User:Benjah-bmm27/degree/3/PB

=Soft matter, PB=

Length scales

 * Specific surface area (total surface area ÷ total mass) is proportional to 1/R
 * Colloid particles have a much higher specific surface area than bulk droplets
 * Colloids particles are therefore much higher in energy, as extra surface area costs energy (&Delta;G = &gamma;&Delta;A)
 * Yield stress is proportional to 1/R3
 * Colloid particles have fewer bonds per unit volume, resulting in much lower yield stresses

VdW attractions in a vacuum

 * Van der Waals forces are quantum mechanical in origin
 * An instantaneous dipole in an atom or molecule (1) can induce a dipole in a nearby atom or molecule (2)
 * The strength of the induced dipole is proportional to the polarizability of atom or molecule 2
 * $$ \mu_{\mbox{ind}} = \alpha \mathbf{E} $$


 * The energy of a van der Waals attraction is proportional to 1/r6
 * VdW attractions are much stronger at short range – they rapidly diminish as the separation, r, between the two interacting atoms or molecules increases

VdW attractions in a medium

 * Molecules in dielectrics – attractions depends on excess polarizability
 * If the difference between the dielectric constant of molecules and of the medium is large, vdW attractions between molecules are strong
 * If the dielectric constants of the molecules and the medium are similar, vdW attractions between molecules are weak
 * The energy of vdW attractions in a medium is proportional to (ε2−ε1)2 and to 1/r6
 * Such energy is usually expressed in terms of the Hamaker constant, A21
 * $$A_{21} \sim \pi^2 \hbar \omega \left ( \epsilon_2 - \epsilon_1 \right )^2$$


 * VdW forces between identical molecules are always attractive
 * The Hamaker constant for vdW attraction (A21) between molecules in a medium depends on the Hamaker constants for the molecules (A2) and the medium (A1) in a vacuum:
 * $$A_{21} = \left ( \sqrt{A_2} - \sqrt{A_1} \right )^2$$


 * In the limit of large separation h between two colloid particles each of radius R,
 * $$U_d(h) = - \frac{A_{21}R}{12h} $$

The electrical double layer

 * Electrical double layer: Stern layer + diffuse ionic atmosphere
 * Competing forces trying to:
 * Minimize charge repulsions
 * Maximize entropy
 * The thickness of the double layer is given the symbol κ−1

The rest

 * Hamaker constant
 * Electrical double layer
 * Bjerrum length
 * DLVO theory

Intermolecular and Surface Forces, 2nd Edition, With Applications to Colloidal and Biological Systems by Jacob Israelachvili
 * Hardcore, detailed, postgraduate-and-beyond-level textbook: