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. By using the original fitting parameter for Z(ϕ), the theoretical PCS in the PS systems investigated here is around 10-9K, too small to be detected, shown as prediction A in Table 1(a). These theoretical results agree with the present measurements that the PCS is negligible compared with the SCS. In the PCS theory, the PCS is inversely proportional to the third power of the particle radius. Moreover, the alumina suspensions are much commonly used in the ice-templating porous ceramics. Here, another system of colloidal suspensions was further designed to reveal the interfacial undercoolings in the freezing of colloidal suspensions. Thealumina powder of d=50nm are used (Wanjing New Material,
Hangzhou, China, ≥99.95% purity, monodispersity). The alumina suspensions were prepared by using HCl (hydrogen chloride) and deionized water as the solvent following Ref.[30]. Also the stable dispersity of alumina suspensions has been confirmed in Ref.[30]. Initial volume fractions are =2.72%, 3.63%, 9.74% (wt%=10, 5 / 23
13, 30) in three different systems, respectively. These measurements were also under the thermal gradient G=7.23K/cm and pulling speed V=0. The SCS and PCS from the measurements are shown in Fig.2. The interfacial position comparisons of static SCS and PCS for alumina suspensions are shown in Fig.S3 (Supplementary Information). By using the improper fitting parameters provided by Ref.[23], the PCS could exceed 100K (prediction B in Fig.2 and Table 1(b)). However, the measured PCS are still extremely small (blue triangular points in Fig.2), and have little contribution to the total interfacial undercoolings compared with the SCS as shown in the inset of Fig. 2. The theoretical calculations of the PCS are around 10-6K (prediction A in Fig.2 and Table 1(b)), still unmeasurable by the present setup, which is consistent with our experimental data. In the limit case, if the particles of d=1nm and ≈p were used, the PCS may be comparable to SCS. However, in most cases, the PCS’s contribution to the interfacial undercooling is neglectable compared with the SCS from the solvent in the solidification of colloidal suspensions. In the above measurements, the static interfacial undercoolings were clarified. The dynamic interfacial undercooling during the freezing of colloidal suspensions, another important aspect related to the pattern formation, have never been reported before. The experimental apparatus can also be used to quantitatively identify the dynamic interfacial undercooling [26]. We used the alumina suspensions of d=50nm,
3.63% to reveal the dynamic interfacial undercooling. The comparison of the colloidal suspensions to its supernatant reveals the dynamic PCS while the comparison of the deionized water to the supernatant reveals the dynamic SCS. Figure 3 shows the steady dynamic interfacial positions of supernatant, deionized water and colloidal suspensions under V=8.217m/s and G=7.23K/cm. The steady state of dynamic PCS was verified as shown in Movie S1 (Supplementary Information). The comparison between the interfacial positions of supernatant and the deionized water reveals the dynamic SCS of 0.090K, as shown in Fig. 3(a). However, Fig. 3(b) shows that the dynamic PCS is almost 0K, although the particles were accumulated in front of the advancing solid/liquid interface forming an obvious concentrated layer. Similar to the static case, the dynamic PCS can be ignored 6 / 23 compared with the obvious dynamic SCS. Therefore, the concentrated layer seems invalid to cause an obvious PCS. Even with different pulling speeds, the results of the dynamic PCS are similar to that of Fig.3 (shown in Supplementary Information, Fig. S4). The concentrated layer of particles in front of the interface scarcely causes dynamic PCS under different pulling speeds. On the contrary, the dynamic SCS varies with pulling speeds. The interfacial position comparisons revealing the dynamic SCS are shown in Fig.S5 (Supplementary Information). Fig.4 shows the variation of dynamic SCS with pulling speeds. The increase of dynamic SCS with the decrease of pulling speeds is consistent with the classical alloy solidification principle [31]. It indicates that on the dynamic case, the