APPLICATION OF PHASE EQUILIBRIA — A PERSPECTIVE

Phase equilibrium is a topic in Chemistry that focuses on studying equilibrium between gas, solid, and liquid. Equilibrium is the state in chemistry in which no change takes place in the chemical potential of components. In chemistry, a phase is an area where there is a uniform intermolecular interaction. The phase rule is a law in thermos dynamics. It was proposed by J. Gibbs. The phase rule is associated with variables involved in thermodynamic equilibrium. The Phase Rule governs the systems which are described and affected by such variables as temperature, volume and pressure, together represented as pVT. Allotropes exist in two distinct phases. The answer to what is phase rule has been discussed in the article.

In a phase equilibrium, a substance and its many phases have a common surface with minimum variation quantitatively. In the study of phase equilibrium, there is no energy loss when any particle in the system goes through a change from one phase to the other. For example, Liquid and saturated vapor have a phase equilibrium. The rule as put forward by Gibbs states that in a component where there are components represented as, only k + 2 components are co-existing at a point. When two systems are having two components, then three phases are at equilibrium with distinct temperatures. The component concentration and the pressure are given in this case. Phase transitions occur at a certain temperature (melting or boiling point) depending on the pressure changes. The Clapeyron equation is used to find out the phase equilibrium when infinitesimal pressure change results in a temperature change.

Thermodynamic Equilibrium

The phase equilibrium is a part of thermodynamic equilibrium. The latter is an axiomatic concept. It is concerned with the internal state of the thermodynamic system. In this theory, there are no macroscopic flows of energy or matter. A thermodynamic system has a spatial temperature that is uniform. Both phase equilibrium and thermodynamic equilibrium at large depend on the Second Law of Thermodynamics.

Phase equilibria is the term used to describe with two or more phases co-exist.

1. Phase equilibrium is the study of the equilibrium between two or more phases of heterogeneous systems.
2. The number of phases that can exist together at equilibrium depends upon the temperature pressure, and composition of various phases.
3. J.W. Gibbs gave a generalization which applicable to all heterogeneous equilibria known a phase rule.

It is mathematically defined as:

F = C — P + 2

Where F = number of degrees of freedom

C= number of components

P = number of phases

Phase : Phase is defined as any homogeneous and physically distinct part of a system which is separated by a well-defined boundary, physically and chemically different from other parts of system.

A system may contain one or more than one phases. For example a system containing ice, Liquid water and water vapour is a three Phase system

The expression of the phase rule, abiding by the rules in thermodynamic equilibrium is F = C — P + 2, where F is freedom degrees, P is phases and C is components. According to the Phase Rule, in a system where there is only a single component, the number of variables is two and any pressure or temperature within reasonable limits can be attained. For a system having one component but having three phases, there are no variables or degrees of freedom. Pressure and temperature in this case are fixed. The point at which they are fixed is known as the triple point.

Criterion For Phase Equilibrium

The conditions of thermal, mechanical, and chemical equilibrium must be met for the various phases of a heterogeneous system to be in equilibrium We know that if two systems are at the same temperature, they are said to be in thermal equilibrium. Heat transfer from one phase to another will occur if various phases are not in thermal equilibrium. Additionally, each phase’s pressure must be the same for mechanical balance; otherwise, one phase’s volume would expand at the expense of the other.

The equality of chemical potential of diverse components in distinct phases can be used to express the criterion of chemical equilibrium. Recall that in order for a process to be spontaneous, the Gibbs energy must also drop, and that the Gibbs energy change at equilibrium, denoted by the symbol dG, should be zero for any minuscule change. We also know that that Chemical potential of species I in a system is the rate of change of the system’s Gibbs energy with the number of the component I assuming that the temperature, pressure, and number of moles of all other components are kept constant.

Additionally, in a mixture, molecules of a component travel on their own from areas of high chemical potential to areas of low chemical potential.

This keeps happening until every component in the system has the same chemical potential. To put it another way, for a component to be in equilibrium, its chemical potential must remain constant in each phase that exists in the system. Consequently, we may sum up the requirements for component 1’s equilibrium between two phases (let’s say phases “alpha” and “beta”) in a system as

Phase equilibria and their applications

Phase behaviour can appear to be magical. For example, the freezing or melting of water occurs at constant temperature, which means that mixtures of water and ice can be used to precisely control temperature. This may appear miraculous at first glance, and possibly even after understanding thermodynamics.

