L S COLLEGE MUZAFFARPUR What are Van der Waals Forces? www lscollege ac in/sites/default/files/e-content/vander_vals_forces pdf Van der Waals forces are weak intermolecular forces that are dependent on the For example, Van der Waals forces can arise from the fluctuation in the
van der Waals Forces - CORE core ac uk/download/ pdf /82486132 pdf VAN DER WAALS FORCES SPECIAL CHARACTERISTICS IN LIPID-WATER SYSTEMS AND A GENERAL METHOD OF CALCULATION BASED ON THE LIFSHITZ THEORY
Bonding in Solids and Liquids - Caltech AUTHORS authors library caltech edu/25050/15/Chapter_14 pdf Molecular solids become compre- hensible as soon as we recognize the contributions of the weak forces known as van der Waals attraction and hydrogen bonding
Bonding, Structure and Properties Lesson 4 – Van der Waal's Forces blogs glowscotland uk/er/public/SNHChemistryWebsite/uploads/sites/2701/2020/06/01075229/1B4-Van-der-Waals-Forces-LDFs pdf London Dispersion Forces are weak forces of attraction which operate between all atoms and molecules LDFs are the weakest Van der Waals forces Even the noble
Chapter 11 Intermolecular Forces - MSU chemistry www2 chemistry msu edu/courses/cem151/Intramolecularforces_Ch11 pdf All weak intermolecular forces are called: van der Waals forces Page 8 van der Waals Forces Two major forms: • Dipole–
Compilation of Definitions “van der Waals interaction” ww2 chemistry gatech edu/~lw26/structure/molecular_interactions/van_der_waals_interactions pdf “Van der Waals forces - the relatively weak attractive forces that act on neutral atoms and molecules that arise because of the electric polarization induced in
REPULSIVE CASIMIR AND VAN DER WAALS FORCES robobees seas harvard edu/files/capasso/files/s0217751x10049529_01 pdf 23 mai 2020 both the Casimir force and the van der Waals force are of quantum Several examples of material systems that obey [Eq 1] exist in nature
the weak interaction: nuclear interaction (responsible for nuclear -decay / electron emission and attractive intermolecular forces ( van der Waals forces) w r A electrons (electron sea) between positively charged atoms over entire sample
Van der Waals Interactions for Point Interactions Before we discuss FD analysis, we first discuss interaction forces, particularly weak interactions between B Covalent Bond: The standard example for a covalent bond is the hydrogen
Graphenes bonding forces in graphite are widely known as an example of the van Weak forces between graphenes suggest that they are the van der Waals
(a) We define precisely what we mean by a van der Waals force and, to put our investigation into For example, and typically when I1 50 A, t,> (3 X 1016) ~ 10166 In the near- to mid-uv, water (14) shows a weak absorption at X = 1650 A or
ABsTRAcTApracticalmethodforexaminingandcalculatingvanderWaalsforcesisderivedfromLifshitz'theory.RatherthantreatthetotalvanderWaalsenergyasasumofpairwiseinteractionsbetweenatoms,theLifshitztheorytreatscomponentmaterialsascontinuainwhichthereareelectromagneticfluctuationsatallfrequenciesovertheentirebody.Itisnecessaryinprincipletousetotalmacroscopicdielectricdatafromcomponentsubstancestoanalyzethepermittedfluctuations;inpracticeitispossibletouseonlypartialinformationtoperformsatisfactorycalculations.Thebiologicallyinterestingcaseoflipid-watersystemsisconsideredindetailforillustration.ThemethodgivesgoodagreementwithmeasuredvanderWaalsenergyofinteractionacrossalipidfilm.Itappearsthatfluctuationsatinfraredfrequenciesandmicrowavefrequenciesareveryimportantalthoughtheseareusuallyignoredinpreferencetouvcontributions."Retarda-tioneffects"aresuchas todampouthighfrequencyfluctuationcontributions;ifinteractionspecificityisduetouvspectra,thiswillberevealedonlyatinteractions
across<200angstrom(A).DependenceofvanderWaalsforcesonmaterialelectricpropertiesisdiscussedintermsofillustrativenumericalcalculations.
