Heat Capacity and Standard Thermodynamic Functions of

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Heat Capacity and Standard Thermodynamic Functions of Triphenylantimony Bis(1-adamantanecarboxylate) over the Range from (0 to 520) K Irina A. Letyanina,†,‡ Alexey V. Markin,*,† Natalia N. Smirnova,† Semen S. Sologubov,† and Vladimir V. Sharutin§ †

Lobachevsky State University of Nizhni Novgorod, 23 Gagarin Avenue, 603950 Nizhni Novgorod, Russia Saint Petersburg State University, 26 Universitetskiy Avenue, Peterhof, 198504 Saint Petersburg, Russia § National Research Southern Ural State University, 76 Lenin Avenue, 454080 Chelyabinsk, Russia ‡

ABSTRACT: Heat capacities of triphenylantimony bis(1-adamantanecarboxylate) Ph3Sb[OC(O)C10H15]2 were measured with a precision adiabatic vacuum calorimeter over the temperature range from T = (6 to 353) K and with differential scanning calorimeter over the temperature range from T = (320 to 520) K. The thermal behavior of the compound under study was investigated over the range from T = (250 to 530) K. It was revealed that triphenylantimony bis(1-adamantanecarboxylate) could exist in crystalline, liquid, glassy, and overcooled liquid states. On the obtained data, the standard thermodynamic functions of molar heat capacity Cp,m, enthalpy H(T) − H(0), entropy S(T), and Gibbs energy G(T) − H(0) of Ph3Sb[OC(O)C10H15]2 were calculated over the range from T = (0 to 498) K. The low-temperature (T < 50 K) heat capacity dependence was analyzed on the basis of Debye’s heat capacity theory of solids and its multifractal model, so the characteristic temperature and the fractal dimension were determined, and chain-layered structure topology was established. The standard entropy of formation at T = 298.15 K of Ph3Sb[OC(O)C10H15]2 (cr) ΔfSm(298.15, Ph3Sb[OC(O)C10H15]2, cr) = (−2885 ± 8) J·K−1·mol−1 was calculated. Some thermodynamic properties of triphenylantimony bis(1-adamantanecarboxylate) were compared with similar data of other organic derivatives of antimony(V) studied earlier.

1. INTRODUCTION The synthesis and investigations of physicochemical properties and search of fields of application of organoantimony(V) complexes has attracted considerable interest of researches recently.1−5 Some unsaturated antimony compounds (acrylates and vinylbenzoates) are used now for the synthesis of organic polymers with an antimony atom as a substituent.6−8 There are a lot of investigations on their biological, including antimicrobial, and optical properties and their thermal-oxidative stability. Organic complexes on a base of antimony(V) with ligands with nitrogen, sulfur, oxygen, chlorine, and other atoms are synthesized actively, and their compositions and structures are analyzed;9−13 however, their physicochemical properties have been studied scarcely.14,15 Thus synthesis and investigation of structures and physicochemical properties of organometallic compounds, particularly highly coordinated antimony compounds, are an actual task. Pentaphenylantimony,16 tetra- and triphenylantimony oximates,17−20 and triphenylantimony diacrylate21 and dimethacrylate22 have been studied by us earlier within the bounds of complex research of antimony(V) organic compounds. The purpose of the present study is to measure the heat capacity with adiabatic calorimetry over the temperature range from T = (6 to 353) K and with differential scanning calorimetry from T = (320 to 520) K of the crystalline © 2013 American Chemical Society

triphenylantimony bis(1-adamantanecarboxylate) Ph3Sb[OC(O)C10H15]2, to investigate the thermal behavior of the compound within the temperature range from T = (250 to 530) K with differential scanning calorimetry, to detect possible phase transitions, to estimate their thermodynamic characteristics, to calculate the standard (p = 0.1 MPa) thermodynamic functions, namely molar heat capacity Cp,m, enthalpy H(T) − H(0), entropy S(T), and Gibbs energy G(T) − H(0) in the range from T = (0 to 498) K, to determine the characteristic temperature and fractal dimension D, to establish the structure topology, to calculate the standard entropy of formation at T = 298.15 K of Ph3Sb[OC(O)C10H15]2 (cr), and to compare obtained results for the compound under study and other organoantimony(V) derivatives.

