# Phase Behavior of Undecane-Dodecane Mixtures Confined in SBA-15

Authors: Xiao Yan; Hai-Rong Pei; Tong-Bo Wang; Wen-Bo Liu; Xiao-Zheng Lan
Journal: Journal of Chemistry
 (2013)

---

## Abstract

Phase behavior of undecane-dodecane mixtures (n-C11H24-C12H26, C11-C12) in bulk and confined in SBA-15 (pore diameters 3.8, 7.8, and 17.2 nm) has been studied by differential scanning calorimetry. Phase diagram of the confined C11-C12 system shows dependence on pore size, indicating simple behavior compared with the bulk. In the three systems, melting points of the confined C11, C12 and the mixtures (xC12 = 0.1–0.9) present a linear relation with the pore diameter from 3.8 to 17.2 nm. Melting behavior of the confined C11-C12 mixtures is closely as the confined C11, C12. Melting temperatures of the three systems have been fitted as a function of mole fraction xC12.


---

## Body

## 1. Introduction

Study on melting and freezing of fluids confined in nanopores materials is important from the theoretical as well as practical point of view [1–5]. The research in this field aims at understanding the influence of size effect and interface interactions on materials [6, 7]. It was found that melting temperatures of some liquids, such as water confined in CPG [6], follow the Gibbs-Thomson (G-T) equation. However, when the pore is very small or pore wall changed, such as activated carbon, carbon nanotubes, and mica, melting points of confined liquids deviated from the G-T equation or even lifted [6–10]. The new phenomena were thought to be related to interface interactions [6, 11].Meanwhile, few investigations have been reported on phase behavior of binary mixtures confined in nanopores. It was found that CaCl2-H2O mixtures confined in silica gel (pore diameter, 15 nm) belong to the same eutectic system with that for the bulk, whereas the phase diagram was shifted down by 10–30 K [12]. A similar phenomenon was observed in C6H5Br-CCl4 system confined in CPGs with pore diameter 7.5 nm [13]. The size effect shows great influence on the phase behavior of C6H5Cl-C6H5Br and n-C12H24-C14H30 mixtures adsorbed in mesoporous silicates [14–16]. At present, the influence of size effect and interface interactions on phase behavior of binary fluids is still not fully understood.Normal alkanes and their mixtures are extensively investigated in petroleum industry. In theoretical aspect, they can offer a good model in study on complex crystallization behavior of polymer materials, surfactants and lipids, and so forth [17]. Among this family, undecane (C11) and dodecane (C12) have medium size carbon chains and same crystal structures [18]. Their crystals have a triclinic unit cell belonging to space group P1-(Z=1) with dimensions (a≈4.3, b≈4.8, c≈20) Å (C11) [19–21], (a=4.3,b=4.8,c=17.3) Å (C12) [18], respectively.C11-C12 bulk system displays a complicated phase behavior [22]. C11-C12 mixtures are only partial miscible in solid states.SBA-15 has ordered cylindrical channels with two-dimensional hexagonal arrangement. It is a new type of silicate mesoporous materials with potential applications in many fields. The tunable pores with narrow size distributions are the ideal adsorbent in study of confinement effect on fluids [23].In this paper, we propose an investigation of phase behavior the odd-even C11-C12 alkane mixtures confined in SBA-15 (pore diameters 3.8, 7.8, and 17.2 nm) by using DSC. Solid-liquid phase diagram of C11-C12/SBA-15 showed dependence on the pore size. Moreover, the alkane mixture inside pores of SBA-15 behaves seemingly as the confined C11, C12.


## 2. Experimental

### 2.1. Materials

Undecane (mass fraction purity≥ 0.98), dodecane (mass fraction purity ≥ 0.98), and tetraethyl orthosilicate (TEOS, mass fraction purity 0.999) were purchased from Aladdin Reagents Co., Shanghai, China. 1, 3, 5-Triisopropylbenzene (TIPB, mass fraction purity 0.97) was bought from Xiya Reagents Co., Chengdu, China. Triblock copolymer Pluronic P123 was obtained from Sigma. All chemicals were used as received without further purification.


### 2.2. Synthesis and Characterization of SBA-15

SBA-15 was synthesized according to literature methods, in which triblock copolymer Pluronic P123 was used as a template and TIPB as a micelle expander for large pore SBA-15 (17.2 nm) [24–26]. After degassed at 433 K for 6 h, nitrogen adsorption and desorption isotherms for SBA-15 were measured at 77 K using an Autosorb-1 system [27].Transmission electron microscopy (TEM) images were recorded on a JEM-1400 (JEOL) operated at 120 kV. Before imaging, SBA-15 powder was dispersed in ethanol through sonication and then deposited on a carbon-coated copper grid.


### 2.3. Sample Preparation and DSC Measurements

SBA-15 powder with a mass of about 10 mg was put in a glass tube and outgas at 423 K under a vacuum of 10−1 Torr for around two hours. Then a certain amount of C11, C12 or their mixtures was transferred into the tube at pure nitrogen atmosphere. The volume of alkanes was taken as 90–100% the pore volume of SBA-15. At last, the glass tube was sealed and equilibrated at room temperature for about 6 hours.SBA-15 with the alkane adsorbed was transferred into DSC aluminum pan and sealed immediately. The sample was analyzed on a TA DSC Q10 under a high purity nitrogen atmosphere at a scanning rate of 5 K·min−1. The temperature scale was calibrated by high purity indium and water for DSC Q10. The mass of samples for DSC analysis was about 1 to 3 mg and measurement at least repeated three times in the temperature range from (173–190) K to room temperature. In most cases the melting temperature was reproducible to within 0.5 K.


## 2.1. Materials

Undecane (mass fraction purity≥ 0.98), dodecane (mass fraction purity ≥ 0.98), and tetraethyl orthosilicate (TEOS, mass fraction purity 0.999) were purchased from Aladdin Reagents Co., Shanghai, China. 1, 3, 5-Triisopropylbenzene (TIPB, mass fraction purity 0.97) was bought from Xiya Reagents Co., Chengdu, China. Triblock copolymer Pluronic P123 was obtained from Sigma. All chemicals were used as received without further purification.


## 2.2. Synthesis and Characterization of SBA-15

SBA-15 was synthesized according to literature methods, in which triblock copolymer Pluronic P123 was used as a template and TIPB as a micelle expander for large pore SBA-15 (17.2 nm) [24–26]. After degassed at 433 K for 6 h, nitrogen adsorption and desorption isotherms for SBA-15 were measured at 77 K using an Autosorb-1 system [27].Transmission electron microscopy (TEM) images were recorded on a JEM-1400 (JEOL) operated at 120 kV. Before imaging, SBA-15 powder was dispersed in ethanol through sonication and then deposited on a carbon-coated copper grid.


## 2.3. Sample Preparation and DSC Measurements

SBA-15 powder with a mass of about 10 mg was put in a glass tube and outgas at 423 K under a vacuum of 10−1 Torr for around two hours. Then a certain amount of C11, C12 or their mixtures was transferred into the tube at pure nitrogen atmosphere. The volume of alkanes was taken as 90–100% the pore volume of SBA-15. At last, the glass tube was sealed and equilibrated at room temperature for about 6 hours.SBA-15 with the alkane adsorbed was transferred into DSC aluminum pan and sealed immediately. The sample was analyzed on a TA DSC Q10 under a high purity nitrogen atmosphere at a scanning rate of 5 K·min−1. The temperature scale was calibrated by high purity indium and water for DSC Q10. The mass of samples for DSC analysis was about 1 to 3 mg and measurement at least repeated three times in the temperature range from (173–190) K to room temperature. In most cases the melting temperature was reproducible to within 0.5 K.


## 3. Results and Discussion

### 3.1. TEM Characterization and Pore Size of SBA-15

Three kinds of ordered mesoporous SBA-15 were synthesized with pore diameters of 3.8, 7.8, and 17.2 nm, respectively, determined by BJH method on basis of adsorption branches of isotherms [16]. Pore volume of the three SBA-15 (3.8, 7.8, and 17.2 nm) is 0.3, 1.0 and 1.4 cm3 g-1, respectively; micropore volume is determined to be ~0, 0.05 and 0.02 cm3 g-1 by V-t methods, respectively. As seen in Figure 1, SBA-15 presents parallel channels on TEM images and cylindrical mesopores with two-dimensional hexagonal arrangements (a, b, and c). The pores show a uniform size under TEM imaging. After adsorbed in the channel of SBA-15, the alkanes would form one-dimensional liquid when the pore is nearly filled. The ordered mesopores in SBA-15 would make the DSC signals sharp. For further study, the regular pore structure should be advantageous when the pore wall of SBA-15 is modified.TEM images of SBA-15: (a) pore diameter 3.8 nm; (b) 7.8 nm; (c) 17.2 nm.Scale bars are 50, 20, and 100 nm, respectively.
(a)
(b)
(c)