forcesinthissystemcanbeanalyzedeasilyandaccuratelybythemacro-scopictheoryofLifshitz(3).Further,severalimportantqualitativefeaturesof
theseforces,unnoticedinearliertreatments,arerevealedbythisanalysis.The approachelaboratedhereallowspredictionofattractiveenergiesinothersystems,electricpolarizationcanariseatacenterduetothemotionofelectrons,moleculardistortion,ormolecularorientation.Thispolarizationwillactonthesurrounding
regiontoperturbspontaneousfluctuationselsewhere.Theinteractionresulting fromthisperturbationissuchastolowertheenergy.Theclassesofsuchinteraction havebeenextensivelyreviewedbyKauzmann(4)andJehle(5). Theresultingattractive"dispersion"forceforelectronicfluctuationswasfirst calculatedbyF.London(6)inhisfamous1930paper.Heshowedthattheforcebetweentwoisolatedatomsisproportionaltotheinverseseventhpowerofdistance,andtheproductoftheirpolarizabilities.London'stheoryprovidedthe
basisforsubsequenttheoreticalestimates(7)ofdispersionforcesbetweencon-onideasofCasimirandPolder(9)whichovercomesthesedifficulties.Histheoryincludesallmany-bodyforcesthroughacontinuumpicture,retainscontributions
fromallinteractionfrequencies,anddealscorrectlywiththeeffectsofintermediate substances.Moreimportant,theinformationrequiredforcalculationsiscontained inthedielectricpropertiesofcomponentmaterials-informationavailableinprin- ciplefromindependentspectroscopicmeasurements. Foracondensedmedium,wheretherangeofstronginteractionexceedsthe distancebetweenatomiccenters,Lifshitzregardstheentiresetoflocalspontaneous electricfieldfluctuationsasanelectromagneticfieldwhichextendsoverthewhole system.Thistime-varyingfieldcanbefrequencyanalyzed;thestrengthofafield ofagivenfrequencyisdirectlydependentontheresponseofthematerialtoan appliedfieldofthatfrequency,i.e.,itsdielectricsusceptibilitye(W).Boundary surfacesbetweenunlikematerialswillaffecttheseelectricfieldsandconsequently theelectromagneticenergyofthesystem.Thisapproachtodispersionforces examinesthechangeinenergyofasystemwithmovementoftheboundarysur- facesbetweenunlikeregions. Itwasthought(10)thatthetheoryofLifshitzcouldnotbeappliedtothecalcu- lationofdispersionforcesintheabsenceofcompletespectralinformation.Wefind thatsuchcompletedataareunnecessary,particularlywhencomponentsubstancesareofsimilarweightdensity.Infact,itispossibletomakeseveralsimplifyingassumptionsregardingspectra.Allthatappearsnecessaryforthecalculationofvan
derWaalsforcesinthepresentthinhydrocarbonfilmsystemaresingleaverage absorptionfrequenciesintheinfraredanduvforwater,oneaveragefrequencyin theuvforhydrocarbon,indicesofrefractionatvisiblefrequencies,alimitingvalueforthedielectricsusceptibilityofwaterbetweenmicrowaveandinfraredfrequencies,andthesimplestformforthedielectricdispersionofliquidwaterinthemicrowaveregion.
FIGURE1Twosemi-infinitemediaofsubstance1separatedbyaplanarslab,thickness1,ofsubstance2.Inthetextweconsiderthecasewhere1iswaterand2ishydrocarbon.
