Graduate
  1. Physical Chemistry  1.1. Thermodynamics  1.1.1. Laws of Thermodynamics  1.1.2. Enthalpy and heat capacity  1.1.3. Entropy and free energy  1.1.4. Phase Equilibrium  1.1.5. Statistical thermodynamics  1.1.6. Thermodynamic cycle  1.1.7. Fugacity and activity  1.2. Quantum Chemistry  1.2.1. Principles of quantum mechanics  1.2.2. Schrödinger Equation  1.2.3. Particle in a box  1.2.4. Operators and eigenvalues  1.2.5. Atomic orbitals  1.2.6. Molecular orbital theory  1.2.7. Perturbation theory  1.2.8. Valence bond theory  1.2.9. Hybridization and chemical bonding  1.3. Chemical kinetics  1.3.1. Rate laws and reaction mechanisms  1.3.2. Collision theory  1.3.3. Transition state theory  1.3.4. Enzyme Kinetics  1.3.5. Chain Reactions and Polymerization  1.3.6. Photochemical reactions  1.4. Statistical mechanics  1.4.1. Partitioning functions  1.4.2. Molecular distribution functions  1.4.3. Boltzmann Distribution  1.4.4. Bose–Einstein and Fermi–Dirac statistics  1.5. Spectroscopy  1.5.1. Rotational Spectroscopy  1.5.2. Vibrational Spectroscopy  1.5.3. Electronic Spectroscopy  1.5.4. Nuclear magnetic resonance spectroscopy  1.5.5. Mass Spectrometry  1.5.6. Raman Spectroscopy  1.5.7. Electron paramagnetic resonance spectroscopy  1.6. Surface and colloidal chemistry  1.6.1. Absorption isotherm  1.6.2. Surface tension and wetting  1.6.3. Colloidal Stability  1.6.4. Catalysis  1.6.5. Emulsions and micelles  1.7. Electrochemistry  1.7.1. Nernst equation  1.7.2. Electrochemical cells  1.7.3. Conductivity and mobility  1.7.4. War  1.7.5. Fuel cells  1.7.6. Electrolysis
  2. Organic chemistry  2.1. Reaction mechanism  2.1.1. Nucleophilic substitution reactions  2.1.2. Electrophilic addition reactions  2.1.3. Elimination reactions  2.1.4. Rearrangement reactions  2.1.5. Radical reactions  2.1.6. Pericyclic reactions  2.2. Spectroscopy and structural determination  2.2.1. UV-Vis Spectroscopy  2.2.2. IR Spectroscopy  2.2.3. NMR Spectroscopy  2.2.4. Mass Spectrometry  2.2.5. X-ray crystallography  2.3. Stereoscopic  2.3.1. Chirality and optical activity  2.3.2. Structural analysis  2.3.3. Geometrical isomerism  2.3.4. Dynamic Stereochemistry  2.4. Organometallic Chemistry  2.4.1. Organolithium and organomagnesium reagents  2.4.2. Palladium-catalyzed cross-coupling reactions  2.4.3. Transition Metal Complexes  2.4.4. Metal–carbon bond  2.5. Polymer chemistry  2.5.1. Polymerization mechanism  2.5.2. Polymer Characteristics  2.5.3. Biodegradable Polymer  2.5.4. Conducting polymer  2.5.5. Supramolecular polymers  2.6. Medicinal chemistry  2.6.1. Drug design and development  2.6.2. Pharmacokinetics and pharmacodynamics  2.6.3. Structure-activity relationships  2.6.4. Molecular docking and drug screening
  3. Inorganic chemistry  3.1. Coordination chemistry  3.1.1. Crystal field theory  3.1.2. Ligand field theory  3.1.3. Spectrochemical Series  3.1.4. Chelation and stability  3.2. Organometallic Chemistry  3.2.1. Metal Carbonyls  3.2.2. Catalysis by organometallic complexes  3.2.3. Metallocenes  3.3. Bio-inorganic chemistry  3.3.1. Metalloproteins and enzymes  3.3.2. The role of metals in biological systems  3.3.3. Metal ion transport and storage  3.4. Solid state chemistry  3.4.1. Crystal Structures  3.4.2. Band theory of solids  3.4.3. Superconductors  3.4.4. Defects in the crystal  3.5. Lanthanides and Actinides  3.5.1. Electronic configuration in lanthanides and actinides  3.5.2. Coordination chemistry of the lanthanides  3.5.3. Magnetic Properties of Lanthanides
  4. Analytical chemistry  4.1. Chromatography  4.1.1. Gas Chromatography  4.1.2. High Performance Liquid Chromatography  4.1.3. Thin Layer Chromatography  4.2. Spectroscopic Techniques  4.2.1. Atomic absorption spectroscopy  4.2.2. X-ray diffraction  4.2.3. Inductively coupled plasma spectroscopy  4.3. Electroanalytical methods  4.3.1. Potentiometry  4.3.2. Voltammetry  4.3.3. Colometry  4.4. Mass Spectrometry  4.4.1. Ionization Technique  4.4.2. Fragmentation Pattern  4.5. Chemometrics  4.5.1. Multidisciplinary analysis  4.5.2. Machine Learning in Chemistry
  5. Theoretical and Computational Chemistry  5.1. Molecular dynamics simulation  5.1.1. Force fields and energy minimization  5.1.2. Monte Carlo simulation in molecular dynamics simulations  5.2. Quantum chemical methods  5.2.1. Hartree–Fock theory  5.2.2. Density functional theory  5.2.3. Semi-empirical methods  5.3. Computational drug design  5.3.1. Molecular Docking  5.3.2. QSAR Modeling  5.3.3. Virtual Screening
  6. Biochemistry  6.1. Enzyme Kinetics  6.1.1. Michaelis-Menten kinetics  6.1.2. Inhibition mechanism  6.2. Metabolism and Bioenergetics  6.2.1. Glycolysis  6.2.2. Citric acid cycle  6.2.3. Electron transport chain  6.3. molecular Biology  6.3.1. DNA replication and repair  6.3.2. Protein synthesis  6.3.3. Gene Regulation  6.4. Structural Biochemistry  6.4.1. Protein Folding  6.4.2. Membrane Biophysics
  7. Environmental Chemistry  7.1. Atmospheric Chemistry  7.1.1. Greenhouse gases  7.1.2. Ozone depletion  7.1.3. Air pollutants and smoke  7.2. Water Chemistry  7.2.1. pH and water hardness  7.2.2. Wastewater treatment  7.2.3. Aquatic Chemistry  7.3. Soil Chemistry  7.3.1. Heavy metal contamination  7.3.2. Soil pH and Buffering  7.3.3. Nutrient cycling  7.4. Toxicology and Chemical Safety  7.4.1. Toxicokinetics  7.4.2. Risk Assessment in Toxicology and Chemical Safety in Environmental Chemistry  7.4.3. Effects of pollutants on the environment

