CHEM-E150 Interfacial Phenomena in Biobased Systems Surface interactions part 1: Van der Waals Forces Monika Österberg Spring 018
Content Colloidal stability van der Waals Forces Surface Forces and their Effect on Colloidal Stability Why is colloidal stability important? Why are surface forces important? Why are van der Waals forces important
About colloidal stability Flocculation: reversible association Coagulation: irreversible association Difference between lyophilic and lyophobic colloids Lyophilic colloids are thermodynamically stable colloids
The Stability of Colloids Flocculation/coagulation: Factors affecting flocculation: Frequency of collision is aff. by: - Concentration - Mixing - Particle shape - Diffusion rate - Sedimentation, convection Energy of collision is affected by: - The interactions between particles - The distance dependence of the interactions 4
Attractive and Repulsive Interactions The total interaction is the sum of several components, some attractive, some repulsive The sum may be a curve with maxima and minima Interaction energy Repulsion We learn about surface forces to be able to predict this behavior. Sum D Should the interaction be repulsive or attractive for colloidal stability? Attraction Stable colloid means that the particles stays apart net repulsive interaction needed D
Structure and Strength of Flocs Fast coagulation, strong adhesion Slow coagulation, weak adhesion Porous, fragile floc Fast percolation Weaker but tighter floc, which percolate poorly
Surface Forces DLVO theory on colloidal stability DLVO = Derjaguin Landau Verwey Overbeck The interactions between two surfaces is the sum of the van der Waals forces and the electrostatic double layer forces Today. van der Waals Forces Next lecture: Electrostatic Double Layer Forces and non DLVO interactions
Why are the Forces between Molecules Important? Forces between molecules forces between surfaces. These surface forces again affect the properties of colloidal dispersions and other technical systems. 8
What are the forces between molecules? Interactions between particles, surface tension, cohesion, adhesion and adsorption are dependent on molecular interactions. The interactions are electromagnetic and can be classified: 1. Interactions between permanent dipoles or ions Ion ion Ion dipole Dipole dipole. Interactions between permanent and induced dipoles or ions Ion induced dipole Dipole induced dipole 3. Interactions between two induced dipoles 4. Overlap of electron clouds 5. Hydrogen bonding bridge between one hydrogen atom bonded to a electronegative atom (F, O, N, Cl) and another electronegative atom 6. Lewis acid/base interactions Donation of electron from one functional group to another 9
Intermolecular forces Interactions between ions (Coulomb forces) + - Van der Waals forces: forces induced by dipole moments Acid/base interactions, + - H H O + - Hydrogen bonds H H O 10
Interactions between ions: Coulomb forces Coulombs law: The force between two charges in vacuum is: q1q Fc o = vacuum permittivity = 8,854 10-1 N -1 m - 4 d o q 1 d q The magnitude and sign of each ionic charge (q 1 and q ) is given in terms of the elementary charge (e o = 1,60 10-19 C ) multiplied by the valency (z 1, z ) q 1 = z 1 e o, q = z e o Coulombs law: The force between two ions in a solvent is: F c q 1 q z 1 z e o 4 o d 4 o d = relative permittivity (or dielectric constant) of solvent The interaction energy of the ions at distance d is: d U c F c ds z 1z e o 4 o d 11
Why does salt dissolve in water? The Coulomb forces keep the ion crystal together. Compare the coloumb force with the kinetic energy Consider two monovalent ions, at a distance d = 0,5 nm from each other. The kinetic energy of the ion (T = 5 o C) = mv In vacuum ( = 1): U c z1ze0 4 d 0 4,610 19 1,6010 1 4 18,85410 C N J >> kt In water = 78,5: U C = - 5,9 10-1 J kt 1 3 1 19-1 m C - 3 kt 0,5 10 3 1,3810 9 m Note: add a minus sign J/K98 K = 6,1710 In water the interaction energy between ions is about the same as the thermal energy. J The forces keeping the ions together in water are so small that the salt dissolves when the mixing entropy increases. 1
Note Positive force = ions repel each other. The electrostatic forces decrease slowly with increasing distance. The Coloumb forces decrease when (ε r ) increase. Question: Why does salt dissolve better in water than in oil? Note: ε r ~ for many nonpolar solvents so the Coloumb force is much stronger in oil than i water 13
Permanent dipole moment polar molecules The dipole moment of a polar molecule consisting of charges +q and -q at a distance r is: q r d The dipole moment is a vector with the direction from the negative to the positive charge. Neutral molecules often have a dipole moment due to the different electronegativity of the atoms. + q 1 A molecules permanent dipole moment is the vector sum of the dipole moments of the bonds _ d i q i r _ i The electric field around a dipole interacts with other molecules. r 3 H O r 1 r + q 3 + q H 14
Interaction between an ion and a permanent dipole Consider an ion and a adjacent water molecule. The water molecule has a permanent dipole moment (6,17 10-30 C m) + d q - Assuming that the water molecule is bound with a permanent angle q. The interaction energy between the ion and the water molecule at a distance d (if d >> r cos qis: zeo cosq Uion dipole 4 d If the water molecule is in contact with a sodium ion d=0,3 nm. Inserting the dipole moment of water and d = 0,3 nm we get: ( = 1) + r o U ion-dipole = - 1,7 10-19 J -40 kt (T = 5 o C ). The first hydration layer is rigidly bonded (the hydration effect). 15
