Thermodynamic Property Study on the Complexes of Rare-Earth Elements with Amino Aids

In this chapter, the following three rare-earth complexes with amino acids, Eu(Glu) (Im) 5 (ClO 4 ) 3 (cid:1) 3HClO 4 (cid:1) 6H 2 O, Nd(Gly) 2 Cl 3 (cid:1) 3H 2 O, and La(Glu)(Im) 6 (ClO 4 ) 3 (cid:1) 4HClO 4 (cid:1) 4H 2 O, are synthesized and characterized by element analysis, infrared (IR) spectrum, and x-ray diffraction (XRD) analysis. The thermodynamic property studies on these complexes are performed. For the first one, Eu(Glu)(Im) 5 (ClO 4 ) 3 (cid:1) 3HClO 4 (cid:1) 6H 2 O, the low temperature heat capacity, phase transition, and thermodynamic functions are determined byadiabatic calorimetry. For the second one, Nd(Gly) 2 Cl 3 (cid:1) 3H 2 O, the molar dissolution enthalpy and standard molar enthalpy of formation are determined by isoperibol solution reaction calorimetry. For the third one, La(Glu)(Im) 6 (ClO 4 ) 3 (cid:1) 4HClO 4 (cid:1) 4H 2 O, the microcalorimetry is used to investigate the interaction between the complex and the Escherichia coli DH5 α to elucidate the biological effects of the complex.


Introduction
Rare-earth (RE) elements and their compounds have been extensively investigated in last several decades, because of their important significance in sciences and the growing practical applications in industries. New frontiers concerned with RE science and technology are increasingly and rapidly developed.
It is well know that China is the country richest in RE minerals all over the world. In order to sufficiently develop and effectively utilize the RE resources, the industries concerned were in urgent need of huge numbers of basic data of RE compounds. Undoubtedly, the thermodynamic property data are absolutely necessary for the study and application of rare-earth compounds. As one part of Chinese national research projects for rare-earth science and technology, in the period of 1990-2006, our Thermochemistry Laboratory in cooperation with Microcalorimetry Research Center of Osaka University well successfully completed the research project "low temperature heat capacity and thermodynamic properties of a series of rare-earth isothiocyanate hydrates, RE(NCS) 3 ÁnH 2 O (RE = La,Ce,Pr,Nd,Sm,Gd,Yb,Y)." The research results concerned were published in international journals [1][2][3][4].
Rare-earth elements have found their applications in many areas nowadays; because of their unique properties, they have been introduced into microfertilizer, pesticide, and antibacterial agent. Accompanying these applications, rare-earth elements inevitably spread into the food chain, the biological chain, and then into the bodies of human beings. This leads people to care about and study the influence and the long-term effect of rare-earth elements on themselves. Rare-earth complexes formed with amino acid were then synthesized for this purpose, because amino acid is the basic unit comprising protein and enzyme, the fundamental and functional materials in the bodies of human beings and animals. In the last 30 years, more than 200 kinds of these complexes were synthesized, and about 50 kinds among them had their own crystallograms. However, the thermodynamic property data of these complexes were seldom reported. As we all well know, only with these data we can quantitatively describe their characteristics in terms of the energetics, for example, stable forms in different temperature range, melting process, thermal anomaly, and so on. Comparisons of these data for a series of complexes comprised by the same RE (or ligands) with different ligands (or RE) may enable us to have a deeper understanding of their properties.
Rare-earth complex coordinated with amino acids possesses many unique physiological and biochemical effects. In 1975, Anghileri et al. reported for the first time that La(Gly) 3 Cl 3 Á3H 2 O was antineoplastic [5]. Since then, the rare-earth complexes coordinated with amino acids have been synthesized and studied intensively by a variety of methods [6][7][8][9][10]. Nowadays, the applications of rare-earth complexes with amino acids have expanded into the fields of medicine, biology, and agriculture more widely. However, the fundamental thermodynamic property data of these complexes have rarely been reported yet, especially the data of low temperature heat capacity and standard thermodynamic functions, and standard enthalpy of formation, although these data are significant for the further applications of the rare-earth complex with amino acids.
Based on previous work about thermodynamic study of rare-earth isothiocyanate hydrates, our thermochemistry laboratory in cooperation with several national academic groups has intensively contributed to this effort for thermodynamic property studies on rare-earth complexes with amino acids, and 28 academic papers concerned with this research project have been published .
In this chapter, we present the following three papers to report our recent research results and describe in detail the modern advanced experimental calorimetric techniques used for thermodynamic property studies of rare-earth complexes.
1. Thermodynamic properties of rare-earth complex with amino acid: Eu(Glu)(Im) 5  Infrared spectra of the complex and L-Glutamic acid were obtained through KBr pellets at room temperature using a Bruker Tensor 27-IR spectrophotometer. The infrared spectrum of the complex was shown in Figure 1. Compared with the IR spectrum of L-Glutamic acid, the νs (carboxyl) band of the complex shifted from 1410 cm À1 to higher wave numbers (1431 cm À1 ), which shows that the carboxyl groups of the ligand have been coordinated to the metal ion [39]. The special absorptions of -NH 2 shifted from 3050 to 3240 cm À1 (ν -NH), from 2750 to 2740 cm À1 (ν -NH), and from 1560 to 1562 cm À1 (δNH 2 + ), because a hydrogen bond formed in the complex. The spectrum also shows the wide peak symmetrical resonance frequencies, νs (N-H), shifted from 3286 to 3425 cm À1 down to 3166 to 3098 cm À1 , which is evidence of the coordination of imidazole molecules [40]. A broad absorption band for ν (hydroxyl) appearing at 3400 cm À1 shows the presence of water molecules in the complex.
Powder X-ray diffraction (XRD) patterns were recorded using Rigaku D/Max 3400 X with Cu Kα radiation at 0.02 steps per second in angle range 2θ = 5-90, and the results were shown in Figure 2. Judging from the shape and number of the peak in the patterns, the sample was a kind of complex with single phase.

