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Avoiding “mud” cracks during drying of thin films from aqueous colloidal suspensions
Journal of Colloid and Interface Science 313 (2007) 160–168 www.elsevier.com/locate/jcis
Avoiding “mud” cracks during drying of thin films from aqueous colloidal suspensions E. Santanach Carreras 1 , F. Chabert, D.E. Dunstan, G.V. Franks ∗ Department of Chemical & Biomolecular Engineering, The University of Melbourne, Vic 3010, Australia Received 4 December 2006; accepted 26 March 2007 Available online 24 April 2007
Abstract The critical cracking thickness of films obtained by drying aqueous alumina suspensions has been investigated. The effects of solution chemistry, binder and binder crosslinking were studied. Films formed from flocculated and dispersed suspensions are compared. The influence of the addition of the polymeric binder, poly(vinyl alcohol) (PVA) was also investigated. In addition, in some of the dispersed suspensions the PVA was covalently crosslinked. The critical cracking thickness is found to be 3 times greater for the films obtained from dispersed suspensions than for the films obtained from flocculated suspensions. The superior mechanical properties are primarily due to the higher final solids concentration in the films obtained from dispersed suspensions. Addition of PVA leads to an increase of the critical cracking thickness by a factor of two for both dispersed and flocculated systems. When the PVA is crosslinked, the mechanical properties of the gel during drying are improved and the critical cracking thickness is increased 10 fold with respect to the suspensions with uncrosslinked PVA. © 2007 Elsevier Inc. All rights reserved. Keywords: Thin film; Cracking; Drying; Suspension; Alumina; PVA; Crosslinking
1. Introduction When a coating of a colloidal suspension is applied to a non-porous rigid substrate and allowed to dry, its volume reduces due to the evaporation of the solvent. Constrained by the rigid substrate, this reduction in volume generates stresses in the drying material. If these stresses exceed the strength of the material, they will be released in the form of cracks. This problem is of great importance in numerous industrial fields for instance, paints, paper coatings, fabrication of ceramic substrates for electronic applications, and drying concrete. The colloids, the suspending media, and the interactions among the different components of the suspension vary depending upon the application; nevertheless, the underlying physics of the drying process and the development of the stresses leading to these cracks remain unchanged. * Corresponding author.
E-mail address: [email protected] (G.V. Franks). 1 Current address: Department of Physics and Division of Applied Science,
Harvard University, USA. 0021-9797/$ – see front matter © 2007 Elsevier Inc. All rights reserved. doi:10.1016/j.jcis.2007.03.076
Following is a brief summary of the three stages of the drying process as described by many investigators [1–6]. Initially a constant drying rate stage occurs in which consolidation of the particles in the suspension and evaporation take place at the same constant rate. Indeed, a layer of liquid covers the film at first, the liquid in the pores does not play a role in the evaporation, and stress build-up is negligible. The air–liquid interface is macroscopically flat during the first stage of drying. The length of time of this stage is proportional to the initial volume fraction of solvent in the suspension [3]. Eventually the particle volume fraction in the drying film increases to the gelpoint (φg ) and a three-dimensional particle network forms [6]. At this point in the drying, the particle network develops a non-zero compressive yield stress which increases as drying continues because the volume fraction of the suspension increases. The particle network is able to resist consolidation if the applied isostatic compressive consolidation pressure is less than the compressive yield stress. The liquid–air interface attempts to penetrate into the top of the powder bed. In order to do so, it must form a curved meniscus between neighboring particles. The curved menisci between particles create an isostatic consolidation pres-
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sure on the particle network and a pressure gradient between the surface of the liquid and the liquid in the interior of the drying body. The liquid rises to the surface as a result of the pressure gradient and continues to evaporate at a constant rate. For colloidal-size particle beds in water that have pore size on order of a micron the isostatic consolidation pressure (which also drives the liquid flow) is on order of 1 MPa based on Laplace’s relationship. During this second stage of constant rate drying, the top of the particle network and the air–water interface recede at the same rate. This is because the consolidation pressure applied to the particle network due to the capillary forces is sufficient to consolidate the powder. As the network continues to consolidate, its compressive yield stress increases as volume fraction increases until the particle network has sufficient strength to withstand the capillary pressure and further consolidation is not possible at the capillary pressure determined by the curvature of the air–water interface. At this point the third and final stage of drying, known as the falling rate period, begins. The liquid/vapor interface penetrates the powder compact and the rate of drying (evaporation) no longer occurs at a constant rate as the liquid/vapor interface recedes into the pores between the particles. At this stage, the liquid/solid interfacial area decreases and so does the capillary pressure. The shrinkage of the solid particle network stops at this point in the drying. There is a significant knowledge base about the development of stresses in drying suspensions and saturated powder compacts and how those stresses can lead to cracking in those drying bodies [1,3,7–12]. Tensile stresses can develop at the surface of a thick section drying body due to the constraint of the drying shrinkage by the interior of the body. Likewise tensile stresses develop in a thin film coating of suspension drying on a rigid substrate. A key factor influencing the development of stresses in a thick section drying body are the rate of evaporation relative to the rate of transport of the liquid to the surface of the body. The rate of evaporation is controlled by the temperature, vapor pressure of the liquid, the ambient pressure and convection effects. The transport of the liquid to the surface is controlled by Darcy’s law which relates the flow rate to the pressure gradient. The flow rate through the porous packed bed is related to the pressure driving the flow, the fluid viscosity, the distance through the packed bed, the particle size and the bed voidage as described by the Carman–Kozeny relationship [13]. If the rate of evaporation is less than the rate of liquid flow through the body (referred to as slow drying in the present paper) the shrinkage of an unconstrained drying body can occur uniformly (moisture is uniform throughout the body). If the rate of evaporation is fast relative to the transport of liquid to the surface (referred to as fast drying in the present paper), a pressure gradient and a moisture gradient will exist within the drying body. These gradients result in non-uniform shrinkage, with the surface (low moisture region) trying to shrink more than the interior of the body which constrains the exterior dryer layer. The constraint of the shrinkage results in tensile stresses at the surface. If the drying suspension is a thin film on a rigid substrate, even when the drying is slow, the body cannot shrink uniformly and isotropically. The rigid substrate constrains shrinkage in the plane of the surface. (Shrinkage normal to the surface is
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not constrained.) The constraint of the drying thin film by the substrate results in bi-axial tensile stresses at the surface of the drying substrate. It is known that a peak stress occurs at the end of the constant rate drying period and this is when cracking will occur if it is energetically favorable [1,3,4,8]. In the case of rigid particles, the film recovers a nearly stress-free state [3,5] once all the liquid has evaporated from the porous body. When thin coatings are considered such that the rigid substrate constrains the shrinkage of the film during the drying process bi-axial tensile stresses occur at the surface of the film. These stresses will lead to cracking if they are greater than a critical value that depends upon the material properties [8]. An energy balance and the use of A.A. Griffith’s concepts of fracture mechanics, which state that a crack in a body will only extend if it decreases the free-energy of the system, allows one to show that cracking will occur only for films with thicknesses exceeding a critical value hc [14], hc = 2Gc E ∗ /(Zσ 2 ), where Gc is the critical strain-energy release rate (a measure of fracture toughness), E ∗ = E/(1 − ν), where E is Young’s modulus and ν is Poisson’s ratio, σ is the biaxial tensile stress and Z is a parameter whose value depends on the geometry of the crack tip and that is of the order of 2 [15]. Cracking is avoided either by keeping the stresses low (slow drying or reducing the surface tension of the liquid), or by increasing the mechanical properties (Gc and E ∗ ) of the drying powder compact. It has been established that cracking often initiates at the end of the constant rate evaporation stage and typically coincides with a peak in stress [1,3,4]. In recent work, Kiennemann and co-workers [4] measured the evolution with time of Young’s modulus of drying aqueous alumina suspensions with ultrasounds using a pulse–echo method in “long-bar mode.” Their results show a negligible Young’s modulus when the stress peak occurs and thus, the lack of stiffness results in a predisposition to cracking. An increase of the critical cracking thickness of gels can be achieved by adding a small amount of elastic binder to the sol–gel precursor solution. The effect of such a binder is illustrated in the work of Roeder and Slamovich [16] who considered titanium di(isopropoxide) bis(ethyl acetocetate) (TIBE) solutions to which they added small quantities, 5 and 10 wt% with respect to the TIBE in the solution, of a styrene–butadiene–styrene block copolymer. Their results show a 5-fold increase of the critical cracking thickness in the case where 5 wt% block copolymer is added. Adding 10 wt% block copolymer results in an increase of the critical cracking thickness that is nearly 10-fold. In ceramic processing, water soluble binders that adhere to particles surfaces during drying and bind the dry particles together are typically added to formulations to improve the mechanical behavior of dry powder bodies [17,18]. They act by strengthening the bond between individual particle pairs in the dried body. When soluble polymers (such as binders) are added to a formulation, a second stress peak results during the falling rate drying period of a thin film on a rigid substrate. This second peak stress has been found to be greater in magnitude than the drying stress when no binder is used and a residual compressive stress will remain in the film
