Per-Olof Åstrand

The quantum-volume Bragg-Williams (qv-BW) equation of state, derived from a lattice gas model and a mean-field approximation for the intermolecular interactions, includes a unique temperature dependence theoretically grounded through the connection to the thermal wavelength for particles. Here, the qv-BW equation of state is extended by deriving equations in a semi-analytical approach (one numerical inversion) for the two-phase region describing the liquid-gas equilibrium below the critical temperature. In more detail, equations are derived for the coexistence curve (vapor pressure), the molar volumes of the liquid and gas phases, the vaporization enthalpy, the isochoric heat capacity and the saturation heat capacity. Results are presented for a simple model system with the focus on argon. The results are promising, but limitations in the present model are also revealed. The molar volume of the liquid branch has a minimum contradicting established results, and the result for the vaporization enthalpy is limited by the mean-field approach for interactions. Future prospects are discussed both with respect to method development and applications.

Molecular properties are important to consider when designing dielectric liquids because breakdown properties are governed by molecular processes such as ionization. The molecular ionization potential varies with applied field strength, as the positive and negative charge centers in the molecule are separated when subject to an applied electric field, aiding ionization. In this work, we apply an analytical expression for the field-dependent molecular ionization potential based on a Taylor expansion of the molecular charge distribution to six representative molecules: cyclohexane, pyrene, N,N-dimethylaniline, trans-azobenzene, butylated hydroxytoluene and trans-5methyl-3-heptene. Thus, the field dependent molecular ionization potential may be calculated from zero-field properties, namely the molecular energy, dipole moment and polarizability. Vertical and adiabatic ionization potentials are calculated. This model replicates results found with other quantum chemical calculations up to 30 MV/cm, with notable exceptions for trans-azobenzene and N,Ndimethylaniline. The model works reasonably well in the field range 0 to 50 MV/cm, which is considered relevant for fields experienced during dielectric breakdown in transformer insulation liquids. The classical Frenkel term is sufficient to calculate the field-dependent ionization potential at this field range, as additional contributions are generally below ± 0.3 eV compared to the Frenkel term, which is 3.39 eV for all molecules at 20 MV/cm. The difference between the vertical and adiabatic ionization potential is between 0.57 and 0.11 eV for the aforementioned field range, compared to gas-phase ionization potentials of around 7-10 eV.

Molecular properties are important to consider when designing dielectric liquids because breakdown properties are governed by molecular processes such as ionization. The molecular ionization potential varies with applied field strength, as the positive and negative charge centers in the molecule are separated when subject to an applied electric field, aiding ionization. In this work, we apply an analytical expression for the field-dependent molecular ionization potential based on a Taylor expansion of the molecular charge distribution to six representative molecules: cyclohexane, pyrene, N,N-dimethylaniline, trans-azobenzene, butylated hydroxytoluene and trans-5methyl-3-heptene. Thus, the field dependent molecular ionization potential may be calculated from zero-field properties, namely the molecular energy, dipole moment and polarizability. Vertical and adiabatic ionization potentials are calculated. This model replicates results found with other quantum chemical calculations up to 30 MV/cm, with notable exceptions for trans-azobenzene and N,Ndimethylaniline. The model works reasonably well in the field range 0 to 50 MV/cm, which is considered relevant for fields experienced during dielectric breakdown in transformer insulation liquids. The classical Frenkel term is sufficient to calculate the field-dependent ionization potential at this field range, as additional contributions are generally below ± 0.3 eV compared to the Frenkel term, which is 3.39 eV for all molecules at 20 MV/cm. The difference between the vertical and adiabatic ionization potential is between 0.57 and 0.11 eV for the aforementioned field range, compared to gas-phase ionization potentials of around 7-10 eV.

The quantum-volume (qv) and Bragg-Williams equations of state, as derived from a lattice gas model, are exploited. The qv equation of state includes a temperature-dependent excluded volume related to the thermal wavelength included in the translational contribution to the molecular partition function, but apart from this contribution intermolecular interactions are not included. The qv equation of state has the correct limiting behavior both in the limit of an ideal gas and in the packing-density limit. It also includes a nonclassical contribution to the internal energy and thereby a many-particle contribution to the kinetic energy, and it supports the view that it is both the position as well as the momentum of a system of particles that are distributed over the volume to maximize the multiplicity of the system. The qv equation of state is extended with intermolecular interactions through the Bragg-Williams mean-field approach, including also a hard-core contribution. For a one-component lattice gas, analytical expressions are presented for the pressure and the critical point as well as for the internal energy, the isochoric heat capacity, and the chemical potential, and results are presented for some simple systems. Given its relative simplicity, essentially on a textbook level, the model shows promising results, in particular for the temperature dependence of the isochoric heat capacity that shows a maximum close to the critical temperature. The presented model is supposed to serve as a foundation for further model extensions as well as for the development of interpretable analytical models in molecular thermodynamics for more complex systems and processes.

