The rate at which the Gibbs energy of a system increases when 1 mol of a component is added (the partial molar Gibbs energy). In phase equilibrium, the chemical potential of each component is equal in all phases.
Japanese name: 化学ポテンシャル
Chemical potential appears in 2 practice questions across 2 topics, including Thin films, surfaces and nanomaterials, Thermodynamics of materials.
Field: Thermodynamics of materials
The chemical potential is the rate at which the Gibbs energy increases when a little of component i is added at constant temperature, pressure and amounts of the other components, µᵢ = (∂G/∂nᵢ). Its unit is J/mol. Moving a small amount of a component from phase α to phase β changes G by (µᵢ(β) − µᵢ(α)) × the amount moved, so components tend to move from where their chemical potential is high to where it is low. Just as a difference in electric potential drives charge and a difference in temperature drives heat, a difference in chemical potential is the driving force that moves matter. For a pure substance, the chemical potential equals the Gibbs energy per mole.
The chemical potential of a component in a solution can be written µ = µ° + RT ln a, using its value in the reference state µ° and the activity a. For an ideal gas a = p/p°, and for an ideal solution a = x. For a binary solution, if G per mole is plotted against composition and a tangent is drawn at a given composition, the values where the tangent meets the vertical axes at x = 0 and x = 1 are the chemical potentials of the components. The chemical potentials of the two components also cannot be changed independently; they are linked by the Gibbs–Duhem equation x_A dµ_A + x_B dµ_B = 0, so measuring the activity of one gives the other.
Diffusion usually proceeds from high to low concentration, but the true driving force is the gradient in chemical potential. In 1949 Darken showed that when two steels with almost the same carbon concentration but different silicon contents are joined and heated, carbon moves into the side with less silicon, creating a large difference in carbon concentration near the interface. Silicon raises the activity of carbon, so carbon on the silicon-rich side had a higher chemical potential and escaped from it. Uphill diffusion in spinodal decomposition is another example of atoms moving because of differences in chemical potential rather than concentration.
The chemical potential also changes with particle size and charge. For a particle of radius r, the surface energy γ raises the chemical potential by 2γV_m/r, where V_m is the molar volume. Supposing γ = 1 J/m² and V_m = 1×10⁻⁵ m³/mol, at r = 10 nm it is about 2 kJ/mol higher, and the solubility into the surroundings at 1000 K is about 1.27 times that at a flat surface. Ostwald ripening, in which small particles dissolve and large ones grow, is driven by this difference. For charged particles, the electrochemical potential, which adds a term for electric potential, is used, and for electrons in a solid this corresponds to the Fermi level.
Answer: A. Smaller particles, around which solubility is higher, dissolve and disappear, and their atoms diffuse to larger particles, which grow
A particle with a small radius of curvature has a chemical potential raised by the interfacial energy, so the equilibrium solubility in the surrounding matrix is higher (the Gibbs–Thomson effect). The solute concentration is therefore high around small particles and low around large ones, and solute diffuses from small particles to large ones. Small particles thus disappear and large ones grow, reducing the total interfacial area (interfacial energy). This is the main cause of softening by overaging in precipitation-strengthened alloys and of the coarsening of nanoparticles. The choice with the solubility relation reversed is wrong, and collision and coalescence of particles is a mechanism distinct from Ostwald ripening.
Answer: C. Taking the pure solid or liquid as the reference (activity 1), the activity of a component in an ideal solution is equal to its mole fraction
Activity a is a "thermodynamic effective concentration" defined so that the chemical potential of a component in a solution can be written μ = μ° + RT ln a. With the pure substance as the reference state, the activity of a pure solid or liquid is 1, and in an ideal solution a = x (the mole fraction) by Raoult's law. For real solutions one writes a = γx, and the activity coefficient γ expresses the deviation from ideality. When unlike atoms attract each other more weakly than like atoms, the component escapes from the solution more easily, giving γ > 1 (positive deviation) and a tendency toward phase separation. When unlike atoms attract strongly, γ < 1, indicating a tendency toward ordering or compound formation. Treating activity as the molar concentration is only an approximation for dilute aqueous solutions.
The Gibbs energy belongs to the whole system and is proportional to the amount of material. The chemical potential is how much it increases when 1 mol of a component is added; it is also called the partial molar Gibbs energy and is an intensive quantity independent of amount. The G of the whole system is the sum of the products of each component's amount and chemical potential, G = Σnᵢµᵢ.
As an energy per mole, it is J/mol. In physics it is sometimes given as an energy per particle, for example in eV, in which case it is the value in J/mol divided by the Avogadro constant. 1 eV per particle corresponds to about 96.5 kJ/mol.
At constant pressure, its rate of change with temperature is minus the partial molar entropy, so the chemical potential falls as temperature rises, and falls faster for phases of higher entropy. So even if the solid has the lower chemical potential at low temperature, at high temperature the liquid or gas has the lower value, and melting or evaporation occurs.
A particle with a small radius of curvature has a chemical potential raised by the interfacial energy, so the equilibrium solubility in the surrounding matrix is higher (the Gibbs–Thomson effect).
When an alloy containing dispersed precipitate particles of…Activity a is a "thermodynamic effective concentration" defined so that the chemical potential of a component in a solution can be written μ = μ° + RT ln a.
Which statement about the activity of a component in a solu…Ostwald ripening Activity Ellingham diagram Entropy of mixing Equilibrium oxygen partial pressure Gibbs energy Regular solution Spinodal decomposition