2. EXPERIMENTAL SECTION 2.1. Synthesis and Characterization of Triphenylantimony Bis(1-adamantanecarboxylate) Ph3Sb[OC(O)C10H15]2. The sample of Ph3Sb[OC(O)C10H15]2 was synthesized according to the method described in ref 23. It is significant to note here that the reaction of oxidative addition with participation of triphenylantimony, hydrogen peroxide, Received: June 5, 2013 Accepted: September 11, 2013 Published: October 2, 2013 3087

dx.doi.org/10.1021/je400535t | J. Chem. Eng. Data 2013, 58, 3087−3095

Journal of Chemical & Engineering Data

Article

by a computer. The speed of the computer-controlled measuring system was 10 measurements per second. To verify the accuracy of the calorimeter, the heat capacities of the reference standard materials (K-3 benzoic acid and αAl2O3)26,27 prepared at the Institute of Metrology of the State Standard Committee of the Russian Federation were measured over the temperature range 6 ≤ (T/K) ≤ 353. The sample masses were (0.5302 and 1.1715) g, respectively. The deviations of our results from the recommended values reported by Archer26 of NIST were within 0.02 Cp,m between T = (6 to 15) K, 0.005 Cp,m between T = (15 to 40) K, and 0.002 Cp,m in the temperature range from (40 to 353) K. Standard uncertainty for temperature was u(T) = 0.01 K and relative standard uncertainty for the enthalpies of transformations was ur(ΔfusHm) = 0.002. Heat capacity measurements were continuously and automatically carried out by means of the standard method of intermittent heating of the sample and alternately measuring of the temperature. The heating rate and temperature increments were controlled at 0.01 K·s−1 and (0.5 to 3) K. The heating duration was about 10 min, and the temperature drift rates of the sample cell measured in an equilibrium period were always kept within 0.01 K·s−1 during the acquisition of all heat capacity results. Liquid helium and nitrogen were used as coolants. The ampule with the substance was filled with dry helium as a heat exchange gas to the pressure of 40 kPa at room temperature. The sample mass used for calorimetric measurement was 0.6790 g, which was equivalent to 0.000954 mol in terms of its molar mass, M = 711.5449 g·mol−1. The molar mass of the object under study was calculated from the International Union of Pure and Applied Chemistry (IUPAC) table of atomic weights.28 The experimental values of Cp,m (192 points) were obtained in two series reflecting the sequence of experiments. The first series of measurements was completed over the temperature range 80 ≤ (T/K) ≤ 353. The second series of Cp,m measurements was carried out between T = (6 to 90) K. The heat capacity of the sample was between (35 and 65) % of the overall heat capacity of the calorimetric ampule with the substance under temperature change from T = (6 to 353) K. 2.3. DSC and TG Analysis. To investigate the thermal behavior of triphenylantimony bis(1-adamantanecarboxylate) over the range from T = (250 to 530) K and measure the heat capacity of the sample under study over the range from T = (320 to 520) K, the differential scanning calorimeter (model: DSC 204 F1 Phoenix, Netzsch Gerätebau, Germany) was used. The calorimeter was calibrated and tested against melting of nheptane, mercury, tin, lead, bismuth, and zinc. Standard uncertainty for temperature was u(T) = 0.5 K and relative standard uncertainty for the enthalpies of transformations ur(ΔfusHm) = 0.01. The temperatures and the enthalpies of transitions were evaluated according to the standard Netzsch Software Proteus procedure. The heat capacity was determined by the “ratio method”, with corundum used as a standard reference sample. The technique for determining of Cp,m according to the data of DSC measurements is described in detail in refs 29 and 30 and the Netzsch Software Proteus. The relative standard uncertainty for the heat capacities was ur(Cp,m) = 0.02. The measurement was carried out in argon atmosphere. A total of (0.016 to 0.025) g of the compound under study was put in the crucible. The thermogravimetric (TG) analysis of Ph3Sb[OC(O)C10H15]2 was done using a thermal microbalance (model TG 209 F1 Iris, Netzsch Gerätebau, Germany). TG analysis was

and 1-adamantylcarboxylic acid (1:1:2 molar ratio) proceeded in ether at room temperature to form Ph3Sb[OC(O)C10H15]2: Ph3Sb + 2HOC(O)C10H15 + H 2O2 Et 2O

⎯⎯⎯⎯→ Ph3Sb[OC(O)C10H15]2 + H 2O

Large colorless crystals of the compound under study well soluble in the organic solvents were isolated from the reaction mixture. The yield of the target product reached 92 %. The compound was identified by elemental analysis: calculated (for formula C40H45O4Sb): C, 67.51 %; H, 6.33 %; found C, 67.32 %; H, 6.30 %. The structure was defined by IR spectroscopy and X-ray diffraction analysis. According to X-ray studies, the antimony atom in the molecules of Ph3Sb[OC(O)C10H15]2 has a distorted trigonal bipyramid coordination with the oxygen atoms of carboxylate ligands in the axial positions. The SbC3 group of atoms has a flat structure. The detailed structure description of Ph3Sb[OC(O)C10H15]2 is given in ref 23. As elemental analysis and IR spectroscopy showed, the content of the main compound in the sample under study was 0.990 molar fraction. The impurities were not identified, but their amount in the sample was irrelevant to the accuracy of the thermodynamic values (taking into account the experimental uncertainty of the calorimetric methods used). The thermal stability of the sample under study was studied by us with thermal microbalance. A considerable mass loss related to the destruction of the compound (∼ 3 %) observed at T = 550 K; thus, the sample of triphenylantimony bis(1adamantanecarboxylate) was thermally stable up to 550 K. The information for the sample used in this study is listed in Table 1. Table 1. Information of the Sample Used in This Study chemical name triphenylantimony bis(1adamantanecarboxylate)

