Introduction

d-Ribose and d-mannose are important carbohydrates which have been widely used in agricultural production, food industry, pharmaceutical industry, and medical treatment [1,2,3,4,5]. d-Ribose (C5H10O5) and d-mannose (C6H12O6) are common biological monosaccharides existing in living cells as energy sources. d-Ribose, belonging to reducing pentoses, exists in living organisms not only as the main component of the nucleotide but also as raw materials of physiological macromolecules such as adenosine triphosphate (ATP) and adenosine diphosphate(ADP). At room temperature, d-ribose is usually white orthorhombic crystal or crystalline powder. d-Mannose is an isomeride of glucose, containing six carbon atoms forming a six-membered ring, which can be utilized to synthesize glycoproteins in plant cell wall. d-Mannose is mainly present in the form of free-state oligosaccharides in fruit epidermis cell wall and in the form of polysaccharides in yeast and red algae.

The studies of d-ribose and d-mannose in the last 40 years have mainly focused on the synthesis of new derivates [6], structure determination [7, 8], and biological activity [9,10,11]. However, the studies of thermodynamic properties of these two compounds are needed for better understanding their roles in synthesis mechanism, structure formation or transition, and biological induction from a view of thermodynamics.

Wilhoit [12] reported the standard enthalpy of combustion and the standard enthalpy of formation for d-ribose. Colbert et al. [13] determined the enthalpy of combustion for d-ribose. Banipal et al. [14] measured the partial molar heat capacities and volumes of d-ribose and d-mannose in water at 298.15, 308.15 and 318.15 K and in NaCl solution at 298.15 K using a Picker flow microcalorimeter, and calculated the partial molar expansion coefficients, isothermal compressibilities, excess partial molecular volumes and partial molar heat capacity coefficients. Robert et al. [15] studied the thermodynamic and transport properties of some carbohydrates at 298.15 K. Saskia et al. [16] discussed the apparent molar heat capacities of some carbohydrates in aqueous solutions versus the molality of carbohydrates at 298.15 K. Zhuo et al. [8] studied the system of electrolyte (NaCl, NaBr and NaI)-monosaccharide(d-Ribose and d-Mannose)-water solutions at 298.15 K and calculated the apparent molar volumes and evaluated the infinite dilution apparent molar volumes of the saccharides and electrolytes. Alberty reported the thermodynamic properties and calculated the standard Gibbs energies of formation and standard enthalpies of formation for d-ribose crystals [17].

However, the heat capacities and the related thermodynamic functions of d-ribose and d-mannose have not been reported especially in a wide temperature region covering their solid–liquid transition. In this work, we have measured the heat capacities of d-ribose and d-mannose in the temperature range from 1.9 to 440 K using the combination of a Physical Property Measurement System and a differential scanning calorimeter. The measured heat capacities have been fitted to a series of theoretical models and empirical equations, and consequently, the corresponding thermodynamic functions have been calculated based on the fitting parameters.

Experimental

The d-mannose and d-ribose samples used in the calorimetric measurements were commercially provided by J & K Scientific Ltd, and their molecular structure and sample information are listed in Fig. 1 and Table 1, respectively. The sample purity was further confirmed by means of HPLC method on a HPAEC system consisting of a Dionex Bio-LC gradient pump with GM-3 (4 mm) gradient mixer, CarboPac PA-10 column (4 × 250 mm), and an electrochemical detector using AgCl as reference electrode. The waveform was carbohydrates (standard Quad) and the following pulse potentials were used for the detection: t = 0 s, E = 0.10 v; t = 0.20 s, E = 0.10 v; t = 0.40 s, E = 0.10 v; t = 0.41 s, E = −2.00 v; t = 0.42 s, E = −2.00 v; t = 0.43 s, E = 0.60 v; t = 0.44 s, E = −0.10 v; t = 0.50 s, E = −0.10 v. The sample injection volume was 20 μL with the column oven temperature maintained at 303 K, while the reference standards were resolved by 18 mM NaOH isocratic elution at a flow rate of 0.5 mL min−1 over a 40 min time interval. The HPLC results listed in Table 1 indicating the mass fraction purity for both compounds to be better than 99%.