SCS still plays a dominant role compared with the negligible dynamic PCS for different pulling speeds. Based on the above systematic measurements, the PCS is usually negligible on both static and dynamic cases. Instead, the effect of SCS caused by additives in the solvent is dominant. Accordingly, the PCS theory is not the fundamental physical mechanism for so many puzzling phenomena with numerous unexplained features. The present experimental results clearly proved the effects of additives in the ice-templating process [12, 13, 17]. Conclusion We settled down the puzzling of interfacial undercoolings in the solidification of colloidal suspensions via quantitative measurements of solute constitutional supercooling (SCS) and particulate constitutional supercooling (PCS). Based on systematic quantitative experimental measurements of both static and dynamic cases within different systems of colloidal suspensions, we show that the interfacial undercooling mainly comes from SCS caused by the additives in the solvent, while the PCS can be ignored. The results imply that the PCS theory is not the fundamental physical mechanism for so many puzzling phenomena with numerous unexplained features. These fundamental findings greatly enhance our understanding of freezing colloidal suspensions in the natural and industrial processes, paving the way to control the pattern formations in freezing colloidal suspensions. 7 / 23
Acknowledgements This research has been supported by National Basic Research Program of China (Grants No.2011CB610401), Nature Science Foundation of China (Grant No. 51371151), Free Research Fund of State Key Laboratory of Solidification Processing
(100-QP-2014), the Fund of State Key Laboratory of Solidification Processing in NWPU (13-BZ-2014) and the Fundamental Research Funds for the Central Universities (3102015ZY020). References [1] M. Vancoppenolle, K.M. Meiners, C. Michel, L. Bopp, F. Brabant, G. Carnat, B. Delille, D. Lannuzel, G. Madec, S. Moreau, J.-L. Tison, P. van der Merwe. Role of sea ice in global biogeochemical cycles: emerging views and challenges, Quaternary Science Reviews 79 (2013) 207-230. [2] S.S.L. Peppin, R.W. Style. The Physics of Frost Heave and Ice-Lens Growth, Vadose Zone Journal 12 (2013). [3] P. Mazur. Freezing of living cells: mechanisms and implications, 1984. [4] U.G.K. Wegst, M. Schecter, A.E. Donius, P.M. Hunger. Biomaterials by freeze casting, 2010. [5] S. Deville, E. Saiz, R.K. Nalla, A.P. Tomsia. Freezing as a Path to Build Complex Composites, Science 311 (2006) 515-518. [6] S. Deville, E. Saiz, A.P. Tomsia. Ice-templated porous alumina structures, Acta Materialia 55 (2007) 1965-1974. [7] S. Deville. Freeze-Casting of Porous Ceramics: A Review of Current Achievements and Issues, Advanced Engineering Materials 10 (2008) 155-169. [8] S. Deville, E. Maire, A. Lasalle, A. Bogner, C. Gauthier, J. Leloup, C. Guizard. In Situ X-Ray Radiography and Tomography Observations of the Solidification of Aqueous Alumina Particles Suspensions. Part II: Steady State, Journal of the American Ceramic Society 92 (2009) 2497-2503. [9] A. Lasalle, C. Guizard, E. Maire, J. Adrien, S. Deville. Particle redistribution and structural defect development during ice templating, Acta Materialia 60 (2012) 4594-4603. [10] S. Deville, J. Adrien, E. Maire, M. Scheel, M. Di Michiel. Time-lapse, three-dimensional in situ imaging of ice crystal growth in a colloidal silica suspension, Acta Materialia 61 (2013) 2077-2086. [11] S. Deville. Ice-templating, freeze casting: Beyond materials processing, Journal of Materials Research 28 (2013) 2202-2219. [12] H. Zhang, I. Hussain, M. Brust, M.F. Butler, S.P. Rannard, A.I. Cooper. Aligned two- and three-dimensional structures by directional freezing of polymers and nanoparticles, Nat Mater 4 (2005) 787-793. [13] L. Qian, H. Zhang. Controlled freezing and freeze drying: a versatile route for porous and micro-/nano-structured materials, Journal of Chemical Technology & Biotechnology 86 (2011) 172-184. [14] U.G.K. Wegst, H. Bai, E. Saiz, A.P. Tomsia, R.O. Ritchie. Bioinspired structural materials, Nat Mater 14 (2015) 23-36. [15] F. Bouville, E. Maire, S. Deville. Self-Assembly of Faceted Particles Triggered by a Moving Ice Front, Langmuir 30 (2014) 8656-8663.