source

state

mass fraction purity

synthesis

powder

0.99

2.2. Adiabatic Calorimetry. A precision automatic adiabatic calorimeter (BCT-3) was used to measure heat capacities over the temperature range of 6 ≤ (T/K) ≤ 353. The principle and structure of the adiabatic calorimeter are described in detail elsewhere.24,25 All of the measurements were performed with a computer-controlled measuring system comprised of an analog-to-digital converter, a digital-to-analog converter, and a switch. The calorimetric cell is a thin-walled cylindrical vessel made from titanium with a volume of 1.5·10−6 m3. Its mass is (1.564 ± 0.005) g. A miniature iron−rhodium resistance thermometer (with the nominal resistance of 100 Ω) was used to measure the temperature of the sample. The thermometer was calibrated on IST-90 (International Temperature Scale of 1990) by the Russian Metrology Research Institute, Moscow region, Russia. The difference in temperature between the ampule and an adiabatic shield was controlled by a four-junction copper−iron−chromel thermocouple. The sensitivity of the thermometric circuit was 1·10−3 K, of the analogto-digital converter 0.1 μV. The energy introduced into the sample cell and the equilibrium temperature of the cell after the energy input were automatically recorded and processed online 3088



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Table 2. Experimental Molar Heat Capacities of Crystalline Triphenylantimony Bis(1-adamantanecarboxylate) Ph3Sb[OC(O)C10H15]2 (M = 711.5449 g·mol−1)a T/K

Cp,m/J·K−1·mol−1

T/K

82.81 84.88 86.94 89.00 91.06 93.12 95.10 97.23 99.29 101.34 103.39 105.44 107.49 109.54 111.58 113.60 115.64 117.68 119.72 121.60 123.78 125.80 127.83 129.85 131.86 133.87 135.88 137.88 139.88 141.88 143.86 145.81 147.78 149.76 152.23 155.20 158.16 161.11

229.3 233.7 238.0 242.4 246.7 251.6 255.9 260.6 265.2 269.7 274.4 279.4 283.8 288.0 292.9 297.5 301.6 306.6 310.6 314.8 319.2 323.9 328.3 332.6 337.5 341.8 346.7 351.3 353.9 360.2 365.0 369.5 373.9 378.3 383.7 391.3 397.8 404.3

164.04 166.97 169.88 172.78 175.68 178.57 181.43 184.29 187.14 189.90 192.72 195.53 198.33 201.12 203.89 212.20 214.96 217.72 220.47 223.23 225.98 228.73 231.48 234.15 236.89 239.63 242.35 245.08 247.81 250.54 253.26 255.99 258.71 261.43 264.15 266.87 269.60 272.32


T/K


411.2 417.6 424.5 430.6 437.0 443.5 450.4 457.3 463.9 470.0 477.1 483.7 489.7 496.2 503.0 523.0 529.5 536.6 543.8 550.0 556.9 564.4 571.2 576.4 583.6 590.6 597.2 603.8 610.3 617.0 623.5 630.5 636.5 643.1 650.3 656.1 662.2 669.0

275.04 277.75 280.46 283.18 285.90 288.62 291.34 294.06 296.83 299.59 302.36 305.06 307.66 310.21 312.71 315.15 317.53 319.66 321.94 324.16 326.33 328.44 330.51 332.48 334.44 336.34 338.20 340.00 341.76 343.47 345.00 346.75 348.10 349.45 350.59 352.03 353.43

675.8 683.5 690.8 697.8 703.7 711.2 717.9 724.7 732.2 739.0 745.1 750.5 756.7 763.5 769.8 776.0 781.5 787.9 792.5 798.1 802.6 808.3 813.0 818.5 823.2 827.3 831.4 835.5 839.5 842.9 846.6 850.4 853.8 857.0 860.6 864.0 868.0

50.00 51.40 53.73 58.14 60.30 62.63 66.95 69.00 71.50 76.10 78.20 81.06 85.96 90.86 92.70 95.66 100.4 105.3 110.2 112.6

49.81 51.54 53.30 55.08 56.92 58.79 60.68 62.61 64.56 65.56 66.56 67.71 68.61 69.83 71.36 72.79 74.91 76.18 77.05 79.88