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after the liquid phase has fully evaporated [3,4]. It is clear that the addition of binder is only useful if the increase in strength of the dried powder compact is greater than the increase in stress developed. A general solution to the problem that can work for a variety of systems is to improve the mechanical properties (Young’s modulus (E) and critical strain-energy release rate (Gc )) of the film during the drying process, and this is particularly important in the initial stages when the first stress peak occurs. The mechanical properties can be improved by increasing the strength of dry bond between individual particle pairs such as by adding polymeric binder. The Young’s modulus, as well as other mechanical properties, increase with and depend strongly on the volume fraction of solids [19]. In turn, the final volume fraction of the dry film will depend on the consolidating pressure and the compressive yield strength of the particle network. The compressive yield stress depends strongly on the particle–particle interactions, which are dictated by solution conditions such as pH [19,20]. Dispersed suspensions consolidate to higher solids contents relative to aggregated suspensions at a particular applied pressure. Another approach is to reduce the stress that develops by the addition of plasticizer (such as ethylene glycol) [8,11] or surfactant [4,10] to the formulation. The aim of this paper is three-fold. Firstly, we investigate the influence of solution chemistry; with that in mind, we consider both flocculated (pH 9) and dispersed (pH 1.75) alumina suspensions. Secondly, we investigate the addition of small amounts of binder to the system in order to increase the modulus and/or fracture toughness of the film. Finally, we add a temperature activated cross-linker in the suspensions [21]. By choosing appropriate processing conditions (humidity, temperature, pH), it is possible to control gelation so that the mechanical properties of the gelled powder compact are improved. The materials used and the experimental procedures are presented in Section 2. Section 3 of this paper presents and discusses the most relevant results. Some concluding remarks are presented in Section 4. 2. Experimental 2.1. Materials The alumina powder used was a commercial high-purity αAl2 O3 (AKP-30, Sumitomo Corp., Tokyo, Japan) with a BET surface area of 7 m2 g−1 , a mean particle diameter of 0.3 µm, and a density of 3.97 g cm−3 . A partially hydrolyzed poly(vinyl alcohol) (PVA, Celanese Chemical, USA) was used. Its glass transition temperature is well above room temperature. Doubledistilled water was used throughout the different experiments of this study. The effects of repulsive and attractive inter-particle interactions on critical cracking thickness were investigated by preparing acidic suspensions (pH ∼ 1.65–1.85) and suspensions near the isoelectric point (iep) of alumina (pH 9). The zeta-potentials of AKP-30 alumina at pH ∼ 2 and at pH 9 (iep) are respectively of around 100 ± 10 mV and 0 ± 5 mV [21]. Hence, the alumina particles are dispersed in the first case, whereas in the second
one, the particles flocculate and gel. The pH of suspensions was adjusted using analytical-grade HNO3 or NaOH. To improve the critical cracking thickness, PVA is added to some of the suspensions. In some cases, the PVA was crosslinked by adding 2,5-dimethoxy-2,5-dihydrofuran (DHF) to the Al2 O3 –PVA suspensions [21]. DHF will decompose and behave as a cross-linker for PVA only in an acidic environment. Therefore, we can only consider films cast from dispersed alumina–PVA suspensions (pH 1.75) in this case. For all gelation experiments, a DHF concentration of 300 mM is used. Suspensions with initial solids concentrations, φi , of 10 and 30 vol% were prepared by ultrasonication under acidic conditions using a sonifier (Model 250, Branson Ultrasonics Corp., Danbury, CT) equipped with a 1.9 diameter horn. The sonifier operates at 20 kHz and was used in the pulsed operation mode with a duty cycle of 50% and at an output control setting of 6 (70 W). With these settings, suspensions were prepared by a series of sonication cycles of 3 min each with about 20 min rest in-between until the suspension is smooth to the eye. Usually, three or four sonication cycles suffice. In order to ensure that the suspension was smooth, a small quantity was spread between two microscope glass slides. If any grinding was felt while rubbing the slides, additional sonication cycles were performed. Once the suspensions were smooth, their pH was adjusted using HNO3 or NaOH. The pH of the suspension was allowed to equilibrate overnight, checked again and re-adjusted if necessary. Once the desired pH was reached, the suspensions were de-aired with a vacuum pump and a few drops of octanol were added to the suspension in order to avoid bubble formation. The suspension was then vigorously mixed and stirred for about 30 s, and films of different thicknesses were cast. 2.2. Methods Drying experiments performed in this study are rather simple yet robust. The suspensions are cast into pools of various depths and are allowed to dry under room temperature and humidity conditions. In general, pools were 75 mm in length and 65 ± 5 mm wide. The base was a glass plate onto which glass microscope slides of thickness 0.8–1.1 mm were fixed in-place using double-sided tape. Stacking up various microscopes slides allowed control of the initial depth of the pool, and thus the initial thickness of the film, hi . Both the glass plate and microscope slides were thoroughly cleaned with doubledistilled water and ethanol before use. For the thicker films, hi > 6 mm, walls machined out of Plexiglas were used. For a few experiments, pools completely machined out of Plexiglas (poly methylmethacrylate) of base dimensions 120 × 120 mm2 and depths between 0.1 and 3.2 mm were used. In order to control hi of these thicker films, the necessary suspension volume to be cast was calculated from the plate’s base dimensions. Using pools facilitates suspension casting and constrains the drying process to be one-dimensional. During experiments, the cast films were protected from possible forced airflows in the room, and the directional drying that comes with crossflow, as well as to avoid deposition of dust onto the films. Any dust particles on
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the film can act as crack nucleation sites and induce cracking at lower thicknesses than the true critical cracking thickness hc . Drying experiments were performed at room temperatures in the range 21–28 ◦ C. However, temperature variations did not exceed 2 ◦ C for one given run. Moreover, to ensure homogeneity of drying conditions, all experiments with one given formulation were carried out simultaneously. A typical range of relative humidity in the room was 45–60%. The drying process took between 4 and 48 h depending on the initial Al2 O3 concentration and hi . We believe that these conditions constitute slow drying conditions as described in the introduction. When very thick (>5 mm) films of the same suspensions were dried very quickly (at 60 ◦ C for instance) cracks occurred in formulations that did not produce cracks under the slow drying conditions described above. This is a result of the constraint of the drying surface by the undried interior of the thick film as described in the introduction. In general, fast drying was avoided in the results presented in this paper. Two different procedures for crosslinking the PVA, that lead to similar results have been used. In the first one, the solution is crosslinked in a water-saturated environment (RH in the order of 95%) at 60 ± 2 ◦ C for 40 min. Relative humidity (RH) measurements show that RH is in the range 90–95% during this stage. Then, and still in a water-saturated environment, the solution is allowed to cool down to room temperature. Once at room temperature, the gelled slurry is dried in conditions similar to those used for Al2 O3 suspensions without binder and with non-crosslinked PVA. In the second method, both the crosslinking of the PVA and the drying took place at room temperature. In this case, the crosslinking stage (in humid environment) took about 24 h followed by the drying stage (at ambient humidity). Once the films were dried, the microscope slides were removed and the final thickness of the film was measured across the length of the film to produce a height profile. This was done at the center of the film and at least at two other positions (one on each side of the center on the film). Measurements were taken 10 mm apart with a Mitutoyo dial indicator (No. 513-404) for films of thicknesses below 800 µm. The accuracy of these measurements is 10 µm, which is less than 10% of the smallest film thicknesses measured. In the case of films thicker than 800 µm, a micrometer was used. As a crosscheck, thickness measurements using both techniques were compared in films of thicknesses in the range 500–800 µm. Measured thicknesses differed by less than 10 µm, which is within measurement uncertainties, thus the measuring procedure was validated. From these measurements, either local thicknesses can be used or an average film thickness h¯ can be calculated. Pictures of dried films were taken by placing them on a rear illumination light-box. The light passing through cracks is seen as white on the pictures whereas the rest of the dried film is opaque, or translucent at best. This technique is a simple way to assess the number, the length, and the width of the cracks. However, it is limited to the case of cracks that penetrate completely through the thickness of the film, referred to here as channeling cracks.
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(a)
(b)
(c) Fig. 1. Pictures of dried films of different final average thickness h¯ obtained from flocculated (pH 9) Al2 O3 aqueous suspensions without binder. (a) h¯ = 113 ± 20 µm < hc , (b) h¯ = 177 ± 40 µm ≈ hc , (c) h¯ = 430 ± 20 µm ≈ 3hc .
