PHD
  1. Inorganic chemistry  1.1. Coordination chemistry  1.1.1. Ligand field theory  1.1.2. Crystal field theory  1.1.3. Molecular Orbital Theory for Coordination Compounds  1.1.4. Stability of Coordination Compounds  1.1.5. Electronic spectra of coordination compounds  1.1.6. Isomerism in Coordination Compounds  1.1.7. Kinetics and mechanism of coordination reactions  1.2. Organometallic Chemistry  1.2.1. Metal Carbonyls  1.2.2. Metal alkyl and aryl  1.2.3. Fischer and Schrock carbonaceans  1.2.4. Oxidative Addition and Reductive Elimination  1.2.5. Metal Hydrides  1.2.6. Catalysis by organometallic compounds  1.2.7. Metallocenes and Sandwich Complexes  1.2.8. CH activation  1.3. Solid state chemistry  1.3.1. Crystal structures and lattices  1.3.2. Band theory and electrical properties  1.3.3. Defects in the crystal  1.3.4. Synthesis of solid state materials  1.3.5. Magnetic and optical properties of solids  1.3.6. Superconductivity  1.3.7. Solid state ionics  1.4. Bio-inorganic chemistry  1.4.1. Metalloproteins and enzymes  1.4.2. Metal ion transport and storage  1.4.3. The role of metals in medicine  1.4.4. Bioinspired catalysis  1.4.5. Metal–DNA interactions  1.4.6. Metal Complexes in Medical Science  1.5. Lanthanides and Actinides  1.5.1. Electronic configuration and oxidation states in lanthanides and actinides  1.5.2. Spectral and Magnetic Properties in Lanthanides and Actinides  1.5.3. Separation and Extraction of Lanthanides and Actinides  1.5.4. Coordination chemistry of f-block elements  1.6. Main Group Chemistry  1.6.1. Chemistry of boron compounds  1.6.2. Chemistry of Silicon and Germanium Compounds  1.6.3. Chemistry of Phosphorus and Sulfur Compounds  1.6.4. Organosilicon chemistry  1.6.5. Noble Gas Chemistry
  2. Organic chemistry  2.1. Reaction mechanism  2.1.1. Nucleophilic substitution reactions  2.1.2. Electrophilic addition and substitution reactions  2.1.3. Elimination reactions  2.1.4. Rearrangement reactions  2.1.5. Radical reactions  2.1.6. Pericyclic Reactions  2.1.7. Photochemical reactions  2.2. Stereoscopic  2.2.1. Chirality and optical activity  2.2.2. Structural analysis  2.2.3. Stereoelectronic effects  2.2.4. Asymmetric synthesis  2.2.5. Dynamic Stereochemistry  2.3. Organometallic Chemistry in Organic Synthesis  2.3.1. Organolithium and organomagnesium reagents  2.3.2. Transition metal catalyzed coupling reactions  2.3.3. Palladium-catalyzed reactions  2.3.4. Olefin Metathesis  2.3.5. Gold and silver catalysis  2.4. Natural products chemistry  2.4.1. Alkaloids and terpenoids  2.4.2. Steroids and Flavonoids  2.4.3. Total synthesis of natural products  2.4.4. Biosynthesis of natural products  2.5. Supramolecular Chemistry  2.5.1. Host-Guest Chemistry  2.5.2. Self-assembly and molecular recognition  2.5.3. Supramolecular Catalysis  2.5.4. Molecular Machines
