Molel, Sfe, nd Continm Isses in the Cpte of Btei Ptiles by Solid Aeosols I ohlbeg, G Boeze, W Gee, nd Good Institte fo Defense Anlyses 4850 Mk Cente Dive Alexndi, VA 3-88 ABSTACT In this stdy, we develop the design pmetes eqied to emove ibone biologil ptiles by impt with svenging eosols The onditions fo pting ibone biologil ptiles fo hed-on ollision e deteed s fntion of eh ptile s mss, dis, inident veloity, nd modls of elstiity, the tttive o eplsive foe between them, nd the ing enegy eted ding impt stimtes of the dii of btei ptiles tht n be pted e deteed s fntion of the mteil pmetes, ing enegy, nd kineti enegy of the inteting ptiles Sfe hemisty ppohes fo eting desied svenge mteils e identified Molel simltions of the intetion between the svenge nd btei ptiles offe ost-etive mnne of ompting sh ftos Designing sfe hemisty to stengthen the bondy intetions is il to imizing svenge pbility Wek vn de Wls nd pi-wise eletostti intetions my not be sffiient to pte ptiles with n ppe nge of kineti enegy eywods: btei, impt theoy, svenging, sfe hemisty, vn de Wls INTODUCTION The ppose of the stdy is ltimtely to delinete the limits of design pmetes tht wold be eqied to svenge the nge of hemil nd biologil ptiles etively A likely mode of delivey fo hemil o biologil ptiles is n ibone lod of mion-sized dy ptiltes (eg, nthx) o liqid eosols (eg, hemil o biologil ptiles) One poposed esponse to sh n ttk is the pid ibone deployment of sbstne tht etively svenges the hemil o biologil ptile nd emoves it fom the tmosphee [,] Fo the svenge to be etive, it mst stik to the ptile pon ollision The onditions fo stiking e deteed by eh ptile s mss, dis, inident veloity, nd modls of elstiity, the tttive o eplsive foe between the ptiles, the ing enegy eted ding impt, nd, to lesse extent, the dissiption modes of the kineti enegy in n inelsti ollision In this initil phse of the stdy, we otline the bsi ssmptions in the simplest ode-of-mgnitde nlysis of the ptile-svenge intetions to detee the onditions fo stiking ding hed-on ollision In this ppe, we desibe the onditions fo the wost-se senio: the tttive foe between the ptiles is shot nge nd of iml mgnitde, thee is long-nge eplsive foe, nd the ptiles hve signifint kineti enegy fo the tmosphei onditions Both the ptile nd the svenge e ssmed to be sphees whose mosopi intetions n be desibed by impt theoy [3] Long-nge eplsive foes n ise fom eletostti intetions fom ptiles with signifint net hge At the miosopi level, the ptile sfes e ssmed to onsist of identil toms sped 3 Å pt The sfe intetions e then desibed in tems of vn de Wls pi potentils between the sfe lyes of toms on eh mosopi ptile The tttive foe ths desibed epesents lowe bond on the el sfe hemisty This model povides simplified fmewok in whih moe elisti tetment of the ptiles, thei dynmis, nd thei sfes n be edily developed xtending the simltion to ove the nge of ptile spet tios, tjetoies, nd distibtion of kineti enegy is stightfowd mehnis The key to optimizing the pefomne of svenge ptiles, howeve, will be moe elisti desiption of the sfe hemisty to imize the stiking oiient to biologil ptiles while tining the bility to be dispesed edily AOSOL CAPTU WITH IMPACT In this setion, we develop the genel physil nd hemil piniples fo svenging eltively smll (- to 5-µm dis) eosols by lge (tens of mion dis) svenge ptiles This pplies, fo exmple, to emoving bteil ptile lod eted in the lowe tmosphee by lying down svenge lod on top of the bteil lod [,] The svenge ptiles, being mh hevie, will fll to the
gond eltively pidly nd will ollide with mny ptiles on the wy down The tik is to get these ptiles to stik togethe Hed-on ollisions e ssmed We do not ttempt to detee the etive pte oss setion sine sh detetion eqies the nlysis of non-hed-on ollisions Fo teting the wost-se senio, we ssme the pesene of long-nge eplsive foe, sh s tht whih n ise if the ptiles y like-net-hges At lose nge, the vn de Wls tttive foes dote The nge of tttive sfe foes is tens of Angstoms nd is qite smll in ompison to the dii of the mion-size ptiles [4] If is the distne between the entes, the enegy ssoited with binging them togethe is int ( ) In this stdy, we ssme the existene of imm