144.3 149.4 154.6 159.8 165.0 170.2 175.3 180.4 185.5 188.2 190.7 194.0 196.1 198.9 203.1 206.9 212.3 214.9 217.4 223.6

series 1

series 2 6.41 6.94 7.48 8.31 9.04 9.66 10.20 10.77 11.22 11.69 12.18 12.78 13.14 13.61 14.14 14.53 15.03 15.43 15.87 16.49

4.28 5.00 6.19 8.15 10.0 11.6 13.1 14.6 16.0 17.3 18.9 20.8 22.0 23.6 25.5 26.8 28.42 29.84 31.16 33.38

21.30 21.81 22.55 23.78 24.30 25.02 26.25 26.83 27.53 28.80 29.43 30.12 31.46 32.84 33.37 34.23 35.64 37.11 38.61 39.32 3089



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Table 2. continued T/K


T/K

17.10 17.71 18.32 18.89 19.52 20.03

35.31 37.46 39.70 41.48 43.60 45.33

40.13 41.68 43.20 44.84 46.46 48.11

Cp,m/J·K−1·mol−1 series 2, continued 115.0 119.9 124.6 129.5 134.4 139.3

T/K


82.03 84.20 87.67 90.77 93.18

228.1 232.4 240.1 246.0 251.3

a Standard uncertainty for temperature u(T) = 0.01 K and relative standard uncertainty for the heat capacities ur(Cp,m) = 0.02 within the temperature range T = (6 to 15) K, ur(Cp,m) = 0.005 between T = (15 and 40) K, and ur(Cp,m) = 0.002 within the temperature range of 40 ≤ (T/K) ≤ 353.

carried out in the range from (300 to 580) K in the argon atmosphere. The thermal microbalance TG 209 F1 Iris allows fixing the mass change in ± 0.1 μg. The mean heating rate was 5 K·min−1. The measuring technique of the TG analysis was standard, according to Netzsch Software Proteus.

3. RESULTS AND DISCUSSION 3.1. Heat Capacity and Phase Transition. All experimental results of the molar heat capacity of Ph3Sb[OC(O)-

Figure 2. Plot of deviations of experimental data from fitted.

C10H15]2 over the range from T = (6 to 353) K (adiabatic vacuum calorimetry, Table 2) and from T = (320 to 520) K (differential scanning calorimetry) are plotted in Figure 1. The tested substance under conditions of the apparatus was cooled from room temperature to the temperature of the measurement onset at a rate of 0.01 K·s−1. The heat capacity of triphenylantimony bis(1-adamantanecarboxylate) rises with temperature increasing. The experimental data were smoothed using least-squares polynomial fits as follows: 9

Figure 1. Experimental molar heat capacity Cp,m of triphenylantimony bis(1-adamantanecarboxylate) as a function of temperature. ○, adiabatic vacuum calorimetry; −, differential scanning calorimetry; ····, extrapolated values of Cp,m.

ln Cp,m =

⎛

i=0

10

Cp,m =

⎛

∑ Ai⎜⎝ln i=0

T⎞ ⎟, 30 ⎠ i

∑ Ai⎜⎝ln

T⎞ ⎟, 30 ⎠

6 ≤ (T /K) ≤ 20 (1)

i

15 ≤ (T /K) ≤ 50 (2)

Table 3. Coefficients of eqs 1 to 3 T/K polynomial coefficients Ai/(J·K−1·mol−1)

6 to 20

15 to 50

40 to 90

80 to 220

200 to 350

320 to 480

−22.2312 −299.545 −1468.66 −4064.86 −7042.44 −7934.32 −5827.1 −2696.59 −715.104 −82.9545

80.5417 109.566 48.0084 −74.7638 −64.4648 423.245 354.602 −1179.05 −1077.56 1339.90 1378.47

−14837.873 58981.236 −100851.58 97270.768 −57786.719 21655.416 −5000.4943 650.71564 −36.549988

1766.238 −2596.899 1731.946 −613.1255 127.5779 −15.60438 1.039368 −0.02910092

218143.64 −168955.43 55723.985 −10132.346 1097.5756 −70.840401 2.5229555 −0.038257409

870404.82 −404182.31 78037.303 −8013.6484 461.68059 −14.148295 0.18018088

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Table 5. Fractal Dimensions D and Characteristic Temperatures Θmax of Some Antimony(V) Organic Compoundsa compound

D

Θmax/K

Ph3Sb[OC(O)C10H15]2 Ph5Sbb Ph4SbONCPh217 Ph4SbONCPhMe18 Ph3Sb(ONCPhMe)219 Ph3Sb(O2CCHCH2)221 Ph3Sb(O2CCMeCH2)222

1.6 1.3 1.5 1.5 1.6 1.4 1.5

201.6 246.7 202.8 218.7 194.8 251.1 227.6

a

Relative standard uncertainty for the characteristic temperature ur(Θmax) = 0.008. bValues of D and Θmax were calculated using data from ref 16.

