Article pubs.acs.org/Langmuir
Wetting Dynamics on Superhydrophilic Surfaces Prepared by Photonic Microfolding Thomas Bahners,*,† Lutz Prager,‡ and Jochen S. Gutmann†,§ †
Deutsches Textilforschungszentrum Nord-West gGmbH (DTNW), Adlerstr. 1, 47798 Krefeld, Germany Leibniz-Institut für Oberflächenmodifizierung e.V. (IOM), Permoserstr. 15, 04318 Leipzig, Germany § Physikalische Chemie and CENIDE, Universität Duisburg-Essen, Universitätsstr. 2, 45141 Essen, Germany ‡
ABSTRACT: The wetting dynamic on microrough and perfectly wetting (superhydrophilic) acrylates was studied. These surfaces were achieved by coating polymer films made of poly(ethyleneterephthalate) (PET) with a hydrophilic acrylate based on hydroxypropylacrylate and polyethyleneglycolmonoacrylate, which was then cured and microroughened by photonic microfolding. The high transparency of the thin acrylate layers and polymer films allowed us to record the spreading of an applied water droplet through the film samples. Subsequently, the dynamic radius of the spreading pattern rc(t) was determined from the video recording. Various models for the wetting dynamics of superhydrophilic surfaces, namely, Tanner’s law and a roughness-modified derivation published by McHale et al. in 2009, were then compared to the experimental results. Basically, the development of rc(t) in time was found to be in good agreement with McHale’s model. Data analysis showed, however, that the initial phase of the spreading, that is, for t < 1 s, was not predicted well. This differing behavior relates well to a theory published by Cazabat and Cohen Stuart, who proposed that, on rough surfaces, spreading follows a power law in three time regimes. In this model, the (very) initial spreading is expected to be similar to the spreading on a smooth surface.
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called “Cassie impregnating” state (cf. de Gennes et al., Erbil, or Bormachenko).6−8 In this state, the rough surface can be described as a composite surface with the liquid penetrating the texture. Consequently, the droplet covers a solid phase with contact angle ΘY and a liquid phase with zero contact angle, with the apparent contact derived from the well-known Cassie−Baxter equation. One consequence of the Cassie impregnating state is that the surface is partially wetted in front of the triple line, which is contrast to the Wenzel state. Independent of the model, two potential cases have to be considered. Depending on the nature of the planar surface, the introduction of a microroughness increases the wettability of an intrinsically hydrophilic surface, but decreases the wettability on an already hydrophobic surface. Given this background, it was proposed to create perfectly wetting surfaces by providing moderately hydrophilic surfaces with a suitable microroughness.9−11 According to Wenzel’s equation, superwetting could also be achieved by increasing the surface free energy of a microrough surface by means of a suitable post-treatment. In recent studies, both ways have been evaluated by the authors for microrough acrylates produced by the described process of photonic microfolding. In a first approach, perfectly
INTRODUCTION Recently, perfectly wetting surfaces were prepared by coating smooth, nonporous substrates such as polymer films or coated fabrics with thin microrough acrylate layers. The microrough topography of the layers was achieved by means of special twostep UV curing process known as photonic microfolding, which was developed at IOM.1−4 The concept of the process is to apply a thin acrylate layer to a substrate by knife-coating or spraying and cure this layer by subsequent exposure to VUV and broadband UV radiation. Due to the very strong absorption in the VUV, the first curing step affects only a skin at the surface of the acrylate layer, which induces shrinkage and folding. This structure is frozen in the second curing step, which affects the full bulk of the acrylate layer. The wetting behavior of a surface is basically determined by the relation of the interfacial energies, namely, the surface free energy (SFE) of the substrate material, and by the surface roughness. In the case of a complete wetting of the liquid− substrate interface, the apparent contact angle is often described by the rather simplified Wenzel model.5 Wenzel’s equation relates the apparent contact angle of the microrough surface Θw to the contact angle of the planar surface of the same material (Young angle) ΘY with the help of a roughness or Wenzel factor r, which is defined as the ratio between the areas of rough and flat surfaces (r ≥ 1). It shall be noted at this point that full wetting is more recently also attributed to the so© 2014 American Chemical Society
Received: January 20, 2014 Revised: March 4, 2014 Published: March 6, 2014 3127
dx.doi.org/10.1021/la500227w | Langmuir 2014, 30, 3127−3131
Langmuir
Article
wetting (superhydrophilic) surfaces could be achieved by using hydrophilic hydroxypropylacrylate and polyethyleneglycolmonoacrylate as the main components of the applied acrylate.12 The experimentally observed wetting behavior followed Wenzel’s equation up to roughness factor of r ≤ 1.2. On a surface of more pronounced roughness, the full wetting was observed. However, spreading of a droplet appeared to be governed by geometric effects such as blockage by the surface. In a second approach, the wettability of microrough acrylate surfaces, inherently hydrophobic or only moderately hydrophilic, could be enhanced by plasma-based or UV-induced grafting post-treatments, both of which increased the surface free energy.13 Again, experiments showed that the wetting behavior was well correlated with the predictions of Wenzel’s model up to a certain roughness factor, above which full wetting occurred. This wetting transition was in agreement with a model proposed by Johnson and Dettre, who predict a transition from partial to full wetting, if the roughness factor r exceeds the inverse of the cosine of the Young angle, that is, r ≥ 1/cos ΘY.14 This was observed in all samples studied by the authors. In the present work, the wetting dynamic on the highly wetting acrylates based on hydroxypropylacrylate and polyethyleneglycolmonoacrylate was studied. The high transparency of the thin acrylate layers applied to equally transparent film made of poly(ethyleneterephthalate) (PET) allowed us to record the spreading pattern through the film samples. These gave good and easy access to quantitative data by determining the radius of the spreading pattern rc (spreading radius) as a function of time from the video recording.
