Phase change materials in the ternary system NH4Cl+CaCl2+H2O

CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 35 (2011) 269–275

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Phase change materials in the ternary system NH4 Cl + CaCl2 + H2 O Ouyang Dong a , Dewen Zeng a,b,∗ , Hongyan Zhou a , Haijun Han a , Xia Yin b , Yong Du c a

Qinghai Institute of Salt Lakes, Chinese Academy of Sciences, Xining, 810007, PR China

b

College of Chemistry and Chemical Engineering, Central South University, Changsha, 410083, PR China

c

Science Center for Phase Diagrams & Materials Design and Manufacture, Central South University, Changsha, 410083, PR China

article

info

Article history: Received 15 January 2011 Received in revised form 3 April 2011 Accepted 3 April 2011 Available online 28 April 2011 Keywords: Phase change materials Pitzer–Simonson–Clegg thermodynamic model Ammonium chloride Calcium chloride

abstract Solubility isotherms of the ternary system (NH4 Cl + CaCl2 + H2 O) were elaborately determined at T = (273.15 and 298.15) K by using the isothermal method. In the equilibrium phase diagram, there are two solubility branches corresponding to the solid phases CaCl2 ·6H2 O and NH4 Cl. Invariant point compositions are 36.32 wt% CaCl2 and 3.4 wt% NH4 Cl at 273.15 K, and 45.86 wt% CaCl2 and 5.22 wt% NH4 Cl at 298.15 K. A Pitzer–Simonson–Clegg thermodynamic model was applied to represent the thermodynamic properties of this ternary system and to construct a partial phase diagram of the ternary system at temperatures between (273.15 and 323.15) K. It was found in the predicted solubility phase diagram that the double salt 2NH4 Cl·CaCl2 ·3H2 O, found by other authors at (323.1 and 348.1) K, will disappear at temperatures below 298.15 K. Besides, it was found that there are two peritectic points in the ternary system with peritectic temperatures at 299.65 K and 298.15 K, and the former peritectic point falls just on the line between the composition points of NH4 Cl and CaCl2 ·6H2 O. According to phase rule, a solution made of this point will begin to crystallize at 299.65 K and end at 298 K and therefore can be acted as a ‘‘pseudo eutectic’’ phase change material (PCM). A heat storing and releasing experiment of 50 grams of the PCM was carried out, obtaining a satisfying result. © 2011 Elsevier Ltd. All rights reserved.

1. Introduction Phase change materials with a phase change temperature at room temperature, which can store energy from heat resources at low temperature, have attracted more and more attention. In previous works [1–3], we have developed a series of Lisalt based phase change materials at room temperatures, which showed excellent behavior of storing and releasing energy at room temperatures. Since lithium salt is expensive, it is desirable that cheaper phase change materials consisting of inorganic salts and water can be found. CaCl2 ·6H2 O with peritectic melting point at 302.7 K is a prospective phase change material. However, it will unnecessarily release heat even at room temperature. If its phase change temperature can be adjusted to room temperature, then it can store heat at room temperature and release heat when the environmental temperature is lower than room temperature. Generally, the melting point of CaCl2 ·6H2 O can be changed by adding a second salt. When KCl is used as adjusting component, peritectic composition points have been found with a phase change among CaCl2 ·6H2 O, CaCl2 ·4H2 O and KCl at about 300 K [4]. The peritectic behavior will lead to the segregation of solid and solution

∗ Corresponding author at: Qinghai Institute of Salt Lakes, Chinese Academy of Sciences, Xining, 810007, PR China. E-mail address: [email protected] (D. Zeng). 0364-5916/$ – see front matter © 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.calphad.2011.04.002

and worsen the function of heat storing of the material after several store-release cycles, besides, the phase change temperature at 300 K is still too high for storage of heat at room temperature. The solubility of ammonia chloride in water, which is higher than that for NaCl or KCl in water, could be a better adjusting agent for CaCl2 ·6H2 O as a room temperature phase change material. In this paper, the solubility isotherms of the system (NH4 Cl + CaCl2 + H2 O) including the corresponding equilibrium solid phase were elaborately determined at T = (273.15 and 298.15) K. Then, a Pitzer–Simonson–Clegg model and BET models were selected to simulate properties of this system. The goal was to make it clear if a room temperature phase change material exists in this ternary system. Just when we finished the manuscript of this work, a kind anonymous reviewer reminded us that Li et al. [5,6] measured solubility isotherms of this system at T = (298.1, 323.1 and 348.1) K. This can act as supplementary material to our work. 2. Experimental 2.1. Materials and apparatus Ammonium chloride and calcium chloride were prepared by three times crystallization of an A.R. reagent (Tianjin Hengxing Industry Co. Ltd.) with 50% salt recovery in each case. Doubly distilled water (S ≤ 1.2 × 10−4 S/m) and silver nitrate (purity in mass fraction >0.999) were used in the experiment.