Adiabatic calorimetry
Adiabatic calorimetry is the most accurate approach to obtain the heat capacity data. In the present study, heat capacity measurements were carried out by a high-precision automatic adiabatic calorimeter over the temperature range of 80-350 K. The adiabatic calorimeter was established by Thermochemistry Laboratory of Dalian Institute of Chemical Physics, Chinese Academy of Sciences in PR China. The structure and principle of the adiabatic calorimeter have been described in detail elsewhere [41]. The schematic diagram of the adiabatic calorimeter is shown in Figure 3. Briefly, the automatic adiabatic calorimeter is mainly composed of a sample cell, a miniature platinum resistance thermometer, an electric heater, the inner and outer adiabatic shields, two sets of six-junction chromel-constantan thermopiles installed between the calorimetric cell and the inner shield and between the inner and the outer shields, respectively, and a high vacuum can. The working temperature range is 78-400 K and, if necessary, it can be cooled by liquid nitrogen. The heat capacity measurements were conducted by the standard procedure of intermittently heating the sample and alternately measuring the temperature. The heating rate and the temperature increments of the experimental points were generally controlled at 0.1-0.4 KÁmin À1 and at 1-4 K, respectively, during the whole experimental process. The heating duration was 10 min, and the temperature drift rates of the sample cell measured in an equilibrium period were kept within 10 À3 -10 À4 KÁmin À1 during the acquisition of heat capacity data. In order to verify the reliability of the adiabatic calorimeter, the molar heat capacities C p,m of the Standard Reference Material (SRM-720) (α-Al 2 O 3 ) were measured in the range of 78-400 K. The deviation of our calibration data from those of NIST [42] was within AE0.1% (standard uncertainty). In the present study, the mass of the complex, Eu(Glu)(Im) 5 (ClO 4 ) 3 Á3HClO 4 Á6H 2 O, used for heat capacity measurement was 2.0352 g.
The result of heat capacity measurement of the complex was listed in Table 1 and shown in Figure 4.

Other thermal analysis
A differential scanning calorimeter (DSCÀ141, SETARAM, France) was used to perform the thermal analysis of Eu(Glu)(Im) 5 (ClO 4 ) 3 Á3HClO 4 Á6H 2 O. In the range 100-300 K, liquid nitrogen was used as cryogen. In the range 300-700 K, nitrogen gas was taken as protective gas with flow rate of 50 cm 3 Ámin À1 , at the heating rate of 10 KÁmin À1 . The masses of the samples used in the above two experiments were 4.03 and 4.26 mg, respectively.
Two aluminum crucibles were used and the reference crucible was empty. The calibrations for the temperature and heat flux of the calorimeter were performed prior to the experimental measurements of the sample. The temperature scale was calibrated by measuring the melting points of Hg, In, Sn, Pb, and Zn, at different heating rates, and the heat flux was calibrated by the Joule effect. Measurements of the melting temperature and the enthalpy of fusion of benzoic acid (NIST, Standard Reference Material 39i) were performed in the laboratory to check the accuracy of the instrument.
The result of DSC measurement was shown in Figure 5.      and positional shifts of TMA ions, and thus the lattice deformation in the relevant region, associated with the orientational change of the ClO 4 À ions. The position of the ClO 4 À ions itself would shift to form preferable ionic interaction.

Phase transitions
It can be seen from Figure 4 that there are two thermal events in the range 80-350 K on the C p,m -T curve. The heat capacity of the sample increases with increasing temperature in a smooth and continuous manner in the temperature range from 80 to 208 K. A little peak occurs at T = 216.98 K on the C p , m -T curve, which is consistent with the peak (T trs = 217.30 K) on the DSC curve ( Figure 5). Such thermal event is deduced to be the phase transition of the complex. The second peak is at 246.08 K, which is also deduced to be the phase transition consistent with the peak (T trs = 245.06 K) on the DSC curve.
It can be proved from Figure 4 that there are two endothermic processes in the temperature range 100-300 K. One is at 217.30 K, and the other is at 245.06 K, which confirms the results of the heat capacity measurements (216.98 and 246.08 K). The temperature ranges and peak values of the endothermic processes correspond to those of the phase transitions in the C p,m -T curve obtained from the heat capacity measurements. It is also verified that there are two phase transitions in the temperature range 100-350 K.
From the view of energy accompanying the process, Yukawa et al. [43] estimated the entropy of the phase transition was to be from 20 to 45 JÁK À1 Ámol À1 in the range. The present work calculated that the molar entropy Δ trans S m of the first-phase transition is 27.86 AE 0.08 J•mol -1• K À1 , which was in the range of entropy of the phase transition estimated by Yukawa et al.
The combined consideration based on the results of AC (adiabatic calorimetric) and DSC (differential scanning calorimetric) measurements, the values of thermodynamic functions, and the report of former documents leads to a conclusion that the phase transition was interpreted as a freezing-in phenomenon of the reorientational motion of perchlorate ions ClO 4 À . The endothermic process at T = 246.86 K was deduced to be the orientational order/ disorder process of ClO 4 À ion [43][44][45][46].

Molar heat capacity, molar enthalpies, and entropies
Experimental molar heat capacities, C p,m against temperature T in the range 80-350 K, were listed in Table 1 and plotted in Figure 4. It can be seen from the figure that no phase change or thermal decomposition was found before 206 K and after 258 K.
None-phase transitions process: Before the solid-solid phase transitions process (from 80 to 208 K): After the solid-solid phase transitions process (from 258 to 350 K): where C p,m (s) is the molar heat capacity of the solid state, T i is the temperature at which the solid-solid phase transition started, and T f is the temperature at which the solid-solid phase transition ended.
The values of the experimental heat capacities except the phase change regions were fitted. One polynomial Eq. (5) was obtained by least squares fitting using the experimental molar heat capacities (C p,m ) and the reduced temperatures (x).
where x = [(T/K) -215]/135, x is the reduced temperature, and T is the experimental temperature. Correlation coefficient of the least squares fitting, R 2 , is 0.9989 (T i = 80 K and T f =350 K).
Phase transitions process (from 206 to 258 K): In the solid-solid phase transitions process (from 206 to 258 K), the temperature T trans, molar enthalpies Δ trans H m , and molar entropies Δ trans S m of the first two-phase transitions are determined according to Eqs. (6)-(10) and listed in Table 3.
where C p,m (trans) is the molar heat capacity during the solid-solid phase transitions process: T trans can be seen as follows: From Eqs. (6) to (9), molar enthalpies, Δ trans H m , and molar entropies, Δ trans S m , of the two solidsolid phase transition processes from 208 to 228 K and from 228 to 252 K were calculated as follows: where C p , m (trans, 1) is the molar heat capacity caused by solid-solid phase transitions. C p , m (trans) is the total molar heat capacity. C p , m (trans, 2) is the molar heat capacity induced by temperature change of substance, and its polynomial equation was obtained by least squares analysis using the experimental molar heat capacities in the non-phase transition regions from 80 to 350 K as in Eq. (5).
The molar enthalpy of the first-phase transition was calculated from 208 to 228 K as follows:  15 ) were calculated in the temperature range from 80 to 350 K with an interval of 5 K at pressure 0.1 MPa, and listed in Table 2, using the above thermodynamic polynomial Eqs. (1)-(12).