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[16] F. Bouville, E. Maire, S. Meille, B. Van de Moortèle, A.J. Stevenson, S. Deville. Strong, tough and stiff bioinspired ceramics from brittle constituents, Nat Mater 13 (2014) 508-514. [17] B. Delattre, H. Bai, R.O. Ritchie, J. De Coninck, A.P. Tomsia. Unidirectional Freezing of Ceramic Suspensions: In Situ X-ray Investigation of the Effects of Additives, ACS Applied Materials & Interfaces 6 (2014) 159-166. [18] H. Bai, A. Polini, B. Delattre, A.P. Tomsia. Thermoresponsive Composite Hydrogels with Aligned Macroporous Structure by Ice-Templated Assembly, Chemistry of Materials 25 (2013) 4551-4556. [19] A. Lasalle, C. Guizard, J. Leloup, S. Deville, E. Maire, A. Bogner, C. Gauthier, J. Adrien, L. Courtois. Ice-Templating of Alumina Suspensions: Effect of Supercooling and Crystal Growth During the Initial Freezing Regime, Journal of the American Ceramic Society 95 (2012) 799-804. [20] J.M. Khodadadi, S.F. Hosseinizadeh. Nanoparticle-enhanced phase change materials (NEPCM) with great potential for improved thermal energy storage, International Communications in Heat and Mass Transfer 34 (2007) 534-543. [21] G. Gay, M.A. Azouni. Forced Migration of Nonsoluble and Soluble Metallic Pollutants ahead of a Liquid−Solid Interface during Unidirectional Freezing of Dilute Clayey Suspensions, Crystal Growth & Design 2 (2002) 135-140. [22] S.S. Peppin, M.G. Worster, J. Wettlaufer. Morphological instability in freezing colloidal suspensions, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science 463 (2007) 723-733. [23] S. Peppin, J. Wettlaufer, M. Worster. Experimental verification of morphological instability in freezing aqueous colloidal suspensions, Physical Review Letters 100 (2008) 238301. [24] W.A. Tiller, K.A. Jackson, J.W. Rutter, B. Chalmers. The redistribution of solute atoms during the solidification of metals, Acta Metallurgica 1 (1953) 428-437. [25] W.W. Mullins, R.F. Sekerka. Stability of a Planar Interface During Solidification of a Dilute Binary Alloy, Journal of Applied Physics 35 (1964) 444-451. [26] J. You, L. Wang, Z. Wang, J. Li, J. Wang, X. Lin, W. Huang. In situ observation the interface undercooling of freezing colloidal suspensions with differential visualization method, Review of Scientific Instruments 86 (2015) 084901. [27] S. Peppin, J. Elliott, M. WORSTER. Solidification of colloidal suspensions, Journal of Fluid Mechanics 554 (2006) 147-166. [28] S. Peppin, A. Majumdar, J. Wettlaufer. Morphological instability of a non-equilibrium ice–colloid interface. Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, vol. 466: The Royal Society, 2010. p.177-194. [29] T. Kozlowski. Soil freezing point as obtained on melting, Cold regions science and technology 38 (2004) 93-101. [30] A.M. Anderson, M.G. Worster. Periodic ice banding in freezing colloidal dispersions, Langmuir 28 (2012) 16512-16523. [31] M.H. Burden, J.D. Hunt. Cellular and dendritic growth. II, Journal of Crystal Growth 22 (1974) 109-116.
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List of figures
Table 1. static undercoolings from measurements and predictions.
Table 1(a). for PS colloidal suspensions of different d and PS colloidal suspensions
d(m) 1 1.73
20% 20% 33% Measured SCS (10-2K) 12.1±0.5 12.3±0.4 12.3±0.4
Measured PCS (10-2K) 0±0.18 0±1.87 0±0.16
PCS theoretical A 3.06×10-7 5.91×10-8 1.69×10-8
-2 predictions (10 K) B 17.2 3.34 19.5
Table 1(b). for alumina suspensions of different alumina suspensions
d(m) 0.05
2.72% 3.63% 9.74% Measured SCS (10-2K) 4.01±0.42 4.02±0.42 4.03±0.42
Measured PCS (10-2K) 0±0.2 0.18±0.22 0.91±0.85
PCS theoretical A 1.93×10-4 6.98×10-4 7.45×10-4
-2 predictions (10 K) B 260 1640 12830 Prediction A is from Ref.[22, 27], while prediction B comes from Ref.[23, 28].