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Figure 1. Radius of the contact area of the droplet (spreading radius) on superhydrophilic samples as a function of time in normal (A) and logarithmic (B) presentation. Data taken from two identically prepared samples are identified by full and open symbols. The dashed line in (B) represents a data fit according to rc ∝ log(t). The inset photograph shows the spreading pattern of two droplets observed on the sample with a mean roughness factor r = 1.62 ± 0.05.
EXPERIMENTAL SECTION
Following the experimental protocol described in a previous paper by the authors,12 the acrylate coating was prepared from hydroxypropylacrylate, polyethyleneglycolmonoacrylate, N,N-methylenebisacrylamide, and ethyl-2,4,6-trimethylbenzoylphenylphosphinate as photoinitiator. A 10 μm thick layer was applied to clear PET film by knife coating. The wet coating was then cured by subsequent irradiation with 172 nm VUV radiation (Xe2* excimer lamp) in nitrogen atmosphere, and a mercury medium pressure lamp emitting broadband UV irradiation with λ > 230 nm. The irradiation doses were 0.7 and 325 mJ/cm2, respectively. The averaged roughness or Wenzel factor of these surfaces was analyzed by white-light interferometry and determined as the ratio between the areas of rough and flat surfaces. The mean roughness factor of the studied samples was r = 1.62 ± 0.05. Notabene (NB): An equilibrium water contact angle of 37° was determined on the corresponding planar surface, that is, identical acrylate cured only using broadband radiation, by the sessile drop method. For the analysis of the dynamic of water on these surfaces, droplets of double distilled water (10 μL) were placed on the sample surface at 20 °C and the spreading of the droplet recorded by video camera. The high transparency of the thin acrylate layers applied to equally transparent film allowed us to record the spreading pattern through the film samples from below. For better visualization of the final contact area of the applied amount of water (“spreading pattern”), the dyestuff Astrazon Blue was added. The actual spreading dynamic was determined as the radius of the circular contact area rc as a function of time.
propagating triple line from simultaneously expected microscopic phenomena in front of the triple line, namely, the precursor film as well as partial wetting in the Cassie impregnating state (see above). One can estimate from the data that (dynamic) contact angles would be of the order of 5° and less after only 1.5 s in our measurements. At this point, spreading is mainly governed by the characteristic topographic features of our samples, which are higher than an idealized droplet (described as a spherical cap).12 Given this background, we refer the observed spreading pattern to the triple-line only and compare the experimental data to the prediction of various theoretical understandings of triple-line propagation on fully wetting surfaces in the following discussion. As can be taken from the graphs, the increase of the contact area radius can basically be described by a logarithmic trend according to rc ∝ log(t). A survey of existing literature, however, provides no theoretical background for this rather simple description. In 2001, De Coninck et al. reviewed mechanisms controlling the dynamics of wetting in partial and complete wetting regimes and related models.15 With regard the complete wetting regime, De Coninck et al. refer to various papers by Heslot, Cazabat and co-workers who used ellipsometric techniques to study the profiles of the spreading drop as a function of time t.16−18 An important observation of these experiments is the appearance of a precursor film in front of the drop, which is often constituted by a few layers of molecular thickness (cf. also Bormashenko).8 The propagation of the base radius is reported to be r ∝ √t on average, which, however,
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RESULTS AND DISCUSSION A complete compilation of all measured spreading pattern radii taken from several identically prepared samples is given in Figure 1 as a function of elapsed time. It is important to point out that it was experimentally not possible to discriminate the 3128
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does not describe the spreading dynamic observed in the experiment reported here. Also reported by De Coninck et al., considerations of molecular dynamics predict a behavior ∝(log(t))1/2. In deference of these models, it has to be acknowledged that effects of surface roughness were not taken into account. A theoretical paper by McHale et al. proposes the description of a dynamic contact angle on rough superhydrophilic surfaces as function of time by a modified Tanner’s law.19,20 Derived from the Navier−Stokes equations, Tanner’s law describes the dynamic spreading of a spherical cap droplet on a smooth surface by 1/10 ⎡ γ ⎛ 4V ⎞⎤ n ⎜ ⎟ rc(t ) = ⎢const ⎥ t ⎣ η ⎝ π ⎠⎦
In order to check McHale’s model against the experimental data, it was feasible to calculate the contact line propagation speed ve = drc/dt and plot it against rc. If we assume a simple proportionality and introduce the (unknown) constant A, we obtain the following equations: rc(t ) = A(t + t0)1/(3p + 1) log rc(t ) = log A +
ve =
⎡ ⎛ A ⎞ ⎤ log ve = ⎢log⎜ ⎟ + log A ⎥ − (3p)log rc ⎢⎣ ⎝ 3p + 1 ⎠ ⎦⎥
(2)
(9)
(10)
(3)
Figure 2. Experimentally determined velocity of contact line propagation as a function of spreading radius versus eq 10, which was derived from McHale’s model of spreading dynamics on fully wetting rough surfaces (dashed line). The parameter p in McHale’s model (eq 6) was determined by the best fit as p = 1.05.
