MODELING OF THE LASER METAL NANOPARTICLES FRAGMENTATION

Transcription

1 MATHEMATICA MONTISNIGRI Vol XXXI (014) MODELING OF THE LASER METAL NANOPARTICLES FRAGMENTATION I.N. ZAVESTOVSKAYA 1,, A.P. KANAVIN 1, 1 P.N. Lbdv Phyical Ititut, RAS, Mocow, , Ruia Natioal Rach Nucla Uivity MEPhI, Mocow, , Ruia Abtact. Th pap coid a phyical modl of mtal aopaticl fagmtatio i liquid ud th actio of fmtocod la pul at th xampl of gold paticl i wat. Th modl i bad o th lctolizatio of mtal aopaticl hatd by a la pul, ad thi diviio ud th dvlopmt of itability of a chagd dop of liquid mtal. Th poc of hot lcto miio fom th ufac of a aopaticl ad futh olvatio i liquid ha b tudid. Th citical fagmtatio paamt, amly a paticl chag, ha b dfid. 1 INTRODUCTION La aotuctuig of matial i impotat i may citific, tchological ad mdical applicatio [1-4]. Of pcial itt a th mtal aopaticl, i paticula th gold o. Thi uiqu optical popti timulat th ach of poibl applicatio i optic, photoic, ad biomdici [5-15]. All th mthod of poducig aopaticl may b covtioally dividd ito two goup: wt chmity i.., th chmity uig liquid compot [16,17] ad dy poc i.., th poc with th u of plama dichag o tho that mak u of th ythi of th dd poduct i flam, a wll a th matial vapoatio ud th actio of a la pul. La ablatio ha maiftd itlf a o of mot ffctiv phyical mthod of aofabicatio [18-5]. Howv, th la mthod fom ath lag-izd aopaticl with a wid iz pctum. I thi coctio, i od to duc th iz of aopaticl thi colloid a additioally tatd by ultahot la pul [5-8]. Th mchaim of la aopaticl fagmtatio i liquid ha ot b much tudid ad th i o cou o thi poblm. Thy am th followig poibl mchaim: th hydodyamic itability of th mltd mtal dop aiig du to it itactio with th liquid vapo [5]; th vapoatio of gold atom ud hatig th aopaticl by la adiatio [6]; th Coulomb xploio [7,8]. A phyical modl of gold aopaticl fagmtatio i wat ud th actio of fmtocod la pul i ptd i thi pap. Wh th colloid of lativly lag gold aopaticl (val t of m) a iadiatd by fmtocod la pul, o ca obv thi fagmtatio ito mall aopaticl (up to val m). I th poc th paticl i hatd up to th mltig tmpatu ad tu ito a dop of liquid. Th hatig i accompaid by thmioic miio fom th dop ufac. Th mittd lcto tak away th gativ chag, ad th dop of mltd mtal tu to b poitivly chagd. Thu th modl of fagmtatio i bad o th lctolizatio of mtal aopaticl hatd by a la 010 Mathmatic Subjct Claificatio: 8D80, 81T80, 37N0. Ky wod ad Pha: Naopaticl fagmtatio, fmtocod la pul, olvatio, paticl chag. 78

2 pul, ad thi diviio ud th dvlopmt of itability of a chagd dop of liquid mtal. A a mchaim of lctolizatio w hav coidd th miio of hot lcto fom th ufac of a aopaticl with futh alvatio i liquid. Th poblm of gold paticl hatig at fmtocod la pul aboptio ha b olvd. Tim dpdc of lcto thmioic miio cut fom th paticl ufac ha b foud. Th paticl fagmtatio paamt ha b dfid. Th timat a giv of aopaticl chag gaid ud th actio of th la pul i wat. EXPERIMENTAL RESULTS La ablatio i a ffctiv mthod of aofabicatio. Th mthod pt a ablatio of a olid tagt by tog la adiatio, ad thi lad to th jctio of th tagt compot, ad fomatio of aoclut ad aotuctu. Gally, th iz ad tuctu of aoobjct poducd with th hlp of la ablatio a iflucd by th followig facto: Th la adiatio chaactitic: itity, pul duatio, ad th wavlgth. Tagt matial popti: aboptio at difft wavlgth, th mltig, vapoizatio ad cytallizatio tmpatu. Th viomt popti: vacuum, ga, liquid. Wh la adiatio i focud oto th olid tagt ufac th tak plac th aboptio of th la gy, which ult i thmal ad othmal hatig of th tagt matial, mltig ad ablatio of th matial i th fom of atom ad aoclut. At th am valu of la itity th ma of paticl poducd by ablatio dpd o th amout of gy abobd fom th la pul. Mico- ad aocod pul cotai mo gy a compad to pico- ad fmtocod o, ad thi mak th ablatio with log pul mo ffctiv to poduc a gat ma of paticl. Howv, o hould ot that ultahot pul ablatio lad to th jctio of paticl of high gy du to high itity of th la pul. Tagt la ablatio may b accompaid by hot plama fomatio. If th plama i poducd a th tagt, it may dca th fficicy of gy taf to th tagt ufac, a wll a giv i to coday ablatio of th matial du to th tagt hatig o cavitatio phoma (i liquid mdia). Th ffct a wll illutatd i [1], i which th autho tudid th dpdc of th iz of aopaticl poducd i wat o th poitio of th focal pla of th l focuig th la adiatio lativ to th tagt ufac. Th poducd aopaticl may b dvidd ito two goup: aow-dipd (paticl avag iz, 10-0 m) aopaticl ad wid-dipd o (paticl avag iz, m). Th autho attibut th oigi of th fit goup to th ablatio du to th la itactio with tagt matial, ad th cod goup i a ult of itactio with th poducd plama. It wa foud that th poducd plama itity colat with th amout of ablatd matial, a wll a th avag iz of aopaticl latd to th wid-dipd goup. Th autho aum that plama hatig of th tagt o mchaical tagt dtuctio du to th collap of plama-iducd cavitatio bubbl a poibl mchaim of coday ablatio coctd with plama. If th tagt i ablatd i vacuum o ga mdium, th aoclut may b tapotd to a ubtat locatd at om ditac fom th tagt ad fom a aotuctud film. Ablatio i 79