Software Proteus. ΔfusHm was calculated from the area between anomalous and normal trends of the curves Cp,m = f(T), and ΔfusSm was calculated according to the second law of thermodynamics. The details of the thermal studies were as follows. Step 1. The sample was heated from T = 320 K (point A, Figure 3a) to T = 530 K (point E, Figure 3a) with a scanning rate of 5 K·min−1. As it can be seen from Figure 3a the compound existed in crystalline (section AB, Figure 3a) and liquid (section DE, Figure 3a) states. It fused over the interval from T = (480 to 515) K (section BCC′D, Figure 3a). Step 2. After that the sample was kept at the indicated temperature (T = 530 K) for 10 min. Then the sample was cooled to T = 250 K (point A′, Figure 3b) with a scanning rate of 20 K·min−1 and again heated to the final temperature (T = 530 K, point E, Figure 3b) with a scanning rate of 5 K·min−1. On heating the devitrification of the compound was revealed over the temperature range from T = (320 to 330) K, Tg = (324 ± 1) K (section FG, Figure 3b). The devitrification internal and temperature were found graphically. Over the interval 390 ≤ (T/K) ≤ 450 K (section HIJ, Figure 3b) the energy output took place that was caused with partial crystallization of the sample. Then within the interval from T = (465 to 500) K, the crystals of the compound fused (section BCC′D, Figure 3b). The point that the sample crystallized partially was indicated with the enthalpy of the fusion of these crystals was less than the enthalpy of the fusion of the initial sample. Step 3. It was interesting to obtain the substance under study in the overcooled liquid state. As it was established in step 2, the crystallization took place within the temperature interval from T = (390 to 450) K, and in this connection the sample was cooled from the final temperature (T = 530 K) until T = 470 K with a rate of 20 K·min−1 and then heated again with a rate of 5 K·min−1. The overcooled liquid state is indicated with a green color in Figure 3b. In cooling to lower temperatures

Figure 3. DSC curves of triphenylantimony bis(1-adamantanecarboxylate) (a) step 1, (b) step 2, and (green line) step 3. 8

Cp,m =

⎛ T ⎞i ⎟, 30 ⎠

∑ Ai⎜⎝ i=0

40 ≤ (T /K) ≤ 480 (3)

The polynomial coefficients Ai for eqs 1 to 3 are given in Table 3. The relative deviations of experimental data from the smoothing functions were listed in Figure 2. Over the range from T = (0 to 6) K the extrapolation was done according to the Debye law in the low-temperature limit. Over the range from T = (480 to 515) K the sample fusion took place. The temperature of the fusion was equal to Tfus = (497.9 ± 0.5) K, and the enthalpy was ΔfusHm = (47.4 ± 0.5) kJ·mol−1 (mean value with respect to three independent measurements are given). The entropy was ΔfusSm = (95.1 ± 0.9) J·K−1·mol−1. The fusion temperature was estimated as the temperature of the transition beginning according to Netzsch

Table 4. Standard Thermodynamic Characteristics of Fusion of Some Antimony(V) Organic Compounds compound

temp range/K

Ph3Sb[OC(O)C10H15]2 Ph5Sb16 Ph4SbONCPh217 Ph4SbONCPhMe18 Ph3Sb(ONCPhMe)219 Ph3Sb(O2CCHC2)221 Ph3Sb(O2CCMeCH2)222

480−520 370−420 400−450 390−430 423−453 390−430 400−440

Tfus/K 497.9 403.3 443.4 409.6 434.5 428.4 418.7 3091

± ± ± ± ± ± ±

0.5 0.5 0.5 0.5 0.5 0.5 0.5

ΔfusHm/ kJ·mol−1

ΔfusSm/ J·K−1·mol−1

47.4 ± 0.5

95.1 ± 0.9

42.0 ± 0.6

96.7 ± 1.4



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Table 6. Calculated Heat Capacities and Thermodynamic Functions of Crystalline Ph3Sb[OC(O)C10H15]2 (M = 711.5449 g· mol−1) at Pressure p = 0.1 MPaa T/K


[H(T) − H(0)]/kJ·mol−1

S(T) /J·K−1·mol−1

−[G(T) − H(0)]/kJ·mol−1

5 10 15 20 25 30 35 40 45 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 298.15 300 310 320 330 340 350 360 370 380 390 400 410 420 430 440 450 460 470 480 490 498