3. Results and discussion Fig. 1 shows representative pictures of the dried films cast from alumina suspensions without binder in the case of flocculated, pH 9 ± 0.15 suspensions. Likewise Fig. 2 shows typical pictures of dry films prepared from dispersed suspensions, pH 1.75 ± 0.10. Figs. 1a, 2a, and 2c correspond to films cast from Al2 O3 suspensions with φi of 0.3 whereas the suspensions used in Figs. 1b, 1c, and 2b had initial Al2 O3 concentration φi of 0.1. Initial solid concentration does not affect the critical cracking thickness of films, hc , but rather the final thickness of the film. Therefore, varying φi is a convenient way to obtain
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Table 1
(a)
(b)
(c) Fig. 2. Pictures of dried films of different final average thickness h¯ obtained from dispersed (pH 1.75) Al2 O3 aqueous suspensions without binder. (a) h¯ = 316 ± 20 µm < hc , (b) h¯ = 430 ± 20 µm ≈ hc , (c) h¯ = 1265 ± 70 µm ≈ 3hc .
films of different final thicknesses from the same initial pool height hi . Fig. 1 corresponds to flocculated suspensions with pH of 9. Under these conditions, attractive forces (van der Waals) between alumina particles exist and the suspension gels naturally and spontaneously resulting in difficult to consolidate particle network. No cracks are observed in Fig. 1a, a film with average thickness h¯ in the order of 113 µm. The vertical fringes with characteristic lengths in the range 1–20 mm that are observable on the film are a consequence of non-constant blade velocity during casting of the film. It is known that such conditions result in variations of film thickness [22]. Thinner marks in the
System
pH
vol. PVA/vol. Al2 O3
hc (µm)
Al2 O3
8.86–9.0 1.65–1.8
0 0
130 ± 20 410 ± 20
Al2 O3 –PVA
8.86–9.0 1.65–1.8
1:10 1:10
240 ± 20 875 ± 75
Al2 O3 –PVA–DHF
1.65–1.8
1:10
>8800
horizontal direction are due to small defects on the Plexiglas blade used. The film in Fig. 1b with h¯ = 177 µm shows multiple cracks. Their spacing is not uniform over the entire film; the cracks are more numerous on the left side and on the bottom of the film, which is explained by local differences in film thickness. Indeed, h¯ is around or greater than 150 µm in the areas with more cracks, whereas in the areas where no cracking occurs, the film thickness is around 120 µm. Thus, as reported in Table 1, the critical cracking thickness hc is considered to be in the order of 130 µm. The number of cracks increases with film thickness and a continuous network of channeling cracks is formed. An example is Fig. 1c that corresponds to h¯ = 430 µm. The cracks have no preferred orientation indicating a rather uniform drying and thickness over the entire film. In fact, either having a directional airflow [23–25] or controlled thickness changes [22] will induce oriented cracks. Let us now discuss the case of films obtained from dispersed (pH 1.75) alumina suspensions without binder as shown in Fig. 2. For these formulations there is repulsion between particles in suspension resulting in high particle packing densities in the dried portions of the body. When the average thickness is below hc , Fig. 2a, no cracks are observed. For uncracked films, deviations of the local film thickness from the average ¯ appear more frequently in the case of films film thickness, h, obtained from solutions of pH 9 than for films obtained from dispersed solution (pH 1.75), see Figs. 1a and 2a, respectively. The reason lays in the different rheological behavior of the solutions. The flocculated suspension used for the film in Fig. 1a (pH 9) has a yield-stress and needed to be spread into a flat film with a blade. The dispersed suspension (pH 1.75), from which the film in Fig. 2a was obtained, had no yield stress and freely flowed homogeneously over the entire pool when cast and gently tapped to level the surface of the film. The critical cracking thickness (hc ) for films obtained from dispersed suspensions is 410 µm (see Table 1), which represents a 3-fold increase compared to films obtained from flocculated suspensions (pH 9). The first cracks in films obtained from dispersed suspensions (pH 1.75) can be seen in Fig. 2b, a film with an average thickness of 430 µm. The channeling cracks, mostly on the top part of the picture, are less obvious and numerous than in Fig. 1b cast from a suspension with a pH of 9. The cracks in Figs. 2b and 2c converge at the last point to dry in the film; the bright spot resulting from a particle deficiency induced by non-homogeneities in drying fluxes over the entire film. The critical cracking thickness (hc ) depends on the mechanical properties of the dried layer on the surface of the film where cracks initiate. The difference in critical cracking thickness of the thin films produced from dispersed and flocculated
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suspensions can be understood in terms of the final volume fraction (φf ) of dried films that depend on the initial suspension conditions. Indeed, the mechanical behavior of the dried film is proportional to the strength of the bond between a particle pair and the number of bonds within the plane of fracture. The strength of the bond for all dried films without added binder is the same and is due to van der Waals forces between two particles in air. Van der Waals force is given by Ar/12d, where A is the Hamaker constant, r is the particle’s radius and d is the distance between the particles [26]. The number of bonds in the fracture plane is inversely proportional to the particle size [27,28] and shows a strong dependence on the particle volume fraction [19,27]. Since primary particle size is constant throughout this study, the strength of the dried films will solely depend on their solid’s concentration. The structure and final volume fraction of solids of the particle network is governed by the inter-particle interactions of the suspension while still saturated. The nature of these interactions, attractive or repulsive, is controlled by the pH of the suspension. For a dispersed system φf is near the maximum random close packing volume fraction (φf ≈ 0.64) and in the case of a flocculated system φf will be substantially lower [6,19,20]. Measurements of the density of dried films using Archimedes’s method yielded average φf values of 0.66 ± 0.02 and 0.55 ± 0.05 in the case of films obtained from dispersed and flocculated suspensions, respectively. These values are consistent with other results [6,19,20] of the final volume fraction of solids consolidated under about 1 MPa pressure which is the approximate value produced by the capillary consolidating pressure. Therefore, the number of interacting particles in the plane of fracture, and in turn the stresses the film can withhold, will be greater for the films cast from dispersed suspensions (pH 1.75) than from flocculated ones (pH 9). Thus, the improved hc of the films obtained from dispersed suspensions is due to the increase in Gc and E that comes with higher solid volume fraction φf . Although we are confident of the mechanism described above to explain the difference in critical cracking thickness of thin films from dispersed and flocculated suspensions during slow drying there is other published work that appears to be contradictory and suggests one additional strengthening mechanism. Work by Cima and co-workers [9,10] found that flocculated alumina suspensions (pH 8) produced greater critical thickness than dispersed suspensions (pH 3.5). These results appear to be opposite to our findings, but the discrepancy is perhaps due to differences in drying rate. Although it is unclear from the publications what the actual drying time of their films was, it appears that it was faster than ours since they indicated that very slow drying over 48 h resulted in an increase in the critical cracking thickness. If their drying was in the fast drying regime, it is possible that the slow drying in our experiments allowed sufficient time for the stresses between the particles in contact with the substrate to relax by sliding and therefore result in a higher critical cracking thickness. Experiments on liquid mercury [9] where stress release at the substrate–suspension interface is facile show large critical cracking thicknesses. Also Cima and co-workers [9,10] noted that for dispersed suspensions, the critical cracking thickness increased as the pH was
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lowered below 2. They attributed this to the precipitation of dissolved aluminum species at low pH during drying that would form strong bonds between particles strengthening the drying surface layer. This mechanism is likely also a factor in the strengthening of the pH 1.75 dispersed suspensions presented in the current paper. A second set of experiments was conducted where the polymer poly(vinyl alcohol) (PVA) was added to the Al2 O3 suspension so that the ratio between the volume of binder and the volume of Al2 O3 is 1:10 regardless of the initial volume fraction of alumina. In weight percentage with respect to the alumina, that is equivalent to about 1.6 wt%. Fig. 3 presents characteristic dried films cast from Al2 O3 –PVA suspensions for both pH 9 and pH 1.75. The film in Fig. 3a allowed us to determine the critical cracking thickness in the case of a flocculated system (pH 9). Two regions are clearly distinct on the film and are separated by the guiding white dashed line in Fig. 3a. One, on the left, where multiple cracks cover the film, and one, on the right, in which very few, localized cracks have initiated. Measurements in each region lead to thickness averages of h¯ bc = 220 ± 20 µm and h¯ ac = 250 ± 20 µm where bc and ac stand for “below cracking” and “above cracking,” respectively. A detailed analysis of all thickness measurements allowed us to determine the hc value of 240 µm reported in Table 1, which is already nearly a 2-fold increase of the critical cracking thickness when compared to the alumina suspensions without binder. It is clear that the PVA is acting to improve the mechanical properties of the film. Moreover, this is obtained with only 1.6 wt% of PVA. In Fig. 3a, some vertical fringes can be observed as well. These are due to a non-uniform blade velocity while casting the film. In both cases, either films obtained by casting dispersed suspensions (pH 1.75) or flocculated ones (pH 9), the increase in critical thickness hc is in the order of a factor 2 as reported in Table 1. This is consistent with the result of Cima and coworkers [9], who found that the critical cracking thickness increased linearly with PVA addition. The PVA acts to increase the strength, critical strain energy release rate and modulus of the dried film. When water is removed during drying, the concentration of PVA in solution is increased sufficiently so that the PVA precipitates out of solution at the particle–particle contact points and therefore strengthens the dried body. Moreover, the shape of the cracks does not seem to change, as illustrated by the picture of Fig. 3d, compared to those observed in films cast from suspensions without binder. They continue to be long and not very numerous for the dispersed films. Visual inspection of the dried films seem to show a layer on top of the dried film cast from acidic suspension that is rich in PVA which might delay cracking. Migration of PVA binder to the surface of dried granules is not uncommon [29]. This phase separation is more important with lower initial solid concentrations and greater initial thickness as the constant rate stage becomes longer and the PVA in solution has more time to come up to the free surface. Thus, it would seem more advantageous to use higher initial solid concentration in order to avoid binder migration and obtain films with homogeneous composition over their entire depth.