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Table 1 Solubility of the ternary system NH4 Cl + CaCl2 + H2 O at 273.15 K. Composition of solutiona

Composition of Wet solid phasea

NH4 Cl

CaCl2

H2 O

NH4 Cl

CaCl2

H2 O

0. 2300 0.1841 0.1443 0.1226 0.0867 0.0671 0.0527 0.0425 0.0338 0.0342 0.0175 0

0 0.0557 0.1109 0.1407 0.2008 0.2413 0.2806 0.3258 0.3633 0.3631 0.3680 0.374

0.7700 0.7602 0.7448 0.7367 0.7125 0.6916 0.6667 0.6317 0.6029 0.6027 0.6145 0.6260

– 0.3178 0.3418 0.3816 0.2650 0.3099 0.2805 0.1294 0.0388 0.0661 0.0111 –

– 0.0464 0.0851 0.0989 0.1618 0.1779 0.2130 0.2961 0.4078 0.3927 0.4197 –

– 0.6358 0.5731 0.5195 0.5732 0.5122 0.5065 0.5745 0.5534 0.5412 0.5692 –

a b

Solid phaseb

A A A A A A A A A+B A+B B B

The mass fraction of the salt. A—NH4 Cl, B—CaCl2 ·6H2 O.

Table 2 Solubility of the ternary system NH4 Cl + CaCl2 + H2 O at 298.15 K. Composition of solutiona

Composition of wet solid phasea

NH4 Cl

CaCl2

H2 O

NH4 Cl

CaCl2

H2 O

0.2837 0.2438 0.2135 0.1673 0.1574 0.1328 0.0888 0.0711 0.0561 0.0558 0.0523 0.0521 0.0344 0.0217 0

0 0.0454 0.0814 0.1391 0.1523 0.1873 0.2625 0.3055 0.3669 0.3798 0.4585 0.4587 0.4528 0.4503 0.4487

0.7163 0.7108 0.7051 0.6936 0.6903 0.6799 0.6487 0.6234 0.5770 0.5644 0.4892 0.4892 0.5128 0.5280 0.5513

– 0.3549 0.2838 0.2853 0.2565 0.2477 0.1925 0.2279 0.2167 0.2037 0.0562 0.0578 0.0257 0.0190 –

– 0.0389 0.0740 0.1194 0.1347 0.1623 0.2327 0.2542 0.3044 0.3209 0.4580 0.4569 0.4638 0.4576 –

– 0.6062 0.6422 0.5953 0.6088 0.5900 0.5748 0.5179 0.4789 0.4754 0.4858 0.4853 0.5105 0.5234 –

a b

Fig. 1. Isothermal solubility in the NH4 Cl + CaCl2 + H2 O system at 273.15 K. (•) saturated solution composition, (◦) corresponding wet solid composition. Solid phaseb

A A A A A A A A A A A+B A+B B B B

The mass fraction of the salt. A—NH4 Cl, B—CaCl2 ·6H2 O.

Solubility measurements were carried out in a thermostat (LAUDA E219, Germany) with temperature stability of ±0.01 K. The temperature was measured by means of a calibrated glass thermometer with an accuracy of ±0.01 K. A Sartorius (CPA225D) balance was used for weighing with an error of ±0.1 mg. Measurement of the heat storing and releasing behavior of the phase change material was carried out in a device reported previously [2]. 2.2. Experimental procedures Solid–liquid Equilibrium experiments were carried out in a ground 250 cm3 Erlenmeyer flask which was immersed in a glycol–water bath in the thermostat. The solution and solid in the flask were stirred with a magnetic stirrer outside the bath. Each sample was stirred at a certain constant temperature for 80 h, and then kept static for about 8 h. The samples of the saturated solution were then taken with a pipette covered with glass cloth as a filter and transferred to a weighed 25 cm3 weighing bottle with internal stoppers. The wet solid was transferred by glass scoop into a weighed 40 cm3 glass-stoppered weighing bottle. The total concentration of NH4 Cl and CaCl2 in ternary system was determined by precipitating Cl− ion with AgNO3 , as described in the literature [7]. The Ca2+ ion concentrations were determined by a titration method with EDTA, as described in the literature [8]. The wet residuals were analyzed in the same way as for the solution. The composition of the solid phase in the wet residues was identified by the Schreinemaker method.