eq 10. The calculation provides p = 1.05, which agrees well with the value for a rough surface in McHale’s model, which assumes p = 1 for rough surfaces. The corresponding power law of the spreading dynamics is derived as
(4)
and rc(t ) ∝ (t + t0)1/(3p + 1)
(8)
Linear regression of eq 10 provides a fit of the form log ve = b + m log rc, where m delivers the parameter p in McHale’s model. The corresponding presentation of the data on hand is given in Figure 2, which also shows the linear fit according to
For a small spherical cap droplet of constant volume, the Hoffmann−de Gennes law further predicts a simple power law for the dynamic contact angle in the form Θ(t) ∝ (t + t0)−3/10, from which rc(t) ∝ (t + t0)1/10, that is, Tanner’s law, is derived. It is worth noting that a constant time shift t0 is introduced in McHale’s presentation of these equations, which depends on volume and initial state of the droplet. In order to evaluate the effect of surface roughness on the spreading dynamics, McHale et al. considered the effect of the Wenzel and Cassie−Baxter equations on the driving forces and also related this to both the hydrodynamic viscous dissipation model and the molecular-kinetic theory of spreading.19 The results of the theoretical consideration suggest a roughness modified Tanner’s law to describe the dependence of contact angle, spreading radius, and spreading velocity on time. In summary, Θ(t ) ∝ (t + t0)−3/(3p + 1)
(7)
Combining eqs 7 and 9 yields
As McHale et al. point out,19 this expression is equivalent to the Hoffmann−de Gennes law, which relates the spreading speed ve = drc/dt with dynamic and equilibrium contact angles Θ(t) and Θe by ve ∝ Θ(t ) (Θ(t )2 − Θe 2)
d r (t ) A (t + t0)−3p /3p + 1 = dt 3p + 1
⎛ A ⎞ −3p log ve = log⎜ log(t + t0) ⎟+ 3p + 1 ⎝ 3p + 1 ⎠
(1)
where rc(t) is the radius of the circular contact area, γ and η are the surface tension and viscosity of the liquid, respectively, and V is the (initial) volume of the droplet. For detailed derivation of eq 1, see Bormashenko.8 In the case of the viscous spreading of small droplets, where gravity can be disregarded, the power n is predicted as 1/10 by Tanner,20 but also by Brenner and Bertozzi,21 and Bonn et al.22 Thus, one obtains rc(t ) ∝ t 1/10
1 log(t + t0) 3p + 1
(6)
(5)
rc(t ) ∝ (t + t0)1/3(1.05 + 1) = (t + t0)0.24
are obtained. We refer to the original paper for the detailed derivation eqs 4 and 5. The important assumption in this model (referred to as “McHale’s model” in the following) is that p = 3, when the surface is flat and smooth, and the original Tanner’s law is obtained. In case of a rough surface, p approaches 1. This is based on the fact that the edge velocity tends to change linear with contact angle (cf. McHale and Newton).23 Under this condition, one obtains
(11)
The parameters of the linear fit basically allow also calculation of the predicted radius rc(t) of the spreading pattern. The corresponding comparison between model and experimental data is shown in Figure 3. As the time shift t0 introduced in McHale’s model is unknown, three fit-curves according to eq 6 present assumed values of t0 = −0.2, 0, and 0.2 s, respectively. It may be taken from the graphs that the model fits the data well for t > 1 s, while the initial phase of the spreading is not predicted well. The nearest fit in the regime of
rc(t ) ∝ (t + t0)1/4 3129
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Figure 3. Comparison of experimentally determined and predicted spreading dynamics. The spreading dynamics is given as radius of the spreading pattern rc(t). Dots give experimental data, while the dashed lines give the prediction of McHale’s model using p = 1.052 and three different time-shifts t0 as indicated.
Figure 4. Comparison of the experimental data to the “three-regimemodel” by Cazabat and Cohen Stuart.25 The data were fitted to log rc(t) = f (log t) individually for small times (initial spreading regime, t < 2 s) and larger times (final spreading regime, t > 5 s). It is assumed that spreading on the superhydrophilic surfaces is extremely fast in the initial time regime, so only the second and third (final) regimes were experimentally accessible.
small t is obtained from negative t0, which would not appear to make physical sense. Extrand tried to explain the different behavior of spontaneous spreading droplet in the very early vis-à-vis later stages of spreading by changing flow geometry from an initial downward movement to an outward movement.24 Extrand assumes the transition from downward to outward flow at a point, when Θ < 80°. With the droplet volume of 10 μL, this relates to a spreading radius of approximately 1.7 mm, which is just at the onset of the data recording in this study, and not sufficiently covered by the available data. Accordingly, the data cannot be supposed to mirror this phenomenon. An alternative interpretation of the initial spreading phase may be found in a paper by Cazabat and Cohen Stuart,25 who propose that, on rough surfaces, spreading follows a power law rc(t) ∝ tn, that is, similar to Tanner’s law, where n ranges between 0.25 and 0.4 in three time regimes: The (very) initial spreading is expected to be similar to the spreading on a smooth surface. From a study of the effects of gravity and capillarity, Cazabat and Cohen Stuart expect the radius of the spreading pattern to follow a 1/8 power law for large droplets, a 1/10 power law for small droplets, the latter corresponding to Hoffmann−de Gennes law, respectively Tanner’s law. This initial spreading is followed by a phase, where the “base” of the droplet spreads in the roughness patterns at a high rate driven by capillary effects. Cazabat and Cohen Stuart assume a power law with 0.25 < n < 0.5. In the final phase, all liquid is consumed in the surface structure, for example, “pools”, and the rate of spreading decreases again. In Figure 4, the data on hand are analyzed in respect to these assumptions by executing linear fits to log rc(t) = f (log t) for small times (initial spreading regime with t < 2 s) and larger times (final spreading regime with t > 5 s) individually. As the graph shows, the data can be described by two time regimes with different power laws. It is assumed that spreading on the superhydrophilic surfaces is extremely fast in the initial time regime, so only the second and third (final) regimes were experimentally accessible. Note that the potential accuracy of the data points for t < 0.5 s is limited by the available analytical tools. The values found for n in the second and third regimes exceed the numbers stated by Cazabat and Cohen Stuart,25 but, as was to be expected, are in accordance with McHale’s model (cf. eq 11) in the final regime. It is to be assumed that this is attributed to surface roughness in both spreading regimes.
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CONCLUSIONS The water wetting dynamics on the highly wetting acrylates based on hydroxypropylacrylate and polyethylenglycolmonoacrylate was studied. The wetted area (contact area) could in good approximation be described as circular with a timedependent radius rc(t). The development of rc(t) in time was found to be in good agreement with a roughness modified Tanner’s law as proposed by McHale et al. While model fits the data well for t > 1 s, the initial phase of the spreading is not predicted well. This differing behavior in the initial spreading phase relates well, however, to a theory published by Cazabat and Cohen Stuart, who propose that, on rough surfaces, spreading follows a power law in three time regimes. In this model, the (very) initial spreading is expected to be similar to the spreading on a smooth surface.
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AUTHOR INFORMATION
Corresponding Author
*Tel. +49 (0)2151 843-156. Fax +49 (0)2151 843-143. E-mail [email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS The research project (AiF no. 16038 BG) of the Forschungskuratorium Textil e. V. was funded by the Bundesministerium für Wirtschaft und Technologie within the program Industrielle Gemeinschaftsforschung (IGF) by the Arbeitsgemeinschaft industrieller Forschungsvereinigungen e. V. (AiF).
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REFERENCES
(1) Bauer, F.; Decker, U.; Dierdorf, A.; Ernst, H.; Heller, R.; Liebe, H.; Mehnert, R. Preparation of moisture curable polysilazane coatings. Part I. Elucidation of low temperature curing kinetics by FT-IR spectroscopy. Prog. Org. Coat. 2005, 53, 183−190. (2) Elsner, C.; Lenk, M.; Prager, L.; Mehnert, R. Windowless argon excimer source for surface modifi cation. Appl. Surf. Sci. 2006, 252, 3616−3624. (3) Prager, L.; Dierdorf, A.; Liebe, H.; Naumov, S.; Stojanović, S.; Heller, R.; Wennrich, L.; Buchmeiser, M. R. Conversion of perhydropolysilazane into a SiOx network triggered by vacuum ultraviolet irradiation: Access to flexible, transparent barrier coatings. Chem.Eur. J. 2007, 13, 8522−8529.
