Computational Analysis of Sugar Alcohols as Phase-Change Material

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Computational Analysis of Sugar Alcohols as Phase-Change Material: Insight into Molecular Mechanism of Thermal Energy Storage Taichi Inagaki, and Toyokazu Ishida J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.5b11999 • Publication Date (Web): 26 Feb 2016 Downloaded from http://pubs.acs.org on March 2, 2016

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The Journal of Physical Chemistry

Computational Analysis of Sugar Alcohols as Phase-Change Material: Insight into Molecular Mechanism of Thermal Energy Storage Taichi Inagaki∗,†,‡ and Toyokazu Ishida∗,†,‡ Research Center for Computational Design of Advanced Functional Materials (CD-FMat), National Institute of Advanced Industrial Science and Technology (AIST), Tsukuba Central 2, 1-1-1 Umezono, Tsukuba, Ibaraki 305-8568, Japan, and Thermal Management Materials and Technology Research Association (TherMAT) E-mail: [email protected]; [email protected]

Phone: +81 (0)29 861 5206. Fax: +81 (0)29 861 3171

∗ To

whom correspondence should be addressed Center for Computational Design of Advanced Functional Materials (CD-FMat), National Institute of Advanced Industrial Science and Technology (AIST), Tsukuba Central 2, 1-1-1 Umezono, Tsukuba, Ibaraki 305-8568, Japan ‡ Thermal Management Materials and Technology Research Association (TherMAT) † Research

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Abstract Sugar alcohols are one promising candidate for phase-change materials (PCMs) in energy industrial societies because of their large thermal storage capacity. In this paper, we investigate melting point and enthalpy of fusion related to the thermal storage of six-carbon sugar alcohols (galactitol, mannitol, sorbitol, and iditol) by molecular dynamics simulations, and elucidate physical principles required for new PCM design. The computational melting points and enthalpies of fusion reproduce the experimental trend qualitatively. Based on the energy decomposition analysis we find that their enthalpies of fusion originate mainly from the decrease in the number and strength of inter-molecular hydrogen bonds upon melting. Furthermore we examine the origin of the difference of enthalpy of fusion between the four isomers. The results show that the larger enthalpy of fusion of galactitol and mannitol comes from their stable solid phases associated with the absence of notable repulsive electrostatic interaction between oxygen atoms in the molecule. In accordance with these results and an additional statistical survey, we propose the threefold guideline for developing new sugar alcohol like PCMs with larger thermal storage: (1) linear elongation of a carbon backbone, (2) separated distribution of OH groups, and (3) even numbers of carbon atoms.


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1 Introduction In the social environment, there is a huge amount of reusable heat wasted from industries, different modes of transportation, and our daily lives. 1,2 Effective handling and managing of this reusable waste heat is one of the key future technologies to reduce energy consumption and promote energy conservation in many aspects of our social systems. Recently, technology for thermal energy storage (or management) has attracted much attention in the field of thermal energy research. 3–5 One promising technology to effectively store and utilize waste heat is to employ phase change materials (PCMs) or latent heat storage materials, 6–9 which make it possible to reutilize unused thermal energy beyond the temporal and spatial limitations. In typical cases, the solid-liquid phase transition is utilized for the purpose. The amount of thermal energy stored in the solid-liquid PCMs corresponds to an enthalpy difference in between the solid and liquid phases, the so-called enthalpy of fusion or latent heat of fusion. These PCMs can store thermal energy through the melting transition, and can release energy through the freezing process in response to the external environment. Sugar alcohols, such as erythritol, xylitol, and mannitol, are reduced forms of carbohydrates in which each carbon atom carries a hydroxyl (OH) group. (In this paper, we define sugar alcohols as acyclic ones.) Due to a variety of physicochemical features, e.g., sweetness, hygroscopicity, and diuretic properties, sugar alcohols are widely used in food and pharmaceutical industries. 10–14 The characteristic properties of sugar alcohols is usually claimed to stem from hydrogen bonds (H-bonds) formed by a number of OH groups. In the solid phase almost all OH groups within molecules are incorporated in their distinctive three-dimensional inter-molecular H-bond networks, which form an H-bonded molecular crystal. On the other hand, in the liquid and solution phases, intra-molecular H-bonds between neighboring OH groups are formed as well as inter-molecular Hbonds. Many experimental 15–18 and theoretical studies 19–22 have shown that these H-bonds play an important role in molecular structures and conformations which are related to fundamental physical properties, such as melting point, 23,24 glass transition temperature, 25 enthalpy change during phase transition, 26 the differences between sugar alcohol stereoisomers, 27,28 and inter-molecular 3 ACS Paragon Plus Environment


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interactions with water molecules in a solution. 29 In recent years, sugar alcohols have also received much attention as a candidate substance for PCM. 8,9,30–32 This is because some sugar alcohols, such as erythritol (one of C4 sugar alcohols) and mannitol (one of C6 sugar alcohols), have inherently large thermal storage densities (∼300 kJ/kg 23,33 ) compared with other organic compounds. 8,9 (It should be noted that the term “thermal storage density” is defined as the enthalpy of fusion per unit mass.) This notable capacity is an essential feature for efficient PCMs. To our knowledge, natural sugar alcohols are up to C8 molecules, 34 of which up to C6 sugar alcohols have a focus of attention as PCMs. Toward the practical use of the sugar alcohols, a number of studies have been performed to solve issues of supercooling phenomena 32,35–37 and low thermal diffusivity coefficients. 38–40 On the other hand, the development of new materials with larger thermal storage density is highly expected to extend the potential ability of PCMs in an industrial field and lead to more efficient recycling of the waste heat. A potential clue of such development is the fact that sugar alcohol isomers can possess large different thermal storage densities each other. 8,9 That is, thermodynamic properties of sugar alcohols are substantially affected by the OH group distribution within a molecule. For example, mannitol has large enthalpy of fusion (12.6-13.4 kcal/mol) whereas, sorbitol, which is an isomer of mannitol, has small one (8.2 kcal/mol) despite the displacement of one OH group position (see Figure 1). The differences of physical property between isomers like this have been reported by a few studies. Lopes et al. showed via density functional theory (DFT) calculations that erythritol has larger enthalpy of sublimation than threitol, which is an isomer of erythritol, due to the lower enthalpy of threitol in the gas phase. 26 Motherwell et al. performed molecular dynamics (MD) simulations and DFT calculations of inositol isomers and explained the melting point difference between the isomers by characterizing inter-molecular H-bond networks. 41,42 However, to our knowledge, enthalpy of fusion and its molecular mechanism of sugar alcohols has not been investigated so far. Therefore, for accelerating the development of new materials, it is highlydesirable to understand, at the atomic level, the origin of enthalpy of fusion of sugar alcohols and


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the difference between the isomers. In this study we perform theoretical investigations based on classical MD simulations to obtain new physical insight into sugar alcohols as PCMs and provide useful information for rational design of new materials. Specifically, we calculate melting points and enthalpies of fusion for four kinds of C6 sugar alcohols, i.e., galactitol, mannitol, sorbitol, and iditol (Figure 1). These isomers are selected because relevant experimental properties have been reported and the isomers are well-known to possess qualitatively different thermodynamic properties: melting points for galactitol and mannitol are much higher than those for sorbitol and iditol. As with the melting points, galactitol and mannitol have larger enthalpy of fusion than sorbitol and iditol. (It should be noted that, in this case, the values of thermal storage density and enthalpy of fusion are parallel because the isomers have the same molecular weight.) Comparison between the four isomers makes it possible to reveal important physical factors associated with large enthalpy of fusion. By performing the energy decomposition analysis, we discuss the origin of the enthalpy of fusion of sugar alcohols and the differences between these isomers. On the basis of the obtained results and an additional statistical survey, we propose useful guidelines for the development of new PCMs which mimic sugar alcohol structure.

