**3.1 Experimental**

610 Thermodynamics – Interaction Studies – Solids, Liquids and Gases

Table 4 lists the purity of ferrocene derivatives determined by adiabatic calorimetry (part 3.2), coefficients *a* and *b* of equations (9) and (10), and enthalpies and entropies of

359.5 115237.0 86.97±1.7 291.7±5.7

373.9 124422.2 90.64±1.8 304.0±5.8 BOF 99.6 *b* 364.8 133682.1 119.9±2.4 402.1±6.3 382.9 133533.0 98.2±2.0 329.4±5.2

320.5 95312.0 69.2±1.4 232.1±4.7

326.6 98138.8 70.7±1.5 237.1±4.9

*<sup>a</sup>* Adiabatic calorimetry; *b* DSC; *c* the value calculated on the basis of correlation

Table 4. The purity, coefficients of equations (9) and (10), enthalpies and entropies of

ferrocenylmethanol [FM], benzylferrocene [BF], benzoylferrocene [BOF], propionylferrocene [POF], *n*-

For testing the uncertainties of transpiration method in applying to FD, a compilation of the literature data on the enthalpy of sublimation of ferrocene were carried in reference

76.78±0.85) kJ·mol-1 was obtained, the most part of the data being focused in the range between (72 and 74) kJ·mol-1. Uncertainties of these quantities were probably the random errors. Taking into account the uncertainties of the initial vapor pressure data making up from (1.5 to 2) per cent, a total value of the random and systematic errors could be 2 %. Therefore, the errors of the enthalpies of vaporization and sublimation as derivative values

**3. The heat capacity and thermodynamic properties of the phase transitions**  A heat capacity is a capability of the substance for absorbing some quantity of the energy that increases its temperature by 1 degree K. A measurement of the heat capacity is performed by adiabatic and isothermal methods. The first one allows attaining the most complete thermodynamic equilibrium or, in any case, the thermal balance in the calorimetric system. The adiabatic method is used for exploring the thermal processes with different times of relaxation and the metastable phases which can exist in wide temperature ranges. The heat capacities and thermodynamic properties of the phase transitions were

of the vapor pressure in the transpiration method were evaluated as ± 2 %.

*<sup>a</sup> <sup>b</sup> <sup>T</sup>* )( *<sup>o</sup> vapHm <sup>T</sup>* )( *<sup>o</sup> subHm <sup>T</sup>* )( *<sup>o</sup> vapSm <sup>T</sup>* )( *<sup>o</sup> subSm*

339.7 111826.0 102.8±2.0 344.8±6.4

359.9 121314.1 109.3±2.0 366.6±6.0

353.7 112812.1 80.8±1.6 99.1±2.8 *<sup>c</sup>* 271.0±5.0 332.4±6.0

*vap mS T* , and sublimation, ( ) *<sup>o</sup>*

kJ·mol-1 J·K-1·mol-1

*subH T <sup>m</sup>* and ( ) *<sup>o</sup>*

*subH K <sup>m</sup>* values ranged from (70.3±1.0 to

*subS T <sup>m</sup>* of

vaporization and sublimation of FD at *T* = 298.15 K.

Comp ounds Purity, mol. %

FM 97.56 *a*; 99.0*<sup>b</sup>*

BF 99.47 *a*; 99.7*<sup>b</sup>*

POF 99.24 *a*; 99.0*<sup>b</sup>*

*n-PF* 98.93 *a*; 99.0*<sup>b</sup>*

*i-BF* 99.41 *a*; 99.0*<sup>b</sup>*

*subH HH m vap m m fus* .

*vap mH T* and ( ) *<sup>o</sup>*

propylferrocene [*n-PF*], *iso*-butylferrocene [*i-BF*] at *T* = 298.15 K

(Emel'yanenko et al., 2007). A series of 21 (298.15 ) *<sup>o</sup>*

vaporization, ( ) *<sup>o</sup>*

The measurements of the heat capacities were conducted in a fully automated setup, consisted of a vacuum adiabatic calorimeter, a data acquisition and control system, AK-9.02, and a personal computer, PC (Fig. 5). The setup was produced in the National Scientific and

Fig. 5. The vacuum adiabatic calorimeter (CA) and cryostat (CR): (1) titanium container (*V*~1 cm3); (2) copper sleeve with the heater of calorimeter; (3) adiabatic shield; (4) bronze lid of the container; (5) the rhodium-iron resistance thermometer; (6) four-junction battery of Cu/Fe - Chromel thermocouples; (7) radiation screen – aluminium- coated Dacron-like film; (8) nylon threads; (9) spring; (10) Teflon tube; (11) plug; (12) vacuum jacket; (13) grooves of the plug 11; (14) valve; (15) and (16) detachable vacuum and cable joists, respectively; (17) steel tubes; (18) coupling nut; (19) charcoal getter; (20) radiation screens.

Research Institute of Physical Technical and Radio-Technical Measurements (Mendeleevo, Moscow Region). The main principles of its construction were published in (Pavese & Malyshev, 1994).

The calorimetric cell consists of a container, 1, a copper sleeve, 2, in which the container is tightly held, and an adiabatic shield, 3. A bronze brass lid, 4, serves for vacuum-tight sealing the container by means of indium gasket and a simple manifold. To decrease the heat capacity of the empty calorimeter, the miniature rhodium-iron resistance thermometer, 5, ( 50 ) <sup>0</sup>*<sup>R</sup>* was mounted on the inner surface of the adiabatic shield. The thermometer, which was calibrated on ITS-90, is destined for temperature measurements from (0.5 to 373) <sup>К</sup> with accuracy <sup>3</sup> 3 10 K. The temperature difference between the calorimeter and the

Thermodynamics of the Phase Equilibriums of Some Organic Compounds 613

four – junction one and employing an additional heater (R ~ 133 Ω) mounted in the upper part of the shield, to which electrical wires of the thermometer and the main heater were connected. Additional heater allows making up a lack of the second adiabatic shield that is usually employed in the adiabatic calorimeters, but cannot be place in our miniature device. Due to small size, the cryostat with the calorimeter was placed in the transport Dewar vessels with refrigerants (liquid helium or nitrogen), that allows us to exclude an intermediate Dewar vessel and, thus, to keep the coolants. There is no constant pumping of the cryostat during the operation, since high vacuum inside the cryostat was kept by means of cry-sorption provided with an efficient charcoal getter. The degree of vacuum in cryostat is controlled by the value of the heater current in the adiabatic shield. This value was determined in a process of the calorimeter production using nitrogen and helium baths. The automatic procedure of the heat capacity measurements is performed by AK – 9.02 system running under PC control (Pvese & Malishev, 1994). The program realizes a method of the discrete input of the energy in two modes: constant increments of temperature, *T* (from 1 to 2) K during measurement of the heat capacity and constant impulses of energy in

studying the phase transitions.

Fig. 6. Temperature, *T,* agains*t* time,

the calorimeter in 4th main (heating) period;

periods of the calorimetric measurement; i *<sup>T</sup>* and f *<sup>T</sup>* are an initial and final temperatures of

The calorimetric experiment consists of six periods (Fig. 6). In the first period the calorimeter is heated to a desired temperature*.* A steady temperature equilibration is attained in the second period. In the third period the temperature of the calorimeter is monitored over a chosen time interval to acquire information about the temperature drift rate, *V*<sup>i</sup> and to obtain the linear relation between the values *V*<sup>i</sup> and the time by the least-squares method. During the fourth (heating) period the electrical energy is supplied to the calorimeter, and the heating-up time is observed. The fifth period is the same as the second one. In the sixth period the linear relation between the temperature drift rate of the calorimeter *V*<sup>f</sup> and the time is established exactly in a similar manner to that in the third period. The initial and the final temperatures of the calorimeter in the main (heating) period are calculated by

m is the midpoint.

