### Laboratory of Applied Thermodynamics

*Physical Chemistry Department, Chemistry building*

#### Research activity

- Thermodynamic properties of pure substances and multicomponent mixtures used in new technologies: ionic liquids, polimers, pharmaceuticals
- Correlation and prediction of the thermodynamic properties of pure substances and their mixtures with the equations of state, group contribution methods (Mod UNIFAC, DISQUAC, ASOG, ERAS, COSMO-RS, SRK EOS, Cell-Hole model)
- The quantum-mechanical calculations of the hydrogen bonded systems. Molecular geometry as a source of chemical information
- Industrial thermodynamics and databases

#### Staff

*prof.*Urszula Domańska-Żelazna -*professor**prof.*Tadeusz Hofman -*lecturer**dr*Marta Królikowska -*lecturer**dr*Marek Królikowski -*lecturer**dr*Kamil Paduszyński -*lecturer**dr*Aneta Pobudkowska-Mirecka -*lecturer**dr*Halina Szatyłowicz -*lecturer**dr*Michał Wlazło -*chemist**dr*Maciej Zawadzki -*lecturer**msc*Patryk Sikorski -*PhD Student**msc*Agnieszka Śliwińska -*PhD Student**msc*Mikołaj Więckowski -*PhD Student*

*from the left: Dr Aneta Pobudkowska, Prof. Urszula Domańska-Żelazna,Dr Małgorzata Marciniak, Dr Marta Kozłowska*

#### Solid-Liquid Equilibria (SLE) and Liquid-Liquid Equilibria (LLE)

##### SLE and LLE apparatus

**1.** Heater

**2.** Vessel

**3.** Thermometer

**4.** Mechanical stirrer

**5.** Thermostat

**6.** Magnetic stirrer

**7.** Magnetic stirrer

##### Solid-Liquid Equilibria

Solid-liquid phase diagram for the (NMP + alcohols): • 1-hexanol, • 1-heptanol, • 1-octanol, • 1-decanol, • 1-undecanol, • 1-dodecanol, • 1-tetradecanol

Solid-liquid phase diagram for the (NMP + organic solvents): • 1-propanol, • cyclopentanone, • 1-pentanol, • 2-pentanone, • THP, • TBME

##### Liquid-Liquid Equilibria

Liquid-liquid phase diagram of [C_{6}H_{13}OCH_{2}MIM][BF_{4}] + aromatic hydrocarbons: • benzene, • toluene, • ethylbenzene

Liquid-liquid phase diagram of [C_{6}H_{13}OCH_{2}MIM][Tf_{2}N] + aromatic hydrocarbons: • benzene, • toluene, • ethylbenzene

#### Vapour-Liquid Equilibria (VLE)

Vapour-liquid phase diagram for the (NMP + alcohols) at *T*=373.15K: • 2-propanol, • 2-butanol, • *iso*-butanol

#### Excess Molar Functions

Correlation with the Redlich-Kister equation:

were *x*_{1} is mole fraction, and *Z*^{E} is either *V*^{E}/(cm^{3}·mol^{-1}) or *H*^{E}/(J·mol^{-1}) or *G*^{E}/*RT*/(J·mol^{-1}). The values of the parameters *X _{r}* have been determined using the method of least squares.

##### Excess Molar Volume

Excess molar volumes for the (NMP + alcohols) at *T*=298.15K: • ethanol, • 1-propanol, • *iso*-butanol, • 1-butanol, • 2-propanol, • 2-butanol, • 1-nonanol, • 1-decanol, • 1-undecanol, --- Redlich-Kister equation

##### Excess Molar Enthalpy

Excess molar enthalpies for the (NMP + alcohols) at *T*=298.15K: • ethanol, • 1-propanol, • 1-butanol, • 1-pentanol, • 1-hexanol, • 1-heptanol, • 1-octanol, • 1-nonanol, • 1-decanol, • 1-undecanol, --- Redlich-Kister equation

#### ERAS and FBT Theories

The Extended Real Associated Solution Model (ERAS), developed by Heintz and the Flory-Benson-Treszczanowicz Theory (FBT) have been applied firstly (1985) to the excess volumes and enthalpies of binary systems formed by mixing an alcohol with an alkane or cycloalkane.

The excess functions are described as sums of two contributions:

• **physical contribution** – comprises free volume effects arising from differences of the Van der Waals interactions between unlike molecules in the mixtures using Flory’s equation of state,

• **chemical contribution** – arising from the self-association of the alcohol, or NMP and is evaluated according to the Kretschmer-Wiebe (for ERAS) or Mecke-Kempter (for FBT) continuous association model.

##### Excess Molar Volume

Excess molar volume for (NMP + TAME) at *T*=298.15K: • experimental data, --- predicted by FBT, --- predicted by ERAS, --- Redlich-Kister equation

##### Excess Molar Enthalpy

Excess molar enthalpy for (NMP + TAME) at *T*=298.15K: • experimental data, --- predicted by FBT, --- predicted by ERAS, --- Redlich-Kister equation

#### Group Contribution Methods

The knowledge of the thermo physical properties, excess functions and phase equilibria of mixtures is important for the synthesis, design, and optimisation of separation processes. Since experimental data are often missing or poor quality, group contribution methods have become increasingly valuable. The great advantage of the group contribution concept is that it is possible to predict a large number of systems using only a relatively small number of group interaction parameters.

