Eur. Phys. J. E (2014) 37: 84 DOI 10.1140/epje/i2014-14084-3
THE EUROPEAN PHYSICAL JOURNAL E
Regular Article
Surface wrinkling and cracking dynamics in the drying of colloidal droplets Yongjian Zhang1 , Yimeng Qian2 , Zhengtang Liu1,a , Zhiguang Li2 , and Duyang Zang2,b 1
2
State Key Laboratory of Solidification Processing, School of Materials Science and Engineering, Northwestern Polytechnical University, Xi’an, 710072, China Functional Soft Matter & Materials Group (FS2M), Key Laboratory of Space Applied Physics and Chemistry of Ministry of Education, School of Science, Northwestern Polytechnical University, Xi’an, 710129, China
Received 26 April 2014 and Received in final form 17 July 2014 c EDP Sciences / Societ` Published online: 26 September 2014 – a Italiana di Fisica / Springer-Verlag 2014 Abstract. The cracking behavior accompanied with the drying of colloidal droplets containing polytetrafluoroethylene (PTFE) nanoparticles was studied. During evaporation, due to the stretching effect of the liquid zone, the receding wet front leads to the formation of radialized surface wrinkling in the gel zone. This indicates the building of a macroscopic stress field with a similar distribution. As a result, the cracks in the deposited films are in a radial arrangement. The propagation velocity of the cracks depends on the thickness of the film, ∼ H 3/5 . In addition, sodium dodecylsulfate (SDS) additives can be used to tune crack behavior by causing a reduction of the capillary force between particles. The results highlight the significance of the receding wet front in building the drying deposition stress field and may be helpful in other fields related to drying and cracking processes.
1 Introduction Evaporation of colloidal droplets is one of the most important and simplest approaches to order colloidal particles, as expected [1,2]. The particles arrange themselves via the capillary force. However, there are two main intrinsic drawbacks of this technique that limit the formation of large-area, ordered structures. One is the coffee ring effect, which was first clearly explained by Deegan et al. [3]. Many studies have been conducted on the ability to control or eliminate this effect [4–6]. For instance, by using non-spherical particles the coffee ring effect was completely suppressed [4]. The other limitation is the formation of cracks, which is a critical problem for the application of the final deposited film [7]. Tremendous efforts have been performed in producing studies to elucidate the cracking mechanisms [8–11]. It is known that evaporation produces compression stress on the deposited film due to the negative Laplace pressure caused by the receding meniscus between particles. Once the generated stress (capillary stress in nature) exceeds a critical value, a crack emerges [10]. Driven by this stress, the crack trajectories a b
e-mail: [email protected] e-mail: [email protected]
may develop to versatile morphologies from parallel patterns [12], circular cracks [7], wavy cracks [13] to spiral crack patterns and craquelures [14]. The propagation of cracks can be arranged with external fields [15,16]. Scientists have tediously researched how to make crack-free depositions via droplet drying, which includes the addition of a halloysite nanotube or using polymer gelbinding [17,18]. A more recent study reported that mixing emulsion droplets (the sizes of the droplets were comparable to that of the particles) with a colloid suspension can completely suppress the cracks. This may provide a novel approach for crack-free evaporation in the paint and ceramics industries [19]. Among the various crack patterns obtained in droplet drying, the radial-like cracks were more frequently observed [7,20,21]. However, the underlying mechanisms responsible for the crack morphology are not fully understood yet, while making insight into crack propagation dynamics is highly desirable [22–24]. The present work is based on the study of the evaporation of aqueous colloidal droplets containing polytetrafluoroethylene (PTFE) particles. Focus is placed on the formation mechanisms and propagation dynamics of the cracks. The explanation of how the cracking behavior is tuned by surfactant additives is also discussed in detail.
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Eur. Phys. J. E (2014) 37: 84
(a)
(c)
(b)
(d)
(e)
Fig. 1. Radialized cracking patterns obtained via evaporation of colloidal droplets containing PTFE particles of varied concentrations. (a) and (b) are showing the overview, enlargement of the center part (marked by the square in panel (a)) of the final deposition (15% wt.); (c)-(e) are the overview patterns of 6% wt., 10% wt. and 30% wt. respectively. The scale bars represent 200 μm.
2 Experimental section 2.1 Materials The colloidal dispersion used in the experiments was diluted from the original condensed dispersion (Shenzhen Kejingstar Technology LTD., China) with a PTFE particle content of 60% wt. (kinematic viscosity was 6 mm2 /s, density, 1.5 g/cm3 ). The average diameter of the PTFE particles was ∼ 50 nm. The particles were stabilized by non-ionic surfactants. The original dispersion was diluted by ultrapure water, which was prepared from an Ultrapure Water System (EPED, China) with a resistivity of 18.25 MΩ cm. The final concentration of the dispersions varied from 6% to 30% wt. Before the experiment, the colloidal dispersion was sonicated for 30 min using an ultrasonic probe (diameter = 6 mm, Bilon-650Y, China) operating at 20.5 kHz with 30% of the maximum oscillation amplitude to avoid formation of particle aggregates. The surfactant used in the experiments was sodium dodecylsulfate (SDS) (Aladdin, purity ≥ 98.5%). It was added to the colloidal dispersion 2 hours before use to ensure complete dissolution. The weight fraction of SDS varied from 0.5% to 3.0%.