, curve in a heat capacity measurement. 1 to 6 are

adiabatic shield is measured by a four-junction thermocouple, 6, (Cu + 0.1 per cent Fe alloy against Chromel), one end of which was mounted on the copper sleeve 2 and the other one was placed on the inner surface of the adiabatic shield, 3. A manganin calorimeter heater *(R =* 300 Ω) was wound non-inductively on the sleeve, 2. A well-known three-lead circuit diagram was employed for wiring the current and potential leads of the heater. Since the resistances of the current leads are equal, this diagram enables us to account for the heat generated in the leads between the calorimeter and the shield. To reduce the level of heat radiation, the shield was wrapped with several layers of aluminium-coated Lavsan film, 7, (ACLF, an analog of Mylar). The container sleeve, 2, is suspended inside the adiabatic shield on three nylon threads, 8, which are stretched by a spring, 9 (Fig. 5). The calorimeter cell has been fixed on an epoxy/fibre-glass tube, 10, of the cryostat, CR. The tube, 10, is fastened to a copper plug, 11, by means of a bayonet joint. The only removable part of the calorimeter cell is the container for the specimen.

The vacuum jacket, 12, is made from oxygen-free copper. The vacuum seal of the cryostat is provided by a KPT-8 silicon/boron nitride paste, which has high thermal conductivity value and gives a stable vacuum junction after freezing. The paste is put between the upper part of the jacket, 12, and the plug, 11, in its grooves, 13.

The top part of the cryostat (CR) has a valve, 14, detachable vacuum, 15, and cable, 16, joints; the latter connects the electrical leads of the calorimeter cell to AK-9.02 and PC. Both parts of the cryostat are jointed by the stainless steel tubes, 17. Due to small size (*l* = 120 mm, *d =* 22.5 mm), the cryostat is immersed directly into a commercial transportation Dewar vessels. This allows us to exclude an intermediate Dewar vessel and, thus, to reserve the coolants. A coupling nut, 18, with a Teflon shell and a rubber ring is used to fasten the cryostat airtight inside the neck of the Dewar vessel. A T-connection, fitted on the neck of the nitrogen Dewar vessel, enables us to pump out nitrogen vapors to lower the bath temperature if necessary.

The calorimeter cell is cooled down by thermal conductivity via electrical leads and by radiation heat transfer. The leads of the thermometer, heaters, and differential thermocouple form a heat shunt with the preset thermal resistance and they provide cooling of the calorimeter from room temperature to approximately T = 78 K, and from T = 78 К down to T = 5 К for about 7 h in each Dewar vessel. The helium heat-exchange gas is not used for this purpose in order to avoid problems, connected with it desorption. To reduce the heat losses by radiation, the additional radiation screens, 20, are used (Fig. 5).

The data acquisition system AK-9.02 is a single unit, connected with a personal computer [PC]. The system AK-9.02 and the PC perform the measurements of all values that are necessary for the determination of the heat capacity, as well as the control of the measurement process and data processing.

The thermometer resistance and the calorimeter power heating are measured by a potentiometer method with cyclic inversion of the direction of thermometer current for excluding the thermal electromotive forces. All the procedures that control the measurement process are carried out by the PC, which has a simple and user-friendly interface. The results of the measurements are printed and displayed on the screen for visual monitoring.

An adiabatic condition in calorimeter is maintained by the AK-9.02 system, which allows keeping the temperature drop between the container and shield on the average within <sup>3</sup> (1 3) 10 K. Owing to modification of the calorimeter , the drop of temperature was reduced to ~ 0.5 mK at the expense of using an eleven - junctions thermocouple instead of

adiabatic shield is measured by a four-junction thermocouple, 6, (Cu + 0.1 per cent Fe alloy against Chromel), one end of which was mounted on the copper sleeve 2 and the other one was placed on the inner surface of the adiabatic shield, 3. A manganin calorimeter heater *(R =* 300 Ω) was wound non-inductively on the sleeve, 2. A well-known three-lead circuit diagram was employed for wiring the current and potential leads of the heater. Since the resistances of the current leads are equal, this diagram enables us to account for the heat generated in the leads between the calorimeter and the shield. To reduce the level of heat radiation, the shield was wrapped with several layers of aluminium-coated Lavsan film, 7, (ACLF, an analog of Mylar). The container sleeve, 2, is suspended inside the adiabatic shield on three nylon threads, 8, which are stretched by a spring, 9 (Fig. 5). The calorimeter cell has been fixed on an epoxy/fibre-glass tube, 10, of the cryostat, CR. The tube, 10, is fastened to a copper plug, 11, by means of a bayonet joint. The only removable part of the calorimeter cell

The vacuum jacket, 12, is made from oxygen-free copper. The vacuum seal of the cryostat is provided by a KPT-8 silicon/boron nitride paste, which has high thermal conductivity value and gives a stable vacuum junction after freezing. The paste is put between the upper part of

The top part of the cryostat (CR) has a valve, 14, detachable vacuum, 15, and cable, 16, joints; the latter connects the electrical leads of the calorimeter cell to AK-9.02 and PC. Both parts of the cryostat are jointed by the stainless steel tubes, 17. Due to small size (*l* = 120 mm, *d =* 22.5 mm), the cryostat is immersed directly into a commercial transportation Dewar vessels. This allows us to exclude an intermediate Dewar vessel and, thus, to reserve the coolants. A coupling nut, 18, with a Teflon shell and a rubber ring is used to fasten the cryostat airtight inside the neck of the Dewar vessel. A T-connection, fitted on the neck of the nitrogen Dewar vessel, enables us to pump out nitrogen vapors to lower the bath temperature if necessary. The calorimeter cell is cooled down by thermal conductivity via electrical leads and by radiation heat transfer. The leads of the thermometer, heaters, and differential thermocouple form a heat shunt with the preset thermal resistance and they provide cooling of the calorimeter from room temperature to approximately T = 78 K, and from T = 78 К down to T = 5 К for about 7 h in each Dewar vessel. The helium heat-exchange gas is not used for this purpose in order to avoid problems, connected with it desorption. To reduce the heat losses

The data acquisition system AK-9.02 is a single unit, connected with a personal computer [PC]. The system AK-9.02 and the PC perform the measurements of all values that are necessary for the determination of the heat capacity, as well as the control of the

The thermometer resistance and the calorimeter power heating are measured by a potentiometer method with cyclic inversion of the direction of thermometer current for excluding the thermal electromotive forces. All the procedures that control the measurement process are carried out by the PC, which has a simple and user-friendly interface. The results of the measurements are printed and displayed on the screen for visual monitoring. An adiabatic condition in calorimeter is maintained by the AK-9.02 system, which allows keeping the temperature drop between the container and shield on the average within <sup>3</sup> (1 3) 10 K. Owing to modification of the calorimeter , the drop of temperature was reduced to ~ 0.5 mK at the expense of using an eleven - junctions thermocouple instead of

is the container for the specimen.

the jacket, 12, and the plug, 11, in its grooves, 13.

by radiation, the additional radiation screens, 20, are used (Fig. 5).

measurement process and data processing.

four – junction one and employing an additional heater (R ~ 133 Ω) mounted in the upper part of the shield, to which electrical wires of the thermometer and the main heater were connected. Additional heater allows making up a lack of the second adiabatic shield that is usually employed in the adiabatic calorimeters, but cannot be place in our miniature device. Due to small size, the cryostat with the calorimeter was placed in the transport Dewar vessels with refrigerants (liquid helium or nitrogen), that allows us to exclude an intermediate Dewar vessel and, thus, to keep the coolants. There is no constant pumping of the cryostat during the operation, since high vacuum inside the cryostat was kept by means of cry-sorption provided with an efficient charcoal getter. The degree of vacuum in cryostat is controlled by the value of the heater current in the adiabatic shield. This value was determined in a process of the calorimeter production using nitrogen and helium baths. The automatic procedure of the heat capacity measurements is performed by AK – 9.02 system running under PC control (Pvese & Malishev, 1994). The program realizes a method of the discrete input of the energy in two modes: constant increments of temperature, *T* (from 1 to 2) K during measurement of the heat capacity and constant impulses of energy in studying the phase transitions.