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(4) Schubert, R.; Scherzer, T.; Hinkefuß, M.; Marquardt, B.; Vogel, J.; Buchmeiser, M. R. VUV-induced micro-folding of acrylate-based coatings. 1. Real-time methods for the determination of the microfolding kinetics. Surf. Coat. Technol. 2009, 203, 1844−1849. (5) Wenzel, R. N. Resistance of solid surfaces to wetting by water. Ind. Eng. Chem. 1936, 28, 988−994. (6) De Gennes, P. G.; Brochard-Wyart, F.; Quéré, D. Capillarity and Wetting Phenomena; Springer: Berlin, 2003. (7) Erbil, H. Y. Surface Chemistry of Solid and Liquid Interfaces; Blackwell: Oxford, 2006. (8) Bormashenko, E. Y. Wetting of Real Surfaces; DeGruyter: Berlin, Boston, 2013. (9) McHale, G.; Shirtcliffe, N. J.; Aqil, S.; Perry, C. C.; Newton, M. I. Topography driven spreading. Phys. Rev. Lett. 2004, 93, 036102 (4 pages). (10) Cebeci, F. C.; Wu, Z.; Zhai, L.; Cohen, R. E.; Rubner, M. F. Nanoporosity-driven superhydrophilicity: A means to create multifunctional antifogging coatings. Langmuir 2006, 22, 2856−2862. (11) Extrand, C. W.; Moon, S. I.; Hall, P.; Schmidt, D. Superwetting of structured surfaces. Langmuir 2007, 23, 8882−8890. (12) Bahners, T.; Prager, L.; Kriehn, S.; Gutmann, J. S. Superhydrophilic surfaces by photo-induced micro-folding. Appl. Surf. Sci. 2012, 259, 847−852. (13) Bahners, T.; Prager, L.; Pender, A.; Gutmann, J. S. Superwetting surfaces by grafting post-treatments of micro-rough acrylate coatings. Prog. Org. Coat. 2013, 76, 1356−1362. (14) Johnson, R. E., Jr.; Dettre, R. H. Contact angle hysteresis. I. Study of an idealized rough surface. In Contact Angle, Wettability, and Adhesion; Fowkes, F. M., Ed.; Advances in Chemistry Series 43; American Chemical Society: Washington, D.C., 1964; pp 112−135. (15) De Coninck, J.; De Ruijter, M. J.; Voué, M. Dynamics of wetting. Curr. Opin. Colloid Interface Sci. 2001, 6, 49−53. (16) Heslot, F.; Fraysse, N.; Cazabat, A. M. Molecular layering in the spreading of wetting liquid drops. Nature 1989, 338, 640−642. (17) Heslot, F.; Cazabat, A. M.; Levinson, P. Dynamics of wetting of tiny drops: ellipsometric study of the late stages of spreading. Phys. Rev. Lett. 1989, 62, 1286−1290. (18) Heslot, F.; Cazabat, A. M.; Levinson, P.; Fraysse, N. Experiments on wetting on the scale of nanometers: Influence of the surface energy. Phys. Rev. Lett. 1990, 65, 599−602. (19) McHale, G.; Newton, M. I.; Shirtcliffe, N. J. Dynamic Wetting and spreading and the role of topography. J. Phys.: Condens. Matter 2009, 21 (464122), 11pages. (20) Tanner, L. H. The spreading of silicone oil drops on horizontal surfaces. J. Phys. D.: Appl. Phys. 1979, 12, 1473−1484. (21) Brenner, M.; Bertozzi, M. Spreading of droplets on a solid surface. Phys. Rev. Lett. 1993, 71, 593−596. (22) Bonn, D.; Eggers, J.; Indekeu, J.; Meunier, J.; Rolley, E. Wetting and spreading. Rev. Mod. Phys. 2009, 81, 739−805. (23) McHale, G.; Newton, M. I. Frenkel’s method and the dynamic wetting of heterogeneous planar surfaces. Colloids Surf., A 2002, 206, 193−201. (24) Extrand, C. W. Spontaneous Spreading of Viscous Liquids. J. Colloid Interface Sci. 1993, 157, 72−76. (25) Cazabat, A. M.; Cohen Stuart, M. A. Dynamics of wetting: effects of surface roughness. J. Phys. Chem. 1986, 90, 5845−5849.
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Wetting Dynamics on Superhydrophilic Surfaces Prepared by Photonic Microfolding Thomas Bahners,*,† Lutz Prager,‡ and Jochen S. Gutmann†,§ †
Deutsches Textilforschungszentrum Nord-West gGmbH (DTNW), Adlerstr. 1, 47798 Krefeld, Germany Leibniz-Institut für Oberflächenmodifizierung e.V. (IOM), Permoserstr. 15, 04318 Leipzig, Germany § Physikalische Chemie and CENIDE, Universität Duisburg-Essen, Universitätsstr. 2, 45141 Essen, Germany ‡
ABSTRACT: The wetting dynamic on microrough and perfectly wetting (superhydrophilic) acrylates was studied. These surfaces were achieved by coating polymer films made of poly(ethyleneterephthalate) (PET) with a hydrophilic acrylate based on hydroxypropylacrylate and polyethyleneglycolmonoacrylate, which was then cured and microroughened by photonic microfolding. The high transparency of the thin acrylate layers and polymer films allowed us to record the spreading of an applied water droplet through the film samples. Subsequently, the dynamic radius of the spreading pattern rc(t) was determined from the video recording. Various models for the wetting dynamics of superhydrophilic surfaces, namely, Tanner’s law and a roughness-modified derivation published by McHale et al. in 2009, were then compared to the experimental results. Basically, the development of rc(t) in time was found to be in good agreement with McHale’s model. Data analysis showed, however, that the initial phase of the spreading, that is, for t < 1 s, was not predicted well. This differing behavior relates well to a theory published by Cazabat and Cohen Stuart, who proposed that, on rough surfaces, spreading follows a power law in three time regimes. In this model, the (very) initial spreading is expected to be similar to the spreading on a smooth surface.