NINHAMANDPARSEGIANVanderWaalsForces:CalculationforLipidWaterSystems649 wherefrequencies.WewilldescribebelowhowthenecessaryconstantsCmwandCy(proportionalto"oscillatorstrengths")andresonancefrequenciescomw,WXmay
bedeterminedfrommeasurementsmadeontherealfrequencyaxisco=WR.On theimaginaryaxis(co=it),wehavefromequation11 +1mwCE1j(13)1+~/cmwjtc)Y Nowthedampingterminyjcoinequation12issignificantonlywhencoCojsincebandwidthsarealwaysmuchlessthanabsorptionfrequencies.Thecontributionofthisterminequation13willbenegligible(1+(/Coj)2>>yjy)sothatwemay
takeX-rayregiondescribedbyequation16,thesimplestprocedureistoconstructaninterpolationformulaforE(it).GiventheconditionthatE(it)bemonotonicde-
creasing,thereislittleambiguityinsodoing. However,becauseofthesimilarityofthesusceptibilitiesofcomponentsubstances inthemid-uv,theintegrandsorsumtermsoftheforceandenergyexpressions tendtozeroveryrapidlyinthisregion,andgivelittlecontribution.Inpractice therefore,itisusuallysufficienttousetheformofequation14forsusceptibilities, andnointerpolationisrequired.Indeed,inspectionofthefullexpressionsequationsDebyerelaxationfromitsstaticvalueof80.4downto5.2withacharacteristicrelaxationwavelength1.78cm.Thus,Cmw=(80.4-5.2)=75.2,andwmw=27rC/XmW=(1.06X1011)=1011.026radians/sec.(Datahere(12)areforT=
Becauseoftheslowvariationofe(it)withtonemayuseanaveragefrequencyw,uvforthenear-tomid-ultravioletregion.Acommonapproximationistousea
frequencyequivalenttothefirstionizationpotential(4).Inthiscase12.62ev-hcouv,orcouv=(1.906X101")=1016.28rad/sec.(Throughoutpaperradusedfor
radian.)Itwillbeshownthatuseoftheionizationpotentialvalueorthestronger absorptionbandvaluehaslittleeffectontheestimatedenergy.ThevalueofCu, forthisrelaxationis(n2-1)=(1.78-1)=0.78.Wehavethenhydrocarbonliquidsbetweenaudioandvisiblefrequencies(12)where(ha=nhe(n=indexofrefraction).Byexaminingthereflectionoflaserbeamsfromathin
lipidfilm,CherryandChapman(15)havemadeaprecisemeasurementofan anisotropicindexofrefraction:nhe=1.486forpolarizationperpendiculartotheplaneofthefilmandnho-Eachofthesenumberswillbeconsideredbelow.Againwewillsummarizerelaxationasoccurringatanaveragefrequencycor-
respondingtotheionizationpotential.Anappropriatevalueofthisforathinhydrocarbonfilmisnoteasilydeterminedfromavailabledata.Valuesfordecane(16),10.19evorCuv=1.54X1016,andforethane(16,14),11.65evorcouv=
derivedfromionizationpotentialsofwateranddecaneorethane,wefindA(50A)byequation8forfourvaluesofn20(TableI).Forthesedata,valuesofA(=50A,
T=20°C)rangefrom5.5to7.1X1014erg.WenotethatAisnotsimplymono- tonicinnhhc NINHAMANDPARSEIGANVanderWaalsForces:CalculationforLipidWaterSystems653Theseestimatesareslightlyhigherthanthoseinferredfromexperimentsonthinlipidfilms(2)(4.7X10-14erg)butmuchlowerthanthosederivedfromex-
perimentsonsuspensionsofparaffinsinaqueoussuspension(17)(r1.6X10-'1 erg).Inprinciplebothexperimentalestimatesshouldbeapproximatelythesame sothattheoreticalestimatesherearelessambiguousthanexperimentsbutwithin thecorrectranges. TableIIAsuggeststhatAisrelativelyinsensitivetotheassumedcUs,aslong astheyarechoseninaconsistentwayforthetwomaterials.Usingstrongestnear- uvabsorptionpeaksorionizationpotentialsforbothmaterialsgiveAestimatesAcarefulattempttousee(it)thatsatisfybothlowandhighfrequencybehavior(equations14and16)makesnegligibledifferencetotheestimatedA.Bystraight-
lineinterpolationbetweenformsfornear-uvandX-rayregionsandusingtheTakelr=5.66X1014rad/sec,C1°r=3.4cow=1.06X1011rad/sec,C;mw=75.2.2.Wuv=1.906X10"rad/sec,n2=1.78.I=50A,T=20°C.