Fig. 2. Solubility isothermal in the NH4 Cl + CaCl2 + H2 O system at 298.15 K. (•) saturated solution composition in this work, (◦) corresponding wet solid composition in this work, (1) literature [6].

On measuring the heat storing and releasing behavior of the phase change material, 50 g phase change material was prepared and then loaded in a 100 ml tube which was placed in center of a 500 ml beaker. The latter was immersed in a water bath. The temperature for the water bath was set to be 303 K for the heat storing process and 293 K for the heat releasing process. A temperature sensor was immersed in the phase change material and the detected temperature was recorded online by a computer. Besides, the temperature of 50 g water was detected as done for the phase change material for comparison. 3. Results and discussion The experimental solubility data at T = (273.15 and 298.15) K are listed in Tables 1 and 2 and plotted in Figs. 1 and 2, respectively. We noticed that the solid phase in equilibrium with saturated solution are CaCl2 ·6H2 O and NH4 Cl at both temperatures. The invariant point compositions are 36.32 wt% CaCl2 and 3.4 wt% NH4 Cl at 273.15 K, and 45.86 wt% CaCl2 and 5.22 wt% NH4 Cl at 298.15 K, as shown by points e in Figs. 1 and 2. No formation branch for CaCl2 ·4H2 O has been found at 298.15 K. The isotherm data from the literature [6] at 298.15 K are also presented in Fig. 2 for comparison. It can be noticed that the literature data are in good agreement with our data on both sides

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Table 3 Binary parameters of the Pitzer–Simonson–Clegg model. Mixture parametersa

System

Bmx

CaCl2 + H2 O NH4 Cl + H2 O a

Bmx1

Wmx

Umx

A

B

A

B

A

6395.679 82.2638

−17.08965 −0.2463

−1804.265

3.88752 0

−70.052

0.09274

18.656

−0.05283

0

B

T /K

Ref.

298–323 298–323

[12,13] [14,15]

Vmx

A

B

A

B

251.348 54.337

−0.697464 −0.14532

−131.648 −40.183

0.45295 0.10981

Parameter value =A + BT .

Table 4 The parameter ln k of solid phases in the ternary NH4 Cl + CaCl2 + H2 O system. Solid phase

ln k

CaCl2 ·6H2 O CaCl2 ·4H2 O CaCl2 ·2H2 O NH4 Cl 2NH4 Cl·CaCl2 ·3H2 O

ln k ln k ln k ln k ln k

= −8458.935 − 2.63134T + 215890.2/T + 1495.3337 ln(T ) = 31707.593 + 8.75989T − 860154.9/T − 5516.4959 ln(T ) = 5916.451 + 1.32993T − 172526.6/T − 1005.0658 ln(T ) = 14.772 − 0.02435T − 3785.1/T = −47.693 + 12600.5/T

T /K

Solubility data for fitting

273–302 303–318 318–333 273–363 323–348

[18] [19] [18] [19] [6]

1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0

1

2

3

4

5

6

7

8

9

10

11

Fig. 3. Calculated water activities of the systems CaCl2 + H2 O compared with literature data. (◦) Ref. [16], (•) Ref. [12], () Ref. [13]; all lines are model values: (—) 273.15 K, (— · —) T = 298.15 K, (- - - -) T = 323.15 K.

Fig. 4. Calculated water activities of the system NH4 Cl + H2 O compared with literature values. (◦) Ref. [14], (•) Ref. [15]; Lines, model values: (—) 298.15 K, (- - - -), 323.15 K.