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(a)
(b)
(c)
(d)
Fig. 3. Pictures of dried films of different final average thickness h¯ obtained from both flocculated (pH 9) and dispersed (pH 1.75) Al2 O3 aqueous suspensions with PVA as a binder. The volume ratio between PVA and Al2 O3 is 1:10, which represents 1.6 wt% of PVA with respect to Al2 O3 . (a) pH ∼ 9, h¯ ac = 250 ± 20 µm, h¯ bc = 220 ± 20 µm; (b) pH ∼ 9, h¯ = 440 ± 20 µm; (c) pH ∼ 1.75, h¯ = 520 ± 20 µm; (d) pH ∼ 1.75, h¯ = 1000 ± 70 µm.
Another interesting observation is that the total length of cracks formed and the number of cracks per unit area is greater for the dried films produced from flocculated slurries compared to those produced from dispersed slurries when compared at the same thickness relative to the critical cracking thickness. This observation is true for thin films produced from suspensions both without and with PVA. When the PVA in the suspension was crosslinked with DHF before drying, the mechanical properties of the slurry are substantially improved even before the initial stages of drying. After crosslinking the binder, films with average thicknesses as high as 8.8 mm have been cast without cracks developing as can be seen in Fig. 4a. This already represents a 10-fold increase in the critical cracking thickness when compared to the non-crosslinked formulation. The picture in Fig. 4a shows a rather thick film, h¯ = 8.8 mm, obtained by crosslinking the PVA in the well-dispersed alumina suspension at room temperature for 24 h and then allowing the film to dry at room temperature. If compared to the pictures presented in Figs. 2b, 2c, and 3d, it is clear that the film of Fig. 4a has yet to reach its critical cracking thickness. However, small cracks and defects can be observed around the edges of the film, as illustrated by the enlargement of one corner of the film presented in Fig. 4b. These cracks are due to edge effects. Indeed, near the edges of the pool, the shrinkage of the film is not only constrained in the x–y plane, but also in the z-direction.
This additional constrain leads to a complex state of stress. The stresses near the edges of the film are higher than at the center of the film, and therefore the cracks initiate near the edges. An easy way to prevent these cracks is to release the wet green film from the pool walls after gelation and before drying. This is rather simple and can be done with a razor blade, for example. As in the case of dispersed Al2 O3 suspensions with uncrosslinked PVA, a thin layer of PVA was observed at the top of the dried film. This layer is not homogeneous over the entire surface of the film as denoted by changes in shade and oval marks observable over the film in Fig. 4a. To better view the thickness of this layer, a 10 mm slab of the film was cut and polished, giving access to the cross-section of the film. The resulting cross-section is presented in Fig. 5. The layer of PVA on top of the film represents at most 2% of the total thickness of the film, meaning that at least 80% of the PVA added has been crosslinked in the bulk of the film. Nevertheless, it might be possible to reduce the thickness of this layer by optimizing the amount of PVA and crosslinking agent used. Fig. 5 also shows how the pool walls constrain the shrinkage of the film’s edges in the z-direction. The reader should keep in mind that the aim of this paper is not to optimize the formulation, but rather to present a procedure to increase the critical cracking thickness of films obtained from aqueous alumina suspensions by strengthening the particle network. Other approaches such as the addition of
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(a)
(b) Fig. 4. Pictures of a dried thick film obtained from a dispersed (pH 1.75) Al2 O3 aqueous suspensions with PVA as a binder that was crosslinked at room temperature using 300 mM DHF before drying. The volume ratio between PVA and Al2 O3 is 1:10, which represents 1.6 wt% of PVA with respect to Al2 O3 . (a) h¯ = 8800 ± 200 µm. (b) Detail of edge region.
Fig. 5. Cross-section of the thick film presented in Fig. 4. An 8.8-mm thick film slab was cut and the polished in order to observe the profile of the film and the thin layer of PVA that formed on the free surface of the dried green body.
plasticizers and surfactants will also be useful in reducing the magnitude of the stress generated. 4. Conclusion Controlling the chemistry of suspensions is important and allows one to improve the critical thickness above which films will crack. By considering successively, aqueous alumina suspensions without and with small amounts of a polymeric binder, which is crosslinked in some cases, we have shown that the critical cracking thickness can be increased by a factor greater than 50 when the worst (flocculated suspension without binder) and best (dispersed suspension with crosslinked PVA) case scenarios are considered.
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For the same given formulation, i.e., concentration of alumina and concentration of binder, the critical thickness is found to be about 3 times greater when a dispersed suspension (pH 1.75), rather than a flocculated one (pH 9), is used during casting. The increase in critical cracking thickness, and mechanical properties, is due to the higher packing density of films obtained from dispersed suspensions. A higher solid concentration means a greater number of particle–particle interactions per unit area, and therefore the stresses that the film can withhold are higher. The addition of a polymeric binder, PVA, also allows one to increase the critical cracking thickness. Although in the present study, we add only 1.6 wt% of binder with respect to alumina, the critical thickness is increased by roughly a factor of 2 for films obtained from both flocculated and dispersed suspensions. Further increases in critical thickness, by a factor of at least 10 with respect to films cast from Al2 O3 –PVA dispersed suspensions, are obtained by crosslinking the polymeric binder with DHF before drying begins. In conclusion, the addition of binder and further crosslinking of binder presented in the study has the potential for nonnegligible increases in critical cracking thickness that may be useful in commercial applications. Plasticizers or other additives such as surfactants could be added to improve the mechanical properties or to decreases the stresses in the film during drying, and in this way, further increase the critical cracking thickness. References [1] G.W. Scherer, J. Am. Ceram. Soc. 73 (1990) 3. [2] Y. Holl, J.L. Keddie, P.J. McDonald, W.A. Winnik, in: T. Provder, M.W. Urban (Eds.), ACS Symposium Series, vol. 790, American Chemical Society, Washington, DC, 2001, p. 2. [3] P. Wedin, C.J. Martinez, J.A. Lewis, J. Daicic, L. Bergström, J. Colloid Interface Sci. 272 (2004) 1. [4] J. Kiennemann, T. Chartier, C. Pagnoux, J.F. Baumard, M. Huger, J.M. Lamérant, J. Eur. Ceram. Soc. 25 (2005) 1551. [5] M.S. Tirumkudulu, W.B. Russel, Langmuir 21 (2005) 4938. [6] L.A. Brown, C.F. Zukoski, L.R. White, AIChE J. 48 (2002) 492. [7] W. Pompe, F.F. Lange, I.B. Sevosianov, in: R.C. Bradt (Ed.), Fracture Mechanics of Ceramics, vol. 11, Plenum Press, New York, 1996, p. 343. [8] P. Wedin, J.A. Lewis, L. Bergstorom, J. Colloid Interface Sci. 290 (2005) 134. [9] R.C. Chiu, T.J. Garino, M.J. Cima, J. Am. Ceram. Soc. 76 (1993) 2257. [10] R.C. Chiu, M.J. Cima, J. Am. Ceram. Soc. 76 (1993) 2769. [11] J.A. Lewis, K.A. Blackman, A.L. Ogden, J.A. Payne, L.F. Francis, J. Am. Ceram. Soc. 79 (1996) 3225. [12] M. Descamps, M. Mascart, B. Thierry, D. Leger, Am. Ceram. Soc. Bull. 74 (3) (1995) 89. [13] M. Rhodes, Introduction to Particle Technology, Wiley, Chichester, 1998. [14] F.F. Lange, Science 273 (1996) 903. [15] J.W. Hutchinson, Z. Suo, in: J.W. Hutchinson, T.Y. Wu (Eds.), Advances in Applied Mechanics, Academic Press, New York, 1991, p. 126. [16] R.K. Roeder, E.B. Slamovich, J. Mater. Res. 14 (1999) 2364. [17] J.S. Reed, Principles of Ceramic Processing, second ed., Wiley, New York, 1995. [18] S. Baklouti, T. Chartier, J.F. Baumard, J. Am. Ceram. Soc. 80 (1997) 1992. [19] G.M. Channell, C.F. Zukoski, AIChE J. 43 (1997) 1700.
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[20] G.V. Franks, F.F. Lange, J. Am. Ceram. Soc. 79 (1996) 3161. [21] S.B. Johnson, D.E. Dunstan, G.V. Franks, J. Am. Ceram. Soc. 85 (2002) 1699. [22] C.M. Stafford, K.E. Roskov, T.H. Epps III, M.J. Fasolka, Rev. Sci. Instrum. 77 (2006) 023908. [23] C. Allain, L. Limat, Phys. Rev. Lett. 74 (1995) 2981. [24] K.A. Shorlin, J.R. de Bruyn, M. Graham, S.W. Morris, Phys. Rev. E 61 (2000) 6950.
