Colloid Chemistry. La chimica moderna e la sua comunicazione Silvia Gross.

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1 Colloid Chemistry La chimica moderna e la sua comunicazione Silvia Gross Istituto Dipartimento di Scienze di e Scienze Tecnologie Chimiche Molecolari ISTM-CNR, Università Università degli Studi degli Studi di Padova di Padova silvia.gross@unipd.it silvia.gross@unipd.it

2 van der Walls forces The Nobel Prize in Physics 1910 was awarded to Johannes Diderik van der Waals "for his work on the equation of state for gases and liquids". Johannes Diderik van der Waals ( )

3 van der Walls forces

4 van der Walls forces in colloids interactions between. - atoms - molecules - particles origin at atomic level: - dipole interactions (permanent polarities) - dipole-induced interactions (induced polarities) in colloidal particles (macroscopic objects) relevant because of the high number of involved atoms/molecules Different types of van der Walls interactions of different origin, one (dispersion) always present

5 van der Walls forces in colloids in colloidal particles van der Walls interactions hardly neglected, though: I. electrostatic interactions may prevail (see electrostatic repulsion preventing coagulation) II. steric stabilisation can «mask» vdw interactions

6 relevance of van der Walls forces I. Non ideality of gases II. Gas adsorption III. Surface tension IV. Colloid stability/coagulation V. Interfacial phenomena

7 van der Walls forces Source of picture:

8 van der Walls forces: typologies 1. Keesom interactions (permanent dipole/permanent dipole interactions) 2. Debye (permanent dipole/induced dipole interactions) 3. London (induced dipole/induced dipole interactions) special role in colloid science (e.g. physical adsorption, surface tension, adhesion, wetting phenomena, structure of macromolecules (proteins), stability of foams)

9 van der Walls forces: relevant features 1. typically attractive (though medium can play a role) 2. relatively long-range compared to others molecular or atomic-level forces ( nm) 3. London force: dispersion force (nothing to do with colloidal dispersions) influenced by the presence of neighbouring particles 4. Perturbation between neighbouring atoms/particles limts additivity of this forces

10 van der Walls forces and colloidal stability - strenght and range of van der Walls attraction between macroscopic bodies - concept of potential energy curves - concept of coagulation (vide infra): particle retain their identity but loose their kinetic independence

11 Colloid stability, vdw forces and potential energy curves Coagulation: the formation of compact aggregates, leading to the macroscopic separation of a coagulum; the individual units (two or more) cluster together to form an aggregate, they retain their identity, but loose their kinetic independence attractive forces between the particles dispersion stable against coagulation evidence that other forces are active and competing coagulation behavior ruled by relative magnitude of these forces

12 van der Walls forces: typologies 1. Keesom interactions (permanent dipole/permanent dipole interactions) 2. Debye (permanent dipole/induced dipole interactions) 3. London (induced dipole/induced dipole interactions) 1. Origin of van der Walls forces 2. How they affect macroscopic behaviour of matter 3. Establish relationship for scaling up the molecular-level forces to forces between macroscopic bodies (Hamaker constant)

13 forces: strenghts and distances Force Strength (kj/mol) (absolute values) Distance (pm) van der Waals Hydrogen Bonds Ionic Interactions (lattice energy) Hydrophobic Interactions <40 varies Covalent bonds Sources: Holleman-Wiberg: Lehrbuch der Anorganischen Chemie, 102 Edition, De Gruyter, Berlin Housecroft- Sharpe, Inorganic Chemistry

14 Colloid stability, vdw forces and potential energy curves Repulsion forces: - effect of the ion atmosphere charge-stabilised colloids - polymer-induced repulsive forces (screen vdw) sterically-stabilised colloids - Born contribution

15 Colloid stability, vdw forces and potential energy curves V~ 1 r 6 V~ 1 r V~ 1 r 12

16 Colloid stability, vdw forces and potential energy curves Born forces (real ion lattice) due to ions finite size Electron-electron repulsions Nucleus-nucleus repulsions DU = LB/r n B= repulsion coefficient n = Born exponent (9-15, typically 12) V~ 1 r 12 Max Born ( )

17 Colloid stability, vdw forces and potential energy curves distance/strenght: decrease repulsion: positive attaction: negative physical & geometrical factors r: variable describing separation separation among surfaces of spheres of radius R s s= r-2r s Source of the figure:

18 Colloid stability, vdw forces and potential energy curves barrier along the path to coagulation Source of the figure: coagulation Review Article Jordi Faraudo, Jordi S. Andreu Juan Camacho Soft Matter, 2013,9,

19 Colloid stability, vdw forces and potential energy curves Understanding origin of attraction between colloidal particles: interactions among molecules (summation of pairwise interactions) - relationship potential energy to distance: inverse relation to r - different relationships: range of interactions quite different - also quadrupole, octapoles, magnetic interactions should be considered (hereby neglected) - electrostatic forces: repulsive or attractive depending on charge/dipole - those dependend on r 6 : always attractive (minus sign) 1. Keesom interactions (permanent dipole/permanent dipole interactions) 2. Debye (permanent dipole/induced dipole interactions) 3. London (induced dipole/induced dipole interactions) vdw interactions

20 Electric field between dipoles m = q*r debye (D) = C m Interaction between dipoles: Electric field (E) produced by dipole 1 on dipole 2 at distance x (x >> r) x

