The Four Forces Of Nature - IFM

The four forces of natureIntermolecular forces, surface forces&the Atomic Force Microscope (AFM) Strong interactionHolds neutrons and protons together in atomic nuclei. Weak interactionβ and elementary particle decay ElectromagnetismAll intermolecular and surface forces can be derived fromelectromagnetic interactions!Reading suggestion: J. N. Israelachvili,Intermolecular and surface forces,Academic Press 2011 GravitationCan be ignored in molecular interactions, but might besignificant for particles of sice µm or larger.Force and energy in molecularinteractionsr -NNBonds in molecules 100-500 kJ/mol- Hold molecules togetherBonds between molecules 10 kJ/mol- Determine physical properties such asboiling and melting points, viscositiessurface tension, and vapour pressures.- Affinities in specific interactions.N HONNBackboneNNOHH NInteraction between two particlesion - ionHBackboneForce- and potential curvesBasparF (r ) W (r ) rF (r ) ForceHGuanine-cytosine base pairW (r ) PotentialMoleculeSurfaceThe equilibrium distance re is at thepotential minimum, where the forcebetween particles is zero!

Forces between atoms andmolecules Quantum mechanical ”forces”Covalent bondsMetal bindingBorn repulsion Electrostatic forcesIon – ion (Coulomb)Ion – dipoleDipole - dipole (Keesom) Polarization forcesIon - induced dipoleDipole - induced dipole (Debye)Forcesbetweenatoms andmolecules Dispersion forces (van der Waals)Induced dipole - induced dipole(London)Dispersion forces, van der Waals forces Hydrogen bondsSpecial case of dipole-dipole �charge (C)dipole moment (Cm)polarizability (C2m2/J)distance (m)elektronic absorptionfrekvens (Hz){Dipole-interactionsIon-dipoleDipole-dipoleFor two particles with charges q1 and q2 :W (r ) q1q24πε 0ε rEx: For Na and Cl- separeted by the distance r 2.8 Å,W(r) - 8 10-19 J 200 kTStrong interaction, which decays slowly with the separation; 1/r. kT at typical interatomic distances,strong enough to bind ions to polarmolecules, and to orient them, at RT.(Hydration of ions!)Of relevance only for very polarmolecules at normaltemperatures.(Hydrogen bonds!)

Hydration of ionsApparent dynamic hydration numbers (ADHN), versus the Jones-Doleviscosity B coefficients (a measure of the affinity of ions for water).Hydrogen bondsDipole momentδ CationsAnionsZavitsas, Curr Opin Colloid Interface Sci, 23 72–81 (2016).Electronegativehydrogen bonddonor 1 ηB 1 c η0 η0 is the viscosity of pure water,η is the viscosity at the concentration c.Hydrogen bonds in waterBond strengths in water (kJ/mol):O-H covalent bond492Hydrogen bond23.3van der Waals-attraction1.3Hydrogen bonds have some covalent character,but it is debated to which extent.Hydrogen bonds are directed, but smalldeviations from linearity (up to approx /- 20degrees) have little influence, but the strengthdecays exponentially with the separation.Water molecules are well separated in condensedphases (water and ice) so there is plenty of roomfor bending and stretching of the bonds.µδ Electronegative acceptorwith unpaired (non-binding)electron pair. Typically O, N or F.D—H A NB! 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 specialphysical and chemical properties of water.See http://www1.lsbu.ac.uk/water/water anomalies.html for alist of anomalous properties of water!Dispersion forces(London-, van der Waals-, electrodynamicor fluctuation forces) Caused by temporary dipoles in atoms or molecules,which generate temporary dipoles in the surroundings,which in turn attrach each other.Boiling points for some compounds Why doesn’t water follow the trend? Always present, therefore of great importance fora number of molecular phenomena. Effective rage 0.1–10 nm; w(r) 1/r6Field off Non-additive; the forces between two moleculesis affected by the presence of a third molecule. London’s approximation:W (r ) 2 α1α 2 I1 I 23 r 6 I1 I 2(α polarizability, Ι ionisation energy)Field on

Atomic and molecularpolarizability, α0bWvdw α0EExample: Surface tensioncomponentsSurface tension is caused by intermolecular forces (or the absence of them acrossthe interface), and surface tension can be divided into contributions from these:Model potentialsThe hard-sphere potentialw( r )Soft potentialsThe power-lawThe Lennard-Jones potentialw(r ) σ w(r ) , 6 n 12 r nσDispersive contributionsLW Lifshitz/van der Waalsγ γ LW γ ABPolar contributionsAB Acid/Base σ w(r ) , n r nThe exponential potentialγ Acceptor contributions (Lewis acid)γ Donator contributions (Lewis base)Model potentials simplifies computations wheredetails of the interaction are less important!r εr 1.12σw(r ) Ce r / σ 0σ0 typically 0.2 Åγ l AB 2 γ γ σWeak theoretical basis, butmathematically convenientw(r ) σ 12 σ 6 A B 6 4ε 12rr r r The attractive term’s inverse sixth-powerterm resembles the van der Waalsattraction. The repulsive term is chosenfor computational convenience.

