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 ↓


Statistical thermodynamics


Statistical thermodynamics, also known as statistical mechanics, is a branch of physical chemistry and physics that combines the principles of statistics with the laws of thermodynamics. This powerful discipline connects the macroscopic properties of systems such as temperature and pressure to the microscopic actions of individual molecules and atoms. By focusing on large groups of particles, statistical thermodynamics transforms the randomness of individual particle actions into predictable and observable macroscopic behavior.

Overview

The main purpose of statistical thermodynamics is to establish relationships between the microscopic properties of matter and macroscopic observations. Macroscopic properties include pressure, temperature, and enthalpy, which are consequences of microscopic behavior such as energy levels, the speed of particles, and molecular forces.

Basic principles

Statistical thermodynamics is based on some fundamental principles:

1. Microstates and macrostates

- Microstates refer to the specific, detailed configurations of all the particles in a system. These include the exact position and velocity of each particle.

- Macrostates describe the overall state of a system, defined by macroscopic properties such as temperature, volume, pressure, etc. A given macrostate may correspond to multiple microstates.

Example: 
Consider a set of dice. The macrostate could be the total amount of states appearing on the faces of the dice, 
And the microstates can be the exact numbers on each die. Multiple microstates (e.g., 1+3+2) 
The result may be the same macrostates (for example, a total of 6).

2. Boltzmann equation

Ludwig Boltzmann made important contributions to this field. Boltzmann's equation is used to relate the entropy of a system to the number of microstates (W) corresponding to a given macrostate:

S = K cdot ln(W)

where: S is the entropy, k is the Boltzmann constant, and W is the number of microstates.

Applications of statistical thermodynamics

1. Ideal gas

The simplest application of statistical thermodynamics is in the ideal gas model, where gas particles are assumed to have no interactions other than elastic collisions.

PV = nRT

This equation of state can be derived from the kinetic theory of gases, which is a classic example of statistical thermodynamics. Each molecule moves randomly, but collectively they follow predictable rules.

2. Internal energy and temperature

In an ideal gas, the internal energy is determined by the kinetic energy of the gas molecules. The distribution of molecular speeds can be described by the Maxwell-Boltzmann distribution.

f(v) = 4pi left( frac{m}{2pi k T} right)^{3/2} v^2 e^{-left( frac{mv^2}{2 k T} right)}

Partition function

The partition function (Z) is central to statistical mechanics. It serves as a key that unlocks many thermodynamic properties:

Z = sum_i e^{-beta E_i}

Where E_i is the energy of state i, and (beta = frac{1}{kT}).

The partition function is the sum of all possible states of a system and provides information about how the energy of the system is distributed among these states.

Usage examples

The partition function allows the calculation of various thermodynamic properties. For example:

  • Entropy: S = k cdot left( ln(Z) + beta left(frac{ partial ln(Z)}{ partial beta} right) right)
  • Free energy: F = -kT ln(Z)

Example: two-tier system

Consider a simple two-level system with energies E_0 and E_1.

Z = e^{-beta E_0} + e^{-beta E_1}

The population of states at different temperatures can be calculated using Z and this gives information about diversification at the macroscopic level.

Quantum effects

At very low temperatures or on very small scales, quantum effects become important. Unlike classical systems, these effects include:

  • Quantized energy levels
  • Wave–particle duality
  • Uncertainty principle effect

Statistical thermodynamics further extends its principles to suit quantum mechanics, leading to quantum statistical mechanics. It is important for low-temperature physics and for predicting behavior in microscopic systems.

Conclusion

Statistical thermodynamics serves as a bridge between microscopic molecular behavior and the macroscopic phenomena observed in the real world. With principles derived from Boltzmann's equation, partition functions, and statistical averaging, it reveals the mechanics of atoms and molecules in a wide range of situations. Its applications range from prediction of gas laws, chemical equilibrium, to more advanced areas such as materials science and kinetic theory. Emphasizing the probabilistic nature of molecular interactions, statistical thermodynamics acknowledges the inherent randomness in molecular systems, facilitating a deeper understanding and accurate predictions of the properties, states, and reactions of matter.


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Statistical thermodynamics

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