21 Colloid stability, vdw forces and potential energy curves

22 Colloid stability, vdw forces and potential energy curves 1. Keesom interactions (permanent dipole/permanent dipole interactions) 2. Debye (permanent dipole/induced dipole interactions) 3. London (induced dipole/induced dipole interactions) - They share dependence upon r -6 - The molecular parameters describing the polarization of a molecule, polarizability and dipole moment, serve as proportionality factor in their expression - Each of the three types contributes to the total vdw forces (but: different contributions)

23 Potential energy curves = z x b x -6 combined effect of vdw and interparticles repulsion at molecular level b: constants in the Debye, Keesom or London equations very short range repulsion, relatively long-range attraction opposing forces: total potential energy function displays a minimum (m) derivative with respect to x = 0 (equilibrium situation) d /dx = 0 = -12z x m b x m -7 = 0-6 x m -7 (2z x -6 b) x m = (b/ 2z) -1/6 b = (x m -6 * 2z) m = z x m b x m -6 = z x m z x m -12 = - z x m -12 = z x b x -6 = - m [(x/x m ) (x/x m ) -6 ] Lennard-Jones potential (numerical values of constant obtained by compressibility of condensed phases, virial coefficient of gases etc.)

24 Colloid stability, vdw forces and potential energy curves = z x b x -6 Methane (2 molecules distant 0.42 nm) z = 6.2 * Jm 12 b = 2.3 *10-77 Jm 6 x m = 0.42 nm = 2.1*10-21 J Source of the figure: very short range repulsion, relatively long-range attraction

25 Molecular origin of vdw forces: Keesom (dipole/dipole) Interaction of freely rotating dipoles (liquid) depends on the thermal energy (kt) and is referred to as Keesom energy (Boltzmann distribution of orientations). preferred over V = 2 3kT μ 1 μ 2 4πε r 6 At 25 C the average interaction energy for pairs of molecules with μ = 1 D is about -1.4 kj mol -1 when the separation is 0.3 nm. The average molar kinetic energy at 25 C is 3/2 RT = 3.7 kj mol -1.

26 Molecular origin of vdw forces: Debye (permanent/induced) A dipole near a polarizable molecule induces a dipole (charge dislocation) in the neutral molecule leading to an attractive interaction, the corresponding potential energy is referred to as Debye energy. equal to V = (α 0,1 μ α 0,2 μ 1 2 ) (4πε 0 ) 2 r 6 The interaction energy is independent of the temperature because the induced dipole follows immediately the motion of the permanent dipole and is thus not affected by thermal motion, and it depends on 1/r 6 (like the dipole / dipole interaction).

27 Molecular origin of vdw forces: Debye equal to V = (α 0,1 μ α 0,2 μ 1 2 ) (4πε 0 ) 2 r 6 For a molecule with μ = 1 D (e.g. HCl) near a molecule with polarizability volume α' = cm 3 (e.g. benzene) the average interaction energy is about -0.8 kj mol -1 at a separation of 0.3 nm.

28 Molecular origin of vdw forces: London Random fluctuations in a polarizable molecule lead to a temporary dipole which induces a corresponding dipole in a nearby molecule, leading to attractive dispersion interactions. The involved potential energy is called the London dispersion energy V = 3h 2 α 0,1 α 0,2 ν 1 ν 2 (4πε 0 ) 2 r 6 (ν 1 +ν 2 ) n is the electronic absorption frequency. In the case of two methane molecules with a' = cm 3 and I = 7 ev the dispersion energy becomes -5 kj mol -1 for a separation of 0.3 nm (comparable to the enthalpy of vaporization of methane DHvapor = 8.2 kj mol -1 ).

29 Molecular origin of vdw forces: London Random fluctuations in a polarizable molecule lead to a temporary dipole which induces a corresponding dipole in a nearby molecule, leading to attractive dispersion interactions. The involved potential energy is called the London dispersion energy V = 3 2 α 1 α 2 4πε r 6 I 1 I 2 I 1 + I 2 = 3 2 α 1 α 2 r 6 I 1 I 2 I 1 + I 2 Alternative expression as a function of ionization energy I In is the ionization energy, with I = hn, n is the electronic absorption frequency. In the case of two methane molecules with a' = cm 3 and I = 7 ev the dispersion energy becomes -5 kj mol -1 for a separation of 0.3 nm (comparable to the enthalpy of vaporization of methane DHvapor = 8.2 kj mol -1 ).

30 Modification of the equation for London forces Φ L = hνα πe 2 x 6 0 general equation for L Several modifications of Equation (24) are also important: 1) When the molecules are capable of vibration in all three dimensions, the numerical constant inequation (24) becomes 4, rather than 2: Φ L = 3hνα πe 0 2 x 6 2) When unlike molecules are involved, their individual frequencies and polarizabilities are involved and the expression equivalent to Equation (24) is: Φ L 3 2 h ν 1 ν 2 ν 1 + ν 2 α 0,1 α 0,2 4πe 0 2 x 6 Note that this result becomes identical to the three-dimensional version of Equation (24) when atoms are identical 3) The quantity hν in Equation (25) may be regarded as some energy that characterizes the system and is sometimes approximated by the ionization energy I: Φ L 3 2 I 1 I 2 I 1 + I 2 α 0,1 α 0,2 4πe 0 2 x 6 adopted equation for L (24) (25) (26) (27) 4) The frequency of a harmonic oscillator, the model for two dipoles, equals (1/2 π)(k/m e ) 1/2, where m e is the mass of the electron. Substituting the value of K yields: Φ L = 3 8 he π α 0 3/2 m e 1/2 4πe0 2 x 6 (28) for two identical molecules, since ν = 1 2π e 2 α 0 m e (29)

31 Contributions to vdw forces Source of the figure: