English

• 0.   Introduction

  At present, the chemical research on lactic acid has gradually shifted from industrial and pharmaceutical applications to basic theoretical research. The research on the coordination of lactic acid with metals is an important aspect^[1]. Lactic acid molecules contain adjacent hydroxyl and carboxyl groups. When coordinated with metal, one oxygen atom in the hydroxyl group and two oxygen atoms in the carboxyl group can participate in coordination. Therefore, metal complexes of lactic acid have the characteristics of many coordination sites, large coordination numbers, and various coordination forms. The molecular structure of lactic acid is small and there is no conjugation in the molecule, so the coordination has little effect on the chemical properties. Lactic acid is often used as a filler to react with other macrocyclic ligands with rare earth to form mixed complexes^[1-4]. In addition, a series of physical properties such as metal solubility can be changed through the water solubility and other properties of lactic acid. Although there are many reports on the synthesis and application of metal complexes of lactic acid^[5-8], these reports mainly focused on food additives and nutrients, such as the effect of zinc lactate additives on protein solubility^[9]. There are few reports on their structural chemistry, thermochemistry, and solution chemistry in the literature, especially the accurate study of lactate electrolyte aqueous solution by isoperibol solution - reaction calorimeter. To deeply understand the thermodynamic regularity between the structure and properties of these complexes^[10-14], it is necessary to study the coordination mode of lactic acid with metal ions and the thermodynamic properties of their interaction in solution.

  The idea of this work is to characterize the structure of the complex by X-ray single crystal diffractometer and to determine its composition and crystal space structure. With the aid of the solution reaction calorimeter, the change of thermal effect in the dissolution process of the complex was accurately measured. According to the theories and methods of solution chemistry, the interaction regularity of complex in solution was deeply studied. It provides data reference for the further study of metal complexes of lactic acid.

  1.   Experimental

  1.1   Synthesis

  Details of the reaction reagents are listed in Table 1. D/L - lactic acid, ammonia, and strontium hydroxide react in a molar ratio of 4:2:1. Lactic acid and strontium hydroxide were weighed respectively according to the molar ratio, dissolved in ultra - pure water, and mixed. The mixture was added into a round bottom flask, and the pH value of the solution was adjusted with approximately a molar amount of ammonia (the pH value was controlled at about 9.0) to make the reaction proceed in an ultra-positive direction. After refluxing for two hours, anhydrous ethanol was added while hot until slightly turbid, and the mixture was filtered while hot. After standing for three weeks, the colorless acicular crystals were precipitated. The resulting equation can be expressed as:

  Table 1

  

  Table 1.  Provenance and purity of the reagents

  下载: 导出CSV

  Chemical name	Chemical formula	Source	Purity (mass fraction)*	CAS No.
  D/L-lactic acid	C3H6O3	Budweiser Chemical Technology Co., Ltd.	90.00%	50-21-5
  Strontium hydroxide	Sr(OH)2	Tianjin Fengchuan Chemical Reagent Technology Co., Ltd.	99.99%	18480-07-4
  Absolute ethanol	C2H5OH	Tianjin Fengchuan Chemical Reagent Technology Co., Ltd.	99.99%	64-17-5
  Ammonia	NH3·H2O	Budweiser Chemical Technology Co., Ltd.	25%	1336-21-6
  Potassium chloride	KCl	Budweiser Chemical Technology Co., Ltd.	99.99%	7447-40-7
  Ultra-pure water	H2O	Laboratory self-made	99.99%	—
  *The purity was provided by the supplier.

  $ \mathrm{Sr}(\mathrm{OH})_2+2 \mathrm{NH}_3 \cdot \mathrm{H}_2 \mathrm{O}+4 \mathrm{C}_3 \mathrm{H}_6 \mathrm{O}_3= \\ \quad\quad\quad\quad\quad\quad \left(\mathrm{NH}_4\right)_2\left[\mathrm{Sr}\left(\mathrm{C}_3 \mathrm{H}_5 \mathrm{O}_3\right)_4\right]+4 \mathrm{H}_2 \mathrm{O} $

  The target complex synthesized was (NH₄)₂[Sr(C₃H₅O₃)₄]. After suction filtration and recrystallization three times, the product was dried in a vacuum drying oven for 12 hours, and then it was put into a clean weighing bottle and placed in the drying oven for testing.

  The sample was placed in a vacuum desiccator at 298 K to dry in a vacuum for six days, then it was put into the weighing bottle and preserved in a desiccator. The actual mass fraction of the sample was more than 90% by a chromatographic method (HPLC) and ion chromatography (for each ion). Through calculation, the yield of the reaction was more than 90%. It should be noted that the yield of the reaction was not the most critical factor, because we had to recrystallize the primary product of the reaction. The X - ray diffraction (XRD) pattern of the sample is shown in Fig. 1. The instrument was an XD - 2700 X - ray diffractometer (Cu Kα₁, λ =0.154 06 nm) with a voltage of 40 kV, current of 35 mA, and scanning range (2 θ) of 5°-45°. The mass fraction (purity) of Sr in the complex was determined by chemical analysis. C, N, and H were determined using element analysis (model: PE-2400, Perkin-Elmer, USA). Elemental analysis Calcd. for (NH₄)₂[Sr(C₃H₅O₃)₄](%): Sr, 18.33; C, 30.01; N, 5.82; H, 5.83. Found(%): Sr, 18.25; C, 30.03; N, 5.84; H, 5.88.

  Figure 1

  

  Figure 1.  XRD pattern of (NH₄)₂[Sr(C₃H₅O₃)₄]

  下载: 全尺寸图片 幻灯片

  1.2   X-ray crystallography

  The crystal with a size of 0.23 mm×0.20 mm×0.18 mm was glued to the fine glass fibers and then mounted on the Bruker Smart-1000 CCD diffractometer with Mo Kα radiation (λ=0.071 073 nm). The intensity data were collected in the φ-ω scan mode at T=298 K. The structure was solved by the direct method and the differential Fourier synthesis, and all non-hydrogen atoms were refined anisotropically on F² by the full - matrix least-squares method. All calculations were performed with the SHELXTL program package. The program used in the building structure was Diamond 3.2 software.

  1.3   Quantum chemical calculation

  The graphics software selected for quantum chemical calculation in this experiment was CrystalExplorer17.5^[15]. CrystalExplorer17.5 provides a new way of visualizing molecular crystals using the full suite of Hirshfeld surface tools^[16]. Hirshfeld surface is the isosurface with a weight coefficient, w(r), equal to 0.5. The average charge density of molecules inside the isosurface should exceed the average charge density of all surrounding molecules (w(r) < 0.5 within the isosurface, w(r)≥0.5 outside the isosurface). This ratio was also approximately the ratio of the charge density of real molecules to that of real crystals. Hirshfeld surface^[16] is a new definition of molecular surface. Hirshfeld surface analysis can get real and continuous 3D visualization, and 2D fingerprint is the 2D representation of Hirshfeld surface analysis.