2 Simulation details In this study, we performed classical MD simulations in order to evaluate melting points and enthalpies of fusion for the sugar alcohols. For melting point calculations we employed the interface/NPT method. In this method, independent NPT simulations with different temperatures are performed via a solid-liquid two-phase configuration. 41,43 This method lowers the nucleation free energy barrier and avoids some superheating by introducing solid-liquid heterogeneous interfaces. Although free-energy based methods such as the pseudo-supercritical path method of Maginn 44 should be employed for accurate prediction of melting point, we employed the efficient and straightforward interface/NPT method because our focus in this study is not to quantitatively



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predict melting points of the sugar alcohols. A two-phase configuration model for the interface/NPT method was prepared by the following procedure: A solid phase simulation model was divided into two regions which have nearly equal numbers of molecules. All atoms inside a half part of the simulation box were constrained to keep their initial positions by adding a strong harmonic potential (with a force constant of 10000 kJ/mol/nm2 ), while the remaining atoms were left free. With this system, an MD simulation was performed in the NVT ensemble at 1000 K until unconstrained molecules melt. The simulation system was then relaxed by NPT simulations (300 K and 1.0 atm) without additional constraints. The resultant system yields the initial configuration used in the interface/NPT simulation (see Figure 2 as an example). Using this initial configuration, NPT simulations with anisotropic cell were carried out at several temperatures ranging 300 K to 540 K with 20 K intervals. The melting phenomenon was observed by an abrupt increase in whole system volume, which is an indicator for phase transitions in this study, and a melting point was determined by identifying the highest temperature before melting phenomenon. For critical regions near the melting temperature, additional NPT simulations with the half intervals (10 K) were performed. A 5 ns trajectory was generated at each temperature and the last 3 ns was used for determining average system volume. These simulations were performed for each configuration which has the two phases (half solid-half liquid) aligned along the lattice a, b, or c axes. (Note that the lattice axes of a, b, and c follow the definition employed in the experimental crystal structures.) The lowest melting point among the three systems was identified as the final melting point. 45 For enthalpy of fusion calculations, NPT simulations were performed in the pure solid and liquid phases at the melting point determined above. In the simulations, anisotropic and isotropic volume fluctuations were allowed in the solid and liquid phases, respectively. Enthalpy of fusion was estimated as the enthalpy difference between the two phases. The enthalpies of the pure phases were obtained from the last 3 ns of a 5 ns trajectory. Mean values of enthalpy of fusion and standard deviations were estimated with ten separate simulations. The simulations for the


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energy decomposition analysis described in the following sections were also performed in the same manner as in the pure phase simulations. The force field for the sugar alcohols was taken from the previous study, 21 that is, the AMBER force field, except for atomic partial charges. In this study, we employed the OPLS charge set 46 which has large absolute values in each atomic site, in particular for interaction sites at OH groups, compared to that of Ref. 21. This is because in our preliminary calculations the atomic partial charge set of Ref. 21 was found to give an underestimate of melting points compared to the experimental values even in the case that the simplest direct heating method for the pure solid phase was employed. For example, the melting point of mannitol was predicted to be 400 K, while the experimental melting point is ∼440 K. It should be noted that the simplest direct heating method usually experiences an overestimate of melting points due to a hysteresis phenomenon. 44,47 We ascribed the underestimate to the small partial charges assigned on OH groups. Indeed, the melting point of mannitol obtained by the simplest direct heating method with the OPLS charge set was found to be 540 K, which is much higher than the experimental value (∼440 K). Therefore, in this study, we employed the force field combined the AMBER force field and the OPLS charge set which seems to be more suitable for melting point calculations. The force field parameters are listed in Supporting Information. In addition, we used 1-4 scaling factors of 0.5 and 0.8333 for the van der Waals and electrostatic interactions, respectively. These parameters are derived from the AMBER force field, which was shown to be more suitable for carbon-chain torsional rotations of sugar alcohols than those from the OPLS force field. The equations of motion were integrated using leap-frog scheme with a time step of 1 fs and C-H and O-H bonds were held rigid by the LINCS method. 48 Periodic boundary conditions were applied and long range electrostatic interactions were calculated using the particle mesh Ewald method 49 with real space cutoff 12.0 Å. To control temperature and pressure in NPT simulations the Nos´e-Hoover 50,51 and Parrinello-Rahman algorithms 52 were used, and the pressure was set to 1.0 atm in all constant pressure simulations. Crystal structures of the sugar alcohols were taken from the experiments. 53–56 Although mannitol and sorbitol have been reported to possess some



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polymorphic forms, we selected the most thermally stable form, that is, β -form for mannitol 54 and Γ-form for sorbitol. 57 In the crystal structure of Γ-sorbitol there are three unique molecules which have the different structures (i.e., Z′ =3), but various values per molecule shown in this paper were averaged over these molecules, unless otherwise noted. In pure phase simulations, we treated simulation systems with 5×4×5 (galactitol), 7×4×2 (mannitol), 2×2×8 (sorbitol), 8×2×5 (iditol) supercells including 400, 224, 384, and 320 molecules, respectively. In the interface/NPT simulations for calculating melting points, the systems were set to be twice in a, b, or c latticeaxis directions as large as pure phase simulations. All MD simulations were carried out with the Gromacs program package. 58

3 Results and Discussion 3.1 Melting points and enthalpies of fusion We first performed the interface/NPT method to determine the melting points of the sugar alcohols. Figure 3 displays volume per molecule (which is an indicator for phase transitions) versus temperature plots obtained by the interface/NPT method. In each plot, approximative melting point is provided by an abrupt increase in volume that describes the first-order phase transition. The melting points seem to somewhat depend on the orientation of solid-liquid contact planes. For example, the melting point of mannitol obtained from the two-phase configuration aligned along the a axis (Figure 3b red marks) is 20 K lower than that aligned along the c axis (Figure 3b blue marks). The difference of melting point may be attributed to the orientations of carbon backbones and H-bond networks against solid-liquid interface planes. As mentioned above, the lowest temperature among the three melting points was identified as the final melting point. This means that we adopted melting points of a (or c) axis for galactitol, a (or b) axis for mannitol, c axis for sorbitol, and b axis for iditol. These melting points are summarized in Table 1. The melting points for galactitol and mannitol are in good agreement with corresponding experimental values while those for sorbitol and iditol overestimate (about 30-50 K) experimental values. 59,60 Nevertheless, the experimental 8 ACS Paragon Plus Environment

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trend that melting points of galactitol and mannitol are higher than those of sorbitol and iditol was correctly reproduced. Using these computational melting points, we next calculated enthalpies of fusion, i.e., enthalpy differences between the pure solid and liquid phases, by performing NPT simulations. The calculated enthalpies of fusion per molecule are also summarized in Table 1 together with experimental values. As with the computations of melting point, the calculated enthalpies of fusion correctly reproduce the experimental trend that galactitol and mannitol have larger enthalpy of fusion compared to sorbitol and iditol. This trend was also observed when enthalpy of fusion was calculated at experimental melting points (see right column of enthalpy of fusion in Table 1). Note that in remaining part of this paper we will discuss enthalpies of fusion obtained from the computational melting points. Except for sorbitol, underestimates of computational enthalpy of fusion (by 1-4 kcal/mol) were observed, which may originate from two factors, i.e., effects of quantum zero-point vibrational energy and electronic polarization. Zero-point vibrational energy in the solid phase are expected to be small compared to that in the liquid phase through stiffer O-H vibrations in the liquid phase. 61 Electronic polarization is more likely to work in the solid phase rather than in the liquid phase through strong inter-molecular interactions such as H-bonds. 22,62 Both two effects relatively stabilize the solid phase and enlarge the enthalpy gap between the solid and liquid phases. Thus the enthalpies of fusion will increase by these effects. From the results of melting point and enthalpy of fusion, we found that the force field used here can qualitatively reproduce the experimental trend of thermodynamic properties of sugar alcohols. In the interface/NPT method using the solid-liquid two-phase configuration, the crystallization phenomenon is also expected to be observed at a lower temperature than the melting point. However, in this study, we obtained only the supercooled liquid state, not the perfect crystal state, from the interface/NPT simulations (see Supporting Information for details). In the viewpoint of PCMs, the crystallization is also important because it corresponds to the heat release process, but the observation of the crystallization using simulation techniques is out of the scope of this study. Therefore, in the present paper, we will show the molecular mechanism of the heat storage on the



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basis of the melting points and enthalpies of fusion obtained above.