vle,, t the nge > +, ssoited with eplsive foe, nd imm vle,, whih os essentilly t the point of impt, + These e shown in Fige int ( ) depends on the dii of the inteting eosols nd the eleto-hemil hteistis of thei sfes [4] nt () t Fige : negy Digm Befoe Impt The kineti enegy vilble fo the ollision is µ V el, /, whee µ mm /( m + m ) is the eded mss, m nd m e the msses of the ptiles, nd V el, V, + V, is the eltive veloity (ssg the ptiles e initilly ppohing one nothe) It is ppent tht the fist ondition fo stiking is tht the kineti enegy vilble fo ollision hs to be gete thn the imm eplsive enegy We eqie µ Vel, /) > ( When q () is not stisfied, n elsti ebond will o t > befoe the ptiles hit one nothe When q () is stisfied, the kineti enegy vilble fo impt t is eded to As the ptiles begin to ppoh eh othe, thee is gin in kineti enegy, (), between the distnes nd The kineti enegy vilble fo impt is then Solving the eqtions of motion fo the inteting ptiles in the nge to detees the veloities V nd V t the point of impt The eltive veloity t impt, V el V + V, is less thn V el, nd is deteed fom the eqtion ( µ /) V el efeene 3 povides n nlysis of the impt of two sphees when only elsti defomtion is onsideed Plsti defomtion nd othe loss mehnisms e negleted This povides less optimisti bsis fo stiking bese something less thn the impt kineti enegy will be vilble fo ebond If the foes ting on the inteting ptiles e deived fom enegy-onseving potentils, pte will not o Ievesible enegy-loss mehnisms e needed to ense tht the ebond kineti enegy fte impt (ie, when the ptiles jst begin to disengge) is less tht the kineti enegy vilble fo impt, s Let the ebond kineti enegy fte impt be witten () b loss The enegy lost ding the impt enggement is loss Fo the smlle ptile to be pted, it mst not be ble to get ove the enegy hmp,, on the wy ot Cpte will o when b < By ombining q () nd q (), we get the following ondition fo pte: + < < loss (3) Given tht > (so tht it stisfies the onditions tht impt will o), the nge of kineti enegies vilble fo pte is loss This ondition my pose seios limittions on svenging in sittions whee the sped in kineti enegies is lge nd loss is smll Fo exmple, if is the ntl sped in kineti enegy in the envionment, the ftion of ptiles tht will be svenged, f, is ppoximted by f loss / Fige shows the onditions ding impt [3] The ptiles lose in on one nothe distne, Unde onditions nomlly onsideed fo svenging, we expet loss to be smll bese the kineti enegy vilble fo the ollision will be smll In this se, the ompession will be smll, eslting in iml oppotnity fo enegy losses bese of plsti flow nd othe mehnil mehnisms
Ptile Ptile F C ompession foe ompession distne S nd S e the espetive vles of the modls of elstiity fo eh ptile, nd ν, ν e the espetive Poisson tios They e typilly bot 03 / / The dis of the ontt sfe is, nd the ontt e, A is A π π (8) Fige : Inteting Ptiles Ding Impt Withot plsti flow nd othe mehnil loss mehnisms, sh s vibtionl dissiption of the kineti enegy, omplete ebond will o Theefoe, fo pte to o, we mst look fo othe thn pely mehnil foes nd/o ete dditionl enegy bies Ceting stong hemil bonds ding the impt poess wold ense pte (stiking) Fo o ode-ofmgnitde nlysis of the wekest possible stiking oiient, howeve, we tet the sfe tttive foes s vn de Wls pi potentils Let be the totl tttive enegy eted ding the impt Using q (3) nd eqting with loss give the following ondition fo pte: + < < (4) We will deive n expession fo bsed, in pt, on the impt model in efeene 3 We biefly eview the fetes nd eqtions of the model nd expess the eslts sing o nottion The ede shold efe to efeene 3 fo the bsi deivtion The instntneos ompessive foe, F, is elted to the losing distne,, vi the eqtion F n 3 / (), 4 n / S 3π (b) (5) In the foegoing expession, is the etive modls of elstiity in tension nd ompession, nd is the etive dis They e defined by the following expessions: S ν π S + ν π S (), + (b) (6) The imm depth of penettion, to eh the imm depth, τ, e / 5 5µ V el (), 4n V el, nd one-wy time 47 τ (b) (9) We ssme tht the nmbe of ing sites, N, eted ding the impt is popotionl to the ontt e If Nb is the nmbe of ing sites pe nit e, we hve N Nb A (0) Let ε be the enegy pe ing site The imm ing enegy,, os when A π N / 5 5 µ V el b επ Nb επ () 4n Using pevios definitions, we get ( ) / 5 β 4 / 5 / 5 6N b ε, nd the following ondition fo pte: / 5 < + ( ) β, < β () The ppe limit to the kineti enegy, pte will o is deteed fom the eqtion / 5 + ( ) β, t whih (3) When β is vey smll, is slightly lge thn its lowe / 5 limit of : + β ( ) Fo lge β (moe likely in the ses of ptil inteest), we neglet both nd in ompison to nd ive t the following ppe limit fo pte, denoted s : β 5 /3 (4)