Note The interaction depends on the angle between the ion and the dipole. The maximum attraction between a cation and a dipole is reached when q = 0, cos q = 1 ; The maximum repulsion is reached when q = 180º, cos q = 0. The interaction decreases faster as a function of the distance than the interaction between two ions. 16
Polarizability The molecules in bulk phase are usually organized so that the electric fields of their dipole moments cancel each other + - + - - + - + + - + + - - + - -+ In an external electric field a substance is polarized. The field attempts to flip the dipole moments of the molecules in the direction of the field. The substance acquires a dipole moment µ s that is proportional to the field E: s s E s = orientational polarizability The orientational polarizability is larger the larger the dipole moment of the molecule is, and decreases with temperature. The total polarizability of a polar molecule is: s s 3kT 17
Induced dipole moment In addition to the orientational polarization molecules can have induced dipole moments close to permanent dipoles or ions. Example: Interaction between water and ion at larger distances If another water molecule is between the ion and the water molecule we can assume that 78 and U ion-dipole decrease to 0,5 kt E The field around the ion induce a dipole moment (µ) on the molecule at distance d: When l << d and the molecule rotate freely. + ze o 4 o d d + - l 18
The interaction energy between the ion and this induced dipole is. ( zeo ) Ci id Uion ind. dipole 4 4 (4 ) d d o U ion-ind. dipole ja U ion-dipole are of about the same magnitude at this distance. Only the first molecular layer around an ion is oriented. 19
Lifshitz-van der Waals interactions Lifshitz-van der Waals interactions are the interactions between permanent and induced dipole moments of molecules. 1) U dipole-dipole (Keesom interactions) The interaction between two freely rotating molecules with permanent dipole moments µ 1 and µ is: U dipoledipole U dipole-dipole is always attractive C 1 d d 6 6 3(4 o ) ktd d ) U dipole-ind.dipole (Debye interaction) The permanent dipoles of molecules induce dipole moments in other molecules. The interaction between two freely rotating molecules is: U dipoleind. dipole 1 1 d id 6 6 3(4 o ) ktd d The molecules have permanent dipole moments µ 1 and µ and their polarizabilities are α 1 and α. The interaction is always attractive but weaker than the Keesom interactions. 0 C
Dispersion interactions (London) Dispersion interactions are always present (even in non-polar molecules) Although the time average dipole moment for a non-polar atom is zero, there exists at any instant a finite dipole moment at a given instantaneous position of the electrons about the nuclear protons. This instantaneous dipole induces a dipole moment in any nearby atom. The dispersion interaction or London interaction is: U ind. dipoleind. dipole 3h1 (4 ) d o 6 I1I I I 1 C d idid 6 1, = polarizability I 1, I = ionization energy d = distance between molecules h = Planck constant, 6,63 10-34 Js 1
U Summary of LW-interactions The interaction between neutral molecules (i.e. the Lifschitz-van der Waals interactions) can be estimated from the following equation: LW U dipoleind. dipole U dipoledipole U ind. dipoleind. dipole C d The interactions are considerably weaker than ion-ion interactions and iondipole interactions. The interaction between single neutral molecules are smaller than the thermal energy already at distances larger than a few molecule diameters. The interaction energy between particles (consisting of many molecules) can be of a significant magnitude at larger distances. The interactions are very important in surface and colloid chemistry because they explain the long-ranged attractions sometimes observed between particles. They also explain the adhesion between particles and surfaces. d id 6 C d d d 6 C d idid 6 C d LW 6
Questions What is the distance dependence of van der Waals interactions between molecules? What forces are present between non-polar molecules? What molecular properties are important for these forces? 3
Van der Waals Forces between Molecules Origin: Attraction between permanent or induced dipoles Molecular properties: dipole moment, polarisability + - + - - + - + + - + + + - - + - - - + Permanent dipoles + - + - Induced dipoles Distance dependence: Interaction energy W 6 D Force F The molecular properties are included in β, D = distance 6 7 D Note: Energy denoted here with W, earlier with U, many possible symbols in literature
Important conclusion: These forces are always present Other names: London force, dispersion force, Keesom force...
Van der Waals Forces between Molecules Name Between Molecular properties Keesom force Debye force Freely rotating permanent dipoles Induced dipole/ permanent dipole Dipole moment Dipole moment, polarisibility London or Dispersion force Induced dipoles polarisability All these forces have the same dependency on distance: W 6 D Interaction energy Force 7 F 6 D D = distance between molecules The molecular properties are included in β Which force is always present?