Fig. 6. Temperature, *T,* agains*t* time, , curve in a heat capacity measurement. 1 to 6 are periods of the calorimetric measurement; i *<sup>T</sup>* and f *<sup>T</sup>* are an initial and final temperatures of the calorimeter in 4th main (heating) period; m is the midpoint.

The calorimetric experiment consists of six periods (Fig. 6). In the first period the calorimeter is heated to a desired temperature*.* A steady temperature equilibration is attained in the second period. In the third period the temperature of the calorimeter is monitored over a chosen time interval to acquire information about the temperature drift rate, *V*<sup>i</sup> and to obtain the linear relation between the values *V*<sup>i</sup> and the time by the least-squares method. During the fourth (heating) period the electrical energy is supplied to the calorimeter, and the heating-up time is observed. The fifth period is the same as the second one. In the sixth period the linear relation between the temperature drift rate of the calorimeter *V*<sup>f</sup> and the time is established exactly in a similar manner to that in the third period. The initial and the final temperatures of the calorimeter in the main (heating) period are calculated by

Thermodynamics of the Phase Equilibriums of Some Organic Compounds 615

solution of impurities with main substance. The efficient coefficient of impurities distribution between the crystal and liquid phases *k* is calculated by Mastrangello's and Dornte's method. The *k* value close to zero, proves an absence of the solid solution. According to (Alexandrov, 1975), melting curves can be concave not only in the case of solid solutions, but also in the absence of equilibrium in the calorimeter at the onset of fusion, when the amount of the liquid phase is small and impurities can therefore be distributed no uniformly, and at the final stage of melting, when sedimentation of crystals to the bottom of container interferes with slow attainment of temperature equilibrium. In conformity with Alexandrov recommendation (Alexandrov, 1975), the tp *<sup>T</sup>* and 2 *<sup>N</sup>* values ought to be estimated on the basis of the linear dependence for the part of melting curve in the range of

In the case of solid solution formation, the mole fraction of impurity, <sup>2</sup> *<sup>N</sup>* , can be determined by the Smit and Alexsandrov method using (1 / ) i i *<sup>T</sup> <sup>f</sup> <sup>F</sup>* experimental data and the equation for 2 *<sup>N</sup>* in a binary system with solid solution formation (Van Wijk & Smit,

<sup>1</sup> ( / ) [(1 ) / ] 0 2

Here, *Ak* is cryoscopic constant for the major substance; and *k* is a distribution coefficient of impurities between the solid and liquid phases. An insufficiency of this equation for calculating 2 *<sup>N</sup>* consists in the need to determine *k* coefficient by an independent method. By differentiating and finding the logarithm, equation (15) was transformed by (Alexandrov et

Equation (16) is used in this work for determination of the *k* coefficient directly from experimental dependence of (1 / ) i i *<sup>T</sup> <sup>f</sup> <sup>F</sup>* and for calculation of the mole fraction, 2 *<sup>N</sup>* , of

experimental data using the linear equation (16). Mole fraction of impurity, <sup>2</sup> *<sup>N</sup>* , was

 0 2 / <sup>0</sup> *A H RT k fus <sup>m</sup>* determined by above mentioned Rossini method. The enthalpy of fusion *fusHm* is determined by calorimetric method using the total enthalpy absorbed during the fusion with following subtraction of the normal heat capacities of the crystal and liquid which the substance has in the fusion region. The *fusHm* value is obtained from the

where *totH* is the total enthalpy absorbed in heating the calorimeter from initial temperature <sup>1</sup>*T* < *Ttp* to final one 2*<sup>T</sup>* <sup>&</sup>gt;*Ttp* ; <sup>1</sup> *<sup>H</sup>* and 2 *<sup>H</sup>* are the changes of enthalpy

impurity. The *k* and <sup>2</sup> *<sup>N</sup>* values were calculated by least-squares fits of the *<sup>i</sup>*

*<sup>k</sup> TT N A kF i i <sup>k</sup>* (15)

<sup>2</sup> ln{ / (1 / )} ln{ (1 ) / } ln(1 / ) <sup>2</sup> *dT d F N k A k F i i <sup>k</sup> <sup>i</sup>* (16)

)1( <sup>2</sup> ln{ *<sup>k</sup> AkN* term using the *k* value and the cryoscopic constant

<sup>123</sup> *H HH H H fus m tot* (17)

*T* and

*i F*

ii *FfT* can be explained by formation of solid

Concave curve of the dependence )/1(

values from 1.2 to about 8-10.

1960) and (Alexandrov et al., 1983):

computed from the }/ <sup>2</sup>

al., 1983) to the form:

equation:

1 /*F*i

extrapolating the linear dependencies of the drift rates *V*<sup>i</sup> and *V*<sup>f</sup> on time to the midpoint ( m) temperature (Fig. 6). This method permits the heat interchange between the calorimeter and surroundings to be taken into account (Varushchenko et al., 1997a). The reliability of this method was proved by a congruence within (0.1 to 0.2) per cent of the heat capacity values of an empty calorimeter, measured in the temperature interval (90 to 110) К using different refrigerants: liquid helium and nitrogen.

The values of the heat capacities, , *<sup>C</sup> s m* , are fitted with polynomials:

$$C\_{S,III} = \sum\_{\dot{l}} A\_{\dot{l}} \{ (T - A\_{\dot{k}}) / \, ^\dagger B\_{\dot{k}} \}^{\dagger} \tag{11}$$

$$C\_{S,III} = \sum\_{\dot{\mathbf{i}}} A'\_{\dot{\mathbf{i}}} \ln \left\{ (T - A'\_{\dot{\mathbf{k}}}) / B'\_{\dot{\mathbf{k}}} \right\}^{\dot{\mathbf{i}}} \tag{12}$$

where {( ) / } *TA B k k* and {( ) / } *TA B k k* are normalizing term, *<sup>i</sup>* is degree of polynomials. The coefficients of the polynomials *Ai* and *A <sup>i</sup>* were estimated by the LSM.

The metrological characteristics of the calorimeter were tested by measuring the heat capacity of pure copper having a mass fraction of 0.99995 and *n-*heptane in the temperature intervals (from 8 to 372) K and (from 6 to 354) K, respectively. Obtained , *<sup>C</sup> s m* values of

copper and *n-*heptane came to an agreement with the precise heat capacities of standard substances within (0.2 to 1.4) % below the temperature 70 К and decrease to (0.01 and 0.3) % above *T*=70 К.

## **3.2 Determination of thermodynamic properties of the phase transitions**

The important characteristics of the substances: a triple point temperature, tp *<sup>T</sup>* , and a mole fraction of impurities, 2 *<sup>N</sup>* , were determined by calorimetrical method of the fractional melting study, developed by Mair, Glasgow and Rossini. A linear dependence between the reciprocal fractions of the sample melted, 1 /*F*i , and the equilibrium fusion temperatures, *T*i , makes it possible to calculate both the tp *<sup>T</sup>* value and mole fraction of impurities, 2 *<sup>N</sup>* , by equations:

$$T\_{\hat{\mathbf{i}}} = d + f \cdot (\mathbf{1} / F\_{\hat{\mathbf{i}}})\_{\prime} \tag{13}$$

$$N\_{\mathbf{2}} = (\Lambda\_{\text{fus}} H\_{\text{m}} \cdot f) / (\mathbb{R} \cdot T\_{\text{tp}}^2) \tag{14}$$

Here <sup>0</sup> *d T* is the triple point temperature, tp *<sup>T</sup>* , of the pure compound, ( ), 1 0 *<sup>f</sup> T T* denotes a depression of the tp *<sup>T</sup>* value caused by impurities, *T1* is the triple point temperature of the completely melted substance (for <sup>1</sup> <sup>i</sup> *F* ), *R* = 8.314472 J K-1 mol-1, and *fusHm* is the enthalpy of fusion, determined by independent method.

extrapolating the linear dependencies of the drift rates *V*<sup>i</sup> and *V*<sup>f</sup> on time to the midpoint

 m) temperature (Fig. 6). This method permits the heat interchange between the calorimeter and surroundings to be taken into account (Varushchenko et al., 1997a). The reliability of this method was proved by a congruence within (0.1 to 0.2) per cent of the heat capacity values of an empty calorimeter, measured in the temperature interval (90 to 110) К

{( ) / } , *<sup>i</sup> C ATA B s m i kk <sup>i</sup>*

ln{( ) / } , *<sup>i</sup> C A TA B s m i kk <sup>i</sup>*

where {( ) / } *TA B k k* and {( ) / } *TA B k k* are normalizing term, *<sup>i</sup>* is degree of polynomials.

