Mesoscopic Phase Behavior of TridecaneâTetradecane Mixtures

Article pubs.acs.org/JPCC

Mesoscopic Phase Behavior of Tridecane−Tetradecane Mixtures Confined in Porous Materials: Effects of Pore Size and Pore Geometry Xiao Yan, Tong Bo Wang, Chun Feng Gao, and Xiao Zheng Lan* College of Chemistry and Materials Science, Shandong Agricultural University, Tai’an 271018, Shandong, China ABSTRACT: Phase behaviors of tridecane−tetradecane (nC13H28−C14H30, C13−C14) system in bulk, and confined in SBA-15 and controlled porous glass (CPG) are investigated using differential scanning calorimetry and temperaturedependent X-ray diffraction. Bulk C13−C14 mixtures exhibit a complicated behavior featuring a special rotator phase RI. Adsorbed in SBA-15 with pore diameters (d) of 3.8 and 7.8 nm, the binary mixtures display a melting boundary of a straight line and a curve, respectively. Within SBA-15 (17.2 nm) and CPG (8.1, 31.8, 46.4, and 300 nm), the mixtures show a similar phase behavior to the bulk, especially in the larger pore CPG than 30 nm. Under confinement, the phase behavior of C13− C14 mixtures varies with the pore size as well as the temperature and composition. XRD analysis reveals that the solid alkane molecules take effectively the 2D closed-packed arrangements inside pores of diameters less than 20 nm. In the large pore CPG (d > 30 nm), the alkane molecules regain lamellar ordering in solid states. Pore geometries of SBA-15 and CPG, one-dimensional channels vs three-dimensional connected pores, may also result in much different influence on the phase behavior of the confined mixtures.

1. INTRODUCTION The effect of confinement on properties of fluids has been extensively investigated in the past decades since Jackson and McKenna’s first work published in 1990.1−3 The studies have found the unique thermodynamic and kinetic properties of liquids confined in porous media such as CPG, SBA-15, and MCM-41.4−11 For water and small molecule organic liquids, the melting and freezing points are depressed in pores with nanometer scale, for example, less than 20 nm.2,5,6,12−18 Melting points may also be elevated when some organic or ionic liquids are adsorbed in carbon nanotubes, mesoporous silica oxide, and on the surface of graphite or mica.6,19,20 On the basis of these new physical phenomena, the Gibbs−Thomson equation is modified to express the relation of melting point and particle size.4−6 Moreover, Gubbins and co-workers have pointed out the transition temperature of a pore solid is driven by the reduced pore width and the ratio of wall−liquid to liquid−liquid interactions, in consideration of the influence of physical size, the pore structure, and reduced dimensionality.21−23 The previous work enriches the understanding of the melting and freezing behaviors of the pure fluids under confinement. However, there are few studies on phase behaviors of confined binary mixtures. It has been reported that CaCl2− H2O mixtures inside silica gel pores (15 nm) show the same eutectic system with the bulk, while the phase diagram is shifted down by 10−30 K.24 A similar phenomenon was found in C6H5Br−CCl4 mixtures adsorbed in CPG (7.5 nm).23 Recently, phase diagrams have been investigated for binary alkane mixtures n-C12H26−C14H30, n-C14H30−C16H34, and n-C11H24− C12H26 confined in SBA-15 (d < 20 nm).25−27 The results of the DSC scans show that the alkane mixtures exhibit only one © 2013 American Chemical Society

melting peak when the pore size is smaller than 9 nm, and in pores larger than 17.2 nm, weak solid−solid (s−s) transitions appear in low temperature range besides the fusion of mixed alkanes. The structures of the pore solids are investigated using XRD, NMR, and ESR, etc., for pure material and the mixtures as well.6,15,16,28,29 When adsorbed in MCM-41, SBA-15, C/SBA15 (covered with carbon film), and CMK3, pure water freezes into its ordinary hexagonal crystals with a lot of defects, which is only slightly affected by pore structure and modification of the pore wall.14−16,28 The alkane molecules in MCM-41 are stacked side by side with the long axes parallel to the pore longitude.30 In Vycor glass (10 nm), solid normal alkane molecules (C12, C14, C16, and C19) are found in an effectively 2D close-packed arrangements with random z coordinates.31−33 Among them, the coexistence of rotator phase RI and stable triclinic crystal of pore C16 in CPG reveals a radial distribution of molecules. The quenching or weakening of lamellar ordering is also observed in pure or mixed microencapsulated alkanes (C17−C20) with particle sizes of 2−5 μm.34−37 Naphthalene and fatty acid or alcohols confined in CPG have the same crystal structures as the bulk.17,38 Generally, the small molecule liquids inside pores tend to crystallize into the same structures as the bulk, while the chain molecules, for example, pure normal alkanes, may display multiphase under confinement. Until now, the structural information is still insufficient for better understanding of the new phase behavior of the pore solids. Received: April 23, 2013 Revised: June 23, 2013 Published: July 25, 2013 17245