3 liquid (.g., wat olutio) lad to th jctio of aopaticl ito th viomt ad to th fomatio of colloidal olutio. Ablatio i liquid mak it poibl to obtai pu aomatial, which a f of ufac cotamiatio typical of chmical mthod. Naopaticl obtaid i a pu wllcotolld mdium a pcially impotat fo th applicatio i vivo biodtctio ad viualizatio. Ablatio i liquid ha a umb of pcific fatu, amly: Th pc of a optical bakdow i a d mdium, which abob a igificat pat of la gy (typical tim up to 50 μm); a ffctiv taf of gy fom th la plama to th ambit liquid ad fomatio of a cavitatio bubbl that i gowig up to μ ad th collapig yildig a lag amout of mchaical gy; Aboptio of a icidt la adiatio by poducd updd aopaticl. May cau vaiou ffct: coday ablatio of th matial [9], fagmtatio of colloidal paticl [30], fomatio of complx chmical tuctu [31]. Th pc of lf-focuig phomo ad gatio of a cotiuum fo ultahot pul. I paticula, th filamtatio may tak plac wh ultahot la pul pa though th optical mdium, ad appa a a ult of a balac btw th la pul lf-focuig ad d-focuig ffct of th plama poducd ud high la itity i lf-focuig aa [3]. La ablatio i liquid i a ffctiv mthod to poduc aopaticl i th fom of colloidal olutio. O hould ot that at ablatio i wat o oth olutio ud th abc of chmically activ compot th poducd aopaticl a of ath lag iz. Thi i aociatd with th coagulatio ad agggatio of atom ubjctd to ablatio. Naocod la pul, fo xampl, giv th paticl of m i iz ad m dipio [33]. Ultahot la pul ablatio off btt chac to cotol th iz ad dipio of aopaticl. A poibility to cotol ffctivly th aopaticl iz by chagig th th la flux dity (F) ha b how i [3]. Th iz of aopaticl vaid fom 4 to 10 m wh F chagd fom 60 up to 1000 J/cm. Two populatio of aopaticl hav b poducd i th xpimt. Th fit o wa poducd ud low dity of th la flux ad icludd th paticl of mall iz ad aow dipio. At avag F valu both populatio w obvd. At high F th paticl had lag avag iz ad wid dipio. Th mtiod populatio a imila to tho poducd i th xpimt o chagig th poitio of th focal ufac of a focuig l dicud abov. So, o ca coclud that difft mchaim a poibl fo th occuc of ach of th populatio: th ablatio du to th icidt adiatio ad ablatio du th ffct caud by plama fomatio. To cotol th iz of poducd aopaticl th wat olutio of ufac-activ agt a ud fqutly, fo xampl, odium dodcyl ulfat, which cov th aopaticl jut aft th ablatio ad pvt futh agglomatio [34]. A dawback of th mthod li i th fact that th aopaticl covd by ufac-activ agt hav o f chmical bod, ad th aa of it futh applicatio i limitd. Pap [14] pt th ult fom th xpimt o th ablatio of gold i wat olutio cotaiig utal α-cyclodxti, β-cyclodxti, o γ- cyclodxti. A Ti/apphi la wa ud i th xpimt (pul duatio, 110 f; wavlgth, 800 m; 80