An intriguing phase behaviour question is the preferential formation of one form of calcium carbonate by shellfish over a more stable form. There is calcium carbonate. How could this be? How does the animal keep a less stable form from forming? How can the animal avoid interconversion to a more stable form? Similar questions arise in the pharmaceutical industry, where formulators must determine the stability of a drug formulation, such as a powder, tablet, or suspension. A patient expects his or her medication to work even after it has been sitting on a bathroom shelf for over a year. This necessitates an understanding of the solid-state behaviour of drugs and drug mixtures and their sensitivity to water. As a result, the FDA (Food and Drug Administration) and the EMA (European Medicines Agency) require the pharmaceutical industry to demonstrate compliance. They can keep their formulation for a set period of time

Similar concerns exist for metal tools used in industry under high pressure, strain, and temperature. When working under difficult conditions, machinery cannot fail because it can lead to dangerous situations and loss of material and profit. Another intriguing issue is the taste and mouth feel of chocolate, which is heavily reliant on the proper crystal form of cocoa butter. It has several different crystal structures, and the most desired form melts just above 30 degrees Celsius. the throat The existence of life is also dependent on phase behaviour, because the lipids that make up cells can form different structures depending on their concentration in water. For that matter, self-assembly is driven by systems seeking equilibrium, even if they remain in a steady state or another non-equilibrium state.

Processes occur as a result of being pushed towards equilibrium. Even if equilibrium is not the ultimate goal of the experimenter or engineer (or life), understanding a system’s equilibrium conditions can help explain why a system changes in certain ways. The case of ritonavir is an intriguing example. It was one of the first drugs discovered to be effective against HIV. As a result, the drug’s formulation was completed as soon as possible and consisted of a suspension based on the only solid form discovered during the development phase. After the drug hit the market, it was discovered that its effectiveness had significantly decreased. Only after extensive research did the researchers realise that the lack of activity was caused by the crystallisation of a previously unknown more stable crystalline form. Because the drug crystallised into a much less soluble form, the amount taken up by the body did not exceed the required minimum concentration to be effective against HIV. If the developers had known, they could have planned ahead of time a formulation to avoid crystallization.

Amontons (1663–1705) in France discovered and considered an absolute zero in the temperature scale, and Black (1728–1799) in Great Britain studied the latent heat of fusion of ice and the heat capacity of water and snow. The push for theoretical understanding and optimization of the first steam engines designed during the industrial revolution in England gave rise to the so-called mechanical theory of heat, the precursor of classical thermodynamics, in the nineteenth century. Carnot (the Carnot cycle) and Clapeyron (Clapeyron equation) in France, and Clausius (second law of thermodynamics) in Germany, to name a few, contributed significantly to this field. However, it was the American Josiah Willard Gibbs (1839–1903) who gathered the available European knowledge by travelling to Great Britain and Germany and managed to distil and describe the essentials of modern day ‘classical’ thermodynamics used in phase equilibria and represented by the equation.

where dU denotes the change in internal energy of the system under study as a function of two variables: the system’s entropy dS and its volume dV. Classical thermodynamics is based on two postulates in addition to this equation.

1) Energy is conserved in an isolated system;

2) for a spontaneous process, entropy must always increase, reaching a maximum when the system reaches equilibrium. Nernst added a third postulate: at zero kelvin (or absolute zero), the entropy of a system is equal to zero.

The work of Gibbs is the foundation for so-called “phase theory” — the thermodynamics of phase equilibria — even though researchers now frequently prefer to use a Legendre transform of equation (1), which is known as the Gibbs free energy in honour of J.W. Gibbs :

The advantage of this equation is that the Gibbs energy variables are temperature and pressure, which are easily controlled in a laboratory setting. Nonetheless, Gibbs’ original equation should not be forgotten, and this special issue shows how both equations are related to each other as well as two other representations of internal energy, the enthalpy and the Helmholtz free energy.

In line with Gibbs, the English researcher Maxwell developed the Maxwell equations, which relate changes in different thermodynamic quantities through partial derivatives, leading to a mathematical interpretation of thermodynamics. Dutch researchers, such as Van der Waals, were inspired by J.W. Gibbs’ work, which resulted in the Van der Waals equation of state of a’real’ gas as opposed to an ideal gas. Bakhuis-Roozeboom proposed the only four possible pressure-temperature phase diagrams of crystalline dimorphism, following Gibbs’ graphical approach.

Moving forward to the present day, it is clear that the theoretical framework of thermodynamics developed in the second half of the nineteenth century is well established. This framework, however, only provides an overall macroscopic description of phase behaviour , whereas the phase behaviour of individual systems remains unsatisfactory, even though computer calculations in the field of crystal structure predictions of organic molecules, for example, have made tremendous progress in the last decade. Nonetheless, chemical systems and their phase behaviour require experimental investigation, either to improve descriptions of phases at the atomic level or due to a general lack of data on the system’s behaviour. Only in this way can we advance science and increase our understanding to the point where, eventually, all phase behaviour in materials can be described mathematically or at least simulated in a computer. One of the primary goals of this special issue is to investigate experimental data and compare it to theoretical approaches. It contains, on the one hand, phenomenological descriptions of the phase behaviour of materials, whether organic or inorganic systems, as well as descriptions of the equipment used to obtain the necessary data, and theoretical descriptions in the form of theoretical approaches and simulations.