The metrological characteristics of the calorimeter were tested by measuring the heat capacity of pure copper having a mass fraction of 0.99995 and *n-*heptane in the temperature

copper and *n-*heptane came to an agreement with the precise heat capacities of standard substances within (0.2 to 1.4) % below the temperature 70 К and decrease to (0.01 and

The important characteristics of the substances: a triple point temperature, tp *<sup>T</sup>* , and a mole fraction of impurities, 2 *<sup>N</sup>* , were determined by calorimetrical method of the fractional melting study, developed by Mair, Glasgow and Rossini. A linear dependence between the

i

, makes it possible to calculate both the tp *<sup>T</sup>* value and mole fraction of impurities, 2 *<sup>N</sup>* ,

Here <sup>0</sup> *d T* is the triple point temperature, tp *<sup>T</sup>* , of the pure compound, ( ), 1 0 *<sup>f</sup> T T* denotes a depression of the tp *<sup>T</sup>* value caused by impurities, *T1* is the triple point

intervals (from 8 to 372) K and (from 6 to 354) K, respectively. Obtained , *<sup>C</sup>*

**3.2 Determination of thermodynamic properties of the phase transitions** 

*s m* , are fitted with polynomials:

*<sup>i</sup>* were estimated by the LSM.

(11)

*s m*

, and the equilibrium fusion temperatures,

*F* ), *R* = 8.314472 J K-1 mol-1, and

(1 / ), i i *T df F* (13)

fus <sup>m</sup> tp <sup>2</sup> ( )/( ) <sup>2</sup> *N H f RT* (14)

(12)

i

values of

using different refrigerants: liquid helium and nitrogen.

The values of the heat capacities, , *<sup>C</sup>*

The coefficients of the polynomials *Ai* and *A*

reciprocal fractions of the sample melted, 1 /*F*

temperature of the completely melted substance (for <sup>1</sup> <sup>i</sup>

*fusHm* is the enthalpy of fusion, determined by independent method.

0.3) % above *T*=70 К.

*T*i

by equations:

( Concave curve of the dependence )/1( ii *FfT* can be explained by formation of solid solution of impurities with main substance. The efficient coefficient of impurities distribution between the crystal and liquid phases *k* is calculated by Mastrangello's and Dornte's method. The *k* value close to zero, proves an absence of the solid solution. According to (Alexandrov, 1975), melting curves can be concave not only in the case of solid solutions, but also in the absence of equilibrium in the calorimeter at the onset of fusion, when the amount of the liquid phase is small and impurities can therefore be distributed no uniformly, and at the final stage of melting, when sedimentation of crystals to the bottom of container interferes with slow attainment of temperature equilibrium. In conformity with Alexandrov recommendation (Alexandrov, 1975), the tp *<sup>T</sup>* and 2 *<sup>N</sup>* values ought to be

estimated on the basis of the linear dependence for the part of melting curve in the range of 1 /*F*values from 1.2 to about 8-10.

In the case of solid solution formation, the mole fraction of impurity, <sup>2</sup> *<sup>N</sup>* , can be determined by the Smit and Alexsandrov method using (1 / ) i i *<sup>T</sup> <sup>f</sup> <sup>F</sup>* experimental data and the equation for 2 *<sup>N</sup>* in a binary system with solid solution formation (Van Wijk & Smit, 1960) and (Alexandrov et al., 1983):

$$T\_{\dot{\mathbf{i}}} = T\_{\mathbf{0}} - (N\_{\mathbf{2}} \, \, / \, A\_{\dot{\mathbf{k}}}) \cdot [(1 - k) \, / \, F\_{\dot{\mathbf{i}}}^{\mathbf{1} - k} \, ] \tag{15}$$

Here, *Ak* is cryoscopic constant for the major substance; and *k* is a distribution coefficient of impurities between the solid and liquid phases. An insufficiency of this equation for calculating 2 *<sup>N</sup>* consists in the need to determine *k* coefficient by an independent method. By differentiating and finding the logarithm, equation (15) was transformed by (Alexandrov et al., 1983) to the form:

$$\ln\{-dT\_{\dot{I}} \;/\ d(1 \;/\ F\_{\dot{I}})\} = \ln\{N\_{\mathcal{D}} \cdot (1 - k)^2 \;/\ A\_{\dot{k}}\} - k \cdot \ln(1 \;/\ F\_{\dot{I}}) \tag{16}$$

Equation (16) is used in this work for determination of the *k* coefficient directly from experimental dependence of (1 / ) i i *<sup>T</sup> <sup>f</sup> <sup>F</sup>* and for calculation of the mole fraction, 2 *<sup>N</sup>* , of impurity. The *k* and <sup>2</sup> *<sup>N</sup>* values were calculated by least-squares fits of the *<sup>i</sup> T* and *i F* experimental data using the linear equation (16). Mole fraction of impurity, <sup>2</sup> *<sup>N</sup>* , was computed from the }/ <sup>2</sup> )1( <sup>2</sup> ln{ *<sup>k</sup> AkN* term using the *k* value and the cryoscopic constant 0 2 / <sup>0</sup> *A H RT k fus <sup>m</sup>* determined by above mentioned Rossini method. The enthalpy of fusion *fusHm* is determined by calorimetric method using the total enthalpy absorbed during the fusion with following subtraction of the normal heat capacities of the crystal and liquid which the substance has in the fusion region. The *fusHm* value is obtained from the equation:

$${}^{\Delta}\_{fus}H\_m = \Delta\_{tot}H - \Delta H\_1 - \Delta H\_2 - \Delta H\_3 \tag{17}$$

where *totH* is the total enthalpy absorbed in heating the calorimeter from initial temperature <sup>1</sup>*T* < *Ttp* to final one 2*<sup>T</sup>* <sup>&</sup>gt;*Ttp* ; <sup>1</sup> *<sup>H</sup>* and 2 *<sup>H</sup>* are the changes of enthalpy

Thermodynamics of the Phase Equilibriums of Some Organic Compounds 617

Freons CF2ClCHFCl 86.5±0.1 *a* 135.74±0.19 - 7.05±0.13 - 51.94±0.71

Derivatives of ferrocene*<sup>c</sup>*

*n-*PF 186.7±0.3 276.83±0.50 1.23±0.01 12.74±0.17 6.59±0.06 46.02±0.61 *i-*BTF 207.4±0.3*a* 294.68±0.40 - 15.05±0.08 - 51.07±0.27

POF - 311.62±0.51 - 19.16±0.12 - 61.48±0.39 *i-*BF - 279.96±0.10 - 15.33±0.04 - 54.76±0.14 BeOF*<sup>d</sup>* - 380.7 - 29.9 - 78.5 FM - 347.80±1.0 - 22.91±0.53 - 65.87±1.52

