–9441 Published on Web 03/18/2010

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 rigidsubstrate. Due to edge-in drying, the stress is usually heterogeneous over the film. Stress peaks play a decisive role in theformation of cracks. This work relies onmembrane bending, a technique that provides spatially resolved stress maps. Inthe experiments reported here, stress fluctuations on the order of 10%on the time scale of a few seconds were found. Thestress fluctuations occur coherently over the entire drying front. Fluctuations go back to slight fluctuations in humidityof the environment (as opposed to local stress relaxations due to reorganizations of the particle network). The stressfluctuations disappearwhen covering the sample with a lid. They can be enhanced by blowing humid or dry air across thesample surface.Modeling builds on the assumption that all stresses go back to capillary pressure created at themenisci inbetween different spheres at the film-air interface. The local radius of curvature changes in response to slight variationsin ambient humidity according to the Kelvin equation. The fluctuations are observed under a wide variety of dryingconditions and should be included in film formation models.

Introduction

Film formation from aqueous polymer dispersions is of out-standing relevance for the coatings industry.1-5 Current environ-mental regulations pose strict limits on the release of volatileorganic compounds (VOC). The market volume of waterbornecoatings is constantly growing. Despite the fact that latexescontain almost only water as solvent, they have the benefitthat the material properties can be tuned over a broad range.Examples for nanostructured composites are manifold, i.e., latexblends6,7 or core-shell particles.8 Of course, the film formationprocess also is challenging in a few ways. The drying film under-goes a series of transformations, which are water evaporation,particle deformation, interparticle boundary break-up, and poly-mer interdiffusion. A number of film defects are related to specificsteps in the drying process. For example, skin formation happens

if water evaporation is so fast that particles accumulate at theair-water interface.9-12 Cracking usually is initiated in theparticle deformation stage, where there is a volume shrinkageon an elastically coupled network of particles.13-16 Due to therigid substrate, the film cannot shrink in all three dimensions.Tensile stress-and possibly even cracks-results. Tensile stress isusually monitored by applying the film to a flexible substrate.Upon drying, the substrate bends upward as first reported byStoney in 1909.17 Today, the beam bending technique is well-established.18-20

A complication in the beam bending technique is the fact thatthe drying of dispersions usually proceeds heterogeneously. In theexperiments reported below, the films experienced edge-in drying.The particles consolidate at the edges first. Later, a drying frontpropagates from the edge toward the center. The stress is largest atthe drying front. Importantly, such heterogeneities are not easilycaptured by the beam bending technique because the latter onlydetects an average stress. We have previously reported on atechnique that allows for spatially resolved stress measurements,termed membrane bending.21 The principle of detection builds on

*Author for correspondence. johannsmann@pc.tu-clausthal.de.(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 ofparticle deformability and continuity of the dispersed phase. Macromolecules2000, 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 viscoelasticproperties of bimodal hard/soft latex blends. Macromolecules 2004, 37, (18),6865-6873.(8) Juhue, D.; Lang, J. Film formation from dispersion of core-shell latex-

particles. 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.

(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 thedeformation and cracking of colloidal packings saturated with liquid. Langmuir2008, 24, (5), 1721-1730.

(15) Singh, K. B.; Bhosale, L. R.; Tirumkudulu, M. S. Cracking in dryingcolloidal 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. Develop-ment 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 duringlatex-silica film formation. Langmuir 2002, 18, (12), 4689-4698.

(20) Petersen, C.; Heldmann, C.; Johannsmann, D. Internal stresses during filmformation of polymer latices. Langmuir 1999, 15, (22), 7745-7751.

(21) von der Ehe, K.; Johannsmann, D. Maps of the stress distributions indrying latex films. Rev. Sci. Instrum. 2007, 78, (11), 5.

9438 DOI: 10.1021/la100454z Langmuir 2010, 26(12), 9437–9441

Article K€onig and Johannsmann

the deformation of a flexible membrane. The back of themembrane serves as an optical mirror. A regular grid is reflectedat the back and imaged by a camera. The distortion of thereflected image can be used to derive the vertical deflectionpattern of the membrane and-and in a second step-the stressdistribution which causes the deformation.

The stress maps acquired with this instrument, generallyspeaking, 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 strongcoffee-stain effect.22

This paper is concerned with stress fluctuations ahead of thedrying front. We elaborate on the mechanism driving thesefluctuations and their relevance for the film formation process.

Experimental Section

Material and Experimental. The results reported here wereobtainedonanacrylic polymerdispersionpreparedbyminiemulsionpolymerization.23,24 Themonomer composition was (49.5:49.5:1) ofbutyl acrylate (BA):methyl methacrylate (MMA):acrylic acid (AA).Acrylic acid acts as a electrosteric stabilizer. The ratio of BA toMMAwas chosen such that the glass transition temperature, Tg, asdetermined by dynamic scanning calorimetry (DSC) was 18 �C.Dowfax 2A1, an anionic sulfonate was used as emulsifier (4 wt %with respect to themonomerphase).The solids contentwas49wt%.The particle diameter, as determined by dynamic light scattering(DLS) was 190 nm. The dispersion was kindly provided by RaquelRodriguez and Maria Barandarian (University of the BasqueCountry).