3.2 Origin of enthalpy of fusion Some sugar alcohols are known experimentally to have especially large enthalpy of fusion compared to other organic compounds. 8 To obtain an insight into the large enthalpy of fusion, it is useful to decompose enthalpy of fusion into intra-molecular and inter-molecular potential energy terms. In simulations based on a classical force field, total energy is easily decomposed since it is given by the sum of each energy term. It should be noted that the pressure-volume product (P∆V ) term has a negligible contribution to enthalpy of fusion at normal pressure. In addition, at a given temperature, the kinetic energy contributes the same amount to enthalpy at any points in a phase diagram. As a result, enthalpy of fusion can be fairly well approximated by the potential energy difference between the solid and liquid phases. For the sugar alcohols, the intra-molecular and inter-molecular potential energy components in enthalpy of fusion are summarized in Table 2. From Table 2, it is clear for each isomer that the total potential energy difference between the solid and liquid phases is mainly attributed to the inter-molecular potential energy difference (∆Uinter ). In contrast, the intra-molecular potential energy difference (∆Uintra ) is small for galactitol and mannitol and is negative for sorbitol and iditol. The negative values mean that the energy term works against increasing enthalpy of fusion. These two potential energies can be further decomposed into several terms. The intra-molecular potential energy term is decomposed into bonded energy (∆UBAD ) including bond, angle, and dihedral angle energies, intra-molecular electrostatic energy (∆Uintra−ES ), and intra-molecular van der Waals energy (∆Uintra−vdW ). Similarly, the inter-molecular potential energy is decomposed into inter-molecular ES energy (∆Uinter−ES ) and inter-molecular vdW energy (∆Uinter−vdW ). These energies are also listed in Table 2. For each isomer, the inter-molecular potential energy is mainly dominated by ∆Uinter−ES (10.2-16.2 kcal/mol). On the other hand, the intra-molecular potential energy consists mainly of ∆UBAD and ∆Uintra−ES which generate positive and negative contributions, respectively. Although the contribution of ∆UBAD is the second largest term (except for iditol), it is canceled out by the negative 10 ACS Paragon Plus Environment

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∆Uintra−ES . Therefore, the balance between the positive contributions (∆Uinter−ES and ∆UBAD ) and the negative one (∆Uintra−ES ) roughly determines the magnitude of enthalpy of fusion for the sugar alcohols. The significant contribution of inter-molecular ES energy can be explained by inter-molecular H-bonds. The sugar alcohols in the solid phase form own inter-molecular H-bond networks. 53–56 Table 3 lists the number of inter-molecular H-bonds per molecule in the solid and liquid phases at the melting points. An H-bond where the distance between a donor oxygen OD and an acceptor oxygen OA atoms is less than 3.5 Å and the angle OD -H· · · OA is larger than 120◦ was counted. This definition was used in Ref. 29. Although the number of H-bonds clearly depends on the criterion, we confirmed by employing another adequate definition of H-bond (e.g., the OD -OA distance less than 3.0 Å and the OD -H· · · OA angle larger than 100◦ ) that the following qualitative observation is retained. From the table it is found for every isomer that there are about six and five inter-molecular H-bonds in the solid and liquid phases, respectively. This means that one inter-molecular H-bond disappears during a melting process. Table 4 summarizes interaction energies related to inter-molecular H-bonds. The values of HB nHB ∆Uinter−ES and ∆Uinter−ES represent the contributions of inter-molecular H-bond and other inter-

molecular ES interaction to enthalpy of fusion, respectively. 63 Note that the sum of the two values corresponds to the inter-molecular ES energy difference ∆Uinter−ES listed in Table 2. From Table 4, HB nHB it is found that the value of ∆Uinter−ES is much larger than ∆Uinter−ES , which indicates that the inter-

molecular ES energy difference originates dominantly from inter-molecular H-bonds. In addition, HB ∆Uinter−ES allow us to calculate ES interaction energy per H-bond (UHB ). The obtained energies

in the solid and liquid phases were about -5.5 and -4.3 kcal/mol, respectively (see Table 4). This result shows that each isomer has stronger inter-molecular H-bonds in the solid phase by about 1 kcal/mol than in the liquid phase. Therefore, the above analyses suggest that the inter-molecular ES energy difference is attributed to the decrease in the number of inter-molecular H-bonds and the reduction in the strength of ES interaction of inter-molecular H-bond itself. As with the inter-molecular ES energy, the intra-molecular ES energy, which contributes in a



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negative manner to enthalpy of fusion, can be qualitatively explained by intra-molecular H-bonds. Table 3 shows that an average of one intra-molecular H-bond is newly formed during a melting process. This indicates that the liquid phase is more stable than the solid phase in terms of the intra-molecular ES interaction. As a result the number of total H-bonds is kept in a similar number during a melting process. However, intra-molecular H-bonds do not necessarily keep comparable strength of the ES interaction to inter-molecular ones. To roughly estimate the relative H-bond strength, we measured average distances between hydrogen and acceptor oxygen atoms of OH groups for inter-molecular and intra-molecular H-bonds in the liquid phase. The H-bond definition is the same as above. The average distance among the four isomers for inter-molecular H-bonds (1.8-2.0 Å) was found to be about 0.3 Å shorter than that for intra-molecular ones (2.2-2.4 Å). This suggests that inter-molecular H-bonds have rather large ES interaction than intra-molecular ones. Hence intra-molecular H-bonds are weaker compared to inter-molecular H-bonds in the liquid phase, which suggests the order of the H-bond strength: (inter-molecular H-bond in the solid phase) > (inter-molecular H-bond in the liquid phase)> (intra-molecular H-bond in the liquid phase). It should be recalled that inter-molecular H-bonds in the solid phase are stronger than those in the liquid phase, as shown in the above result. Therefore, even if the decrease in the number of inter-molecular H-bonds is largely compensated by the increase in that of intra-molecular ones, the inter-molecular ES energy is supposed not to be completely canceled out by the intra-molecular ES energy. Overall, these two opposite ES interactions, ∆Uinter−ES and ∆Uintra−ES , are thus explained by the characteristic H-bonds in sugar alcohols.

3.3 Difference of enthalpy of fusion between isomers In this section, we reveal why the sugar alcohol isomers have large different enthalpy of fusion. The results obtained in this section are also quite useful for molecular design of PCMs which mimic sugar alcohols. Here, we consider two factors that influence the difference of enthalpy of fusion between isomers. One is the difference of enthalpic (or energetic) stability between isomers in a concerned phase at a given temperature, which directly links to the enthalpy of fusion difference. 12 ACS Paragon Plus Environment

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Enthalpy of fusion is generally determined by a balance between enthalpies in the solid and liquid phases. This means that enthalpy of fusion becomes large (small) when a system has a stable (an unstable) solid phase or an unstable (a stable) liquid phase. The other is the difference of melting point between isomers, which is indirectly related to the enthalpy of fusion difference. Heat capacity, which is described as a temperature derivative of enthalpy, of sugar alcohols is known to be larger in the liquid phase than in the solid phase. 23 Thus, in sugar alcohols with high melting point, the enthalpy gap between the solid and liquid phases becomes large, resulting in the increase in enthalpy of fusion. Indeed, since the sugar alcohols treated here have different melting points each other, the melting point difference should be taken into account on discussion of the enthalpy of fusion difference between the isomers. However, in this study, we assume that the effect of melting point on the enthalpy of fusion difference is not the essential factor. Concretely, the melting point difference between the isomers originates from the difference of enthalpic stability between the isomers, not that of entropic stability. On the basis of this assumption, we will investigate the stabilities of the isomers in the solid and liquid phases at given temperatures to reveal the origin of the difference of enthalpy of fusion between the isomers. This assumption will be partially justified by the investigation of the energetic stability in the solid phase.