2.2 Evaporation and observation In the experiments, the colloidal droplets (∼ 0.2 μL) were deposited with a microsyringe (total volume = 1 μL) on a standard glass slide, which was cleaned thoroughly by
alcohol and distilled water and dried in a drying oven. The evaporation process and the final deposited pattern were observed using a brightfield optical microscope (Olympus, BX51) illuminated by transmitted light with either a 20× NA 0.40 objective or a 10× NA 0.25 objective. For the evaporation process, the images were recorded by means of a video recorder at 25 fps. All the experiments and observation were carried out at room temperature ∼ 22 ◦ C with a relative humidity of ∼ 40%. To obtain more information of the morphology and structure of the evaporated deposition, the deposited patterns were also studied with a scanning electron microscope (SEM) (TESCAN VEGA3LMH). To enhance the SEM image quality, the deposited patterns were obtained by evaporation of colloidal droplets on a silicon substrate at the same condition as the experiments on glass substrate. It was verified that the obtained patterns were similar to those on the glass substrate due to the very close contact angle and surface roughness.
3 Results and discussion 3.1 Formation of radial cracks For the colloidal droplets containing only PTFE particles, the final evaporation depositions are characterized by crack patterns in a radial arrangement with a loose particle network in the center (fig. 1(b)). As observed by SEM, the thicknesses of the deposited films are of tens of microns. Apparently, the crack length and the space between cracks increase with the increase of particle volume
Eur. Phys. J. E (2014) 37: 84
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(a)
(b) (b)
(c)
(d)
(f)
(g)
(h)
Wet front Gel (e)
Fig. 2. In situ observation of the drying process of a colloidal droplet (30% wt.). (a) Instability inside the liquid zone; (b) wet front undulation; (c) and (d) appearance of surface wrinkling in the gel zone, before the emergence of cracks which reflects the stress field built in the deposited film; (e) crack nucleates at the edge of the deposition; (f)-(h) propagation of the cracks from outside to the center. The scale bars represent 100 μm.
fraction. The final deposition patterns, as illustrated in fig. 1, suggest the presence of the coffee ring effect, due to the pinning of the contact line in the evaporation process [3]. Generally, it is necessary that the thickness of the deposition exceeds a critical value Hc for the formation of cracks [25]. A higher volume fraction leads to larger area deposition that is thicker than Hc , resulting in longer cracks. To further understand the cracking behavior, an in situ observation of the evaporation process with a bright-field microscopy was conducted, as shown in fig. 2. A gel zone was formed at the periphery of the droplet with the receding of the wet front, clearly causing instability inside the liquid zone (fig. 2(a)) [26]. This may result from the balance of the normal component of the liquid surface tension, which is often neglected in Young’s equation [27]. Furthermore, the surface tension of the liquid zone develops a stretching effect (radial stress σrr ) to the outside gel zone, i.e., causes a ring of materials at radial distance r to move to a ring of smaller radius [27]. This eventually leads to the formation of surface wrinkling in the outside gel zone (fig. 2(d)). With further evaporation, cracks originate from the flaws at the troughs of the wrinkle and propagate with the receding wet front (fig. 2(e)-(h)) [21]. The wrinkling instability is a result of the energy minimum between bending and stretching of the deposited gel film. The wavelength of wrinkling λ depends on the distance from droplet center r, which can be written as [28] λ∼
B σrr
1/4 r1/2 ,
(1)
where B is the bending modulus of the film [29], B=
EH 3 , 12(1 − Λ2 )
(2)
where E, H and Λ are the Young modulus, thickness and Poisson ratio of the materials, respectively.
Tensile stress
Compression stress
Fig. 3. Schematic view of stress and colloidal distribution in the surface wrinkle.
Based on eqs. (1) and (2), it could be reasoned that λ ∝ H 1/2 r1/2 . This indicates that the increase of film thickness leads to a larger wavelength of wrinkling, which is consistent with our experiment results. It should be noted that the direct driving force for cracking is the large tensile stress induced by the shrinkage of the gel phase that sticks on to the substrate [30]. The macroscopic radialized stress field built by the surface wrinkling does not result in the cracks itself. However, the stress field may lead to a different colloidal distribution at the trough and peak of a wrinkle due to the local compression and tensile stress, as illustrated in fig. 3. The colloids are more disposed to reaching a close-packed state at the troughs where the colloid distance is shorter. Once a closepacked state is reached, further evaporation would lead to the receding of the meniscus. Whereas, at the peaks of the wrinkling, evaporation may first cause capillary attraction between particles resulting in reduction in their distances prior to the meniscus receding. Therefore, at the troughs it is faster for the meniscus to recede below the first layer of particles, which directly renders the binded colloid particles to be stretched apart by the adjacent tensile stress, i.e., the nucleation of cracks. For this reason, once a crack nucleates, it propagates along the troughs of the wrinkling. It should be noted that the number of cracks is much less than the amount of wrinkling. It is
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Eur. Phys. J. E (2014) 37: 84
Fig. 4. (a) Propagation dynamics of the cracks in the drying of droplets of different volume fractions; the inset graph plots the crack velocity vs. film thickness. (b) Schematic view of a crack tip.