[25] E.R. Dufresne, E.I. Corwin, N.A. Greenblatt, J. Ashmore, D.Y. Wang, A.D. Dinsmore, J.X. Cheng, X.S. Xie, J.W. Hutchinson, D.A. Weitz, Phys. Rev. Lett. 91 (2003) 224501. [26] D.J. Shaw, Introduction to Colloid and Surface Chemistry, fourth ed., Butterworth–Heinemann, Oxford, 1992. [27] G.V. Franks, F.F. Lange, Colloids Surf. A 146 (1999) 5. [28] O. Molerus, Powder Technol. 12 (1975) 259. [29] U. Kim, W.M. Carty, Ceram. Eng. Sci. Proc. 23 (2002) 33.
Avoiding “mud” cracks during drying of thin films from aqueous colloidal suspensions E. Santanach Carreras 1 , F. Chabert, D.E. Dunstan, G.V. Franks ∗ Department of Chemical & Biomolecular Engineering, The University of Melbourne, Vic 3010, Australia Received 4 December 2006; accepted 26 March 2007 Available online 24 April 2007
Abstract The critical cracking thickness of films obtained by drying aqueous alumina suspensions has been investigated. The effects of solution chemistry, binder and binder crosslinking were studied. Films formed from flocculated and dispersed suspensions are compared. The influence of the addition of the polymeric binder, poly(vinyl alcohol) (PVA) was also investigated. In addition, in some of the dispersed suspensions the PVA was covalently crosslinked. The critical cracking thickness is found to be 3 times greater for the films obtained from dispersed suspensions than for the films obtained from flocculated suspensions. The superior mechanical properties are primarily due to the higher final solids concentration in the films obtained from dispersed suspensions. Addition of PVA leads to an increase of the critical cracking thickness by a factor of two for both dispersed and flocculated systems. When the PVA is crosslinked, the mechanical properties of the gel during drying are improved and the critical cracking thickness is increased 10 fold with respect to the suspensions with uncrosslinked PVA. © 2007 Elsevier Inc. All rights reserved. Keywords: Thin film; Cracking; Drying; Suspension; Alumina; PVA; Crosslinking
1. Introduction When a coating of a colloidal suspension is applied to a non-porous rigid substrate and allowed to dry, its volume reduces due to the evaporation of the solvent. Constrained by the rigid substrate, this reduction in volume generates stresses in the drying material. If these stresses exceed the strength of the material, they will be released in the form of cracks. This problem is of great importance in numerous industrial fields for instance, paints, paper coatings, fabrication of ceramic substrates for electronic applications, and drying concrete. The colloids, the suspending media, and the interactions among the different components of the suspension vary depending upon the application; nevertheless, the underlying physics of the drying process and the development of the stresses leading to these cracks remain unchanged. * Corresponding author.
E-mail address: [email protected] (G.V. Franks). 1 Current address: Department of Physics and Division of Applied Science,
Harvard University, USA. 0021-9797/$ – see front matter © 2007 Elsevier Inc. All rights reserved. doi:10.1016/j.jcis.2007.03.076
Following is a brief summary of the three stages of the drying process as described by many investigators [1–6]. Initially a constant drying rate stage occurs in which consolidation of the particles in the suspension and evaporation take place at the same constant rate. Indeed, a layer of liquid covers the film at first, the liquid in the pores does not play a role in the evaporation, and stress build-up is negligible. The air–liquid interface is macroscopically flat during the first stage of drying. The length of time of this stage is proportional to the initial volume fraction of solvent in the suspension [3]. Eventually the particle volume fraction in the drying film increases to the gelpoint (φg ) and a three-dimensional particle network forms [6]. At this point in the drying, the particle network develops a non-zero compressive yield stress which increases as drying continues because the volume fraction of the suspension increases. The particle network is able to resist consolidation if the applied isostatic compressive consolidation pressure is less than the compressive yield stress. The liquid–air interface attempts to penetrate into the top of the powder bed. In order to do so, it must form a curved meniscus between neighboring particles. The curved menisci between particles create an isostatic consolidation pres-
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sure on the particle network and a pressure gradient between the surface of the liquid and the liquid in the interior of the drying body. The liquid rises to the surface as a result of the pressure gradient and continues to evaporate at a constant rate. For colloidal-size particle beds in water that have pore size on order of a micron the isostatic consolidation pressure (which also drives the liquid flow) is on order of 1 MPa based on Laplace’s relationship. During this second stage of constant rate drying, the top of the particle network and the air–water interface recede at the same rate. This is because the consolidation pressure applied to the particle network due to the capillary forces is sufficient to consolidate the powder. As the network continues to consolidate, its compressive yield stress increases as volume fraction increases until the particle network has sufficient strength to withstand the capillary pressure and further consolidation is not possible at the capillary pressure determined by the curvature of the air–water interface. At this point the third and final stage of drying, known as the falling rate period, begins. The liquid/vapor interface penetrates the powder compact and the rate of drying (evaporation) no longer occurs at a constant rate as the liquid/vapor interface recedes into the pores between the particles. At this stage, the liquid/solid interfacial area decreases and so does the capillary pressure. The shrinkage of the solid particle network stops at this point in the drying. There is a significant knowledge base about the development of stresses in drying suspensions and saturated powder compacts and how those stresses can lead to cracking in those drying bodies [1,3,7–12]. Tensile stresses can develop at the surface of a thick section drying body due to the constraint of the drying shrinkage by the interior of the body. Likewise tensile stresses develop in a thin film coating of suspension drying on a rigid substrate. A key factor influencing the development of stresses in a thick section drying body are the rate of evaporation relative to the rate of transport of the liquid to the surface of the body. The rate of evaporation is controlled by the temperature, vapor pressure of the liquid, the ambient pressure and convection effects. The transport of the liquid to the surface is controlled by Darcy’s law which relates the flow rate to the pressure gradient. The flow rate through the porous packed bed is related to the pressure driving the flow, the fluid viscosity, the distance through the packed bed, the particle size and the bed voidage as described by the Carman–Kozeny relationship [13]. If the rate of evaporation is less than the rate of liquid flow through the body (referred to as slow drying in the present paper) the shrinkage of an unconstrained drying body can occur uniformly (moisture is uniform throughout the body). If the rate of evaporation is fast relative to the transport of liquid to the surface (referred to as fast drying in the present paper), a pressure gradient and a moisture gradient will exist within the drying body. These gradients result in non-uniform shrinkage, with the surface (low moisture region) trying to shrink more than the interior of the body which constrains the exterior dryer layer. The constraint of the shrinkage results in tensile stresses at the surface. If the drying suspension is a thin film on a rigid substrate, even when the drying is slow, the body cannot shrink uniformly and isotropically. The rigid substrate constrains shrinkage in the plane of the surface. (Shrinkage normal to the surface is
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not constrained.) The constraint of the drying thin film by the substrate results in bi-axial tensile stresses at the surface of the drying substrate. It is known that a peak stress occurs at the end of the constant rate drying period and this is when cracking will occur if it is energetically favorable [1,3,4,8]. In the case of rigid particles, the film recovers a nearly stress-free state [3,5] once all the liquid has evaporated from the porous body. When thin coatings are considered such that the rigid substrate constrains the shrinkage of the film during the drying process bi-axial tensile stresses occur at the surface of the film. These stresses will lead to cracking if they are greater than a critical value that depends upon the material properties [8]. An energy balance and the use of A.A. Griffith’s concepts of fracture mechanics, which state that a crack in a body will only extend if it decreases the free-energy of the system, allows one to show that cracking will occur only for films with thicknesses exceeding a critical value hc [14], hc = 2Gc E ∗ /(Zσ 2 ), where Gc is the critical strain-energy release rate (a measure of fracture toughness), E ∗ = E/(1 − ν), where E is Young’s modulus and ν is Poisson’s ratio, σ is the biaxial tensile stress and Z is a parameter whose value depends on the geometry of the crack tip and that is of the order of 2 [15]. Cracking is avoided either by keeping the stresses low (slow drying or reducing the surface tension of the liquid), or by increasing the mechanical properties (Gc and E ∗ ) of the drying powder compact. It has been established that cracking often initiates at the end of the constant rate evaporation stage and typically coincides with a peak in stress [1,3,4]. In recent work, Kiennemann and co-workers [4] measured the evolution with time of Young’s modulus of drying aqueous alumina suspensions with ultrasounds using a pulse–echo method in “long-bar mode.” Their results show a negligible Young’s modulus when the stress peak occurs and thus, the lack of stiffness results in a predisposition to cracking. An increase of the critical cracking thickness of gels can be achieved by adding a small amount of elastic binder to the sol–gel precursor solution. The effect of such a binder is illustrated in the work of Roeder and Slamovich [16] who considered titanium di(isopropoxide) bis(ethyl acetocetate) (TIBE) solutions to which they added small quantities, 5 and 10 wt% with respect to the TIBE in the solution, of a styrene–butadiene–styrene block copolymer. Their results show a 5-fold increase of the critical cracking thickness in the case where 5 wt% block copolymer is added. Adding 10 wt% block copolymer results in an increase of the critical cracking thickness that is nearly 10-fold. In ceramic processing, water soluble binders that adhere to particles surfaces during drying and bind the dry particles together are typically added to formulations to improve the mechanical behavior of dry powder bodies [17,18]. They act by strengthening the bond between individual particle pairs in the dried body. When soluble polymers (such as binders) are added to a formulation, a second stress peak results during the falling rate drying period of a thin film on a rigid substrate. This second peak stress has been found to be greater in magnitude than the drying stress when no binder is used and a residual compressive stress will remain in the film