of the isotherms, except for the data near the invariant point. The invariant point of our work is lower in water content than the literature data. We notice that the temperature stability ±0.1 K of the water bath reported in the literature [6] isn’t as high as ours ±0.01 K, and their equilibrium time 12 h may be insufficient. 4. Modeling As we discussed previously [1], the Pitzer–Simonson–Clegg model [9–11] is especially good for describing the properties of the titled highly soluble salt aqueous system NH4 Cl + CaCl2 + H2 O. Activity expressions of all components in a mixing system by the Pitzer–Simonson–Clegg model are given in the Appendix section of this work. Binary model parameters for CaCl2 and NH4 Cl were determined by fitting to water activity data [12–16] at (298.15 and 323.15) K, and are listed in Table 3. The associated constant α is set to be 13 for both salts, however α1 = 0 for NH4 Cl and α1 = 2 for CaCl2 . The calculated water activities in Figs. 3 and 4 show that the model can represent the binary activity property quite well. The ln k parameters for each solid phase were determined by calculating the component activities (Eq. (1)) at its saturated solutions. In our previous work [17], the solubility data for CaCl2 ·6H2 O [18], CaCl2 ·4H2 O(alpha) [19] and CaCl2 ·2H2 O [18] are considered as reliable. These data are used for determination of the ln k parameters. The solubility data for NH4 Cl are taken from Ref. [19]. The obtained ln k parameters are listed in Table 4. MX · nH2 O(s) = M(+aq) + X(−aq) + nH2 O(aq) ln k = ln(aM + aX − anH2 O ). (aq)

(aq)

(1)

Fig. 5. Calculated phase diagram of the system CaCl2 + H2 O compared with the literature data. (◦, ) Ref. [18], (1) Ref. [19], (—) model value.

The recalculated liquidus of the two binary systems CaCl2 + H2 O and NH4 Cl + H2 O are shown in Figs. 5 and 6. Applying the pure solution parameters in Tables 3 and 4, we predicted the solubility isotherms of the ternary system NH4 Cl + CaCl2 + H2 O at 273.15 K and 298.15 K, which deviate largely from the experimental data, as shown by the dashed lines in Fig. 7. Meanwhile, we calculated water activities in the ternary system with the binary parameters only and compared them

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Table 5 Comparison of experimental and calculated water activities in the ternary system NH4 Cl + CaCl2 + H2 O at 298.15 K. m/mol kg−1

aw

Deviation

NH4 Cl

CaCl2

Exp [20]

calc1

calc2

delta1

delta2

0.3 0.45 0.6 0.75 0.9 1.05 1.2 1.5 1.8 2.1 2.4 2.7 3 0.3 0.45 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 3 3.6 4.2 0.6 1.2 1.5 1.8 2.1 2.4 2.7 3 3.3 3.6 3.9 4.2 4.8 Average

0.2 0.3 0.4 0.5 0.6 0.7 0.8 1 1.2 1.4 1.6 1.8 2 0.1 0.15 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.2 1.4 0.1 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.8

0.9807 0.9707 0.9600 0.9490 0.9380 0.9260 0.9140 0.8890 0.8620 0.8350 0.8070 0.7780 0.7500 0.9856 0.9783 0.9708 0.9560 0.9400 0.9230 0.9070 0.8890 0.8720 0.8540 0.8360 0.8000 0.7660 0.9759 0.9510 0.9390 0.9260 0.9130 0.8990 0.8860 0.8730 0.8590 0.8460 0.8330 0.8190 0.7940

0.9753 0.9635 0.9520 0.9406 0.9289 0.9168 0.9041 0.8769 0.8473 0.8157 0.7829 0.7494 0.7159 0.9825 0.9736 0.9650 0.9480 0.9309 0.9134 0.8953 0.8763 0.8567 0.8365 0.8159 0.7742 0.7327 0.9724 0.9452 0.9316 0.9178 0.9038 0.8895 0.8750 0.8603 0.8454 0.8305 0.8155 0.8006 0.7711

0.9768 0.9665 0.9570 0.9479 0.9388 0.9295 0.9196 0.8981 0.8739 0.8472 0.8184 0.7880 0.7567 0.9832 0.9752 0.9676 0.9534 0.9398 0.9260 0.9117 0.8966 0.8806 0.8639 0.8463 0.8095 0.7712 0.9738 0.9499 0.9384 0.9268 0.9151 0.9032 0.8910 0.8785 0.8657 0.8526 0.8394 0.8260 0.7989

0.0054 0.0072 0.0080 0.0084 0.0091 0.0092 0.0099 0.0121 0.0148 0.0193 0.0242 0.0286 0.0341 0.0031 0.0047 0.0058 0.0080 0.0091 0.0096 0.0117 0.0127 0.0153 0.0175 0.0201 0.0259 0.0333 0.0035 0.0058 0.0074 0.0082 0.0093 0.0095 0.0110 0.0127 0.0136 0.0155 0.0175 0.0184 0.0229 0.0134

0.0039 0.0042 0.0030 0.0011 −0.0008 −0.0035 −0.0056 −0.0091 −0.0119 −0.0122 −0.0114 −0.0100 −0.0067 0.0024 0.0031 0.0032 0.0026 0.0002 −0.0030 −0.0047 −0.0076 −0.0086 −0.0099 −0.0103 −0.0095 −0.0052 0.0021 0.0011 0.0006 −0.0008 −0.0021 −0.0042 −0.0050 −0.0055 −0.0067 −0.0066 −0.0064 −0.0070 −0.0049 0.0053

calc1: calculated by binary parameters only. calc2: calculated by both binary and ternary mixture parameters. delta1 = aw∑ (exp) − aw (calc1); delta2 = aw (exp) − aw (calc2). n average = i |delta_i| /n.