  1.4   Isoperibol solution-reaction calorimetry

  The model of the isoperibol solution-reaction calorimeter used in this work is SRC - 100. This model of the calorimeter was developed and improved by Yu and Dong et al.^[17] based on summing up years of experience in thermochemistry and calorimetry and referring to the work of their counterparts at home and abroad. It has the characteristics of simple operation and high precision. To obtain a certain experimental accuracy, the SRC-100 requires a sample mass of 0.2-0.6 g each time. The total mass of each sample was 1 - 3 g when calculated five times in parallel according to each group of experiments. After weighing the sample, we dissolved it in a Dewar bottle filled with 100 mL of ultra - pure water. The Dewar bottle needed to be preheated in a constant-temperature water bath for several minutes before the test. The test process might produce a certain degree of uncertainty. This uncertainty was a comprehensive uncertainty considering factors such as mass weighing, electric energy calibration (including current, resistance, time), and temperature rise change. The precision and accuracy of the instrument needed to be checked and corrected by chemical calibration. In this experiment, the KCl calibrator was dissolved in ultra-pure water for calibration. The details were as follows: an electronic balance with an accuracy of more than 0.001 g was used to weigh 0.365 g of treated highpurity KCl, and the KCl was dissolved in 100 mL of ultra - pure water and then measured. The enthalpy of dissolution of KCl obtained was (17.602±0.014) kJ·mol^-1, as shown in Table 2. This result was close to the literature value^[18] of (17.597±0.017) kJ·mol^-1.

  Table 2

  

  Table 2.  Molar enthalpy of solution of KCl in water at 298 K

  下载: 导出CSV

  No.	m / g	n / mmol	ΔsHm/(kJ·mol-1)
  1	0.374 7	5.026 2	17.559
  2	0.374 7	5.026 2	17.628
  3	0.374 8	5.027 5	17.580
  4	0.375 2	5.032 9	17.629
  5	0.374 6	5.0248	17.612

  1.5   Differential thermal analysis

  The detection instrument used for thermogravimetric (TG) and differential thermogravimetric (DTG) analysis was the DTA - 1700 differential thermal analyzer. The measurement was taken in the Al₂O₃ crucible with the sample mass of 5 mg under air atmosphere (40 mL·min^-1). Dynamic scans were performed at the heating rate of 10 ℃ ·min^-1 in a temperature range of 20-800 ℃. From the TG curve, relevant data such as thermal stability and thermal analysis product of the sample could be obtained, and the relationship between the sample mass change rate and temperature could also be obtained.

  2.   Results and discussion

  2.1   Description of crystal structure

  Table 3 shows that the crystal of (NH₄)₂[Sr(C₃H₅O₃)₄] is monoclinic, and the space group is C2/c. The selected bond lengths and angles of the complex are listed in Table 4. The information on hydrogen bonds is shown in Table 5.

  Table 3

  

  Table 3.  Crystallographic data of the complex

  下载: 导出CSV

  Parameter	(NH4)2[Sr(C3H5O3)4]
  Empirical formula	C12H28SrN2O12
  Formula weight	479.98
  Crystal system	Monoclinic
  Space group	C2/c
  a / nm	1.799 02(16)
  b / nm	1.047 00(11)
  c / nm	1.074 31(13)
  β/(°)	93.581 0(10)
  Volume / nm3	2.019 6(4)
  Z	4
  Dc / (g·cm-3)	1.579(2)
  Absorption coefficient / mm-1	2.73
  F(000)	992
  θ range for data collection / (°)	2.25-25.02
  Limiting indices	-21 ≤ h≤ 21, -12 ≤ k≤ 10, -12 ≤ l≤ 9
  Reflection collected, unique	5 061, 1 793 (Rint=0.051 5)
  Completeness to θ=25.02°/ %	99.9
  Absorption correction	Semi-empirical from equivalents
  Max. and min. transmission	0.639 3 and 0.448 3
  Data, restraint, number of parameters	1 793, 0, 155
  Goodness-of-fit on F2	1.037
  Final R indices [I > 2σ(I)]	R1=0.042 0, wR2=0.108 0
  R indices (all data)	R1=0.051 4, wR2=0.112 2
  (Δρ)max and (Δρ)min / (e·nm-3)	714 and -514

  Table 4

  

  Table 4.  Selected bond lengths (nm) and angles (°) of the complex

  下载: 导出CSV

  Sr1—O1	0.256 3(3)	Sr1—O6	0.2540(3)	Sr1—O3	0.257 0(3)
  Sr1—O4	0.251 2(3)	O5—C4	0.130 6(11)	O6—C5	0.143 2(19)
  O1—C1	0.123 0(5)	C1—C2	0.1527(5)	O2—C1	0.125 7(4)
  C2—C3	0.151 4(7)	O3—C2	0.1427(4)	C4—C5	0.150(2)
  O4—C4	0.119 5(5)
  O1—Sr1—O1ⅰ	91.20(13)	O1ⅰ—Sr1—O3	94.29(9)	O6ⅰ—Sr1—C4ⅰ	44.56(10)
  O4ⅰ—Sr1—O4	78.68(15)	O6—Sr1—C4ⅰ	97.58(11)	O4—Sr1—O6ⅰ	82.77(10)
  C4ⅰ—Sr1—C1ⅰ	157.69(11)	O1—Sr1—O3	59.84(8)	O4—Sr1—O6	61.71(9)
  C1—O1—Sr1	122.9(2)	C2—O3—Sr1	121.0(2)	O1ⅰ—Sr1—C1ⅰ	17.73(9)
  C4—O4—Sr1	124.5(3)	O1—Sr1—C1ⅰ	99.88(9)	O4—Sr1—C1ⅰ	84.64(10)
  C5—O6—Sr1	124.1(8)	O1—Sr1—C4ⅰ	92.95(11)	O4ⅰ—Sr1—C1ⅰ	163.05(10)
  O1—C1—O2	124.9(4)	O1ⅰ—Sr1—C4ⅰ	175.00(11)	O4—Sr1—C4ⅰ	78.31(12)
  O1—C1—C2	119.3(3)	O3—Sr1—O3ⅰ	144.41(15)	O3ⅰ—Sr1—C1ⅰ	44.28(9)
  O4ⅰ—Sr1—C4ⅰ	17.15(10)	O2—C1—C2	115.8(3)	O3—Sr1—C1ⅰ	112.01(10)
  O6—Sr1—O1	133.67(8)	O3—C2—C1	106.8(3)	O3—Sr1—C4ⅰ	90.20(11)
  O6ⅰ—Sr1—O1	81.49(10)	O3—C2—C3	111.1(4)	O3ⅰ—Sr1—C4ⅰ	117.01(10)
  O6—Sr1—O1ⅰ	81.49(10)	C3—C2—C1	110.0(4)	O4—Sr1—O1ⅰ	96.99(10)
  O6—Sr1—O3	119.64(9)	O4—C4—O5	122.2(8)	O4—Sr1—O1	163.83(9)
  O6—Sr1—O3	75.08(9)	O4—C4—C5	123.6(8)	O4—Sr1—O3	132.84(10)
  O6—Sr1—O6ⅰ	134.37(13)	O5—C4—C5	113.4(8)	O4—Sr1—O3ⅰ	78.04(10)
  O6ⅰ—Sr1—C1ⅰ	119.36(9)	O6—C5—C4	106.1(12)	C4—C5—C6	105.1(13)
  O6—Sr1—C1ⅰ	86.70(9)	O6—C5—C6	106.7(10)
  Symmetry code: ⅰ -x, y, -z+1/2.