Fig. 1
figure 1

The molecular structures of d-ribose and d-mannose

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Table 1 Information of the studied samples used in this study
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The phase purity was examined using a powder X-ray diffraction instrument with a Cu Ka radiation (0.15418 nm) (PANalytical Co. X’pert PRO, Netherlands) operated under a voltage of 40 kV and a current of 40 mA. The XRD patterns collected for these two compounds are presented in Fig. 2. It can be seen that the diffraction peaks of d-ribose and d-mannose are well consistent with the standard patterns (PDF card No. 00-029-1898) and (PDF card No. 00-039-1836), respectively, from International Centre for Diffraction Data, indicating that these samples measured in this work are phase pure. The thermal stability of d-mannose and d-ribose was inspected using a thermogravimetric analyzer (SETSYS 16/18, SETARAM Co., France) from room temperature to 1073 K with a heating rate of 10 K min−1 and a high-purity Nitrogen atmosphere. The sample mass used in the measurement is 0.02313 g for d-ribose and 0.02228 g for d-mannose.

Fig. 2
figure 2

The XRD patterns of d-ribose and d-mannose

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The low-temperature heat capacities were measured using a Quantum Design Physical Property Measurement System (PPMS) with a logarithmic spacing from 1.9 to 100 K and a 10 K temperature interval from 100 to 300 K. The accuracy of the PPMS heat capacity measurement was estimated, by measuring the heat capacities of a high-purity copper pellet, α-Al2O3 (SRM720) and benzoic acid (SRM39j), and comparing the measured data to the standard values, to be ± 3% in the temperature region from 1.9 to 20 K and ± 1% from 20 to 300 K [18]. The powdered sample was prepared into a pellet to meet the PPMS requirement using a method developed by Shi et al., and the detailed sample preparation process and measurement procedure can be found in previous publications [19, 20]. The sample amounts used in the measurements were 0.01152 and 0.00880 g for d-ribose and d-mannose, respectively.

The heat capacities of d-ribose and d-mannose in the melting region were measured in the temperature range from 188 to 440 K using a heat-flux differential scanning calorimeter (Discovery DSC2500 from TA Instruments). The temperature calibration was performed by determining the melting temperature of indium. The extrapolated onset of indium was compared to the known melting point, and the difference was recorded for temperature calibration. The uncertainty for the enthalpy measurement in the DSC instrument is within ± 3%. The DSC heat capacity measurement accuracy was estimated, by measuring the heat capacity of α-Al2O3 (SRM720), to be within ± 3% in the temperature range from T = 183 to 673 K. The temperature intervals in the measurement were set to be 1 K in non-transition region and 0.1 K in transition region with a heating rate of 10 K min−1 and a high-purity nitrogen purge gas flow rate of 50 cm3 min−1. The sample amounts used in the measurements were 0.0937 and 0.0767 g for d-ribose and d-mannose, respectively.

Results and discussion

TG analysis

The thermal stability of d-ribose and d-mannose was evaluated using the TG measurement, and the TG curve is presented in Fig. 3. It can be seen from Fig. 3 that these two compounds both behave a thermal decomposition process with a three-step weight loss in the entire temperature region. d-ribose exhibits a percent weight loss of 19.75, 42.7 and 9.92% in the temperature region from 451 to 523, 523 to 618 and 618 to 705 K, respectively. d-mannose appears to decompose at a little higher temperature with percent weight loss of 15.27, 40.51 and 12.1% in the region from 462 to 519, 519 to 611 and 611 to 708 K, respectively. Based on these results, it can be concluded that both d-ribose and d-mannose are thermally stable in the heat capacity measurement region below 440 K.

Fig. 3
figure 3

TG–DTG curves of d-ribose and d-mannose

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PPMS heat capacities

The heat capacities of d-ribose and d-mannose measured using the PPMS in the temperature range from 1.9 to 300 K are plotted in Fig. 4 and listed in Table 2. It is clearly seen that the heat capacities of both compounds increase with the temperature increasing, and no phase transition, decomposition or other thermal anomalies can be detected in this temperature region. Also, d-mannose has a larger heat capacity than that of d-ribose due to its larger molecular weight.

Fig. 4
figure 4

Plot of the experimental and fitted heat capacities of d-ribose and d-mannose measured with PPMS

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Table 2 Experimental molar heat capacities \(C_{\text{p,m}}^{o}\) at constant pressure (p = 1.2 mPa) for d-ribose and d-mannose from T = 1.9 to 300 K
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In order to calculate the thermodynamic functions, the measured heat capacities of these two compounds were fitted to a series of empirical and theoretical models in the related temperature region. The heat capacities below 10 K were fitted to the theoretical model below [21],

$$C^{\rm o}_{\text{p,m}} = \gamma T + B_{3} T^{3} + B_{5} T^{5} + B_{7} T^{7}$$
(1)

where the linear term represents the contribution from defects and oxygen vacancies in insulating materials, and the odd power terms in temperature represent the contribution from lattice vibration. The fitting parameters from Eq. (1) are listed in Table 3, and the corresponding percent fitting deviation curve is presented in Fig. 5. It can be seen the percent root-mean-square deviation (%RMS) and fitting deviation are within 0.841 and ± 1%, respectively, indicating that the theoretical model of Eq. (1) could exactly express the heat capacity data of these two compounds below 10 K.