3.3.1 Liquid phase First, we investigated the relative stability of the liquid phase at 500 K among the isomers. The temperature of 500 K was selected because every isomer is in the stable liquid phase at the temperature. Table 5 lists total potential energies and each energy component introduced in the above section. Although iditol has slightly lower total potential energy (75.8 kcal/mol) than other isomers (76.5-76.8 kcal/mol), which may somewhat influence a decrease in enthalpy of fusion, no crucial potential energy differences are observed in the liquid phase. Indeed, detailed analysis of each energy component shows that deviations between the isomers are less than 1 kcal/mol. From these results it is clearly suggested that the stability in the liquid phase has no apparent difference between the isomers.



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This energetic result is supported by several structural properties in the liquid phase. We characterized inter-molecular H-bonds which are associated with inter-molecular ES interactions. Table 3 lists the number of such H-bonds in the liquid phase at 500 K. Each isomer is found to have almost the same number of H-bonds (∼4.3). In addition, the character of inter-molecular H-bond is examined by radial distribution functions (RDFs). Figure 4 presents RDFs between the hydrogen atom of a terminal OH group (H1) and oxygen atoms of six OH groups (O1-O6). From the figure we can see that the RDFs of the isomers have a quantitatively similar height and position of the first peak. Intra-molecular H-bonds associated with intra-molecular ES interactions were also examined, which gives similar results between the isomers. Table 3 shows that intra-molecular H-bonds have a similar number (1.3) for each isomer. Besides, in the type of intra-molecular H-bonds, we obtained the same trend between the isomers (Table S2 in Supporting Information). Overall, these results of the inter- and intra-molecular H-bond analyses have a clear relation to the fact that there are little differences in the ES interactions between the isomers. Furthermore, the liquid densities again are almost identical between the isomers (Table S3 in Supporting Information), which can be linked to the same degree of inter-molecular vdW interactions. Therefore, we conclude that the distribution of OH groups has little effect on the liquid structure and the difference of enthalpy of fusion between the isomers is not due to physical properties of the liquid phase. The experimental study also suggests that the liquid phases of sugar alcohol isomers do not differ in their physicochemical properties. 23 It should be noted that the same conclusion for the liquid properties was also obtained at the temperature of 450 K. This indicates that the above conclusion for the liquid phase does not depend on temperatures at which the liquid phase is stable.

3.3.2 Solid phase From the liquid phase analyses, it can be expected that the stability in the solid phase is different from each isomer. We next investigated the relative stability of the solid phase at 300 K as in the case of the liquid phase. In the following, although the results at 300 K are displayed, the same conclusion was obtained by the analysis at 350 K where each isomer is also in the stable solid


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phase. Table 6 summarizes total potential energies in the solid phase. This table shows some difference of total potential energy between the isomers. The isomers with large enthalpy of fusion (galactitol and mannitol) have a 1-2 kcal/mol lower total potential energy than those with small one (sorbitol and iditol). For the difference of enthalpy of fusion between the isomers, this result is interpreted from the two different viewpoints mentioned above. The first one is the difference of energetic stability between the isomers at the same temperature, which contributes directly to the enthalpy of fusion difference. The result that galactitol and mannitol have the energetically more stable solid phases is qualitatively consistent with the trend of enthalpy of fusion, that is, the more stable solid phase provides larger enthalpy of fusion. The second is related to melting points: an isomer with the energetically-stable solid phase has a high melting point. As mentioned above, since the heat capacity of the liquid phase is known to be larger than that of the solid phase, 23 large enthalpies of fusion of galactitol and mannitol are attributed partially to the high melting points which originates from the energetically-stable solid phase. Thus, the difference of enthalpy of fusion between the isomers originally stem from the difference between stabilities of the solid phase. The more remarkable difference between the isomers is clarified by decomposing the total potential energy into the intra-molecular and inter-molecular potential energies. At first, we expected that galactitol and mannitol with higher melting point and larger enthalpy of fusion would be stabilized by strong inter-molecular interactions (such as inter-molecular H-bonds) which bind neighboring molecules. In reality, this is not the case, and the solid phase stability of galactitol and mannitol was found to be caused by the intra-molecular interaction. From Table 6, we can see that the intra-molecular potential energies of galactitol and mannitol are 6-9 kcal/mol lower than those of sorbitol and iditol. This critical difference of intra-molecular potential energy originates mainly from the ES interactions. In contrast, in terms of inter-molecular potential energy, stabilities of sorbitol and iditol are 5-6 kcal/mol larger than those of galactitol and mannitol. The result is also attributed mainly to the ES interactions. Thus, intra-molecular and inter-molecular ES energies in the solid phase seem to be in the rough trade-off relationship.



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A next question is where the stability of the intra-molecular interaction energy for galactitol and mannitol comes from. Here we focus on the intra-molecular ES interaction energy which is a major cause of the stability. Intra-molecular ES interaction is directly related to the molecular structure in the solid phase, and the distribution of six OH groups plays a crucial role in the ES interaction because those functional groups have large partial charges (see Table S1 in Supporting Information). Figure 5 depicts typical snapshots of molecular structures of the isomers in the solid phase obtained from MD simulations at 300 K. It can be seen, from the structures of galactitol and mannitol, that one of the two hydrogen atoms in each gauche-type OH group pair surely turn to the other oxygen atom. For example, the H4 (H1) hydrogen atom turns to the O5 (O2) oxygen atom in galactitol (mannitol), which may be regarded as a quite weak intra-molecular Hbond. (These intra-molecular H-bonds are discussed below.) This is supported by Table 7, which summarizes inter-atomic distances involving these OH groups. Galactitol and mannitol show a similar trend that each hydrogen-oxygen distance R(H-O) is much shorter than the corresponding oxygen-oxygen distance R(O-O). These OH group orientations have clear advantages in decreasing the ES repulsion between the closest oxygen atoms with large negative charges. For sorbitol, we found that the ES repulsion between oxygen atoms is not alleviated by their hydrogen atoms. Even though the circled oxygen atoms in Figure 5c are located in an adjacent OH pair, the attached hydrogen atoms are oriented in the nearly opposite directions. 64 Indeed, the O2-O3 distance (2.78 Å) is shorter than the relevant H2-O3 (3.70 Å) and H3-O2 (3.02 Å) distances (Table 7). As in the case of sorbitol, an iditol molecule in the solid phase has a characteristic OH pair, which is also displayed in Figure 5d. Compared to sorbitol, the pair shows the apparent ES repulsion between O2 and O3 atoms. We can see from Table 7 that the average H2-O3 and H3-O2 distances are about 4.0 Å , which is much longer than the corresponding O2-O3 distance (3.10 Å). This means that the two OH groups orient their hydrogen atoms in the opposite directions as shown in Figure 5d. Thus, sorbitol and iditol have less stable intra-molecular energies due to these unfavorable ES repulsions. Indeed, these ES repulsive interactions between oxygen atoms are so-called 1-4 interactions defined in dihedral angle rotations, so that the interactions are scaled


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down by a factor of 0.8333 65 in this study. Nevertheless these ES repulsions are expected to play a critical role to distinguish the isomers with the more stable solid phase (galactitol and mannitol) from those with the less stable solid phase (sorbitol and iditol). Here, one may ask if the bending conformations of sorbitol and iditol are responsible for the bare ES repulsions. Certainly, it is important to focus on molecular conformations for understanding the stability of sugar alcohols, and such bending conformations may be related to the ES repulsions. However, extended conformations for sorbitol and iditol are more likely to cause instability than the bending ones. This is because 1-3 parallel interaction between oxygen atoms 15 (noted 1-3 O//O interaction here) is generated in the extended conformations for the two isomers, that is, the interaction between a C-O bond and a second neighboring C-O bond which has a parallel bond direction to the former one. The 1-3 O//O interaction is well-known to destabilize the conformation through the repulsive interaction caused by a remarkably short distance between oxygen atoms (∼2.5 Å). 15 (It should be recalled that the larger O-O distances (2.8-3.1 Å) are observed in the bending molecular conformations.) Therefore, sorbitol and iditol molecules in the solid phase possess the bending conformations to avoid the energetically-unfavorable 1-3 O//O interaction. Furthermore, one may argue that intra-molecular H-bonds largely influence the stability of intra-molecular ES energy. Table 3 lists the number of intra-molecular H-bonds in the solid phase at 300 K. From the table, we find that the number of intra-molecular H-bonds is significantly small, which indicates the relatively minor importance of intra-molecular H-bonds. In addition, in another intra-molecular H-bond analysis using a looser H-bond definition than that showed earlier, the number of intra-molecular H-bonds was shown to correlate poorly with the stability of intramolecular ES interaction (see Supporting Information). Thus, these observations indicate that intra-molecular H-bonds in the solid phase are less significant than the O-O repulsive interaction as for the stability of intra-molecular ES interaction.