  Table 5

  

  Table 5.  Hydrogenbond parameters of the complex

  下载: 导出CSV

  D—H…A	d(D—H) /nm	d(H…A) /nm	d(D…A) /nm	∠(DHA)/(°)
  O6—H6…O1ⅱ	0.082	0.194	0.275 5(4)	174.8
  O3—H3…O2ⅲ	0.082	0.190	0.270 1(4)	164.8
  Symmetry codes: ⅱ x, -y+1, z+1/2; ⅲ -x+1/2, -y+1/2, -z.

  Fig. 2 shows the molecular structure of (NH₄)₂ [Sr(C₃H₅O₃)₄]. Strontium ion (Sr²⁺) coordinates with the oxygen atom of carboxyl and the hydroxyl oxygen atom of four lactic acid molecules to form an eight-coordinated complex with a triangular dodecahedron configuration (Fig. 3). Four fivemembered ring structures are formed around Sr²⁺. Four five - membered rings form an axial symmetric suspension structure to increase the stability of the complex. It can be seen that some carbon and oxygen atoms are disordered in the molecule. It can be seen from Table 4 that the bond length of the Sr—O is not the same, and Sr²⁺ and oxygen in the coordination group form an irregular coordination triangular dodecahedron of the inner orbit type. Fig. 4 is the crystal cell diagram of (NH₄)₂ [Sr(C₃H₅O₃)₄]. The molecules of (NH₄)₂ [Sr(C₃H₅O₃)₄] are mainly combined by coordination bonds, and the molecules are arranged regularly in space mainly by intermolecular hydrogen bonds. Hydrogen bonds O6—H6…O1^ⅱ, O3—H3…O2^ⅲ (Table 5) and van der Waals forces exist simultaneously in the crystal to stabilize the structure. NH₄⁺ plays no role in coordination, and its main role is to balance the charge of the whole system.

  Figure 2

  

  Figure 2.  Molecular structure of (NH₄)₂[Sr(C₃H₅O₃)₄]

  Symmetry code: ^ⅰ-x, y, 1/2-z

  下载: 全尺寸图片 幻灯片

  Figure 3

  

  Figure 3.  Coordination environment diagram of Sr²⁺

  下载: 全尺寸图片 幻灯片

  Figure 4

  

  Figure 4.  Unit cell diagram of (NH₄)₂[Sr(C₃H₅O₃)₄]

  下载: 全尺寸图片 幻灯片

  2.2   Hirshfeld surface analysis

  The Hirshfeld surface and 2D fingerprint plot of the complex were created using CrystalExplorer17.5 software. d_e and d_i in the 2D fingerprint plot represent the length from the Hirshfeld surface to the outer distance of the nearest atom and from the surface to the inner distance of the nearest atom, respectively. d_norm is the normalized contact distance calculated from d_e and d_i^[16]. All of them represent intermolecular interactions of the complex. Fig. 5a-5c show the Hirishfeld surface drawn according to d_norm, d_e, and d_i, respectively. Among them, the red region and orange region represent the region with the strongest intermolecular force. It can be seen from Fig. 5a-5c that the title compound is a metal complex with more active sites. Fig. 5d is a 2D fingerprint plot corresponding to Fig. 5a. Fig. 6 shows how the breakdown of the 2D fingerprint plot can be used to identify the patterns associated with specific interactions (H…H, H…O, etc.). Fig. 6a and 6b show the close interaction of H…H (accounting for 46.5%), indicating that the intermolecular interaction of the complex mainly depends on hydrogen bond. Fig. 6c and 6d show the H…O interaction (accounting for 20.3%), which is part of the hydrogen bond. It can be seen from the 2D fingerprint plot that the hydrogen bond donor is located inside the Hirshfeld surface. Fig. 6e and 6f show the O…H interaction (accounting for 30.9%), which is part of the hydrogen bond. It can be seen from the 2D fingerprint plot that the hydrogen bond donor is located outside the Hirshfeld surface. The two interactions of H…O and O…H lead to distinct red - spotted areas on the Hirshfeld surface of the complex, which is consistent with the data in Table 5. The intermolecular interaction of the complex mainly depends on O—H…O hydrogen bonding. The Hirshfeld surface and 2D fingerprint plots reveal that the complex has many coordination sites and strong coordination activity. More coordination sites and stronger activity enhance the solubility and chemical reactivity of the complex.

  Figure 5

  

  Figure 5.  Hirshfeld surface for (NH₄)₂[Sr(C₃H₅O₃)₄] mapped with d_norm (a), d_i (b), and d_e (c) over a range of 0-0.38 nm; (d) 2D fingerprint plot corresponding to the three pictures

  下载: 全尺寸图片 幻灯片

  Figure 6

  

  Figure 6.  Fingerprint plots for H in (NH₄)₂[Sr(C₃H₅O₃)₄], broken down into contributions from specific pairs of atom-types: (a, b) H…H; (c, d) H…O; (e, f) O…H

  For each plot, the grey shadow is an outline of the complete fingerprint plot

  下载: 全尺寸图片 幻灯片

  2.3   Calculation of lattice potential energy

  The lattice energy of the complex was calculated by the following formula^[19]:

  $ U_{\text {РОT }}=\left|z_{+}\right|\left|z_{-}\right| v\left(\alpha^{\prime} / V_m^{1 / 3}+\beta^{\prime}\right) $

  (1)

  where z₊ and z_- are the valences of cations and anions respectively, v represents the total number of anions and cations in each molecule, V_m represents the molecular volume of the complex (V_m can be calculated by the formula V_mN_A=M_m/ρ, where N_A is Avogadro constant, M_m is the relative molar mass, ρ is the density, the values of M_m and ρ can be obtained from Table 1), and α' and β' are fitting coefficients. The charge ratio of cation to the anion of the di-valence metal salt of lactic acid is 1:2, z₊=3, z_-=1, v=4, α'=133.5 kJ·mol^-1·nm, β'=60.9 kJ·mol^-1. The lattice energy of the samples could be deduced from the crystallographic data of the metal complex of lactic acid. In addition, for a salt of molecular formula M_pX_q,

  $ V_{\mathrm{m}}\left(\mathrm{M}_p \mathrm{X}_q\right)=p_1 V_{1+}+p_2 V_{2+}+q V_{-} $

  (2)

  where V₁₊, V₂₊, and V_- are the volumes of the metal cation (M²⁺), ammonium ion (NH₄⁺), and lactate ion (C₃H₅O₃^-), p₁ =1, p₂=2, and q=4 for (NH₄)₂[Sr(C₃H₅O₃)₄]. According to relevant literature reports^[20], V_{Sr^{2 +}} and V_NH4⁺ are 0.020 1, 0.021 3 nm³ respectively. When substituted into Eq. 2, the volume size of the anion (C₃H₅O₃^-) was 0.103 1 nm³. The values of lattice energy and volumes of anion and cation were listed in Table 6.