### 3.2. Phase Behavior of C11-C12, C11-C12/SBA-15 (3.8, 7.8, and 17.2 nm)

Phase behavior of C11-C12 bulk system was investigated using differential scanning calorimetry. DSC curves of the mixtures at mole fractions of dodecane, xC12=0-1, are shown in Figure 2. The signals in low-temperature range (dash lines) are enlarged in aid of observation. Solid-liquid phase diagram of C11-C12 system was determined by “shape factor method” [28] and shown in Figure 3, very close to the diagram in [22]. Different phases in the figure are designated by citing the results from the literature [22]. The phase diagram has shown two invariants, a peritectic and a eutectic point. The bulk system shows a relatively complicated behavior because of the special rotator phase in normal alkanes.Figure 2
DSC curves of C11-C12 bulk system at different mole fractions of C12(xC12). The low-temperature region (dash line) is enlarged for easy observation.Figure 3
Experimental solid-liquid phase diagram of bulk C11-C12 system. T represents triclinic crystal, R rotator phase.In Figure4, DSC curves show the melting behavior of C11-C12 system confined in SBA-15 (3.8 nm). Only one endothermic peak was observed for all the samples, including C11 which has solid-liquid (s-l) and solid-solid (s-s) phase transitions in the bulk. To make sure the phenomena, the samples had been cooled down about 50 K below the melting point of each peak; however, no more thermal anomaly was found. Experimental phase diagram was established for C11-C12/SBA-15 (3.8 nm) system on basis of the onset point of each peak as shown in Figure 5. The s-l boundary is a straight line, where melting points are proportional to xC12. This is a system of miscible both in solid and liquid state according to classification of phase diagrams of bulk system. The behavior is very different with the bulk system.Figure 4
DSC curves of C11-C12 system confined in SBA-15 (pore diameter 3.8 nm) as a function of mole fractions of C12(xC12).Figure 5
Experimental phase diagram of C11-C12 system confined in SBA-15 (3.8 nm).When the pore size of SBA-15 comes to 7.8 nm, the alkane adsorbed also displays a single endothermic melting peak on DSC curve scanned from very low temperature at mole fractions ofxC12 as shown in Figure 6. By onset points of these peaks, the experimental phase diagram of C11-C12/SBA-15 system was decided as in Figure 7. The diagram comprises of a curved line and also means a system of completely miscible both in solid and liquid state according to classification of phase diagrams of bulk system too.Figure 6
DSC curves of C11-C12 system confined in SBA-15 (7.8 nm) as a function of mole fractions of C12(xC12).Figure 7
Experimental phase diagram of C11-C12 system confined in SBA-15 (7.8 nm).As the pore diameter reaches 17.2 nm, the alkanes inside channel of SBA-15 show some changing in melting behavior as shown in Figure8. All the samples display melting peaks in higher-temperature region. In the low temperature range, C11 and the mixtures at xC12=0.1–0.4 present solid-solid phase transitions, indicated as dash line next to the complete curve. Experimental phase diagram of the confined mixtures was determined on connection of onset points of the s-l and s-s transition peaks and shown in Figure 9. Perhaps, the absence in s-s boundary over the range xC12=0.5–1 might result from incomplete crystallization or supercooling of the alkane mixtures.Figure 8
DSC curves of C11-C12 system confined in SBA-15 (17.2 nm) as a function of mole fractions of xC12. From 200 to 230 K, the solid-solid transitions are enlarged as the dash lines, next to the main DSC curves at xC12=0–0.4 in aid of observation.Figure 9
Experimental phase diagram of C11-C12 system confined in SBA-15 (17.2 nm). ∘ experimental melting points at mole fractions xC12; • solid-solid transition temperatures.