probable that the internal stress is significantly released by cracking, which prevents the formation of a new crack at adjacent troughs. The wrinkling instability is a result of the stretching effect of the inside liquid zone [27,28]. The stretching effect is universal in all drying sessile colloidal droplets. However, surface wrinkling occurs only if the gel film has proper mechanical properties. If the compression modulus of the gel phase is too small, i.e., the gel film is highly compressible, the gel zone will be compressed/stretched evenly rather than forming wrinkles. Therefore, no remarkable surface wrinkling was observed in the drying of very dilute colloidal droplets(concentration < 2% wt.). If the gel phase is too rigid, for instance, the particles stick to the substrate too tightly and bending will be energetically unfavorable. In this case, it is hard for surface wrinkling to appear, which is indeed the case for the silica colloidal system [22]. In a recent work, it has been observed that wrinkling on an elastic sheet induced by the stretching of the underside of a liquid drop may turn into a crumpled state due to distinct symmetry-breaking instabilities [31]. However, in our experiments, the wrinkle-to-crumple transition does not occur due to different experiment conditions. The observed phenomenon in which surface wrinkling leads to a small number of cracks is probably generated by energy release rather than an instability transition. Macroscopic stress induced by surface wrinkling is also an important factor in the propagation direction of the cracks, even though the crack occurs fundamentally when the capillary stress is greater than the critical value [10, 32]. This finding suggests that, in addition to the compression stress due to negative Laplace pressure arising from the receding meniscus between colloidal particles, the stretching effect of the inner liquid phase on the outside gel phase can not be neglected.
3.2 Crack propagation dynamics Propagation dynamics are also important to understand the crack behavior in addition to the direction of crack growth. To avoid the influence of evaporation rate, all experiments were performed at fixed relative humidity and temperature. The wet front velocities for different droplets were very close. However, it is clearly seen from fig. 4(a) that the propagation velocity V of the cracks increases with increasing volume fraction. This can be explained by energy analysis based on Griffith’s criterion, i.e. the released stress energy is equaled with the newly emerged gas-solid interfacial energy for a steady growing crack [32]. In a unit time period, the energy balance for a growing crack with tip angle 2θ (fig. 4(b)), is written as ΔPc · V 2 tan θ · H = Γ ·
V · H, cos θ
(3)
where ΔPc is the critical Laplace pressure to open the crack, Γ is the interfacial energy per unit area. ΔPc is given by [10] 2/5 −HΔPc /γ ∼ = 2.16 [φN GH/2π(1 − Λ)γ] ,
(4)
where N is the number of contacting neighbors, φ is the volume fraction of the colloidal packing, G is the shear modulus of the particles, and γ is the surface tension of the liquid. Equation (4) suggests that a thinner film is tougher since it needs a larger ΔPc to open a crack. From eqs. (3) and (4), it can be deduced that V ∝ H 3/5 Γ.
(5)
The experimental data (data in the inset graphic in fig. 4(a), velocities were extracted from the linear region in L ∼ t plots, H was the average film thickness corresponding to the linear region) is in good agreement with
Eur. Phys. J. E (2014) 37: 84
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(b)
(d)
(e)
(c)
(f)
Fig. 5. Reversed propagation (from the inner part to periphery of the droplet) of cracks in the colloidal droplet with 0.5% wt. SDS. The arrows indicate the receding wet front (a) and the reversed propagation of cracks (b), respectively. The scale bars represent 200 μm.
(a)
(c)
(b)
(d)
Fig. 6. Complete suppression of cracks with 3% SDS in the droplets. (a)-(d) correspond to particle concentrations of 6%, 10%, 15% and 30% wt., respectively. The scale bars represent 200 μm.
the H 3/5 scaling of crack velocity. It should be mentioned that the thickness of the deposition is not uniform over the whole area. The crack propagation becomes slower when it approaches the center where the thickness becomes thinner. The H 3/5 scaling suggests that the energy dissipation accompanying the moving crack tip is negligible. The
crack behavior is mainly dominated by the surface energy of the newly emerged crack. The crack velocity in the present study is ∼ 102 μm/s, which is about one order of magnitude lower than that for the silica colloid system [22]. As indicated by eq. (5), the decreased crack velocity may be due to the decreased surface energy of the PTFE particles.
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3.3 Crack patterns tuned by SDS additives A crack may nucleate from the inner part of the droplet and propagate toward the periphery with the addition of surfactant (0.5% SDS) to the colloid suspension (fig. 5), which contrasts the case without surfactant. This distinct crack propagation direction can be related to the reduced surface tension with SDS. For nucleation of an individual crack, the binded particles (by capillary bridge) must be torn open by the tensile stress. The bound force between particles is the capillary force, which is proportional to the surface tension of the liquid. Inward Marangoni flow, from the droplet periphery to the center, results in a higher concentration of SDS in the inner part of the droplet, hence much lower surface tension and weaker bound forces between particles. Therefore, the stress built within the deposited film may first be released at the inner part followed by nucleation of a crack. A similar phenomenon has been observed in particle rafts systems, where cracks propagate outward due to Marangoni stresses caused by surfactant spreading [33,34]. Interesting periodic crack patterns were also witnessed in these systems, which may originate from the compression effect stimulated by a surfactant shock whose front has ramified finger morphology due to concentration fluctuation [34], while in the present study, the stresses were intrinsically the capillary force [25]. As a consequence, different mechanisms were responsible for the crack propagation and pattern formation occurring in our system. When adding more SDS (3%) into the suspension, the cracks can be completely suppressed, as shown in fig. 6. The coffee ring effect was eliminated by inwards Marangoni flow [35]. Moreover, the outward capillary flow may be significantly retarded due to the formation of larger-sized aggregates, because the presence of ionic surfactant may reduce the electrostatic screen length surrounding the PTFE particles. Here the surface wrinkling behavior has not been observed, suggesting that the surface tension is too low to generate sufficient stretching for wrinkling instability of the deposited film. No macroscopic stress could be built to favor crack growth in a preferential direction. On the contrary, the drying stress could be released without any delay due to the greatly reduced capillary force between particles. This eventually leads to a rough surface morphology. The surfactant-particle interaction may influence the stability of the suspension. For instance, the decrease of the electrostatic screen length can enhance coagulation and possibly restrain the coffee ring effect. For the tuning of the crack pattern, the effect of surfactant additive is mainly attributed to the change of surface tension and hence the capillary force.
4 Conclusions In summary, we have observed the radialized surface wrinkling and cracking behavior in the evaporation of PTFE colloidal droplets. The surface wrinkling arises from the stretching of the surface tension of the receding liquid
Eur. Phys. J. E (2014) 37: 84
zone, which plays an important role in building a macroscopic radial-like stress field. The macroscopic stress field, in turn, determines the final radialized distribution of cracks. With the increase of volume fraction/film thickness, the crack space decreases, whereas its propagation velocity increases as ∼ H 3/5 . The final deposition can be tuned by SDS additives, from reversed crack propagation (with 0.5% SDS) to complete crack elimination (with 3% SDS) due to the reduction of capillary force between particles. This study emphasizes the importance of the receding wet front in developing the stress field in deposited film. This work was supported by the National Natural Science Foundation of China (Grant No. 51301139), Shaanxi Provincial Natural Science Foundation (Grant No. 2012JQ1016), NPU Foundation for Fundamental Research (JCY20130147) and Specialized Research Fund for the Doctoral Program of Higher Education (Grant No. 20126102120058).
References 1. F.R. Alexander, Rep. Prog. Phys. 76, 046603 (2013). 2. K. Sefiane, R. Bennacer, Sci. Adv. Colloid Interface Sci. 147-148, 263 (2009). 3. R.D. Deegan, O. Bakajin, T.F. Dupont, G. Huber, S.R. Nagel, T.A. Witten, Nature 389, 827 (1997). 4. P.J. Yunker, T. Still, M.A. Lohr, A.G. Yodh, Nature 476, 308 (2011). 5. T. Still, P.J. Yunker, A.G. Yodh, Langmuir 28, 4984 (2012). 6. R.G. Larson, Angew. Chem. Int. Edi. 51, 2546 (2012). 7. G. Jing, J. Ma, J. Phys. Chem. B 116, 6225 (2012). 8. K.I. Dragnevski, A.F. Routh, M.W. Murray, A.M. Donald, Langmuir 26, 7747 (2010). 9. K.B. Singh, M.S. Tirumkudulu, Phys. Rev. Lett. 98, 218302 (2007). 10. W. Man, W.B. Russel, Phys. Rev. Lett. 100, 198302 (2008). 11. S. Kitsunezaki, Phys. Rev. E 87, 052805 (2013). 12. L. Pauchard, M. Adda-Bedia, C. Allain, Y. Couder, Phys. Rev. E 67, 027103 (2003). 13. L. Goehring, W.J. Clegg, A.F. Routh, Soft Matter 7, 7984 (2011). 14. V. Lazarus, L. Pauchard, Soft Matter 7, 2552 (2011). 15. L. Pauchard, F. Elias, P. Boltenhagen, A. Cebers, J.C. Bacri, Phys. Rev. E 77, 021402 (2008). 16. T. Khatun, T. Dutta, S. Tarafdar, Langmuir 29, 15535 (2013). 17. T. Kanai, T. Sawada, Langmuir 25, 13315 (2009). 18. J. Qiao, J. Adams, D. Johannsmann, Langmuir 28, 8674 (2012). 19. Q. Jin, P. Tan, A.B. Schofield, L. Xu, Eur. Phys. J. E 36, 28 (2013). 20. L. Xu, S. Davies, A.B. Schofield, D.A. Weitz, Phys. Rev. Lett. 101, 094502 (2008). 21. J. Ma, G. Jing, Phys. Rev. E 86, 061406 (2012). 22. Y. Zhang, Z. Liu, D. Zang, Y. Qian, K. Lin, Sci. China Phys. Mech. Astron. 56, 1712 (2013). 23. E.R. Dufresne, E.I. Corwin et al., Phys. Rev. Lett. 91, 224501 (2003).