  Table 6

  

  Table 6.  Lattice energy (U_POT) and volumes (V_m) of anion and cation of the complex

  下载: 导出CSV

  Complex	Vm / nm3	UPOT / (kJ·mol-1)	V+ / nm3	V- / nm3
  (NH4)2[Sr(C3H5O3)4]	0.504 7	2 742.9	0.092 5	0.103 1

  2.4   Molar enthalpies of dissolution at infinite dilution and Pitzer parameters

  The molar enthalpies of dissolution of lactate at different concentrations at 298 K were determined by an isoperibol solution - reaction calorimeter, and the molar enthalpy of dissolution of the lactate complex can be expressed as^[21]:

  $ \Delta_{\mathrm{s}} H_{\mathrm{m}}=\Delta_{\mathrm{s}} H_{\mathrm{m}}^{\infty}+{ }^{\varPhi} L $

  (3)

  Where Δ_sH_m^∞ represents the infinite dilution molar dissolution enthalpy of the sample and ^ΦL is the apparent relative molar enthalpy. For 2:1 lactate complexes (i.e. divalent metal complexes), the aqueous solution can be represented by Pitzer's electrolyte solution theory^[21-23]:

  $ { }^{\varPhi} L=2.5 A_{\mathrm{H}} \ln \left(1+1.2 I^{1 / 2}\right)-\\4 R T^2\left[m\left(\beta_{\mathrm{MX}}^{(0) L}+y^{\prime} \beta_{\mathrm{MX}}^{(1) L}\right)+1.4 m^2 1.4 m^2 C_{\mathrm{MX}}^{\varPhi_L}\right] $

  (4)

  $ \beta_{\mathrm{MX}}^{(0) L}=\left(\partial \beta_{\mathrm{MX}}^{(0)} / \partial T\right)_P $

  (5)

  $ \beta_{\mathrm{MX}}^{(1) L}=\left(\partial \beta_{\mathrm{MX}}^{(1)} / \partial T\right)_P $

  (6)

  $ C_{\mathrm{MX}}^{\varPhi_L}=\left(\partial C_{\mathrm{MX}}^{\varPhi} / \partial T\right)_P $

  (7)

  Among them, β_MX^(0)L and β_MX^(1)L represent various short-range forces between ions and the three - ion action term, and C_MX^Φ_L only shows its important role when the solution concentration is high. The values of β_MX^(0)L, β_MX^(1)L, and C_MX^Φ_L can be obtained by fitting the measured data in this experiment by the least square method. A_H represents the Debye - Huckel parameter of enthalpy, A_H=1 986 J·mol^-1 at 298 K. m represents the mass molar concentration of the sample (mol·kg^-1). For general electrolytes, the absolute values of the β_MX^(0)L and β_MX^(1)L parameters are very small (between 10^-2 and 10^-4), and there is a tendency to increase with the increase of the volume and number of ions.

  After substituting Eq.4 into Eq.3 and rearranged, the equation can be derived as follows:

  $ \begin{aligned} Y & =\left[\Delta_{\mathrm{s}} H_{\mathrm{m}}-2.5 A_{\mathrm{H}} \ln \left(1+1.2 I^{1 / 2}\right)\right] /\left(2 R T^2\right) \\ & =\alpha_0-2 m \beta_{\mathrm{MX}}^{(0) L}-2 m y^{\prime} \beta_{\mathrm{MX}}^{(1) L} \end{aligned} $

  (8)

  where Y represents the extrapolation function, which can be calculated from experimental data, and α₀ and y' are respective:

  $ \alpha_0=\Delta_{\mathrm{s}} H_{\mathrm{m}}^{\infty} /\left(2 R T^2\right) $

  (9)

  $ y^{\prime}=\left[1-\left(1+2 I^{1 / 2}\right) \exp \left(-2 I^{1 / 2}\right)\right] /(2 I) $

  (10)

  The experimental value of Δ_sH_m^∞ is subjected to multivariate linear fitting according to Eq. 8, then parameters α₀, β_MX^(0)L, β_MX^(1)L, and fitted standard deviation s are obtained. The infinite dilution molar dissolution enthalpy Δ_sH_m^∞ of lactate complex in water was calculated by Eq.9.

  The relative partial molar enthalpies (L₁ and L₂) of the solvent and the solute are important thermodynamic data of the electrolyte solution. Generally speaking, there are many ways to determine the relative partial molar enthalpy. The equations used in this article are as follows:

  $ \bar{L}_1=-M_{\mathrm{H}_2 \mathrm{O}} m^2\left(\partial^{\varPhi} L / \partial m\right)_{T, P} $

  (11)

  $ \bar{L}_2={ }^{\varPhi} L+m\left(\partial^{\varPhi} L / \partial m\right)_{T, P} $

  (12)

  Under constant temperature and pressure, the partial derivative of Eq.4 for concentration was obtained:

  $ \left(\partial^{\Phi} L / \partial m\right)_{T, P}=2.6 A_{\mathrm{H}} /\left(m^{1 / 2}+2.08 m\right)- \\ 4 R T^2\left[\beta_{\mathrm{MX}}^{(0) L}+\beta_{\mathrm{MX}}^{(1) L} \exp \left(-3.46 m^{1 / 2}\right)+2.8 m C_{\mathrm{MX}}^{\varPhi_L}\right] $

  (13)

  The relative partial molar enthalpy L₁ of solvent water and the relative partial molar enthalpy L₂ of the sample were calculated. The details are listed in Table 7.