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3.4 Discussion Relevance with other related studies In the preceding section, we have seen that the difference of enthalpy of fusion between the C6 sugar alcohol isomers is attributed to the solid phase, not to the liquid phase. The isomers in the liquid phase have almost the same energetic character (Table 5). Here, consider an enthalpy change in phase transitions: enthalpy of fusion and enthalpy of sublimation, which may be not completely unrelated each other. They differ from each other only in the higher-enthalpy phases, i.e., the liquid or gas phases. Lopes et al. investigated enthalpy of sublimation of two C4 sugar alcohols, erythritol and threitol, and showed that the most important contribution to the difference between the two isomers is intra-molecular H-bond conformations in the gas phase. 26 This argument is inconsistent with the present work which showed that the liquid phase is of less importance. This discrepancy may be responsible for the difference of the environment that surrounds a molecule between the liquid and gas phases. A molecule in the liquid phase is surrounded by numerous molecules, so that a conformation of the molecule is greatly influenced by interactions with neighboring molecules (such as inter-molecular H-bonds). In this situation, the distribution of OH groups in a molecule is not so essential for properties in the concerned phase. In contrast to the liquid phase, a molecule is isolated in the gas phase. An isolated molecule prefers the conformations which stabilize itself by intra-molecular H-bonds, which depends significantly on the distribution of OH groups. Thus, a difference of molecular structure between isomers is less critical in the liquid phase than in the gas phase. Another interesting observation in this study is the fact that isomers with stable intra-molecular energy have higher melting points. Melting point differences among analogous organic compounds have often been discussed in terms of inter-molecular interactions. 42,66 This idea may be based on the lattice binding energy which describes attractive interaction between molecules. For example, Simperler et al. explained the melting point difference between inositol isomers in terms of the strength of the inter-molecular H-bond networks in the solid phase, 42 which suggests that strong inter-molecular interaction by H-bonds leads to high melting point. In that study, an infinite H18 ACS Paragon Plus Environment

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bonded double chain, which is two infinite · · · O-H· · · O-H· · · O-H· · · chains constructed by two adjacent OH groups in an inositol molecule, was shown to play a critical role in strong intermolecular H-bond networks. This observation in inositols is inconsistent with the propensity of melting points of the sugar alcohol isomers treated here. The sugar alcohol isomers with strong inter-molecular interaction in the solid phase were shown to have low melting point. Indeed, the crystal structures of the sugar alcohols have the infinite H-bonded single chains and the H-bond rings, 53–56 not the infinite H-bonded double chains observed in inositols. Unfortunately, only the infinite single chains and rings may be insufficient to easily describe the order of melting point in the sugar alcohols. In our case, thus, the strength of inter-molecular interactions is not an appropriate indicator for melting point. Therefore, strong inter-molecular interaction is not necessarily required for higher melting point. It is important to consider the total energy including not only inter-molecular energy but also intra-molecular energy for characterizing melting points. This consideration is expected to be widely accepted when melting points of organic compounds with large intra-molecular degrees of freedom are discussed, since in that case intra-molecular energies influence the stabilities in the solid and liquid phases as well as inter-molecular energies. guidelines for molecular design of new PCMs As mentioned in Introduction, sugar alcohols have attracted much attention as phase-change materials (PCMs) or latent heat storage materials in energy industries because these molecules have inherently large enthalpy of fusion. To improve the ability of sugar alcohols as PCMs, i.e., to increase the enthalpy of fusion, the results obtained in this study will be quite valuable. In this section, we discuss molecular design of new PCMs which mimic sugar alcohol structures. A straightforward strategy to the goal is to elongate a carbon backbone linearly and increase the number of OH groups. As noted in Section 3.2, the dominant part of enthalpy of fusion of sugar alcohols is the inter-molecular ES interactions which is closely related to inter-molecular H-bonds. That is, a large decrease in inter-molecular H-bonds in the melting process results in large enthalpy of fusion. Based on this observation, the above elongation strategy is associated with the simulation results in this study as follows. Here we consider an arbitrary Cn sugar alcohol



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molecule (n > 6). In the solid phase of the molecule, the number of inter-molecular H-bonds will increase compared to C6 sugar alcohols since every OH group is expected to be incorporated in inter-molecular H-bond networks. Indeed, the four C6 sugar alcohols in this paper have almost six inter-molecular H-bonds in their solid phases (Table 3 and S4 in Supporting Information). In the liquid phase, on the other hand, it is quite unlikely that the number of inter-molecular H-bonds increases in the same extent in the solid phase. This is because strong inter-molecular H-bonds in the liquid phase stem mainly from the terminal OH groups of the carbon backbone due to the relatively low steric hindrance, which is the key point of this strategy. This is supported by the fact that RDFs between terminal OH groups (e.g., RDFs of the H1-O1 or H1-O6 pairs) have a higher first peak compared to those between other OH groups (see Figure 4). We also found that first peaks between mid OH groups become much lower than the first peaks between other OH groups (Figure S3 in Supporting Information). Furthermore, the number of inter-molecular H-bonds in the liquid phase was decomposed into the contributions of each OH group, which shows that the mid OH groups have smaller number of H-bonds compared with the terminal OH groups (Table S4 in Supporting Information). Since the linear elongation of a carbon backbone increases mid OH groups, the number of H-bonds in the liquid phase would not increase as many as that in the solid phase and the increase ratio of inter-molecular H-bond in the liquid phase would decrease gradually. Thus, the change of the number of H-bonds in the melting process would increase and provide resulting large enthalpy of fusion. In addition, the elongation of a carbon backbone increases the internal degrees of freedom, such as stretching, bending, and torsional vibrations. This increase will also contribute to large enthalpy of fusion in terms of the bond-angle-dihedral bonded energy term, which is the second largest contribution to that enthalpy (see Table 2). This anticipation may be related to an effect of carbon-chain elongation in n-alkanes. Both melting point and enthalpy of fusion of n-alkanes increase with the number of carbon atoms. 67 The same trend has been shown in ionic liquids with longer alkyl chains. 68 In the study of the ionic liquids, it has been reported that the melting process of large molecules with C10, C12, or C14 alkyl chains involves more significant intra-molecular


