9428
Langmuir 2004, 20, 9428-9431
Topographical Parameters for Specifying a Three-Dimensional Surface Jouko Peltonen,* Mikael Ja¨rn, Sami Areva, Mika Linden, and Jarl B. Rosenholm Department of Physical Chemistry, Åbo Akademi University, Porthaninkatu 3-5, FIN-20500 Turku, Finland Received February 17, 2004. In Final Form: August 25, 2004 The importance of different surface geometries and thereby the need for versatile surface identification by describing a number of different surface features is emphasized. A set of topographical parameters for the description of the amplitude and spatial and hybrid properties of surfaces was utilized for a versatile three-dimensional surface characterization of sol-gel samples with different topographies. The image data were measured by atomic force microscopy. The results demonstrate the power of the roughness parameters to identify surfaces according to their specific characteristics. An example is also given about how certain surface topographical properties may control the material reactivity.
Introduction Wenzel reported on the interdependence of wettability and surface roughness for polar surfaces as early as 1936.1 The roughness-dependent water repellency from nonpolar surfaces was first studied by Cassie and Baxter.2 The phenomenon gained very little scientific interest until recent years, despite the fact that fluid-solid interactions have been extensively studied during recent decades (see, for example, the book by Mittal).3 By using rotating glass plates, the transition from complete to partial wetting as a function of changing shape of the solid surface was recently demonstrated by Wapner and Hoffman.4 The paper actually demonstrates how certain topographical features may give rise to the birth of air pockets and thereby, for example, explains the formation of nanobubbles5,6 when such a surface is covered by a liquid. Depending on the surface chemistry, the surface geometry either improves (polar surface) or reduces (nonpolar surface) wetting.7-11 It is through this interdependence of topography and chemistry that a surface may turn from “normal” hydrophobic to superhydrophobic. Nature utilizes this phenomenon, for example, in self-cleaning plant leaves (the so-called lotus effect).12,13 The presented examples show that true three-dimensional description of a surface for well-defined surface specification is in great demand. It has been demonstrated that even molecular scale topography contributes to contact angle hysteresis;11 therefore, the topographical characterization has to be carried out with high resolution * To whom correspondence should be addressed. E-mail:
[email protected]. (1) Wenzel, R. W. Ind. Eng. Chem. 1936, 28, 988. (2) Cassie, A. B. D.; Baxter, S. Trans. Faraday Soc. 1944, 40, 546. (3) Mittal, K. L., Ed. Contact Angle, Wettability and Adhesion; VSP: Utrecht, 1993. (4) Wapner, P. G.; Hoffman, W. P. Langmuir 2002, 18, 1225. (5) Attard, P.; Moody, M. P.; Tyrrell, J. W. G. Physica A 2002, 314, 696. (6) Tyrrell, J. W. G.; Attard, P. Langmuir 2002, 18, 160. (7) Bico, J.; Thiele, U.; Que´re´, D. Colloids Surf., A 2002, 206, 41. (8) Minko, S.; Mu¨ller, M.; Motornov, M.; Nitschke, M.; Grundke, K.; Stamm, M. J. Am. Chem. Soc. 2003, 125, 3896. (9) Shibuichi, S.; Onda, T.; Satoh, N.; Tsujii, K. J. Phys. Chem. 1996, 100, 19512. (10) O ¨ ner, D.; McCarthy, T. J. Langmuir 2000, 16, 7777. (11) Fadeev, A. Y.; McCarthy, T. J. Langmuir 1999, 15, 3759. (12) Holloway, P. J. Pestic. Sci. 1970, 1, 156. (13) Barthlott, W.; Neinhuis, C. Planta 1997, 202, 1.