  Table 7

  

  Table 7.  Summary of the molar dissolution enthalpy^a (Δ_sH_m), relative partial molar enthalpy^b (L₁) and (L₂) of (NH₄)₂[Sr(C₃H₅O₃)₄] in water at 298 K

  下载: 导出CSV

  mc/(mol·kg-1)	ΔsHm/(kJ·mol-1)	(∂ΦL/∂m)T, Pd	L1 / (J·mol-1)	L2 / (kJ·mol-1)
  0.66×10-4	110.919	-1.141 11×109	-2.620	5.269
  2.31×10-4	104.031	-1.080 41×109	9.323	-3.221
  3.80×10-4	98.844	-1.030 67×109	26.534	-9.763
  6.12×10-4	92.472	-9.616 2×108	64.334	-18.113
  7.70×10-4	89.161	-9.196 5×108	96.959	-22.719
  9.18×10-4	86.705	-8.834 7×108	131.999	-26.382
  1.048×10-3	84.997	-8.538 0×108	165.980	-29.176
  1.225×10-3	83.250	-8.160 0×108	216.474	-32.488
  1.483×10-3	81.667	-7.647 1×108	297.308	-36.681
  1.669×10-3	81.068	-7.293 1×108	359.689	-39.541
  1.957×10-3	80.745	-6.746 9×108	460.699	-44.297
  2.245×10-3	80.853	-6.172 6×108	564.085	-50.205
  2.847×10-3	81.31	-4.729 3×108	772.909	-70.036
  3.468×10-3	80.964	-2.619 9×108	950.814	-107.942
  4.285×10-3	79.250	-1.692 7×108	1 070.059	-199.092
  a The ratio of the enthalpy of dissolution of the complex to the amount n of the substance under standard pressure is called their standard molar enthalpy of dissolution, written as ΔsHm; b The relative partial molar enthalpies of solvent and solute are expressed as L1 and L2 respectively, which are important thermodynamic parameters of electrolyte solution. The formula used in this work is as follows: L1=-MH2Om2(∂ΦL/∂m)T, P and L2=ΦL+m(∂ΦL/∂m)T, P; c m is the mass molar concentration; d (∂ΦL/∂m)T, P is the partial derivative of relative partial molar enthalpy to m, and its formula is expressed as Eq.13.

  Fig. 7 shows the tendency of molar enthalpy of dissolution of the complex with concentration. The fitting function expression of molar enthalpy of dissolution is y=112.337 1-40 110.8x+15 766 900x²-1 924 210 000x³, where the fitting similarity is equal to 0.991 5. It can be seen from the curve that its molar enthalpy of dissolution Δ_sH_m was positive, indicating that the dissolution of the complex is an endothermic process. The infinite dilution molar enthalpy of dissolution Δ_sH_m^∞ of the complex is listed in Table 8, which was (114.01±0.04) kJ·mol^-1, considering the relative standard deviation of fitting s. The 3D structure diagram of the extrapolation function Y of the complex varying with -2m and -2my' is drawn in Fig. 8, indicating that the extrapolation function Y has a good linear fitting relationship with the mass molar concentration m. the value of m was brought into Eq. 11, 12, and 13 respectively to calculate the relative partial molar enthalpy sum of solvent and solute, which are listed in Table 7.

  Figure 7

  

  Figure 7.  Functional relationship of measured enthalpy of dissolution of (NH₄)₂[Sr(C₃H₅O₃)₄] with molar concentration m at 298 K

  下载: 全尺寸图片 幻灯片

  Table 8

  

  Table 8.  Summary of infinite dilution molar enthalpy of solution and Pitzer's parameters of the complex at 298 K

  下载: 导出CSV

  Complex	α0	βMX(0)L	βMX(1)L	s	ΔsHm∞/(kJ·mol-1)
  (NH4)2[Sr(C3H5O3)4]	0.077 17	-8.394	105.196	1.999×10-6	114.01±0.04

  Figure 8

  

  Figure 8.  Three-dimensional diagram of extrapolation function Y of (NH₄)₂[Sr(C₃H₅O₃)₄] with -2m and -2my'

  下载: 全尺寸图片 幻灯片

  Pitzer's theory was used to obtain the parameters α₀, β_MX^(0)L, β_MX^(1)L, and the fitting standard deviation s. The data were listed in Table 8. It can be seen from Table 7 that the dissolution enthalpy of the complex was positive, indicating that the dissolution process is entropydriven endothermic. This is mainly due to the need to break the coordinate bond (lattice energy) and hydrogen bonds in the complex during the dissolution process, so a large amount of heat needs to be absorbed. In the complex, β_MX^(0)L was negative, i.e. (∂β_MX⁽⁰⁾/∂T)_P < 0, indicating that the value of β_MX^(0)L decreases with the increase of temperature. This indicates that the repulsion force decreases between ions with the increase in temperature. Pitzer parameters (β_MX^(0)L and β_MX^(1)L) of the complex were much larger than those of ordinary electrolytes (mostly in a range of 10^-4-10^-2). This is mainly because the volume of salt ions in the complex is much larger than that of ordinary electrolytes in this work, which also indicates that there is a strong short-range interaction between positive and negative ions in the solution.

  2.5   Enthalpy of hydration

  The thermodynamic cycle in Scheme 1 was to calculate the hydration enthalpy of the complex. The thermal effect of the formation of C₃H₅O₃^- (aq), NH₄⁺ (aq), and Sr²⁺ (aq) in solution comes from the sum of the hydration enthalpies of the corresponding gaseous ions C₃H₅O₃^- (g), NH₄⁺ (g), and Sr²⁺ (g). According to the thermochemical cycle, the calculation formula of hydration enthalpy of the complex of lactic acid is expressed as^[24]:

  $ \Delta_{\mathrm{s}} H_{\mathrm{m}}^{\infty}=U_{\mathrm{POT}}+2 R T+\Delta H_{+}+\Delta H_{-} $

  (14)

  Scheme 1

  

  Scheme 1.  Designed thermodynamic cycle to calculate the hydration enthalpy of (NH₄)₂[Sr(C₃H₅O₃)₄]

  下载: 全尺寸图片 幻灯片

  In the formula, ΔH₊ is the hydration enthalpy of cations, ΔH_- is the hydration enthalpy of anions, and (ΔH₊+ ΔH_-) is the sum of the hydration enthalpies of corresponding ions. Substituting the values of infinite dilution molar enthalpy and lattice energy of the complex into Eq. 14, it can be deduced that the sum of hydration enthalpies of cation and anion in (NH₄)₂[Sr(C₃H₅O₃)₄] was calculated to be -2 633.85 kJ·mol^-1. According to the literature^[25], the enthalpies of hydration of Sr²⁺ and NH₄⁺ were -1 470 and -329 kJ·mol^-1, respectively. Substituting the lattice energy of the complex and the hydration enthalpy of the corresponding metal cations into Eq. 14, the hydration enthalpy of D/L - lactate ion of (NH₄)₂[Sr(C₃H₅O₃)₄] was calculated to be -834.85 kJ·mol^-1.

  2.6   TG/DTG analysis

  The TG curve (Fig. 9) shows that the non-isothermal degradation, in a dynamic air atmosphere, of the sample occurred through three successive decomposition processes accompanied by mass losses. The weight loss rate from 70 to 230 ℃ was about 7.32%, which is caused by the decomposition of two ammonium ions in the complex and the decomposition of a small number of solvent molecules. From 250 to 520 ℃, the weight loss rate of this process was about 35.41%, which was close to the proportion of lactate ions coordinated by two molecules in the complex structure. From 550 to 750 ℃, the weight loss rate of this process was about 36.32%, which was close to the proportion of lactate ions coordinated by two molecules in the complex structure. There were three obvious peaks in the DTG curve. The corresponding temperatures of the bottoms of the three peaks were 162, 350, and 645 ℃, respectively. This also indirectly proves that the decomposition of the complex is a three continuous decomposition process. It's strong evidence to prove the molecular structure of the complex.