Eur. Phys. J. E (2014) 37: 84 24. E.R. Dufresne, D.J. Stark et al., Langmuir 22, 7144 (2006). 25. R.C. Chiu, T.J. Garino, M.J. Cima, J. Am. Ceram. Soc. 76, 2257 (1993). 26. P. Xu, A.S. Mujumdar, B. Yu, Dry. Technol. 27, 636 (2009). 27. D. Vella, M. Adda-Bedia, E. Cerda, Soft Matter 6, 5778 (2010). 28. J. Huang, M. Juszkiewicz, W.H. de Jeu, E. Cerda, T. Emrick, N. Menon, T.P. Russell, Science 317, 650 (2007). 29. L. Landau, E. Lifshitz, Theory of Elasticity. Course of Theoretical Physics, 3rd edition, Vol. 7 (ButterworthHeinemann, 1986).
Page 7 of 7 30. C. Allain, L. Limat, Phys. Rev. Lett. 74, 2981 (1995). 31. H. King, R.D. Schroll, B. Davidovitch, N. Menon, Proc. Natl. Acad. Sci. U.S.A. 109, 9716 (2012). 32. M.S. Tirumkudulu, W.B. Russel, Langmuir 20, 2947 (2004). 33. D. Vella, H.Y. Kim, P. Aussillous, L. Mahadevan, Phys. Rev. Lett. 96, 178301 (2006). 34. M.M. Bandi, T. Tallinen, L. Mahadevan, EPL 96, 36008 (2011). 35. H. Hu, R.G. Larson, J. Phys. Chem. B 110, 7090 (2006).
THE EUROPEAN PHYSICAL JOURNAL E
Regular Article
Surface wrinkling and cracking dynamics in the drying of colloidal droplets Yongjian Zhang1 , Yimeng Qian2 , Zhengtang Liu1,a , Zhiguang Li2 , and Duyang Zang2,b 1
2
State Key Laboratory of Solidification Processing, School of Materials Science and Engineering, Northwestern Polytechnical University, Xi’an, 710072, China Functional Soft Matter & Materials Group (FS2M), Key Laboratory of Space Applied Physics and Chemistry of Ministry of Education, School of Science, Northwestern Polytechnical University, Xi’an, 710129, China
Received 26 April 2014 and Received in final form 17 July 2014 c EDP Sciences / Societ` Published online: 26 September 2014 – a Italiana di Fisica / Springer-Verlag 2014 Abstract. The cracking behavior accompanied with the drying of colloidal droplets containing polytetrafluoroethylene (PTFE) nanoparticles was studied. During evaporation, due to the stretching effect of the liquid zone, the receding wet front leads to the formation of radialized surface wrinkling in the gel zone. This indicates the building of a macroscopic stress field with a similar distribution. As a result, the cracks in the deposited films are in a radial arrangement. The propagation velocity of the cracks depends on the thickness of the film, ∼ H 3/5 . In addition, sodium dodecylsulfate (SDS) additives can be used to tune crack behavior by causing a reduction of the capillary force between particles. The results highlight the significance of the receding wet front in building the drying deposition stress field and may be helpful in other fields related to drying and cracking processes.
1 Introduction Evaporation of colloidal droplets is one of the most important and simplest approaches to order colloidal particles, as expected [1,2]. The particles arrange themselves via the capillary force. However, there are two main intrinsic drawbacks of this technique that limit the formation of large-area, ordered structures. One is the coffee ring effect, which was first clearly explained by Deegan et al. [3]. Many studies have been conducted on the ability to control or eliminate this effect [4–6]. For instance, by using non-spherical particles the coffee ring effect was completely suppressed [4]. The other limitation is the formation of cracks, which is a critical problem for the application of the final deposited film [7]. Tremendous efforts have been performed in producing studies to elucidate the cracking mechanisms [8–11]. It is known that evaporation produces compression stress on the deposited film due to the negative Laplace pressure caused by the receding meniscus between particles. Once the generated stress (capillary stress in nature) exceeds a critical value, a crack emerges [10]. Driven by this stress, the crack trajectories a b
e-mail: [email protected] e-mail: [email protected]
may develop to versatile morphologies from parallel patterns [12], circular cracks [7], wavy cracks [13] to spiral crack patterns and craquelures [14]. The propagation of cracks can be arranged with external fields [15,16]. Scientists have tediously researched how to make crack-free depositions via droplet drying, which includes the addition of a halloysite nanotube or using polymer gelbinding [17,18]. A more recent study reported that mixing emulsion droplets (the sizes of the droplets were comparable to that of the particles) with a colloid suspension can completely suppress the cracks. This may provide a novel approach for crack-free evaporation in the paint and ceramics industries [19]. Among the various crack patterns obtained in droplet drying, the radial-like cracks were more frequently observed [7,20,21]. However, the underlying mechanisms responsible for the crack morphology are not fully understood yet, while making insight into crack propagation dynamics is highly desirable [22–24]. The present work is based on the study of the evaporation of aqueous colloidal droplets containing polytetrafluoroethylene (PTFE) particles. Focus is placed on the formation mechanisms and propagation dynamics of the cracks. The explanation of how the cracking behavior is tuned by surfactant additives is also discussed in detail.
