Solidification and Super-cooling Behaviors of Silica Nanofluids based on the Molten Eutectic Nitrate Salt

SiO2 nano-powders with different particle sizes were used to fabricate nitrate-based nanofluids with the nano-particle concentration arranged from 0.5-4.0 wt.%. The crystallization process of the as-prepared composite and the influence of nanoparticles on the cooling kinetics was analyzed based on experimental data. The research results show that Johnson-Mehl-Avrami equation can be only used to describe the crystallization process of pure eutectic salt, but not suit for nanofluids since the nanoparticles addition can alter the crystallization kinetics of the composites. Depending on the particle size and concentration, nanoparticles addition was found to be able to improve the degree of supercooling and reduce the crystallization completion time by varying degrees. Further verification by a modified JMAK equation shows that with the nanoparticle addition, the component ‘n’ would fluctuate within a certain range, which indicates that the nanoparticles can improve the crystallization process by altering the nucleation mechanism and adjusting the cooling rate resulted from the increased thermal conductivities of the nano-fluids.


Introduction
Molten salt has been wildly used in concentrated solar power (CSP) facilities due to its higher operating temperature since increasing the operating temperature can improve the efficiency and reliability of solar thermal energy conversion systems.The use of molten salt as a heat transfer fluid can improve the Rankine cycle efficiency of the power steam turbine and reduce the physical size of the heat storage system at a given capacity [1][2] .
Recent studies demonstrated that an innovative heat transfer fluids called nanofluids has been exploited in a variety of areas.By dispersing nanoparticles in conventional heat transfer fluids, the formed composites show the potential to significantly improve heat transfer rates.A significant number of studies in this area has been conducted by many researchers and all these researches suggested nano-fluid technique might be a good alternative for molten salt performance modification, which are expected to enhance the molten salt"s thermal conductivities significantly.Hence, a variety of nanoparticles, such as Al 2 O 3 , SiO 2 , CuO, ZnO, Fe 2 O 3 , TiO 2 , etc. have been tried and investigated in the past decades with the molten salts chosen as the based materials [3][4][5][6][7][8][9][10][11] .All these studies further confirmed that nanofluid, as a new-type heat transfer way, is very effective to improve the thermal performance of the molten salt.However, to the knowledge of the authors, most of the researches on the molten salt based nanofluid are mainly focused on the performance optimization, almost no research papers focus their emphasis upon the dynamic crystallization behaviour and especially the effects of nanoparticles on the crystallization process of the composites.Therefore, in an effort to enhance the performance optimization of molten salt based nanofluids, a series of parametric studies in this study were conducted to investigate the effects of the eutectic salt ratio, cooling rates, particle

Molten salt nanofluid preparation
In this study, we used the liquid solution method proposed by Shin et al. to formulate the nanofluids [12]   .Both KNO 3 and NaNO 3 (Beijing Chemical factory Co., Ltd., China) with the purity of 99% were chosen for this experimental research.
In order to show the possible effects of nanoparticles on supercooling behavior of nanofluid, a binary nitrate with a eutectic ratio of NaNO 3 : KNO 3 as 45:55 was selected.Firstly, 20 mg of SiO 2 nanoparticles (provided by Shanghai Maclean Biochemical Technology Co., Ltd.) were added to 60 ml of deionized water and then stirred for 10 minutes to form a suspension.The suspension was then ultrasonic treated in an ultra-so nicator (KQ-500DE, Kunshan Ultrasonic Instrument Co., Ltd., China) at a frequency of 40 kHz for 60 minutes to ensure good dispersion and to minimize the potential agglomeration of nanoparticles.Afterwards, different weights of the dried binary nitrate salt were dissolved in the suspension, causing the mass fraction of nanoparticles to vary from 0.5% to 4%.The mixture was ultrasonic treated for another 200 minutes to ensure the uniformity of the mixture.After ultrasonic treatment, the solution was evaporated in a drying oven with a temperature setting of 70℃, due to that lower temperature could avoid agglomeration [13] .In addition, the sample powders were kept at 120℃ constantly for at least 4 hours to remove all the crystal water before DSC measurement.Nanofluids doped with Al 2 O 3 and TiO 2 nanoparticles were also prepared by the same steps for further comparison.

