ABSTRACT
Waals-London(dispersion)forces,onamacroscopicscale(3-5).Theseforcesarecollectively alludedtoasLifshitz-vanderWaals(LW)forces.
2.LWFreeEnergies Lifshitz-vanderWaalsinteractionsbetweenatomsand/ormolecules,whenoccurringin medium-sizedtolargemoleculesorparticles,aretoasignificantdegreeadditive.Theirfree energyofinteraction,~GLW(intheconfigurationoftwosemi-infiniteflatparallelbodies),may thusbeexpressedas
whereAistheHamakercoefficient(whichislinkedtophysicalpropertiesoftheinteracting materials,includingthoseoftheliquid,whentheinteractiontakesplaceinaliquidmedium) andeisthedistancebetweenthetwoparallelbodiesormolecules.Foranumberofmaterials, theHamakercoefficientscanbemeasuredand/orcalculated(6).VanderWaals-London interactionscanbeestimatedviatheLifshitzapproach(6)orviadeterminationsofthe Lifshitz-vanderWaalssurfacetensioncomponents(4).Thefreeenergy,~Gy~,ofthe Lifshitz-vanderWaalspartoftheinteractionbetweentwomaterials1and2(inaliquidmedium 3)canbedeterminedasfollows.Fore=eo(f0istheminimumequilibriumdistancebetween twoparallelbodiesormolecules;eo=1.57A[4])~Gr~GisexpressedbymeansoftheDupre equationincondensedmedia:
where'Yhwstandsfortheinterfacialtensionsbetweenthematerialsindicatedbythesubscripts andwhere~Gr~isthesameat~aLwgiveninEq.1.OncetheLWcomponentsofthesurface tensionsof,e.g.,Ag(1),Ab(2),andoftheliquidmedium(3),'Yiw,'Y~w,and'Y~w,are known,theinterfacialtensionsofEq.2canbeobtainedfromtheLWcomponentsofthesurface tensions,withanerroroflessthanre2%(5):
(3)
BasedontheDupreequation(Eq.2),itcanalsobeshownthattheinteractionbetweentwo similarmolecules,orcells,1,immersedinaliquid,3,canbeexpressedas:
~ar:rr=-2-Yif(4) Eq.4isofimportancewhenstudyingthestabilityofcellssuspendedinliquids;e.g.,m connectionwithhemagllutination(seeSect.VIbelow).