Alkylderivatives of adamantane 1,3,5-TMA 234.4±0.1 255.61±0.05 8.19±0.03 2.06±0.03 34.94±0.13 8.06±0.11 1,3-DMA 223.38±0.01 247.79±0.01 9.31±0.01 1.54±0.01 41.68±0.06 6.21±0.02 1-EA - 225.56±0.02 - 11.22±0.03 - 49.74±0.08 Bicyclic hydrocarbons

*trans*-C9H16 - 213.86 - 10.90±0.02 - 50.97 *cis-*C10H18 216.1 230.18±0.05 2.136 9.489±0.006 9.88 41.22 *trans-*C10H18 242.78±0.05 14.414±0.001 59.37 Bicyclic perfluorocarbons

*trans-*C9F16 236.63±0.02 248.05±0.04 8.90 2.63±0.02 37.6 10.60±0.10 *cis-*C10F18 232.5±0.2 266.95±0.02 4.24±0.01 10.30±0.01 18.24±0.06 38.58±0.15 *trans-*C10F18 - 294.83±0.02 - 17.96±0.04 - 60.92±0.14 C5F10N-C6F10-CF3 - 293.26±0.20 - 8.32±0.02 - 28.37±0.06 *<sup>a</sup>* Glass like transition, *Tg*; *b*(Kolesov, 1995) *<sup>c</sup> n-*propylferrocene [*n*-PF], *iso-*butyrylferrocene [*i-*BTF], benzylferrocene [BeF], propionylferrocene [POF], *iso-*butylferrocene [*i-*BF], benzoylferrocene [BeOF],

*fusSm* of the solid-to-solid transitions and fusions, respectively, for some freons,

*trsHm* <sup>0</sup>

*<sup>b</sup>* 82.5±0.5 236.92±0.02 0.83±0.01 2.47±0.01 10.1±0.2 10.42±0.04

K kJmol-1 JK-1mol-1

2.63±0.01 1.51±0.01 11.1±0.1

46.1±0.4 25.54±0.94 0.54±0.01

0.40±0.002 1.40±0.004 45.3

1.27 2.72±0.03 43.66±0.04

*fusHm* , and entropies,

*trsHm* , <sup>0</sup>

*fusHm* <sup>0</sup>

*trsSm* <sup>0</sup>

19.54±0.04 8.36±0.04

0.83±0.01 73.06±2.70

2.2 5.92

5.17 9.34±0.09

*fusSm*

*Ttrs Ttp* <sup>0</sup>

134.6±0.1 180.62±0.02 1.21±0.01

51.1±0.3 349.57±0.10 23.8±0.2

184.9 236.48 8.26±0.004

245.63±0.04 291.27±0.09 8.76±0.03

Compounds

CF2ClCFCl2

*cis-*C9H16

*cis-*C9F16

0

*trsSm* , <sup>0</sup>

CF2ClCF2Cl *<sup>b</sup>* 109.3±0.2

BeF 44.3±0.2

182.28

200.64±0.03

ferrocenylmethanol [FM]; *d* values were measured by DSC.

Table 5. The temperatures, *Ttrs* , *Ttp* , enthalpies, <sup>0</sup>

ferrocene derivatives, cyclic hydrocarbons, and perfluorocarbons.

calculated from the normal heat capacities of the crystal and liquid in the temperature intervals from 1*<sup>T</sup>* to*Ttp* and from *Ttp* to 2*<sup>T</sup>* , respectively; *Hemp* is the enthalpy increment need for heating the empty calorimeter from 1*<sup>T</sup>* to <sup>2</sup>*<sup>T</sup>* .

### **3.3 Crystal phase transitions and molecular dynamics**

The solid state transitions revealed in the molecular crystals can be explained by different polymorphous transformations, caused by changing the crystal structure, different location of the molecules and their orientational and conformational disorder in the crystal lattice. In this chapter, some thermodynamic properties of solid state transitions and fusion are reviewed for some compounds, which were studied in the Luginin's Thermochemistry Laboratory of the Moscow State University and in some other thermodynamic Laboratories. An interpretation of the solid-state transitions in organic crystals was successfully fulfilled in a set of outstanding researcher's works (Westrum & McCullough, 1965; Kolesov, 1995; Adachi, et al., 1968) and the others. An interpretation of calorimetric measurements was carried out very often on the basis of the order – disorder concept. Understanding these processes requires sometimes exploring the molecular crystals by X-ray crystallography and IR and Raman spectroscopy. In this work, the solid state transitions will be discussed including some additional physico-chemical properties of the compounds.

The values of thermodynamic properties of the phase transitions are given in Table 5.

It was found by exploring IR-spectra of CF2ClCFCl2, that this substance comprises a mixture of *trans*- and *gauche*- conformers in solid (crystal I) and liquid states (Fig. 7). The sum 0 *trsSm* <sup>+</sup> <sup>0</sup> *fusSm* = 20.52 JK-1mol-1 for CF2ClCFCl2 is small, while such sum used to be from (42 to 50) JK-1mol-1 for organic crystals. By comparesing the calorimetric and spectroscopic <sup>0</sup>*Sm* values, it was found that CF2ClCFCl2 has residual entropy, *S*(0) = 10.1 JK-1mol-1 at T= 198.15 K (Higgins & Lielmers, 1965; Kolesov, 1995).

Fig. 7. Heat capacities and phase transitions of CF2ClCFCl2 **(a)** and CF2ClCHCl2 **(b)**. Freon CF2ClCHCl2 was in following states: glass (AB) and supercooled liquid (CE) ( = 0); partially crystalline state (BD) and supercooled liquid (DE) (= 0.076); and liquid (EF)

calculated from the normal heat capacities of the crystal and liquid in the temperature intervals from 1*<sup>T</sup>* to*Ttp* and from *Ttp* to 2*<sup>T</sup>* , respectively; *Hemp* is the enthalpy increment

The solid state transitions revealed in the molecular crystals can be explained by different polymorphous transformations, caused by changing the crystal structure, different location of the molecules and their orientational and conformational disorder in the crystal lattice. In this chapter, some thermodynamic properties of solid state transitions and fusion are reviewed for some compounds, which were studied in the Luginin's Thermochemistry Laboratory of the Moscow State University and in some other thermodynamic Laboratories. An interpretation of the solid-state transitions in organic crystals was successfully fulfilled in a set of outstanding researcher's works (Westrum & McCullough, 1965; Kolesov, 1995; Adachi, et al., 1968) and the others. An interpretation of calorimetric measurements was carried out very often on the basis of the order – disorder concept. Understanding these processes requires sometimes exploring the molecular crystals by X-ray crystallography and IR and Raman spectroscopy. In this work, the solid state transitions will be discussed

need for heating the empty calorimeter from 1*<sup>T</sup>* to <sup>2</sup>*<sup>T</sup>* .

198.15 K (Higgins & Lielmers, 1965; Kolesov, 1995).

0

*trsSm* <sup>+</sup> <sup>0</sup>

**3.3 Crystal phase transitions and molecular dynamics** 

including some additional physico-chemical properties of the compounds.

The values of thermodynamic properties of the phase transitions are given in Table 5. It was found by exploring IR-spectra of CF2ClCFCl2, that this substance comprises a mixture of *trans*- and *gauche*- conformers in solid (crystal I) and liquid states (Fig. 7). The sum

(42 to 50) JK-1mol-1 for organic crystals. By comparesing the calorimetric and spectroscopic <sup>0</sup>*Sm* values, it was found that CF2ClCFCl2 has residual entropy, *S*(0) = 10.1 JK-1mol-1 at T=

Fig. 7. Heat capacities and phase transitions of CF2ClCFCl2 **(a)** and CF2ClCHCl2 **(b)**. Freon

= 0);

= 0.076); and liquid (EF)

CF2ClCHCl2 was in following states: glass (AB) and supercooled liquid (CE) (

partially crystalline state (BD) and supercooled liquid (DE) (

*fusSm* = 20.52 JK-1mol-1 for CF2ClCFCl2 is small, while such sum used to be from


*<sup>a</sup>* Glass like transition, *Tg*; *b*(Kolesov, 1995) *<sup>c</sup> n-*propylferrocene [*n*-PF], *iso-*butyrylferrocene [*i-*BTF], benzylferrocene [BeF], propionylferrocene [POF], *iso-*butylferrocene [*i-*BF], benzoylferrocene [BeOF], ferrocenylmethanol [FM]; *d* values were measured by DSC.