When one considers the incredible diversity of the subjects covered in this special issue, the importance of understanding phase behaviour in materials becomes clear. among the More difficult fields are likely biological systems, which may not have a clearly defined equilibrium state due to their complex makeup. There may be many local minima in internal energy, and living organisms maintain a steady state driven by potentials defined with respect to equilibrium states that are never reached. A simple and very practical example of water vapour equilibria and biological matter in relation to mint sorption isotherms is presented here. In this regard, biological matter can also be used to absorb other molecules such as dyes.

Another applied issue in the realm of phase equilibria is water treatment and desalination, which will only become more important as the world’s water scarcity grows. Geochemical studies of the solubility of aluminium hydroxy sulphates from aluminosilicate ores for processing applications are related to this topic.

Of course, many of the papers in this special issue are from more traditional areas of phase equilibria research, such as metal systems, which have clear technological applications: the aluminium-barium phase diagram , local order in molten steel for control over its properties , metal glass-forming mixtures , the holmium-germanium phase diagram , mixtures of a rare earth and gold for use in new technologies , phase diagrams of Ag-In and Cu-In , thermodynamic modelling of Ni-C-Cr-Si-B fluxing alloys , and crystallisation of Al-Co-Dy(Ho) amorphous alloys .

Mixtures of small (often carbon-containing) molecules are another industrially important area, particularly in the petroleum industry. Understanding the phase behaviour of such systems aids in improving fuel transportation and storage, as well as carbon capture. Theoretical approaches to liquid-vapor behaviour in mixtures and argon are two examples in this special issue. Equipment for determining A quartz crystal resonator has been used to describe the vapour pressure of complicated mixtures .

Polymorphism in organic crystals is a significant issue for the pharmaceutical and food industries, as demonstrated by some of the preceding examples. Polymorph experimental studies are also important for providing the field of crystal structure calculation with the necessary experimental data for comparison and fine-tuning. In particular, incorporating the influence of temperature in crystal structure calculations and obtaining accurate energy estimates remain difficult tasks. The relative stability of polymorphs can be investigated using differential scanning calorimetry and X-ray diffraction, which can also be used to determine a pressure-temperature phase diagram, as shown here for fluoxetine nitrate. Related to the polymorphism issue is pharmaceutical solubility, for which, as is often the case nowadays, algorithms are being developed to predict solubility, which may aid in the selection of the active molecule to develop.

One of the more difficult experimental questions concerning phase behaviour is how and whether the amorphous phase evolves into a stable crystal form. In this regard, it is unclear whether the amorphous phase should be regarded as a continuous series of ‘metastable’ states with a continuum of different thermodynamic properties, or whether polymorphism is even possible. Nonetheless, the amorphous (or viscous) phase allows the study of almost stationary molecules and can thus be used to investigate nucleation and local order in some cases. The paper on the mobility of ()-methocarbamol contains an example. An article on griseofulvin provided another example of how crystallisation occurs in the amorphous phase. In this context, it is also critical to be able to obtain the amorphous phase in order to study its — crystallisation — behaviour. This special issue describes the equipment used to create amorphous water and salt mixtures.

The separation of racemic mixtures is an important issue in phase equilibria. Even though both enantiomers have the same energetic probability of crystallisation, additives can be used to change the crystallisation kinetics, allowing only one enantiomer to crystallise, demonstrating a delicate interplay between thermodynamic equilibrium requirements and crystallisation kinetics .

The phase diagrams of impurities with the main compound can be studied for purification purposes. The binary phase diagrams of 9,10-dihydroanthracene and carbazole with phenanthrene are an example.

The formation of mixed crystals, such as cocrystals and solvates, is an important topic because the conditions for formation and the resulting properties of the crystals differ in each case. Buckminsterfullerene, which forms solvates with many different solvents, is a very useful subject of investigation in this regard .

In accordance with J.W. Gibbs’ graphical approach, this special issue shows how the various representations of the internal energy, U, H, F, and G (respectively the internal energy itself, the enthalpy, the Helmholtz free energy, and the Gibbs free energy) are graphically related to each other and how each of them can be related to characteristic experimental variables . Another contribution to this rather theoretical treatise shows how the combination of simple thermodynamic rules and graphical extrapolations allows for consistent topological pressure — temperature phase diagrams . A similar approach is used to investigate the degrees of freedom in the pressure melting of plastic crystals. A temperature-volume diagram (a projection of the Helmholtz energy) is also shown in the ascorbic acid paper.

Finally, it can be demonstrated that these thermodynamic approaches and phase diagrams, which are typically applied to ‘simple’ matter, can also be applied to plasma.

Authors: CH-A GP-4

Nishant Chavhan, Prasad Bongarde, Sharda Chandak, Bhushan Chaware and @Sanket Bodhe

Vishwakarma Institute of Technology, Pune.