2.04 12.5 28.4 45.29 62.48 80.54 98.30 114.6 130.0 144.9 173.4 199.7 223.8 244.7 266.9 289.1 311.3 333.5 356.0 378.8 401.7 424.6 447.4 470.3 493.6 517.7 542.3 567.3 591.6 615.4 639.5 664.0 689.1 714.3 734.7 739.3 763.8 787.8 811.6 835.4 859 882 904 926 949 972 996 1020 1044 1067 1091 1118 1152 1201 1251 1289

0.00260 0.0356 0.136 0.3199 0.5893 0.9465 1.394 1.927 2.539 3.226 4.820 6.687 8.808 11.15 13.71 16.49 19.49 22.71 26.16 29.83 33.74 37.87 42.23 46.82 51.64 56.69 61.99 67.54 73.34 79.37 85.65 92.16 98.93 105.9 111.8 113.2 120.7 128.5 136.5 144.7 153 162 171 180 189 199 209 219 229 240 251 262 273 285 297 307

0.683 4.85 12.8 23.24 35.18 48.15 61.92 76.14 90.53 105.0 134.0 162.7 191.0 218.6 245.5 272.0 298.1 323.9 349.4 374.7 399.9 425.0 449.9 474.7 499.4 524.1 548.7 573.4 598.0 622.7 647.3 671.9 696.5 721.1 741.2 745.7 770.4 795.0 819.6 844.2 869 893 918 942 966 991 1015 1039 1064 1088 1112 1136 1161 1186 1211 1231

0.000855 0.0129 0.0555 0.1449 0.2903 0.4982 0.7732 1.118 1.535 2.024 3.219 4.703 6.472 8.520 10.84 13.43 16.28 19.39 22.76 26.38 30.25 34.37 38.75 43.37 48.24 53.36 58.72 64.33 70.19 76.29 82.64 89.24 96.08 103.2 109.1 110.5 118.1 125.9 134.0 142.3 151 160 169 178 188 197 207 218 228 239 250 261 273 284 296 306

a Standard uncertainty for temperature u(T) = 0.01 K and relative standard uncertainty for the heat capacities ur(Cp,m) = 0.02 within the temperature range T = (6 to 15) K and T = (350 to 498) K, ur(Cp,m) = 0.005 between T = (15 and 40) K, and ur(Cp,m) = 0.002 within the temperature range of 40 ≤ (T/K) ≤ 353.

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than T = 470 K, stopping there and following heating the compound crystallized and then fused. Thus crystalline, liquid, glassy, and overcooled liquid states of triphenylantimony bis(1-adamantanecarboxylate were obtained via calorimetrical experiment. The fusion was observed for antimony(V) organic compounds researched by us earlier, such as Ph5Sb,16 Ph4SbONCPh2,17 Ph4SbONCPhMe,18 Ph3Sb(ONCPhMe)2,19 Ph3Sb(O2CCHCH2)2,21 and Ph3Sb(O2CCMeCH2)2.22 As it can be seen from Table 4, just two of them, Ph3Sb(ONCPhMe)2 and Ph3Sb[OC(O)C10H15]2, fuse without decomposition. Table 4 shows that all compounds under study fuse over comparatively close temperature ranges, but triphenylantimony bis(1-adamantanecarboxylate) is an exception because of the influence of large substitutes. Nevertheless, the values of enthalpy and entropy of fusion of triphenylantimony bis(acetophenoneoximate) and bis(1-adamantanecarboxylate) are close. Low-temperature heat capacity data were used to calculate a value of a fractal dimension D.31 The fractal dimension is an exponent at temperature in the basic equation in the fractal model of Debye’s theory of heat capacity of solids. The value of D allows us to draw certain conclusions about the type of structure topology of solids and can be derived from the plot of ln Cv vs ln T.31 It follows from eq 4: Cv = 3D(D + 1)kNγ(D + 1)ξ(D + 1)(T /Θmax )D

Θmax (Ph3Sb[OC(O)C10H15]2 ) ≈ Θmax (Ph3Sb(ONCPhMe)2 ) ≈ Θmax (Ph4SbONCPh 2) < Θmax (Ph4SbONCPhMe) < Θmax (Ph3Sb(O2 CCMeCH 2)2 ) < Θmax (Ph5Sb) < Θmax (Ph3Sb(O2 CCHCH 2)2 )