Table 5. The temperatures, *Ttrs* , *Ttp* , enthalpies, <sup>0</sup> *trsHm* , <sup>0</sup> *fusHm* , and entropies,

 0 *trsSm* , <sup>0</sup> *fusSm* of the solid-to-solid transitions and fusions, respectively, for some freons, ferrocene derivatives, cyclic hydrocarbons, and perfluorocarbons.

Thermodynamics of the Phase Equilibriums of Some Organic Compounds 619

The nature of this transition was studied by the X-ray crystallography. Table 6 lists crystallographic data of *n*-propylferrocene in vicinity of the "order-disorder" transition. The structure of *n*-propylferrocene at 200 K contains a propyl- group disordered between two positions (in ca. 2:1 ratio) obviously due to thermal motion (Fig. 9). The transition of the crystal II (*T* = 150 K) to the crystal I (*T* = 200 K) occurred with significant changes of the lattice parameters: basis vectors, *a*, *b*, *c,* angle, *β,* the volume, *V,* the number of molecule in

Fig. 9. The structure of the ferrocenyl-*n*-propane crystal at the temperatures 150 K (II) and

13.738 (4) 7.541(1) 10.660(2) 99.76 (3) 1088.4(4)

200 13.977 (4) 7.621(1) 10.521(2) 96.87 (3) 1112.6(4) 0.064 0.136

While both *a* and *b* parameters became larger during phase transition II to I, the *c* parameter and *β* angle slightly decreased (Table 6). Structure solution of the crystals I and II revealed that lower temperature modification of the *n*-propylferrocene molecule has only one orientation of the propyl group. Apparently, the transitions in reverse order occurred when cooling the crystals from (150 to 200) K. Thus, the solid-state anomaly of *n*-propylferrocene is caused by the onset of the internal rotation of propyl groups in the molecules and also by a small shift of the pentadienyl cycles around the axis passed through their centers. These

The order-disorder conception is successfully used in exploring the plastic crystals. Adamantane and some of its derivatives form disordered plastic crystalline phases. The fusion of such substances occurs some times in two stages. First, an orientational disorder proceeds in the crystalline lattice because of high mobility of the molecules, and then the plastic crystals fuse owing to a translational molecular motion at higher temperature. In this

Table 6. Crystallographic data of *n*-propylferrocene crystal at the temperatures 150 K and

variations led to some orientation disorder of the crystal phase II (Fig. 9).

10-10*a* / m 10-10*b*/ m 10-10 *c* / m *β* / 0 10-30*V* / m3 *Z R1 wR2*

4

0.061 0.112

200 K (I)

symmetry, space group

150 monoclinic *Р*21/*с*

*Т*/К

200 K

the unit cell, *Z,* and the factors of the crystal structure quality, *R1* and *wR2*.

A characteristic feature of solid state transition of organic crystals is a slow thermal equilibrium between co-existing phases which very often promote to formation of metastable phases existing in a wide temperature range. In Fig. 7(b), the heat capacity *Cs m*, of 1,1-difluoro-1,2,2-trichloroethane, CF2ClCHCl2, is shown in the temperature interval studied. Similar ( ) *C* ,*s m f T* dependence has been obtained for isomer of 1,1-difluoro-1,2,2 trichloroethane: CFCl2CHFCl. Both isomers were in the forms of glasses, supercooled liquids, and partially crystalline states. The latter was attained after annealing the specimen at temperatures from (110 to 114) K during 3 days, followed by quenching it at *T* 78 K over a period of 12 h. The heat capacity jumps, accompanying *G*-transitions, are observed on the *C T s* curves of both freons. Taking into account this typical transitions for the glasses, the authors of reference (Adachi, et al., 1968) proposed a term "glassy crystal" for the frozen – in disordered states (AB) (Fig.7, (b)). The temperatures of the glass transition *Tg* 95.7 K and fusion, *<sup>T</sup> fus* 123.1±0.4 K have been obtained. The degrees of crystallinity, , appropriated to the mole fraction of crystalline samples, equal to 0.076 and 0.116 for CF2ClCHCl2 and CFCl2CHFC , respectively, were calculated on the basis of calorimetric data on *Cs* jumps by studying the *G*-transitions (Varushchenko et al., 1997b).

Fig. 8 presents the*C T s* curve of ferrocenyl-*n*-propane, which exhibits a fusion and a gradual solid-to-solid transition in the temperature range from (156 to 204) K. The temperature of the gradual transition of crystal II to crystal I of ferrocenyl-*n*-propane was ascribed to that of the maximum *Cs* -value in the peak of solid state transition. A test of the calorimetric experiment showed that -anomaly was accompanied by decreasing the heat capacity, *Cs* =-2.7 JK-1mol-1 and continuance changing the enthalpy and entropy. Thus, the solid-state anomaly is the phase transition of the second order and can be interpreted as the "order-disorder" transformation. The changes of the enthalpy, <sup>0</sup> *trsHm* , and entropy, 0 *trsSm* of the thermal anomaly were evaluated by summing up these values in each experimental *Cs* point with subtracting changes of appropriate functions for the empty calorimeter and those ones for the hypothetic normal parts of the crystals I and II.

Fig. 8. Molar heat capacity, *Cs* , of ferrocenyl-*n*-propane as a function of temperature, *T*, where *Ttp ,* and *Ttrs* denote the triple point and temperature of -like transition.

A characteristic feature of solid state transition of organic crystals is a slow thermal equilibrium between co-existing phases which very often promote to formation of metastable phases existing in a wide temperature range. In Fig. 7(b), the heat capacity *Cs m*, of 1,1-difluoro-1,2,2-trichloroethane, CF2ClCHCl2, is shown in the temperature interval studied. Similar ( ) *C* ,*s m f T* dependence has been obtained for isomer of 1,1-difluoro-1,2,2 trichloroethane: CFCl2CHFCl. Both isomers were in the forms of glasses, supercooled liquids, and partially crystalline states. The latter was attained after annealing the specimen at temperatures from (110 to 114) K during 3 days, followed by quenching it at *T* 78 K over a period of 12 h. The heat capacity jumps, accompanying *G*-transitions, are observed on the *C T s* curves of both freons. Taking into account this typical transitions for the glasses, the authors of reference (Adachi, et al., 1968) proposed a term "glassy crystal" for the frozen – in disordered states (AB) (Fig.7, (b)). The temperatures of the glass transition *Tg* 95.7 K and fusion, *<sup>T</sup> fus* 123.1±0.4 K have been obtained. The degrees of crystallinity,

 , appropriated to the mole fraction of crystalline samples, equal to 0.076 and 0.116 for CF2ClCHCl2 and CFCl2CHFC , respectively, were calculated on the basis of calorimetric data

Fig. 8 presents the*C T s* curve of ferrocenyl-*n*-propane, which exhibits a fusion and a gradual solid-to-solid transition in the temperature range from (156 to 204) K. The temperature of the gradual transition of crystal II to crystal I of ferrocenyl-*n*-propane was ascribed to that of the maximum *Cs* -value in the peak of solid state transition. A test of the

capacity, *Cs* =-2.7 JK-1mol-1 and continuance changing the enthalpy and entropy. Thus, the solid-state anomaly is the phase transition of the second order and can be interpreted as

*trsSm* of the thermal anomaly were evaluated by summing up these values in each experimental *Cs* point with subtracting changes of appropriate functions for the empty



*trsHm* , and entropy,

on *Cs* jumps by studying the *G*-transitions (Varushchenko et al., 1997b).

the "order-disorder" transformation. The changes of the enthalpy, <sup>0</sup>

calorimeter and those ones for the hypothetic normal parts of the crystals I and II.