Graduate → Physical Chemistry → Surface and colloidal chemistry ↓


Absorption isotherm


Absorption isotherms are important for understanding how substances stick to surfaces. By studying these curves, we gain information about the ongoing interactions and the surface's ability to hold molecules. This knowledge is particularly important in areas such as catalysis, the design of sensors, and environmental cleanup efforts.

What is adsorption?

Adsorption is a process in which molecules (the "adsorbent") accumulate on the surface of a solid or liquid (the "adsorbent"). This process is different from absorption, where a substance penetrates a larger portion of the substance.

Understanding absorption isotherms

The adsorption isotherm shows the relationship between the amount of adsorbent on the adsorbent and the concentration (or pressure) of the adsorbent at a constant temperature. By investigating the adsorption isotherm, we can obtain valuable information about the adsorption process and the characteristics of the adsorbent material.

Types of absorption isotherms

There are several well-known models for adsorption isotherms. The most common ones are the Langmuir, Freundlich, and BET isotherms.

Langmuir isotherm

This model assumes a single layer of adsorbent molecules on a homogeneous adsorbent surface that has a finite number of identical sites. The Langmuir isotherm equation is:

θ = (K * P) / (1 + K * P)

Where:

  • θ is the fraction of the surface covered by the adsorbate.
  • P is the pressure of the adsorbed substance.
  • K is the Langmuir constant.
Langmuir Point Pressure(P) Surface coverage (θ) Illustration of the Langmuir isotherm

Freundlich isotherm

Unlike the Langmuir model, the Freundlich isotherm describes adsorption on heterogeneous surfaces. The equation is:

q_e = K_F * C_e^(1/n)

Where:

  • q_e is the amount of adsorbate per unit mass of adsorbent.
  • C_e is the equilibrium concentration of the adsorbate.
  • K_F and n are empirical constants.
Equilibrium concentration (C e ) Absorbed dose (qe) Illustration of the Freundlich isotherm

BET isotherm

The BET (Brunauer, Emmett and Taylor) isotherm extends the Langmuir theory to multilayer adsorption and is commonly used for surfaces containing clusters of identical adsorption sites. The BET equation is:

(1/X)((P_0/P) - 1) = 1/(X_m * C) + ((C - 1)/(X_m * C))(P/P_0)

Where:

  • X is the mass of the adsorbed substance.
  • P is the pressure of the adsorbed substance.
  • P_0 is the saturation pressure of the adsorbate.
  • X_m is the mass of a single layer of adsorbate.
  • C is the BET constant.
(P/P0) 1/(x ((p0/p) - 1)) Illustration of the BET isotherm

Applications of adsorption isotherm

Adsorption isotherms are widely used in various scientific and industrial applications. They help in:

  • Designing efficient catalysts.
  • Purification of gases and liquids.
  • Preparation of pharmaceuticals and cosmetics.
  • Environmental pollution control.

Conclusion

Understanding adsorption isotherms is essential for a variety of scientific disciplines. Whether you're studying their theoretical basis or applying them to real-world problems, these tools provide valuable information about how molecules interact with surfaces.


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Absorption isotherm

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