Experimental method
In the current work, the cooling rates were designed to be 5, 10 and 20°C/min, respectively, in order to study the influences of the cooling rates.a different scanning calorimeter (DSC, STA 499 F5, NETZSCH) was used to evaluate thermal performance of the as-prepared nanocomposite fluids.The supercooling degree is calculated by subtracting the value of melting peak temperature and freezing peak temperature.For the purpose of accuracy, the final value of supercooling degree is the average of three calculation results.

Results and discussions
The relative crystallinity (α) could be determined by the following equation, in which α equals to partial integration of the crystallization exotherm at specific temperature intervals divided by the total area of the crystallization exotherm.
Where T 0 and T e are the initial and final temperature of crystallization.T represents the crystallization temperature at time t, H c is the enthalpy of crystallization.Depending upon the above equation ( 1), relative crystallinity Vs. both crystallization temperature and crystallization time under various conditions were calculated and the results given in Figure 1 and 2, respectively.All the plotted curves in Figure 1 show similar trends and the time for complete crystallization changed obviously with the changed cooling rate.The time for complete crystallization increases with the decreased cooling rate.
When the cooling rate is 20 o C/min, the obviously increased crystallization time should be connected closely with better diffusivity provided in the slow cooling rate and final crystallization morphology [14-15]   .Besides, Figure 1 also reveals the relative crystallinity values of the composites in the curves were above that of pure eutectic salt, in other words, the time required to complete the crystallization process decreased with SiO 2 nanoparticles addition.However, a relatively limited influence of the particle size on the non-isothermal crystallization process is found in Figure 1.For further clarity, the crystallization time under various conditions were estimated.The following equation was used to calculate the crystallization time (t): where T represents temperature at time t , T 0 is the initial temperature of crystallization at t=0, and φ is the cooling rate.The experimentally determined the crystallization time for 50% crystallinity in the case of non-isothermal crystallization temperature is displayed in Table 1.Table 1 reveals that the composites with SiO 2 nanoparticles addition have minimized time for 50% crystallization by 38% compared with the pure eutectic salt.For effects of the particle size on the crystallization time, Table 1 suggests silica with larger particle sizes can prolong the crystallization time.The largest reduction in crystallization time caused by particle size changes is about 13%.  Figure 2 shows dependence of relative crystallinity on crystallization temperature under various conditions.With respect to the pure eutectic salt, both the initial freezing points and curve steepness of the composites with nanoparticles addition shown in figure 2 are higher.This indicates the nanoparticle can reduce the degree of supercooling and meanwhile achieve a higher solidification cooling rate under the same conditions, which should be connected closely with both change in nucleation rate and the enhanced thermal conductivity by Brownian motion of nanoparticles.
Figure 1 and 2 also indicate both the relatively large particle size and low concentration of SiO 2 have a limit effect on the crystallization kinetics.For example, with the nanoparticle concentration as 0.5 wt.%, no matter for the temperature-crystallinity or time-crystallinity analyses, all the curves of the composites become almost coincident despite different particles sizes, indicating less effect of the particle size on the crystallization kinetics.With the nanoparticle concentration increased, the curves would become separated.For example, the curve steepness of the composite with 60 nm-sized nanoparticle addition tend to decrease, indicating a weakened impact produced on crystallization kinetics compared with the small-size nanoparticles.These observations are consistent to the previous discussions.Here g is determined by the shape of the growing crystal and m has close relations with the mechanism of growth and the dimensionality of the crystal.In case of isothermal crystallization with nucleation rate and growth rate independent of time, the equation (3) can be revised as below: Where n=m+1 for I v ≠ 0 and g' is a new shape factor.Equation ( 4) can be used as a detailed case of the Johnson-Mehl-Avrami Relation, which has been used to describe crystallization kinetics extensively and is usually written in the following form,  = 1 − exp −  # 5 Where α has the same meaning as that in equation ( 2), k and n are constants relative to time, t.Although Eq. ( 5) is generally offered to quantify the transformation kinetics of many isothermal solid-state processes, practice researches show this theoretical model is not suit for the non-isothermal transformations.Johnson-Mehl-Avrami equation is valid only in some special cases when it is applied to the description of non-isothermal thermal-analytical data.Therefore, before it can be employed for the analyses on non-isothermal process, a simple, quick and reliable test on the its further applicability becomes necessary.According to suggestions by Henderson, the below simplified expression for the Z(α) function can be used to test the applicability of the JMA equation: Depending upon the above equation, it is very easily to establish an association of the fractional extent of crystallization α with Z(α).If the normalized plots have the similar shapes with a maximum   ∞ of the z(α) function falling in the scale of 0.62-0.64,then Johnson-Mehl-Avrami equation becomes valid to describe thermal analytical data in non-isothermal process [16][17][18] .The Z(α) values against the fractional conversion α in various cases were plotted and shown in Figure 3.