Page 2 of 7
Eur. Phys. J. E (2014) 37: 84
(a)
(c)
(b)
(d)
(e)
Fig. 1. Radialized cracking patterns obtained via evaporation of colloidal droplets containing PTFE particles of varied concentrations. (a) and (b) are showing the overview, enlargement of the center part (marked by the square in panel (a)) of the final deposition (15% wt.); (c)-(e) are the overview patterns of 6% wt., 10% wt. and 30% wt. respectively. The scale bars represent 200 μm.
2 Experimental section 2.1 Materials The colloidal dispersion used in the experiments was diluted from the original condensed dispersion (Shenzhen Kejingstar Technology LTD., China) with a PTFE particle content of 60% wt. (kinematic viscosity was 6 mm2 /s, density, 1.5 g/cm3 ). The average diameter of the PTFE particles was ∼ 50 nm. The particles were stabilized by non-ionic surfactants. The original dispersion was diluted by ultrapure water, which was prepared from an Ultrapure Water System (EPED, China) with a resistivity of 18.25 MΩ cm. The final concentration of the dispersions varied from 6% to 30% wt. Before the experiment, the colloidal dispersion was sonicated for 30 min using an ultrasonic probe (diameter = 6 mm, Bilon-650Y, China) operating at 20.5 kHz with 30% of the maximum oscillation amplitude to avoid formation of particle aggregates. The surfactant used in the experiments was sodium dodecylsulfate (SDS) (Aladdin, purity ≥ 98.5%). It was added to the colloidal dispersion 2 hours before use to ensure complete dissolution. The weight fraction of SDS varied from 0.5% to 3.0%.
2.2 Evaporation and observation In the experiments, the colloidal droplets (∼ 0.2 μL) were deposited with a microsyringe (total volume = 1 μL) on a standard glass slide, which was cleaned thoroughly by
alcohol and distilled water and dried in a drying oven. The evaporation process and the final deposited pattern were observed using a brightfield optical microscope (Olympus, BX51) illuminated by transmitted light with either a 20× NA 0.40 objective or a 10× NA 0.25 objective. For the evaporation process, the images were recorded by means of a video recorder at 25 fps. All the experiments and observation were carried out at room temperature ∼ 22 ◦ C with a relative humidity of ∼ 40%. To obtain more information of the morphology and structure of the evaporated deposition, the deposited patterns were also studied with a scanning electron microscope (SEM) (TESCAN VEGA3LMH). To enhance the SEM image quality, the deposited patterns were obtained by evaporation of colloidal droplets on a silicon substrate at the same condition as the experiments on glass substrate. It was verified that the obtained patterns were similar to those on the glass substrate due to the very close contact angle and surface roughness.
3 Results and discussion 3.1 Formation of radial cracks For the colloidal droplets containing only PTFE particles, the final evaporation depositions are characterized by crack patterns in a radial arrangement with a loose particle network in the center (fig. 1(b)). As observed by SEM, the thicknesses of the deposited films are of tens of microns. Apparently, the crack length and the space between cracks increase with the increase of particle volume
Eur. Phys. J. E (2014) 37: 84
Page 3 of 7
(a)
(b) (b)
(c)
(d)
(f)
(g)
(h)
Wet front Gel (e)
Fig. 2. In situ observation of the drying process of a colloidal droplet (30% wt.). (a) Instability inside the liquid zone; (b) wet front undulation; (c) and (d) appearance of surface wrinkling in the gel zone, before the emergence of cracks which reflects the stress field built in the deposited film; (e) crack nucleates at the edge of the deposition; (f)-(h) propagation of the cracks from outside to the center. The scale bars represent 100 μm.