and at scales of different lengths. Compared with artificial textured surfaces,7,10 the description of the form and shape of real surfaces9,13 with complex topography sets high requirements for surface microscopy and especially for image analysis. Obviously, root-mean-square (RMS) roughness or peak-to-valley height parameters may be regarded as only indicative when considering, for example, surface porosity14 or topography-corrected wetting behavior.8 Taniguchi and Belfort have considered the correction of contact angles for surface roughness by introducing a model with horizontal and vertical length scales and thereby the mean surface slope.15 The three-dimensional image data were captured by atomic force microscopy (AFM).16 Also, this model represented an artificial surface. The challenge to be met is to quantify a real surface not only by RMS roughness but also, for example, by the effective surface area, height asymmetry, surface porosity, and number, size, and form of local maxima. In this way, the understanding of the role of topography in phenomena such as wetting, adsorption/precipitation, and liquid penetration can be considerably enhanced. Here, a set of topographical parameters for the description of the amplitude and spatial and hybrid properties of surfaces are utilized for a versatile three-dimensional surface characterization of sol-gel samples with different topographies. Our aim is to demonstrate that different sets of parameters describe and identify surfaces of different character. We also demonstrate the topographydependent functionality of the studied surfaces. Experimental Section Preparation of the Sol-Gel Samples. Sol-gel technology enables the production of novel materials with varying morphological and chemical properties. Several process parameters (pH, temperature, aging time) and additives (templates of various kinds and amounts) may be utilized to tune the properties of the end product. Here, coatings of different surface morphologies were produced by tuning the calcination time and by using poly(ethylene glycol) (PEG) as a template. A more systematic study about the influence of process parameters on the sample morphology will be reported soon. The titania coatings on the glass substrates were prepared by the sol-gel dip-coating technique as described previously17,18 (14) Roizard, X.; Wery, M.; Kirmann, J. Compos. Struct. 2002, 56, 223. (15) Taniguchi, M.; Belfort, G. Langmuir 2002, 18, 6465. (16) Binnig, G.; Quate, C. F.; Gerber, C. Phys. Rev. Lett. 1986, 56, 930.
10.1021/la0400252 CCC: $27.50 © 2004 American Chemical Society Published on Web 09/28/2004
Letters
Langmuir, Vol. 20, No. 22, 2004 9429 Table 1. List of Selected Roughness Parameters symbol Sq Sy Sz
Figure 1. AFM top-view images (3 µm × 3 µm) of TiO2 samples synthesized in the presence of PEG to obtain morphologically different model surfaces. The mass ratios of PEG for the samples from left to right were 1:1.75:1.25. The height (dark-light ) low-high) scale of the images is given by the Sy parameter listed in Table 2. but with slight modifications. Briefly, the sol was prepared by dissolving tetraisopropyl orthotitanate [Ti(OCH(CH3)2)4] into absolute ethanol (solution I). Solution II was prepared by mixing ethylene glycol monoethyl ether (C2H5OCH2CH2OH), deionized water, and 1 M hydrochloric acid (37%) with absolute ethanol. Solutions I and II were mixed at 0 °C with vigorous stirring. The clear sol was kept at 0 °C during aging and the dip-coating process. The coated substrates were calcined at 500 °C for 10 min, 1 h, and 2 h to obtain morphologically different surfaces. For part of the samples, various amounts of PEG were added to the clear sol which was aged at 40 °C prior to dip-coating (details given in the caption of Figure 1). During the dipping process PEG and the Ti sol phase separate forming porous structures as a result of 1 h of calcination at 500 °C.18 Contact Angle Measurements. The contact angle of a water drop against the studied substrate was measured optically by using DAT 1100 Fibro System equipment. The Milli-Q filtration system (Millipore Corp.) was used for water purification. The drop volume was within 2-4 µL. The reported values are mean values of at least 10 measurements. AFM Measurements and Image Analysis. The AFM images were recorded with a Nanoscope IIIa atomic force microscope (Digital Instruments, Santa Barbara, CA) equipped with an extender electronics module which enables phase imaging in tapping mode. All the images were recorded in tapping mode using silicon cantilevers with a resonance frequency between 250 and 300 kHz. The scan rate was typically 0.7-2 Hz. The free tapping amplitude was 70-100 nm for the high-kinetic-energy tapping measurements. The damping ratio rsp ()Asp/A0) controlling the level of forced damping was chosen by tuning the setpoint amplitude, Asp. All images (512 × 512 pixels) were measured in air without filtering. The microscope was placed on an active vibration isolation table (MOD-1M, JRS Scientific Instruments, Switzerland), which was further placed on a massive stone table to eliminate external vibrational noise. The Scanning Probe Image Processor (SPIP, Image Metrology, Denmark) software was used for the roughness analysis of the images. Roughness Parameters. A set of roughness parameters has been developed and standardized for versatile characterization of various surface properties in three dimensions.19 The parameters are available, for example, in the commercial SPIP image analysis software20 that we have utilized here. The parameters we have analyzed in this paper are listed in Table 1. The RMS roughness Sq is the most widely used amplitude roughness parameter that gives the standard deviation of height. Amplitude parameters Sz and Sy give the extreme height differences for an image. Obviously, the peak-to-peak height Sy is more sensitive to noise than Sz being calculated as a mean height value of five local maxima and five local minima. For a normally behaving surface the value of Sz is about 10-20% lower than that of Sy. A larger difference refers to a noisy image. (17) Jokinen, M.; Pa¨tsi, M.; Rahiala, H.; Peltola, T.; Ritala, M. J. Biomed. Mater. Res. 1998, 42, 295. (18) Kajihara, K.; Yao, T. J. Sol.-Gel Sci. Technol. 1998, 12, 185. (19) Stout, K. J.; Sullivan, P. J.; Dong, W. P.; Mainsah, E.; Luo, N.; Mathia, T.; Zahouani, H. The development of methods for the characterization of roughness on three dimensions; Publication no. 15178 EN; Commission of the European Communities: Luzemburg, 1994. (20) The Scanning Probe Image Processor, SPIP, User’s and Reference Guide; Image Metrology: Copenhagen, 2001.