Fig. 6. Predicted solubility of the system NH4 Cl + H2 O and the comparison with the literature. (◦) Ref. [19], (—) model value.

with the experimental data [20] (see Fig. 8 and Table 5), finding large deviations between them too. It seems that the ternary model parameters are necessary to describe the properties of the system. Therefore, we fit the parameters to the solubility isotherms

Fig. 7. Solubility isotherm of the system NH4 Cl + CaCl2 + H2 O. Symbols, experimental data: (◦) 273.15 K, (•) 298.15 K, (- - - -) predicted isotherms with binary parameters only, (—) predicted isotherms with both binary and ternary parameters.

Fig. 8. Water activity in the system NH4 Cl + CaCl2 + H2 O against total molality m at different ionic-strength fractions y = INH4 Cl /{INH4 Cl + ICaCl2 } at T = 298.15 K. Symbols, experimental data from Ref. [20]: (•) y = 0.67, () y = 0.5, (1) y = 0.33, (—) model value calculated with both binary and ternary parameters, (- - - -) model value calculated with pure salt parameters only.

at 273.15 K and 298.15 K, obtaining the ternary parameters as a function of temperature (see set number 2 of parameters in Table 6). Solubility isotherms and water activities were calculated again with the binary and ternary model parameters, both of which are in good agreement with the experimental values at (273.15 and 298.15) K, see solid lines in Figs. 7 and 8. Since the solubility isotherms at (323.1 and 348.1) K were reported in literatures [5,6], we predicted the isotherm at 323.1 K and found that it obviously deviates from the experimental data [5,6], as shown in Fig. 9. Possibly, the extrapolation ability of the model is insufficient, or the experimental data are not accurate enough. Besides, the authors [5,6] found the formation field of a double salt 2NH4 Cl·CaCl2 ·3H2 O in this ternary system at (323.1 and 348.1) K. We are interested to know below which temperature the double salt phase will disappear. At least, determined by our experiment and the authors, the double salt will disappear at 298.15 K [5,6]. The question can be answered by thermodynamic modeling. To obtain a ‘better’ set of model parameters, we fitted them again to the experimental water activities [20] at 298.15 K and solubility isotherms at (273.15 and 298.15) K from this work and that at 323.1 K from the literatures [5,6], obtaining the set 3 of model parameters in Table 6. The new parameter ln k for the double salt is fitted to the experimental data at (323.1 and 348.1) K [6]

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Table 6 Mixing parameters of the Pitzer–Simonson–Clegg model for the system NH4 Cl + CaCl2 + H2 O. Set

Mixture parametersa

Exp. data for parameter determination

Wmnx A 1 2 3 a

0

−28.31 75.33

Qmnx B

A

0 0.1476 −0.2000

−40.31 −103.05

0

Umnx B

A

B

0 0.0396 0.2500

0 2.841 −59.890

−0.0104

0 0.2000

– Solubility data at (273.15 and 298.15) K [this work], water activities from Ref. [20] Solubility data at (273.15 and 298.15) K [this work] and at 323.1 K [5,6], water activities [20]

Parameter value = A + BT .

Fig. 9. Solubility phase diagram of the system NH4 Cl + CaCl2 + H2 O. All lines are calculated by binary model parameters and the ternary parameters (set number 2 in Table 6), ( ) polytherm, (- - - -) isotherm at 273.15 K, (—) isotherm at 298.15 K, (—·—) isotherm at 323.1 K, () exp. values at 273.15 K in this work, (◦) exp. values at 298.15 K in this work, (1) exp. values at 323.1 K [5,6]. Table 7 Predicted compositions of peritectic points in the ternary system NH4 Cl + CaCl2 + H2 O. Composition (in mass fraction) CaCl2