fraction. The final deposition patterns, as illustrated in fig. 1, suggest the presence of the coffee ring effect, due to the pinning of the contact line in the evaporation process [3]. Generally, it is necessary that the thickness of the deposition exceeds a critical value Hc for the formation of cracks [25]. A higher volume fraction leads to larger area deposition that is thicker than Hc , resulting in longer cracks. To further understand the cracking behavior, an in situ observation of the evaporation process with a bright-field microscopy was conducted, as shown in fig. 2. A gel zone was formed at the periphery of the droplet with the receding of the wet front, clearly causing instability inside the liquid zone (fig. 2(a)) [26]. This may result from the balance of the normal component of the liquid surface tension, which is often neglected in Young’s equation [27]. Furthermore, the surface tension of the liquid zone develops a stretching effect (radial stress σrr ) to the outside gel zone, i.e., causes a ring of materials at radial distance r to move to a ring of smaller radius [27]. This eventually leads to the formation of surface wrinkling in the outside gel zone (fig. 2(d)). With further evaporation, cracks originate from the flaws at the troughs of the wrinkle and propagate with the receding wet front (fig. 2(e)-(h)) [21]. The wrinkling instability is a result of the energy minimum between bending and stretching of the deposited gel film. The wavelength of wrinkling λ depends on the distance from droplet center r, which can be written as [28] λ∼
B σrr
1/4 r1/2 ,
(1)
where B is the bending modulus of the film [29], B=
EH 3 , 12(1 − Λ2 )
(2)
where E, H and Λ are the Young modulus, thickness and Poisson ratio of the materials, respectively.
Tensile stress
Compression stress
Fig. 3. Schematic view of stress and colloidal distribution in the surface wrinkle.
Based on eqs. (1) and (2), it could be reasoned that λ ∝ H 1/2 r1/2 . This indicates that the increase of film thickness leads to a larger wavelength of wrinkling, which is consistent with our experiment results. It should be noted that the direct driving force for cracking is the large tensile stress induced by the shrinkage of the gel phase that sticks on to the substrate [30]. The macroscopic radialized stress field built by the surface wrinkling does not result in the cracks itself. However, the stress field may lead to a different colloidal distribution at the trough and peak of a wrinkle due to the local compression and tensile stress, as illustrated in fig. 3. The colloids are more disposed to reaching a close-packed state at the troughs where the colloid distance is shorter. Once a closepacked state is reached, further evaporation would lead to the receding of the meniscus. Whereas, at the peaks of the wrinkling, evaporation may first cause capillary attraction between particles resulting in reduction in their distances prior to the meniscus receding. Therefore, at the troughs it is faster for the meniscus to recede below the first layer of particles, which directly renders the binded colloid particles to be stretched apart by the adjacent tensile stress, i.e., the nucleation of cracks. For this reason, once a crack nucleates, it propagates along the troughs of the wrinkling. It should be noted that the number of cracks is much less than the amount of wrinkling. It is
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Fig. 4. (a) Propagation dynamics of the cracks in the drying of droplets of different volume fractions; the inset graph plots the crack velocity vs. film thickness. (b) Schematic view of a crack tip.
probable that the internal stress is significantly released by cracking, which prevents the formation of a new crack at adjacent troughs. The wrinkling instability is a result of the stretching effect of the inside liquid zone [27,28]. The stretching effect is universal in all drying sessile colloidal droplets. However, surface wrinkling occurs only if the gel film has proper mechanical properties. If the compression modulus of the gel phase is too small, i.e., the gel film is highly compressible, the gel zone will be compressed/stretched evenly rather than forming wrinkles. Therefore, no remarkable surface wrinkling was observed in the drying of very dilute colloidal droplets(concentration < 2% wt.). If the gel phase is too rigid, for instance, the particles stick to the substrate too tightly and bending will be energetically unfavorable. In this case, it is hard for surface wrinkling to appear, which is indeed the case for the silica colloidal system [22]. In a recent work, it has been observed that wrinkling on an elastic sheet induced by the stretching of the underside of a liquid drop may turn into a crumpled state due to distinct symmetry-breaking instabilities [31]. However, in our experiments, the wrinkle-to-crumple transition does not occur due to different experiment conditions. The observed phenomenon in which surface wrinkling leads to a small number of cracks is probably generated by energy release rather than an instability transition. Macroscopic stress induced by surface wrinkling is also an important factor in the propagation direction of the cracks, even though the crack occurs fundamentally when the capillary stress is greater than the critical value [10, 32]. This finding suggests that, in addition to the compression stress due to negative Laplace pressure arising from the receding meniscus between colloidal particles, the stretching effect of the inner liquid phase on the outside gel phase can not be neglected.
3.2 Crack propagation dynamics Propagation dynamics are also important to understand the crack behavior in addition to the direction of crack growth. To avoid the influence of evaporation rate, all experiments were performed at fixed relative humidity and temperature. The wet front velocities for different droplets were very close. However, it is clearly seen from fig. 4(a) that the propagation velocity V of the cracks increases with increasing volume fraction. This can be explained by energy analysis based on Griffith’s criterion, i.e. the released stress energy is equaled with the newly emerged gas-solid interfacial energy for a steady growing crack [32]. In a unit time period, the energy balance for a growing crack with tip angle 2θ (fig. 4(b)), is written as ΔPc · V 2 tan θ · H = Γ ·
V · H, cos θ
(3)
where ΔPc is the critical Laplace pressure to open the crack, Γ is the interfacial energy per unit area. ΔPc is given by [10] 2/5 −HΔPc /γ ∼ = 2.16 [φN GH/2π(1 − Λ)γ] ,
(4)
where N is the number of contacting neighbors, φ is the volume fraction of the colloidal packing, G is the shear modulus of the particles, and γ is the surface tension of the liquid. Equation (4) suggests that a thinner film is tougher since it needs a larger ΔPc to open a crack. From eqs. (3) and (4), it can be deduced that V ∝ H 3/5 Γ.