tardationfactorofA(1)/A(0)isalsolistedforcomparisonwiththefunctionusedincolloidchemistry(19).Clearlytheneglectofnon-uvfrequencyfluctuations,typical
oftheoldertheory,givesvastlylowerestimatesatlargeseparationdistances. NINHAMANDPARSEGIANVanderWaalsForces:CalculationforLipidWaterSystems655 Theproperanalysisofretardationeffectsisdiscussedinthefollowingsectionand intheAppendix.AtverylargedistancesthecalculationofAisdominatedbythe n=0terminequation8;thistermisthesubjectofthesucceedingpaper(two).FIGURE2SpectrumofrelativeinfraredanduvcontributionstovanderWaalsenergyinthelimitI=0.Useequations17,18,and10withdataforwaterandethane.Datafordecanegivesharplyreduceduvpeak.Notelargeinfraredcontribution,sharpdecreasein
uvcontributionwhenn2h,isreducedfrom2.208to2.0tobringitclosertontO2=1.78for water.ThefactortmultiplyingI(Q,I=0)intheordinateistocorrectforthelogarithmicscaleintheabscissa.ForfixedIandfixedwatercomposition,theonlytwoparameterswhichcan2-hoaltersignificantlywithhydrocarboncompositionarenhoand&Dhc.TheplotsofI(Q,1)inFig.2alsoshowthattheeffectofchangingn20istoaltertheentirespectrum
ofcontributingfrequencies.Similarly,variationinabsorptionfrequenciescO, willshiftthepositionofmaximaofthespectrum,andaltertheheightofpeaks. Forthepresentexamplec,>Elhiintheinfrared,butc,fluctuationsignalacrossthegapiscomparabletoafluctuationfrequency(21E2'12)/c1/i,thecorrelationinfluctuationsbetweeneithersideisdiminished.Thein-
tegrandI(Q,I)satisfiestheunequalityI(Q,I)1=0,50Aand500A,andfornh0=2.208and2.0;theyillustratetheprogressive removalofhighfrequencymodeswithincreasing1.Onthesameabscissawehave alsoplotted(Fig.3c)theratioI(Q,I)/I(I,0)<1.Thisrathercomplicatedfunction isweaklydependentonmaterialpropertiesandisthemultiplicativefactorfordampingthesehighfrequencymodes. Thefrequencyregimeoverwhichtheintegrandintisdampedoutisaboutonedec- NINHAMANDPARSEGIANVanderWaalsForces:CalculationforLipidWaterSystems657 -infrared--FIGuRE3aTheinfluenceofthefinitevelocityofpropagationonthespectrumofinfraredanduvcontributionstovanderWaalsenergies.n2hc=2.208,dataforethaneandwater.LargeuvcontributionatI=0andsignificantdecreaseofAwith1.
FIGURE3bTheinfluenceofthefinitevelocityofpropagationonthespectrumofinfraredanduvcontributionstovanderWaalsenergies.nfhc=2.0,dataforethaneandwater.SmalluvcontributionatI=0andweakdependenceofAon1.
FIGURE3cTheinfluenceofthefinitevelocityofpropagationonthespectrumofinfraredanduvcontributionstovanderWaalsenergies.Retardationfactorfordampingcontribu-tionsatdifferentfrequencies.ArrowsIindicatefrequencyatwhichE=c/21.NotethatretardationdampingiseffectivelyashiftofthecurveI(t;I)/I(I;0)tothelefttocutouthigherfrequencies.Therangeofdampingisapproximatelyonedecadewideandcenteredaboutt=c/21.