### 3.3. Comparison of the Phase Behavior of C11-C12/SBA-15 (3.8, 7.8, and 17.2 nm)

In preparation of samples, the volume of alkanes was added nearly the same as pore volume of SBA-15. In analysis, no thermal anomalies from the bulk, pure alkanes, or the mixtures were observed on heat flow signals. It means that the alkanes should be adsorbed into pores of SBA-15 with no extra liquids left. In this case, interference of bulk alkane was avoided, and DSC signals reflected only properties of pore liquids. In addition, influence of equilibrium time and temperature on preparation of samples had been examined. There almost no difference in the melting points of samples equilibrated at room temperature to 323 K during a period about 1–6 hours. It indicates that the alkanes entered pores of SBA-15 by wetting. In this condition, no discrimination in adsorption of C11 and C12 molecules exists inside pores of SBA-15 [29, 30], considering that the micropore volume takes a small portion in total pore volume. Accordingly, DSC analysis could provide correct information of C11-C12 binary mixtures in present experiments.From Figures5, 7, and 9, the development of phase diagram can be observed among the systems C11-C12/SBA-15 (3.8, 7.8, and 17.2 nm). With the increasing of the size, phase diagram of the confined system grows from a straight line (3.8 nm, s-l), a curve (7.8 nm, s-l) to a loop line (17.2 nm, s-l plus s-s). In the bulk scale, it would attain the complicated phase diagram showing all the specific characteristics of rotator phase in the system [22].It is known that the cross-section of pure normal alkanes (σ) is around 0.49 nm in the most stable configuration [20]. Therefore, SBA-15 with pore diameter (3.8, 7.8, and 17.2) nm has a channel of about 8σ, 16σ, and 35σ in radial direction of the pore. Perhaps, alkane molecules in pores of 3.8 and 7.8 nm would partially crystallize on cooling under the criterion of 10 or 20σ for complete crystallization [3, 6, 7].Meanwhile, the alkane within pore of a size 17.2 nm could crystallize completely in consideration of a size of 20 nm for complete crystallization [6]. It is in this difference in the size of alkane liquids that might lead to distinct phase behavior among the above three systems.According to the DSC curves of C11-C12/SBA-15 (17.2 nm), the size of 17.2 nm may close to a threshold value that confined mixtures start to possess solid-solid transition property. In this case, the DSC curve shows weak but definite endothermic signal in the low-temperature region. A larger pore size should make the s-s transition more prominent. That would be the interest in next stage.