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structural reorganization and the bonded energy contributes significantly to enthalpy of fusion as well as the non-bonded energy. However, it should be noted that enthalpy of fusion in practical use is measured in energy per unit mass such as kJ/kg, that is thermal storage density, not that per unit mole such as kJ/mol and kcal/mol. This requirement indicates that long carbon backbones have disadvantages for thermal storage density since addition of heavy atoms largely increases molecular weight. Therefore, we hope that thermal storage density converges to a certain value as a carbon backbone becomes longer or has a maximum value in a certain carbon backbone length. Besides the above strategy, it is important to select isomers with the energetically-stable solid phase. Even if the above elongation strategy is achieved successfully, enthalpy of fusion depends significantly on the distribution of OH groups. We showed that in the case of the C6 sugar alcohols the stability of intra-molecular potential energy plays an important role for the stability of the solid phase. Based on the result we should determine an ideal distribution of OH groups. In other words we should select the best stereoisomer for the stable solid phase. In practical procedure, we propose two strategies: the first one is that the 1-3 O//O interactions are avoided and the second is that vicinal OH groups are arranged in an anti-conformation. These two will avoid the significant O-O repulsive interaction as much as possible. These are based on the idea that isomers which are likely to have unfavorable conformations should be removed. This is because we cannot control the molecular conformation in the solid phase. Indeed, these two rules are consistent with the molecular structures of galactitol and mannitol. Therefore we should design isomers with the separated distribution of OH groups according to the above two guidelines. Furthermore, a statistical survey using the Reaxys database 69 shows melting point alternation of polyalcohols, which is widely known for n-alkanes. 66,70,71 Figure 6 displays the population of melting points of Cn polyalcohols (n = 4 − 8). It should be noted that polyalcohols listed in the figure have more than n − 3 OH groups to the each Cn molecule and do not have any branch of the carbon backbone. The line in Figure 6 connects between the highest melting points of Cn isomers, which is shown to be a zig-zag line, not a straight line. This means that molecules with even



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carbons melt at a relatively higher temperature than those with odd carbons. Since other physical properties are known to have a similar trend as melting point, 71 enthalpy of fusion is also expected to have such alternative character. Although this alternative character has not been investigated by simulation or theoretical studies, it may be essential to develop new PCMs which mimic sugar alcohol structure. Therefore we should design molecules with even numbers of carbon atoms in order to increase enthalpy of fusion. Besides, we found from this survey that polyalcohols with the same number of carbon and oxygen atoms have the highest melting point among the same carbon number groups (except for n=5) and the highest melting points get higher with increasing the number of carbon atoms n. This observation partially supports the strategy of linear elongation mentioned above.

4 Concluding remarks In this paper we investigated the two major thermophysical properties (melting point and enthalpy of fusion) of C6 sugar alcohol isomers (galactitol, mannitol, sorbitol, and iditol) by using molecular dynamics simulations. Melting points were calculated by the interface/NPT method, and the experimental trend that the melting points of galactitol and mannitol are higher than those of sorbitol and iditol was correctly reproduced. As for enthalpy of fusion, calculations also predicted the experimental trend properly. This suggests that the force field used here is reasonable to describe both the solid and liquid phases of sugar alcohols. We investigated the origin of inherently large enthalpy of fusion of sugar alcohols by the energy decomposition analysis and showed that the inter-molecular ES interaction is the dominant component of enthalpy of fusion. The change of the inter-molecular ES interaction during the melting transition was interpreted by the decrease in the number of inter-molecular H-bonds and the reduction in the strength of inter-molecular H-bond itself. This observation indicates that inter-molecular H-bonds play a critical role in the large enthalpy of fusion of sugar alcohols. Furthermore we examined the difference of enthalpy of fusion between the isomers. We found that the difference is attributed to the stability of the solid phase,


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not the liquid phase. The energy decomposition analysis again illustrated that the stability of the solid phase originates mainly from the ES interactions. In the case of C6 sugar alcohols, stable intra-molecular ES interaction, not inter-molecular one, leads to the favorable solid phase. As a result, galactitol and mannitol have the high melting point and large enthalpy of fusion. Sorbitol and iditol, in contrast, have low melting point and small enthalpy of fusion owing to the large ES repulsion between vicinal OH groups. From this result we also showed that it is important to consider the total energy including not only inter-molecular energy but also intra-molecular energy when the stabilities of the solid and liquid phases related to enthalpy of fusion and melting point are discussed. Based on the simulation results and the statistical survey, we proposed molecular design of new PCMs derived from sugar alcohol structures. The threefold strategy was suggested: (1) linear elongation of a carbon backbone, (2) separated distribution of OH groups, and (3) even numbers of carbon atoms in a carbon backbone. The first suggestion will achieve the increase in enthalpy of fusion in terms of inter-molecular ES interaction and bond-angle-dihedral bonded interaction. The second will select favorable isomers to increase enthalpy of fusion. The third guarantees that even members will lead to higher melting point and the resulting larger enthalpy of fusion than odd members. In fact, we proposed the guideline (1) on the basis of the MD simulation results, but the proposition may be insufficient to put it into practice. To make the guideline incontrovertible we should construct non-natural sugar alcohols with a long carbon backbone and estimate their enthalpies of fusion in silico. In addition, the guideline (3) should also be justified by theoretical studies. These further studies are indeed currently ongoing for validating the guidelines and computational design of new PCMs based on sugar alcohol structures, which will demonstrate the future potential of sugar alcohols as PCMs.

Acknowledgement This work was supported by New Energy and Industrial Technology Development Organization (NEDO), and Future Pioneering Projects of Ministry of Economy, Trade and Industry (METI), 23 ACS Paragon Plus Environment


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Japan. Molecular figures are created with VMD. 72

Supporting Information Available Force field parameters for C6 sugar alcohols; Additional data of interface/NPT simulations at low temperatures and intra-molecular hydrogen bond analysis in the solid phase; and supplementary materials as noted in text.

This material is available free of charge via the Internet at http:

//pubs.acs.org/.

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(46) Damm, W.; Frontera, A.; Tirado-Rives, J.; Jorgensen, W. L. OPLS All-Atom Force Field for Carbohydrates. J. Comput. Chem. 1997, 18, 1955–1970. (47) Alavi, S.; Thompson, D. L. Simulations of Melting of Polyatomic Solids and Nanoparticles. Mol. Simul. 2006, 32, 999–1015. (48) Hess, B.; Bekker, H.; Berendsen, H. J. C.; Fraaije, J. G. E. M. LINCS: A Linear Constraint Solver for Molecular Simulations. J. Comput. Chem. 1997, 18, 1463–1472. (49) Essmann, U.; Perera, L.; Berkowitz, M. L.; Darden, T.; Lee, H.; Pedersen, L. G. A Smooth Particle Mesh Ewald Method. J. Chem. Phys. 1995, 103, 8577–8593. (50) Nose, S. A Molecular Dynamics Method for Simulations in the Canonical Ensemble. Mol. Phys. 1984, 52, 255–268. (51) Hoover, W. G. Canonical Dynamics: Equilibrium Phase-Space Distributions. Phys. Rev. A 1985, 31, 1695–1697. (52) Parrinello, M.; Rahman, A. Polymorphic Transitions in Single Crystals: A New Molecular Dynamics Method. J. Appl. Phys. 1981, 52, 7182–7190. (53) Berman, H. M.; Rosenstein, R. D. The Crystal Structure of Galactitol. Acta Crystallogr. Sect. B 1968, 24, 435–441. (54) Fronczek, F. R.; Kamel, H. N.; Slattery, M. Three Polymorphs (α , β , and δ ) of D-Mannitol at 100 K. Acta Crystallogr. Sect. C-Cryst. Struct. Commun. 2003, 59, o567–o570. (55) Rukiah, M.; Lefebvre, J.; Hernandez, O.; van Beek, W.; Serpelloni, M. Ab Initio Structure Determination of the Γ Form of D-Sorbitol ( D-Glucitol) by Powder Synchrotron X-Ray Diffraction. J. Appl. Crystallogr. 2004, 37, 766–772. (56) Kopf, J.; Morf, M.; Zimmer, B.; Bischoff, M.; Koll, P. Structure of D,L-Iditol. Acta Crystallogr. Sect. C 1992, 48, 339–342. 29 ACS Paragon Plus Environment


