Units, Symbols, Useful Quantities and Relations Much of the published literature and equations on intermolecular and surface forces are based on the CGS system of units. In this book the Système International (SI) is used. In this system the basic units are the kilogram (kg) for mass, the meter (m) for length, the second (s) for time, the kelvin (K) for temperature, the ampére (A) for electrical quantities, and the mole (mol) for quantity of mass. Some old units such as gramme (1 gm = 1 g = 10 -3 kg) , centimeter (1 cm = 10 -2 m), ångstrom (1 Å = 10 -10 m) and degree centigrade (°C) are still commonly used, although they are not part of the SI system. The SI system has many advantages over the CGS, not least when it comes to forces. For example, force is expressed in newtons (N) without reference to the acceleration due to the earth's gravitation, which is implicit in some formulae based on the CGS system. Note that units, prefixes, words, and abbreviations are usually unitalicized-that is, in text format (e.g., J, K, m, N, volts V), whereas variables are italicized (e.g., stiffness K, mass m, number N, maximum number Nmax, velocity or volume V). Derived SI Units

Quantity SI Unit Symbol Definition of Unit Energy Joule J kg m 2 s -2 (also Nm and CV) Force Newton N J m -1 = kg m s -2 Power Watt W J s -1 = kg m 2 s -3 Pressure Pascal Pa N m -2 Electric charge Coulomb C A s Electric potential Volt V J A -1 s -1 = J C -1 Electric field Volt/meter V m -1 Frequency Hertz Hz s -1 Fraction 10 12 10 9 10 6 10 3 10 -1 10 -2 10 -3 10 -6 10 -9 10 -12 10 -15 10 -21 Prefix symbol T G M k d c m µ n p f z

Definitions of Terms and Symbols Used in the Text

a Atomic or molecular radius (m), surfactant headgroup area (m 2) a, b Constants in equations of state a0 Bohr radius, atomic unit (a.u.) of length 0.053 nm, optimum headgroup area (m 2) A, Aijk Hamaker constant for media i and k interacting across medium j (J), area (m 2), Helmholtz free energy c, C Interaction constant (J m 6), aqueous solute concentration in mole fraction units (mol dm -3/55.5 or M/55.5), concentration number density (m -3), volume fraction d Distance, diameter (m) D Distance between two surfaces (m) Da Dalton unit of molecular weight (same as MW) E Electric field strength (V m -1), energy (J, eV, erg) F Force (N) or, when between two planar surfaces, force per unit area (N m -2) G Gibbs free energy h, H Height (m), enthalpy, hardness (Pa), hour (also hr) I Ionization potential (J) i ka Area compressibility modulus (J m -2 or N m -1) kb Bending or curvature modulus (J) k, K Elastic modulus (N m -2), spring constant or stiffness (N m -1) Ka Reaction constant, association constant (M -1) Kd Dissociation constant ( Kd = 1/ Ka) l, l Length (m), unit segment length in polymer chain (m) lP Persistence length of worm-like chain polymer (m) lc Critical hydrocarbon chain length (m) L Latent heat (J mol -1), thickness of polymer brush layer (m) m, M Mass (kg), molarity, molar mass, molecular weight (also MW), mean aggregation number M Concentration (mol dm -3, 10 3 mol m -3, moles/liter) M W, M, MW Molecular weight, molar mass (g mol -1), atomic mass (g), mass of atom or molecule × N o, mass of atom or molecule/mass of of 12C atom, Da (if not specified, e.g., PEO 1,000, assume Da) n, N Refractive index; number of atoms, molecules, moles, bonds, segments in a polymer chain, micelle aggregation number p, P Pressure (N m -2) PL, PY Laplace pressure, yield stress (Pa) pK -log 10[concentration or activity of H + ions in M] Q, q Charge (C) r, R Radius (m) , interatomic distance (m), atomic or molecular radius (m) rK Kelvin radius (m) Rg, RF Radius of gyration of polymer (m), Flory radius of polymer (m) s Mean distance between polymer anchoring sites (m) S Entropy, solubility t Time (s) T Temperature (K) TM, TB Melting or boiling points (K or °C) Tc, Tm Lipid chain melting temperature u Dipole moment (C m) U Molar cohesive energy (J mol -1), internal energy (J mol -1) v, V Volume (m 3), velocity or speed (m s -1), molar volume (m 3) w, W, W0 Interaction free energy, pair potential (J). Between two planar surfaces: Work of adhesion, cohesion or interaction free energy per unit area (J m -2) x, y, z Position along the x-, y- or z- axis, arbitrary variables Time derivative of variable x, for example, velocity = d x/d t (m s -1) Acceleration, = d 2x/d t2 (m s -2) X Dimensionless concentration (e.g., mole fraction) Y Young's modulus (N m -2) z Valency a Polarizability (C 2 m 2 J -1), interaction energy parameter (J or J m -1) ? Surface tension (N m -1), surface energy (J m -2), tanh( e?0/4 kT) tanh[ ?0(mV)/103] at 298 K ?i, ?AB Interfacial energy (J m -2) G Surface coverage, surface density, 2D density (number per m 2) d Stern layer thickness (m), elastically or plastically deformed distance (m) ?( ?) Dielectric permittivity at frequency ? ? Relative permittivity, static dielectric constant at zero frequency ?(0), strain ? Energy (J or J m -1) ?, ?, ?, a Angle (deg or rad), contact angle (deg) ? Theta temperature of solvent (°C, K) ? Inverse Debye length (m -1) ?, ?o, ?0 Characteristic exponential decay length, wavelength (m), line tension (N) ? Correlation length (m) µ Chemical potential, coefficient of friction (COF) µi, µo Standard part of chemical potential due to molecular interactions ?, ?I Frequency (s -1 or Hz), ionization frequency (s -1) ? Number density (m -3) or mass density (kg m -3) s Atomic or molecular diameter (m), surface charge...