Proc. of the 5th Asian Thermophysical Properties Conference, Aug. 30 - Sep. 2, Seoul, Korea, pp. 583-586, 1998.

Vladimir S. Iorish

Glushko Thermocenter of Russian Academy of Sciences

"IVTAN" Association of RAS, HEDRC

Izhorskaya 13/19

Moscow, 127412, Russian Federation

Critical constants are important thermophysical parameters of substances in the field of chemical process design. They are used, for example, in extrapolating the vapor pressures from the normal boiling point to the critical temperature or in some other properties estimations [1].

Polychlorinated dibenzo-p-dioxins (PCDDs) and dibenzofurans (PCDFs) are the most acutely toxic compounds in the environment. These pollutants are known to be by-products in chemical technology and also under various fuel and waste combustion. The availability of thermodynamic data for these compounds is of fundamental importance for understanding of the mechanism of their formation in order to assist in design of strategies to effectively control or eliminate their emission.

There are 75 isomers of PCDDs and 135 isomers of PCDFs. In absence of experimental data on critical constants some estimations should be made [2].

In this paper group contribution technique is used to estimate the critical constants for all isomers of PCDDs and PCDFs.

2378T4CDD 2,3,7,8 - tetrachlorodibenzo-p-dioxin

C_p^o isobaric heat capacity

C_pG^o isobaric heat capacity of gas phase

C_pL isobaric heat capacity of liquid phase

C_pS isobaric heat capacity of solid phase

DD dibenzo-p-dioxin

DF dibenzofuran

D_mH^o=_mH^o(T_m) enthalpy of fusion at T_m

D_sH^o=_sH^o(298.15) enthalpy of sublimation

M molecular weight

n number of atoms in a molecule

N_p pressure index of a molecule

n_p pressure index of group

N_t temperature index of a molecule

n_t temperature index of group

N_v volume index of a molecule

n_v volume index of group

P_c critical pressure

PCDDs polychlorinated dibenzo-p-dioxins

PCDFs polychlorinated dibenzofurans

R gas constant

S^o= S^o(298.15) standard entropy

T_b normal boiling temperature

T_c critical temperature

T_m melting temperature

T_r = T/T_c

V_c critical volume

w acentric factor

x chlorine substitution

The procedures for the estimation of critical constants of organic compounds have been recently reviewed by Somayajulu [3] and modified approach to the calculation has been proposed.

The equations for the estimation of the critical properties developed in [3] and used in this study are the following.

T_c = T_b + T_b / (a_t + b_t N_t ) (K) (1)

P_c = M / (a_p + b_p N_p )² (bar) (2)

V_c = (a_v + b_v N_v ) (cm³ mol^-1) (3)

where N_t = S n_t , N_p = S n_p, N_v = S n_v, a_t = 1.242, b_t = 0.138, a_p = 0.339, b_p = .226 , a_v = 40.0, b_v = 55.0.

Chirico et al. [4] demonstrated excellent agreement between the experimental values and those calculated by equations (1) - (3) for dibenzofuran that is shown in Table 1.

Table 1. Critical constants of dibenzofuran

The calculation requires molecular weight, normal boiling point and group indices. I used group indices listed by Somayajulu [3] and the additional increments for the macro group of dibenzofuran based on experimental data [4].

The normal boiling points are calculated from far extrapolation of vapor pressures measured over solid compounds [5]. The procedure requires thermodynamic functions estimation for gaseous and condensed phases [6]. I calculated also acentric factor w which is closely related to critical properties and defined as {-lg(P/P_c) - 1}, where P is the vapor pressure at T = 0.7T_c.

Molecular indices for dibenzo-p-dioxin, dibenzofuran and their chlorinated derivatives are calculated from three group indices, listed in Table 2:

N_a(PCDDs) = n_a1 + n_a2 + x n_a3, (4)

N_a(PCDFs) = n_a1 + x n_a3, where a = p, t, v (5)

Table 2. Indices of groups

There are no experimental data on boiling points of DD, PCDDs and PCDFs. I calculated them from enthalpies of sublimation, experimental and estimated heats of fusion and thermodynamic functions of solid, liquid and gaseous substances obtained recently from combined consideration of all experimental and theoretical data about these compounds [6]. The procedures used for these estimations are briefly outlined below.

The values of the ideal gas entropy derived from calorimetric measurements are known for DF only[4]. The entropies and heat capacities of gaseous DD, PCDDs and PCDFs were estimated by group additivity approach and by statistical thermodynamics method [7,8,9]. The S ^o(T) and C_p^o(T) values evaluated in these works differ from one another by 10 - 60 J^.K^-1.mol^-1. Recent ab initio calculation of vibrational spectra of four tetrachlorodibenzo-p-dioxins [10] makes it possible to predict the values of entropy and heat capacity of PCDDs and PCDFs more reliably.

