The four forces of nature. Intermolecular forces, surface forces & the Atomic Force Microscope (AFM) Force- and potential curves
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1 Intermolecular forces, surface forces & the Atomic Force Microscope (AFM) The four forces of nature Strong interaction Holds neutrons and protons together in atomic nuclei. Weak interaction β and elementary particle decay Electromagnetism All intermolecular forces can be derived from electromagnetic interactions! Reading suggestion: J.. Israelachvili, Intermolecular and surface forces, Academic Press 2011 Gravitation Can be ignored in molecular interactions, but might be significant for particles of sice ~ µm or larger. Force and energy in molecular interactions Force- and potential curves Bonds in molecules ~ kj/mol Bonds between molecules <~ 10 kj/mol Backbone r + - H O H H Guanine-cytosine base pair O H H ion - ion Backbone Baspar Molecule W ( r) F( r) = r F( r ) = Force W ( r ) = Potential Interaction between two particles Surface The equilibrium distance r e is at the potential minimum, where the force between particles is zero!
2 Forces between atoms and molecules Quantum mechanical forces Covalent bonds Metal binding Born repulsion Electrostatic forces Ion ion (Coulomb) Ion dipole Dipole - dipole (Keesom) Hydrogen bonds Special case of dipole-dipole interaction Polarization forces Ion - induced dipole Dipole - induced dipole (Debye) Dispersion forces (van der Waals) Induced dipole - induced dipole (London) Dispersion forces, van der Waals forces Forces between atoms and molecules { { Q charge (C) u dipole moment (Cm) α polarizability (C 2 m 2 /J) r distance (m) ν elektronic absorption frekvens (Hz) { kt Coulomb-interaction For two particles with charges q 1 and q 2 : q1q2 W ( r) = 4πε εr 0 Ion-dipole Dipole-interactions Dipole-dipole Ex: For a + and Cl - separeted by the distance r = 2.8 Å, W(r) = J 200 kt Strong interaction, which decays slowly with the separation; ~ 1/r. >> kt at typical interatomic distances, strong enough to bind ions to polar molecules, and to orient them, at RT. (Hydration of ions!) Of relevance only for very polar molecules at normal temperatures. (Hydrogen bonds!)
3 Cations Hydration of ions Apparent dynamic hydration numbers (ADH), versus the Jones-Dole viscosity B coefficients (a measure of the affinity of ions for water). Anions Dipole moment Electronegative hydrogen bond donor Hydrogen bonds Electronegative acceptor with unpaired (non-binding) µ electron pair. Typically O, or F. δ δ + D H A Zavitsas, Curr Opin Colloid Interface Sci, (2016). 1 η B = 1 c η0 η 0 is the viscosity of pure water, η is the viscosity at the concentration c. B! A hydrogen bond acceptor is an electron donor! A dipole-dipole bond, with covalent contribution. May create short-range order in liquids, which are then termed associated. Of considerable importance for the very special physical and chemical properties of water. See for a list of anomalous properties of water! Hydrogen bonds in water Some bond strengths in water (kj/mol): O-H covalent bond 492 Hydrogen bond 23.3 van der Waals-attraction 1.3 Hydrogen bonds have some covalent character, but it is debated to which extent. Hydrogen bonds are directed, but small deviations from linearity (up to approx +/- 20 degrees) have little influence, but the strength decays exponentially with the separation. Water molecules are well separated in condensed phases (water and ice) so there is plenty of room for bending and stretching of the bonds. Dispersion forces (London-, van der Waals-, electrodynamic- or fluctuation forces) Caused by temporary dipoles in atoms or molecules, which generate temporary dipoles in the surroundings, which in turn attrach each other. Always present, therefore of great importance for a number of molecular phenomena. Effective rage ~ nm; w(r) ~ 1/r 6 on-additive; the forces between two molecules is affected by the presence of a third molecule. London s approximation: 2 α1α 2 I1I2 W ( r) = 6 3 r I + I (α = polarizability, Ι = ionisation energy) 1 2 Field off Field on
4 Atomic and molecular polarizability, α 0 b W vdw α 0 E Example: Surface tension components Surface tension is caused by intermolecular forces (or the absence of them across the interface), and surface tension can be divided into contributions from these: Forces between surfaces Forces between particles or surfaces cannot be considered only as the sum of the forces acting between individual molecules: γ = γ LW + γ AB Dispersive contributions LW = Lifshitz/van der Waals AB γ l = 2 γ + γ Polar contributions AB = Acid/Base γ + = Acceptor contributions (Lewis acid) γ = Donator contributions (Lewis base) Interactions which depend on molecular size solvent structure entropic effects and osmotic pressure are apparent, and are of particular importance in aqueous solutions. Electrostatic Dispersion (vdw) Steric Undulation Structural Hydration Entropic Bridging Osmotic Depletion Capillary forces Hydrodynamic Hydropfobic forces Casimir forces...
5 van der Waals forces between surfaces / particles B! The relations in the figure yield the potential W. A can be determined either by Hamaker s (A constant) or Lifshitz (A distance dependent) method. van der Waals forces between surfaces / particles II There are two routes from van der Waals forces between individual molecules to vdw-forces between surfaces: Hamaker s additive method: Assume that the force between surfaces can be considered a sum of the forces between individual atoms. (Does not work well with a medium between the surfaces.) Lifshitz continuum method: Consider the electric fields between two polarizable surfaces, and sum the energies from all these contributions. vdw-forces between atoms/molecules are always attractive, but might be repulsive between macroscopic surfaces (rarely!). i 1 i j 2 ΣΣ F ij j A native silicon oxide film will grow on silicon if left exposed to air. This native oxide is self-limiting. In dry oxygen, the film will only grow to 1 nm, whereas in humid air, the film will grow to 2 nm. Thickness versus time for oxide growth in contact with various media. Langmuir 2015, 31, DOI: /acs.langmuir.5b00251 Hamaker constant versus oxide thickness for silicon-silicon oxide-contacting material systems Casimir interaction Two conducting plates in vakuum attract each other due to the absence of electromagnetic fields with λ > d between them, while these are present on the outside, causing a radiation pressure from the outside! 2 F( d) π hc = A 240d 4 A phenomenom of relevance for e.g. cosmology, atomic spectroscopy and particle physics, but also of relevance for micromechanical structures which are predicted to become more and more important for chemical analysis and biosensing!
6 The electrostatic double layer A surface in water is almost always charged: Ionization of acids or bases on the surface Adsorption of ions (ex. OH ). Asymmetric dissociation from the surface. Electrostatic double layer forces Two equally charged surfaces repel each other; in air this is a purely electrostatic effect, while in water, where counter-ions screen the surface charges, the charges at the surfaces do not interact directly with each other. Surface charges create a surplus of counter-ions near the surface, more strongly bound nearer the surface. In water the repulsion is primarily an effect of repulsion between the counterions: As the surfaces are brought closer together, the available volume for each ion is reduced, this increases electrostatic interaction, reduces the entropy, and increases the total free energy. DLVO-forces (Derjaguin-Landau-Verwey-Overbeek) The sum of van der Waals and electrostatic forces (=DLVO) is of great importance in water-based systems, where both always are present, and it decides the stability of colloidal systems. The total force can be modulated e.g. by varying the salinity, or the surface charge. Forces caused by solvent structure Molecules near a smooth interfaces tend to order themselves in layers; the order reaches a few molecular diameters from the surface. Forces between SiO 2 surfaces in P85: An oscillating force appear between the surfaces. (Of relevance e.g. for lubrication!) P85 is a polymer which formes aggregates near room temperature. Pluronics P85 (EO 27 PO 39 EO 27 ) Thormann, Phys. Chem. Chem. Phys., 12, (2010)
7 Hydration Steric stabilization with polymers Water is often strongly bound to surfaces or ions... Strong hydrogen bonds in water increases the tendency to molecular order, especially near charged interfaces. Force measurements between mica surfaces in water with 1 mm KCl (inset shows a theoretical calculation for the same system), showing the removal of layers of adsorbed hydrated ions. Compression Polymers with molecular weight > ~ 10 kda have a size typically extending beyond the range of van der Waals forces. Such a polymer can prevent two surfaces from coming close enough for attraction to be significant if it is adsorbed to the surfaces, and if the solvent is good enough so that the chains do not attract each other. Poly(etylene glycol)-modified surfaces are frequently used to prevent non-specific protein adsorption, by steric repulsion. Interpenetration Attractive bridging of polymers Depletion forces Long polymers which adsorb to two surfaces result in attraction since it is entropically unfavourable for the chains to be stretched. Requires low surface concentration of the polymer, so that a chain has a reasonable chance to bind to both surfaces. At high surface concentration (forcing chains into the solution) long polymers with high affinity will form bridges. Interactions with a polymer chain gives more possible configurations than what is possible for interactions with the solvent alone, increasing entropy. Effect of surface concentration and solvent quality on forces between surfaces with adsorbed polymers. T < θ Interaction between monomers is attractive. T > θ Repulsion between monomerers. If the two large surfaces come close enough, small particles are excluded from the volume between them, resulting in a lower osmotic pressure between the surfaces, forcing the large particles closer to each other.