dx.doi.org/10.1021/jp4040198 | J. Phys. Chem. C 2013, 117, 17245−17255

The Journal of Physical Chemistry C

Article

Normal alkanes are widely used in many fields, such as the petroleum industry, energy storage materials, and lubricants.35,36 In theoretical study, they are suitable models in the research of complex crystallization behavior of polymer materials, surfactants, and lipids relating to alkane chain strutures.36,37,39,40 In their family, tridecane and tetradecane have medium size chains, which allows them crystallize into stable orthorhombic (O13) and triclinic (T14) structures, respectively, at low temperatures.41,42 As a special feature of C13, an equilibrium rotator phase RI exists between the stable crystal form and isotropic liquid, which has an orthorhombic face-centered Bravais lattice from the stacking of AB bilayers. RI phase is a metastable modification that has end defects, such as end gauche, in which the end groups rotate around their long axes to a limited angle with short-range correlations.40,43−47 C13−C14 mixtures belong to an odd−even numbered system with multiple phases in solid states.48−50 RI solid solution can be stabilized by mixing, which covers the composition range of xC14 = 0−0.7. Mesoporous materials SBA-15 and CPG are often chosen as nanoconfinement media with narrow pore size distributions but different pore geometry. SBA-15 possesses ordered cylindrical channels aligned in two-dimensional hexagon, connected by micropores. The simple pore geometry and tunable pore size in the range of ca. (3.8 to 20) nm makes it a good matrix for a well-defined (quasi) one-dimensional liquid.51 CPG has disordered three-dimensional connected pores with sizes from (∼7.5 to 300) nm, which is suitable for the study of a wide mesoscopic scope of pore materials.6,7 In this work, we report an investigation on the phase behaviors of C13−C14 binary mixtures in the bulk and confined in SBA-15 (3.8, 7.8, and 17.2 nm) and CPG (8.1, 31.8, 46.4, and 300 nm). Phase diagrams of these systems are established on the basis of DSC analysis, which vary with temperature, composition, and pore size. Some representative solid phases are measured using temperature-dependent powder X-ray diffractions to characterize the structures of the pore alkanes. The combined DSC and XRD techniques present an efficient way to understand the new phase behaviors of the confined alkane mixtures.

Table 1. Specifications of Controlled Pore Glass As Provided by the Manufacturer product name

mean pore diameter (nm)

pore size distribution (%)

specific pore volume (cm3/g)

specific surface area (m2/g)

CPG75 CPG300 CPG500 CPG3000

8.1 31.8 46.4 300

9 4.0 3 6

0.49 0.97 1.31 1.08

>120 70.5 64 10

were measured at 77 K using an Autosorb-1 system (Quantachrome Instruments) from nitrogen adsorption branches, which were described in details elsewhere.26,27 The as-synthesized SBA-15 powder shows ordered cylindrical pores in hexagonal arrangements under transmission electronic microscopy imaging on a JEM-1400 (JEOL) operated at 120 kV.26,27 DSC and XRD Measurements. Samples of SBA-15 or CPG with adsorbed alkanes were prepared by the following procedure. SBA-15 or CPG powder of a mass of about 10 mg was put into a glass tube and outgassed at 423 K under a vacuum of 10−1 Pa for 2 h. A certain amount of the alkane liquid was transferred into the glass tube by a clean glass capillary under protection of dried nitrogen atmosphere in a plastic bag. The alkane introduced occupied 95−100% percent of pore volume of SAB-15 or CPG for avoiding interference of excess liquid with the pores. At last, the glass tube was sealed on a Bunsen burner and equilibrated for 2 h at room temperatures. Thermal analysis of the samples was performed on a DSC Q10 (TA Instruments) under a high purity nitrogen atmosphere. In a typical procedure, the sample was cooled first at a rate of (2 to 5) K min−1 from room temperature down to, for example, 180−220 K; then a thermogram was recorded in the heating process with a scanning rate of 5 K min−1. The temperature scale was calibrated using high purity adamantine, water, and indium. In most cases, the transition temperatures were reproducible to within 0.5 K. Temperature-dependent X-ray diffraction (XRD) experiments were carried out on a Philips X’Pert Pro MPD type diffractometer in the same temperature range as that for the DSC measurement of the samples. The diffractometer uses Cu Kα radiation (1.54 Å) at a power of 40 mA/40 kV and scans in the rotating angle 2θ = 5−40°. The sample was placed in an aluminum vessel 2 × 1.6 × 1 mm3. Diffraction patterns of the samples were recorded in a series of temperature intervals during the heating process. Before each measurement, the sample was equilibrated about 3−5 min. The cooling and heating rates of the samples were 5 K min−1 in the case of SBA15 (3.8, 7.8 nm) and CPG (8.1 nm), and 5−10 K min−1 for the bulk solution and in pores of larger than 17 nm.

2. EXPERIMENTAL SECTION Materials. The alkane tridecane and tetradecane, with a purity in mass fractions larger than 0.98, used in this study were purchased from Aladdin Reagents Co. The starting materials used in preparation of SBA-15 are tetraethyl orthosilicate (TEOS, 0.999, Aladdin Reagents Co.), triblock copolymer Pluronic P123 (Sigma), and 1,3,5-triisopropylbenzene (TIPB, 0.97, Xiya Reagents Co.). All the chemicals were used as received. Four kinds of controlled pore glass (CPG, Millipore) were used as confinement media with nominal pore sizes from (7.5 to 300) nm. The specifications of the CPG as provided by the manufacturer are listed in Table 1. The CPG powder was cleaned with concentrated nitric acid with a method recommended by the supplier. The treatment was reported to result in negligible variation in pore diameter and distributions.1 SBA-15 with pore sizes of 3.8, 7.8, and 17.2 nm was synthesized as the reference methods, where P123 was used as a template for pore formation and TIPB as a micelle expander for the large pore SBA-15 (17.2 nm).26,27,52,53 The pore diameter, pore volume, and specific surface area of the SBA-15