  Figure 9

  

  Figure 9.  TG/DTG curves of (NH₄)₂[Sr(C₃H₅O₃)₄]

  下载: 全尺寸图片 幻灯片

  3.   Conclusions

  The five-memberedring structure is the basic unit of (NH₄)₂[Sr(C₃H₅O₃)₄], and the suspension structure strongly enhancesthe stability of the complex. The metalion Sr²⁺ of the complex coordinate with the oxygen atoms of the lactate ion to form an eight-coordinated structure. The Hirshfeld surface and 2D fingerprint plot reveal thatthe complex has many coordination sites and strong coordination activity. The lattice energy of the complex wasderived to be 2 742.9 kJ·mol^-1. The volume of the D/L - lactate ion was 0.103 1 nm³. The molar enthalpy of dissolution Δ_sH_m of the complex of lactic acid was positive, indicating that the dissolution process of the complex is entropy-driven and endothermic. The infinite dilution molar enthalpy of dissolution Δ_sH_m^∞ and Pitzer's parameters (β_MX^(0)L and β_MX^(1)L) of the complex were calculated and obtained at 298 K. The hydration enthalpy of the complex and its D/L - lactate ion was determined to be -834.85 kJ·mol^-1.

  
  Acknowledgments: This work was financially supported by the National Natural Science Foundations of China (Grant No.21873063).
• 1. [1]

     Zhai S X, Liu Q Y, Zhao Y L, Sun H, Yang B, Weng Y X. A review: Research progress in modification of poly (lactic acid) by lignin and cellulose[J]. Polymers, 2021, 13(5):  776-791. doi: 10.3390/polym13050776

  2. [2]

     Siakeng R, Jawaid M, Ariffin H, Sapuan S M, Asim M, Saba N. Natural fiber reinforced polylactic acid composites: A review[J]. Polym. Compos., 2019, 40(2):  446-463. doi: 10.1002/pc.24747

  3. [3]

     Carlotti S J, Giani-Beaune O, Schué F. Characterization and mechani-cal properties of water-soluble poly (vinyl alcohol) grafted with lactic acid and glycolic acid[J]. J. Appl. Polym. Sci., 2001, 80(2):  142-147. doi: 10.1002/1097-4628(20010411)80:2<142::AID-APP1082>3.0.CO;2-4

  4. [4]

     Cao X J, Lee H J, Yun H S, Koo Y M. Crystallization and dissolution behavior of L (+) calcium and zinc lactate in ethanol-water solvent[J]. Korean J. Chem. Eng., 2002, 19(2):  301-304. doi: 10.1007/BF02698418

  5. [5]

     Duan C L, Song J L, Wang B Y, Li L, Wang R F, Zhang B W. Lactic acid assisted solvothermal synthesis of BiOCl_xI_1-x solid solutions as excellent visible light photocatalysts[J]. Chem. Res. Chin. Univ., 2019, 35(2):  277-284. doi: 10.1007/s40242-019-8274-7

  6. [6]

     Womersley R A. Metabolic effects of prolonged intravenous adminis-tration of magnesium lactate to the normal human[J]. J. Physiol., 1958, 143(2):  300-306. doi: 10.1113/jphysiol.1958.sp006060

  7. [7]

     Gu L Q, Qiu J H, Sakai E. Effect of DOPO-containing flame retardants on poly (lactic acid): Non-flammability, mechanical properties and thermal behaviors[J]. Chem. Res. Chin. Univ., 2017, 33(1):  143-149. doi: 10.1007/s40242-017-6196-9

  8. [8]

     Porciani P F, Grandini S, Chazine M. The effect of zinc lactate and magnolia bark extract added tablets on volatile sulfur-containing compounds in the oral cavity[J]. J. Clin. Dent., 2014, 25(3):  53-56.

  9. [9]

     Cao X J, Lee H J, Yun H S, Koo Y M. Solubilities of calcium and zinc lactate in water and water-ethanol mixture[J]. Korean J. Chem. Eng., 2001, 18(1):  133-135. doi: 10.1007/BF02707210

  10. [10]

      Štejfa V, Rohlíček J, Červinka C. Phase behaviour and heat capacities of selected 1-ethyl-3-methylimidazolium-based ionic liquids Ⅱ[J]. J. Chem. Thermodyn., 2021, 160:  106392. doi: 10.1016/j.jct.2021.106392

  11. [11]

      Xu D, Di Y Y, Kong Y X, Dou J M. Crystal structure and thermo-chemical properties of 2-pyrazine carboxylate lithium monohydrate[Li (pyza)(H₂O)]_n(s)(pyza=2-pyrazine carboxylate)[J]. Chem. Res. Chin. Univ., 2015, 31(2):  253-260. doi: 10.1007/s40242-015-4438-2

  12. [12]

      Guo J J, Huang J, Song J R, Miao K H, Cao W L. Three new compounds based on 4, 4'-azo-1, 2, 4-triazol-5-one: Synthesis, crystal structure and thermal properties[J]. Chem. Res. Chin. Univ., 2016, 32(5):  812-817. doi: 10.1007/s40242-016-6114-6

  13. [13]

      Zhang Y H, Di Y Y, Tan Z C, Dou J M. Synthesis, crystal structure and thermochemistry of the coordination compound of pyridine-2, 6-dicarboxylic acid with barium ion[J]. Thermochim. Acta, 2014, 575:  173-178. doi: 10.1016/j.tca.2013.10.034

  14. [14]

      Di Y Y, Chen J T, Tan Z C. Low-temperature heat capacities and standard molar enthalpy of formation of the solid-state coordination compound trans-Cu (Ala)₂(s)(Ala=L-α-alanine)[J]. Thermochim. Acta, 2008, 471(1):  70-73.

  15. [15]

      Spackman P R, Turner M J, McKinnon J J, Wolff S K, Grimwood D J, Jayatilaka D, Spackman M A. CrystalExplorer: A program for Hirshfeld surface analysis, visualization and quantitative analysis of molecular crystals[J]. J. Appl. Crystallogr., 2021, 54(3):  1006-1011. doi: 10.1107/S1600576721002910

  16. [16]

      Spackman M A, Jayatilaka D. Hirshfeld surface analysis[J]. CrystEngComm, 2009, 11(1):  19-32. doi: 10.1039/B818330A

  17. [17]

      Yu H G, Liu Y, Tan Z C, Dong J X, Zou T J, Huang X M, Qu S S. A solution-reaction isoperibol calorimeter and standard molar enthalpies of formation of Ln (hq)₂Ac (Ln=La, Pr)[J]. Thermochim. Acta, 2003, 401(2):  217-224. doi: 10.1016/S0040-6031(02)00566-X

  18. [18]

      Di Y Y, Tan Z C, Zhang G Q, Chen S P, Liu Y, Sun L X. Low-temperature heat capacity and standard molar enthalpy of formation of the complex Zn (Thr) SO₄·H₂O (s)[J]. Thermochim. Acta, 2003, 400(1):  43-49.