### 3.4. Melting Points of C11, C12 and the Mixtures as a Function of Pore Size

In Figure10, the melting points (Tm,d) are displayed for pure C11, C12 and the mixtures at xC12=0-1 confined in SBA-15 of pore diameter d = (3.8, 7.8, and 17.2) nm, respectively.Figure 10
Melting points of pure (C11; C12), C11-C12 system (xC12=0-1) confined in SBA-15 with pore diameter d = (3.8, 7.8 and 17.2) nm; ■ C11; • C12; mole fraction xC12: □ (0.1); ▴ (0.2); ▾ (0.3); ◆ (0.4); ⊲ (0.5); ⊳ (0.6); ∘ (0.7); ☆ (0.8); Δ (0.9).In the experiments, melting points of C11, C12 confined in SBA-15 (3.8, 7.8 and 17.2 nm) are depressed compared with the bulk. This may be understood qualitatively on basis of previous works by Gubbins and coworkers (1) [6, 31, 32] and a modified G-T equation described in [11] as follows:
(1)Ttr*≈f(H*,α),(2)ΔTm=Tm,bulk-Tm,r=2VTm,bulk(γcw-γlw)rΔHm,
where in (1) transition temperature (freezing/melting) Ttr* is a function of the reduced pore size H*= H/σ (H is the pore width, and σ is the diameter of pore liquid molecule) and the ratio of the wall/fluid (wf) to the fluid/fluid (ff) interactions, α ~ Cρwεwf/εff, where ρw and ε are the density of wall atoms and the potential well depth, respectively, and C is a constant depending on the wall geometry; in (2) Tm,bulk is bulk melting point; Tm,r is melting point of particle with radius r; Vm represents the crystal molar volume; γcw and γlw are crystal-wall and liquid-wall interaction energy; ΔHm the enthalpy of fusion of the crystal. As it is known, SBA-15 is comprised of silica tetrahedrons with nearly neutral or weakly polar pore wall because of surface hydroxyl groups. When nonpolar alkane molecules are adsorbed, an intermediate strength interaction produces between them. In this case, the value of α in (1) is less than 1, that is, α < 1, which results in a depression of freezing/melting temperatures for C11, C12 confined in SBA-15, [31, 32]. This also means that a relation exists, γcw>γlw, indicating in a depletion of transition temperatures either according to (2). From Figure 10, Tm,d of C11, C12 shows a good linear relation with 1/dover the size range from 3.8 to 17.2 nm, Tm,d∝1/d. Moreover, at each size C11 melts in a lower temperature than C12. This reflects the influence of Tm,bulk, ΔHm and surface tension of the two alkanes besides the pore size.It is clearly that the G-T equation cannot be used to predict phase behavior ofC11-C12 binary system in confinement. However, in the scale of 3.8 nm to 17.2 nm in Figure 10, Tm,d of the mixtures also shows a good linear relation with 1/d, Tm,d∝1/d. The straight fitting lines for Tm,d of the mixtures do not overlap and are almost parallel to each other. It seems that melting behavior of the mixtures can be compared to the pure alkane qualitatively under confinement.In the size of 3.8 to 17.2 nm, theTm,d of C11, C12 and the mixtures (xC12 = 0.1–0.9) are fitted as a function of xC12 by the following equation:
(3)Tm,d(C11,C12)=C1-C2d,
where the pore diameter d of SBA-15 is (3.8 to 17.2) nm; dimension of C1 and C2 is K nm−1. As for C12, C1=254.23; C2=99.11; R≈0.9984; for C11, C1=243.83; C2=108.70; R≈0.9999. The C1 and C2 values at each mole fractions are listed in Table 1.Table 1
Coefficients (C1, C2)a in expression for melting points of C11, C12 and the mixtures(xC12) with pore diameter (d) of 3.8~17.2, and correlation coefficients (Rb).
x
C12
C
1
C
2
0 (C11)
243.83
108.70
1 (C12)
254.23
99.11
0.100
243.98
103.52
0.193
244.43
99.93
0.301
245.35
98.89
0.410
245.76
94.66
0.503
246.69
93.67
0.604
247.11
91.02
0.699
248.77
92.63
0.800
250.92
96.26
0.900
252.19
95.98
aMelting point and pore diameter d is fitted as Tm,d = C1 − C2/d.
bCorrelation coefficients R = 0.9984~1.0000.


### 3.5. Melting Points of C11-C12/SBA-15 (3.8, 7.8 and 17.2 nm) as a Function of Composition

The experimental melting temperatures of C11-C12/SBA-15 (3.8, 7.8 and 17.2 nm) systems have been fitted as the following expressions: (a)
C11-C12/SBA-15 (3.8 nm) system: Tm,d=12.8777x+215.43, R=0.9998,(b)
C11-C12/SBA-15 (7.8 nm) system: Tm,d=9.3898x2+1.6199x+229.83, R=0.9990, and(c)
C11-C12/SBA-15 (17.2 nm) system: Tm,d=9.3495x2 + 1.7128x + 237.76, R = 0.9952,where Tm,d represents melting point of the mixture (x); x is the mole fraction of C12. On basis of these linear or polynomial relations, melting points of a certain composition of C11-C12 system can be predicted at the three-pore size of 3.8, 7.8 and 17.2 nm.