NH4 Cl

H2 O

0.482 0.459

0.047 0.051

0.471 0.490

T /K

Presentation

299.65 298.15

point p1 in Fig. 10 point p2 in Fig. 10

and given in Table 4. The new calculated regional phase diagram of the ternary system is presented in Fig. 10. It can be observed that there are two peritectic points in the ternary system below 303 K, the points p1 and p2 in Fig. 10. The predicted exact compositions of the peritectic points are given in Table 7. The most important information drawn from the predicted phase diagram is that the point p1 falls on the line between the composition point of NH4 Cl and CaCl2 ·6H2 O. According to the phase rule, the following two peritectic reactions happen CaCl2 ·4H2 O + Lp1 = CaCl2 ·6H2 O + 2NH4 Cl·CaCl2 ·3H2 O

(point p1 at 299.65 K)

(2)

2NH4 Cl·CaCl2 ·3H2 O + Lp2 = NH4 Cl + CaCl2 ·6H2 O

(point p2 at 298.15 K).

(3)

Below 299.65 K, the phase CaCl2 ·4H2 O disappears and below 298.15 K the phase 2NH4 Cl·CaCl2 ·3H2 O disappears. The latter agree very well with our experimental isotherm at 298.15 K where no double salt formation field was found. According to the predicted phase diagram, when a mixture with composition at p1 in Fig. 10 is cooled down from high temperatures, the following reaction (4) will happen Lp1 = CaCl2 ·6H2 O + 2NH4 Cl·CaCl2 ·3H2 O

(4)

Fig. 10. Solubility phase diagram of the system NH4 Cl + CaCl2 + H2 O. All lines are calculated by binary model parameters and the ternary parameters (set number 3 in Table 6). ( ) polytherm, (- - - -) 273.15 K, (—) 298.15 K, (—·—) 299.65 K, (– · ·–) 323.15 K, (◦) exp. values at 323.1 K [5,6].

during the temperature range (299.65–298) K, at about 298 K the reaction (3) will happen until exhausting of the double salt 2NH4 Cl·CaCl2 ·3H2 O together with the liquid phase Lp2 at the same time, when the solid phases composite of CaCl2 ·6H2 O and NH4 Cl and the whole solidification process ends. Shortly, a mixture solution with composition at p1 will begin to crystallize at 299.65 K and end at about 298 K. Although a peritectic reaction arises in the single crystallization process, the whole crystallization process looks like a ‘pseudo eutectic process’ since it happens in a quite narrow temperature interval of 1.5 K. To check the pseudo eutectic behavior, an experiment of 50 grams grade has been carried out. As described in the experimental procedure section, 50 g phase change material consisting of 4.7 wt% NH4 Cl and 95.3 wt% CaCl2 ·6H2 O (p1 in Fig. 10) was prepared and its heat storing and releasing behavior was measured. The obtained results were presented in Fig. 11. While the temperatures of pure water reach environmental temperatures rapidly, two platforms arise in the temperature curves for the phase change material in the temperature decreasing and increasing processes. The heat storing and releasing capacity of the predicted PCM is much higher than pure water. The phase change temperatures, 298.35 K in the temperature-decreasing process and 299.45 K in the temperatureincreasing process fall in the predicted range. The measured results show that the predicted eutectic composition (4.7 wt% NH4 Cl and 95.3 wt% CaCl2 ·6H2 O) could be used as a prospective PCM. 5. Conclusions Solubility isotherms in the ternary system NH4 Cl + CaCl2 + H2 O at T = (273.15 and 298.15) K were determined by the isothermal method. It was found that there are two solubility branches for CaCl2 ·6H2 O and NH4 Cl at both temperatures.

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and anion X : ln fX = −zX2 Ax [(2/ρ) ln(1 + ρ Ix1/2 )

+ Ix1/2 (1 − 2Ix /zX2 )/(1 + ρ Ix1/2 )] + xM BMX g (αMX Ix1/2 ) − xM xX BMX [zX2 g (αMX Ix1/2 )/(2Ix ) + (1 − zX2 /(2Ix )) exp(−αMX Ix1/2 )] 1 1 + xM B1MX g (αMX Ix1/2 ) − xM xX B1MX [zX2 g (αMX Ix1/2 )/(2Ix ) 1 + (1 − zX2 /(2Ix )) exp(−αMX Ix1/2 )] + x1 ((zM + zX )/(2zM ) − xI )W1,MX + x1 xI ((zM + zX )/zM − 2xI )U1,MX

1

+ 4x2I xM (1 − 3xX )V1,MX − [(zM + zX )/zM ]W1,MX

(A.3)

2

Fig. 11. Heat storing and releasing behavior of the phase change material (4.7 wt% NH4 Cl + 95.3 wt% CaCl2 ·6H2 O) and pure water.