A volume of 150 μL of the dispersion was spread onto themembrane surface. The wet film was circular in shape witha diameter of 2.5 cm, which corresponds to a wet thickness of300μm.Since the diameter of the filmgreatly exceeds the capillarylength, lcap= (γ/(Fg))1/2, the film is essentially flat. The curved rimhas awidthof about lcap≈ 2mm.Unlessmentionedotherwise, thefilm 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 roomwith no otheruse. The climate conditions were the same for all experiments.

Stress Mapping. The instrument used to acquire the stressmaps is described in ref 21. The latex film is deposited ona flexible,partially reflectivemembrane,which is fixed ina supporting frameand stretchedbya tension ring (Figure 1). Themembranematerialis a PET foil which is coated with an aluminum layer. Under theinfluence of the drying-induced surface stress, the membranedeforms. The deformation is monitored by imaging a regularobject (a grid) across the back of the membrane. The membraneserves as a distorted mirror. A second camera acquires images ofthe sample from the top simultaneously.

Automated image analysis leads to a map of vertical displace-ment of the membrane, uz(x, y). Assuming that the stress is thesame along x and y (in-plane isotropy) and, further, that thebending stiffness of the membrane is negligible, one can convertuz(x, y) to a surface stress, σf(x, y), (in units of N/m) via therelation21

σf ðx, yÞ ¼ 2Γdm

uzðx, yÞ ð1Þ

Γ is the lateral tension of the membrane (in units of N/m) anddm is the membrane thickness. Since the bending stiffness of a

membrane scales with the cube of its thickness, the membraneshould be as thin as possible. A membrane’s extensibility scaleslinearly with the inverse thickness. The membrane must be strongenough to support a tension Γ larger than the film stress, σf. Forthat reason, a practical lower limit for the membrane thickness isaround 10 μm.Γwas calibrated by placing knownweights onto themembrane. Γ and dmwere around 70N/m and 12 μm, respectively.

In principle, one might convert the surface stress, σf, to anaverage bulk stress, Æσæ, by dividing by the film thickness. How-ever, since the stress distribution along the vertical may very wellbe heterogeneous, such a conversion is potentiallymisleading.Wetherefore discuss the surface stress only.

Results and Discussion

A typical stress map is shown in Figure 2D. Usually, the stressfront originates at the rim and later propagates toward the center(Figure 3). The stress front coincides with the drying front, wherethe latter is identified as the border between the white and thetransparent portions of the sample. At the drying front, the stressis at a maximum. Stress fluctuations reported below occur onlyclose to the drying front. Neither the wet center nor the dry areasfluctuate in stress.

Figure 4 shows subsections of the raw images separated by timeintervals of 2 s. The location of the stress front is indicated by avertical line. The lateral displacements of the dots correspond tochanges in the stress gradients. Clearly, the encircled dots moveback and forth. Note that the apparent position of a dot reflectsthe local deflection of the membrane, it therefore is proportionalto the stress gradient at the respective position. The absolute stress(cf. Equation 1) results from integration over the vector field oflocal deflections.

Figure 1. Sketch of the experimental setup.

Figure 2. (A,B)Photographsof the setup. (C)Distorted imageof agrid. The lateral displacement of the dots is proportional to a localstress gradient. Integration provides the stress map (panel D).

(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.

DOI: 10.1021/la100454z 9439Langmuir 2010, 26(12), 9437–9441

K€onig and Johannsmann Article

Figure 4A shows images taken under typical drying conditions(nominally stagnant air), whereas Figure 4B shows a case wherehumid air was blown across the sample surface. Image IIcorresponds to the time of high local humidity. The movementof the dot is much stronger in Figure 4B. However, in Figure 4Athe movement of the dot exceeds the signal-to-noise ratio by afactor of 1000, as well. After covering the sample with a lid, thestress fluctuations are below the accuracy of the image analysissoftware, which is 10-4 pixels.

Figure 5 displays the lateral displacement of a single dot vstime. Figure 6 shows the same data converted to surface stress.Panel A in both Figures 5 and 6 correspond to Figure 4A (typicaldrying conditions). Panels B and C show experiments wherehumid air (B) and dry air (C) were blown across the samplesurface. Roman numbers in Figure 5B and Figure 6B correspondto the same numbers in Figure 4B. Arrows indicate the time whenhumid or dry air was blown across the sample surface.