Fig. 8. Molar heat capacity, *Cs* , of ferrocenyl-*n*-propane as a function of temperature, *T*,

where *Ttp ,* and *Ttrs* denote the triple point and temperature of

calorimetric experiment showed that

0

The nature of this transition was studied by the X-ray crystallography. Table 6 lists crystallographic data of *n*-propylferrocene in vicinity of the "order-disorder" transition. The structure of *n*-propylferrocene at 200 K contains a propyl- group disordered between two positions (in ca. 2:1 ratio) obviously due to thermal motion (Fig. 9). The transition of the crystal II (*T* = 150 K) to the crystal I (*T* = 200 K) occurred with significant changes of the lattice parameters: basis vectors, *a*, *b*, *c,* angle, *β,* the volume, *V,* the number of molecule in the unit cell, *Z,* and the factors of the crystal structure quality, *R1* and *wR2*.

Fig. 9. The structure of the ferrocenyl-*n*-propane crystal at the temperatures 150 K (II) and 200 K (I)


Table 6. Crystallographic data of *n*-propylferrocene crystal at the temperatures 150 K and 200 K

While both *a* and *b* parameters became larger during phase transition II to I, the *c* parameter and *β* angle slightly decreased (Table 6). Structure solution of the crystals I and II revealed that lower temperature modification of the *n*-propylferrocene molecule has only one orientation of the propyl group. Apparently, the transitions in reverse order occurred when cooling the crystals from (150 to 200) K. Thus, the solid-state anomaly of *n*-propylferrocene is caused by the onset of the internal rotation of propyl groups in the molecules and also by a small shift of the pentadienyl cycles around the axis passed through their centers. These variations led to some orientation disorder of the crystal phase II (Fig. 9).

The order-disorder conception is successfully used in exploring the plastic crystals. Adamantane and some of its derivatives form disordered plastic crystalline phases. The fusion of such substances occurs some times in two stages. First, an orientational disorder proceeds in the crystalline lattice because of high mobility of the molecules, and then the plastic crystals fuse owing to a translational molecular motion at higher temperature. In this

Thermodynamics of the Phase Equilibriums of Some Organic Compounds 621

spectra is in agreement with the low values of transition entropies measured by adiabatic calorimetry for alkylderivatives of adamantane. The *cis*- and *trans*- isomers of perfluorobicyclo(4,3,0)nonane are almost spherical "globular" molecules, which are able to form the plastic crystals due to unusually high molecular mobility. The thermodynamic properties of compounds are known to change when going from fluoroorganic compounds to their hydrogen containing analogous. With this in mind, the thermodynamic properties of the solid state transitions of perfluorocarbons are compared with those of appropriate

Fig. 11. Molar heat capacity, *Cs* , of *cis-*perfluorobicyclo(4,3,0)nonane as function of

solid transitions and *Ttp* is the temperature of triple point

temperature, *T*, where *Ttrs* (III to II) and *Ttrs* (II to I) denote the temperatures of the solid-to-

Fig. 11 presents a temperature dependence of the heat capacity of *cis*perfluorobicyclo(4,3,0)nonane. Two solid states transitions can be interpreted as the orderdisorder transformation caused by orientation disorder. Taking into account the high entropy

this solid phase conversion can be attributed to an anisotropic molecular reorientation about preferential common C-C axis. According to the empirical Timmerman's criterion, small

onset of the isotropic molecular reorientation and, thus the formation of the plastic crystals. As is seen from Table 5, the *cis-*bicyclo(4,3,0)nonane has thermodynamic properties of the solid-state transition, analogous to its perfluorated counterpart, and forms plastic crystals. The *trans*-perfluorobicyclo(4,3,0)nonane exhibits one solid-state transition and also forms the plastic crystals, but its hydrogen analogous, *trans*-bicyclo(4,3,0)nonane do not form the plastic crystals. These properties of the *trans-*isomers can be explained by their less spherical

*trsSm* = 43.66±0.04 Jmol-1K-1 (Table 5) for transition of the crystal III-to- crystal II,

*fusSm* = 9.34±0.09 Jmol-1K-1 of *cis-*C9F16 (Table 5) indicates the

hydrocarbons.

values of <sup>0</sup>

values of the fusion entropy, <sup>0</sup>

shapes as compared with the *cis*-isomers.

case, the magnitudes of enthalpy and entropy of the solid-to-solid transition are several times larger than those of the fusion. In accordance with the empirical Timmerman's criterion, the <sup>0</sup> *fusSm* values for the plastic crystals are usually less than 20 Jmol-1K-1. There

are two modifications of the plastic crystals with different molecular reorientations, isotropic and anisotropic. Some substances are known to form both of reorientations.

Fig. 10 presents *C T s* curve of 1,3,5-trimethyladamantane (1,3,5-TMA) explored in this work (a) and the Raman spectrum of the substance (b). A spectroscopic investigation of 1,3,5-TMA was carried out together with that of 1,3-dimethyladamantane (1,3-DMA), which also formed plastic crystals. Both compounds have low values of the entropy of fusion, <sup>0</sup> *fusSm* = 8.1 (6.2) JK-1mol-1 and narrow temperature intervals of existence of the

high temperature crystal I, *T* = 21 (24.2) K, respectively. According to adiabatic calorimetry, these properties are typical for the plastic crystals. Distinct bands were observed in their spectra at the low temperatures. As it follows from joint spectra discussion, the number of bands for 1,3,5-TMA is about haft of that for the 1,3-DMA crystal. This suggests that more symmetric molecules of the former compound compose the lattice of higher symmetry and/or with the less quantity of units in a primitive cell. In the vicinity of the phase transitions, the changes in spectra become more pronounced. At the transition points, all the bands disappear and transform into the wing of a broad Rayleigh scattering. This implies that all of them were caused by the librational modes in the low-temperature crystals of 1,3- DMA and 1,3,5- TMA and that the character of molecular motion is different in high-temperature solid phases. The absence of the preferential axes of molecular reorientation in the latter implies that there are isotropic plastic crystals. Analysis of Raman

Fig. 10. **(a)** The heat capacity of 1,3,5-trimethyladamantane in dependence on temperature, *T*, where *Ttp ,* and *Ttrs* denote temperatures of the triple point and the solid-to-solid transition. **(b)** The temperature dependence of low-frequency Raman spectrum of 1,3,5 trimethyladamantane.

case, the magnitudes of enthalpy and entropy of the solid-to-solid transition are several times larger than those of the fusion. In accordance with the empirical Timmerman's

are two modifications of the plastic crystals with different molecular reorientations,

Fig. 10 presents *C T s* curve of 1,3,5-trimethyladamantane (1,3,5-TMA) explored in this work (a) and the Raman spectrum of the substance (b). A spectroscopic investigation of 1,3,5-TMA was carried out together with that of 1,3-dimethyladamantane (1,3-DMA), which also formed plastic crystals. Both compounds have low values of the entropy of

high temperature crystal I, *T* = 21 (24.2) K, respectively. According to adiabatic calorimetry, these properties are typical for the plastic crystals. Distinct bands were observed in their spectra at the low temperatures. As it follows from joint spectra discussion, the number of bands for 1,3,5-TMA is about haft of that for the 1,3-DMA crystal. This suggests that more symmetric molecules of the former compound compose the lattice of higher symmetry and/or with the less quantity of units in a primitive cell. In the vicinity of the phase transitions, the changes in spectra become more pronounced. At the transition points, all the bands disappear and transform into the wing of a broad Rayleigh scattering. This implies that all of them were caused by the librational modes in the low-temperature crystals of 1,3- DMA and 1,3,5- TMA and that the character of molecular motion is different in high-temperature solid phases. The absence of the preferential axes of molecular reorientation in the latter implies that there are isotropic plastic crystals. Analysis of Raman

Fig. 10. **(a)** The heat capacity of 1,3,5-trimethyladamantane in dependence on temperature, *T*, where *Ttp ,* and *Ttrs* denote temperatures of the triple point and the solid-to-solid transition. **(b)** The temperature dependence of low-frequency Raman spectrum of 1,3,5-

*fusSm* = 8.1 (6.2) JK-1mol-1 and narrow temperature intervals of existence of the

isotropic and anisotropic. Some substances are known to form both of reorientations.