Ssk Sku Sds Ssc Sdq Sdr Sci Svi
name
description
RMS roughness
standard deviation of the height values peak-peak height height difference between highest and lowest pixel ten point height average of five highest local maxima and five deepest local minima skewness height distribution asymmetry kurtosis height distribution sharpness (peakedness) density of summits number of local maxima per unit area mean summit curvature principal curvature of local maxima RMS slope RMS value of the surface slope surface area ratio ratio between the interfacial and projected areas core fluid retention index measure of fluid volume in the core zone valley fluid retention index measure of fluid volume in the valley zone
Surface skewness Ssk describes the asymmetry of the height distribution. A skewness value equal to 0 represents a Gaussianlike surface. Negative values of Ssk refer to a surface-porous sample; that is, the valleys dominate over the peak regimes. Respectively, the local summits dominate over the valleys when Ssk > 0. Surface kurtosis Sku, a measure of the sharpness of the surface height distribution, equals 3.0 for a Gaussian-like surface. Values smaller than 3.0 indicate a broad (heterogeneous) height distribution whereas values much larger than 3.0 refer to a surface with almost quantized height values. The number of local maxima per unit area is given by the spatial parameter Sds. In addition to the number, the form of the local maxima (summits) is also of interest. Two hybrid parameters have been developed to specially describe the form of the summits: the mean summit curvature, Ssc, and the RMS value of the surface slope, Sdq. Most of the above parameters contribute to the effective surface area: the absolute height difference and the number and form of local maxima, among others. A measure for the effective surface area with respect to the projected area is given in percent by the surface area ratio parameter Sdr. Considering the wetting/nonwetting characteristics of a surface, two more parameters deserve to be included. The fluid (or gas) retention indexes indicate the ability of the surface for fluid/gas retention. For a more accurate evaluation, the surface is subdivided into two regions in the height scale represented by two different parameters: the core fluid retention index Sci (the core zone ) 20-95% of the total height scale calculated from the absolute minimum) and the valley fluid retention index Svi (the valley zone ) 0-20% of the total height scale calculated from the absolute minimum). The Gaussian values for these parameters are 1.56 and 0.11, respectively.
Results and Discussion TiO2 sol-gel substrates with different morphologies and porosities were synthesized by varying the sintering time and the amount of the doping agent. Typical AFM images of three different samples are presented in Figure 1.21 The top-view images directly show that the substrates represent different morphologies with characteristic surface textures. A calculation and closer analysis of the selected roughness parameters (Table 2) reveal many interesting features. (21) The topography of the samples was well reproducible, the standard deviation of the roughness values being 20% as a maximum, typically well below 10%, calculated for six to eight sites on each surface.
