Surface properties of nanoparticle

Transcription

1 Sufac popts of nanopatcl th sufac of suspn nanopatcls s lctcally chag n many cass count ons a asob onto th sufac, mo o lss to compnsat th lctcal chags th lay of sufac chags th lay of count ons mol of th lctochmcal oubl lay on th patcl sufac Ogn of sufac chags: O O O O S S l O O O O lattc fcts by substtut atoms asopton of ons onto sufac of th sol patcl asopton of molculs wth functonal goups whch hav lctcal chags an/o a ssocabl chmcal.g. ac / basc actons on th sufac of th sol patcls.g. by ssocaton sol patcl BaSO BaSO Ba Ba Ba Ba sol patcl

2 Mchansm of spson pptaton an stablsaton Stablsaton of nano - s ttanum o O - OH OH O -- T O - OH - OH T bas OH H ac OH T OH O - OH OH c / basc actons on sufac of sol patcls by ssocaton Zta - potntal of TO angng fom mv to mv ph < 3. of mtal o nanopatcls ttanum o

3 Inn an out Hlmholt lay.g. ngatvly chag sol nanopatcl Nnst - potntal aft patcl fomaton / suspnng an asopton of ngatvly / postvly chag count ons onto th patcl sufac whl asobng anons lost th hyat nvlop, van Waals focs omnats nn Hlmholt - lay postvly chag cat ons a boun onto th ngatv mono lay of anons, lctostatc an van Waals focs omnat out Hlmholt - lay nn an out Hlmholt - lay Stn - lay Stn - potntal

4 Gouy - hapman lay.g. ngatvly chag sol nanopatcl boun count ons n th Stn - lay compnsat th lctcal chag of th sol patcl only patally fo a whol chag compnsaton of patcl sufac th s th n of mo count ons conton of lctcal chag nutalty count ons fom a ffusv clou aoun th patcl, count ons can mov npnntly, concntaton of count ons gows n cton to th patcl sufacs Gouy - hapman lay bgns on th fm boun Stn - lay an ns n th nfnt totally compnsaton of patcl sufac chag

5 Hlmholt mol Gouy-hapman mol Stn mol 3 Stn lay Stn - lay Gouy - hapman lay ngatvly chag patcl sufac nn Hlmholt lay 3 out Hlmholt lay 879 Hlmholt 9, 97 Gouy, 93 hapman 3 9 Stn

6 lctochmcal oubl lay mol ngatvly _ chag _ patcls Gouy - hapman lay Nnst potntal ψ φ Stn lay sha plan Stn potntal Zta potntal φ S ψ S ζ Z P φψ S / / δ ffus lay stanc

7 lctochmcal potntal a potntal s th wok n fo tanspotng a chag fom th nfnt to a fn plac v by chag a sufac potntal of a suspn patcl s a potntal on th sufac n compason to th nfnt n a suspnson th s th conton of lctcal chag nutalty, that mans th absolut potntal can b tmn φ φ S φ stanc fom patcl sufac φ Nnst potntal φ nn Hlmholt potntal ncas by asob anons φ S out Hlmholt potntal low by asob catons Stn potntal

8 lctochmcal potntal lctcal nutalty of chags n nfnt stanc fom patcl fo pactcal calculatons : th thcknss of th lctochmcal oubl lay s th Dby lngth δ к th cas of th potntal to / of th sufac potntal ϕ ϕ S p δ κ mt δ κ ε N ε k T c wth φ S Stn potntal ε absolut lctc constant φ potntal at stanc ε latv lctc constant stanc fom th patcl sufac k Boltmann constant δ к Dby lngth lmntay chag N vogao constant c concntaton of ons T tmpatu valnc of ons

9 How to uc th lctochmcal potntal ncasng lctolyt concntaton ucng Dby lngth ncasng on valnc ucng Dby lngth stablsaton of suspnson.g. wth aton of 3 o l 3 ons potntal ε ε k T δ κ N c compsson of ffus oubl lay van Waals attacton hgh than lctostatc pulson φ φ S φ φ S / lctolyt concntaton stanc fom patcl sufac n mol / L 3 Dby lngth δ κ of ffnt typs of lctolyts n nm,,,, Gouy-hapman lay a n nm fo ffnt salt typs n wat at 98 K

10 Dtmnaton of th sufac potntal of nano patcls masuabl potntals potntal at th sha plan ta potntal stn potntal masung of lctcal potntal : ζ - potntal φ φ S potntal sha ons wth ffnt sha vlocts suspn patcls sms to b nutal, chags of th ffus oubl lay a compnsat by a splacmnt of a pat of th chag clou ass a masuabl potntal ffnc φ sha focs caus by ffuson only a too low, th s th n of a hgh sha vlocty φ S / a movng of th complt oubl lay s mpossbl, only appomatly th Stn potntal masuabl stanc fom patcl sufac

11 Dtmnaton of th ta - potntal fo nanopatcl chaactsaton Zta potntal: lctcal potntal of a chag patcl at th shang plan chag patcl n moton caus by an lctcal fl o by ffuson loss a poton of ts count ons of th lctcal oubl play It s assum that th ta - potntal cospons to th Stn - lay potntal Masumnt of th ta potntal: tmnaton of th lctophotcal moblty Hlmholt Smoluchowsk quaton: ζ v η ε ε ζ ta - potntal lctcal ntnsty v patcl vlocty η vscosty ε ε lctc constant

12 Stcal stablsaton of nanopatcls on th sufac th a polyms wth hyophlc goups, polyms fom shot has towng nto th spsant stablsaton ntopc ffcts, numbs of possbl confguatons woul b low by coagulaton ngtc ffcts, polyms hav n th spsant a low ngy contnt than bng n contact ach oth

13 lctostatc stablsaton of nanopatcls DLVO thoy: vlop by Dagun, Lanau, Ovbk an Vwy combns van Waals attacton an lctostatc pulson focs Bos Dagun Lw Lanau vt J.W. Vwy J.T.G. Tho Ovbk B. Dagun, L.Lanau 9: Thoy of th stablty of stongly chag lyophobc sols an of th ahson of stongly chag patcls n solutons of lctolyts, cta Phys. hm. USSR, 633.J.W. Vwy, J.T.G. Ovbk 98: Thoy of th stablty of lyophlc collos. Th ntacton of sol patcls havng an lctc oubl lay, lsv Publshng ompany

14 Stablsaton of sps systms a suspnson of nanopatcls s thn stabl, f pmay patcls stay solat th stablty s nflunc by th ntacton of attactv an pulsv focs attactv van Waals focs spson focs nuctv focs pol - pol focs - - δ δ - δ δ - δ - δ pol nonpola molcul pol pol - - fast lcton motons la to chag fluctuatons δ δ - δ δ - pol nuc pol lctostatc attacton btwn patal chags wth ffnt algbac sgn

15 Stablsaton of sps systms bnay systm of ntactng patcls: van--waals ntacton thos: a Lonon-van--Waals attacton - Lonon 93, Hamak 937 classcal mcoscopc appoach Lonon: atom - atom a: cnt-to-cnt stanc Hamak: patcl - patcl att a a 6 mt π ε α μ Dby μ 3kT Ksom 3hν α Lonon att a v N N v 6 a atoms cm 3 att 6 SLS ln π N Hamak mt N N ρ M SLS SS L SL SL SS L SS L b Lfscht 956 macoscopc appoach fo - lctomagntc popts of ma ε statc lctc constant 3 ε S ε L ε S ε 3 h L ε S ν ε ν L S LS kt ν ε ε ε ε π ε ν ε ν ε ν ε at magnay fquncy S L S L ν S L contbuton of th fluctuatng, nuc pols Ksom, Dby contbuton of spson quantum mchancs

16 Stablsaton of sps systms bnay systm of ntactng patcls: van--waals ntacton ngy sph - sph sph - plat plat - plat S S sph-sph: att 6 SLS ln fo a clos appoach << : fo : sph-plat: att 6 SLS att SLS att 6 SLS ln plat-plat: fo a fnt thcknss δ P : fo a nfnt thcknss: att SLS π δ P δ P att SLS π

17 Stablsaton of sps systms Hamak constant SLS pns on matal: sol S - lqu L - sol S att SLS SLS SS L SL SL SLS SS L SS L S S S S L L Xylol can stabl suspnsons spsng agnt SLS SS L f S S L follows SLS no attacton Hamak mtals J constants: os J halogns J ogancs J toluol 5. - J p..7 - J cal. n vy cas attacton S S L > f S > L > S SLS coul b ngatv! van Waals foc s pulsv that s only thoy!!! Hamak constant pns only on th matals, but not fom gomty!

18 Stablsaton of sps systms pulsv Bon foc caus by asopton of wat hyat clou aoun th patcl o oth lqus ngy s n to mov th covng lqus nflunc of Bon pulson on th stablsaton of nanopatcls s low pulsv lctostatc foc nflunc by th changng of th Dby lngth ϕ εε k T p mt δκ ϕs δκ N c φ S Stn potntal φ potntal at stanc stanc fom th patcl sufac δ к N Dby lngth vogao constant k Boltmann constant T tmpatu ε ε c absolut lctc constant latv lctc constant lmntay chag valnc of ons concntaton of ons

19 Ovvw: ppoach an Soluton of th Posson-Boltmann quaton ϕ ρ ² ϕ ² N ² ε ε ϕ p kt Posson quaton Boltmann stbuton ϕ ² ² ε ε N, ϕ p kt N, ² ² ϕ Lnas Posson-Boltmann quaton Dby aus: δ κ I ² ϕ ε ε kt ε ε kt N ²I c ² N, ² Posson-Boltmann quaton ϕ p πε ε [ κ a ] κ a fo nanopatcls wth a, s cnt-to-cnt stanc p κ a ϕ πε a ε πεε κ ontbuton of th cntal on an th on clou Lnasaton: p ϕ << kt N,! κ - s th Dby lngth

20 DLVO - thoy Stablsaton of sps systms Intfnc of attactng an pulsng ntactons: fo a systm of two sphs of th a an th ntacton ngy T a att a p a wth a bng th sufac-to-sufac stanc Dagun 93: Lna supposton appomaton LS - ntacton ngy p a btwn two closly spac sphs π pa vp mt vp potntal ngy p unt aa pa vp wth > 5 an a << κ a fo th att a attactv van--waals ntacton ngy an p a pulsv lctostatc potntal ngy of th oubl lay π T a SLS 6a 8π c, N κ kt Γ Γ κ a N c κ ε ε kt an Γ ϕs p kt ϕs p kt tanh ϕs kt van--waals attacton lctostatc pulson ϕs p kt Γ ϕs p kt ϕs tanh kt

21 potntal Stablsaton of sps systms lctostatc pulson Bon pulson aton of actng potntals potntal ba van Waals attacton stanc fom th patcl sufac aton of actng potntals nclung Bon pulson

22 Intacton ngy stanc pofls fom DLVO thoy a stong pulson of sufacs nanopatcl suspnson s stabl b sufacs com nto a stabl qulbum na th scon mnmum, f p nough suspnson s kntcally stabl c sufacs com nto th scon mnmum, slow coagulaton of nanopatcls ctcal coagulaton concntaton ccc: sufacs stay n th scon mnmum, o coagulat, fast coagulaton of nanopatcls fast coagulaton of nanopatcls

23 DLVO - thoy an Schul - Hay ul Stablsaton of sps systms ctcal coagulaton concntaton ccc s cpocal popotonal to 6 th pow of on valnc at th ccc fo th ntacton ngy s val: T a an T a a 8π kt Γ SLS, κ a 6a κ c N Γ SLS 6a 8 π c, N κ kt Γ Γ κ a o a a κ a a a T att p att a N pa follows a κ κ ccc ε ε kt ccc 9.85 ε N 3 ε 6 5 kt 6 SLS Γ Γ ϕs kt ϕs kt >> << Γ ccc 6 ϕs Γ Γ ccc kt Dby Hückl appomaton : : :.6 :.5 : : 3

24 lctochmcal oubl lay Posson-Boltmann quaton - Basc appoach statng fom Posson s an Boltmann s quaton Mawll: lctostatc potntal,y, v D, y, D ga, y, v D, y, f vgnc opato lctc splacmnt lctc 8.85 chag fl pmttvty vacuum, mum / m v ga, y,, y, v ga, y,, y, Posson s quaton: fl nsty v,y, ga,y,,y, y lctochmcal qulbum btwn NP an all ons G S T V P ~ I n Q W Q aaay cons tant N 96,85.3 / mol ~ II ~ wth T,P ln, y, ~ T,P ln, y, l n Boltmann s quaton: ~ an nt gaton of T,P, y,, y,, y, follows fom to ln, y,, y, an fom bulk concntaton to, y, p Posson-Boltmann s quaton:, y,, y, on valnc p possblts to solv PB quaton:, y, s a non-lna patal ffntal quaton - no analytca soluton, but appomatons.g. Dby 3,y, s small p!! 3!,y, fo p ch ag nutalty lnasaton possbl

25 lctochmcal oubl lay q : potntal oulomb fo D ansat p p thus, p p p p T k T k p countons of ch ag lctc NP of ch ag lctc Posson-Boltmann quaton - Dby-Hückl s appomaton,y,,y, an,y,,y, p y,, p,y, Lna PB quaton: T k wth y,, y,, T k y,, cntal NP aus at th ogn, lctc fl has sphcal symmty, thus lna PB quaton as: p thus, p B follows an as fo p B p ansat ns th cntal NP < Laplac s quaton s val

26 lctochmcal oubl lay Posson-Boltmann quaton - Gouy - hapman s appomaton D an fo D : fo Soluton of PB quaton fo chag plans: p obvously, S II I an ln : thus ln T,P ~ wth ~ ~ : stat w p gvs gaton nt p p p p p fo a symmtc : lctolyt follows p p snh wth p p p p snh 8

27 Posson-Boltmann quaton - Gouy - hapman s appomaton - Gaham quaton sufac ch ag nt gaton suf Gaham quaton suf 8 8 snh, u sn g snh substtutng, thus snh snh u wth u follows nt gaton las to snh u ln tanh u ln tanh 8 snh snh Mathmatcal hnt : snh snh f ln f, thus f tanh p tanh, actanh snh cosh snh ln cosh cosh ln tanh, at th sufac : p ln p tanh cosh tanh ta potntal Intacton ngy btwn two nanopatcls Quston: Why o w hav a pulson foc btwn lctcally qual chag nanopatcls? Plas mmb, th oppost lctcally chag count-ons a scnng th chag of th cntal nanopatcl. nsw: Whn th onc oubl lays stat to ovlap, th s an css of ons n th ovlap gon spct to th lctochmcal potntal. To compnsat ths, an osmotc pssu vlops btwn th bulk soluton an th ovlap gon.

28 Intacton ngy btwn nanopatcls - osmoss an osmotc pssu Osmoss: ffuson of solvnts though a smpmabl mmban nto a gon of hgh solut concntaton ntal stat H O tanspotaton fnal stat H O tanspotaton chmcal potntal of th solvnt l at th ntal stat fo osmotc pssu P P P nt gaton : l l phas P P P l l P appomaton : ln X l l P ln X l P ln X, wth X pu solvnt follows : l P l P ln X G V l S T V P P T const. n n n V n V n ln P P P, phas as : thus ln X X ons X ons Osmotc pssu: ntal stat fnal stat ΔP osmotc pssu : V ovlappng potntal btwn two nanopatcls l ln D ovlappng potntal sufac potntal suf X H O tanspotaton H O tanspotaton lctostatc potntal of sngl ovlappng nanopatcls as flat plans

29 Intacton ngy btwn nanopatcls - pulson pssu u to osmotc pssu calculaton of osmotc pssu ΔPD: pulsv pssu P P D P D wth p p wth P snh P bulk D at p p p p snh p p p a patcl s tan c D : p p osmotc pssu n th ml plan compa fo a symmtcal : lctolyt : s calculaton fo to bulk flat pssu plan th s tanh fo tanh, s Gouy hapman thoy 3 compa : tanh 3 5 p wth snh cosh snh cosh 6 D cosh! sufac cosh follows! p,! p s tan c btwn 5 an fo D NPs ta, D potntal p follows fo, wak ovlap appomaton : at, ovlappng s th sum of ach of sngl NPs! nt acton W D ngy p sufac aa D 6 P D D : p D

30 Intacton ngy btwn sphcal nanopatcls - Dagun appomaton ntacton ngy btwn sphcal NPs wth a an D an follows an fo, D thus, : tangl gn Pythagoa n thom on D D p 6 D D P P D wth P P D D D kt c N an kt tanh kt p kt p kt tanh kt p kt p wth 8 6 a a a s th stanc btwnth sphs: an a btwntwo sphswthth a totalntactonngy 8 a potntal ta, tanh potntal ta, tanh potntals: wthffntta 8 D D a, a btwntwo sphswtha pulson ngy plans flat pulson ngy p sufacaaof D a SLS T T a p a D p p pulsv foc btwn sphcal NPs: D y annul -