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called “Cassie impregnating” state (cf. de Gennes et al., Erbil, or Bormachenko).6−8 In this state, the rough surface can be described as a composite surface with the liquid penetrating the texture. Consequently, the droplet covers a solid phase with contact angle ΘY and a liquid phase with zero contact angle, with the apparent contact derived from the well-known Cassie−Baxter equation. One consequence of the Cassie impregnating state is that the surface is partially wetted in front of the triple line, which is contrast to the Wenzel state. Independent of the model, two potential cases have to be considered. Depending on the nature of the planar surface, the introduction of a microroughness increases the wettability of an intrinsically hydrophilic surface, but decreases the wettability on an already hydrophobic surface. Given this background, it was proposed to create perfectly wetting surfaces by providing moderately hydrophilic surfaces with a suitable microroughness.9−11 According to Wenzel’s equation, superwetting could also be achieved by increasing the surface free energy of a microrough surface by means of a suitable post-treatment. In recent studies, both ways have been evaluated by the authors for microrough acrylates produced by the described process of photonic microfolding. In a first approach, perfectly
INTRODUCTION Recently, perfectly wetting surfaces were prepared by coating smooth, nonporous substrates such as polymer films or coated fabrics with thin microrough acrylate layers. The microrough topography of the layers was achieved by means of special twostep UV curing process known as photonic microfolding, which was developed at IOM.1−4 The concept of the process is to apply a thin acrylate layer to a substrate by knife-coating or spraying and cure this layer by subsequent exposure to VUV and broadband UV radiation. Due to the very strong absorption in the VUV, the first curing step affects only a skin at the surface of the acrylate layer, which induces shrinkage and folding. This structure is frozen in the second curing step, which affects the full bulk of the acrylate layer. The wetting behavior of a surface is basically determined by the relation of the interfacial energies, namely, the surface free energy (SFE) of the substrate material, and by the surface roughness. In the case of a complete wetting of the liquid− substrate interface, the apparent contact angle is often described by the rather simplified Wenzel model.5 Wenzel’s equation relates the apparent contact angle of the microrough surface Θw to the contact angle of the planar surface of the same material (Young angle) ΘY with the help of a roughness or Wenzel factor r, which is defined as the ratio between the areas of rough and flat surfaces (r ≥ 1). It shall be noted at this point that full wetting is more recently also attributed to the so© 2014 American Chemical Society
Received: January 20, 2014 Revised: March 4, 2014 Published: March 6, 2014 3127
dx.doi.org/10.1021/la500227w | Langmuir 2014, 30, 3127−3131
Langmuir
Article
wetting (superhydrophilic) surfaces could be achieved by using hydrophilic hydroxypropylacrylate and polyethyleneglycolmonoacrylate as the main components of the applied acrylate.12 The experimentally observed wetting behavior followed Wenzel’s equation up to roughness factor of r ≤ 1.2. On a surface of more pronounced roughness, the full wetting was observed. However, spreading of a droplet appeared to be governed by geometric effects such as blockage by the surface. In a second approach, the wettability of microrough acrylate surfaces, inherently hydrophobic or only moderately hydrophilic, could be enhanced by plasma-based or UV-induced grafting post-treatments, both of which increased the surface free energy.13 Again, experiments showed that the wetting behavior was well correlated with the predictions of Wenzel’s model up to a certain roughness factor, above which full wetting occurred. This wetting transition was in agreement with a model proposed by Johnson and Dettre, who predict a transition from partial to full wetting, if the roughness factor r exceeds the inverse of the cosine of the Young angle, that is, r ≥ 1/cos ΘY.14 This was observed in all samples studied by the authors. In the present work, the wetting dynamic on the highly wetting acrylates based on hydroxypropylacrylate and polyethyleneglycolmonoacrylate was studied. The high transparency of the thin acrylate layers applied to equally transparent film made of poly(ethyleneterephthalate) (PET) allowed us to record the spreading pattern through the film samples. These gave good and easy access to quantitative data by determining the radius of the spreading pattern rc (spreading radius) as a function of time from the video recording.
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Figure 1. Radius of the contact area of the droplet (spreading radius) on superhydrophilic samples as a function of time in normal (A) and logarithmic (B) presentation. Data taken from two identically prepared samples are identified by full and open symbols. The dashed line in (B) represents a data fit according to rc ∝ log(t). The inset photograph shows the spreading pattern of two droplets observed on the sample with a mean roughness factor r = 1.62 ± 0.05.
EXPERIMENTAL SECTION
Following the experimental protocol described in a previous paper by the authors,12 the acrylate coating was prepared from hydroxypropylacrylate, polyethyleneglycolmonoacrylate, N,N-methylenebisacrylamide, and ethyl-2,4,6-trimethylbenzoylphenylphosphinate as photoinitiator. A 10 μm thick layer was applied to clear PET film by knife coating. The wet coating was then cured by subsequent irradiation with 172 nm VUV radiation (Xe2* excimer lamp) in nitrogen atmosphere, and a mercury medium pressure lamp emitting broadband UV irradiation with λ > 230 nm. The irradiation doses were 0.7 and 325 mJ/cm2, respectively. The averaged roughness or Wenzel factor of these surfaces was analyzed by white-light interferometry and determined as the ratio between the areas of rough and flat surfaces. The mean roughness factor of the studied samples was r = 1.62 ± 0.05. Notabene (NB): An equilibrium water contact angle of 37° was determined on the corresponding planar surface, that is, identical acrylate cured only using broadband radiation, by the sessile drop method. For the analysis of the dynamic of water on these surfaces, droplets of double distilled water (10 μL) were placed on the sample surface at 20 °C and the spreading of the droplet recorded by video camera. The high transparency of the thin acrylate layers applied to equally transparent film allowed us to record the spreading pattern through the film samples from below. For better visualization of the final contact area of the applied amount of water (“spreading pattern”), the dyestuff Astrazon Blue was added. The actual spreading dynamic was determined as the radius of the circular contact area rc as a function of time.
