Symbols Free

Indicator of difference or change in a variable, often used to represent a finite increment in mathematics and in physical sciences to denote a change in state or condition.

Partial derivative or infinitesimal difference symbol, often used in calculus to denote a small change in a variable. In equations, it indicates that the derivative is taken with respect to one variable while holding others constant. May also refer to chemical shift in NMR measurements

Total polarizability of an atom or molecule

Electronic polarizability of a molecule or atom

Dipolar polarizability of a molecule

Dielectric constant, aka relative permittivity of a material with respect to the permittivity of vacuum. ε may also be used to refer to engineering strain, the fractional increase in length from a starting length, L₀

Absolute dielectric permittivity of vacuum, ε₀ ≈ 8.854 × 10⁻¹² F m⁻¹

Permanent dipole moment of a molecule

Induced dipole moment of a molecule or atom

Atomic number of an atom: number of protons in the atomic nucleus

Boltzmann’s constant, also written as k_B, 1.380649 × 10⁻²³ J K⁻¹. May also refer to the spring constant, a measure of the stiffness of a spring, indicating the force required to displace the spring by a unit length.

Thermal energy at temperature T, a useful value for contextualizing covalent and noncovalent interactions at the nanoscale. At room temperature, kT = 4.01 × 10⁻²¹ J

Ionization energy, the energy required to eject the most loosely held electron from the atom or molecule under consideration

Constant, used as a general form to represent larger expressions, particularly for components of the van der Waals force, e.g., C_VDW represents the total van der Waals constant, C_dip–dip represents the dipole–dipole component of the van der Waals constant, etc.

The van der Waals diameter of an atom, 2× the van der Waals radius

A measure of the acidity of a substance, specifically the negative logarithm of the acid dissociation constant K_a. It indicates the tendency of a molecule to lose a proton H⁺ in a solution. Lower pK_a values correspond to stronger acids.

LJ attractive coefficient for van der Waals energy; it controls the depth of the potential well

LJ repulsive coefficient for van der Waals energy; it controls how hard particles repel each other at close distances

Attractive parameter in van der Waals equation of state; it represents corrections to the ideal gas equation due to intermolecular attraction

Repulsive parameter in van der Waals equation of state; it represents corrections to the ideal gas equation due to finite size of molecules

Electrostatic charge, which is a property of matter that gives rise to electrostatic force

Valency of an ion, indicating the number of charges gained or missing from an atom to form the ion

Charge of one electron, approximately −1.6 × 10⁻¹⁹ Coulombs

Interparticle separation, typically refers to the center-to-center distance between two particles

Distance between macroscopic surfaces, commonly used in continuum mechanics. May also refer to an arbitrary linear dimension that characterizes the size of an object

Avogadro’s number, approximately 6.022 × 10²³ molecules per mole

Mass density of a material, generally expressed in terms of kg m⁻³

Number density of a material, generally expressed in terms of N_particles m⁻³, where the particles maybe atoms or molecules depending on the material

Surface tension, also referred to as γ, the energy required to increase the surface area of a liquid by a unit area, typically measured in mN m⁻¹ or dyne cm⁻¹

Surface energy of a solid–liquid interface

Surface energy of a gas–solid interface

The imbibition parameter, or “thirsty parameter”. If I is greater than 0, liquid will rise in a capillary tube

Gravitational constant, the acceleration due to gravity near the surface of Earth, approximately 9.81 m s⁻²

Number-average molecular weight, the arithmetic mean of molecular weights of individual chains in a polymer sample

Weight-average molecular weight; a “weighted” mean of molecular weights that takes into account not only the size of each molecular species but also its relative abundance by mass in the sample

Dispersity, a dimensionless measure of the distribution of molecular mass in a given polymer sample, defined as the ratio $Đ= M w M n$

Radius of gyration, a measure of the size of an object, like a polymer chain or a colloidal particle, in a way that takes into account its shape and mass distribution. For a polymer, it provides an average distance of the monomer units from the center of mass of the polymer chain.

Melting temperature; the temperature at which a material transitions from a solid to a liquid, during which it loses its ordered structure.

Boiling temperature; the temperature at which a material transitions from a liquid to a gas

Glass transition temperature in polymers; the temperature at which the polymer transitions from a hard, glassy material to a soft, rubbery material, marking the onset of segmental motion in the polymer chain.

Crystallization temperature in polymers; the temperature between T_g and T_m where the crystallization degree of a polymer is maximum

Planck’s constant, a fundamental constant that sets the scale of quantum effects, 6.62607015 × 10⁻³⁴, m² kg s⁻¹.

Frequency of a wave, often measured in hertz (Hz).

Speed of light in vacuum, exactly 299, 792, 458, m s⁻¹.

Wavelength of a wave, often measured in meters (m) or nanometers (nm). May also refer to the skin depth, the distance into the bulk to which the loss of multibody effects impacts the properties of the material

Reduced Planck’s constant, defined as h/(2π), where h is Planck’s constant. It is a fundamental constant that appears in quantum mechanics, 1.0545718 × 10⁻³⁴, m² kg s⁻¹.

Wavefunction in quantum mechanics, a complex-valued function that encodes the probability amplitude distribution of a quantum system. The square of its magnitude, $|ψ | 2$ ⁠, gives the probability density for finding a particle at a given position and time.

The intermolecular pair potential for atoms or molecules of the substance at contact

Melting temperature of a nanoparticle, which is reduced from the bulk melting temperature due to scaling laws

Surface tension or energy of a nanoscale droplet or particle, which is reduced from the bulk value due to scaling laws

Gibbs free energy change, indicating the thermodynamic potential for a process to occur spontaneously at constant pressure and temperature

Activation energy, the minimum energy required for a chemical reaction to proceed

Pre-exponential factor in the Arrhenius equation, which is a measure of the rate of a reaction without the energy barrier

Mean free path, the average distance a particle travels between successive collisions

Concentration, the amount of a component in a mixture or solution, often expressed in moles per liter, weight percent, etc.

Work function, the minimum energy required to remove an electron from the surface of a material into a vacuum.

Fermi level; the energy level below which all electronic states are filled and above which all states are empty at absolute zero temperature.

Energy of the conduction band; the lowest energy level that is free to move and conduct electricity in a material.

Energy of the valence band; the highest energy level that is normally filled with electrons in a material.

Bandgap energy; the energy difference between the top of the valence band and the bottom of the conduction band, indicating the energy required to move an electron from the valence band to the conduction band.

Interplanar spacing in Bragg’s law; the distance between crystal planes that results in constructive interference of X-rays scattered off those planes.