Interatomic Forces. Overview

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Jane Blankenship
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1 Inteatomic Foces Oveview an de Walls (shot ange ~1/ 6, weak ~ e) Ionic (long ange, ~1/, stong ~510 e) Metallic (no simple dependence, ~0.1e) Covalent (no simple dependence, diectional,~3 e) Hydogen (patially ionic and covalent) Inteatomic Foces 1

2 an de Waals: elated to dipoledipole inteactions Fluctuation sepaates chage Induced chage sepaation E + + l l l l q p 1 +q q p 2 +q Sepaate the molecules by some distance, a weak ATTRACTION is poduced due to molecula stuctue and Coulomb s law. The intenal motion of the nucleus and electon cloud that can give attaction. This foce is called the AN DER WAALS foce and is the attactive pat of the LJ potential Inteatomic Foces 2

3 Fom obsevation we know that: Molecules epel if too close togethe due to electostatic epulsion of electon clouds (~12 Å) In solids and liquids the molecules tend to stick togethe so at some molecules must attact each othe At vey lage thee is no discenable foce Expessed gaphically: F() Stong epulsion due to electon ovelap anishing foce Take some standad length a as a unit of 2a a 3a 4a Attaction Inteatomic Foces 3

4 o Mathematical epesentation: E electic field, p dipole moment, q chage E ~ p 1 / 3 (follows fom F~ qe ~ q 2 / 2 ), hence p 2 ~ αp 1 / 3, α polaisability ~ pe ~ A/ 6 ()= Repulsive ()+ Attactive () 1 1 ( ) = A B ( ) = n σ 4ε n σ 6 6,n>9 () ε Repulsive () a 0 Attactive () Most commonly n=12 is used ( 6 12 potential mostly fo convenience of calculations). In geneal symbols p and q can be used ( pq potential) Fo epulsion ~e /a dependence is also sometimes used (due to fall off in chage density in the oute edge of electon clouds of each molecule as they ovelap) Inteatomic Foces 4

5 The pq potential is just one example of an infinate set of mathematical functions that might epesent a molecula paipotential Fo INERT GASES this is a good epesentation of potential between molecules because these gases compise single atoms Often use the LENNARDJONES potential (often called the 612 potential) to descibe inet gases: ( ) = σ 4ε 12 σ 6 This is sometimes witten in tems of the distance a at which () is zeo Inteatomic Foces 5

6 IONIC FORCES: in substances like Sodium Chloide o the alkali halides geneally, the effect of intenal stuctue is diffeent. Instead of metal Na and Cl atoms, it is enegetically favouable fo an electon to leave the Sodium cloud to joint the chloine electon cloud leaving two chaged ions: F ( ) = F + F Repulsion ( ) = + Repulsion Coulomb Coulomb Na Cl ( ) λ 2 e 4πε o = Constants p + _ Inteatomic Foces 6

7 + + F ( ) = q1q2 4πε 0 2 The fundamental foce hee is the ELECTROSTATIC COULOMB foce between point chages. + + Electon clouds ovelap DENSITY of ve chage in the oute edge of the molecule vaies apidly ( exp[/a]) stong epulsion Inteatomic Foces 7

8 van de Waals binding enegies in the ange e Coulomb enegy is typical of the enegy it takes to pull an electon out of an atom 5 10 e IONIC FORCES ae much stonge than van de Waals vdw () << Coulomb () vdw (a 0 )= ε a 0 a 0 a 0 vdw vdw (2a 0 6 a0 ε ) 2ε 0. 03ε 2a a0 2ε ( 3a0 ) 2ε ε 6 3a0 3 Inteatomic Foces 8

9 Coulomb ( a 0 ) 2 e = 4πε a 1 Coulomb( 2a0) = Coulomb( a0) 2 1 Coulomb( 10a0) = Coulomb( a0) an de Waals foces ae SHORT RANGED Coulomb foces ae LONG RANGED A neutal molecule will exet significant foce only on its neaest neighbou A chaged ion can exet a stong foce on anothe ion many neighbous away (causes poblems in calculations) Inteatomic Foces 9

10 METALLIC BONDING: anothe fom of bonding by electon eaangement. Thee is no simple LJ type expession fo metallic bonding (some textbooks do use a 612 potential but it has no fundamental meaning as is the case fo inet gases fo example) Electon.. gas Metals: One o moe loosely bound electons Electons detach (delocalisation) to fom electon gas suounding the +ve ion Metal cystal behaves like a single giant molecule Repulsion on compession and attaction on extension Metallic bonding stong, ~ 0.1 e A FULL EXPLANATION OF METALLIC BONDING REQUIRES QUANTUM PHYSICS Inteatomic Foces 10

11 COALENT FORCES: elated to electostatics and the intenal stuctue of the molecules, e.g. H 2 molecule: + + H 2 molecule Binding enegy~ 3 e H H Enegetically favouable stuctue: + + a 0 The electon cloud edistibutes The exta electon cloud between the nuclei SCREANS the stong epulsion ceating a stong COALENT foce A FULL EXPLANATION OF COALENT BONDING REQUIRES QUANTUM PHYSICS Inteatomic Foces 11

12 E.g. Cabon: covalently bonded mateial C IA H IIA IIIB IB B I B II B III B He 4 moveable oute electons Li Be B C N O F Ne Na Mg Al Si P S Cl A Tiple bond 6 electons C C 4 electons 180º C Double bond Single bond 2 electons C C C C C 120º C 109.5º Inteatomic Foces 12

13 Cabon allotopes Diamond Gaphite covalent Fulleenes d=0.7 nm vdw Cabon nanotubes Cabyne C C C C C d~1.4 nm Inteatomic Foces 13

14 Polymes C C C C C C C C The COENT BOND is: Due to electon eaangement Stong Highly diectional Cannot be epesented by any simple mathematical foce expession Inteatomic Foces 14

15 HYDROGEN BOND: H atoms fom single covalent bond to fom H 2, but fully o patially ionised can fom essentially ionic bonds with e.g. O (H 2 O), N (NH 3 ) o F (HF). Bond is pat (about 90%) electostatic and pat (about 10%) The wate molecule 0.7e Inteatomic Foces 15

16 Summay LENNARDJONES (612) POTENTIAL AN DER WAALS bonding Between neutal atoms and molecules Stength ~ 0.01 e 0.1 e Shot ange ( ) = 4ε E.g. A, K σ 12 Oigin in fluctuation of electon cloud σ 6 IONIC bonding Between chaged atoms Stength ~ 5 e Long ange E.g. Na +, Cl ( ) = λ p Oigin in electon tansfe 2 e 4πε o Inteatomic Foces 16

17 Summay contd. COALENT bonding Oigin in electon eaangement (quantum mechanical) Stength ~ 3 e Shot ange Diectional METALLIC bonding Oigin in electon eaangement (quantum mechanical) Stength ~ 0.1 e Shot ange Next Topic: Inteatomic foces contd Inteatomic Foces 17

Electric Field. y s +q. Point charge: Uniformly charged sphere: Dipole: for r>>s :! ! E = 1. q 1 r 2 ˆr. E sphere. at <0,r,0> at <0,0,r>

Electric Field. y s +q. Point charge: Uniformly charged sphere: Dipole: for r>>s :! ! E = 1. q 1 r 2 ˆr. E sphere. at <0,r,0> at <0,0,r> Electic Field Point chage: E " ˆ Unifomly chaged sphee: E sphee E sphee " Q ˆ fo >R (outside) fo >s : E " s 3,, at z y s + x Dipole moment: p s E E s "#,, 3 s "#,, 3 at