A Pitzer–Simonson–Clegg model was selected to represent thermodynamic properties of this system. Successful correlation of the solubility phase diagram and water activities has been achieved and reasonable model parameters have been obtained. A partial solubility phase diagram of the ternary system was predicted within the temperature range of 273.15–323.15 K. It was found that based on the predicted solubility phase diagram there are two ternary peritectic points at temperatures below 300 K with one peritectic temperature at 299.65 K and the other at 298.15 K. According to the phase rule, when a solution composed of 0.482 CaCl2 , 0.047 NH4 Cl and 0.471 H2 O in mass fraction is cooled down, it will begin to crystallize at 299.65 K and the crystallization process ends at 298.15 K. This crystallization process can be acted as a pseudo eutectic process. At last, a heat storing and releasing experiment of a 50 gram sample has been carried out and this has proved the correctness of the predicted phase diagram. The predicted phase diagram of the ternary system forms a foundation to develop other room temperature phase change materials.

where ρ = 2150(d1 /DT )1/2 ; xI = xM + xX = 1 − x1 ; Ax and Ix are Debye–Hückel parameter and ionic strength based on mole fraction; xX , xM , d1 , D and T are mole fractions of anion and cation, density of the solvent water, dielectric constant of the solvent and thermodynamic temperature, respectively; BMX , B1MX , W1,MX , 1 U1,MX , V1,MX , αMX and αMX are model parameters. For a symmetrical or unsymmetrical ternary system MX–NX– H2 O, one has ln f1 = 2Ax Ix3/2 /(1 + ρ Ix1/2 ) − xM xX BMX exp(−αMX Ix1/2 ) 1 − xM xX B1MX exp(−αMX Ix1/2 ) − xN xX BNX exp(−αNX Ix1/2 ) 1 1/2 ′ − xN xX B1NX exp(−αNX Ix ) − 2xM xN (vMN + Ix vMN ) + (1 − x1 )(1/F ){EM (zM + zX )/(zM zX )W1,MX + EN (zN +z X )/(zN zX )W1,NX }

+ (1 − 2x1 )xX {xM (zM + zX )2 /(zM zX )U1,MX + xN (zN + zX )2 /(zN zX )U1,NX } + 4x1 (2 − 3x1 )xX × (xM V1,MX + xN V1,NX ) − 2xM xN WMNX − 4xM xN (xM /vM (X ) − xN /vN (X ) )UMNX + 4(1 − 2x1 )xM xN Q1,MNX ln fM = −

Acknowledgments This work was financially supported by the 100 top talents project of the Chinese Academy of Sciences and Innovative Project of Chinese Academy of Sciences (KJCX2-YW-H2O).

+ +

[( /ρ) ( + ρ

×

/

( −

/( [

(−α

))

ln f1 = 2Ax Ix3/2 /(1 + ρ Ix1/2 ) − xM xX BMX exp(−α Ix1/2 )

−

[

(α

/(

))

−

exp(−α

)+

+( −

(W1,MX

+ (xI − x1 )U1,MX ) + 4x1 xM xX (2 − 3x1 )V1,MX .

(A.1)

Cation M: 2 ln fM = −zM Ax [(2/ρ) ln(1 + ρ Ix1/2 )

+ Ix1/2 (1 − 2Ix /zM2 )/(1 + ρ Ix1/2 )] + xX BMX g (αMX Ix1/2 ) 1 + (1 − zM2 /(2Ix )) exp(−αMX Ix1/2 )] + xX B1MX g (αMX Ix1/2 ) 1 − xM xX B1MX [zM2 g (αMX Ix1/2 )/(2Ix ) 1 + (1 − zM2 /(2Ix )) exp(−αMX Ix1/2 )] + x1 ((zM + zX )/(2zX ) − xI )W1,MX + x1 xI ((zM + zX )/zX − 2xI )U1,MX

1 2

)/(

(A.2)

)

)]

)/(

)+( − (α

[

(−α

)/(

(α

(α

/(

)/(

)]

)

(−α

)]

+ (v − (v + v ( − / ))) + x1 [(zM + zX )/zX W1,MX − (zM /2 + 1/F )(EM (zM + zX )/(zM zX )W1,MX ) + EN (zN + zX )/(zN zX )W1,NX ] + x1 xX [(zM + zX )2 /(zM zX )U1,MX