*fusSm* values for the plastic crystals are usually less than 20 Jmol-1K-1. There

criterion, the <sup>0</sup>

fusion, <sup>0</sup>

trimethyladamantane.

spectra is in agreement with the low values of transition entropies measured by adiabatic calorimetry for alkylderivatives of adamantane. The *cis*- and *trans*- isomers of perfluorobicyclo(4,3,0)nonane are almost spherical "globular" molecules, which are able to form the plastic crystals due to unusually high molecular mobility. The thermodynamic properties of compounds are known to change when going from fluoroorganic compounds to their hydrogen containing analogous. With this in mind, the thermodynamic properties of the solid state transitions of perfluorocarbons are compared with those of appropriate hydrocarbons.

Fig. 11. Molar heat capacity, *Cs* , of *cis-*perfluorobicyclo(4,3,0)nonane as function of temperature, *T*, where *Ttrs* (III to II) and *Ttrs* (II to I) denote the temperatures of the solid-tosolid transitions and *Ttp* is the temperature of triple point

Fig. 11 presents a temperature dependence of the heat capacity of *cis*perfluorobicyclo(4,3,0)nonane. Two solid states transitions can be interpreted as the orderdisorder transformation caused by orientation disorder. Taking into account the high entropy values of <sup>0</sup> *trsSm* = 43.66±0.04 Jmol-1K-1 (Table 5) for transition of the crystal III-to- crystal II, this solid phase conversion can be attributed to an anisotropic molecular reorientation about preferential common C-C axis. According to the empirical Timmerman's criterion, small values of the fusion entropy, <sup>0</sup> *fusSm* = 9.34±0.09 Jmol-1K-1 of *cis-*C9F16 (Table 5) indicates the onset of the isotropic molecular reorientation and, thus the formation of the plastic crystals. As is seen from Table 5, the *cis-*bicyclo(4,3,0)nonane has thermodynamic properties of the solid-state transition, analogous to its perfluorated counterpart, and forms plastic crystals. The *trans*-perfluorobicyclo(4,3,0)nonane exhibits one solid-state transition and also forms the plastic crystals, but its hydrogen analogous, *trans*-bicyclo(4,3,0)nonane do not form the plastic crystals. These properties of the *trans-*isomers can be explained by their less spherical shapes as compared with the *cis*-isomers.

Thermodynamics of the Phase Equilibriums of Some Organic Compounds 623

conducted by (18), provided the parameters *n* and are adjusted thus to allow one to obtain zero *Cs,m* values at *T* = 0 K. The ( / )( / ) *C C TV T* , , *p m sm p p T s* difference evaluated at *T* = 298.15 K was smaller than uncertainties of *Cs m*, for the substances under study and was not taken into account. The smoothed values of *Cp,m* and thermodynamic functions *<sup>0</sup>S T <sup>m</sup>*( ) , *0 0* { ( ) (0)} *HT H m m* , and *0 0* { ( ) (0)} *GT H m m* for the condensed states were calculated by numerical integrating the *Cp,m f* ( ) *T* functions obtained by equations (18) and (11) and adding the enthalpies and entropies of the solid-to-solid transition and fusion. The errors of thermodynamic functions were estimated by the law of random errors accumulation using the uncertainties of the heat capacity measurements. The ideal gas absolute entropy, *<sup>0</sup>S T <sup>m</sup>*( ) , the changes of the enthalpy and the free Gibbs energy at 298.15 K were calculated using the appropriate functions in the liquid state, enthalpies and entropy of vaporization and the entropy of the ideal gas compression,

The ideal gas absolute entropy and heat capacity were calculated by statistical thermodynamics, additive principle (Poling et al., 2001; Domalski et al., 1993; Sabbe et al.,

The statistical thermodynamic method was used with quantum mechanical [QM] calculation on the basis of the density functional theory [DFT]. The QM calculation was performed on the level B3LYP/6-31G(d,p) using the Gaussian 98 and 03 software packages (Frisch et al., 2003). As a result, the following constants can be calculated: the moments of inertia of the entire molecule, the moments of inertia for internal rotors, the normal vibrational frequencies, and the barrier to internal rotation. The potential functions of internal rotation were determined by scanning the torsion angles from (0 to 360)o at 10o increments and allowing all other structural parameters to be optimized at the same level with the subsequent frequency calculation. The calculated potential energies were fitted to

> ( ) 0.5 (1 cos ) 0 *VV V n n n*

The ideal gas entropies and heat capacities in dependence on the temperature were calculated by standard statistical thermodynamics formulae using the rigid-rotor harmonic oscillator [RRHO] approximation. To account for the internal rotation processes, the torsional frequencies were omitted in the calculation of thermodynamic function. A contribution of the internal rotation for each rotor was calculated by direct summation over the energy levels obtained by diagonalization of the one-dimensional Hamiltonian matrix associated with potential function from equation (20). The RRHO approximation, is known, results in overestimated entropy values for flexible molecules due to coupling the internal rotations. One-dimensional hindered rotor correction has been applied by (Vansteenkiste et

The method of group equation is suitable for calculation of some additive properties of a

is torsional angle.

*<sup>f</sup> Hm* values on the basis of reliable appropriate

, (20)

2008), and empirical difference method of group equations (Cohen & Benson, 1993).

0, appropriate extending of the heat capacity could be

*S R pT* ln{ ( ) /(101.325) } <sup>k</sup> <sup>P</sup> <sup>a</sup> calculated from the vapor pressure data.

**4.1 Theoretical calculations of the thermodynamic functions** 

al., 2003; Van Speybroeck et al., 2000) assuming decoupled internal rotations.

)( denotes potential energy function,

compound, namely *S T <sup>m</sup>*( ) , *C T*( ) *p,m* , *<sup>o</sup>*

*s,m* <sup>3</sup> *C AT* . But, in the case

the cosine-based Fourier series:

where *V*

Fig. 12. Molar entropies of fusion <sup>0</sup> *fusSm* for some bicyclic perfluorocarbons and appropriate hydrocarbons: *cis-* [1] and *trans-* [2] perfluorobicyclo(4,3,0)nonanes; *cis-* [3] and *trans*- [4] bicyclo (4,3,0) nonanes; *cis-* [5] and *trans-* [6] perfluorobicyclo(4,4,0)decanes; *cis-* [7] and *trans-* [8] bicyclo(4,4,0)decanes

Analysis of the entropies of fusion for *cis-* and *trans-*isomers of perfluorobicyclo (4,3,0)nonanes and -(4,4,0) decanes and appropriate values of hydrogen - containing analogous (Table 5, Fig. 12) permits to interpret the influence of the structure and chemical nature on molecular mobility and thermodynamic properties of the solids. Comparesing the entropies of fusion shows that the mobility of the molecules increases in going from hydrocarbons to appropriate perfluorocarbons and from the *cis*-isomers to the *trans*-ones. The larger molecular mobility of the perfluorocarbons can be explained by more weak intermolecular interactions for these compounds compared with the hydrocarbons. The greater ability of the molecules of *cis*-isomer to reorient in the solid state seems to be due to the steric factors. The nature of the solid-to-solid transitions in *cis-* [7] and *trans*- [8] bicyclodecanes and *cis-* [5] and *trans-* [6] perfluorobicyclodecanes (Fig. 12) were discussed in the order-disorder concept in reference (Kolesov, 1995).