Table 3 Fitting parameters of heat capacities of d-ribose and d-mannose
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Fig. 5
figure 5

Plot of deviations (100 × (Cexp−Cfitted)/Cfitted) of the experimental heat capacities from the fitted values against temperatures for d-ribose and d-mannose below 10 K

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In the middle temperature range of 10–55 K, the heat capacities were fitted to the following polynomial function [22],

$$C^{\rm o}_{\text{p,m}} = A_{0} + A_{1} T + A_{2} T^{2} + A_{3} T^{3} + A_{4} T^{4} + A_{5} T^{5} + A_{6} T^{6} + A_{7} T^{7} + A_{8} T^{8} + A_{9} T^{9}$$
(2)

As for the high-temperature region above 50 K, the heat capacities were fitted to a combination of Debye and Einstein function,

$$C^{\rm o}_{\text{p,m}} = n_{\text{D}} D\left( {\theta_{\text{D}} } \right) \, + n_{\text{E}} E\left( {\theta_{\text{E}} } \right) \, + aT + bT^{2}$$
(3)

where θD and θE are Debye and Einstein temperatures, D(θD) and E(θE) are Debye and Einstein functions, and nD and nE are Debye and Einstein parameters, respectively, and the term of (aT + bT2) is used for the correction of (Cv–Cp) [23].

All the fitting parameters and %RMS in the corresponding temperature regions are listed in Table 3, and the fitted heat capacities using these parameters are plotted as dashed lines in Fig. 4. The fitting %RMS are 0.841, 0.221, and 0.174 for d-ribose, and 0.586, 0.268, and 0.208 for d-mannose in low-, middle- and high-temperature region, respectively, indicating that these fits can be representative of the measured heat capacity data.

DSC heat capacities

To further study the thermodynamic property at higher temperatures, the heat capacities of d-ribose and d-mannose were measured using the DSC in the temperature range from 180 K up to 440 K. The measurement results are shown in Fig. 6, and the corresponding heat capacity data are provided in Supporting Information (SI). The heat capacities measured by PPMS are also shown in Fig. 6 to compare with the DSC data in the overlapping temperature region. It can be seen in the heat capacity curve that both compounds behave a solid–liquid transition in this temperature region. The heat flows recorded in the DSC measurements are presented in Fig. 7, and the melting onset temperature, peak temperature and transition enthalpy could be determined to be 355.27, 366.23 and 26.02 kJ mol−1 for d-ribose, and 403.09, 412.26 and 26.41 kJ mol−1 for d-mannose.

Fig. 6
figure 6

Plot of the experimental heat capacities of d-ribose and d-mannose within the temperature range from 1.9 to 440 K from DSC and PPMS measurements

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Fig. 7
figure 7

Plot of the experimental heat flows for d-ribose and d-mannose from DSC measurement

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Also, it can be noted that the DSC data is a little larger than the PPMS data, and their deviations are determined in Fig. 8 to be within 3 and 5% for d-ribose and d-mannose, respectively. These deviations are likely reasonable since these two sets of data were measured using two different calorimetric methods, and also the DSC measurement uncertainties may be easily affected by many factors, such as sample amounts, morphologies, conductivities, as well as experimental conditions [24]. In order to avoid the effect of these deviations on the thermodynamic function calculation over the entire temperature region, we have scaled the DSC heat capacity data by multiplying a scaling factor to match the PPMS data. The scaling factors are 0.975 and 0.961 for d-ribose and d-mannose, respectively. The scaled DSC heat capacities in the solid and liquid phase temperature region were fitted to a polynomial function of Eq. (2), and the data in the melting transition region were fitted using a spline fitting method. The fitting parameters and corresponding RMS% are listed in Table 4.