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after the liquid phase has fully evaporated [3,4]. It is clear that the addition of binder is only useful if the increase in strength of the dried powder compact is greater than the increase in stress developed. A general solution to the problem that can work for a variety of systems is to improve the mechanical properties (Young’s modulus (E) and critical strain-energy release rate (Gc )) of the film during the drying process, and this is particularly important in the initial stages when the first stress peak occurs. The mechanical properties can be improved by increasing the strength of dry bond between individual particle pairs such as by adding polymeric binder. The Young’s modulus, as well as other mechanical properties, increase with and depend strongly on the volume fraction of solids [19]. In turn, the final volume fraction of the dry film will depend on the consolidating pressure and the compressive yield strength of the particle network. The compressive yield stress depends strongly on the particle–particle interactions, which are dictated by solution conditions such as pH [19,20]. Dispersed suspensions consolidate to higher solids contents relative to aggregated suspensions at a particular applied pressure. Another approach is to reduce the stress that develops by the addition of plasticizer (such as ethylene glycol) [8,11] or surfactant [4,10] to the formulation. The aim of this paper is three-fold. Firstly, we investigate the influence of solution chemistry; with that in mind, we consider both flocculated (pH 9) and dispersed (pH 1.75) alumina suspensions. Secondly, we investigate the addition of small amounts of binder to the system in order to increase the modulus and/or fracture toughness of the film. Finally, we add a temperature activated cross-linker in the suspensions [21]. By choosing appropriate processing conditions (humidity, temperature, pH), it is possible to control gelation so that the mechanical properties of the gelled powder compact are improved. The materials used and the experimental procedures are presented in Section 2. Section 3 of this paper presents and discusses the most relevant results. Some concluding remarks are presented in Section 4. 2. Experimental 2.1. Materials The alumina powder used was a commercial high-purity αAl2 O3 (AKP-30, Sumitomo Corp., Tokyo, Japan) with a BET surface area of 7 m2 g−1 , a mean particle diameter of 0.3 µm, and a density of 3.97 g cm−3 . A partially hydrolyzed poly(vinyl alcohol) (PVA, Celanese Chemical, USA) was used. Its glass transition temperature is well above room temperature. Doubledistilled water was used throughout the different experiments of this study. The effects of repulsive and attractive inter-particle interactions on critical cracking thickness were investigated by preparing acidic suspensions (pH ∼ 1.65–1.85) and suspensions near the isoelectric point (iep) of alumina (pH 9). The zeta-potentials of AKP-30 alumina at pH ∼ 2 and at pH 9 (iep) are respectively of around 100 ± 10 mV and 0 ± 5 mV [21]. Hence, the alumina particles are dispersed in the first case, whereas in the second
one, the particles flocculate and gel. The pH of suspensions was adjusted using analytical-grade HNO3 or NaOH. To improve the critical cracking thickness, PVA is added to some of the suspensions. In some cases, the PVA was crosslinked by adding 2,5-dimethoxy-2,5-dihydrofuran (DHF) to the Al2 O3 –PVA suspensions [21]. DHF will decompose and behave as a cross-linker for PVA only in an acidic environment. Therefore, we can only consider films cast from dispersed alumina–PVA suspensions (pH 1.75) in this case. For all gelation experiments, a DHF concentration of 300 mM is used. Suspensions with initial solids concentrations, φi , of 10 and 30 vol% were prepared by ultrasonication under acidic conditions using a sonifier (Model 250, Branson Ultrasonics Corp., Danbury, CT) equipped with a 1.9 diameter horn. The sonifier operates at 20 kHz and was used in the pulsed operation mode with a duty cycle of 50% and at an output control setting of 6 (70 W). With these settings, suspensions were prepared by a series of sonication cycles of 3 min each with about 20 min rest in-between until the suspension is smooth to the eye. Usually, three or four sonication cycles suffice. In order to ensure that the suspension was smooth, a small quantity was spread between two microscope glass slides. If any grinding was felt while rubbing the slides, additional sonication cycles were performed. Once the suspensions were smooth, their pH was adjusted using HNO3 or NaOH. The pH of the suspension was allowed to equilibrate overnight, checked again and re-adjusted if necessary. Once the desired pH was reached, the suspensions were de-aired with a vacuum pump and a few drops of octanol were added to the suspension in order to avoid bubble formation. The suspension was then vigorously mixed and stirred for about 30 s, and films of different thicknesses were cast. 2.2. Methods Drying experiments performed in this study are rather simple yet robust. The suspensions are cast into pools of various depths and are allowed to dry under room temperature and humidity conditions. In general, pools were 75 mm in length and 65 ± 5 mm wide. The base was a glass plate onto which glass microscope slides of thickness 0.8–1.1 mm were fixed in-place using double-sided tape. Stacking up various microscopes slides allowed control of the initial depth of the pool, and thus the initial thickness of the film, hi . Both the glass plate and microscope slides were thoroughly cleaned with doubledistilled water and ethanol before use. For the thicker films, hi > 6 mm, walls machined out of Plexiglas were used. For a few experiments, pools completely machined out of Plexiglas (poly methylmethacrylate) of base dimensions 120 × 120 mm2 and depths between 0.1 and 3.2 mm were used. In order to control hi of these thicker films, the necessary suspension volume to be cast was calculated from the plate’s base dimensions. Using pools facilitates suspension casting and constrains the drying process to be one-dimensional. During experiments, the cast films were protected from possible forced airflows in the room, and the directional drying that comes with crossflow, as well as to avoid deposition of dust onto the films. Any dust particles on
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the film can act as crack nucleation sites and induce cracking at lower thicknesses than the true critical cracking thickness hc . Drying experiments were performed at room temperatures in the range 21–28 ◦ C. However, temperature variations did not exceed 2 ◦ C for one given run. Moreover, to ensure homogeneity of drying conditions, all experiments with one given formulation were carried out simultaneously. A typical range of relative humidity in the room was 45–60%. The drying process took between 4 and 48 h depending on the initial Al2 O3 concentration and hi . We believe that these conditions constitute slow drying conditions as described in the introduction. When very thick (>5 mm) films of the same suspensions were dried very quickly (at 60 ◦ C for instance) cracks occurred in formulations that did not produce cracks under the slow drying conditions described above. This is a result of the constraint of the drying surface by the undried interior of the thick film as described in the introduction. In general, fast drying was avoided in the results presented in this paper. Two different procedures for crosslinking the PVA, that lead to similar results have been used. In the first one, the solution is crosslinked in a water-saturated environment (RH in the order of 95%) at 60 ± 2 ◦ C for 40 min. Relative humidity (RH) measurements show that RH is in the range 90–95% during this stage. Then, and still in a water-saturated environment, the solution is allowed to cool down to room temperature. Once at room temperature, the gelled slurry is dried in conditions similar to those used for Al2 O3 suspensions without binder and with non-crosslinked PVA. In the second method, both the crosslinking of the PVA and the drying took place at room temperature. In this case, the crosslinking stage (in humid environment) took about 24 h followed by the drying stage (at ambient humidity). Once the films were dried, the microscope slides were removed and the final thickness of the film was measured across the length of the film to produce a height profile. This was done at the center of the film and at least at two other positions (one on each side of the center on the film). Measurements were taken 10 mm apart with a Mitutoyo dial indicator (No. 513-404) for films of thicknesses below 800 µm. The accuracy of these measurements is 10 µm, which is less than 10% of the smallest film thicknesses measured. In the case of films thicker than 800 µm, a micrometer was used. As a crosscheck, thickness measurements using both techniques were compared in films of thicknesses in the range 500–800 µm. Measured thicknesses differed by less than 10 µm, which is within measurement uncertainties, thus the measuring procedure was validated. From these measurements, either local thicknesses can be used or an average film thickness h¯ can be calculated. Pictures of dried films were taken by placing them on a rear illumination light-box. The light passing through cracks is seen as white on the pictures whereas the rest of the dried film is opaque, or translucent at best. This technique is a simple way to assess the number, the length, and the width of the cracks. However, it is limited to the case of cracks that penetrate completely through the thickness of the film, referred to here as channeling cracks.
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(a)
(b)
(c) Fig. 1. Pictures of dried films of different final average thickness h¯ obtained from flocculated (pH 9) Al2 O3 aqueous suspensions without binder. (a) h¯ = 113 ± 20 µm < hc , (b) h¯ = 177 ± 40 µm ≈ hc , (c) h¯ = 430 ± 20 µm ≈ 3hc .