Thermal decomposition properties
It can be seen from Figure 6 that there are two peaks on the DSC curve from 300 to 700 K. One is a little endothermic peak (T trans = 485.57 K), which was caused by decomposition of amino, and the other is a wide exothermic peak from 530 to 600 K, which was contributed to decomposition of the complex. It was consistent with the results of TG analysis.
The result of TG analysis was showed in Figure 7. It can be seen from the TG curve that mass loss of Eu(Glu)(Im) 5 (ClO 4 ) 3 Á3HClO 4 Á6H 2 O began at about 298 K and ended at about 900 K. The whole process was divided into three stages. The mechanism of the decomposition was deduced as following:  Table 3. Temperature, enthalpy, and entropy of the phase transitions of the complex obtained by the heat capacity measurements from 80 to 350 K.
with glycine in the molar ratio of 1:2 at about pH = 2.5 for 7-8 h. After that, the mixed solution was concentrated in a thermostat bath at 323 K until most of the water was evaporated, and then the concentrated solution was dried in a vacuum desiccator over phosphorus pentoxide for several weeks until lavender crystals appeared.
The actual amount of C, H, and N in the as-prepared sample was confirmed by elemental analysis instrument (model PE-2400 II, USA  Figure 8. Compared with the IR spectrum of glycine, the νs(carboxyl) band of Nd(Gly) 2 Cl 3 Á3H 2 O shifted from 1394 cm À1 to higher wave numbers (1418 cm À1 ), which reveals that the carboxyl groups of the ligand have been coordinated to the metal ion. The special absorption of NH 2 shifted from 3105 À1 to 3420 cm À1 (νN-H), from 2604 to 2580 cm À1 (νN-H), and from 1500 to 1477 cm À1 (υ NH2 ) indicates a hydrogen bond formed in the complex. A broad absorption band for νs(hydroxyl) appearing at 3400 cm À1 suggests the presence of water molecules in the complex. Meanwhile, it can be observed that main diffraction peaks of Nd

DSC and TG measurements
Thermal analysis of Nd(Gly) 2 Cl 3 Á3H 2 O was performed using a differential scanning calorimeter (DSC-141, SETARAM, France) and a thermogravimetric analyzer (model DT-20B, Shimadzu, Japan). The DSC measurement was carried out with a heating rate of 10 K À1 min À1 under high-purity nitrogen with a flow rate of 50 mL À1 min À1 . The mass of the sample used in the experiment was 3.36 mg. The calibrations for the temperature and heat flux of the calorimeter were performed prior to the experiment. The temperature scale was calibrated by measuring the melting points of Hg, In, Sn, Pb, and Zn at different heating rates, and the heat flux was calibrated using the Joule effect. Measurement of the melting temperature and the enthalpy of fusion of benzoic acid (NIST, SRM 39i) were carried out in this laboratory to check the accuracy of the instrument. The TG measurement of the complex was conducted at a heating rate of 10 K À1 min À1 under high-purity nitrogen with a flow rate of 120 mLÁmin À1. The mass of the sample used in the experiment was 9.47 mg. The reference crucible was filled with α-Al 2 O 3 . The TG-DTG equipment was calibrated by the thermal analysis of the SRM, CaC 2 O 4 ÁH 2 O(s).