Fig. 8
figure 8

Plot of deviations (100 × (Cdsc−Cppms)/Cppms) of PPMS heat capacities from those of DSC in the region of T = 180 to 300 K

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Table 4 Fitting parameters in solid–liquid transition region for the experimental molar heat capacity of d-ribose and d-mannose measured by DSC
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Thermodynamic functions

Based on the heat capacity fitting parameters listed in Tables 3 and 4, the thermodynamic functions of d-ribose and d-mannose have been calculated using the thermodynamic relationship of Eqs. (4) and (5) in the temperature range from 0 to 440 K, and the calculated results are listed in Table 5. The standard molar heat capacity, entropy and enthalpy at 298.15 K and 0.1 MPa have been determined to be \(C_{\text{p, m}}^{\rm o}\) = 185.66 ± 1.86 J K−1 mol−1, \(S_{\text{m}}^{\rm o}\) = 176.72 ± 1.77 J K−1 mol−1 and \(H_{\text{m}}^{\rm o}\) = 278.41 ± 2.78 kJ mol−1 for d-ribose, and \(C_{\text{p, m}}^{\rm o}\) = 223.44 ± 2.23 J K−1 mol−1, \(S_{\text{m}}^{\rm o}\) = 216.53 ± 2.17 J K−1 mol−1 and \(H_{\text{m}}^{\rm o}\) = 339.39 ± 3.39 kJ mol−1 for d-mannose.

Table 5 Standard thermodynamic functions of d-ribose and d-mannose as a function of temperature T at the standard pressure po = 0.1 MPa
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$${\text{S}}_{\text{m}}^{o} (T) = \mathop \smallint \limits_{0}^{T} \frac{\left( T \right)}{T}{\text{d}}T$$
(4)
$$\frac{{\Delta \frac{T}{0}\left( T \right)}}{T} { = }\frac{{ \mathop \smallint \nolimits_{0}^{T} \left( T \right){\text{dT}}}}{T}$$
(5)

Comparison to previous results

Torres et al. performed heat capacity measurements in 2009 on d-ribose and d-mannose in the temperature range from 288.15 to 358.15 K using a power-compensation differential scanning calorimeter [25]. Also, Kawaizumi et al. determined the heat capacities of these two compounds using a laboratory-constructed isoperibol twin calorimeter of dry shield type at room temperature as early as 1981[26]. These previous data have been plotted in Fig. 9 to compare with our measured data. It can be seen that the deviations of our d-ribose DSC data are within about −0.01 and 3% from the data of Torres and Kawaizumi, respectively, indicating that our data agree well with these previous results. For d-mannose, our PPMS data deviate from Kawaizumi’s data to be about 4%. However, the DSC data from Torres are not smoothed below 303 K, and the deviations of their data above 303 K from our DSC data are within about 7%.

Fig. 9
figure 9

Comparison of measured heat capacities in this work from those reported in literature

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It should pointed out that, as far as we known, the thermodynamic properties of the melting transition have not been reported for d-ribose and d-mannose, except that Goldberg and Tewari [15] indicated their melting temperature to be 360 and 406 K for d-ribose and d-mannose, respectively. These melting temperature are in roughly agreement with our DSC onset temperature of 355.27 and 403.09 K. However, we could not find the related report on the melting transition enthalpy for these two compounds in previous literatures.

Conclusions

In summary, the heat capacities of d-ribose and d-mannose have been measured in the temperature range from 1.9 to 440 K using a combination of PPMS and DSC calorimeter, and the thermodynamic functions of these two compounds have been calculated based on the fitting parameters as well as the theoretical and empirical models used in the heat capacity data fitting. The standard molar heat capacity, entropy and enthalpy at 298.15 K and 0.1 MPa have been determined to be \(C_{\text{p, m}}^{\rm o}\) = 185.66 ± 1.86 J K−1 mol−1, \(S_{\text{m}}^{\rm o}\) = 176.72 ± 1.77 J K−1 mol−1 and \(H_{\text{m}}^{\rm o}\) = 278.41 ± 2.78 kJ mol−1 for d-ribose, and \(C_{\text{p, m}}^{\rm o}\) = 223.44 ± 2.23 J K−1 mol−1, \(S_{\text{m}}^{\rm o}\) = 216.53 ± 2.17 J K−1 mol−1 and \(H_{\text{m}}^{\rm o}\) = 339.39 ± 3.39 kJ mol−1 for d-mannose. Also, using the DSC heat flows, the melting onset temperature, peak temperature and transition enthalpy have been determined to be 355.27, 366.23 and 26.02 kJ mol−1 for d-ribose, and 403.09, 412.26 and 26.41 kJ mol−1 for d-mannose.