4 pul maximum gy, 1 mj). A hap dca i th iz of aopaticl wa obvd i compaio with th xpimt i wat. Th aopaticl poducd at ablatio i th olutio of β-cyclodxti (10 mmol) had th avag iz.1-.3 m, th dipio did ot xcd 1 m. Th olutio wa of atuatd d colo. Th poducd colloid tud to b vy tabl. To mak mall th aopaticl poducd by ablatio i a liquid mdium th colloid a additioally tatd by ultahot la pul. I [7] th 11±5 m aopaticl w poducd by la ablatio of a gold plat i a odium dodcyl ulfat olutio. Th, uig a pay, th colloid 80 μm doplt w poducd ad ubjctd to tuctual chag with th hlp of igl aocod la pul (wavlgth, 53 m; pul duatio, 10 ; pul gy, 30 mj). Th xpimt ultd i obtaiig th aopaticl of 3.7 m avag iz. Th autho aum that, a a ult of la gy aboptio, aopaticl a hatd up to th tmpatu of mtal mltig, ad th a ioizd du to thmal miio. Th lcto mittd fom th paticl ufac a tmpoaily olvatd i wat. A a ult, a multiply chagd gold aopaticl bcom utabl ad fagmtd owig to th Coulomb xploio. A imila caio of fagmtatio i coidd i [8]. At th fit tag th 8±5 m aopaticl w poducd by ablatio of a gold plat i odium dodcyl ulfat olutio. Th, th aopaticl w ubjctd to la adiatio (th wavlgth, 355 m; pul duatio, 10 ; pul gy, 50 mj; pul ptitio at, 10 Hz). Th aopaticl ducd i iz to 1.5 m. I [15], a a ult of gold hll ablatio i pu dioizd wat th poducd gold aopaticl had a avag iz of 55 m ad 34 m dipio. At th cod tag, th obtaid colloid w ubjctd to la iadiatio with th followig chaactitic: (pul duatio, 140 f; wavlgth, 800 m; pul gy, 500 mj; pul ptitio at, 1 khz). Aft 30 miut of iadiatio of th colloid, th avag iz of aopaticl ducd to 11±5 m. Figu 1 ad illutat iz ditibutio of aopaticl bfo ad aft iadiatio. Ud futh tatmt (up to two hou) th aopaticl avag iz icad gadually, ad fially tabilizd at 0-30 m. Th obtaid colloid dmotatd xcllt tability up to val moth. Th autho coid th aopaticl fagmtatio to b a coquc of Coulomb xploio. Oigially th iz of aopaticl duc haply du to th aboptio of th icidt 800 m la adiatio. Futh dca i caud by aboptio of gy fom th whit cotiuum, which occu du to olia optical itactio btw th icidt adiatio ad mdium. A abc of aopaticl of itmdiat iz v at a vy hot tim of iadiatio pak i favo of a cocpt of Coulomb xploio. Th pc of uch paticl i typical fo aopaticl iz ductio du to thmal vapoatio of matt. I [6] th colloid of gold 5-50 m aopaticl w obtaid by th mthod of chmical ductio. Lat, a la with th wavlgth of 53 m, pul duatio 7 ad flux dity 10 mj/cm wa ud i th xpimt o aopaticl iz ductio. Th tim of la iadiatio wa 10 miut. A a ult, th aopaticl havig th iz of 0 to 50 m diappad, ad th umb of aopaticl of th iz up to 10 m haply icad. TEM pictu of aopaticl bfo ad aft la iadiatio a how i Fig

5 Fig. 1. TEM pictu of Au aopaticl poducd by tagt ablatio i wat. Siz ditibutio of aopaticl. Fig.. TEM pictu of Au aopaticl aft 30 miut of iadiatio by fmtocod la pul. Siz ditibutio of aopaticl. Fig. 3 TEM pictu of Au aopaticl bfo (a) ad aft (b) 10 miut of la iadiatio; th la flux dity 10 mj/cm - 8