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(57) Nezzal, A.; Aerts, L.; Verspaille, M.; Henderickx, G.; Redl, A. Polymorphism of Sorbitol. J. Cryst. Growth 2009, 311, 3863–3870. (58) Pronk, S.; Pall, S.; Schulz, R.; Larsson, P.; Bjelkmar, P.; Apostolov, R.; Shirts, M. R.; Smith, J. C.; Kasson, P. M.; van der Spoel, D.; Hess, B.; Lindahl, E. GROMACS 4.5: A High-throughput and Highly Parallel Open Source Molecular Simulation Toolkit. Bioinformatics 2013, 29, 845–854. (59) Quinquenet, S.; Ollivon, M.; Grabielle-Madelmont, C.; Serpelloni, M. Polimorphism of Hydrated Sorbitol. Thermochim. Acta 1988, 125, 125–140. (60) Siniti, M.; Carre, J.; an J. P. Bastide, J. M. L.; Claudy, P. Etude du Comportement Thermique des Hexitols: Partie 1. Vitrification et Cristallisation de Fiditol, du Mannitol, du Sorbitol et du Dulcitol. Thermochim. Acta 1993, 224, 97–104. (61) Wohlert, J. Vapor Pressures and Heats of Sublimation of Crystalline β -Cellobiose from Classical Molecular Dynamics Simulations with Quantum Mechanical Corrections. J. Phys. Chem. B 2014, 118, 5365–5373. (62) Baker, C. M.; Anisimov, V. M.; MacKerell, A. D. Development of CHARMM Polarizable Force Field for Nucleic Acid Bases Based on the Classical Drude Oscillator Model. J. Phys. Chem. B 2011, 115, 580–596. (63) The inter-molecular H-bond energy in each phase was estimated by the ES interaction energy between molecules which form inter-molecular H-bonds. In the solid phase, the ES interaction energy between the regular molecules with inter-molecular H-bonds was calculated because the inter-molecular H-bond pattern is unchanged in the stable solid phase. On the other hand, in the liquid phase, there is no regular inter-molecular H-bond pattern, so that the molecular pairs whose ES interaction is calculated were determined in each timestep in accordance with the H-bond definition used in the preceding section. The contribution of inter-molecular H-bonds to enthalpy of fusion was estimated by the difference between the 30 ACS Paragon Plus Environment

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inter-molecular H-bond energies in the two phases while that of the other inter-molecular ES interactions was calculated by subtracting the H-bond one from ∆Uinter−ES listed in Table 2. (64) In fact, sorbitol molecules in the solid phase have three distict conformations in a reflection of Z′ =3. Although the molecular structure introduced in the main text is one of them, other conformations also have the characteristic OH pairs which generate such ES repulsion. (65) Wang, J.; Cieplak, P.; Kollman, P. A. How Well Does a Restrained Electrostatic Potential (RESP) Model Perform in Calculating Conformational Energies of Organic and Biological Molecules? J. Comput. Chem. 2000, 21, 1049–1074. (66) Thalladi, V. R.; Boese, R.; Weiss, H.-C. The Melting Point Alternation in α , ω -Alkanediols and α , ω -Alkanediamines: Interplay between Hydrogen Bonding and Hydrophobic Interactions. Angew. Chem. Int. Ed. 2000, 39, 918–922. (67) Sharma, A.; Tyagi, V. V.; Chen, C. R.; Buddhi, D. Review on Thermal Energy Storage with Phase Change Materials and Applications. Renew. Sust. Energ. Rev. 2009, 13, 318–345. (68) Zhang, Y.; Maginn, E. J. Molecular Dynamics Study of the Effect of Alkyl Chain Length on Melting Points of [CnMIM][PF6] Ionic Liquids. Phys. Chem. Chem. Phys. 2014, 16, 13489– 13499. (69) Goodman, J. Computer Software Review: Reaxys. J. Chem. Inf. Model. 2009, 49, 2897–2898. (70) Boese, R.; Weiss, H.-C.; Blaser, D. The Melting Point Alternation in the Short-Chain nAlkanes: Single-Crystal X-Ray Analyses of Propane at 30 K and of n-Butane to n-Nonane at 90 K. Angew. Chem. Int. Ed. 1999, 38, 988–992. (71) Thalladi, V. R.; Boese, R. Why is the Melting Point of Propane the Lowest Among nAlkanes? New J. Chem. 2000, 24, 579–581. (72) Humphrey, W.; Dalke, A.; Schulten, K. VMD - Visual Molecular Dynamics. J. Molec. Graphics 1996, 14, 33–38. 31 ACS Paragon Plus Environment


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Table 1: Melting points (K) and enthalpies of fusion (kcal/mol) for four C6 sugar alcohols obtained by molecular dynamics simulationsa . Thermal storage density (kJ/kg) is obtained by multiplying enthalpy of fusion (kcal/mol) by 22.98. sugar alcohol galactitol mannitol sorbitol iditol

melting point Calc. Exp. 460 460c 450 439c 420 372e 380 353 f

enthalpy of fusion Calc.b Exp. 11.89(1) / 11.89(1) 14.4d , 15.6c 11.57(4) / 11.25(4) 12.6d , 13.4c 9.10(6) / 7.32(9) 8.2e 5.53(9)/ 4.73(9) 7.4 f

a

The statistical errors are indicated in the parentheses for the last digits (i.e., 11.89(1) = 11.89±0.01). b The left and right values are enthalpies of fusion calculated at the computational and experimental melting points, respectively. c Reference 23. d Reference 33. e Reference 59. f Reference 60.


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∆Uintra−ES -3.01(2) -4.60(11) -9.22(14) -9.59(13)

∆Uintra−vdW 1.96(1) 1.03(1) 1.39(1) 1.86(3)

∆Uinter−ES 10.18(1) 11.60(11) 15.51(16) 16.23(21)

∆Uinter−vdW -0.83(1) -0.45(3) -1.51(2) -3.11(5)

The short-hand notation for the each energy term represents total potential energy (Utot ), total intra-molecular energy (Uintra ), total inter-molecular energy (Uinter ), bond-angle-dihedral bonded energy(UBAD ), intra-molecular electrostatic energy (Uintra−ES ), intra-molecular van der Waals energy (Uintra−vdW ), inter-molecular electrostatic energy (Uinter−ES ), and inter-molecular van der Waals energy (Uinter−vdW ). b The difference between the solid and liquid phases is represented by delta symbol (∆). c The statistical errors are indicated in the parentheses for the last digits (i.e., 11.89(1) = 11.89±0.01).

a

sugar alcohol ∆Utot ∆Uintra ∆Uinter ∆UBAD galactitol 11.89(1) 2.54(2) 9.35(2) 3.60(1) mannitol 11.57(4) 0.41(14) 11.15(13) 3.99(3) sorbitol 9.10(6) -4.90(12) 14.00(16) 2.92(3) iditol 5.53(9) -7.59(12) 13.12(21) 0.13(8)

Table 2: Summary of the decomposition analysis of enthalpy of fusion (kcal/mol) for four C6 sugar alcohols calculated by molecular dynamics simulationsa,b,c .

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Table 3: Number of hydrogen bonds (H-bonds) at melting points (in the solid and liquid phases), 300 K (in the solid phase) and 500 K (in the liquid phase) for four C6 sugar alcoholsa . sugar alcohol galactitol mannitol sorbitol iditol galactitol mannitol sorbitol iditol galactitol mannitol sorbitol iditol galactitol mannitol sorbitol iditol a

total H-bond intra-H-bond inter-H-bond solid phase at melting point 5.89 0.12 5.77 6.12 0.29 5.82 6.25 0.24 6.01 6.29 0.02 6.27 liquid phase at melting point 5.85 1.31 4.54 5.89 1.14 4.75 6.04 1.15 4.88 6.21 1.03 5.18 solid phase at 300 K 5.98 0.03 5.95 6.14 0.15 5.99 6.26 0.19 6.07 6.28 0.00 6.28 liquid phase at 500 K 5.63 1.35 4.28 5.61 1.20 4.41 5.61 1.25 4.36 5.59 1.26 4.33

intra-H-bond and inter-H-bond represents intra-molecular H-bond and inter-molecular H-bond, respectively.