van der Waalsforcesbetweensurfaces /particlesForces between surfacesForces between particles or surfaces cannot be considered only as the sumof the forces acting between individual molecules:Between particles,interactions which depend onmolecular sizesolvent structureentropic effects andosmotic pressureare present, and are ofparticular importance inaqueous solutions. ElectrostaticDispersion (vdW)Steric – UndulationStructural – HydrationEntropic – BridgingOsmotic – DepletionCapillary forcesHydrodynamicHydropfobic forcesCasimir forces.NB! The relations in the figure yield thepotential W. A can be determined eitherby Hamaker’s (A constant) or Lifshitz’ (Adistance dependent) method.Langmuir 2015, 31, 4862 4867.DOI: 10.1021/acs.langmuir.5b00251van der Waals forces betweensurfaces / particles IIThere are two routes from van der Waals forces betweenindividual molecules to vdW-forces between surfaces: Hamaker’s additive method:Assume that the force betweensurfaces can be considered a sumof the forces between individualatoms. (Does not work well with amedium between the surfaces.)iA native silicon oxide film will grow onsilicon if left exposed to air. This nativeoxide is self-limiting. In dry oxygen, thefilm will only grow to 1 nm, whereas inhumid air, the film will grow to 2 nm.ΣΣ 1 Fiji j 2j Lifshitz’ continuum method:Consider the electric fields betweentwo polarizable surfaces, and sum theenergies from all these contributions.vdW-forces between atoms/molecules are always attractive,but might be repulsive between macroscopic surfaces (rarely!).Thickness versus timefor oxide growth incontact with variousmedia.Hamaker constant versus oxide thickness forsilicon-silicon oxide-contacting material systems

Casimir interactionTwo conducting plates in vakuum attract each other due to the absence ofelectromagnetic fields with λ d between them, while these are present onthe outside, causing a radiation pressure from the outside!A phenomenom of relevance fore.g. cosmology, atomicspectroscopy and particle physics,but also of relevance formicromechanical structures whichare predicted to become more andmore important for chemicalanalysis and biosensing!F (d )π 2 ℏc A240d 4Electrostatic double layer forcesThe electrostatic double layerA 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.Surface charges create a surplus of counter-ionsnear the surface, more strongly bound nearer the ek)Two equally charged surfaces repel eachother; in air this is a purely electrostaticeffect, while in water, where counter-ionsscreen the surface charges:thus, the charges at the surfaces do notinteract directly with each other.In water the repulsion is primarily an effect ofrepulsion between the counterions: As thesurfaces are brought closer together, theavailable volume for each ion is reduced, thisincreases electrostatic interaction, reducesthe entropy, and increases the total freeenergy.The sum of van der Waals andelectrostatic forces ( DLVO) is ofgreat importance in water-basedsystems, where both always arepresent, and it decides thestability of colloidal systems.The total force can be modulatede.g. by varying the salinity, or thesurface charge.

Forces caused by solvent structureMolecules near asmooth interfacestend to orderthemselves inlayers; the orderreaches a fewmoleculardiameters fromthe surface.HydrationWater is often strongly bound tosurfaces or ions.An oscillating force appearbetween the surfaces.(Of relevance e.g. forlubrication!)Strong hydrogen bonds in waterincreases the tendency to molecularorder, especially near chargedinterfaces.Forces between SiO2 surfaces in P85:P85 is a polymer which formesaggregates near room temperature.Pluronics P85 (EO27PO39EO27)Force measurements between micasurfaces in water with 1 mM KCl(inset shows a theoretical calculationfor the same system), showing the removalof layers of adsorbed hydrated ions.Thormann, Phys. Chem. Chem. Phys., 12, 10730 (2010)Steric stabilization with polymersAttractive ”bridging”of polymersLong polymers which adsorb to twosurfaces result in attraction since it isentropically unfavourable for thechains to be stretched.Requires low surface concentration ofthe polymer, so that a chain has areasonable chance to bind to bothsurfaces.Polymers with molecular weight 10 kDahave a size typically extending beyond therange of van der Waals forces.CompressionSuch a polymer can prevent two surfacesfrom coming close enough for attraction tobe significant if it is adsorbed to thesurfaces, and if the solvent is good enoughso that the chains do not attract each other.InterpenetrationPoly(etylene glycol)-modified surfaces are frequently used to preventnon-specific protein adsorption, by steric repulsion.At high surface concentration (forcingchains into the solution) long polymerswith high affinity will form ”bridges”.Interactions with a polymer chain givesmore possible configurations than whatis possible for interactions with thesolvent alone, increasing entropy.Effect of surface concentrationand solvent quality on forcesbetween surfaces with adsorbedpolymers.T θ Interaction betweenmonomers isattractive.T θ Repulsion betweenmonomerers.

Rayleigh-instabilityDepletion forcesA water jet breaks upin droplets through(Plateau-)Rayleighinstability, driven bythe surface tension.If the two large surfaces comeclose enough, small particlesare excluded from the volumebetween them, resulting in alower osmotic pressurebetween the surfaces, forcingthe large particles closer toeach other.The same effect hasbeen observed infalling streams ofpowders!Cluster formation through van der Waalsforces and capillary bridges betweennm-sized roughness on the surfaces.These forces correspond to anequivalent surface tension about fiveorders of magnitude weaker than inwater.Royer, Nature 459, 1110 (2009)Measurement of forcesbetween surfaces Indirect methods, e.g.– Adsorption isotherms– Contact angle measurements– Rheology or sedimentation rate (colloids)Scanning Probe Microscopy,SPM A family of methods for ”imaging” of surfaces, where a probe isscanned over a surface in a regular pattern.The probe can be sensitive to topography, surface elasticity, electrondensity, surface charge, hydrophobicity, heat conductivity, specificchemical interactions (e.g. gen-antigen), magnetism etc. Direct methods, e.g.– Adhesion tests– Surface force measurements, R cm– Atomic force microscope, R nm-µmTopographic imageof a DVD masterMagnetic image ofa hard disk storage