9430
Langmuir, Vol. 20, No. 22, 2004
Letters
Table 2. Values of Roughness Parameters and Contact Angles for Samples of Figure 1 sample no. 1
sample no. 2
sample no. 3
Sq (nm) Sy (nm) Sz (nm) Ssk Sku Sds (µm-2) Sdr (%) Sci Svi
4.2 37.5 34.4 -0.50 3.4 234 2.2 1.40 0.148
20.9 245 230 -0.08 4.64 343 7.3 1.61 0.123
33.2 270 262 -0.63 3.67 119 11.1 1.38 0.137
Θm (deg) ΘY (deg)
48.6 49.7
49.8 52.2
31.4 39.8
Figure 2. AFM top-view images (3 µm × 3 µm) of TiO2 samples prepared from a clear sol without any PEG. The coated substrates were sintered at 500 °C for 10 min (left image), 60 min (image in the middle), and 120 min (right image). The height (dark-light ) low-high) scale of the images is given by the Sy parameter listed in Table 3.
The RMS roughness and absolute height (Sy) are increasing from sample 1 to sample 3. The average height parameter Sz is only slightly smaller than Sy for all samples. Therefore, the values may be regarded as reliable: no erratic pixels seem to distort the height scale. Looking at the images, all of the samples look porous. According to the skewness values, however, this is the case only for samples 1 and 3 [a clearly negative value means that the valleys (surface pores) dominate over the peaks]. It is worth noting that surface porosity does not follow RMS roughness. For sample 2, despite the large depth of the pores it is their small volume that is not enough to contribute to the height asymmetry. This conclusion is supported by the volume index parameters Sci and Svi which both are close to the Gaussian values for sample 2. Also the kurtosis (Sku) and density of summits (Sds) show that it is actually the high areas that dominate over the valleys for sample 2. Despite the small pore volume of sample 2, the deep pores, because having rather long perimeters and, hence, a large wall area, do contribute to the effective surface area. The Sdr values indeed demonstrate an increasing trend from sample 1 to sample 3, following increasing RMS roughness. Next, the wetting properties of the samples of Figure 1 were studied by measuring the contact angles of water. The values are included in Table 2. According to the Wenzel’s roughness equation1 the relation between the roughness-dependent measured contact angle Θm and Young’s contact angle ΘY corresponding to an ideally flat surface may be written as
cos Θm ) r cos ΘY
(1)
where r denotes the ratio between the real and the projected surface areas of the sample. We may utilize one of the roughness parameters to calculate r from
r ) 1 + Sdr/100
(2)
The calculated values of ΘY are included in Table 2. The correction is largest for the most porous sample and quite minimal for sample 1 with the smallest height differences. The result clearly demonstrates the dependence of wetting on topography. As expected for a polar surface, topography (i.e., a surface with a certain real roughness in contrast to an ideally flat surface) enhances wetting.2,7-9 The samples of Figure 2 represent, in contrast to those of Figure 1, clearly nonporous surfaces, as a result of not using any doping agent during the sol-gel synthesis. The absence of surface pores is nicely described by the clearly positive values of the skewness parameter. Also, the values of Svi being clearly smaller than the Gaussian value 0.11, together with the values of Sci being higher than the Gaussian 1.56, demonstrates that the core zone dominates the surface. The heat treatment of TiO2 is used to modify
Table 3. Values of Roughness Parameters and Contact Angles for Samples of Figure 2 sample no. 1
sample no. 2
sample no. 3
Sq (nm) Sy (nm) Sz (nm) Ssk Sku Sds (µm-2) Ssc (nm-1) Sdq (nm-1) Sdr (%) Sci Svi
2.1 20.8 17.6 1.80 7.0 573 0.000 086 0.15 1.2 2.21 0.038
2.1 20.2 18.3 2.34 10.3 955 0.000 071 0.09 0.4 2.31 0.036
1.2 23.7 20.3 4.01 31.0 1088 0.000 16 0.11 0.6 1.62 0.069
Θm (deg)
33.7
29.2
48.5
the crystallographic properties of the material from amorphous to crystals of various symmetries. The RMS roughness parameter seems to be rather insensitive to the exposure time of the heat treatment at 500 °C. The most informative parameter for this series of surfaces is kurtosis. It nicely demonstrates how the local summits develop with temperature and become more and more identical to each other. A value as high as 31 (cf. the Gaussian value 3.0) is observed for the sample of longest temperature treatment, meaning that the peaks have a very narrow height distribution. The peaks increase in amount from sample 1 to sample 3 (Sds), but the changes in curvature (Ssc) and slope (Sdq) of the local maxima are more irregular and difficult to interpret. According to the values of Sdr the contribution of the low peaks (as indicated by Sq, Sy, and Sz) to the effective surface area is negligible. Therefore, the Wenzel’s equation does not need to be taken into account in this case. The contact angle values included in Table 3, hence, purely relate to differences in