3. RESULTS AND DISCUSSION 3.1. DSC Analysis and Phase Diagrams of the Bulk and Confined C13−C14 Mixtures. In the experiments, eight systems are analyzed with the DSC method: C13−C14 bulk mixtures, C13−C14/SBA-15 (3.8, 7.8, and 17.2 nm), and C13− C14/CPG (8.1, 31.8, 46.4, and 300 nm). For clarity, some representative DSC curves are displayed in Figure 1. Obviously, the alkanes show first-order solid−liquid (s−l) and solid−solid phase transitions as a function of the temperature, composition, and pore size. The thermal responses of the transitions tend to be weak in smaller pores but are strong enough even in the very 17246



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Figure 1. DSC curves recorded in the heating process of C13 (left column), C14 (right column), and the mixture (xC14 = 0.5, middle column) in the bulk, and confined in SBA-15 (3.8, 7.8, and 17.2 nm) and CPG (8.1, 31.8, 46.4, and 300 nm). The dotted lines near the main curves are enlarged in aid of observation.

Figure 2. Solid−liquid phase diagrams of C13−C14 system in the bulk (a) and confined in SBA-15 of pore diameters of 3.8 (b), 7.8 (c), and 17.2 nm (d), respectively. The phases are designated with reference to literature and XRD measurements in section 3.2.

small pores of SBA-15 (3.8 nm). Only the s−s transitions in SBA-15 (17.2 nm) and CPG (8.1 nm) are a bit weak. It seems

the alkanes can be easily crystallized in pores of SBA-15 and CPG to show clear thermal anomalies on heating.6,42,49 As is 17247



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Figure 3. Solid−liquid phase diagrams of C13−C14 system confined in CPG with pore diameters of 8.1 (a), 31.8 (b), 46.4 (c), and 300 nm (d), respectively. The phases are designated with reference to the bulk and XRD analysis in section 3.2.

known, crystallization of liquids can be significantly affected by the cooling process in the bulk and may be hindered largely under confinement.4−6,9−11 Probably, the crystallization of the pore alkanes can be favored by the uniform molecular cross sections and fairly strong attractions from molecular chains in lateral packings. The pore molecules are thus prone to be parallel with each other in energetically stable forms upon cooling and show the clear phase transformations in DSC heating scans. To obtain the equilibrium phase diagram, DSC and XRD measurements of the samples are tracked on heating. It is found the s−l and s−s transition temperatures of DSC scans of the bulk or confined alkanes are well reproduced when cooled at a rate of (2 to 5) K min−1 before analysis. Phase diagrams of these systems are established on the basis of the DSC analysis, as shown in Figures 2 and 3. The phase diagram of the bulk mixtures (Figure 2a) is determined according to the shape factor method,54,55 which is comparable to the previous results.42,48,49 In doing this, two basic “shape factors” need to be calculated first from the difference of melting peak temperature to the intersection points from both sides of the peak extrapolated to the baseline for each pure component. The liquidus line is thus deduced by the two shape factors. The solid boundary line in the diagram is drawn among onset points of DSC curves of the related s−s phase transitions. The

multiple solid phases of the bulk system are assigned in reference to previous work and XRD measurements of some representative components in section 3.2, which will be discussed later. The specific rotator phase RI manifests itself in the phase diagram as in the other binary normal alkanes.43,45,57 C13−C14 mixtures confined in SBA-15 (3.8 and 7.8 nm) shows only one melting peak in each component during DSC heating scans. The melting boundary is obtained by fitting onset points of the endothermic peaks, which turns out to be a straight and a slightly curved line for the two systems, as depicted in Figure 2b,c. In them, the melting point increases with an average step about 1 K in mole fraction interval ΔxC14 = 0.1. In the classification of the phase diagram for the bulk, this simple melting behavior should correspond to a system of complete miscibility in the two components. The mixtures in the pores of SBA-15 (17.2 nm) show not only s−l but s−s phase transitions in all the compositions. The phase diagram of this system is decided from onset points of the transitions as shown in Figure 2d, where the dotted line is estimated from XRD analysis afterward. Under confinement of the SBA-15, the phase diagram of the mixtures shrinks to a single melting boundary in very small pores (d < 8 nm), whereas it gains some outline as the bulk in SBA-15 (17.2 nm). The phenomena are 17248



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Table 2. The Solid−liquid Phase Transition Temperatures (Ts‑l)*, Eutectic (Teu) and Peritectic (Tp) temperatures of C13−C14 Systems in the Bulk, and Confined in SBA-15 and CPG with Different Pore Sizes (d, nm) Ts‑l/K

Ts‑l/K

in SBA-15 (d, nm)

in CPG (d, nm)

mole fraction xC14

Ts‑l/K (bulk)

(3.8)

(7.8)

(17.2)

(8.1)

(31.8)

(46.4)