Compared with the samples with SiO 2 addition, the curves of the Z(α) function of the pure eutectic salt are broader, especially at the maximum values interval.However, they are unambiguously in the theoretical value interval of 0.62-0.64,which indicates the JMA model is suitable for the pure eutectic salt.Figure 3 also indicates that the JMA model seems to be invalid for describing a more complex crystallization process in the samples with SiO 2 addition.Many different treatments on the above referred JMA equation have been reported for extending its application to non-isothermal crystallization.The relatively classic models include Ozawa-Chen, Kissinger, Augis-Bennett, Takhor, etc [19] .However, all these models are complicated and suited to limited applications.By contrast, Jeziorny proposed a simple modification by incorporating the cooling rate in to "k" in equation ( 4) [20] .The detailed procedure can be described as below.Firstly, the logarithmic form of equation ( 5) is below: Where is relative crystallinity, n is the Avrami exponent, and the k is over crystallization rate constant.Secondly, considering the non-isothermal process, value of k can be modified by incorporating the cooling rate, φ.
Where k c is the modified overall crystallization rate constant.the parameter "k c " describes the rate at which crystallization growth occurs under the non-isothermal crystallization process.Further the equation ( 7) can be revised as below: ln − ln 1 −  = φ ln   + ln # 9 According to Andrzej Jeziorhy"s report [20] , both k c and Avrami exponent "n" can be used for characterizing the poikilothermic crystallization kinetics.The former depends exclusively on the specific chemical features and crystallization structure of the composite investigated while the latter is used to describe both the crystal nucleation & growth mechanism and crystallization geometry.The calculated k c and "n" for pure eutectic salt and composites were displayed in Figure 4 and 5.Both parameters k c and the Avrami exponent "n" become obviously linear in Figure 4. Since k c is not sensitive to the conditions of the crystallization process, no obvious influences of the colling rates on it is found in Figure 4, in which its values are kept to be nearly constant despite various cooling rates.But, the "n" values change significantly with the changed cooling rates and its value increases almost linearly with the increased cooling rates.This phenomenon implies for the pure eutectic salt investigated in our studies, nucleation in the non-isothermal crystallization cannot be activated thermally and the transformation only can take place with the help of the changing thermodynamic driving force.In this case, the final product morphology is usually decided by the cooling rate, which has been observed in previous SEM pictures shown in Figure 4. Depending the extrapolation method, the straight line representing the Avrami exponent "n" can be extended to intersect the vertical axis, obtaining the "n" value for the "zero" cooling rate, which is regarded as a typical characteristic of the isothermal conditions.The obtained "n" value is larger than 2, but obviously not integer.According to the JMA theory, this indicates the crystallization process is not a single, but composite nucleation and growth mechanism, which should connect closely with the impurities and the cooling container [21] .rates. Figure 5(a) shows that SiO 2 addition generally increases the k c value with respect to pure salt.As the nano-particle size increases, the k c value keeps a downward trend; but when the concentration is low, such as 0.5%, the trend is not obvious with the line tended to be level.The dependence of k c value on the nano-particle concentrations is not significant.For example, when the concentration changes from 0.5 to 4%, the fluctuations in the k c value are only 0.36.0.72, 1.4 and 2.7%, corresponding to the particle size of 15, 30, 40 and 60 nanometers, respectively although the fluctuation scale increases as the particle size decreases.k c is called the rate constant, which is mainly used to describe the nucleation rate and growth rate.Therefore, compared to pure salt, the change in k c value is obviously related to the promoted nucleation rate by SiO 2 addition.Since SiO 2 addition can significantly enhance both the nucleation rate and growth rate, the k c value increases significantly compared to pure salt.At the higher concentration, the k c value decreases with the increased particle size, indicating that the large particle size has a certain negative effect on the crystal growth rate, resulting in a slow growth rate and nucleation rate, and a prolonged crystallization completion time, which is consistent to the previous analysis in figure 1. Figure 5(b) shows the exponent "n" has a different trend on both the concentration and particle size, which is totally different from that shown in figure 5(a).The exponent "n" is mainly affected by external cooling conditions and nucleation mechanism.Figure 5(b) indicates that SiO 2 addition can make the exponent "n" value fluctuate significantly with a scale of about 12%.With the particle concentration changed from 0.5 to 4 wt.%, the fluctuation scale is from 2.2 to 2.5.Assuming that all the external conditions are the same during the sample preparation, the changed exponent "n" value of the composite should be related to the changed heterogeneous nucleation mechanisms, such as secondary nucleation, caused by the nanoparticle size and agglomeration during the crystallization process; on the other hand, as previously speculated based on kinetics, the changed cooling rate due to the increased thermal conductivity caused by the addition of nanoparticles also have chance to contribute the changed exponent "n" value.