## 3.1. TEM Characterization and Pore Size of SBA-15

Three kinds of ordered mesoporous SBA-15 were synthesized with pore diameters of 3.8, 7.8, and 17.2 nm, respectively, determined by BJH method on basis of adsorption branches of isotherms [16]. Pore volume of the three SBA-15 (3.8, 7.8, and 17.2 nm) is 0.3, 1.0 and 1.4 cm3 g-1, respectively; micropore volume is determined to be ~0, 0.05 and 0.02 cm3 g-1 by V-t methods, respectively. As seen in Figure 1, SBA-15 presents parallel channels on TEM images and cylindrical mesopores with two-dimensional hexagonal arrangements (a, b, and c). The pores show a uniform size under TEM imaging. After adsorbed in the channel of SBA-15, the alkanes would form one-dimensional liquid when the pore is nearly filled. The ordered mesopores in SBA-15 would make the DSC signals sharp. For further study, the regular pore structure should be advantageous when the pore wall of SBA-15 is modified.TEM images of SBA-15: (a) pore diameter 3.8 nm; (b) 7.8 nm; (c) 17.2 nm.Scale bars are 50, 20, and 100 nm, respectively.
(a)
(b)
(c)


## 3.2. Phase Behavior of C11-C12, C11-C12/SBA-15 (3.8, 7.8, and 17.2 nm)

Phase behavior of C11-C12 bulk system was investigated using differential scanning calorimetry. DSC curves of the mixtures at mole fractions of dodecane, xC12=0-1, are shown in Figure 2. The signals in low-temperature range (dash lines) are enlarged in aid of observation. Solid-liquid phase diagram of C11-C12 system was determined by “shape factor method” [28] and shown in Figure 3, very close to the diagram in [22]. Different phases in the figure are designated by citing the results from the literature [22]. The phase diagram has shown two invariants, a peritectic and a eutectic point. The bulk system shows a relatively complicated behavior because of the special rotator phase in normal alkanes.Figure 2
DSC curves of C11-C12 bulk system at different mole fractions of C12(xC12). The low-temperature region (dash line) is enlarged for easy observation.Figure 3
Experimental solid-liquid phase diagram of bulk C11-C12 system. T represents triclinic crystal, R rotator phase.In Figure4, DSC curves show the melting behavior of C11-C12 system confined in SBA-15 (3.8 nm). Only one endothermic peak was observed for all the samples, including C11 which has solid-liquid (s-l) and solid-solid (s-s) phase transitions in the bulk. To make sure the phenomena, the samples had been cooled down about 50 K below the melting point of each peak; however, no more thermal anomaly was found. Experimental phase diagram was established for C11-C12/SBA-15 (3.8 nm) system on basis of the onset point of each peak as shown in Figure 5. The s-l boundary is a straight line, where melting points are proportional to xC12. This is a system of miscible both in solid and liquid state according to classification of phase diagrams of bulk system. The behavior is very different with the bulk system.Figure 4
DSC curves of C11-C12 system confined in SBA-15 (pore diameter 3.8 nm) as a function of mole fractions of C12(xC12).Figure 5
Experimental phase diagram of C11-C12 system confined in SBA-15 (3.8 nm).When the pore size of SBA-15 comes to 7.8 nm, the alkane adsorbed also displays a single endothermic melting peak on DSC curve scanned from very low temperature at mole fractions ofxC12 as shown in Figure 6. By onset points of these peaks, the experimental phase diagram of C11-C12/SBA-15 system was decided as in Figure 7. The diagram comprises of a curved line and also means a system of completely miscible both in solid and liquid state according to classification of phase diagrams of bulk system too.Figure 6
DSC curves of C11-C12 system confined in SBA-15 (7.8 nm) as a function of mole fractions of C12(xC12).Figure 7
Experimental phase diagram of C11-C12 system confined in SBA-15 (7.8 nm).As the pore diameter reaches 17.2 nm, the alkanes inside channel of SBA-15 show some changing in melting behavior as shown in Figure8. All the samples display melting peaks in higher-temperature region. In the low temperature range, C11 and the mixtures at xC12=0.1–0.4 present solid-solid phase transitions, indicated as dash line next to the complete curve. Experimental phase diagram of the confined mixtures was determined on connection of onset points of the s-l and s-s transition peaks and shown in Figure 9. Perhaps, the absence in s-s boundary over the range xC12=0.5–1 might result from incomplete crystallization or supercooling of the alkane mixtures.Figure 8
DSC curves of C11-C12 system confined in SBA-15 (17.2 nm) as a function of mole fractions of xC12. From 200 to 230 K, the solid-solid transitions are enlarged as the dash lines, next to the main DSC curves at xC12=0–0.4 in aid of observation.Figure 9
Experimental phase diagram of C11-C12 system confined in SBA-15 (17.2 nm). ∘ experimental melting points at mole fractions xC12; • solid-solid transition temperatures.