While these findings suggest that a variable ambient humidity isthe cause of the stress fluctuations, one might also consider localrearrangements of the particle network (void collapse) as apossible origin. Such void collapses might, for instance, be caused

by themechanismdescribed in refs 25 and 26, whereHolmes et al.dried electrostatically stabilized silica dispersions. Theymeasuredthe height of drying dispersions versus time and conclude thatcharged particles may form an elastically coupled (metastable)network without actually touching each other. Later, the increas-ing pressure forces the particles into direct (van der Waals)contact, they overcome the electrostatic DLVO barrier. Onecan argue that such collapse events should lead to sudden dropsof local stress in consequence to stress fluctuations.

This scenario can be excluded as a driving mechanism for thefluctuations reported here. Figure 7 shows differences betweensuccessive stress maps. Gray scales are the differences in stressbetween successive images. The time interval was 0.5 s. The sign ofthe difference is reversed between panels A and B. Figure 7 reflectsa transient peak in stress. Importantly, the stress peak occurscoherently over the entire stress front. This finding is incompatiblewith 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 ofstress fluctuation is derived from the details of the fluctuationpattern. Local void collapse should cause a sudden drop in stressand a slow, subsequent increase, as the sample keeps drying.

Figure 3. Stress profiles along a cut through the image at differenttimes. Clearly, tensile stress evolves at the rim and later propagatestoward the center.

Figure 4. Raw images of the grid at the stress front. The lateraldisplacement reflects the stress gradient. Vertical lines indicate thelocation of the stress front. Panel A shows a sequence of threeimages (time interval 2 s) for a film drying under ambient condi-tions (45%RH, 25 �C). The dots move horizontally. The sequenceshown in panel B shows the same experiment, a few seconds later.At the time corresponding to image II, a stream of humid air wasblown across the sample surface. Clearly, the magnitude of themovement is greatly increased compared to panel A. Romannumbers in panel B correspond to the same numbers in Figures 5and 6.

Figure 5. Lateral displacement of dots at the stress front versustime. The lateral displacement is proportional to the stress gradi-ent. (A) Ambient conditions (45% RH, 25 �C). (B) Humid air(>95%RH)blownacross the sample surface at the times indicatedby arrows. (C) Dry air (

9440 DOI: 10.1021/la100454z Langmuir 2010, 26(12), 9437–9441

Article K€onig and Johannsmann

Plotting the local stress versus time, we find no such sudden drops(Figure 6A). We applied statistical analysis to Figure 6A (and alarger data set of that type) to search for suddendrops.Weproduceda histogram of stress differences between successive data points andcalculated the skewness of this distribution. Sudden collapse shouldmake this histogram asymmetric (skewed). However, the skewnesswas always compatible with zero.Note that the sudden drops visiblein Figure 6B are not caused by void collapse. At the times indicatedby vertical arrows, humid airwas blownacross the sample. The localhumidity abruptly increases and the stress decreases accordingly. Ittakes a few seconds to recover to the previous state. Therefore, thepeaks have an asymmetric shape. The asymmetry is caused by anabrupt increase of humidity rather than void collapse. Figure 6Cshows the analogous experiment with dry air.

In the following,we argue that even slight changes of humidity caneasily cause stress fluctuations of the magnitude observed in experi-ment. A related phenomenon is known from the field of moistgranular media.23 The forces of capillary adhesion are difficult topredict, partly because small fluctuations in humidity lead to largefluctuations in capillarypressure.Themodel builds ona combinationof theKelvin and the Laplace equation.27 It assumes that the stress isgoverned by capillary pressure. The analysis below shows thatcapillary pressure-rather than dry or wet sintering-is the mecha-nism for particle deformation. Capillary pressure, Δp, is given by

Δp ¼ 2γrK

ð2Þ

where γ is the air-water interfacial tension and rK is the radius ofcurvature at the meniscus; see Figure 8. The radius of curvature, inturn, is governed by the Kelvin equation

lnpsat, curved

psat, planar¼ 2γV

rKRTð3Þ

where V is the molar volume of the solvent (18 cm3/mol), psat,curvedand psat,planar are the equilibrium vapor pressures above a curved anda planar surface, respectively, R is the gas constant, and T is thetemperature. As shown below, the vapor pressure above a curvedinterface,psat,curved, is almost equal to the instant local vaporpressure,pvap. While the vapor pressure might, in principle, be different fromthe saturated vapor pressure, equilibration is fast, and saturation isquickly achieved. Note: this argument applies to vapor pressureimmediately above the water surface. This pressure above the watersurface is governed by the rate of transfer between the liquid and thevapor.A finitediffusivity in thevaporphase is unessential.Becauseof

fast equilibration, the relative humidity, RH = pvap/psat,planar, istherefore close to psat,curved/psat,planar, at any time. Combination of eq2 and eq 3 leads to the relation