Structural parameters and vibrational frequencies needed for statistical thermodynamics calculation were estimated in this work using the similarity transference procedure. Based on X-ray diffraction and theoretical data for DD, DF and some of PCDDs and PCDFs, the structural parameters were evaluated to be the same for all PCDDs and PCDFs. Available vibrational assignments for DF, PCDDs as well as for chlorinated benzenes, anthracene, 1,4-dioxin, and furan were used in this work to develop the simplified force field approximation for PCDDs. The distinguishing feature of proposed method is that the force constants are calculated to best fit not only the vibrational frequencies, but also the experimental data on entropy or heat capacity if the later are known in the literature. Twenty-six force constants were obtained by a least-squares refinement to provide a satisfactory fit to known fundamentals of DF, PCDDs, PCDFs, chlorinated benzenes and to the experimental values of entropy of DF. Using estimated structural parameters and vibrational frequencies, the thermodynamic functions of all isomers of PCDDs and PCDFs were calculated in this work by rigid-rotor harmonic-oscillator approximation.

The only experimental information on thermodynamic functions of DD, PCDDs and PCDFs in condensed phase is indirectly contained in several vapor pressure measurements for solid [5] and overcooled liquid [11] compounds. To extract the data on thermodynamic functions from these experimental results some assumptions on heat capacity of solid and liquid phases should be made. Domalsky and Hearing[12] showed the possibility of satisfactory estimation of the heat capacity for solid organic compounds at 298.15K by group additivity method. In the absence of all required increments for the heat capacity of PCDDs and PCDFs estimation, "difference method" was used, which is fully consistent with the group additivity approach. Using experimental heat capacity values for several related compounds C_pS^o(DD, 298.15) = 215 5 J^. K^-1. mol^-1 was estimated. From this value and increments for chlorine substitutions developed by Domalsky and Hearing[12] heat capacities(in J^. K^-1. mol^-1) for all solid PCDDs and PCDFs were estimated by equations:

C_pS(xCl-DD) = C_pS(DD) + 13.42 x,

C_pS(xCl-DF) = C_pS(DF) + 13.42 x, (6)

where C_pS(DF) = 199.01 J^. K^-1. mol^-1 [4].

To extrapolate the heat capacity from room temperature up to the melting point the linear equation derived from experimental data for related compounds is used:

C_pS(T)/R = C_pS(298.15)/R + 1.51^. n^. (T – 298.15)/T_m (7)

Bondi-Rowlinson equation [1], the heat capacities for gases, critical temperatures and acentric factors were used for heat capacity estimation of liquid DD, PCDDs and PCDFs:

C_pL /R= C_pG^o/R + 2.56 + 0.436^. (1 – T_r)^-1 + w^. [2.91 +

4.28^. (1 – T_r)^1/3T_r^-1 + 0.296^. (1 – T_r)^-1] (8)

So several iterations were needed to agree the data. The final heat capacities were approximated by linear dependence on temperature (see Table 4).

Vapor pressure data for several PCDDs and PCDFs [5] were treated by "Third Law" and "Second Law" techniques taking into account direct determination the enthalpy of sublimation for some of PCDDs[13,14]. As a result of these treatments standard entropy values and enthalpies of sublimation were estimated for the considered solid PCDDs and PCDFs. Rordorf's procedure [5] for enthalpies of fusion estimation is used for the cases where the values were not known from experiment.

The thermodynamic functions were correlated with chlorine substitution and the following equations allow estimate the same data for all other PCDDs:

S^o(298.15) = 214.8 + 23.02 x J^. K^-1. mol^-1 ,

D_sH^o(298.15) = 91.6 + 7.93 x kJ^. mol^-1 ,

D_mH^o = 15.7 + 5.37 x kJ^. mol^-1 ,

a_L = 149.9 +31.42 x J^. K^-1. mol^-1 ,

b_L = 3971 - 292.0 x J^. mol^-1. 10000,

and PCDFs:

S^o(298.15) = 196.2 + 21.625 x J^. K^-1. mol^-1,

D_sH^o(298.15) = 88.5 + 8.14 x kJ^. mol^-1,

D_mH^o = 21.4 + 3.87 x kJ^. mol^-1,

a_L = 124.0 + 32.82 x J^. K^-1. mol^-1

b_L = 4045 - 320.74 x J^. mol^-1. 10000. (9)

Selected data for DD, 2378-T4CDD and 2378-T4CDF are presented in Tables 3 and 4 as an example.

Table 4. Thermodynamic functions for condensed phase (in J^. K^-1. mol^-1 : S^o,a_S, a_L and in kJ^. mol^-1: _sH^o and _mH^o)