## 3.3. Comparison of the Phase Behavior of C11-C12/SBA-15 (3.8, 7.8, and 17.2 nm)

In preparation of samples, the volume of alkanes was added nearly the same as pore volume of SBA-15. In analysis, no thermal anomalies from the bulk, pure alkanes, or the mixtures were observed on heat flow signals. It means that the alkanes should be adsorbed into pores of SBA-15 with no extra liquids left. In this case, interference of bulk alkane was avoided, and DSC signals reflected only properties of pore liquids. In addition, influence of equilibrium time and temperature on preparation of samples had been examined. There almost no difference in the melting points of samples equilibrated at room temperature to 323 K during a period about 1–6 hours. It indicates that the alkanes entered pores of SBA-15 by wetting. In this condition, no discrimination in adsorption of C11 and C12 molecules exists inside pores of SBA-15 [29, 30], considering that the micropore volume takes a small portion in total pore volume. Accordingly, DSC analysis could provide correct information of C11-C12 binary mixtures in present experiments.From Figures5, 7, and 9, the development of phase diagram can be observed among the systems C11-C12/SBA-15 (3.8, 7.8, and 17.2 nm). With the increasing of the size, phase diagram of the confined system grows from a straight line (3.8 nm, s-l), a curve (7.8 nm, s-l) to a loop line (17.2 nm, s-l plus s-s). In the bulk scale, it would attain the complicated phase diagram showing all the specific characteristics of rotator phase in the system [22].It is known that the cross-section of pure normal alkanes (σ) is around 0.49 nm in the most stable configuration [20]. Therefore, SBA-15 with pore diameter (3.8, 7.8, and 17.2) nm has a channel of about 8σ, 16σ, and 35σ in radial direction of the pore. Perhaps, alkane molecules in pores of 3.8 and 7.8 nm would partially crystallize on cooling under the criterion of 10 or 20σ for complete crystallization [3, 6, 7].Meanwhile, the alkane within pore of a size 17.2 nm could crystallize completely in consideration of a size of 20 nm for complete crystallization [6]. It is in this difference in the size of alkane liquids that might lead to distinct phase behavior among the above three systems.According to the DSC curves of C11-C12/SBA-15 (17.2 nm), the size of 17.2 nm may close to a threshold value that confined mixtures start to possess solid-solid transition property. In this case, the DSC curve shows weak but definite endothermic signal in the low-temperature region. A larger pore size should make the s-s transition more prominent. That would be the interest in next stage.