3. Results and discussion Fig. 1 shows representative pictures of the dried films cast from alumina suspensions without binder in the case of flocculated, pH 9 ± 0.15 suspensions. Likewise Fig. 2 shows typical pictures of dry films prepared from dispersed suspensions, pH 1.75 ± 0.10. Figs. 1a, 2a, and 2c correspond to films cast from Al2 O3 suspensions with φi of 0.3 whereas the suspensions used in Figs. 1b, 1c, and 2b had initial Al2 O3 concentration φi of 0.1. Initial solid concentration does not affect the critical cracking thickness of films, hc , but rather the final thickness of the film. Therefore, varying φi is a convenient way to obtain
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Table 1
(a)
(b)
(c) Fig. 2. Pictures of dried films of different final average thickness h¯ obtained from dispersed (pH 1.75) Al2 O3 aqueous suspensions without binder. (a) h¯ = 316 ± 20 µm < hc , (b) h¯ = 430 ± 20 µm ≈ hc , (c) h¯ = 1265 ± 70 µm ≈ 3hc .
films of different final thicknesses from the same initial pool height hi . Fig. 1 corresponds to flocculated suspensions with pH of 9. Under these conditions, attractive forces (van der Waals) between alumina particles exist and the suspension gels naturally and spontaneously resulting in difficult to consolidate particle network. No cracks are observed in Fig. 1a, a film with average thickness h¯ in the order of 113 µm. The vertical fringes with characteristic lengths in the range 1–20 mm that are observable on the film are a consequence of non-constant blade velocity during casting of the film. It is known that such conditions result in variations of film thickness [22]. Thinner marks in the
System
pH
vol. PVA/vol. Al2 O3
hc (µm)
Al2 O3
8.86–9.0 1.65–1.8
0 0
130 ± 20 410 ± 20
Al2 O3 –PVA
8.86–9.0 1.65–1.8
1:10 1:10
240 ± 20 875 ± 75
Al2 O3 –PVA–DHF
1.65–1.8
1:10
>8800
horizontal direction are due to small defects on the Plexiglas blade used. The film in Fig. 1b with h¯ = 177 µm shows multiple cracks. Their spacing is not uniform over the entire film; the cracks are more numerous on the left side and on the bottom of the film, which is explained by local differences in film thickness. Indeed, h¯ is around or greater than 150 µm in the areas with more cracks, whereas in the areas where no cracking occurs, the film thickness is around 120 µm. Thus, as reported in Table 1, the critical cracking thickness hc is considered to be in the order of 130 µm. The number of cracks increases with film thickness and a continuous network of channeling cracks is formed. An example is Fig. 1c that corresponds to h¯ = 430 µm. The cracks have no preferred orientation indicating a rather uniform drying and thickness over the entire film. In fact, either having a directional airflow [23–25] or controlled thickness changes [22] will induce oriented cracks. Let us now discuss the case of films obtained from dispersed (pH 1.75) alumina suspensions without binder as shown in Fig. 2. For these formulations there is repulsion between particles in suspension resulting in high particle packing densities in the dried portions of the body. When the average thickness is below hc , Fig. 2a, no cracks are observed. For uncracked films, deviations of the local film thickness from the average ¯ appear more frequently in the case of films film thickness, h, obtained from solutions of pH 9 than for films obtained from dispersed solution (pH 1.75), see Figs. 1a and 2a, respectively. The reason lays in the different rheological behavior of the solutions. The flocculated suspension used for the film in Fig. 1a (pH 9) has a yield-stress and needed to be spread into a flat film with a blade. The dispersed suspension (pH 1.75), from which the film in Fig. 2a was obtained, had no yield stress and freely flowed homogeneously over the entire pool when cast and gently tapped to level the surface of the film. The critical cracking thickness (hc ) for films obtained from dispersed suspensions is 410 µm (see Table 1), which represents a 3-fold increase compared to films obtained from flocculated suspensions (pH 9). The first cracks in films obtained from dispersed suspensions (pH 1.75) can be seen in Fig. 2b, a film with an average thickness of 430 µm. The channeling cracks, mostly on the top part of the picture, are less obvious and numerous than in Fig. 1b cast from a suspension with a pH of 9. The cracks in Figs. 2b and 2c converge at the last point to dry in the film; the bright spot resulting from a particle deficiency induced by non-homogeneities in drying fluxes over the entire film. The critical cracking thickness (hc ) depends on the mechanical properties of the dried layer on the surface of the film where cracks initiate. The difference in critical cracking thickness of the thin films produced from dispersed and flocculated
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suspensions can be understood in terms of the final volume fraction (φf ) of dried films that depend on the initial suspension conditions. Indeed, the mechanical behavior of the dried film is proportional to the strength of the bond between a particle pair and the number of bonds within the plane of fracture. The strength of the bond for all dried films without added binder is the same and is due to van der Waals forces between two particles in air. Van der Waals force is given by Ar/12d, where A is the Hamaker constant, r is the particle’s radius and d is the distance between the particles [26]. The number of bonds in the fracture plane is inversely proportional to the particle size [27,28] and shows a strong dependence on the particle volume fraction [19,27]. Since primary particle size is constant throughout this study, the strength of the dried films will solely depend on their solid’s concentration. The structure and final volume fraction of solids of the particle network is governed by the inter-particle interactions of the suspension while still saturated. The nature of these interactions, attractive or repulsive, is controlled by the pH of the suspension. For a dispersed system φf is near the maximum random close packing volume fraction (φf ≈ 0.64) and in the case of a flocculated system φf will be substantially lower [6,19,20]. Measurements of the density of dried films using Archimedes’s method yielded average φf values of 0.66 ± 0.02 and 0.55 ± 0.05 in the case of films obtained from dispersed and flocculated suspensions, respectively. These values are consistent with other results [6,19,20] of the final volume fraction of solids consolidated under about 1 MPa pressure which is the approximate value produced by the capillary consolidating pressure. Therefore, the number of interacting particles in the plane of fracture, and in turn the stresses the film can withhold, will be greater for the films cast from dispersed suspensions (pH 1.75) than from flocculated ones (pH 9). Thus, the improved hc of the films obtained from dispersed suspensions is due to the increase in Gc and E that comes with higher solid volume fraction φf . Although we are confident of the mechanism described above to explain the difference in critical cracking thickness of thin films from dispersed and flocculated suspensions during slow drying there is other published work that appears to be contradictory and suggests one additional strengthening mechanism. Work by Cima and co-workers [9,10] found that flocculated alumina suspensions (pH 8) produced greater critical thickness than dispersed suspensions (pH 3.5). These results appear to be opposite to our findings, but the discrepancy is perhaps due to differences in drying rate. Although it is unclear from the publications what the actual drying time of their films was, it appears that it was faster than ours since they indicated that very slow drying over 48 h resulted in an increase in the critical cracking thickness. If their drying was in the fast drying regime, it is possible that the slow drying in our experiments allowed sufficient time for the stresses between the particles in contact with the substrate to relax by sliding and therefore result in a higher critical cracking thickness. Experiments on liquid mercury [9] where stress release at the substrate–suspension interface is facile show large critical cracking thicknesses. Also Cima and co-workers [9,10] noted that for dispersed suspensions, the critical cracking thickness increased as the pH was
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lowered below 2. They attributed this to the precipitation of dissolved aluminum species at low pH during drying that would form strong bonds between particles strengthening the drying surface layer. This mechanism is likely also a factor in the strengthening of the pH 1.75 dispersed suspensions presented in the current paper. A second set of experiments was conducted where the polymer poly(vinyl alcohol) (PVA) was added to the Al2 O3 suspension so that the ratio between the volume of binder and the volume of Al2 O3 is 1:10 regardless of the initial volume fraction of alumina. In weight percentage with respect to the alumina, that is equivalent to about 1.6 wt%. Fig. 3 presents characteristic dried films cast from Al2 O3 –PVA suspensions for both pH 9 and pH 1.75. The film in Fig. 3a allowed us to determine the critical cracking thickness in the case of a flocculated system (pH 9). Two regions are clearly distinct on the film and are separated by the guiding white dashed line in Fig. 3a. One, on the left, where multiple cracks cover the film, and one, on the right, in which very few, localized cracks have initiated. Measurements in each region lead to thickness averages of h¯ bc = 220 ± 20 µm and h¯ ac = 250 ± 20 µm where bc and ac stand for “below cracking” and “above cracking,” respectively. A detailed analysis of all thickness measurements allowed us to determine the hc value of 240 µm reported in Table 1, which is already nearly a 2-fold increase of the critical cracking thickness when compared to the alumina suspensions without binder. It is clear that the PVA is acting to improve the mechanical properties of the film. Moreover, this is obtained with only 1.6 wt% of PVA. In Fig. 3a, some vertical fringes can be observed as well. These are due to a non-uniform blade velocity while casting the film. In both cases, either films obtained by casting dispersed suspensions (pH 1.75) or flocculated ones (pH 9), the increase in critical thickness hc is in the order of a factor 2 as reported in Table 1. This is consistent with the result of Cima and coworkers [9], who found that the critical cracking thickness increased linearly with PVA addition. The PVA acts to increase the strength, critical strain energy release rate and modulus of the dried film. When water is removed during drying, the concentration of PVA in solution is increased sufficiently so that the PVA precipitates out of solution at the particle–particle contact points and therefore strengthens the dried body. Moreover, the shape of the cracks does not seem to change, as illustrated by the picture of Fig. 3d, compared to those observed in films cast from suspensions without binder. They continue to be long and not very numerous for the dispersed films. Visual inspection of the dried films seem to show a layer on top of the dried film cast from acidic suspension that is rich in PVA which might delay cracking. Migration of PVA binder to the surface of dried granules is not uncommon [29]. This phase separation is more important with lower initial solid concentrations and greater initial thickness as the constant rate stage becomes longer and the PVA in solution has more time to come up to the free surface. Thus, it would seem more advantageous to use higher initial solid concentration in order to avoid binder migration and obtain films with homogeneous composition over their entire depth.