(300)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Teu Tp

267.5 267.3 267.6 268.6 270.3 270.4 270.8 272.0 275.0 276.8 278.4 239.6 270.5

239.0 240.3 240.8 241.9 242.8 244.1 244.6 245.6 246.5 247.8 248.5

251.0 251.6 252.3 253.2 254.0 255.1 255.9 257.0 257.8 258.9 260.2

259.1 259.0 259.9 260.3 261.1 262.0 262.7 263.6 264.6 266.0 266.3 223.7

259.6 259.8 260.4 260.8 261.3 262.4 263.3 264.1 265.4 265.9 267.5 223.3

266.2 266.5 266.9 267.2 267.8 268.6 269.2 270.3 271.2 273.9 276.2 237.8 270.7

267.2 267.2 267.4 268.2 268.7 269.4 270.1 271.1 271.7 274.6 277.5 238.7 271.4

267.9 268.0 268.3 268.7 269.3 270.2 271.0 271.8 274.7 275.3 278.4 239.5 272.2

*

The mean deviations of the phase transition temperatures are mostly in the range of (0.1 to 0.2) K, except three data points in the range of (0.2 to 0.3) K.

similar with those observed in C12−C14, C14−C16, and C11−C12 mixtures confined in SBA-15.25−27 Inside pores of CPG (8.1, 31.8, 46.4, and 300 nm), the mixtures display not only melting but at least one s−s phase transition in each composition during DSC heating scans. Also, the s−s phase boundary is fitted from the onset points of the corresponding transitions as shown in Figure 3. In Figure 3b− d, the shape factor method is used to determine the liquidous lines, where the shape factors are calculated in the same way as defined in the bulk from C13 and C14 melting peaks at each pore size. The melting and eutectic temperature of the mixtures in CPG (8.1 nm) (Figure 3a) are in the temperature range of about 6−8 K, and 18−20 K lower than in CPG (31.8, 46.4, and 300 nm). All four diagrams resemble the bulk system, especially with the recovery of peritectoid in the large pores of CPG (31.8, 46.4, and 300 nm). In fact, the latter three systems appear at a very close temperature range as the bulk. As in the case of SBA-15, the mixtures in CPG also show the behaviors from the simple to complicated with the increasing pore size. Still, the solid phases at each system are ascribed to the analysis of DSC and XRD, and the bulk phase behaviors. The dotted lines are depicted with some uncertainty. 3.2. XRD Measurements on Representative Alkane Solid Phases. C13, C14, and some mixtures in the mentioned systems have been selected for temperature-dependent XRD measurements to confirm the crystalline structures of solid alkanes in different regions. The samples are listed as follows: (i) bulk C13, C14, and the mixtures of mole fraction xC14 = 0.05, 0.2, 0.5 and 0.8 (ii) C13−C14/SBA-15 (d): xC14 = 0.5 (3.8 nm), 0.5 (7.8 nm), 0.05, 0.2, and 0.8 (17.2 nm) (iii) C13−C14/CPG (d): xC14 = 0.2 and 0.8 (8.1 nm), 0.5 (31.8 nm), and 0.5 (46.4 nm) In Figure 4a,b, diffraction patterns of C13 and C14 are recorded at different temperatures during the heating process. C14 only shows reflections of its stable triclinic crystals (T14), shifting slightly to lower angles at higher temperatures (Figure 4b). The indexes of C14 diffractions are assigned to the peaks according to the JCPDS standard values in a JCPDS card no. 030-1955. In Figure 4a, the bottom two lines correspond to the

stable ordered form of C13, orthorhombic crystal O13, where the indexes of diffractions are described with cell parameters a = 4.97 Å, b = 7.48 Å, c = 36.85 Å of a space group Pbcm.41,56 In the upper two lines, the in-plane reflection of the rotator phase RI appears at 2θ = ∼21.13° and 23.45°, where the latter shifts obviously to lower angle with the increasing temperature. The reflection angles from (00l) planes in C13 and C14 are very close, for example, at 2θ = ∼9.6 and 14.4°, for the rotator and crystalline forms (or solid solutions described later) as well. This indicates the almost same thickness of an alkane molecular layer in these solid phases. It is reasonable since the tilted carbon chains of C14 are likely to give nearly the same length as the untitled C13 in projection to the z axis. Figure 4 panels c−f show diffraction patterns of the mixtures xC14 = 0.05, 0.2, 0.5, and 0.8, respectively, during the heating process. Just below the melting temperatures, the first three mixtures show the RI phases (solid solutions) with the in-plane reflection at angles 2θ = 21−21.2° and 23.2−23.9°, which agree well with those in C13. For the mixture xC14 = 0.8, the RI solid solution appears at the same angle range at lower temperatures while the solid solution with C14 packing comes up above the peritectic temperature. Here, the solid solutions with O13 or T14 packings are recognized in reference to reflection patterns of pure C13 or C14, which may have slight shift because of a minute change in unit cell parameters. The diffraction patterns of C13−C14 mixtures confined in SBA-15 (3.8, 7.8, and 17.2 nm) are displayed in Figure 5 in the heating processes. The solid mixture (xC14 = 0.5) in SBA-15 (3.8 nm) exhibits broad humps of the amorphous crystals (Figure 5a). As this sample has a melting peak in the DSC scan, the absence of reflections is probably due to too small sizes of the pore solid alkanes. In Figure 5b, the mixture (xC14 = 0.5) in SBA-15 (7.8 nm) shows a bit weak but clear reflections at angles 2θ = ∼19.16°, 21.05°, 23.44°, 24.59° and 25.72°, respectively, at 255.2 K, among which the second and third belong to the RI solid solution and the rest comes from solid solution with T14 packing. In other temperatures, diffraction peaks appear also at angles 2θ = ∼19−26°, with a little shift with the temperature. In view of the patterns, the in-plane ab lattice reflections of the RI phase come up at 2θ = ∼21−21.2° 17249



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Figure 4. Temperature-dependent XRD patterns of C13 (a), C14 (b), and C13−C14 mixtures of xC14 = 0.05 (c), 0.2 (d), 0.5 (e), 0.8 (f), respectively, recorded in the heating process. Rotator phase RI and low-temperature stable crystal T14 and O13 are noted to each diffraction line.