6 Th ifluc of la iadiatio tim ad la flux dity o aopaticl iz ditibutio wa alo tudid i th pap. At a fixd la flux dity of 140 mj/cm, th maximum iz of aopaticl aft 5 miut of iadiatio wa m. Futh iadiatio did ot chag thi valu, ad thi how that aopaticl maximum iz valu may b coidd a a ctai thhold valu. Wh la flux dity icad fom 30 up to 500 mj/cm, th wa obvd a dca i aopaticl maximum iz. Th autho uggtd a a mchaim of aopaticl iz ductio th vapoatio of Au atom ud aopaticl hatig by la adiatio up to th tmpatu xcdig th gold mltig tmpatu. A poibility to duc th aopaticl iz by ma of la tatmt ha b dmotatd fo ilv a wll [35]. Th colloid of ilv m aopaticl w obtaid by th mthod of chmical ductio of AgNO 3 i wat with a additio of odium citat at a tmpatu clo to th boilig tmpatu. Th, th poducd aopaticl w ubjctd to la adiatio: pul duatio, 18 p; wavlgth, 355 ad 53 m; pul gy, -3 mj. A a ult, 5-10 m aopaticl w poducd. It wa tablihd that th choic of la wavlgth affct th lctivity of clut fagmtatio. Fo xampl, wh th wavlgth wa chagd fo 53 m, th wa obvd th fagmtatio of lag aopaticl oly, o igula-hapd aopaticl. Th autho tatd that th tak plac a lcto photomiio a a ult of la actio o ilv aopaticl. Th aopaticl bcom chagd ad diitgat ito th mall o. 3 THEORETICAL MODELING Th pap a availabl which coid vaiou apct of la itactio with mtal aopaticl. Pap [36] i dvotd to umical imulatio of th itactio btw hot la pul ad gold aopaticl i wat. Th autho mad u of a hydodyamic modl, which dcib, with th hlp of Navi-Stok quatio, th hat ad ma taf i th ytm, ad iclud th quatio of tat (EOS) fo wat, two-tmpatu dciptio of lcto-phoo quilibium i a mtal aopaticl, a wll a th dciptio of thmolatic po of th paticl matt. Th modlig wa mad fo modat la flux (F < 100 J/m ), wh th tmpatu i low o lightly high tha th citical tmpatu i wat; aopaticl adiu li withi th limit 5-00 m; pul duatio i p. It wa foud that iadiatio of aopaticl by fmtocod la pul ult i a popagatio of a compio wav i th dictio fom th paticl, ad th width of th wav dpd o th vicoity ad hat coductivity of th ambit liquid. Fo 50 m aopaticl iadiatd by 00 f la pul ad F = 60 J/m, th vapo fomatio o th ufac of th paticl tat at t 3 p, ad th vapo lay i poducd up to th tim t 84 p. It wa tablihd that a total amout of vapoatd matt mai lativly mall, ad th ffct ofvapo fomatio o th tmpatu pofili iigificat. Th wat tmpatu a th aopaticl ufac ach th boilig tmpatu at flux dity of 18 J/cm, ad th citical tmpatu at 7 J/cm. At high flux th i obvd a cotiuou taitio fom liquid to th vapo without vapo-liquid commo xitc a th ufac of a aopaticl. Pap [37] pt a kitic thoy of la-mtal aopaticl itactio i a matix of a wid-bad dilctic (SiO ). Th fomalim i bad o Boltzma quatio fo th lcto of a op ytm adaptd to th dciptio of aopaticl lcto lo owig to 83

7 thmioic miio ad photolctic ffct. Th imulatio of gy taf ad ditibutio a ptd, a wll a tho of lcto miio withi th famwok of th tudy ito th dtuctio poc ultig fom la-gold aopaticl itactio i a SiO matix. Th calculatio w mad fo 1.3 m ad.6 m aopaticl i SiO matix iadiatd by 351 m la pul with pul duatio 0.5 ad 50 p, ad flux dity 0.3 J/cm ad 0.15 J/cm, pctivly. It wa how that ud uch gim a coidabl umb of lcto ca b jctd fom th aopaticl du to thmioic miio. I both ca th lcto ffctiv tmpatu i aoicluio achd atuatio at > 1V ( К), ad th gatig tmpatu wa lativly low (60К ad 390К, pctivly) du to gy taf to th aambit gla ad th miio of high-gy lcto. Pap [38] pt a modl which allow o to dtmi th dyamic of lcto ad io tmpatu i a gold aopaticl dippd ito dilctic of a fiit volum ud th actio of ubpicocod la pul. Th modl i bad o a two-tmpatu modl dtid fo th calculatio of aopaticl tmpatu ad ballitic-diffuio appoximatio (BDA) fo th timatio of hat taf fom th paticl ad it popagatio i a dilctic viomt. Th modl wa applid to gold 10 m aopaticl i Al O 3 hll, ad th hll thick vaid fom 0.54 to 54 m. Th la pul duatio cotitutd 110 f. Tim dpdc of lcto ad gatig tmpatu w foud with th hlp of Foui law ad BDA fo 5.4 m thick hll. W coid uch caio of gold aopaticl fagmtatio i wat ud th actio of fmtocod la pul. Wh th colloid of lativly lag gold aopaticl (val t of m) a iadiatd by fmtocod la pul, o ca obv thi fagmtatio ito mall aopaticl (up to val m). I th poc th paticl i hatd up to th mltig tmpatu ad tu ito a dop of liquid. Th hatig i accompaid by thmioic miio fom th dop ufac. Th mittd lcto tak away th gativ chag, ad th dop of mltd mtal tu to b poitivly chagd. Thu th modl of fagmtatio i bad o th lctolizatio of mtal aopaticl hatd by a la pul, ad thi diviio ud th dvlopmt of itability of a chagd dop of liquid mtal. A a mchaim of lctolizatio w hav coidd th miio of hot lcto fom th ufac of a aopaticl with futh alvatio i liquid. Th poblm of gold paticl hatig at fmtocod la pul aboptio ha b olvd. Tim dpdc of lcto thmioic miio cut fom th paticl ufac ha b foud. Th paticl fagmtatio paamt ha b dfid. Th timat a giv of aopaticl chag gaid ud th actio of th la pul i wat. To dvlop a phyical modl ad optimiz th gim of la iadiatio fo poducig aopaticl o d to olv th followig poblm: Th poblm of aopaticl hatig ud th actio of la adiatio; Fid th cut of lcto thmioic miio fom th ufac of a aopaticl; Calculat th fagmtatio paamt fo gold aopaticl; Evaluat th chag gaid by th aopaticl a a ult of thmioic miio ad lcto alvatio 4 THE PROBLEM OF NANOPARTICLE HEATING A two-tmpatu modl [3] ha b ud to olv th poblm of mtal aopaticl hatig by fmtocod la pul: 84