  3. Physical Chemistry  3.1. Thermodynamics  3.1.1. Laws of Thermodynamics  3.1.2. Chemical Potential and Equilibrium  3.1.3. Statistical thermodynamics  3.1.4. Non-equilibrium thermodynamics  3.2. Quantum Chemistry  3.2.1. Schrödinger equation and its applications  3.2.2. Molecular orbital theory  3.2.3. Density functional theory  3.2.4. Post-Hartree–Fock methods  3.3. Chemical kinetics  3.3.1. Reaction rate theory  3.3.2. Mechanism and rate laws  3.3.3. Catalysis and enzyme kinetics  3.3.4. Reaction dynamics  3.4. Spectroscopy and molecular structure  3.4.1. Infrared Spectroscopy  3.4.2. UV-visible spectroscopy  3.4.3. Nuclear Magnetic Resonance Spectroscopy  3.4.4. Mass Spectrometry  3.4.5. Raman Spectroscopy  3.5. Surface and Colloid Chemistry  3.5.1. Absorption and Catalysis  3.5.2. Surfactants and micelles  3.5.3. Colloidal Stability  3.5.4. Nanomaterials and Interfaces
  4. Analytical chemistry  4.1. Chromatography  4.1.1. Gas Chromatography  4.1.2. High Performance Liquid Chromatography  4.1.3. Thin Layer Chromatography  4.1.4. Ion Chromatography  4.2. Electroanalytical techniques  4.2.1. Voltammetry and Polarography  4.2.2. Conductometry and potentiometry  4.2.3. Colometry  4.3. Spectroscopic Methods  4.3.1. Atomic absorption spectroscopy  4.3.2. Fluorescence Spectroscopy  4.3.3. X-ray diffraction  4.3.4. Electron paramagnetic resonance spectroscopy  4.4. Chemometrics  4.4.1. Data processing and statistical methods  4.4.2. Multidisciplinary analysis  4.4.3. Machine Learning in Analytical Chemistry
  5. Theoretical and Computational Chemistry  5.1. Molecular dynamics simulation  5.2. Quantum chemistry methods  5.3. Computational drug design  5.4. Machine Learning in Chemistry  5.5. Ab initio molecular dynamics
  6. Biophysics and Medicinal Chemistry  6.1. Drug discovery and design  6.2. Enzyme kinetics and inhibition  6.3. Chemical biology approach  6.4. Protein-ligand interactions  6.5. Bioorthogonal chemistry
  7. Materials chemistry  7.1. Polymer chemistry  7.1.1. Polymerization mechanism  7.1.2. Functional Polymers  7.1.3. Biodegradable Polymer  7.1.4. Conducting and semiconducting polymers  7.2. Nano Chemistry  7.2.1. Nanoparticles and nanostructures  7.2.2. Carbon-based nanomaterials  7.2.3. Quantum dots  7.3. Energy and Environmental Chemistry  7.3.1. Battery and Fuel Cell Chemistry  7.3.2. Green chemistry and sustainable materials  7.3.3. Photocatalysis