23.8°, with a little change with the temperatures and compositions. For the mixtures of xC14 = 0.2 and 0.8 in CPG (8.1 nm), the reflections emerge in the range of 2θ = ∼20−25°, still without obvious layering order from (00l) planes. In CPG (31.8 nm), the mixture (xC14 = 0.5) shows reflections from not only the in-plane ab lattice at 2θ = ∼20−25° but also the lamellar ordering, for example, the peaks at 2θ = 9−10° and 14−15° of the (00l) planes. In the case of CPG (46.4 nm), the mixture (xC14 = 0.5) displays almost all the reflections as those observed in the bulk of a same composition. The results suggest the recovery of the long-range ordering or the complete crystallization starting from a pore size of ca. 30 nm (CPG). One can expect some larger complete crystals of the solid alkane in CPG (300 nm). Indeed, the phase diagram of the mixtures resembles the bulk in every aspect as the pore diameter reaches near 300 nm.

and 23.3−23.6°, which is in the same range as the bulk. It should be noticed that reflections from the (00l) planes are not observed in the three pore sizes, indicating a quenching or heavily perturbation of layering order in these mixtures.31−33 Figure 5 panels c−e show the reflection patterns of three mixtures (xC14 = 0.05, 0.2, and 0.8) confined in SBA-15 (17.2 nm), which focus mainly in the angle range of 2θ = ∼19−26°. At low temperatures, some weak reflections come out at angles 2θ = 34−36°, probably indicating somewhat layered ordering. The RI phase in these mixtures reflects at 2θ = ∼20−21° and 23.1−23.6° from the in-plane ab lattice. The solid phase of O13 or T 14 packing is identified in comparison with the corresponding bulk mixture, marked beside each line. Figure 6 presents the XRD patterns during the heating processes of the mixtures in CPG (8.1, 31.8, and 46.4 nm). At high temperatures, the RI phase may be identified by the two peaks of the in-plane ab lattice at 2θ = ∼21−21.2° and 23.1− 17250



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Figure 5. Temperature-dependent XRD patterns recorded during the heating process of C13−C14 mixtures of xC14 = 0.5 confined in SBA-15 (3.8 nm) (a), and SBA-15 (7.8 nm) (b); xC14 = 0.05 (c), 0.2 (d), and 0.8 (e) confined in SBA-15 (17.2 nm), respectively. Rotator phase RI and lowtemperature stable crystal T14 and O13 are labeled to each diffraction line.

higher temperatures, for example, xC14 > ∼0.8. This solubility break in triclinic packing is related to the packing densities of its end groups (−CH3).32 Principally, the longer chain C14 molecules can accommodate the shorter C13 in the triclinic packing in the form of a solid solution but at a compromise of reduced packing densities of the end groups. As C13 molecules increase to a certain proportion, the triclinic packing would lose its advantage in the packing densities of the tilted structure compared with, for example, the (untilted) twisted hexagonal phase RI packing. This leads to the appearance of two-phase region, (RI + T), and further the solid solution RI. Furthermore, a peritectiod, (RI + T14 + L), is formed at the temperature Tp = ∼270.5 K. When C14 molecules dissolve in C13, the extrusion of the longer C14 chains from the alkane layer would inevitably distort the O13 packing in any amount. Accordingly, the onephase region of solid solution with O13 packing can only exist within a narrow composition range at lower temperatures as observed in the experiments. 3.4. Molecular Packings of the Solid Alkanes under Confinement. A knowledge of the solid structures of the pore alkanes is essential to understanding the confinement effect. As seen in the diffraction patterns (Figure 4), the bulk solutions (C13, C14, and the mixtures) can be frozen into 3D or complete crystals with both the layering order of (00l) planes and lateral order of in-plane ab lattice at 2θ = 19−25°. Under confinement, the structures of pore alkane solids are strongly affected by the matrix. Inside SBA-15 (7.8, and 17.2 nm) and

The above XRD measurements confirm the components and crystalline structures of some important phases in the above phase diagrams. Under confinement, the reflection angles of solid solutions with RI, O13, and T14 packings only shift slightly compared with those in the bulk. This means the pore confinement does not change the in-plane lattice parameters. In the experiments, the thermal analysis can detect almost all the phase transformations of the bulk or pore solids although the latter are normally weak, which may be verified or compensated by the XRD measurements. 3.3. Phase Behavior of C13−C14 Bulk System. As shown in Figure 2a, the bulk system shows a special RI one-phase region. The RI phase of C13 exists in the temperature range of (255 to 267.8) K. In the solid solution, the RI phase covers compositions up to xC14 = ∼0.7 and extends in temperature down to 239 K, twice the span of C13. The stabilization of the rotator RI phase by the mixing is a typical phenomenon in alkane binary mixtures.57,58 The other five solid phase regions are of two kinds: the solid solutions with O13, T14 packings; the two-phase regions (RI + O13), (RI + T14), and (O13 + T14). As for an odd−even numbered system, the phase behavior of the bulk mixtures may be understood in terms of molecular packing densities, molecular symmetry, and linear chain structures. Because of the difference in molecular symmetry of C13 and C14, a continuous solid solution is not expected in their binary mixtures. As a case, the one-phase region of T14 solid solution can only exist in a certain composition range at 17251



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Figure 6. Temperature-dependent XRD patterns recorded in heating process of C13−C14 mixtures of xC14 = 0.2 (a), 0.8 (b) confined in CPG (8.1 nm); xC14 = 0.5 confined in CPG (31.8 nm) (c), and CPG (46.4 nm) (d), respectively. Rotator phase RI and low-temperature stable crystal T14 and O13 are marked to each diffraction line.