According to our results, the most rigid compound among studied ones is triphenylantimony diacrylate, and the least rigid compound is triphenylantimony bis(1-adamantanecarboxylate). 3.2. Standard Thermodynamic Functions of Ph3Sb[OC(O)C10H15]2. To calculate the standard thermodynamic functions (Table 6) of Ph3Sb[OC(O)C10H15]2, the smoothed molar heat capacities Cp,m were extrapolated from the temperature of the measurement beginning at approximately T = 6 K to T → 0 K with the Debye law in the low-temperature limit:14 Cp,m = n D(ΘD/T )

where n = 6 is the number of degrees of freedom, D is the Debye function, and ΘD = 61.9 K refers to the Debye characteristic temperature. Using the above parameters,14 eq 6 describes the Cp,m values of the compound over the range 6 ≤ (T/K) ≤ 12 with relative standard uncertainty ur(Cp,m) = 0.012. In calculating the functions, it was assumed that eq 6 reproduced the Cp,m values of Ph3Sb[OC(O)C10H15]2 at T ≤ 6 K with the same uncertainty. The calculations of [H(T) − H(0)] and S(T) were made by numerical integration of the curves with respect to T and ln T, respectively. The Gibbs energy [G(T) − H(0)] was calculated from [H(T) − H(0)] and S(T) values at corresponding temperatures. The zero entropy of crystalline Ph3Sb[OC(O)C10H15]2 was assumed to be zero. The calculation procedure was described in detail in ref 33. Using the value of the absolute entropy of Ph3Sb[OC(O)C10H15]2 in Table 6 and the elemental substances, namely carbon,34 hydrogen,34 oxygen,34 and antimony,35 the standard entropy of formation of triphenylantimony bis(1-adamantanecarboxylate) at T = 298.15 K was estimated. ΔfSm(298.15, Ph3Sb[OC(O)C10H15]2, cr) = (−2885 ± 8) J·K−1·mol−1. The obtained value fits the equation

(4)

where N is the number of atoms in a molecular unit, k is the Boltzmann constant, γ(D + 1) is the γ-function, ξ(D + 1) is the Riemann ξ-function, and Θmax is the characteristic temperature. For a particular solid 3D(D + 1)kNγ(D + 1)ξ(D + 1)(1/Θmax)D = A is a constant value, and eq 4 can be written as eq 5: ln Cv = ln A + D ln T

(6)

(5)

At T < 50 K, the experimental values of Cp,m are equal to Cv. Thus, using experimental heat capacities in the range from (20 to 50) K and eq 5 the value of the fractal dimension was obtained for Ph3Sb[OC(O)C10H15]2 (Table 5). According to the multifractal model of the theory of heat capacity of solids,32 D = 1 corresponds to the solids with a chain structure, D = 2 corresponds to ones with a layered structure, and D = 3 corresponds to ones with a spatial structure. The D value obtained for Ph3Sb[OC(O)C10H15]2 points to the chain-layered topology of structure. The values of D and Θmax for studied earlier organic derivatives of pentavalent antimony16−19,21,22 are presented in Table 5. Apparently, the chain-layered topology of structures is typical for all compounds under research. The values of the characteristic temperatures Θmax calculated for the same number of degrees of freedom and temperature range allow us to draw some conclusions on the relative rigidity of the structures of solids. The results are presented as the rank:

40C(gr) + 22.5H 2(g) + 2O2 (g) + Sb(cr) → Ph3Sb[OC(O)C10H15]2 (cr)

where gr, cr, and g are graphite, crystal, and gas, respectively.

4. CONCLUSIONS This work reports heat capacities of the crystalline triphenylantimony bis(1-adamantanecarboxylate) Ph3Sb[OC(O)C10H15]2 within the temperature range 6 ≤ (T/K) ≤ 520. The standard thermodynamic functions of Ph3Sb[OC(O)C10H15]2 (cr) over the range from T = (0 to 498) K and the standard entropy of formation at T = 298.15 K ΔfSm(298.15, Ph3Sb[OC(O)C10H15]2, cr) = (−2885 ± 8) J·K−1·mol−1 were derived from these experimental results. The low-temperature (T ≤ 50 K) dependence of the heat capacity was analyzed on the basis of the heat capacity theory of 3093