The quantum-volume (qv) and Bragg-Williams equations of state, as derived from a lattice gas model, are exploited. The qv equation of state includes a temperaturedependent excluded volume related to the thermal wavelength included in the translational contribution to the molecular partition function, but apart from this contribution intermolecular interactions are not included. The qv equation of state has the correct limiting behaviour both in the limit of an ideal gas and in the packing-density limit. It also includes a non-classical contribution to the internal energy and thereby a manyparticle contribution to the kinetic energy, and it supports the view that it is both the position as well as the momentum of a system of particles that are distributed over the volume to maximize the multiplicity of the system. The qv equation of state is extended with intermolecular interactions through the Bragg-Williams mean-field approach, including also a hard-core contribution. For a one-component lattice gas, analytical expressions are presented for the pressure and the critical point as well as for the internal energy, the isochoric heat capacity, and the chemical potential, and results are presented for some simple systems. Given its relative simplicity, essentially on a textbook level, the model shows promising results, in particular for the temperature dependence of the isochoric heat capacity that shows a maximum close to the critical temperature. The presented model is supposed to serve as a foundation for further model extensions as well as for the development of interpretable analytical models in molecular thermodynamics for more complex systems and processes.

The quantum-volume (qv) and Bragg-Williams equations of state, as derived from a lattice gas model, are exploited. The qv equation of state includes a temperaturedependent excluded volume related to the thermal wavelength included in the translational contribution to the molecular partition function, but apart from this contribution intermolecular interactions are not included. The qv equation of state has the correct limiting behaviour both in the limit of an ideal gas and in the packing-density limit. It also includes a non-classical contribution to the internal energy and thereby a manyparticle contribution to the kinetic energy, and it supports the view that it is both the position as well as the momentum of a system of particles that are distributed over the volume to maximize the multiplicity of the system. The qv equation of state is extended with intermolecular interactions through the Bragg-Williams mean-field approach, including also a hard-core contribution. For a one-component lattice gas, analytical expressions are presented for the pressure and the critical point as well as for the internal energy, the isochoric heat capacity, and the chemical potential, and results are presented for some simple systems. Given its relative simplicity, essentially on a textbook level, the model shows promising results, in particular for the temperature dependence of the isochoric heat capacity that shows a maximum close to the critical temperature. The presented model is supposed to serve as a foundation for further model extensions as well as for the development of interpretable analytical models in molecular thermodynamics for more complex systems and processes.

The field-dependent ionization potential of six molecules relevant for transformer insulating liquids has been examined by an analytical expression based on a multipole expansion. Molecular properties were calculated by density functional theory at zero field. We found that many molecules are explained well by a classical Frenkel model at low to moderate field strengths. Large molecules and molecules with a significant permanent dipole moment require additional terms, especially the interactions between the electron and the dipole and polarizability of the cation.

Local electric field factors have been calculated for cyclohexane and ethyl laurate liquids by using a force-field model for the local field response to an external field based on liquid configurations generated from molecular dynamics simulations. For cyclohexane, we found field factors up to around 1.5 and 2.0 at the carbon and hydrogen atoms, respectively. Ethyl laurate has larger local field factors, up to 3.5 at the carbon atoms and 2.4 at the oxygen atoms, respectively. The local field factors at the hydrogen atoms in ethyl laurate are similar to those of cyclohexane. The electric fields in liquids arising from the electronic polarization of the molecules by the external field can thus be considerably larger, here with up to a factor 3.5, than the applied electric field.

Lattice models are a central idea in statistical thermodynamics, as they allow for the introduction of a configurational entropy by counting the multiplicity of placing indistinguishable particles on a lattice. In this work we use a lattice model to show that the configurational entropy needs to be merged with the molecular translational entropy in order to have a consistent model. This is achieved by replacing the volume of a lattice site with a quantum volume (i.e., the cube of the thermal wavelength). This modified lattice model allows us to derive a new equation of state, referred to as the Bragg-Williams equation state, from which we may also derive a generalized version of the van der Waals equation of state. In contrast to the standard van der Waals equation of state, the heat capacity of the new models has temperature dependence.

Guanidine-containing molecules are an interesting class of compounds within both medicinal and material sciences. Having knowledge of their tautomerism is key in designing guanidines that interact with biological and chemical receptors. However, there are limited data on the solid-phase structure of N,N′-substituted guanidines. Thus, eleven guanidines bearing a 4,6-dimethylpyrimidyl at one end and substituents of varying sizes and electronic properties at the other side, were synthesised, crystallised, and analysed by X-ray crystallography. Calculations of isolated molecules of tautomer energies and bond lengths were performed for comparison. One class of guanidines crystallised as a cis–trans tautomer with the shorter bond directed towards the pyrimidyl unit. When more electron-deficient aniline substituents were inserted, the crystallised tautomer changed to a cis–cis form where the shorter bond was directed towards the aniline. The switch in the tautomer structure is concluded to be due to both the electronic properties of the substituents and the intermolecular hydrogen bonding in the crystal lattice.