− xM xX BMX [zM2 g (αMX Ix1/2 )/(2Ix )

+ 4x2I xX (1 − 3xM )V1,MX − [(zM + zX )/zX ]W1,MX

(−α

)] −

/(

x2I

[

(α

+( −

1/2 1 Ix

)] +

)−

))

For a single-electrolyte solution, the Pitzer–Simonson–Clegg model [9–11] describes the solvent activity coefficient f1 as below: xM xX B1MX

)

)/( + ρ

(α

+( − −

Appendix

(A.4)

2 zM Ax 2 ln 1 Ix1/2 2 1 Ix1/2 xX BMX g MX Ix1/2 Ix1/2 1 2Ix zM 1 1 1/2 2 xX BMX g MX Ix xM xX BMX zM g MX Ix1/2 2Ix 2 1/2 1 zM 2Ix exp MX Ix 2 1 2 xM xX B1MX zM g MX Ix1/2 2Ix 1 zM 2Ix 1 1/2 2 1/2 exp xN xX BNX zM g NX Ix 2Ix MX Ix 2 1/2 1 zM 2Ix exp I NX x 2 1 1/2 xN xX B1NX zM g NX Ix 2Ix 2 1 1/2 1 zM 2Ix exp NX Ix ′ 2 2xN MN xM MN zM 2 MN Ix

− 2(xM (zM + zX )2 /(zM zX )U1,MX + xN (zN + zX )2 /(zN zX )U1,NX )] + 4x21 xX (V1,MX − 3xM V1,MX − 3xN V1,NX ) + 2(xN WMNX − xM xN WMNX ) + 2[xN (2xM /vM (X ) − xN /vN (X ) ) × UMNX − 2xM xN (xM /vM (X ) − xN /vN (X ) )UMNX ] + 4x1 (xN Q1,MNX − 2xM xN Q1,MNX )

))

)

)

O. Dong et al. / CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry 35 (2011) 269–275

− [(1 − EM /2)(zM + zX )/zX W1,MX 1

− zM EN (zN + zX )/(zN zX )W1,NX ]

ln fX

2 = −zX2 Ax [(2/ρ) ln(1 + ρ Ix1/2 )

References (A.5)

+ Ix1/2 (1 − 2Ix /zX2 )/(1 + ρ Ix1/2 )] 1 + xM BMX g (αMX Ix1/2 )xM B1MX g (αMX Ix1/2 ) 1 1/2 + xN BNX g (αNX Ix1/2 ) + xN B1NX g (αNX Ix )

− xM xX BMX [zX2 g (αMX Ix1/2 )/(2Ix ) + (1 − zX2 /(2Ix )) exp(−αMX Ix1/2 )] 1 − xM xX B1MX [zX2 g (αMX Ix1/2 )/(2Ix ) 1 + (1 − zX2 /(2Ix )) exp(−αMX Ix1/2 )]

− xN xX BNX [zX2 g (αNX Ix1/2 )/(2Ix ) + (1 − zX2 /(2Ix )) exp(−αNX Ix1/2 )] 1 1/2 − xN xX B1NX [zX2 g (αNX Ix )/(2Ix ) 1 1/2 + (1 − zX2 /(2Ix )) exp(−αNX Ix )]

′ (Ix − zX2 /2)) − 2xM xN (vMN + vMN + x1 EM [(zM + zX )/zM W1,MX − (zX /2 + 1/F )(zM + zX )/(zM zX )W1,MX ] + x1 EN [(zN + zX )/zN W1,NX − (zX /2 + 1/F )(zN + zX )/(zN zX )W1,NX ]

+ x1 xM [(zM + zX )2 /(zM zX )U1,MX − 2xX (zM + zX )2 /(zM zX )U1,MX ] + x1 xN [(zN + zX )2 /(zN zX )U1,NX − 2xX (zN + zX )2 /(zN zX )U1,NX ] + 4x21 xM (V1,MX − 3xX V1,MX ) + 4x21 xN (V1,NX − 3xX V1,NX ) − 2xM xN WMNX − 4xM xN (xM /vM (X ) − xN /vN (X ) )UMNX 1

− 8x1 xM xN Q1,MNX − [EM (zM + zX )/zM W1,MX 2

+ EN (zN + zX )/zN W1,NX ]

275

(A.6)

where WMNX , Q1,MNX and UMNX are ternary model parameters. In Eqs. (A.1)–(A.6) all print failures in the original paper [11] have been corrected.

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