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lantimony chlorate: Syntheses and structures. Russ. J. Inorg. Chem. 2009, 54, 389−395. (13) Dodonov, V. A.; Gushchin, A. V.; Vorob’ev, O. G.; Zinov’eva, T. I. A one-step synthesis of trimethylantimony(V) diacrylates. Russ. Chem. Bull. 1994, 43, 497−498. (14) Rabinovich, I. B.; Nistratov, V. P.; Telnoy, V. I.; Sheiman, M. S. Thermochemical and thermodynamic properties of organometallic compounds; Begell House: New York, 1999. (15) Stull, D. R.; Westrum, E. F.; Sinke, G. C. The chemical thermodynamics of organic compounds; John Wiley & Sons, Inc.: New York, 1969. (16) Smirnova, N. N.; Letyanina, I. A.; Larina, V. N.; Markin, A. V.; Sharutin, V. V.; Senchurin, V. S. Thermodynamic properties of pentaphenylantimony Ph5Sb over the range from T → 0 to 400 K. J. Chem. Thermodyn. 2009, 41, 46−50. (17) Smirnova, N. N.; Letyanina, I. A.; Markin, A. V.; Larina, V. N.; Sharutin, V. V.; Molokova, O. V. Thermodynamic properties of tetraphenylantimony benzophenoxymate in the region of 0−450 K. Rus. J. Gen. Chem. 2009, 79, 717−723. (18) Letyanina, I. A.; Smirnova, N. N.; Markin, A. V.; Ruchenin, V. A.; Larina, V. N.; Sharutin, V. V.; Molokova, O. V. Thermodynamics of tetraphenylantimony acetophenoneoxymate. J. Therm. Anal. Calorim. 2011, 103, 353−363. (19) Markin, A. V.; Letyanina, I. A.; Smirnova, N. N.; Sharutin, V. V.; Molokova, O. V. Thermodynamic characteristics of triphenylantimony bis(acetophenoneoximate). Rus. J. Phys. Chem. 2011, 85, 1315−1321. (20) Markin, A. V.; Letyanina, I. A.; Smirnova, N. N.; Sharutin, V. V.; Molokova, O. V. Standard thermochemical characteristics of formation of triphenylantimony bis(acetophenoneoximate). J. Therm. Anal. Calorim. 2013, 111, 1499−1502. (21) Letyanina, I. A.; Markin, A. V.; Smirnova, N. N.; Gushchin, A. V.; Shashkin, D. V. Thermodynamic characteristics of triphenylantimony diacrylate. Rus. J. Phys. Chem. 2012, 86, 1189−1195. (22) Markin, A. V.; Letyanina, I. A.; Ruchenin, V. A.; Smirnova, N. N.; Gushchun, A. V.; Shashkin, D. V. Heat capacity and standard thermodynamic functions of triphenylantimony dimethacrylate over the temperature range from (0 to 400) K. J. Chem. Eng. Data 2011, 56, 3657−3662. (23) Sharutin, V. V.; Senchurin, V. S.; Sharutina, O. K.; Pakusina, A. P.; Smirnova, S. A. Synthesis and structure of tetraphenylantimony 1adamantanecarboxylate and triphenylantimony bis(1-adamantanecarboxylate). Rus. J. Gen. Chem. 2009, 79, 2131−2136. (24) Varushchenko, R. M.; Druzhinina, A. I.; Sorkin, E. L. Low temperature heat capacity of 1-bromoperfluorooctane. J. Chem. Thermodyn. 1997, 29, 623−637. (25) Malyshev, V. M; Milner, G. A.; Sorkin, E. L.; Shibakin, V. F. An automatic and low-temperature calorimeter. Instr. Exp. Technol. 1985, 6, 195−197. (26) Archer, D. G. Thermodynamic properties of synthetic sapphire (α-Al2O3), standard reference material 720 and the effect of temperature-scale differences on thermodynamic properties. J. Phys. Chem. Ref. Data 1993, 22, 1441−1453. (27) Gatta, G. D.; Richardson, M. J.; Sarge, S. M.; Stolen, S. Standards, calibration, and guidelines in microcalorimetry. Part 2. Calibration standards for differential calorimetry. Pure Appl. Chem. 2006, 78, 1455−1476. (28) Wieser, M. E.; Coplen, T. B. Atomic weights of the elements 2009 (IUPAC Technical Report). Pure Appl. Chem. 2011, 83, 359− 396. (29) Höhne, G. W. H.; Hemminger, W. F.; Flammersheim, H.-J. Differential scanning calorimetry, 2nd ed.; Springer: Heidelberg, 2003. (30) Drebushchak, V. A. Calibration coefficient of heat-flow DSC. Part II. Optimal calibration procedure. J. Therm. Anal. Calorim. 2005, 79, 213−218. (31) Lazarev, V. B.; Izotov, A. D.; Gavrichev, K. S.; Shebershneva, O. V. Fractal model of heat capacity for substances with diamond-like structures. Thermochim. Acta 1995, 269−70, 109−116. (32) Tarasov, V. V. Theory of heat capacity of chain and layer structures. J. Fiz. Him. 1950, 24, 111−128.

solids of Debye and the multifractal model, and as a results, a chain-layered structure topology was established. The thermal behavior of the compound under study was investigated over the range from T = (250 to 530) K. It was revealed that triphenylantimony bis(1-adamantanecarboxylate) could exist in crystalline, liquid, glassy, and overcooled liquid states. Some obtained results were compared for triphenylantimony bis(1-adamantanecarboxylate) and other organic derivatives of pentavalent antimony.

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AUTHOR INFORMATION

Corresponding Author

*Fax: +7-831-4345056. E-mail: [email protected]. Funding

The work was financially supported by Ministry of Education and Science of the Russian Federation (Contract No. 14.B37.21.0799). Notes

The authors declare no competing financial interest.

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REFERENCES

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