adewideandroughlycenteredabout=c/(21E'12)-'(c/21)whereeho--s1.Byvirtue ofthelargeinfraredcontributiontotheenergy,evenat500A(where,10155< uvfrequencies),almosthalftheoriginalintegralisintactwhennh.,=2.208(Fig.isintimatelyconnectedwiththemagnitudesofoscillatorstrengthsaswellasab-sorptionfrequencies;bothmaterialpropertiesandgeometricfactorssetsimul-
taneousconditionsontheenergyspectrumandmustbeconsideredtogetherin addingupthemodalenergies.forces.WefindthatfittingthesimpleformE(ic)=1+(Cmw/[l+(Q/cmmw)])+2(Cj/[I+(/lwj)2])givesanadequaterepresentationforthedielectricdispersion
asitisneededhere. Thereisaverystrongcontributiontothetotaldispersionenergyfromthein- fraredspectrumofwater.Thisfeature,certaintoholdinbiologicalsituations,is usuallyignoredinpreferencetotheuvcontributionsandisimportantincalculating thelong-distancebehaviorofthevanderWaalsforce. Ontheotherhand,twophenomenamilitateagainstimportantcontributions fromthefar-uvfluctuationfrequenciesinbiologicalsystems.First,materialsof similarweightdensitywillhavesimilardielectricsusceptibilitiesathighfrequencies (i.e.far-uvtoX-rayregion).Sincetheinteractingsurfacesareelectromagnetically definedonlywhentherearedifferencesindielectricsusceptibilityofinteracting speciesandinterveningmedium,therewillnotbeimportantbehaviorfromthe far-uv.Thisisqualitativelydifferentfromthecasewherebodiesinteractatshort distanceacrossavacuum. Second,thefinitevelocityoflight,c,causesretardationdampingacrossgaps1 atandabovefrequenciestsuchthat1/t<21/corwavelengthsX<4irl.This saysthatatlongdistance,e.g.I=50m,u=500A,thematerialpropertiesonlyfor X<500m,u=5000Aareneeded.Atshortdistancesshorterwavelengthsbegin tocontribute. Itisclearthatsubstancesthatchangetheindexofrefractionofwatercanchange thedispersionforces.Wehavecalculatedelsewhere2bythepresentmethod thatproteinorsaccharidematerialsonthebiologicalcellsurfacecangreatlyin- creaseintercellattractiveforces. Ifthecoatingmaterialsondifferentkindsofcells havedifferentuvspectra,weexpectspecificityinattractiveforcestoappearfor intercellulardistanceslessthan200A.(Itwouldbemostfortunateifthedistinctive spectrawereintheeasilyaccessible150m,uandsimpleprocedureforexaminingvanderWaalsforcesquantitatively.Webelieveitwillbeusefulinmanyconnections.
ItisourhopethattheLifshitztheorycanbeusedforausefultheoreticalandexperimentalframeworkinwhichtoviewelectromagneticforcesinawidevariety
TheprecisenatureofthedampingduetoretardationdiscussedinAnalysisofIntegralscanbemadeexplicitbyacarefulanalysisoftheintegralI(t,1)whichgivesthespectrumoffrequencycontributions.Werecalleq.(8)intheform
ToagoodapproximationthelogarithmswhichoccurinequationA1canbereplacedbytheirleadingterms,andweconsiderfirst
Forafixedfrequencyi,thefunction([SE2-PEL]/[SE2+pei])isslowlyvaryingasafunctionofp.Sincetheexponentialisadecreasingfunctionofpwhilepisincreasing,theintegrandofequationA4hasamaximumatp=pogivenby
dcdp(Inp-[p/l.81)=O;POrl%W/=2tl-,*/e2(A5)Thismeansthatforafixedvalueof1,andsmalli,themajorcontributiontothepintegralcomesfromlargevaluesofp.Ontheotherhandforthesamegivenvalueof1,forlarget,Po<1andthemaincontributiontothepintegralcomesfromtheregionp-1.Two
casesthenarise (a)t2v1.ThiscorrespondstothecaseofsmalldistancesdiscussedbyLifshitz(3).Forthesevaluesoftwemayputptsintheintegrandofequation19.Thefirsttermdisappears.Inthe
NINHAMANDPARSEGIANVanderWaalsForces:CalculationforLipidWaterSystems661 remainingintegrandthelowerlimitcanbereplacedbyzeroandwehaveAtI=50A,t8t3X1016whichhesinthemid-uv.Fort>3X1016thefunction(1C2-1lJ/[E2+El])2isalreadyverysmallcomparedwithitsmaximumvalue,sothateffectsofretardationarealsosmall.OntheotherhandforI=500A,t8liesinthenear-uvandweexpectthesehighfrequencycontributionstobediminished.
(b)t/A="<<1Afterafurtherchangeofvariabletoxt/l8=y,notingthatthemajorcontributioncomesfromtheregiony=0,wecanexpandtheintegrandinascendingpowersofytoget