PHD → Physical Chemistry → Thermodynamics ↓


Non-equilibrium thermodynamics


Non-equilibrium thermodynamics is a branch of thermodynamics that deals with systems that are not in thermodynamic equilibrium. Unlike classical thermodynamics, which generally assumes that the systems being studied are in equilibrium or close to equilibrium, non-equilibrium thermodynamics applies to more general situations, taking into account the flow of matter and energy over time.

Introduction

In classical thermodynamics, systems are typically studied when they are in equilibrium. At equilibrium, the macroscopic properties of a system do not change over time. However, many real-world processes are far from equilibrium, such as chemical reactions, biological processes, and heat transfer. Non-equilibrium thermodynamics provides tools and concepts to study such processes.

Basic concepts of discontinuous thermodynamics

Balance vs. unbalance

A common way to understand equilibrium is to consider a cup of hot coffee left in a room. In the beginning, the coffee is at a higher temperature than the surrounding air, and over time, it loses heat until it reaches the same temperature as the room. When the temperatures equalize and there is no further net exchange of heat, the system is said to be in equilibrium.

In contrast, non-equilibrium conditions can be observed when coffee is constantly stirred or when heat is applied to it. These are dynamic situations where macroscopic properties are constantly changing.

Irreversible processes

Non-equilibrium thermodynamics is often concerned with irreversible processes. These are processes that cannot reverse on their own. For example, heat flows from a hot object to a cold object without any external work; this process is irreversible because the reverse does not occur naturally. To make heat flow from a cold object to a hot object we need external work (e.g. a refrigerator).

Thermodynamic forces and fluxes

An essential concept in non-equilibrium thermodynamics is the relationship between thermodynamic forces and flows. Thermodynamic forces are gradients, such as temperature gradients, concentration gradients, or chemical potential gradients, that drive changes in a system. Flows represent the flow of quantities such as heat or matter in response to these forces.

J = L * X

Here, J is the flux, X is the thermodynamic force, and L is the incidence coefficient, a proportionality constant that describes the response of the system.

Linear non-equilibrium thermodynamics

Linear non-equilibrium thermodynamics is a field that focuses on systems where forces and flows are linearly related, which is a useful approximation near equilibrium. In linear systems, the principle of superposition applies, making the mathematical analysis more manageable.

Applications in physical chemistry

Chemical reactions

Consider a simple chemical reaction where reactants A and B combine to form product C:

A + B → C

In a non-equilibrium state, the concentrations of A, B, and C change over time. The rates of these changes can be described by reaction kinetics. Non-equilibrium thermodynamics gives information about how changes in external conditions, such as temperature or pressure, affect the reaction rate and direction.

Spread

An everyday example of diffusion as a non-equilibrium process is the spreading of ink in water. Initially localized, the ink molecules move randomly due to thermal motion, leading to diffusion. This process is driven by the concentration gradient and can be studied using Fick's laws of diffusion.

INK

In the above illustration, ink spreads in water, illustrating diffusion driven by a concentration gradient.

Convection

Convection is the bulk motion of groups of molecules within fluids (gases and liquids) and is another non-equilibrium process. It is essential in situations where heat needs to be transferred in the fluid, such as in boiling water. Here, convection currents are set up, which transfer heat efficiently away from the heat source.

Convection cell

This visual illustration shows a convection cell, where heat causes fluid to move in a circular pattern, allowing for efficient heat transfer.

Entropy production

In non-equilibrium systems, entropy production is constant, which is in contrast to equilibrium systems where entropy is maximum and production stops. The second law of thermodynamics asserts that entropy in an isolated system has a tendency to increase, which is consistent with many non-equilibrium processes.

Consider the melting of ice in open air; when this happens, there is no net exchange of heat with the surroundings, the entropy of the water (system) and the air (surroundings) increases, indicating irreversible processes driven by gradients.

Prigogine's theorem

Ilya Prigogine furthered the understanding of non-equilibrium systems through his theorem on minimum entropy production, which states that for linear systems close to equilibrium, the entropy production rate is minimal. This principle helps in understanding and predicting the direction of processes in non-equilibrium thermodynamics.

Biological systems and non-equilibrium thermodynamics

Living systems are prime examples of non-equilibrium thermodynamic systems. They are open systems that exchange matter and energy with their environment, allowing for evolution and maintenance far from equilibrium.

Metabolism

The metabolic pathway consists of a series of biochemical reactions that take place within the cell, requiring a constant input of energy and mass. The energy currency ATP is produced and consumed, which drives these processes and maintains a state far from equilibrium.

Homeostasis

Homeostasis is a biological principle whereby living systems maintain stable internal conditions despite external changes. This regulation ensures that variables such as temperature, pH and ion concentrations are controlled, demonstrating key non-equilibrium thermodynamics in action.

Non-equilibrium thermodynamics can be used to analyze these highly regulated and energy-expensive processes, and to model how effectively organisms cope with environmental variations.

Conclusion

Non-equilibrium thermodynamics broadens the scope of traditional thermodynamics by taking into account the dynamic nature of real-world processes. By understanding and applying the principles of non-equilibrium thermodynamics, scientists can better describe and predict the behavior of a wide variety of systems, from simple physical systems to complex biological organisms.


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Non-equilibrium thermodynamics

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