## 3.4. Melting Points of C11, C12 and the Mixtures as a Function of Pore Size

In Figure10, the melting points (Tm,d) are displayed for pure C11, C12 and the mixtures at xC12=0-1 confined in SBA-15 of pore diameter d = (3.8, 7.8, and 17.2) nm, respectively.Figure 10
Melting points of pure (C11; C12), C11-C12 system (xC12=0-1) confined in SBA-15 with pore diameter d = (3.8, 7.8 and 17.2) nm; ■ C11; • C12; mole fraction xC12: □ (0.1); ▴ (0.2); ▾ (0.3); ◆ (0.4); ⊲ (0.5); ⊳ (0.6); ∘ (0.7); ☆ (0.8); Δ (0.9).In the experiments, melting points of C11, C12 confined in SBA-15 (3.8, 7.8 and 17.2 nm) are depressed compared with the bulk. This may be understood qualitatively on basis of previous works by Gubbins and coworkers (1) [6, 31, 32] and a modified G-T equation described in [11] as follows:
(1)Ttr*≈f(H*,α),(2)ΔTm=Tm,bulk-Tm,r=2VTm,bulk(γcw-γlw)rΔHm,
where in (1) transition temperature (freezing/melting) Ttr* is a function of the reduced pore size H*= H/σ (H is the pore width, and σ is the diameter of pore liquid molecule) and the ratio of the wall/fluid (wf) to the fluid/fluid (ff) interactions, α ~ Cρwεwf/εff, where ρw and ε are the density of wall atoms and the potential well depth, respectively, and C is a constant depending on the wall geometry; in (2) Tm,bulk is bulk melting point; Tm,r is melting point of particle with radius r; Vm represents the crystal molar volume; γcw and γlw are crystal-wall and liquid-wall interaction energy; ΔHm the enthalpy of fusion of the crystal. As it is known, SBA-15 is comprised of silica tetrahedrons with nearly neutral or weakly polar pore wall because of surface hydroxyl groups. When nonpolar alkane molecules are adsorbed, an intermediate strength interaction produces between them. In this case, the value of α in (1) is less than 1, that is, α < 1, which results in a depression of freezing/melting temperatures for C11, C12 confined in SBA-15, [31, 32]. This also means that a relation exists, γcw>γlw, indicating in a depletion of transition temperatures either according to (2). From Figure 10, Tm,d of C11, C12 shows a good linear relation with 1/dover the size range from 3.8 to 17.2 nm, Tm,d∝1/d. Moreover, at each size C11 melts in a lower temperature than C12. This reflects the influence of Tm,bulk, ΔHm and surface tension of the two alkanes besides the pore size.It is clearly that the G-T equation cannot be used to predict phase behavior ofC11-C12 binary system in confinement. However, in the scale of 3.8 nm to 17.2 nm in Figure 10, Tm,d of the mixtures also shows a good linear relation with 1/d, Tm,d∝1/d. The straight fitting lines for Tm,d of the mixtures do not overlap and are almost parallel to each other. It seems that melting behavior of the mixtures can be compared to the pure alkane qualitatively under confinement.In the size of 3.8 to 17.2 nm, theTm,d of C11, C12 and the mixtures (xC12 = 0.1–0.9) are fitted as a function of xC12 by the following equation:
(3)Tm,d(C11,C12)=C1-C2d,
where the pore diameter d of SBA-15 is (3.8 to 17.2) nm; dimension of C1 and C2 is K nm−1. As for C12, C1=254.23; C2=99.11; R≈0.9984; for C11, C1=243.83; C2=108.70; R≈0.9999. The C1 and C2 values at each mole fractions are listed in Table 1.Table 1
Coefficients (C1, C2)a in expression for melting points of C11, C12 and the mixtures(xC12) with pore diameter (d) of 3.8~17.2, and correlation coefficients (Rb).
x
C12
C
1
C
2
0 (C11)
243.83
108.70
1 (C12)
254.23
99.11
0.100
243.98
103.52
0.193
244.43
99.93
0.301
245.35
98.89
0.410
245.76
94.66
0.503
246.69
93.67
0.604
247.11
91.02
0.699
248.77
92.63
0.800
250.92
96.26
0.900
252.19
95.98
aMelting point and pore diameter d is fitted as Tm,d = C1 − C2/d.
bCorrelation coefficients R = 0.9984~1.0000.


## 3.5. Melting Points of C11-C12/SBA-15 (3.8, 7.8 and 17.2 nm) as a Function of Composition

The experimental melting temperatures of C11-C12/SBA-15 (3.8, 7.8 and 17.2 nm) systems have been fitted as the following expressions: (a)
C11-C12/SBA-15 (3.8 nm) system: Tm,d=12.8777x+215.43, R=0.9998,(b)
C11-C12/SBA-15 (7.8 nm) system: Tm,d=9.3898x2+1.6199x+229.83, R=0.9990, and(c)
C11-C12/SBA-15 (17.2 nm) system: Tm,d=9.3495x2 + 1.7128x + 237.76, R = 0.9952,where Tm,d represents melting point of the mixture (x); x is the mole fraction of C12. On basis of these linear or polynomial relations, melting points of a certain composition of C11-C12 system can be predicted at the three-pore size of 3.8, 7.8 and 17.2 nm.


## 4. Conclusion

Physical size has a great influence on phase behavior of C11-C12 binary mixtures inside one-dimensional channels of SBA-15. In the scale of 3.8 to 17.2 nm, the solid-liquid phase diagram grows from a straight line (3.8 nm), a curve line (7.8 nm) to a loop line comprising of a curved solid-liquid and solid-solid boundary (17.2 nm). Melting temperatures of the mixtures with the three systems are depressed in a similar way with the pure C11, C12, which vary in consistent with mole fraction and pore diameter. The different behavior shows the dependence on the size of alkane.



---

*Source: 476236-2012-09-04.xml*