propagating triple line from simultaneously expected microscopic phenomena in front of the triple line, namely, the precursor film as well as partial wetting in the Cassie impregnating state (see above). One can estimate from the data that (dynamic) contact angles would be of the order of 5° and less after only 1.5 s in our measurements. At this point, spreading is mainly governed by the characteristic topographic features of our samples, which are higher than an idealized droplet (described as a spherical cap).12 Given this background, we refer the observed spreading pattern to the triple-line only and compare the experimental data to the prediction of various theoretical understandings of triple-line propagation on fully wetting surfaces in the following discussion. As can be taken from the graphs, the increase of the contact area radius can basically be described by a logarithmic trend according to rc ∝ log(t). A survey of existing literature, however, provides no theoretical background for this rather simple description. In 2001, De Coninck et al. reviewed mechanisms controlling the dynamics of wetting in partial and complete wetting regimes and related models.15 With regard the complete wetting regime, De Coninck et al. refer to various papers by Heslot, Cazabat and co-workers who used ellipsometric techniques to study the profiles of the spreading drop as a function of time t.16−18 An important observation of these experiments is the appearance of a precursor film in front of the drop, which is often constituted by a few layers of molecular thickness (cf. also Bormashenko).8 The propagation of the base radius is reported to be r ∝ √t on average, which, however,
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RESULTS AND DISCUSSION A complete compilation of all measured spreading pattern radii taken from several identically prepared samples is given in Figure 1 as a function of elapsed time. It is important to point out that it was experimentally not possible to discriminate the 3128
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does not describe the spreading dynamic observed in the experiment reported here. Also reported by De Coninck et al., considerations of molecular dynamics predict a behavior ∝(log(t))1/2. In deference of these models, it has to be acknowledged that effects of surface roughness were not taken into account. A theoretical paper by McHale et al. proposes the description of a dynamic contact angle on rough superhydrophilic surfaces as function of time by a modified Tanner’s law.19,20 Derived from the Navier−Stokes equations, Tanner’s law describes the dynamic spreading of a spherical cap droplet on a smooth surface by 1/10 ⎡ γ ⎛ 4V ⎞⎤ n ⎜ ⎟ rc(t ) = ⎢const ⎥ t ⎣ η ⎝ π ⎠⎦
In order to check McHale’s model against the experimental data, it was feasible to calculate the contact line propagation speed ve = drc/dt and plot it against rc. If we assume a simple proportionality and introduce the (unknown) constant A, we obtain the following equations: rc(t ) = A(t + t0)1/(3p + 1) log rc(t ) = log A +
ve =
⎡ ⎛ A ⎞ ⎤ log ve = ⎢log⎜ ⎟ + log A ⎥ − (3p)log rc ⎢⎣ ⎝ 3p + 1 ⎠ ⎦⎥
(2)
(9)
(10)
(3)
Figure 2. Experimentally determined velocity of contact line propagation as a function of spreading radius versus eq 10, which was derived from McHale’s model of spreading dynamics on fully wetting rough surfaces (dashed line). The parameter p in McHale’s model (eq 6) was determined by the best fit as p = 1.05.
eq 10. The calculation provides p = 1.05, which agrees well with the value for a rough surface in McHale’s model, which assumes p = 1 for rough surfaces. The corresponding power law of the spreading dynamics is derived as
(4)
and rc(t ) ∝ (t + t0)1/(3p + 1)
(8)
Linear regression of eq 10 provides a fit of the form log ve = b + m log rc, where m delivers the parameter p in McHale’s model. The corresponding presentation of the data on hand is given in Figure 2, which also shows the linear fit according to
For a small spherical cap droplet of constant volume, the Hoffmann−de Gennes law further predicts a simple power law for the dynamic contact angle in the form Θ(t) ∝ (t + t0)−3/10, from which rc(t) ∝ (t + t0)1/10, that is, Tanner’s law, is derived. It is worth noting that a constant time shift t0 is introduced in McHale’s presentation of these equations, which depends on volume and initial state of the droplet. In order to evaluate the effect of surface roughness on the spreading dynamics, McHale et al. considered the effect of the Wenzel and Cassie−Baxter equations on the driving forces and also related this to both the hydrodynamic viscous dissipation model and the molecular-kinetic theory of spreading.19 The results of the theoretical consideration suggest a roughness modified Tanner’s law to describe the dependence of contact angle, spreading radius, and spreading velocity on time. In summary, Θ(t ) ∝ (t + t0)−3/(3p + 1)
(7)
Combining eqs 7 and 9 yields
As McHale et al. point out,19 this expression is equivalent to the Hoffmann−de Gennes law, which relates the spreading speed ve = drc/dt with dynamic and equilibrium contact angles Θ(t) and Θe by ve ∝ Θ(t ) (Θ(t )2 − Θe 2)
d r (t ) A (t + t0)−3p /3p + 1 = dt 3p + 1
⎛ A ⎞ −3p log ve = log⎜ log(t + t0) ⎟+ 3p + 1 ⎝ 3p + 1 ⎠
(1)
where rc(t) is the radius of the circular contact area, γ and η are the surface tension and viscosity of the liquid, respectively, and V is the (initial) volume of the droplet. For detailed derivation of eq 1, see Bormashenko.8 In the case of the viscous spreading of small droplets, where gravity can be disregarded, the power n is predicted as 1/10 by Tanner,20 but also by Brenner and Bertozzi,21 and Bonn et al.22 Thus, one obtains rc(t ) ∝ t 1/10
1 log(t + t0) 3p + 1
(6)
(5)
rc(t ) ∝ (t + t0)1/3(1.05 + 1) = (t + t0)0.24
are obtained. We refer to the original paper for the detailed derivation eqs 4 and 5. The important assumption in this model (referred to as “McHale’s model” in the following) is that p = 3, when the surface is flat and smooth, and the original Tanner’s law is obtained. In case of a rough surface, p approaches 1. This is based on the fact that the edge velocity tends to change linear with contact angle (cf. McHale and Newton).23 Under this condition, one obtains
(11)
The parameters of the linear fit basically allow also calculation of the predicted radius rc(t) of the spreading pattern. The corresponding comparison between model and experimental data is shown in Figure 3. As the time shift t0 introduced in McHale’s model is unknown, three fit-curves according to eq 6 present assumed values of t0 = −0.2, 0, and 0.2 s, respectively. It may be taken from the graphs that the model fits the data well for t > 1 s, while the initial phase of the spreading is not predicted well. The nearest fit in the regime of
rc(t ) ∝ (t + t0)1/4 3129
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Figure 3. Comparison of experimentally determined and predicted spreading dynamics. The spreading dynamics is given as radius of the spreading pattern rc(t). Dots give experimental data, while the dashed lines give the prediction of McHale’s model using p = 1.052 and three different time-shifts t0 as indicated.