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(a)
(b)
(c)
(d)
Fig. 3. Pictures of dried films of different final average thickness h¯ obtained from both flocculated (pH 9) and dispersed (pH 1.75) Al2 O3 aqueous suspensions with PVA as a binder. The volume ratio between PVA and Al2 O3 is 1:10, which represents 1.6 wt% of PVA with respect to Al2 O3 . (a) pH ∼ 9, h¯ ac = 250 ± 20 µm, h¯ bc = 220 ± 20 µm; (b) pH ∼ 9, h¯ = 440 ± 20 µm; (c) pH ∼ 1.75, h¯ = 520 ± 20 µm; (d) pH ∼ 1.75, h¯ = 1000 ± 70 µm.
Another interesting observation is that the total length of cracks formed and the number of cracks per unit area is greater for the dried films produced from flocculated slurries compared to those produced from dispersed slurries when compared at the same thickness relative to the critical cracking thickness. This observation is true for thin films produced from suspensions both without and with PVA. When the PVA in the suspension was crosslinked with DHF before drying, the mechanical properties of the slurry are substantially improved even before the initial stages of drying. After crosslinking the binder, films with average thicknesses as high as 8.8 mm have been cast without cracks developing as can be seen in Fig. 4a. This already represents a 10-fold increase in the critical cracking thickness when compared to the non-crosslinked formulation. The picture in Fig. 4a shows a rather thick film, h¯ = 8.8 mm, obtained by crosslinking the PVA in the well-dispersed alumina suspension at room temperature for 24 h and then allowing the film to dry at room temperature. If compared to the pictures presented in Figs. 2b, 2c, and 3d, it is clear that the film of Fig. 4a has yet to reach its critical cracking thickness. However, small cracks and defects can be observed around the edges of the film, as illustrated by the enlargement of one corner of the film presented in Fig. 4b. These cracks are due to edge effects. Indeed, near the edges of the pool, the shrinkage of the film is not only constrained in the x–y plane, but also in the z-direction.
This additional constrain leads to a complex state of stress. The stresses near the edges of the film are higher than at the center of the film, and therefore the cracks initiate near the edges. An easy way to prevent these cracks is to release the wet green film from the pool walls after gelation and before drying. This is rather simple and can be done with a razor blade, for example. As in the case of dispersed Al2 O3 suspensions with uncrosslinked PVA, a thin layer of PVA was observed at the top of the dried film. This layer is not homogeneous over the entire surface of the film as denoted by changes in shade and oval marks observable over the film in Fig. 4a. To better view the thickness of this layer, a 10 mm slab of the film was cut and polished, giving access to the cross-section of the film. The resulting cross-section is presented in Fig. 5. The layer of PVA on top of the film represents at most 2% of the total thickness of the film, meaning that at least 80% of the PVA added has been crosslinked in the bulk of the film. Nevertheless, it might be possible to reduce the thickness of this layer by optimizing the amount of PVA and crosslinking agent used. Fig. 5 also shows how the pool walls constrain the shrinkage of the film’s edges in the z-direction. The reader should keep in mind that the aim of this paper is not to optimize the formulation, but rather to present a procedure to increase the critical cracking thickness of films obtained from aqueous alumina suspensions by strengthening the particle network. Other approaches such as the addition of
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(a)
(b) Fig. 4. Pictures of a dried thick film obtained from a dispersed (pH 1.75) Al2 O3 aqueous suspensions with PVA as a binder that was crosslinked at room temperature using 300 mM DHF before drying. The volume ratio between PVA and Al2 O3 is 1:10, which represents 1.6 wt% of PVA with respect to Al2 O3 . (a) h¯ = 8800 ± 200 µm. (b) Detail of edge region.
Fig. 5. Cross-section of the thick film presented in Fig. 4. An 8.8-mm thick film slab was cut and the polished in order to observe the profile of the film and the thin layer of PVA that formed on the free surface of the dried green body.
plasticizers and surfactants will also be useful in reducing the magnitude of the stress generated. 4. Conclusion Controlling the chemistry of suspensions is important and allows one to improve the critical thickness above which films will crack. By considering successively, aqueous alumina suspensions without and with small amounts of a polymeric binder, which is crosslinked in some cases, we have shown that the critical cracking thickness can be increased by a factor greater than 50 when the worst (flocculated suspension without binder) and best (dispersed suspension with crosslinked PVA) case scenarios are considered.
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For the same given formulation, i.e., concentration of alumina and concentration of binder, the critical thickness is found to be about 3 times greater when a dispersed suspension (pH 1.75), rather than a flocculated one (pH 9), is used during casting. The increase in critical cracking thickness, and mechanical properties, is due to the higher packing density of films obtained from dispersed suspensions. A higher solid concentration means a greater number of particle–particle interactions per unit area, and therefore the stresses that the film can withhold are higher. The addition of a polymeric binder, PVA, also allows one to increase the critical cracking thickness. Although in the present study, we add only 1.6 wt% of binder with respect to alumina, the critical thickness is increased by roughly a factor of 2 for films obtained from both flocculated and dispersed suspensions. Further increases in critical thickness, by a factor of at least 10 with respect to films cast from Al2 O3 –PVA dispersed suspensions, are obtained by crosslinking the polymeric binder with DHF before drying begins. In conclusion, the addition of binder and further crosslinking of binder presented in the study has the potential for nonnegligible increases in critical cracking thickness that may be useful in commercial applications. Plasticizers or other additives such as surfactants could be added to improve the mechanical properties or to decreases the stresses in the film during drying, and in this way, further increase the critical cracking thickness. References [1] G.W. Scherer, J. Am. Ceram. Soc. 73 (1990) 3. [2] Y. Holl, J.L. Keddie, P.J. McDonald, W.A. Winnik, in: T. Provder, M.W. Urban (Eds.), ACS Symposium Series, vol. 790, American Chemical Society, Washington, DC, 2001, p. 2. [3] P. Wedin, C.J. Martinez, J.A. Lewis, J. Daicic, L. Bergström, J. Colloid Interface Sci. 272 (2004) 1. [4] J. Kiennemann, T. Chartier, C. Pagnoux, J.F. Baumard, M. Huger, J.M. Lamérant, J. Eur. Ceram. Soc. 25 (2005) 1551. [5] M.S. Tirumkudulu, W.B. Russel, Langmuir 21 (2005) 4938. [6] L.A. Brown, C.F. Zukoski, L.R. White, AIChE J. 48 (2002) 492. [7] W. Pompe, F.F. Lange, I.B. Sevosianov, in: R.C. Bradt (Ed.), Fracture Mechanics of Ceramics, vol. 11, Plenum Press, New York, 1996, p. 343. [8] P. Wedin, J.A. Lewis, L. Bergstorom, J. Colloid Interface Sci. 290 (2005) 134. [9] R.C. Chiu, T.J. Garino, M.J. Cima, J. Am. Ceram. Soc. 76 (1993) 2257. [10] R.C. Chiu, M.J. Cima, J. Am. Ceram. Soc. 76 (1993) 2769. [11] J.A. Lewis, K.A. Blackman, A.L. Ogden, J.A. Payne, L.F. Francis, J. Am. Ceram. Soc. 79 (1996) 3225. [12] M. Descamps, M. Mascart, B. Thierry, D. Leger, Am. Ceram. Soc. Bull. 74 (3) (1995) 89. [13] M. Rhodes, Introduction to Particle Technology, Wiley, Chichester, 1998. [14] F.F. Lange, Science 273 (1996) 903. [15] J.W. Hutchinson, Z. Suo, in: J.W. Hutchinson, T.Y. Wu (Eds.), Advances in Applied Mechanics, Academic Press, New York, 1991, p. 126. [16] R.K. Roeder, E.B. Slamovich, J. Mater. Res. 14 (1999) 2364. [17] J.S. Reed, Principles of Ceramic Processing, second ed., Wiley, New York, 1995. [18] S. Baklouti, T. Chartier, J.F. Baumard, J. Am. Ceram. Soc. 80 (1997) 1992. [19] G.M. Channell, C.F. Zukoski, AIChE J. 43 (1997) 1700.
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