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HB Table 4: Contributions of inter-molecular hydrogen bonds ∆Uinter−ES and other inter-molecular nHB electrostatic interaction ∆Uinter−ES energies to enthalpy of fusion, and electrostatic interaction ensolid and liquid U liquid phases (kcal/mol)a . ergies per hydrogen bond in the solid UHB HB

sugar alcohol galactitol mannitol sorbitol iditol a

HB ∆Uinter−ES 10.57(2) 10.08(8) 14.33(9) 13.62(7)

nHB ∆Uinter−ES -0.39(2) 1.52(4) 1.18(11) 2.61(10)

liquid

solid UHB UHB -5.15(0) -4.22(0) -5.22(2) -4.28(1) -5.93(1) -4.35(1) -5.92(5) -4.45(2)

The statistical errors are indicated in the parentheses for the last digits (i.e., 10.57(2) = 10.57±0.02).

Table 5: Summary of the decomposition analysis of potential energy (kcal/mol) in the liquid phase at 500 K for four C6 sugar alcohols by molecular dynamics simulationsa,b . sugar alcohol Utot Uintra Uinter UBAD Uintra−ES Uintra−vdW galactitol 76.80(1) 112.68(1) -35.88(1) 30.73(0) 75.37(1) 6.58(0) mannitol 76.83(2) 113.01(2) -36.19(2) 30.48(0) 76.30(2) 6.23(0) sorbitol 76.45(2) 112.68(1) -36.23(2) 30.32(1) 76.11(2) 6.25(0) iditol 75.76(1) 111.92(1) -36.16(1) 29.97(1) 75.73(1) 6.22(0)

Uinter−ES Uinter−vdW -21.75(1) -14.14(0) -22.17(2) -14.01(1) -22.18(2) -14.05(1) -22.07(1) -14.09(1)

a

b

The short-hand notation for the each energy term is the same as Table 2. The statistical errors are indicated in the parentheses for the last digits (i.e., 76.80(1) = 76.80±0.01).

Table 6: Summary of the decomposition analysis of potential energy (kcal/mol) in the solid phase at 300 K for four C6 sugar alcohols by molecular simulationsa,b . Uintra sugar alcohol Utot Uinter UBAD Uintra−ES Uintra−vdW galactitol 49.58(0) 100.73(1) -51.14(1) 18.52(1) 78.48(0) 3.73(0) mannitol 49.64(0) 102.01(0) -52.37(0) 17.09(0) 80.59(0) 4.34(0) sorbitol 50.72(2) 108.39(3) -57.65(6) 18.02(0) 86.42(3) 3.96(1) iditol 51.79(1) 109.68(3) -57.88(3) 20.23(3) 86.29(0) 3.16(0) a

b

Uinter−ES Uinter−vdW -38.11(1) -13.04(0) -38.47(0) -13.91(0) -44.79(1) -12.87(1) -46.52(3) -11.36(0)

The short-hand notation for the each energy term is the same as Table 2. The statistical errors are indicated in the parentheses for the last digits (i.e., 100.73(1) = 100.73±0.01).



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Table 7: Selected geometrical parameters (oxygen-oxygen distance, R(O-O), and hydrogenoxygen distance, R(H-O)) for four C6 sugar alcohols calculated by molecular dynamics simulations in the solid phase at 300 Ka . pair

O-O

1 2 3 4

O1-O2 O2-O3 O4-O5 O5-O6

1 2 3

O1-O2 O3-O4 O5-O6

1 2 3 4 5

O1-O2 O2-O3 O2-O3 O3-O4 O5-O6

1 2 3 4 5

O1-O2 O2-O3 O2-O3 O3-O4 O4-O5 a

R(O-O) (Å) H-O galactitol 2.864 H1-O2 2.858 H3-O2 2.869 H4-O5 2.832 H6-O5 mannitol 2.808 H1-O2 2.768 H3-O4 2.781 H6-O5 sorbitol 2.777 H2-O1 2.782 H2-O3 2.782 H3-O2 2.840 H3-O4 2.888 H6-O5 iditol 3.036 H2-O1 3.099 H2-O3 3.099 H3-O2 2.804 H3-O4 2.855 H5-O4

R(H-O) (Å)

See Figure 5 for atom indices.


2.652 2.524 2.518 2.693 2.356 2.352 2.396 2.273 3.697 3.018 2.490 2.756 2.808 3.968 3.991 2.630 2.697

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Figure 1: Chemical structures and reported experimental melting points and enthalpies of fusion of C6 sugar alcohol isomers : (a) galactitol, (b) mannitol, (c) sorbitol, and (d) iditol. (See Table 1 for references of experimental values.)



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Figure 2: Two-phase configuration model in a periodic box used in the interface/NPT method. The simulation box is shown as a blue line lattice. Only model for mannitol with a solid-liquid two-phase configuration aligned along the c lattice axis is displayed in this figure. Similar models have been prepared for other isomers and interface plane orientations.


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Figure 3: Plot of volume per molecule versus temperature obtained by the interface/NPT method: (a) galactitol, (b) mannitol, (c) sorbitol, and (d) iditol. The red, green, and blue marks respectively represent the results of the solid-liquid configurations aligned along the a, b, and c lattice axes. Each curve is a guide for eye. It is difficult to distinguish three marks in the liquid phase since they are almost identical.

235

235

galactitol

230

225

3

Volume (Å )

3

Volume (Å )

230

220 215

a axis b axis c axis

210 205 400

420

440

500 460 480 Temperature (K)

520

230

mannitol

225 220 215


210 205 400

540

235

420

440


520

540

225

sorbitol

iditol 220

225

3

Volume (Å )

3

Volume (Å )

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


220 215 210


215 a axis b axis c axis

210

205 340 360 380 400 420 440 460 480 500 520 Temperature (K)

205 340

360



440

460


Figure 4: Radial distribution functions (RDFs) in the liquid phase at 500 K for four C6 sugar alcohols: (a) galactitol, (b) mannitol, (c) sorbitol, and (d) iditol. The RDFs between the hydrogen atom of a terminal OH group (H1) and oxygen atoms of six OH groups (O1-O6) are plotted. It should be noted that the RDFs of the H1-O1 pair almost overlap with those of the H1-O6 pair as a result of the roughly symmetric molecular structure. The similar overlap is observed between RDFs of the H1-O2 (H1-O3) and H1-O5 (H1-O4) pairs. (See Figure5 for atom indices.)

1.4

1.4

galactitol

1.2

g(r)

g(r)

1

0.8 H1-O1 H1-O2 H1-O3 H1-O4 H1-O5 H1-O6

0.6 0.4 0.2 0 0

mannitol

1.2

1

1

2

3

4

5 r (Å)

6

7

8

9

0.8 H1-O1 H1-O2 H1-O3 H1-O4 H1-O5 H1-O6

0.6 0.4 0.2 0 0

10

1.4

1

2

3

4

5 r (Å)

6

8

9

10

iditol

1.2

1.2

1

1 g(r)

0.8 H1-O1 H1-O2 H1-O3 H1-O4 H1-O5 H1-O6

0.6 0.4 0.2 0 0

7

1.4

sorbitol

g(r)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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1

2

3

4

5 r (Å)

6

7

8

9

0.8 H1-O1 H1-O2 H1-O3 H1-O4 H1-O5 H1-O6

0.6 0.4 0.2 0 0

10

1

2

3


4

5 r (Å)

6

7

8

9

10

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Figure 5: Representative molecular structures in the solid phase: (a) galactitol, (b) mannitol, (c) sorbitol, and (d) iditol and atom indices. These structures are obtained from molecular dynamics simulations at 300 K. The circled oxygen pairs in sorbitol and iditol have large electrostatic repulsive interaction (see main text for details).



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Figure 6: The population of melting point of Cn sugar alcohols (n = 4 − 8) which have more than n − 3 oxygen atoms to the each Cn sugar alcohol and do not have any branch of the carbon chain. The line connects between the highest melting points of Cn isomers. Even members possess relatively higher melting points compared to the corresponding odd members.


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Table of Contents (TOC) graphics.



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Cover Art.


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Computational Analysis of Sugar Alcohols as Phase-Change Material

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