Figure 2 .
Figure 2. Dependence of relative crystallinity on crystallization temperature under various conditions.The theoretical study on crystallization kinetics depending DSC results was initially provided by the classic mathematical models, Johnson-Mehl-Avrami equation.In its basic form, the theory describes the evolution with time, t, of the volume fraction crystallized, α, in terms of the nucleation frequency per unit volume, I v , and the crystal growth rate, u:

Figure 4 .
Figure 4. (a) Plots of ln [-ln (1-α)] Vs. ln (t) for non-isothermal crystallization at different concentrations; (b) Dependence of both parameters k c and the Avrami exponent "n" on the coolingrates.Figure5(a) shows that SiO 2 addition generally increases the k c value with respect to pure salt.As the nano-particle size increases, the k c value keeps a downward trend; but when the concentration is low, such as 0.5%, the trend is not obvious with the line tended to be level.The dependence of k c value on the nano-particle concentrations is not significant.For example, when the concentration changes from 0.5 to 4%, the fluctuations in the k c value are only 0.36.0.72, 1.4 and 2.7%, corresponding to the particle size of 15, 30, 40 and 60 nanometers, respectively although the fluctuation scale increases as the particle size decreases.k c is called the rate constant, which is mainly used to describe the nucleation rate and growth rate.Therefore, compared to pure salt, the change in k c value is obviously related to the promoted nucleation rate by SiO 2 addition.Since SiO 2 addition can significantly enhance both the nucleation rate and growth rate, the k c value increases significantly compared to pure salt.At the higher concentration, the k c value decreases with the increased particle size, indicating that the large particle size has a certain negative effect on the crystal growth rate, resulting in a slow growth rate and nucleation rate, and a prolonged crystallization completion time, which is consistent to the previous analysis in figure1.Figure5(b) shows the exponent "n" has a different trend on both the concentration and particle size, which is totally different from that shown in figure5(a).The exponent "n" is mainly affected by external cooling conditions and nucleation mechanism.Figure5(b)indicates that SiO 2 addition can make the exponent "n" value fluctuate significantly with a scale of about 12%.With the particle concentration changed from 0.5 to 4 wt.%, the fluctuation scale is from 2.2 to 2.5.Assuming that all the external conditions are the same during the sample preparation, the changed exponent "n" value of the composite should be related to the changed heterogeneous nucleation mechanisms, such as secondary nucleation, caused by the nanoparticle size and agglomeration during the crystallization process; on the other hand, as previously speculated based on kinetics, the changed cooling rate due to the increased thermal conductivity caused by the addition of nanoparticles also have chance to contribute the changed exponent "n" value.

Figure 5 .
Figure 5. (a) dependence of parameters k c on both the particle size and concentration; (b) dependence of the Avrami exponent "n" on both the particle size and concentration.4. Conclusions SiO 2 nano-powders with different particle sizes were used to fabricate nitrate-based nanofluids with nano-particle concentration arranged from 0.5-4.0wt.%.With the help of DSC techniques, both the solidification and supercooling behaviors of molten salt based SiO 2 nanofluid was investigated using Johnson-Mehl-Avrami equation.The results indicated both the particle size and concentration have effects on the degree of supercooling and Johnson-Mehl-Avrami equation valid to describe the crystallization process of pure eutectic salt, but not suit for nanofluids since the nanoparticles addition can alter the crystallization kinetics of the salt.Nanoparticles can increase the initial crystallization temperature and effectively shorten the crystallization time.Further verification by a modified JMAK equation shows that with the nanoparticle addition, the component "n" would fluctuate within a certain range, which indicates that the nanoparticles can improve the crystallization process by altering the nucleation mechanism and adjusting the cooling rate resulted from the increased thermal conductivities of the nano-fluids.

Table 1 .
Time for 50% Crystallinity of different samples.