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Fig.1 The static interfacial positions in two side-by-side Hele-Shaw cells of the deionized water and the supernatant from PS colloidal suspensions of d=1.73m,
33% (a); and two side-by-side Hele-Shaw cells of the colloidal suspensions and its supernatant (b) in a uniform thermal gradient of G=7.23K/cm. The distance of the static interfacial positions reveal the static interfacial undercoolings. The pulling speed V=0 and scale bar is 200m.
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prediction A
120 0.04 prediction B measured PCS 0.03
90 measured PCS
0.02 measured SCS
)
K
( 60 0.01
T 0.00 30 0.02 0.04 0.06 0.08 0.10
0 0.02 0.04 0.06 0.08 0.10 Fig.2 measured PCS compared with the theoretical predictions A and B (both for theoretical PCS). Prediction A is from Ref.[22, 27], while prediction B comes from Ref.[23, 28]. The inset is the measured value of SCS and PCS for alumina suspensions with d=50nm under G=7.23K/cm and V=0.
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Fig.3 The steady-state interfacial positions in two side-by-side Hele-Shaw cells of the deionized water and the supernatant from alumina suspensions of d=50nm,
3.63% (a); and two side-by-side Hele-Shaw cells of the alumina suspensions and its supernatant (b) in a uniform thermal gradient of G=7.23K/cm. The distance of the steady-state interfacial positions reveal the dynamic interfacial undercoolings. The pulling speed V=8.217m/s and scale bar is 200m.
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0.100
0.075
0.050
T (K) T dynamic PCS dynamic SCS 0.025
0.000
0 5 10 15 V (m/s) Fig.4 measured dynamic SCS and PCS for alumina suspensions with d=50nm,
3.63% under different pulling speeds, G=7.23K/cm.
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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
Supplementary Information
Figures S1-S5 and Movie S1
Corresponding author. Tel.:86-29-88460650; fax: 86-29-88491484 E-mail address: [email protected] (Zhijun Wang) 15 / 23
Fig.S1 Schematic of horizontal directional freezing stage (the upper part) and the gauging method (the lower part) for the interfacial undercooling. The experimental platform we adopted is known as a horizontal Bridgeman directional freezing stage. This platform can avoid the convection interference caused by gravity. Furthermore, it aims at producing a constant and uniform thermal gradient along which samples of colloidal suspensions are pushed mechanically at a constant pulling speed. The sample cell of colloidal suspensions (sample 1) is placed side by side with a cell of its solvent (sample 2) under an identical thermal gradient, shown as the lower part of Fig.S1. Interface gaps between two samples are recorded and measured through snapshot. The separation distance between melting front of the solvent (red dash line in Sample 2) and interface position of suspensions (blue dash line in Sample 1) indicates the interfacial undercooling of colloidal suspensions. Through the difference of pixels (ΔS) between these two lines on the photograph combined with image scale (M) and temperature gradient (G), the interfacial undercooling (ΔT) of colloidal suspensions is calculated as ΔT=S×G (S=ΔS×M is the real distance of the interface gap).
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Fig.S2 The static interfacial positions in two side-by-side Hele-Shaw cells of the deionized water and the supernatant from PS colloidal suspensions with d=1m and
0=20% (1a); and two side-by-side Hele-Shaw cells of the colloidal suspensions and its supernatant with d=1m and 0=20% (1b); and two side-by-side Hele-Shaw cells of the deionized water and the supernatant from PS colloidal suspensions with d=1.73m and 0=20% (2a); and the colloidal suspensions and its supernatant with d=1.73m and 0=20% (2b) in a uniform thermal gradient of G=7.23K/cm. The distance of the static interfacial positions reveal the static interfacial undercoolings. The pulling speed V=0 and scale bar is 200m. Figure S2 (1a) shows the measurement of static SCS for PS suspensions through the interfacial position comparison between the deionized water (left cell of Fig.S2 (1a)) and the supernatant (right cell of Fig.S2 (1a)). The discrepancy of the solid/liquid interface positions between the deionized water and the supernatant is 167.36m, which indicates that the value of SCS is 0.121K in the consideration of
G=7.23K/cm. Fig.S2 (1b) shows the measurement of static PCS for PS suspensions with d=1m and 0=20%, through the interfacial position comparison between the suspensions (left cell of Fig.S2 (1b)) and its own supernatant (right cell of Fig.S2
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(1b)). 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 results of Fig.S2 (2a) and (2b) for PS suspensions with d=1.73m and 0=20% are similar to those of Fig.S2 (1a) and (1b). Note that the brightness of Figure S2 (1a) is obviously higher than that of (1b). It is from the different light brightness of the microscope in different measurements. However, the interfacial positions are not affected by the different brightness from the optical microscope. We test different systems using the different colloidal suspension and its own supernatant by centrifugation each time. The measured data of PCS and SCS are shown in Table 1(a).