(5)
The experimental data (data in the inset graphic in fig. 4(a), velocities were extracted from the linear region in L ∼ t plots, H was the average film thickness corresponding to the linear region) is in good agreement with
Eur. Phys. J. E (2014) 37: 84
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(a)
(b)
(d)
(e)
(c)
(f)
Fig. 5. Reversed propagation (from the inner part to periphery of the droplet) of cracks in the colloidal droplet with 0.5% wt. SDS. The arrows indicate the receding wet front (a) and the reversed propagation of cracks (b), respectively. The scale bars represent 200 μm.
(a)
(c)
(b)
(d)
Fig. 6. Complete suppression of cracks with 3% SDS in the droplets. (a)-(d) correspond to particle concentrations of 6%, 10%, 15% and 30% wt., respectively. The scale bars represent 200 μm.
the H 3/5 scaling of crack velocity. It should be mentioned that the thickness of the deposition is not uniform over the whole area. The crack propagation becomes slower when it approaches the center where the thickness becomes thinner. The H 3/5 scaling suggests that the energy dissipation accompanying the moving crack tip is negligible. The
crack behavior is mainly dominated by the surface energy of the newly emerged crack. The crack velocity in the present study is ∼ 102 μm/s, which is about one order of magnitude lower than that for the silica colloid system [22]. As indicated by eq. (5), the decreased crack velocity may be due to the decreased surface energy of the PTFE particles.
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3.3 Crack patterns tuned by SDS additives A crack may nucleate from the inner part of the droplet and propagate toward the periphery with the addition of surfactant (0.5% SDS) to the colloid suspension (fig. 5), which contrasts the case without surfactant. This distinct crack propagation direction can be related to the reduced surface tension with SDS. For nucleation of an individual crack, the binded particles (by capillary bridge) must be torn open by the tensile stress. The bound force between particles is the capillary force, which is proportional to the surface tension of the liquid. Inward Marangoni flow, from the droplet periphery to the center, results in a higher concentration of SDS in the inner part of the droplet, hence much lower surface tension and weaker bound forces between particles. Therefore, the stress built within the deposited film may first be released at the inner part followed by nucleation of a crack. A similar phenomenon has been observed in particle rafts systems, where cracks propagate outward due to Marangoni stresses caused by surfactant spreading [33,34]. Interesting periodic crack patterns were also witnessed in these systems, which may originate from the compression effect stimulated by a surfactant shock whose front has ramified finger morphology due to concentration fluctuation [34], while in the present study, the stresses were intrinsically the capillary force [25]. As a consequence, different mechanisms were responsible for the crack propagation and pattern formation occurring in our system. When adding more SDS (3%) into the suspension, the cracks can be completely suppressed, as shown in fig. 6. The coffee ring effect was eliminated by inwards Marangoni flow [35]. Moreover, the outward capillary flow may be significantly retarded due to the formation of larger-sized aggregates, because the presence of ionic surfactant may reduce the electrostatic screen length surrounding the PTFE particles. Here the surface wrinkling behavior has not been observed, suggesting that the surface tension is too low to generate sufficient stretching for wrinkling instability of the deposited film. No macroscopic stress could be built to favor crack growth in a preferential direction. On the contrary, the drying stress could be released without any delay due to the greatly reduced capillary force between particles. This eventually leads to a rough surface morphology. The surfactant-particle interaction may influence the stability of the suspension. For instance, the decrease of the electrostatic screen length can enhance coagulation and possibly restrain the coffee ring effect. For the tuning of the crack pattern, the effect of surfactant additive is mainly attributed to the change of surface tension and hence the capillary force.
4 Conclusions In summary, we have observed the radialized surface wrinkling and cracking behavior in the evaporation of PTFE colloidal droplets. The surface wrinkling arises from the stretching of the surface tension of the receding liquid
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zone, which plays an important role in building a macroscopic radial-like stress field. The macroscopic stress field, in turn, determines the final radialized distribution of cracks. With the increase of volume fraction/film thickness, the crack space decreases, whereas its propagation velocity increases as ∼ H 3/5 . The final deposition can be tuned by SDS additives, from reversed crack propagation (with 0.5% SDS) to complete crack elimination (with 3% SDS) due to the reduction of capillary force between particles. This study emphasizes the importance of the receding wet front in developing the stress field in deposited film. This work was supported by the National Natural Science Foundation of China (Grant No. 51301139), Shaanxi Provincial Natural Science Foundation (Grant No. 2012JQ1016), NPU Foundation for Fundamental Research (JCY20130147) and Specialized Research Fund for the Doctoral Program of Higher Education (Grant No. 20126102120058).
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