##### UNIFAC Model

In UNIFAC model (Fredenslund et al. 1975, 1977) the required activity coefficients consist of two terms:

The combinatorial part takes into account the size and the form of the molecules. In the residual part the interactions betwen the various groups are considered.

For the calculation of the residual part the "solution of groups" concept is used. In this concept the activity coefficient *γ _{i}* is obtained from the group activity coefficients

*Γ*in the mixture and the pure compound

_{k}*i Γ*

_{k}^{(i)}.

##### Modified UNIFAC (Dortmund)

One of the main differences between original UNIFAC and Mod. UNIFAC (Dortmund) (Weidlich and Gmehling, 1987) is the introduction of temperature-dependent interaction parameters to permit a more reliable description of the real phase behaviour as a function of temperature:

The combinatorial part was changed in an empirical way to make it possible to deal with compounds very different in size:

The parameter *V _{i}*' can be calculated by using the relative van der Waals volumes

*R*of the different groups.

_{k}##### DISQUAC Model

The main features of dispersive-quasichemical group contribution (DISQUAC) model are:

• the partition function is factorised into two terms, in such way that the excess functions are calculated as the sum of two contributions; a dispersive term (DIS) which represents contributions from the dispersive forces; a quasichemical (QUAC) term which arises from the anisotropy of the field forces created by the solution molecules; in the case of *G*^{E}, the combinatorial entropy is represented by the Flory-Huggins equation,

• the interaction parameters are assumed to be dependent on the molecular structure.

The temperature dependence of the interaction parameters *g _{st}*,

*h*,

_{st}*cp*, has been expressed in terms of the DIS and QUAC interchange coefficients:

_{st}

Vapour-liquid phase diagram for the NMP + 2-butanol at *T*=373.15K: • experimental data, --- Mod UNIFAC, --- DISQUAC

Excess Molar Gibbs Energy for NMP + dipropyl ether at *T*=353.15K: • calculated from VLE experimental data, --- Mod UNIFAC, --- DISQUAC

#### Ternary Liquid-Liquid Equilibria

Ternary liquid-liquid equilibria apparatus

Ternary liquid-liquid equilibria diagram for the system [emim][EtSO_{4}](1) + limonene(2) + linalool(3) at *T*=318.15K

#### Activity Coefficients at Infinite Dilution *γ*_{13}^{∞}

*Prof. Trevor Letcher (South Africa) and Dr Andrzej Marciniak*

Experimental activity coefficients at infinite dilution for the solutes pentane, hexane, heptane, octane in [bmim][MDEGSO_{4}] ionic liquid at *T*=298.15K (•), *T*=303.15K (•), *T*=308.15K (•)

#### Solid-Liquid Equilibria at High Pressure

*Prof. Urszula Domańska-Żelazna, Dr J. A. P. Coutinho (Portugal), Dr Piotr Morawski*

Solid-Liquid Equilibria at High Pressure apparatus

Solid-liquid equilibria at high pressure for the system tridecane + cyclohexane

Solid-liquid equilibria at high pressure for the system [EMIM][TOS] ionic liquid + benzene

#### Cell-Hole Model

*Dr Tadeusz Hofman*

• Modelling of the thermodynamic properties of pure non-electrolytes and their mixtures.

• The models based on molecular theories are being developed and tested. Their aim is to predict thermodynamic and volumetric properties of pure chain-like compounds and their mixtures. They include: the pVT properties, saturated vapour pressures, enthalpies of vaporization, mixing functions and fluid-phase equilibria in solutions.

• The group-contribution method based on the cell-hole theory was developed. It can be applied for pure normal alkenes, chloroalkanes, aliphatic monoethers, and ketones and their mixtures with alkanes.

Prediction of vapor-liquid equilibria for the propane +
*n*-pentane systems at 71.1, 87.8, 104.4, and 121.1 °C with respect to a
mole fraction of the first component in both phases (*x*_{1},*y*_{1}). Circles denote experimental data. Lines are predicted by the cell-hole model (solid) and the simplified Smirnova-Victorov model (dashed)

#### Molecular Geometry as a Source of Chemical Information

• Influence of hydrogen bond on different chemical and physicochemical properties is widespread investigated. Is it possible to model H-bonded system with variable H-bond strength. The question is: how distant are the structural consequences of H-bonding?

• The models based on molecular theories are being developed and tested. Their aim is to predict thermodynamic and volumetric properties of pure chain-like compounds and their mixtures. They include: the pVT properties, saturated vapour pressures, enthalpies of vaporization, mixing functions and fluid-phase equilibria in solutions.

• Comparison of the results of theoretical calculations with X-ray data for phenol, pyridine and aniline derivatives is very promising.

Dependence of HOMA on the C–O bond length, *d*_{C-O}, for phenol/phenolate derivatives involved in H-bonding complexation (experimental, CSD, and modelling, B3LYP, data).

Krygowski T. M., Zachara J. E., Szatyłowicz H., J. Org. Chem., 2004, 69, 7098.
Krygowski T. M., Szatyłowicz H., Zachara J. E., J. Chem. Inf. Model., 2005, 45, 652.