CPG (8.1 nm), the pore solids lose the lamellar ordering as evidenced from the absence of (00l) plane reflections and effectively take the 2D close-packed arrangements in molecules. In pores of CPG (31.8, and 46.4 nm), the mixture (xC14 = 0.5) regains the lamellar order of the 3D crystals as observed in the diffractions. On the basis of the results, the alkane molecules might be speculated to stack in an image as shown in Figure 7a as frozen in pores of SBA-15 or CPG. It should be noted that the lateral packing of alkanes always exists in the bulk or confined states, which, as mentioned above, may be favored by the relative strong attractions among alkane

chains, although the strength of attraction might vary with overlapping or disordered conformations of the chains. This is proved by the ever existing 2D close-packed arrangements of molecules under confinement of SBA-15 or CPG. On the rough surface of pores in SBA-15 or CPG, the alkane molecules would be adsorbed onto the irregular or uncorrelated sites on cooling, from which the lateral packing is propagated into 2D structures with random z coordinates. In the vicinity of the pore wall, the packing of alkane molecules might be more disordered in both the lamellar and lateral directions, for example, in SBA-15 or CPG with pore diameters less than 20 nm. Meanwhile, some weak attractions could be expected among adjacent 2D domains and result in somewhat lamellar ordering, for example, as seen from the appearance of some small peaks at angles 2θ = 34−36° in SBA-15 (17.2 nm) (Figure 5c−e). In the larger pores of CPG (d > 30 nm), the lamellar ordering may be energetically favored among the 2D domains as in the bulk in the regions fairly far away from the pore surface. Clearly, these specific structures of the pore alkanes accompany the phase behaviors dramatically changed at different pores. It is known that interface interactions and pore geometry are the main sources of confinement effect on liquids by porous matrix. In a same medium of SBA-15 or CPG, the phase behavior of the mixtures shows dependence merely on the pore size, because the other two factors remain constant in this condition. But when the phase behavior in different media is compared, the pore size cannot be interpreted as the only

Figure 7. Schemic view of possible stackings of solid state alkane molecules in pores of SBA-15 and CPG with different sizes in the radial direction where the pore diameters locate at the centers of pores (a), and in 3D connected pores of CPG, where the packing of molecules could extend outside one pore to the others indicated by the dotted circles (b). 17252



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According to the DSC and XRD analysis, the RI phase might exist in all the solid mixtures inside SBA-15 (7.8, and 17.2 nm). However, this breaks the rule of crystallization in an alkane bulk system which has a T14 solid solution in the high mole fraction region. As mentioned in a previous section, the existence of a triclinic solid solution needs enough packing densities of the end groups of C14 in addition to C13 molecules. However, the 2D close-packed arrangements of molecules in pores of SBA-15 (7.8, or 17.2 nm) do not guarantee the packing densities of the end groups. To the contrary, the molecular chains (and thus the end groups) might be aligned more randomly in SBA-15 than in the bulk because of the rough pore walls and limitations in the space, as depicted in Figure 7a. The pores act as a heterogeneous source for molecules packing and thereby may cause a distribution of packings along the radial direction, as reported in a previous work.32 In these conditions, the mixtures with triclinic structures originally in the bulk lose the advantage in molecular packing densities under confinement and are replaced by the untitled RI phase, partially in SBA-15 (7.8 nm) or fully in SBA-15 (17.2 nm). It is estimated that the pores of SBA-15 (7.8 nm) can accommodate at most 15 ab plane lattices of the solid alkane in the cross section. In such a small space, the 2D close-packed molecules with random z positions could not form 3D structured crystals and thus lose their rich-phase behaviors as the bulk. The alkane molecules can only be frozen into solid mixtures because of the different molecular symmetry of C13 and C14. In the larger pores of SBA-15 (17.2 nm), the 2D closepacked molecules probably could be allowed somewhat lamellar ordering in the core part of the channels, although actually weak. As a consequence, the mixtures could exhibit some behaviors as the bulk, for example, the appearance of the RI phase and O13 and T14 packings. However, the expanded RI phase region indicates that the influence of pore confinement is still strong. Moreover, as observed in the experiments the s−s transitions of the pore solid are weak in small pores (d < 20 nm). This is probably because thermal energy only needs to excite the in-plane transformations of the 2D structures, which also might be related to the less steric hindrance from the lamellar interactions. 3.6. Phase Behaviors of C13−C14/CPG (8.1, 31.8, 46.4, and 300 nm). The phase diagrams of C13−C14 mixtures in CPG are easier to understand because of their resemblance to the bulk system, especially in larger pores (d > 30 nm). In CPG (8.1 nm), the mixtures display a possible continuous RI phase covering the whole compositions as in SBA-15 (17.2 nm), which may be attributed to the 2D packed molecules of the solid alkanes. The solid phases in other regions are similar to those in the bulk. In the diffraction patterns, the pore alkane solids inside CPG (31.8 and 46.4 nm) show both lamellar ordering and in-plane lateral packing. The complete 3D crystallization of the pore solid signifies the recovery of the phase behavior of the bulk. The features belonging to the bulk system are mostly detected in thermal analysis such as the RI phase, the two-phase region, and two invariants (eutectic, peritectic point). But some other phase behaviors in the bulk are still not observed in thermal analysis. For example, the two phase region (RI + O13) is invisible in xC14 < 0.3 in DSC analysis. This means the considerable influence of CPG pore confinement is still in effect.