8 Rayleigh-instability A water jet breaks up in droplets through (Plateau-)Rayleigh instability, driven by the surface tension. Measurement of forces between surfaces Indirect methods, e.g. Adsorption isotherms Contact angle measurements Rheology or sedimentation rate (colloids) The same effect has been observed in falling streams of powders! Cluster formation through van der Waals forces and capillary bridges between nm-sized roughness on the surfaces. These forces correspond to an equivalent surface tension about five orders of magnitude weaker than in water. Royer, ature 459, 1110 (2009) Direct methods, e.g. Adhesion tests Surface force measurements, R ~ cm Atomic force microscope, R ~ nm-µm Scanning Probe Microscopy, SPM A family of methods for imaging of surfaces, where a probe is scanned over a surface in a regular pattern. The probe can be sensitive to topography, surface elasticity, electron density, surface charge, hydrophobicity, heat conductivity, specific chemical interactions (e.g. gen-antigen), magnetism etc. The atomic force microscope (AFM) Topographic images of surfaces over dimensions from 1 nm to 100 µm. Commonly used method for direct measurement of forces between surfaces. Sensitivity ~10-12, (covalent bonds have strengths of ~ 10-9 ). Topographic image of a DVD master Magnetic image of a hard disk storage A sharp tip is mounted on a spring (cantilever) and scanned over the surface. The deflection is recorded, and is assumed to reflect the topography of the surface. In force measurements, the tip is only moved vertically, and the deflection vs separation is recorded. The spring stiffness then gives the force via Hooke s law.
9 Functionalization of probes Mechanical strength in proteins Colloidal particles 5 µm Molecules Proteins with mechanical functions (e.g. muscles) can be investigated by AFM to provide information about their function or mechanisms. (M. Rutland) Gives the probe a well-defined radius, for quantitative force measurements. Surface coatings Chemical modification of the probe to vary the surface charge, surface energy, polarity, etc. Molecules for specific interactions or recognition, e.g. antibodies, oligonucleotides for DA recognition, or other ligands. Unfolding of immunoglobulin domains in the muscle protein titin, ~ 200 p/domain. Rief m.fl. J. Mol. Biol. 286, 553 (1999) Avidin-biotin bindning Protein-membrane receptor recognition Ligand-receptor F (p) H (kcal/mol) G (kcal/mol) Avidin-iminobiotin Avidin-destiobiotin Streptavidin-iminobiotin + 135? Avidin-biotin Streptavidin-biotin Adhesive forces are proportional to H but not G, implying that the separation is adiabatic (isoentropic). Entropic changes occur after the separation of the ligand-receptor pair. Moy, Science 266, 257 (1994) Luckham, Faraday Discuss., 111, 307 (1998)
10 Enzyme activity: Lipid hydrolysis via Phospholipase A 2 Före 2 min 4 min 6 min Grandbois, Biophys. J. 74, 2398 (1998) Soft Matter 2014, 10, 7769 DOI: /c3sm52785a Cell adhesion (contact radius) Real cells or model membranes (above) on micropipettes can be used to measure cell adhesion or the strength in membrane bound molecules. Histogram for the force in one biotin-streptavidin bond. (1) Prior to moving together, (2) compressed during thin film drainage, (3) adhering due to depletion attraction, (4) being stretched during separation, and (5) after separation while they are still moving apart. DOI: /c3sm52785a See video in the Supporting Information! (Biotin is a vitamin, and streptavidin a protein receptor. This pair forms one of the strongest non-covalent bonds in biology.) Evans, Biophysical Chemistry 82, 83 (1999)
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