Isoperibol solution reaction calorimeter
The Isoperibol solution reaction calorimeter (SRC-100) used for this study was constructed in our thermochemistry laboratory and has been used for measuring enthalpies of solid-liquid, liquid-liquid dissolution reactions enthalpies of the reactant, and the product to obtain the formation enthalpies of the complex. The principle and structure of the instrument were described elsewhere [47]. The schematic diagram of the calorimeter is shown in Figure 9.
The calorimeter mainly consisted of a water thermostat, a pyrex-glass Dewar with volume of 100 mL, a glass sample cell with volume of 2 mL, a heater for calibration and equilibration purposes, a glass-sheathed thermistor probe, an amplifier, a circuit used as an A/D converter, and a personal computer for data acquisition and processing. The Dewar vessel, equipped with a twin-blade stirrer, served as a mixing chamber, was submerged in the water thermostat. The precisions of controlling and measuring the temperature of the calorimeter are AE0.001 and AE0.0001 K, respectively. The measurements of solution-reaction enthalpy of samples were conducted under atmospheric pressure. The calorimeter was tested by measuring the dissolution enthalpies of the KCl (calorimetric primary standard) in water at 298.15 K. The mean dissolution enthalpies obtained from five experiments are 17515 AE 12 JÁmol À1 , which are in conformity with the reported data (17536 AE 9 JÁmol À1 ) [48].

Dissolution and formation enthalpy measurements
The dissolution enthalpies of reactants and the products, and standard molar enthalpy of formation of Nd(Gly) 2 Cl 3 Á3H 2 O were determined through the proposed Hess thermochemical cycle, which is demonstrated in Figure 10. As illustrated in Figure 10, the molar enthalpy of formation of Nd(Gly) 2 Cl 3 Á3H 2 O(s) is given as: Figure 10. Hess thermochemical cycle.
The mixture of NdCl 3 Á6H 2 O(s) and Gly(s) at mole ratio of n(NdCl 3 Á6H 2 O):n(Gly) = 1:2 was dissolved in 100 mL of 2 molÁL À1 HCl at 298.15 K. The final solution obtained was named as Solution A. Dissolution enthalpy of 1 mol Nd(Gly) 2 Cl 3 Á3H 2 O (s) in 100 mL of 2 molÁL À1 hydrochloric acid was determined under the same condition as above. The final solution obtained was named as Solution A'. Finally, UV-vis spectroscopy and the data of the refrangibility were applied to confirm whether Solution A was in the same thermodynamic state as that of Solution A'. These results mentioned above indicated that chemical components and physical-chemistry properties of Solution A were consistent with those of Solution A'. In this chapter, UV-vis spectrum and the data of the refrangibility of Solution A obtained agreed with those of Solution A'. These results demonstrated that the designed thermochemical cycle is reasonable and reliable, hence can be used to calculate the standard molar enthalpy of formation of Nd(Gly) 2 Cl 3 Á3H 2 O(s).