Δp ¼ RTV

lnpsat, curved

psat, planar� RT

Vln RH ð4Þ

Pressure fluctuations, δ(Δp), can be expressed as

δðΔpÞ ¼ dðΔpÞd RH

δRH ð5Þ

According to eq 4, the derivative is

dðΔpÞd RH

¼ RTV

1

RHð6Þ

Inserting ahumidity fluctuation,δRH/RH,of 1% leads to apressurefluctuation of δ(Δp) = 1.3 � 106 N/m2. In order to convert frompressure (same as bulk stress) to surface stress, one multiplies bythe film thickness, h. Using h ≈ 150 μm leads to Δσf ≈ 200 N/m,which is two decades above the values shown in Figure 6A. Thisestimate shows that even minute fluctuations of humidity causesizable fluctuations of surface stress. This mechanism is illustrated inFigure 8. Interstitial volumes at the top of the film are partially filledwith serum and the curved surface exerts a capillary force onto theparticles. The curvature, in turn, responds to variations in ambienthumidity above the surface.

In the following, we prove that the capillary pressure respondsto variations in humidity on the time scale of less than a second-as suggested by the experiments. According to kinetic gas theory,

Figure 7. Differences between three stressmaps 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.

Figure 8. Sketch of the postulated mechanism leading to stressfluctuations. Interstitial volumes of the particles at the top of thefilm are filled with serum. The curved surface exerts a capillaryforce onto the particles. The local curvature responds to smallvariations in ambient humidity which, in turn, causes fluctuationsin capillary pressure and film stress.

(27) Adamson, A.W.Physical Chemistry of Surfaces, 4th ed.; JohnWiley & Sons:New York, 1982.

DOI: 10.1021/la100454z 9441Langmuir 2010, 26(12), 9437–9441

K€onig and Johannsmann Article

the flux of molecules, Zw, colliding with a surface is given by28

Zw ¼ NApffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2πMRT

p ð7Þ

where NA is Avogadro’s number, pvap is the vapor pressure, andM is themolarmass (18 g/mol for water). Using the values pvap=31 mbar and T= 298 K leads to 1026 collisions per square meterper second. Assuming a size of the water molecule of 0.3 nm leadsto a growth rate of 107 monolayers (3 mm) per second. Clearly,the recondensation of water equilibrates the vapor pressure andthe local curvature of the air-water interface (eq 3) very quickly.

When blowing humid air across the sample surface, reconden-sation is evident from the optical appearance of the film (seeFigure 9). The dry region closely behind the drying front (whitesquare in panel B) turns turbid in high humidity. After thecessation of flow, the area quickly becomes transparent again(panels C-E).

The fluctuations reported here differ compared to thosereported in refs 15 and 16. Singh et al. related the fluctuationsto cracking, while we observed stress fluctuations depending onlocal relative humidity above the drying film. These have norelation to cracking.

The current film formation models predict a monotonousincrease of stress ahead of the drying front and stress relaxationbehind the drying front. Our work shows that the detailed stressevolution is more complex. Even at nominally stagnant air, theresidual slight fluctuations in humidity cause stress fluctuationson the order of 10%. Any single sphere does not experience asingle peak in stress but rather a series of stress maxima. Such acomplex stress history should affect the film formation process.

Conclusions

Applying membrane bending, one finds that the local stress atthe drying front fluctuates by up to 10%. The stress fluctuationsare caused by small variations in the local humidity. Kinetic gastheory in conjunction with the Laplace and the Kelvin equationshows that recondensation of water can explain these findings.The fluctuations have two consequences for the film formationprocess. On the one hand, a sudden drop in stress can allow for arearrangement of the packed network of particles which, in turn,would lead to a more homogeneous film. On the other hand, asudden maximum in stress can lead to the formation of micro-cracks. Stress fluctuations should be included in the models offilm formation.

Acknowledgment. This work was funded by the EU undercontract IP 011844-2 (Napoleon). We thank Raquel Rodriguezand Maria Barandarian (University of the Basque Country, SanSebastian) for preparing the latex, HVB (Hoch-Vakuum-Beschichtungs GmbH, Berlin) for providing the PET foil, andAlexander F. Routh for helpful discussions.

Figure 9. Images acquired from above the sample. ), dry portion;�, wet portion; O, drying front. The time interval between theimages was 2 s. Humid air was blown across the sample surfaceshortly before the acquisition of the photograph shown in panel B.Parts of the film which had turned clear already became turbidagain, which is a consequence of recondensation. The area indi-cated by the dotted ellipse stays dark due to an artifact in imageacquisition. This portion of the surface is inclined and thereforereflects the light less efficiently than the rest of the sample. For anillustration, see sketch below panel B. The transparency is recov-ered within a few seconds.

(28) Somorjai, G. A. Introduction to Surface Chemistry and Catalysis; JohnWiley& Sons: New York, 1994.