factor. For example, pure C13 experiences a phase sequence O13 → RI → L in CPG (8.1 nm) in the heating process. However, in a similar pore size of SBA-15 (7.8 nm), the s−s transition O13 → RI is suppressed. In the binary mixtures, the phase diagram of the C13−C14 system in CPG (8.1 nm) resembles more the phase diagram of the bulk than that of the system in SBA-15 (17.2 nm), although the latter has a pore size of more than twice that of the former. Understanding these phenomena requires a consideration of all the possible reasons associated with the confinement effect. As the pore wall−alkane molecule interactions are similar in SBA-15 and CPG, the influence of the pore geometries of SBA-15 and CPG in addition to the pore size has to be considered. The image in Figure 7b might provide a rough structural estimation for the confined solid alkanes inside the pores of CPG. With the well-defined 1D channels, SBA-15 can provide a uniform space for the molecular packing of alkanes. In contrast, CPG has the 3D connected cylindrical pore network, which probably could allow the stacking of alkane molecules outside the range of “one” pore, as indicated in Figure 7b. That is, the crystallization of alkane molecules inside CPG might propagate into a larger space of neighboring pores, leading to an “expansion” of the nominal pore size to some extent. According to the thermal analysis results, CPG (8.1 nm) could provide a space equivalent to SBA-15 (17.2 nm) for the pore solid alkane. On the basis of this assumption, C13 or the mixtures would manifest themselves more like the bulk inside CPG than in SBA-15. In a word, the 2D domains of solid alkane molecules prevail in small pores of sizes less than 20 nm. In this case, the pore size guides the phase behavior of the confined alkanes in SBA15 or in CPG. When the general influence of confinement among different media is compared, the pore geometry, for example, dimensionality of the pores, as well as the pore size should be taken into account. 3.5. Phase Behaviors of C13−C14/SBA-15 (3.8, 7.8, and 17.2 nm). Within SBA-15 (7.8 nm) (Figure 5b), the pore solid (x14 = 0.5) is composed of two components, RI phase and triclinic crystal of T14 packing. Their intensities or the relative amounts vary with the temperatures. The T14 component takes up a larger portion at low temperatures, probably because of its larger packing densities of molecules, than the RI subcells and thus are energetically suitable. Just below the melting point, the RI phase dominates the solid mixture while the T14 component is almost invisible in the reflection patterns. Therefore, the melting of the pore solid is actually due to the transition RI → L. From this phenomenon, a one-phase region of RI solid solution might be expected within a very narrow temperature region before fusion. If so, the same situation should happen to the other mixtures considering the regular variation of melting points as a function of mole fractions in this system. Following this, the single line of the melting boundary is understandable for C13−C14 mixtures confined in SBA-15 (7.8 nm). In this system, only RI and T14 packings are observed and the orthorhombic O13 crystals are absent. As a result, the phase regions related to O13 packing in the bulk would disappear in this confined system, for example, the two-phase region (O13 + T14) or (O13 + RI). When in a smaller space of SBA-15 (3.8 nm), a simpler phase behavior should be predicted. Indeed, the mixtures in pores of SBA-15 (3.8 nm) merely show a straight line of the melting boundary from the DSC scans (Figure 2b). Herein, the size effect displays a significant influence on the phase behaviors of the mixed alkanes. 17253