  19. [19]

      Jenkins H D B, Tudela D, Glasser L. Lattice potential energy estimation for complex ionic salts from density measurements[J]. Inorg. Chem., 2002, 41(9):  2364-2367. doi: 10.1021/ic011216k

  20. [20]

      Glasser L, Jenkins H D B. Internally consistent ion volumes and their application in volume-based thermodynamics[J]. Inorg. Chem., 2008, 47(14):  6195-6202. doi: 10.1021/ic702399u

  21. [21]

      Liu Y P, Di Y Y, He D H, Zhou Q, Dou J M. Crystal structures, lat-tice potential energies, and thermochemical properties of crystalline compounds (1-C_nH_2n+1NH₃)₂ZnCl₄(s)(n=8, 10, 12, and 13)[J]. Inorg. Chem., 2011, 50(21):  10755-10764. doi: 10.1021/ic2012974

  22. [22]

      Zhang L J, Tan Z C, Chen J T, Di Y Y. Crystal structures and thermo-chemical properties of n-nonylammonium dihydrogen phosphate C₉H₁₉NH₃·H₂PO₄(s) and n-octylammonium dihydrogen phosphate C₈H₁₇NH₃·H₂PO₄(s)[J]. J. Chem. Eng. Data, 2011, 56(12):  4491-4498. doi: 10.1021/je200352g

  23. [23]

      Yang J Z, Pitzer K S. Thermodynamics of electrolyte mixtures. Activity and osmotic coefficients consistent with the higher-order limiting law for symmetrical mixing[J]. J. Solut. Chem., 1988, 17(10):  909-924. doi: 10.1007/BF00649736

  24. [24]

      Zhang L J, Di Y Y, Lu D F. Crystal structure and thermochemical properties of 1-decylammonium hydrobromide (C₁₀H₂₁NH₃Br)(s)[J]. J. Chem. Thermodyn., 2011, 43(11):  1591-1596. doi: 10.1016/j.jct.2011.05.016

  25. [25]

      Housecroft C E, Brooke Jenkins H D. Absolute ion hydration enthalpies and the role of volume within hydration thermodynamics[J]. RSC Adv., 2017, 7(45):  27881-27894. doi: 10.1039/C6RA25804B

• 

  Figure 1  XRD pattern of (NH₄)₂[Sr(C₃H₅O₃)₄]

  下载: 全尺寸图片 幻灯片
  

  Figure 2  Molecular structure of (NH₄)₂[Sr(C₃H₅O₃)₄]

  Symmetry code: ^ⅰ-x, y, 1/2-z

  下载: 全尺寸图片 幻灯片
  

  Figure 3  Coordination environment diagram of Sr²⁺

  下载: 全尺寸图片 幻灯片
  

  Figure 4  Unit cell diagram of (NH₄)₂[Sr(C₃H₅O₃)₄]

  下载: 全尺寸图片 幻灯片
  

  Figure 5  Hirshfeld surface for (NH₄)₂[Sr(C₃H₅O₃)₄] mapped with d_norm (a), d_i (b), and d_e (c) over a range of 0-0.38 nm; (d) 2D fingerprint plot corresponding to the three pictures

  下载: 全尺寸图片 幻灯片
  

  Figure 6  Fingerprint plots for H in (NH₄)₂[Sr(C₃H₅O₃)₄], broken down into contributions from specific pairs of atom-types: (a, b) H…H; (c, d) H…O; (e, f) O…H

  For each plot, the grey shadow is an outline of the complete fingerprint plot

  下载: 全尺寸图片 幻灯片
  

  Figure 7  Functional relationship of measured enthalpy of dissolution of (NH₄)₂[Sr(C₃H₅O₃)₄] with molar concentration m at 298 K

  下载: 全尺寸图片 幻灯片
  

  Figure 8  Three-dimensional diagram of extrapolation function Y of (NH₄)₂[Sr(C₃H₅O₃)₄] with -2m and -2my'

  下载: 全尺寸图片 幻灯片
  

  Scheme 1  Designed thermodynamic cycle to calculate the hydration enthalpy of (NH₄)₂[Sr(C₃H₅O₃)₄]

  下载: 全尺寸图片 幻灯片
  

  Figure 9  TG/DTG curves of (NH₄)₂[Sr(C₃H₅O₃)₄]

  下载: 全尺寸图片 幻灯片

  Table 1.  Provenance and purity of the reagents

  Chemical name	Chemical formula	Source	Purity (mass fraction)*	CAS No.
  D/L-lactic acid	C3H6O3	Budweiser Chemical Technology Co., Ltd.	90.00%	50-21-5
  Strontium hydroxide	Sr(OH)2	Tianjin Fengchuan Chemical Reagent Technology Co., Ltd.	99.99%	18480-07-4
  Absolute ethanol	C2H5OH	Tianjin Fengchuan Chemical Reagent Technology Co., Ltd.	99.99%	64-17-5
  Ammonia	NH3·H2O	Budweiser Chemical Technology Co., Ltd.	25%	1336-21-6
  Potassium chloride	KCl	Budweiser Chemical Technology Co., Ltd.	99.99%	7447-40-7
  Ultra-pure water	H2O	Laboratory self-made	99.99%	—
  *The purity was provided by the supplier.

  下载: 导出CSV

  Table 2.  Molar enthalpy of solution of KCl in water at 298 K

  No.	m / g	n / mmol	ΔsHm/(kJ·mol-1)
  1	0.374 7	5.026 2	17.559
  2	0.374 7	5.026 2	17.628
  3	0.374 8	5.027 5	17.580
  4	0.375 2	5.032 9	17.629
  5	0.374 6	5.0248	17.612

  下载: 导出CSV

  Table 3.  Crystallographic data of the complex

  Parameter	(NH4)2[Sr(C3H5O3)4]
  Empirical formula	C12H28SrN2O12
  Formula weight	479.98
  Crystal system	Monoclinic
  Space group	C2/c
  a / nm	1.799 02(16)
  b / nm	1.047 00(11)
  c / nm	1.074 31(13)
  β/(°)	93.581 0(10)
  Volume / nm3	2.019 6(4)
  Z	4
  Dc / (g·cm-3)	1.579(2)
  Absorption coefficient / mm-1	2.73
  F(000)	992
  θ range for data collection / (°)	2.25-25.02
  Limiting indices	-21 ≤ h≤ 21, -12 ≤ k≤ 10, -12 ≤ l≤ 9
  Reflection collected, unique	5 061, 1 793 (Rint=0.051 5)
  Completeness to θ=25.02°/ %	99.9
  Absorption correction	Semi-empirical from equivalents
  Max. and min. transmission	0.639 3 and 0.448 3
  Data, restraint, number of parameters	1 793, 0, 155
  Goodness-of-fit on F2	1.037
  Final R indices [I > 2σ(I)]	R1=0.042 0, wR2=0.108 0
  R indices (all data)	R1=0.051 4, wR2=0.112 2
  (Δρ)max and (Δρ)min / (e·nm-3)	714 and -514