surface chemistry between the samples. In fact, the largest contact angle value observed for sample 3 may be interpreted by the burning off of the OH groups during the heat treatment, thereby decreasing the polarity of the surface. An important aspect about the novel sol-gel materials is to consider their reactivities with other materials. In previous investigations we have found that the surface topography influences the precipitation.22 The peaks (local maxima) may, thus, be interpreted as precipitation nuclei of highly energetic surface imperfections. Indeed, it is known that surface precipitation occurs at lower concentrations than bulk precipitation.23 Moreover, it seems that the depth and angle of the idealized surface peaks may govern crystal growth to particular crystal habits.24-26 (22) Jokinen, M. Ph.D. Thesis, A° bo Akademi University, Turku, Finland, 1999. (23) James, R. O.; Healy, T. W. J. Colloid Interface Sci. 1972, 40, 61. (24) Teng, H. H.; Dove, P. M.; De Yoreo, J. J. Geochim. Cosmochim. Acta 2000, 64, 2255. (25) Liu, X. Y.; Lim, S. W. J. Am. Chem. Soc. 2003, 125, 888. (26) Guo, X.-C.; Madix, R. J. J. Phys. Chem. B 2003, 107, 3105.
Letters
Langmuir, Vol. 20, No. 22, 2004 9431
conclusions, this phenomenon needs to be studied in greater detail in terms of larger data sets in continued studies. It is obvious that various roughness parameters enable many surface properties to be quantified and to be distinguished from each other; thereby, the samples can be classified accordingly. The results of Figure 1 demonstrate that the topographical characteristics of sol-gel materials may be changed by varying the amount of the doping agent. The surface properties of the end products may be further tuned, for example, by heat treatment (Figure 2). These properties can be of importance for applications of these materials, for example, as photocatalytic films where the structural parameters of the surface may influence the activity of the films through changes in the specific surface area. Conclusions Figure 3. Precipitation (exposure time was 2 weeks) of CaP onto different TiO2 samples with varying topography. The formation index is calculated as the change of CaP concentration in solution multiplied by the time during which the concentration changed. The solid line describes the linearily increasing precipitation of CaP with increasing amount of local summits. For values of Sds smaller than about 470, the precipitation is negligible (dashed line).
Therefore, we tested the precipitation of calcium phosphate (CaP) on sol-gel substrates having similar surface polarities but varying topographical characteristics. The correlation between the amount of precipitated CaP and the different roughness parameters was then studied. The best fit is shown in Figure 3. The number of local maxima per unit area (Sds) gave the best correlation (solid line) with CaP precipitation beyond a certain value (ca. 470 maxima/µm2) that seems to act as a threshold value. It is worth mentioning that the commonly used RMS roughness value gave no such correlation. The appearance of the critical threshold value indicates that it is not enough to have just any small number of adsorption sites to initiate nucleation. Instead, a certain critical density of summits seems to be required to give rise to meaningful precipitation. This result may also be utilized the other way around: when aiming at developing a sample with minimized ability for nucleation and growth, a surface with a small density of local summits (the dashed line of Figure 3) seems preferential. However, to draw more general
Roughness parameters such as those listed in Table 1 have been available for image analysis for some time but they have been utilized surprisingly little in image analysis of AFM data. We believe that when aiming at a versatile identification of various surfaces, these parameters will be of great help. The most commonly used parameters such as RMS roughness are not specific enough to describe the complex relation between various surface features and phenomena such as precipitation and wetting. Regarding the samples in this paper, one of the future goals is to utilize the topographical parameters in sol-gel synthesis for enhanced tuning of materials properties. It will also be of great interest to study the topography-chemistry interdependence of nonpolar, hydrophobized sol-gel materials. A combination of various roughness parameters should also be considered in revising the topographical factor used in the Wenzel’s equation, that is, correcting for the possible underestimation caused by using the effective surface area.27 Acknowledgment. Financial support from the National Technology Agency of Finland (Grant 40245/02) is gratefully acknowledged. S.A. also acknowledges the Graduate School of Materials Research (GSMR) for financial support. LA0400252 (27) Jia, X.; McCarthy, T. J. Langmuir 2003, 19, 2449.