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Fig.S3 The static interfacial positions in two side-by-side Hele-Shaw cells of the deionized water and the supernatant from alumina suspensions with d=50nm (a); and two side-by-side Hele-Shaw cells of the colloidal suspensions and its supernatant with
0=2.72% (b); and two side-by-side Hele-Shaw cells of the colloidal suspensions and its supernatant with 0=3.63% (c); and two side-by-side Hele-Shaw cells of the colloidal suspensions and its supernatant with 0=9.74% (d) in a uniform thermal gradient of G=7.23K/cm. The distance of the interfacial positions reveal the interfacial undercoolings. The pulling speed V=0 and scale bar is 200m. Note that each suspensions have been compared with their own supernatant. However the static interfacial positions of SCS for different suspensions are similar, and one static interfacial positions of static SCS is presented here to represent the four different static SCS. Figure S3 (a) shows the measurement of SCS for alumina suspensions. The discrepancy of the solid/liquid interface positions between the deionized water and the supernatant is 55.60m, which indicates that the value of SCS is 0.0402K in the consideration of G=7.23K/cm. Fig.S2 (b), (c) and (d) show the measurement of PCS for alumina suspensions with 0=2.72%, 3.63%, 9.74% and d=50nm, respectively.
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Several measurements of these systems were taken and the average measured PCS for
0=2.72%, 3.63%, 9.74% and d=50nm are shown in Table 1(b).
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Fig.S4 the interfacial positions in two side-by-side Hele-Shaw cells of the deionized water and the supernatant (i.e. the solvent) from alumina suspensions with d=50nm and 3.63% under different pulling speeds, G=7.23K/cm. Fig.S4 shows that the dynamic PCS for alumina suspensions under different pulling speeds were almost zero, although the particles were obviously accumulated in front of the advancing solid/liquid interface forming a clear concentrated layer. Accordingly, the concentrated layer seems invalid to cause an obvious PCS. Although the bubbles formed in front of the advancing solid/liquid interface in Fig.S4 D, it is far away from the steady-state interface and doesn’t affect the advancing interface as well as the dynamic PCS.
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Fig.S5 the interfacial positions in two side-by-side Hele-Shaw cells of the deionized water and the supernatant of alumina suspensions under different pulling speeds and G=7.23K/cm, d=50nm, 3.63%. The scale bar is 200m Fig.S5 shows the measurement of SCS for alumina suspensions. Left cell of each small picture is the deionized water and right cell of each small picture is the supernatant. The distance of the solid/liquid interface positions between the deionized water and the supernatant decreased with the increase of pulling speeds, which indicates that the dynamic SCS decreased with the increase of pulling speeds. The results are consistent with the classical alloy solidification principle [31].
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Movie S1 (Multimedia view) the steady dynamic interface position of PCS for alumina suspensions under V=8.217m/s and G=7.23K/cm, d=50nm, 3.63%. The scale bar is 200m. It is easy to check the steady dynamic interface. We kept track of the position of the interface through snapshot. If the interface doesn't move in the visual field, the interface position will be at steady state. Also the stability of the method for dynamic pulling test has already been verified by Ref.[26]. Although the bubble formed in front of the advancing solid/liquid interface, it is far away from the steady-state interface and doesn’t affect the advancing interface as well as the dynamic PCS.
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