  下载: 导出CSV

  Table 4.  Selected bond lengths (nm) and angles (°) of the complex

  Sr1—O1	0.256 3(3)	Sr1—O6	0.2540(3)	Sr1—O3	0.257 0(3)
  Sr1—O4	0.251 2(3)	O5—C4	0.130 6(11)	O6—C5	0.143 2(19)
  O1—C1	0.123 0(5)	C1—C2	0.1527(5)	O2—C1	0.125 7(4)
  C2—C3	0.151 4(7)	O3—C2	0.1427(4)	C4—C5	0.150(2)
  O4—C4	0.119 5(5)
  O1—Sr1—O1ⅰ	91.20(13)	O1ⅰ—Sr1—O3	94.29(9)	O6ⅰ—Sr1—C4ⅰ	44.56(10)
  O4ⅰ—Sr1—O4	78.68(15)	O6—Sr1—C4ⅰ	97.58(11)	O4—Sr1—O6ⅰ	82.77(10)
  C4ⅰ—Sr1—C1ⅰ	157.69(11)	O1—Sr1—O3	59.84(8)	O4—Sr1—O6	61.71(9)
  C1—O1—Sr1	122.9(2)	C2—O3—Sr1	121.0(2)	O1ⅰ—Sr1—C1ⅰ	17.73(9)
  C4—O4—Sr1	124.5(3)	O1—Sr1—C1ⅰ	99.88(9)	O4—Sr1—C1ⅰ	84.64(10)
  C5—O6—Sr1	124.1(8)	O1—Sr1—C4ⅰ	92.95(11)	O4ⅰ—Sr1—C1ⅰ	163.05(10)
  O1—C1—O2	124.9(4)	O1ⅰ—Sr1—C4ⅰ	175.00(11)	O4—Sr1—C4ⅰ	78.31(12)
  O1—C1—C2	119.3(3)	O3—Sr1—O3ⅰ	144.41(15)	O3ⅰ—Sr1—C1ⅰ	44.28(9)
  O4ⅰ—Sr1—C4ⅰ	17.15(10)	O2—C1—C2	115.8(3)	O3—Sr1—C1ⅰ	112.01(10)
  O6—Sr1—O1	133.67(8)	O3—C2—C1	106.8(3)	O3—Sr1—C4ⅰ	90.20(11)
  O6ⅰ—Sr1—O1	81.49(10)	O3—C2—C3	111.1(4)	O3ⅰ—Sr1—C4ⅰ	117.01(10)
  O6—Sr1—O1ⅰ	81.49(10)	C3—C2—C1	110.0(4)	O4—Sr1—O1ⅰ	96.99(10)
  O6—Sr1—O3	119.64(9)	O4—C4—O5	122.2(8)	O4—Sr1—O1	163.83(9)
  O6—Sr1—O3	75.08(9)	O4—C4—C5	123.6(8)	O4—Sr1—O3	132.84(10)
  O6—Sr1—O6ⅰ	134.37(13)	O5—C4—C5	113.4(8)	O4—Sr1—O3ⅰ	78.04(10)
  O6ⅰ—Sr1—C1ⅰ	119.36(9)	O6—C5—C4	106.1(12)	C4—C5—C6	105.1(13)
  O6—Sr1—C1ⅰ	86.70(9)	O6—C5—C6	106.7(10)
  Symmetry code: ⅰ -x, y, -z+1/2.

  下载: 导出CSV

  Table 5.  Hydrogenbond parameters of the complex

  D—H…A	d(D—H) /nm	d(H…A) /nm	d(D…A) /nm	∠(DHA)/(°)
  O6—H6…O1ⅱ	0.082	0.194	0.275 5(4)	174.8
  O3—H3…O2ⅲ	0.082	0.190	0.270 1(4)	164.8
  Symmetry codes: ⅱ x, -y+1, z+1/2; ⅲ -x+1/2, -y+1/2, -z.

  下载: 导出CSV

  Table 6.  Lattice energy (U_POT) and volumes (V_m) of anion and cation of the complex

  Complex	Vm / nm3	UPOT / (kJ·mol-1)	V+ / nm3	V- / nm3
  (NH4)2[Sr(C3H5O3)4]	0.504 7	2 742.9	0.092 5	0.103 1

  下载: 导出CSV

  Table 7.  Summary of the molar dissolution enthalpy^a (Δ_sH_m), relative partial molar enthalpy^b (L₁) and (L₂) of (NH₄)₂[Sr(C₃H₅O₃)₄] in water at 298 K

  mc/(mol·kg-1)	ΔsHm/(kJ·mol-1)	(∂ΦL/∂m)T, Pd	L1 / (J·mol-1)	L2 / (kJ·mol-1)
  0.66×10-4	110.919	-1.141 11×109	-2.620	5.269
  2.31×10-4	104.031	-1.080 41×109	9.323	-3.221
  3.80×10-4	98.844	-1.030 67×109	26.534	-9.763
  6.12×10-4	92.472	-9.616 2×108	64.334	-18.113
  7.70×10-4	89.161	-9.196 5×108	96.959	-22.719
  9.18×10-4	86.705	-8.834 7×108	131.999	-26.382
  1.048×10-3	84.997	-8.538 0×108	165.980	-29.176
  1.225×10-3	83.250	-8.160 0×108	216.474	-32.488
  1.483×10-3	81.667	-7.647 1×108	297.308	-36.681
  1.669×10-3	81.068	-7.293 1×108	359.689	-39.541
  1.957×10-3	80.745	-6.746 9×108	460.699	-44.297
  2.245×10-3	80.853	-6.172 6×108	564.085	-50.205
  2.847×10-3	81.31	-4.729 3×108	772.909	-70.036
  3.468×10-3	80.964	-2.619 9×108	950.814	-107.942
  4.285×10-3	79.250	-1.692 7×108	1 070.059	-199.092
  a The ratio of the enthalpy of dissolution of the complex to the amount n of the substance under standard pressure is called their standard molar enthalpy of dissolution, written as ΔsHm; b The relative partial molar enthalpies of solvent and solute are expressed as L1 and L2 respectively, which are important thermodynamic parameters of electrolyte solution. The formula used in this work is as follows: L1=-MH2Om2(∂ΦL/∂m)T, P and L2=ΦL+m(∂ΦL/∂m)T, P; c m is the mass molar concentration; d (∂ΦL/∂m)T, P is the partial derivative of relative partial molar enthalpy to m, and its formula is expressed as Eq.13.

  下载: 导出CSV

  Table 8.  Summary of infinite dilution molar enthalpy of solution and Pitzer's parameters of the complex at 298 K

  Complex	α0	βMX(0)L	βMX(1)L	s	ΔsHm∞/(kJ·mol-1)
  (NH4)2[Sr(C3H5O3)4]	0.077 17	-8.394	105.196	1.999×10-6	114.01±0.04

  下载: 导出CSV
•