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(8) Vogelsberg, C. S.; Bracco, S.; Beretta, M.; Comotti, A.; Sozzani, P.; Garcia-Garibay, M. A. Dynamics of Molecular Rotors Confined in Two Dimensions: Transition from a 2D Rotational Glass to a 2D Rotational Fluid in a Periodic Mesoporous Organosilica. J. Phys. Chem. B 2012, 116, 1623−1632. (9) Koh, Y. P.; Simon, S. L. Crystallization and Vitrification of a Cyanurate Trimer in Nanopores. J. Phys. Chem. B 2012, 116, 7754− 7761. (10) Koh, Y. P.; Simon, S. L. Kinetic Study of Trimerization of Monocyanate Ester in Nanopores. J. Phys. Chem. B 2011, 115, 925− 932. (11) Koh, Y. P.; Simon, S. L. Trimerization of Monocyanate Ester in Nanopores. J. Phys. Chem. B 2010, 114, 7727−7734. (12) Schreiber, A.; Ketelsen, I.; Findenegg, G. H. Melting and Freezing of Water in Ordered Mesoporous Silica Materials. Phys. Chem. Chem. Phys. 2001, 3, 1185−1195. (13) Findenegg, G. H.; Jahnert, S.; Akcakayiran, D.; Schreiber, A. Freezing and Melting of Water Confined in Silica Nanopores. Chem. Phys. Chem. 2008, 9, 2651−2659. (14) Deschamps, J.; Audonnet, F.; Brodie-Linder, N.; Schoeffel, M.; Alba-Simionesco, C. A Thermodynamic Limit of the Melting/Freezing Processes of Water under Strongly Hydrophobic Nanoscopic Confinement. Phys. Chem. Chem. Phys. 2010, 12, 1440−1443. (15) Morishige, K.; Iwasaki, H. X-ray Study of Freezing and Melting of Water Confined within SBA-15. Langmuir 2003, 19, 2808−2811. (16) Kittaka, S.; Sou, K.; Yamaguchi, T.; Tozaki, K. Thermodynamic and FTIR Studies of Supercooled Water Confined to Exterior and Interior of Mesoporous MCM-41. Phys. Chem. Chem. Phys. 2009, 11, 8538−8543. (17) Ha, J.-M.; Hamilton, B. D.; Hillmyer, M. A.; Ward, M. D. Phase Behavior and Polymorphism of Organic Crystals Confined within Nanoscale Chambers. Cryst. Growth. Des. 2009, 9, 4766−4777. (18) Chen, S. M.; Liu, Y. S.; Fu, H. Y.; He, Y. X.; Li, C.; Huang, W.; Jiang, Z.; Wu, G. Z. Unravelling the Role of the Compressed Gas on Melting Point of Liquid Confined in Nanospace. J. Phys. Chem. Lett. 2012, 3, 1052−1055. (19) Sliwinska-Bartkowiak, M.; Jazdzewska, M.; Gubbins, K. E.; Huang, L. L. Melting Behavior of Bromobenzene within Carbon Nanotubes. J. Chem. Eng. Data 2010, 55, 4183−4189. (20) Chen, S.; Kobayashi, K.; Miyata, Y.; Imazu, N.; Saito, T.; Kitaura, R.; Shinohara, H. Morphology and Melting Behavior of Ionic Liquids inside Single-Walled Carbon Nanotubes. J. Am. Chem. Soc. 2009, 131, 14850−14856. (21) Coasne, B.; Czwartos, J.; Sliwinska-Bartkowiak, M.; Gubbins, K. E. Effect of Pressure on the Freezing of Pure Fluids and Mixtures Confined in Nanopores. J. Phys. Chem. B 2009, 113, 13874−13881. (22) Coasne, B.; Czwartos, J.; Sliwinska-Bartkowiak, M.; Gubbins, K. E. Freezing of Mixtures Confined in Silica Nanopores: Experiment and Molecular Simulation. J. Chem. Phys. 2010, 133, 084701−084709. (23) Czwartos, J.; Sliwinska-Bartkowiak, M.; Coasne, B.; Gubbins, K. E. Melting of Mixtures in Silica Nanopores. Pure Appl. Chem. 2009, 81, 1953−1959. (24) Aristov, Y. I.; Marco, G. D.; Tokarev, M. M.; Parmon, V. N. Selective Water Sorbents for Multiple Applications, 3. CaCl2 Solution Confined in Micro-and Mesoporous Silica Gels: Pore Size Effect on the ″Solidification-Melting″ Diagram. React. Kinet. Catal. Lett. 1997, 61, 147−154. (25) Lan, X. Z.; Pei, H. R.; Yan, X.; Liu, W. B. Phase Behavior of Dodecane−Tetradecane Binary System Confined in SBA-15. J. Therm. Anal. Calorim. 2012, 110, 1437−1442. (26) Pei, H. R.; Yan, X.; Liu, W. B.; Lan, X. Z. Phase Behavior of Tetradecane−Hexadecane Mixtures Confined in SBA-15. J. Therm. Anal. Calorim. 2013, 112, 961−967. (27) Yan, X.; Pei, H. R.; Wang, T. B.; Liu, W. B.; Lan, X. Z. Phase Behavior of Undecane−Dodecane Mixtures Confined in SBA-15. E-J. Chem. 2013, 2013, Article ID 476236. (28) Hansen, E. W.; Gran, H. C.; Sellevold, E. J. Heat of Fusion and Surface Tension of Solids Confined in Porous Materials Derived from

4. CONCLUSION The bulk C13−C14 mixtures possess complicated phase behavior with the addition of the special rotator phase in normal alkanes. The multiphase feature of the system is displayed with a variation of temperatures and compositions such as the RI region and triclinic and orthorhombic solid solution. Under the confinement of the mesoscopic scale, physical size and pore geometry show significant influence on the phase behavior of the confined mixtures. Inside the quasione-dimensional channels of SBA-15, the phase diagram is shrunk into the single melting boundary in the small pore size of 3.8 and 7.8 nm. In SBA-15 (17.2 nm), the mixtures gain some features of the bulk such as the RI region and two-phase regions. The diffraction patterns reveal the structures of some pore solid alkanes. The pore geometry can have a much different effect on phase behaviors of the mixtures confined in SBA-15 or CPG. The 3D connected pores in CPG cause the solid alkanes to appear within them much more than they do in SBA-15. The effectively 2D close-packed arrangement of molecules in pores is the source of the new phase behaviors otherwise forbidden in the bulk. The absence of one-phase or two-phase regions of the confined mixtures in low temperature range is attributed to the 2D structure of pore alkane solids and the suppressed s−s transition. Generally, in the mesoscopic scale the phase diagram evolves with the physical size from simple to complicated, which could be understood in terms of temperature, composition, pore size, and geometry.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel: +86-538-8247753. Fax: +86538-8242251. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank the financial support from National Natural Science Found of China (No. 21273138) and Natural Science F ou n d a t io n of Sh a n d on g P r ovi n c e , Ch in a ( N o . ZR2010BM035).

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REFERENCES

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