Figure 4. Comparison of the experimental data to the “three-regimemodel” by Cazabat and Cohen Stuart.25 The data were fitted to log rc(t) = f (log t) individually for small times (initial spreading regime, t < 2 s) and larger times (final spreading regime, t > 5 s). It is assumed that spreading on the superhydrophilic surfaces is extremely fast in the initial time regime, so only the second and third (final) regimes were experimentally accessible.
small t is obtained from negative t0, which would not appear to make physical sense. Extrand tried to explain the different behavior of spontaneous spreading droplet in the very early vis-à-vis later stages of spreading by changing flow geometry from an initial downward movement to an outward movement.24 Extrand assumes the transition from downward to outward flow at a point, when Θ < 80°. With the droplet volume of 10 μL, this relates to a spreading radius of approximately 1.7 mm, which is just at the onset of the data recording in this study, and not sufficiently covered by the available data. Accordingly, the data cannot be supposed to mirror this phenomenon. An alternative interpretation of the initial spreading phase may be found in a paper by Cazabat and Cohen Stuart,25 who propose that, on rough surfaces, spreading follows a power law rc(t) ∝ tn, that is, similar to Tanner’s law, where n ranges between 0.25 and 0.4 in three time regimes: The (very) initial spreading is expected to be similar to the spreading on a smooth surface. From a study of the effects of gravity and capillarity, Cazabat and Cohen Stuart expect the radius of the spreading pattern to follow a 1/8 power law for large droplets, a 1/10 power law for small droplets, the latter corresponding to Hoffmann−de Gennes law, respectively Tanner’s law. This initial spreading is followed by a phase, where the “base” of the droplet spreads in the roughness patterns at a high rate driven by capillary effects. Cazabat and Cohen Stuart assume a power law with 0.25 < n < 0.5. In the final phase, all liquid is consumed in the surface structure, for example, “pools”, and the rate of spreading decreases again. In Figure 4, the data on hand are analyzed in respect to these assumptions by executing linear fits to log rc(t) = f (log t) for small times (initial spreading regime with t < 2 s) and larger times (final spreading regime with t > 5 s) individually. As the graph shows, the data can be described by two time regimes with different power laws. It is assumed that spreading on the superhydrophilic surfaces is extremely fast in the initial time regime, so only the second and third (final) regimes were experimentally accessible. Note that the potential accuracy of the data points for t < 0.5 s is limited by the available analytical tools. The values found for n in the second and third regimes exceed the numbers stated by Cazabat and Cohen Stuart,25 but, as was to be expected, are in accordance with McHale’s model (cf. eq 11) in the final regime. It is to be assumed that this is attributed to surface roughness in both spreading regimes.
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CONCLUSIONS The water wetting dynamics on the highly wetting acrylates based on hydroxypropylacrylate and polyethylenglycolmonoacrylate was studied. The wetted area (contact area) could in good approximation be described as circular with a timedependent radius rc(t). The development of rc(t) in time was found to be in good agreement with a roughness modified Tanner’s law as proposed by McHale et al. While model fits the data well for t > 1 s, the initial phase of the spreading is not predicted well. This differing behavior in the initial spreading phase relates well, however, to a theory published by Cazabat and Cohen Stuart, who propose that, on rough surfaces, spreading follows a power law in three time regimes. In this model, the (very) initial spreading is expected to be similar to the spreading on a smooth surface.
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AUTHOR INFORMATION
Corresponding Author
*Tel. +49 (0)2151 843-156. Fax +49 (0)2151 843-143. E-mail [email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS The research project (AiF no. 16038 BG) of the Forschungskuratorium Textil e. V. was funded by the Bundesministerium für Wirtschaft und Technologie within the program Industrielle Gemeinschaftsforschung (IGF) by the Arbeitsgemeinschaft industrieller Forschungsvereinigungen e. V. (AiF).
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