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Interfacial Undercooling in the Solidification of Colloidal Suspensions

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Interfacial Undercooling in the Solidification of Colloidal Suspensions Interfacial undercooling in the solidification of colloidal suspensions Jiaxue You1, Lilin Wang2, Zhijun Wang1, Junjie Li1, Jincheng Wang1, Xin Lin1, and Weidong Huang1 1-State Key Laboratory of Solidification Processing, Northwestern Polytechnical University, Xi’an 710072, P. R. China 2-School of Materials Science and Engineering, Xi'an University of Technology, Xi'an 710048, P. R. China Abstract: Interfacial undercooling is of significant importance on microscopic pattern formation in the solidification of colloidal suspensions. Two kinds of interfacial undercooling are supposed to be involved in freezing colloidal suspensions, i.e. solute constitutional supercooling (SCS) caused by additives in the solvent and particulate constitutional supercooling (PCS) caused by particles. However, quantitatively identification of the interfacial undercooling of freezing colloidal suspensions is still absent and it’s still unknown which undercooling is dominant. The revealing of interfacial undercooling is closely related to the design of ice-templating porous materials. Based on quantitative experimental measurements, we show that the interfacial undercooling mainly comes from SCS caused by the additives in the solvent, while the PCS can be ignored. This finding implies that the PCS theory is not the fundamental physical mechanism for patterning in the solidification of colloidal suspensions. Instead, the patterns in ice-templating method can be controlled effectively by adjusting the additives. Key words: interfacial undercooling, freezing colloidal suspensions, pattern formation, quantitative experiments. The solidification of colloidal suspensions is commonly encountered in a variety of natural processes such as the growth of sea ice[1] and frost heave[2], and engineering situations such as cryobiology[3], tissue engineering[4], the Corresponding author. Tel.:86-29-88460650; fax: 86-29-88491484 E-mail address: [email protected] (Zhijun Wang) 1 / 23 ice-templating bio-inspired porous materials and composites[5-19], thermal energy storage[20] and soil remediation[21]. Especially, ice-templating porous material has attracted more and more attention due to the novel micro-aligned structures that can be easily produced for a wide range of practical applications [5-16, 18]. One of the key issues therein is the pattern formation. The formation of the microstructures is closely related with the interfacial instability of freezing colloidal suspensions and the subsequent development of the interfacial morphologies [22, 23]. The freezing interfacial instability strongly depends on the interfacial undercooling which has been extensively revealed by research community of solidification [24, 25]. Accordingly, it is believed that the interfacial undercooling is also of significant importance on microscopic pattern formation of freezing colloidal suspensions. Two kinds of interfacial undercooling have been proposed in the solidification of colloidal suspensions, i.e. solute constitutional supercooling (SCS) caused by additives in the solvent [12, 13, 17] and particulate constitutional supercooling (PCS) caused by particles [22, 23]. The theory of SCS is based on classical alloy solidification principle [12, 24, 25]. The theory of PCS is from multi-particle thermodynamics [22], a characteristic of the colloidal suspensions system. Up to now, there are no reports on the quantitative measurement of interfacial undercooling during the solidification of colloidal suspensions, much less do the distinction for these two interfacial undercoolings. It’s still unrevealed but important that which undercooling is dominant in the solidification of colloidal suspensions. Figuring out the individual effects of SCS and PCS during freezing colloidal suspensions is much helpful on the scientific issue of fundamentally understanding the physical mechanism of pattern formation in this complex system. It will further pave the way for controlling the microscopic pattern formation. For example, if the PCS is dominant, the freezing pattern can be adjusted via the particle size or particle shape; otherwise, it can be adjusted by changing the additives. In this letter, interfacial undercoolings were quantitatively measured based on a novel experimental method and the contributions of SCS and PCS were confirmed respectively. A detailed description of the experimental apparatus and gauging method 2 / 23 is given in Ref.