Van der Waals Forces between Surfaces the Hamaker Method Assumption The force between two macroscopic bodies is the sum of the forces between the individual atoms Restrictions The principle of pairwise additivity ignores the influence of the neighboring atoms Retardation effects are neglected Temperature effects are neglected The properties of the medium are neglected
The Hamaker constant (A H ) A H N M A ρ = density N A = Avogadro constant M = molecular weight Using the Hamaker constant the vdw interactions can be written: W W AH 1D AHR 6D Between two flat surfaces D = distance between particles Between a sphere with radius R and a flat surface The vdw interaction energy depends on the chemistry (the Hamaker constant) and the geometry of the system
Force (F(D)) = d W(D)/dD W AHR 6D Between a sphere with radius R and a flat surface The force R D F( D) dw ( D) dd AHR 1D Laitoksen nimi 1..018 9
The Lifshitz Theory for van der Waals Interactions The theory: In the Lifshitz theory the atomic structures are ignored and the forces between large bodies, now treated as continuous media, are derived in terms of such bulk properties such as their dielectric constants and refractive indices. Advantages with the Lifshitz theory: The medium is taken into account The temperature effects are included The retardation effects are included (not in the formulas shown here, though) Easy to calculate the Hamaker constant Drawbacks Difficult to derive the Lifshitz theory
The Lifshitz theory surface or particle medium surface or particle 1 3 The materia 1 is interacting with materia 3 across materia ε 1, n 1 ε, n ε 3, n 3
The Hamaker constant according to Lifshitz theory 3 1 3 1 3 1 3 3 1 1 8 3 4 3 n n n n n n n n n n n n h kt A H k= Boltzmann constant T = temperature h= Planck constant ν = UV absorption frequency ε = static dielectric constants for the three media n = refractive indices for the three media
Conclusions about the van der Waals Force Always attractive in vacuum Always attractive between similar surfaces Can be repulsive between different surfaces Question: Why do these conclusions hold?
Values of Hamaker Constants Hamaker constants/10-0 J Material (M) M air M M water air M water M Pentane 3,75 0,153 0,363 Hexane 4,07-0,0037 0,360 Dodecan 5,04-0,344 0,50 Quartz, crystal 8,83-1,83 1,70 Calcite 7,0 -,6,3 Polystyren 6,58-1,06 0,950 Polytetrafluorethylene 3,80 0,18 0,333 Water 3,70 Cellulose 0,84 8.4 0,086 0.8 (i) The attraction between two particles in water is smaller than in air (ii) The attraction between air bubbles and other particles is weak in aqueous solutions and the interaction might even be repulsive (negative Hamaker constant)
You should know: That the van der Waals forces are always present The most important contributions to the van der Waals force Understand (not know by heart) the Lifshitz equation for the Hamaker constant When are the vdw forces attractive? When are the vdw forces repulsive? What is the effect of the media? Why are van der Waals forces important? Note: Many symbols for energy: U, W, E,
Example: Alumina particles across decalin Ceramic components are often formed from a concentrated suspension of ceramic particles. The suspension is flocculated into a mould, the solvent is driven off and the material is sintered. For maximum strength and hardness, the particle concentration in the mould should be as high as and homogeneous as possible. If not, material tensions able to induce fraction, are formed. How to make a homogeneous particle suspension?
Example: Alumina particles across decalin cont. 1. What forces are important? ε(decalin) =.1, ε(aluminium oxide) = 11.6, n(decalin)=1.475 and n(aluminiumoxide)=1.75 What does these data tell about a) the van der Waals force? b) the electrostatic forces?
Calculate the vdw interaction Strong vdw attraction, rigid open structure, poor packing. How should the interaction energy be changed to achieve close packing? We need to decrease the vdw attraction
Adsorption of an Amphiphile to the Surface Attraction Repulsion Distance between two particles (nm)
Test The ceramic suspension is allowed to settle, whereafter the particle concentration in the sedimentation tube is measured as a function of the distance from the bottom. Conclusion: It is possible to influence the vdw force by covering the particles with a layer with dielectrical properties similar to those of the medium. In this way the properties, such as the homogeneity of the ceramic suspension, can be improved which leads to increased strength of the moulded ceramic item. Questions: What would be the effect of adding surfactant if the adsorbed layer had the same dielectrical properties as the particles? Which force causes the sedimentation? How can the speed of the sedimentation be increased?
Useful reading Simplified: Between molecules: http://www.chemguide.co.uk/atoms/bonding/vdw.html Everything (and more than) you need to know: Israelachvili Intermolecular and Surface Forces Intermolecular and Surface Forces - (Third Edition) ScienceDirect Chapter 6: van der Waals forces If you are interested: Review on surface forces in lignocellulosics (no theory): Österberg, M.* and Valle-Delgado, JJ. (016) Surface forces in lignocellulosic systems Current Opinion in Colloid and Interface Science 7, 33-4 DOI: 10.1016/j.cocis.016.09.005 /1/018 41