8 C C ph T div t Tph = g t P ( λ gadt ) = g( T T ) ( T T ) T, i th lcto ubytm tmpatu; T ph, th phoo ubytm tmpatu; С,, th lcto ad phoo hat capacity; g, th facto of lcto-phoo couplig, C ph which dcib th at of gy xchag btw th lcto ad th lattic; λ, th cofficit of hat coductivity; P, th la adiatio pow abobd by a aopaticl; V, th aopaticl volum. Each of th quatio pt th gy covatio law. Th quatio fo th lcto illutat th chag i thi tmpatu du to th hat taf to th phoo, ad la adiatio ad la adiatio aboptio. Th phoo tmpatu chag oly du to th hat xchag with lcto, ic th phoo do ot abob th la adiatio. O ca u a appoximatio of homogouly hatd aopaticl fo th aopaticl with th adii mall tha th ditac covd by th hat fom th icidt adiatio duig th pul actio. Th ditac covd by th hat duig th pul i: l = χ τ, ph υ F χ = 3ν wh τ i th pul duatio; χ th tmpatu coductivity of th mtal lcto ubyt; υ F, th Fmi vlocity; ν, th fqucy of lcto colliio. Fo th mtal th lcto colliio fqucy coit of th lcto-phoo ad lcto-lcto colliio. Th gatig tmpatu При температурах решетки T big high tha Dby tmpatu Θ D (fo Au Θ D = 170K ), th fqucy of lcto-phoo colliio i popotioal to T ph. Wh th lcto thmal gy k BT i all tha Fmi gy ε F, th fqucy of lcto-lcto colliio ν dpd quadatically o th lcto tmpatu. Baig thi i mid, lt u glct th cotibutio of lcto-phoo colliio ad coid 14 ν v. At ν = , υ F = cm/, w gt χ = 70 cm/. At 100 f pul duatio w gt l = 5 m. So, fo th paticl havig th adii mall tha 5 m, o ca glct th thmal flux dictd fom th aa with high tmpatu to th aa with low tmpatu. Fially w hav th followig ytm of quatio: ph V T P C = g( T Tph ) + t V Tph C ph = g( T Tph) t () ph (1) Th iitial coditio: T (0) = Ti Tph(0) = T i 85

9 H T i i th tmpatu of th viomtal aa coidd to b qual to 300K. If th lcto ubytm tmpatu i much low tha Fmi tmpatu (fo Au T F = ), oly th lcto a Fmi ufac a chagd, ad th lcto hat capacityi ptd i th fom of lia tmpatu dpdc: wh = π kb F ( ) ' C T = C T C ε ad i th coctatioof f lcto; k B, th Boltzma cotat; ε F, th Fmi gy. Thotical ad xpimtal ach how that th Au d zo, locatd clo to Fmi lvl, ha a vy complx tuctu. Th lcto of U d zo itoduc igificat coctio ito th umb of thmally xcitd lcto, ad, hc, ifluc th lcto hat coductivity [39]. Th u of lia appoximatio fo tmpatu dpdc of lcto hat coductivity may lad to a tial ovtimatio of lcto ubytm tmpatu i a tat of patial thmodyamic quilibium with th phoo ubytm. Such quilibium i uually alizd ud th actio of fmtocod la pul oto th mtal. Thmally xcitd lcto of d zo alo mak cotibutio ito th itactio btw th lcto ad phoo ubytm. That i why th tmpatu dpdc of g wa tak ito accout i th olutio of th thmal poblm. Figu 4 illutat th tmpatu dpdc of g facto. (3) Fig.4. Dpdc of lcto-phoo couplig facto o th lcto ubytm tmpatu. Dfi th dpdc of lcto maximum tmpatu o th la pul gy dity uig a lia dpdc btw th lcto hat coductivity ad tmpatu. At th tag of hatig by th la pul (100 f) o ca glct th tm poibl fo th gy xchag btw th lcto ad phoo i th fit quatio of ytm (). W gt: T V C = P = σ ab q, (4) t 86

10 wh V i th aopaticl volum; P, th abobd la adiatio; σ ab, th aboptio coctio coidd to b qual to a gomtical coctio π a ; ad a, th aopaticl adiu; q, th la flux. Aft tim itgatio of quatio (4) to th pul duatio w gt th ( 0) atiobtw th lcto maximum tmpatu T o th la pul gy dity F: T (0) = 3 F a C ' (0) Th obtaid dpdc btw th maximum lcto tmpatu T ad la pul gy dity a giv i Fig. 5. A fom th figu, th maximum lcto tmpatu calculatd with th u of lia appoximatio fo lcto hat capacity i twic a much a th o obtaid with accout fo d-lcto cotibutio to hat coductivity. (5) Fig. 5 Elcto ubytm tmpatu v flux dity. Solid li: d-lcto cotibutio tak ito accout; dahd li: lia appoximatio with o accout fo d-lcto cotibutio. At th iitial tag of hatig th lcto ubytm tmpatu i much high tha th tmpatu of phoo ubytm ( T >> T ), ad, o, w may glct th gatig tmpatu i th ytm (): е ph ' T C T = g T t Tph C ph = g T t (6) Th olutio of th ytm (6) ha th followig fom: 87

11 (0) g t (0) t T ( t) = T 1 1 ' (0) = T C T τ c (0) g T t Tph ( t ) = t C ph τ c (7) τ c, th typical tim of lcto ubytm coolig. Fo Au w hav g = W/cm 3 K, C = J/cm 3 K. Fom th fit quatio of th ytm (7) w may timat th typical (0) 4 tim of lcto ubytm coolig: if T 10 К, th τ с 5пс. Figu 6 illutat th ult fom olutio of ytm () ad (6) fo th la pul gy dity 100 mj/cm. Fig.6 Tim tmpatu pofil of th lcto (A,B) ad phoo (C,D) ubytm. Solid li umical olutio; dahd li aalytical olutio. I th calculatio th aboptio co-ctio wa aumd to b qual to th gomtical co-ctio π a, wh а = 100 m i th paticl adiu. A fom Fig.1, aft th d of th la pul th lcto tmpatu ach about t thouad dg, ad th dop lialy duig th tim of t of picocod. Th fial tmpatu of th aopaticl lattic xcd th mltig tmpatu of gold (T=1337 K), i.. th aopaticl i tafomd ito a liquid tat. 5 DEPENDENCE ON THE SIZE OF NANOPARTICLES Th aboptio coctio σ ab fo th aopaticl dpd o thi iz. Th σ ab fficicy of la adiatio aboptio Q ab i dfid a follow: Qab =. Th πa 88

12 dpdc of th fficicy of la adiatio (800 m) aboptio by gold aopaticl i wat i how i Fig. 7. Fig.7. Th dpdc of aboptio fficicy fo fo th icidt la adiatio with λ=800 m. Fo th calculatio w hav ud th pogam packag MatLab [40], bad o th Mi cattig thoy of a pla lctomagtic wav o a homogou ph of adom iz. A fom th figu 7, th aboptio coctio ica with a ica i th aopaticl iz, ad ach it maximum fo th aopaticl with th adiu of about 75 m. Th icidt la gy i abobd by th mtal lcto ubytm ad lad to it hatig. Thi ma that that th chag i th aboptio coctio ud th chag of aopaticl iz ult i th chag of lcto tmpatu. Figu 8 pt th dpdc of lctom maximum tmpatu o th iz of aopaticl fo difft diti of th th icidt la flux obtaid by quatio (4). Maximum tmpatu of th hatd lcto ubytm copod to th aboptio maximum fficicy, ad fall at 75 m aopaticl. Th lcto ubytm taf th gy to th gatig, ad thi lad to th tmpatu gowth. Lt u timat timat th amout of hat H, which i cay fo th H = C T T0 + ΔH, gold aopaticl to b mltd ud th actio of a la pul. Au ( пл ) пл h С Au = 5. 4 J/mol K i th gold hat capacity; T пл, th mltig tmpatu of Au; T 0 = 300K, th iitial tmpatu; H = 3 = 3.8kJ / mol K 37, kj / cm. ΔH = 3 пл J/mol, th mltig mola hat. Th 89

13 Fig. 8. Maximum lcto tmpatu v aopaticl iz fo th la flux dity of 00 mj/cm (dottd li), 50 mj/cm (dahd li), 300 mj/cm (olid li). If o kow th H valu, th, by uig fomula (4) it i poibl to fid th dpdc btw th thhold flux dity of th la flux F th ad th aopaticl iz. Ud th thhold dity of th la flux w ma h it miimal valu dd to taf to th paticl th amout of hat ufficit to mlt it. Fig. 9. La flux thhold dity v aopaticl iz. O ca fom Fig. 9 that th F th valu li withi th limit of 300 to 800 mj/cm fo 100 m aopaticl. Th mall i th aboptio fficicy th mo gy hould b giv to th aopaticl i od to ach th mtal mltig tmpatu. Thi i wll fom a compaio of Fig.8 ad Fig. 9: th gowth of aboptio fficicy copod to th dca i la flux dity. 90

14 6 THERMIONIC EMISSION A thmioic miio fom th ufac of hatd gold aopaticl i obvd. Th valu of lcto thmioic miio cut i dfid by th tmpatu of th mtal lcto ubytm: W j = A T xp( ) kt (8) A H А, i th Richado cotat; A 10, W=5,1 V, th wok of th gold сm K yild; Т, th lcto tmpatu. Fig. 10. Tim pofil of thmioic miio cut. Solid li aalytical olutio, dahd li umical olutio. Fig. 10 illutat tim dpdc of thmioic miio cut fo la fluc F = 100 mj/cm. Maximal dity of thmioic cut i ~ 10 6 А/cm. O ca fom th Fig. 10 that, i accodac with th umical ad aalytical olutio, th cut dop xpotially aft th d of th la pul duig a typical tim of val picocod. 7 SALVATION OF ELECTRONS IN WATER Th lcto mittd fom th ufac of a aopaticl a apidly thmolizd. Th itactio lctotatic foc occu bw th wat dipol ad lcto mittd fom th aopaticl ufac du to thmioic miio. Wat molcul a polaizd by lcto ad captud, i.. th lcto a olvatd i wat. Typical tim of alvatio i about 50 f [3]. Th mobility of lcto haply dop h. A a ult, a lctic doubl lay of a pac chag i fomd a th aopaticl ufac. Pu dioizd wat pt a amophou dilctic with th fobidd zo E g =6.5±0.5 V [3]. Hc, th motio of mittd lcto i wat ca b coidd a lcto motio i a micoducto i th pac chag lf-fild. 91

15 Thi fild gow with th gowth of th umb of mittd lcto, ad it bcom mo ad mo difficult fo th w lcto to lav th aopaticl ufac. A a ult, th miio cut dca, ad, hc, th fild bcomd wak. Wh th fild dca, it i ai fo th lcto to lav th aopaticl ufac, ad th miio cut gow. Such lctic fild i calld a lf-coitt fild. Wat molcul a havi tha lcto, ad, o, th captu of lcto by wat molcul i alvatio pvt th lcto motio by th lctic fild. Coqutly, th molility ad th dpdig (by Eiti latio) diffuio cofficit of lvatd lcto haply dop dow to ~ 10-4 cm / [3]. I thi ca alvatio i imila to lcto captu o a captu ct. Th abov coidatio allow o to u th lmt of th olid body thoy to dcib th lcto motio i wat. Namly, th quatio of lcto motio i a dilctic mdium with accout fo th pac lf-chag hav th fom [41]: = DΔ μ div t = DΔ μ div t ε 0Δϕ = 4π( + ) E = gadϕ ( E) ( E) τ + τ i th lcto chag;, th coctatio of lcto; D, th lcto diffuio cofficit i wat; μ, th lcto mobility i wat; Е, th lcto patial lfcoitt fild; ε 0, th dilctic cotat of wat; φ, th lctic pottial of th lffild of lcto, th idic ad f to th mittd ad olvatd lcto, pctivly. Th fit two quatio i (9) dcib th motio of th mittd ad olvatd lcto du to th diffuio ad dift i a lf-coitt lctic fild ad th olvatio i wat, pctivly. Th thid quatio of th ytm i divd fom th Maxwll quatio fo th oto of th magtic fild vcto povidd that ou poblm i a phically ymmtic o (aum th aopaticl to b ph-hapd). Th bouday coditio a a follow: H j T i th miio cut ad jt = = a υt D μ E υ T = a = 0, th avag vlocity of th mittd lcto. Th fit quatio of ytm (10) how that th coctatio of lcto mittd at aopaticl bouday i dfid by th miio cut oly; th cod o how that th cut at th bouday of a aopaticl qual zo. (10) (9) 9

16 Sic th mobility ad diffuio cofficit of olvatd lcto a mall, w glct th tm copodig to th diffuio ad dift of olvatd lcto. Fially, itad of ytm (9) w gt th followig ytm of quatio: ( ) ( ) + = Δ = Δ = t E div D t π ϕ ε τ τ μ 4 0 (11) Sytm (10) ad (11) dtmi th lctic fild E(,t) ad (,t), at th giv paamt j T ad T υ, ad th paamt ε 0, μ ad T. Fo futh olutio of th ytm it i covit to itoduc dimiol fuctio ad vaiabl. I a dimiol fom i a phical ytm of coodiat w hav th ytm of quatio wh all th valu a dimiol: ( ) ( ) + = = = E t E t τ τ (1) Numical olutio of (1) ultd i obtaiig tim dpdc of a pac chag lfcoitt fild valu. It i wll kow that th fild valu ad th valu of th gatig chag a latd a follow: a Z E =, E i th lctic fild; Z, th chag, а, th iz of a aopaticl. Fig.10. Elctic chag (i lativ uit) v tim. 93

17 Figu 10 illutat th tim of a pac chag. Th obtaid tim dpdc of th pac chag idicat that a hap gowth of th lctic fild i obvd fo th tim of ~1 p, i.., th tim copodig to a hap gowth of th thmioic miio cut ( Fig. 10). Aft thi o ca obv a xpotial dop of th thmioic miio cut, ad th lctic chag ach th atuatio. Th timatd lctic chag gaid by a aopaticl a a ult of lcto miio fom it ufac Z FRAGMENTATION PARAMETER It ha b how that ud iadiatio of colloid of lativly lag gold aopaticl (val t of ) by fmtocod la pul o obv th fagmtatio of th aopaticl ito mall aopaticl (up to val ). Th aopaticl i hatd to up to th mtal boilig tmpatu ad tu ito a dop of liquid. Th hatig i accompaid by lcto thmioic miio fom th ufac of a dop. Th mittd lcto tak away th gativ chag, ad th dop of mltd mtal bcom poitivly chagd. Th poblm of chagd phical dop tability dpdig o th atio btw th ufac ad Coulomb gy wa olvd by Rayligh i 188 [4]. Th fiio paamt X i dfid a follow: Ec X = E wh E c, i th Coulomb pulio foc, E, th ufac tio foc. It wll kow that th fagmtatio i obvd at X 1; at 0.3 < X < 1 o ca obv both th fagmtatio ad vapoatio of igl atom fom th th aopaticl ufac; at X < 0. 3 oly th vapoatio of igl atom i obvd [43]. q Th fiio paamt fo th mtal (gold) aopaticl i dfid a X = A, q, th ρ paticl chag;, th umb of atom i th aopaticl; A = ;, th 6 σ 3 3 lcto chag; ρ = 19.3g / cm, th gold dity; σ = g / cm, th ufac tio cofficit of mltd gold; M a = g / mol, th gold mola ma. Th dop i tabl i th fac of xtm dfomatio plittig ito two idtical pat at Q 16π 3 c = 0,36 a σ, wh a - paticl iz, Q=Z, σ, ufac tio cofficit of th liquid. O ca timat th miimal umb of lcto, q mi, which hould lav th dop ufac to mak it utabl ad fagmtd. Figu 1 pt th dpdc of q mi o th iz of aopaticl. Mimimum umb / 3 of lcto dd fo fagmtatio gow a fuctio a, wh a i th aopaticl adiu. Th typical valu of q mi fo th aopaticl at a diamt a=100m hould b a od Z c=10 4. Compaig th typical valu with th chag timat obtaid fom umical olutio of (9), o ca obtai that M a 94

18 Z0 / Z c >> 1 Th chag gaid by th aopaticl fom th lcto thmioic miio i ufficit to mak th paticl utabl ad fagmtd. Fig. 1. Miimum umb of lcto dd fo fagmtatio v aopaticl iz.. 9 CONCLUSION Thotical modlig of mtal aopaticl fagmtatio i wat ud th actio of fmtocod la pul i dicud. Th poblm of hatig a gold aopaticl by la pul of fmtocod duatio ha b olvd. Th valu ad typical tim of th dop of thmioic miio cut fom th aopaticl ufac du to th hatig of th paticl by th la adiatio fild ha b foud. O th bai of th Rayligh dop modl th citio of aopaticl fagmtatio ha b foud. Th timat of th chag gaid by th aopaticl du to th lcto thmioic miio ad thi futh olvatio hav b obtaid. It wa how that th chag xcd th thhold valu giv by th Rayligh citio. It i poibl to coclud that a a ult of th ifluc of la adiatio th paticl bcom utabl ad th aopaticl fagmtatio tak plac. Th ult of thotical modlig may b ud to optimiz th la opatio gim dtid to poduc th aopaticl of th giv iz. Ackowldgmt. Thi wok wa uppotd by th Ruia Acadmy of Scic (gat 1P ad 7OF) ad Ruia Foudatio fo Baic Rach (gat ) REFERENCES [1] I.N. Zavtovkaya, La-aitd mtal ufac mico- ad aotuctuizatio, La ad Paticl Bam, 8, 437 (010). [] I.N. Zavtovkaya, La Naotuctuizatio of mtal ufac, Quatum Elctoic, 40, 94 (010). 95

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