Thermal analysis
The thermal analysis results of Nd(Gly) 2 Cl 3 Á3H 2 O are shown in Figures 11 and 12, respectively. The DSC curve ( Figure 11) reveals that the two endothermic peaks appear at 146.68 and 282.21 C, which are in agreement with those obtained from the TG-DTG (thermogravimetricdifferential thermogravimetric) experiments at 147.5 and 283.0 C.
The mass loss of Nd(Gly) 2 Cl 3 Á3H 2 O was mainly divided to two steps. Based on the TG curve and the structure of Nd(Gly) 2 Cl 3 Á3H 2 O, the conclusion can be drawn that from 59 to 188 C the three coordinating water molecules break away from the complex. The experimental mass loss (%) of the first step was found to be 8.9%. The result is consistent with the theoretical mass loss, 11.9%, of the three water molecules. The second step of the mass loss from 262 to 904 C should be due to the glycine being separated from the Nd 3+ cations, and the residue of the TG experiment should be NdCl 3 and Nd. The experimental mass loss (%) of the decomposition is 52.8%, which is in accord with the theoretical mass loss, 48.6%. The possible mechanism of the thermal decompositions was deduced as The experimental values of the dissolution enthalpies of the mixture prepared at the mole ratio of the reactants were measured. Dissolution enthalpies Δ s H 1 and Δ s H 2 were determined by the dissolution process tested. The experiment was repeated five times in the same condition, and  the results were listed in Table 4. The enthalpy change Δ r H θ m could be calculated in accordance with expression (19) as follows: The experimental values of the dissolution enthalpies of the reactants and products in the thermochemical cycle are combined with the following auxiliary thermodynamic data: According to the expression (20), the standard molar enthalpy of formation of the complex Nd (Gly) 2 Cl 3 Á3H 2 O (s) at 298.15 K can be calculated as follows: After the pH value of the reaction mixture was carefully adjusted to 6.0 by adding 0.1 molÁL À1 NaOH slowly, imidazole was added as the same molar as glutamic acid. The reaction was performed at 60 C in water bath for 5 h. Then the solution was condensed at 80 C for 5 h and put into desiccator in the fridge at À4 C. The crystal was obtained after about one month. was determined to be La(Glu)(Im) 6 (ClO 4 ) 3 Á4HClO 4 Á4H 2 O, and the purity obtained from the EDTA titration under the same conditions was found to be 99.79%.
IR spectra were obtained using KBr pellets with a Tensor 27 (Bruker) spectrometer. It can be seen from the IR spectra of the complex that the symmetrical resonance frequencies, ν s (COO-) , shifted from 1431 to 1413 cm À1 , which suggests that the carboxyl group of Glu has coordinated to the metal ions.
The E. coli DH5α was provided by Biomass Conversion Technology Group, Dalian Institute of Chemical Physics, CAS, Dalian 116023, PR China. The strain of E. coli DH5α was stored in 10% glycerol solution at À20 C.
The E. coli DH5α used in the present research was prepared as follows. A single colony of E. coli DH5α from LB(Luria-Bertani) plates was inoculated into a 10 mL LB culture medium and cultivated at 37 C in a rotary shaker (220 rpm) for 12 h under aerobic condition. Then, 200 μL of the above suspension was inoculated into 10 mL LB culture medium at 37 C in a rotary shaker (220 rpm) for 2.5 h once again. The value of optical density (OD) of the E. coli DH5α suspension was measured to be about 0.6 by spectrophotometry at λ = 600 nm. Per 200 mL of LB culture medium contained 2 g tryptone, 1 g yeast extract powder, 2 g and NaCl (pH 7.0-7.2). It was sterilized in high-pressure steam at 120 C for 20 min before experiment.

Microcalorimeter
Thermal Analysis Microcalorimeter (TAM) Air is a type of eight-channel twin isothermal microcalorimeters that originally was developed for the study of the hydration process of cement and concrete. TAM represents an ultra-sensitive heat flow measurement which is complementary to TA instruments differential scanning calorimeters (DSC). "Air" means the thermostat type. However, the high sensitivity and excellent long-term stability make TAM Air useful also for other applications such as stability testing of energetic materials, determining the shelf life of food and monitoring biological processes [51].
A TAM Air Isothermal Microcalorimeter (see Figure 13) manufactured by Thermometric AB Company of Sweden ( incorporated by TA Instruments in 2006) was used to measure the power-time curves of the metabolism of E. coli DH5α at 37 C. The main structure of the instrument is eight channels, each of which consists of aluminum heat sink, vessel holder, and thermocouple plate, and each two of them are twin. Glass reaction vessel of 20 mL was used in each channel. The working temperature in the instrument was 5-60 C controlled by air thermostat. The deviation of the controlled temperature is within AE0.02 C. A computer was employed to record the voltage-time signals continuously which were converted to powertime signals through calibration. Thermal power detection limit was stated to be AE 2 μW. The development and theory of many kinds of multi-channel isothermal microcalorimeters have been studied by Wadsö [52,53].
The ampoule method was used for the microcalorimetric measurement in this work. Luria-Bertani (LB) culture medium (10 mL) containing object compound with different concentrations was put into eight sample ampoules, which had been cleaned and sterilized. Then, the E. coli DH5α suspension was inoculated into the above eight ampoules. At last, the ampoules were sealed with ampulla cap by ampoule filler. The working temperatures of the calorimeter were set and controlled at 37 C. The power-time signals were recorded at intervals of 1 min.
The ampoule method was used for the microcalorimetric measurement in this work. LB culture medium (10 mL) containing object compound with different concentrations was put into eight sample ampoules, which had been cleaned and sterilized. Then, the E. coli DH5α suspension was inoculated into the above eight ampoules. At last the ampoules were sealed with ampulla cap by ampoule filler. The working temperatures of the calorimeter were set and controlled at 37 C. The power-time signals were recorded at intervals of 1 min.