[26]. The sketch of the method is shown in the Figure S1 (Supplementary Information). In the proposed method, the interfacial undercooling is visualized through the discrepancy of solid/liquid interfacial positions in two adjacent Hele-Shaw cells of the colloidal suspensions and its compared counterpart in an uniform thermal gradient apparatus. The SCS and PCS can be well distinguished by designing the different compared counterparts. We quantitatively measured the SCS and PCS in different systems of colloidal suspensions. The results were thoroughly discussed based on the theoretical predictions. The first system we chose is PolyStyrene microspheres (PS) suspensions (Bangs Lab, USA). The norminal solvent of the PS suspensions is deionized water. The density of PS particles is almost the same as water. The mean diameter of the particles is d=1.73m with poly-dispersity smaller than 5% and the initial volume fraction of particles is 33%. The PS suspensions system is stable with weak sedimentation, an idea system to investigate the freezing of colloidal suspensions. Although the solvent of deionized water is marked on the nominal label of PS suspensions, we believe that there are still very small quantity residual solutes from the synthetic process of PS particles even after great effort of purification in these commercial PS suspensions. The residual solutes will cause SCS during the freezing of PS suspensions. Therefore, in the measurement, we firstly verified this kind of SCS by comparing the deionized water with the supernatant from the same PS suspensions by centrifugation. Furthermore, we compared the PS suspensions with its supernatant to confirm the individual contribution of PCS. The combination of SCS and PCS will present the whole interfacial undercooling of the colloidal suspensions. Figure 1(a) shows the measurement of SCS through the interfacial position comparison between the deionized water (left cell of Fig. 1(a)) and the supernatant (right cell of Fig. 1(a)) with a microscopy. The upper end of the cell is the heating zone, while the bottom end of the cell is the cooling zone, building a linear thermal gradient G=7.23K/cm. The pulling speed V is 0. In Fig. 1(a), the position of solid/liquid interface in the deionized water cell is much higher than that of the supernatant. It indicates that the freezing point of the deionized water is higher than 3 / 23 that of the supernatant. The discrepancy of the solid/liquid interfacial positions between the deionized water and the supernatant is 170.64m, which indicates that the value of SCS is 0.123K in the consideration of G=7.23K/cm. The comparison of the interfacial positions between the colloidal suspensions and its supernatant is shown in Fig. 1(b), which exhibits the measurement of PCS. The interfacial position of the supernatant is almost parallel to that of its suspensions, which means that the freezing point of the supernatant is almost the same as that of its suspensions. Therefore, the PCS is undetectable and smaller than 0.01K, if it exists in this PS colloidal suspensions system (the precision of the experimental method has been proved to be 0.01K by Ref.[26]). Consequently, in Fig.1, the interfacial undercooling of colloidal suspensions mainly comes from the SCS. The interfacial undercoolings of PS suspensions systems with particles of different diameters and different volume fractions were further tested. All results are similar to that in Fig.1. The interfacial position comparisons of these results are shown in Fig.S2 (Supplementary Information). Their interfacial undercoolings of SCS and PCS are shown in Table 1(a). Surprisingly, the PCS almost has no contribution to the interfacial undercooling of PS colloidal suspensions. However, the 5K PCS is reported in the Ref.[23] under d=1m and 50%. These unexpected results deserve further analysis in considering the PCS theory [22, 23, 27, 28]. In PCS theory, the particle-induced interfacial undercooling is described as П(ϕ) ∆TPCS = Tm − Tf = Tm , (1) ρwLf ϕ where П(ϕ) = kBTmZ(ϕ) is the osmotic pressure caused by the concentrated vp 1+푎 ϕ+푎 ϕ2+푎 ϕ3+푎 ϕ4 layer of particles, and Z(ϕ) = 1 2 3 4 is the dimensionless 1−ϕ/ϕp compressibility factor. The maximum volume fraction of particles is ϕp = 0.64. 0≤≤0.64. 푎1, 푎2, 푎3 and 푎4 are fitting parameters of П. Tm is the melting point of ice. Tf is the depressed melting point. ρw is the density of water. Lf is the latent heat, andis the volume fraction of particles. kB is the Boltzmann constant and vp is the 4 / 23 volume of a particle. The PCS comes from the depressed equilibrium melting point by the osmotic pressure of concentrated particles ahead of the solid/liquid interface. The PCS theory is with consolidated physical foundation. However, the determination of the dimensionless compressibility factor in osmotic pressure is casual in Ref.[23, 28]. The variation of Z(ϕ) with different ϕ has been well investigated. Originally, the fitting parameters from Ref.[22, 27] are 푎1 = 2.4375, 푎2 = 3.75, 푎3 = 2.375, 푎4 = −14.1552. However, the fitting parameters used in Ref.[23, 28] were 7 9 9 9 푎1 = 1 × 10 , 푎2 = 2 × 10 , 푎3 = 3 × 10 , 푎4 = −8 × 10 , in order to give way to the experimental depressions of freezing point [23]. The huge discrepancies of several orders of magnitude among these fitting parameters are unaccountable and without physical foundation. The root of this problem is the improper use of experimental data in the analysis of PCS. Firstly, the colloidal suspensions contain a large number of ions which can dramatically depress the freezing point of water [29]. Secondly, the bentonite used is a mixture of a variety of different size particles, while the PCS theory emphasizes the importance of particle radius since the PCS is inversely proportional to the third power of the particle radius.
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