Thermokinetics
In the log phase of growth, the growth of E. coli DH5α cells is exponential [54]. It can be expressed as follows: Where t is the incubation time, n t is the cell number at time t, n 0 is the initial cell number, and k is the constant of cell growth rate. If the power output of each cell is denoted as Pw, then We define P 0 as the initiative power output and P t as the power output at time t, then Eq. (2) can be rewritten as follows: Figure 13. Practicality and cutaway views of TAM Air 8-channel isothermal calorimeter.
For thermokinetic parameters, inhibitory ratio (I) is defined as: Where k 0 is the rate constant of the control, and k c is the rate constant of E. coli DH5α growth inhibited by the complex with a concentration of C. The relationships among the concentration (C), the rate constant (k), and the maximum heat power (P m ) were plotted in Figure 16 at different concentrations (0, 0.1, 0.5, and 1.0 μgÁmL À1 ) based on the data of Table 5. It can be seen from Figure 16 that the rate constant (k) and the maximum heat power (P m ) were both increasing with the increase of the concentration from Thermodynamic Property Study on the Complexes of Rare-Earth Elements with Amino Aids http://dx.doi.org/10.5772/intechopen.69473 0 to 0.5 μg mL À1 , which indicated that the complex could speed up the growth of E. coli DH5α.

Thermokinetic parameters
When the concentration (C) reached 0.5 μg mL À1 , the value of rate constant (k) showed a highest value. It demonstrated that the complex could promote clearly the growth of E. coli   Table 6. Thermodynamic parameters of growth of E. coli DH5α at different concentrations of the complex.
DH5α at this time. At the concentration (C) from 0.5 to 1.0 μg mL À1 , the line decreased, which was consistent with Figure 17. Figure 17 was plotted from the data of Table 6, when the concentration (C) was from 0.5 to 5.0 μg mL À1 . It showed that the rate constant (k) and the maximum heat power (P m ) were both decreasing with the increase of the concentration (C), which indicated that the complex inhibited the growth of E. coli DH5α at this range of concentrations (C). When the concentration reached 5.0 μg mL À1 , E. coli DH5α almost could not grow.  Thermodynamic Property Study on the Complexes of Rare-Earth Elements with Amino Aids http://dx.doi.org/10.5772/intechopen.69473

Conclusions
In this chapter, the following three rare-earth complexes with amino acids were synthesized and characterized by element analysis, infrared(IR) spectrum, and x-ray diffraction (XRD) analysis. The thermodynamic property studies on these complexes were performed. For the first rare-earth complex, Eu(Glu)(Im) 5 (ClO 4 ) 3 Á3HClO 4 Á6H 2 O, the low-temperature molar heat capacity was measured by adiabatic calorimetry. Two thermal abnormalities interpreted as phase transitions were discovered at 216. 18 15 ] were derived in the temperature range from 80 to 320 K. The mechanism of thermal decomposition was deduced in terms of the results of TG. For the second rare-earth complex, Nd(Gly) 2 Cl 3 Á3H 2 O, the standard molar enthalpy of formation was determined to be (À3081.3 AE 1.08) kJÁmol À1 by an isoperibol solution-reaction calorimeter in terms of a designed thermochemical cycle. For the third rareearth complex, Eu(Glu)(Im) 5 (ClO 4 ) 3 Á3HClO 4 Á6H 2 O, the microcalorimetry was used to investigate the interaction between the complex and the Escherichia coli DH5α to elucidate the biological effects of the complex. The thermokinetic parameters of growth of the E. coli DH5α were obtained. The results show that the complex has a stimulatory effect on the growth of E. coli DH5α below the concentration 0.5 μg mL À1 , and the complex could inhibit its growth in the concentration range between 0.5 and 5.0 μg mL À1 .