3 NUMICAL CONSIDATIONS In this setion, we exe the nge of pmetes tht stisfy the onditions of q (4) The nmbe of pmetes is lge, bt we need to fos mostly on those tht we n ontol nd those tht hve lge impt on the dii of the btei eosols tht n be pted We ppoximte those pmetes tht e not expeted to hnge by moe thn fto of two o thee The fist step is to expess q (4) in tems of the bsi pmetes Fo o model, we ssme tht the svenge is mh lge thn the btei nd tht both hve ppoximtely the sme density, ρ q (5b) then gives We lso 3 obtin µ mm /( m + m ) m ρ4π / 3 Fom o pevios stdies [,], we se eltive veloity, V el, of bot m/se Assg tht the btei density, ρ, is 3 3 ompble to tht of wte ( ρ 0 kg / m ) nd expessing ˆ 6 0 in mions give the following expession fo the kineti enegy, : µ V 5 ˆ 3 el 0 Joles (5) Assg the ing sites e septed by distne d 3 Å, the nmbe of ing sites pe nit e, N b, is given by the ppoximtion 9 N b / d 0 (6) The ing enegy pe ing ente (lttie ptile), ε, is highly vible Fo ses whee the intetion between ptiles is doted by eletostti nd vn de Wls intetions, it n nge fom 04 kj/mol to 0 kj/mol Sine thee e 6 0 3 lttie ptiles pe mol, ε n be witten s ε 0 0 J, whee n nge fom 007 to 6 The eing fto we need to ddess is the etive modls of ompessibility, If we ssme tht the mteils e fto of to 3 moe ompessible thn wood 0 o plsti, we ive t vle of S 0 N/m q (6) shows tht modls of ompessibility,, is ontolled by the lest ompessible of the inteting ptiles Being ble to design svenge with lowe ompessibility will deese if tht beomes neessy Combining the pevios ftos, we get 5/ 3 ˆ 5 β 06 0 (7) 5 /3 4/ 3 Inseting qs (5) nd (7) into q (4) gives the imm dis in mions fo whih pte n o The eslt is ˆ, 05 (8) Using the lgest vle of 6 ppopite fo eletostti nd vn de Wls intetions shows tht the lgest dis fo pte will be bot µm This my not be deqte fo mny pplitions On the othe hnd, if the eltive veloity is less thn m/se nd/o the etive modls of 0 ompessibility is less thn 0 N/m, the imm dis will be gete thn mion 4 SUFAC CHMISTY CONSIDATIONS The nmeil vles obtined in the pevios setion wee bsed on estimtes of diffeent pmetes ven thogh the eslts seem to be esonble, it is le tht pplying the model pesented in this ppe to elisti poblems will eqie moe systemti ppoh in deteing these ftos Molel simltions of the intetion between the svenge nd btei ptiles offe ost-etive mnne fo ompting sh ftos Althogh no eslts bsed on these simltions e shown in this ppe, we biefly toh pon the isses egding the simltions nd o plns fo pefog them in the ne fte The nte of the hemil fntionl gops pesent on the sfe of the dy ptilte o eosol detees the stength of the tttive foes between netl ptiles, nd this stength n nge ove sevel odes of mgnitde Using molel simltions, we popose to onstt seies of model sfes nd llte the tttive foe pe nit e s the hemil fntionl gops e vied thogh the nge of polity nd possible bonding intetions In n ttempt to bket the limiting behvio fo eh se, oienttions of the gops on the sfes will be vied to llow fo imm nd imm intetions An impotnt qestion to ddess befoe pefog molel simltions is this: Wht is the hemil fntionlity on the sfe of the biologil ptiles tht needs to be onsideed? Biologil ptiles, sh s btei nd vises, hve omplex ote otings tht enble them to tth to ell wlls The following fts egding the nte of some biologil ptiles e vilble:
Thogh expeiments in the qeos phse (eletophoesis), we know these ptiles e negtively hged bese of idi sgs lled sili ids Fom eletophoesis, it is possible to estimte the nmbe of hged boxylte gops pe nit e In the gs phse, ptiles will be netl nless they e poessed in mnne to be hged (eg, sing tibohging o oon dishge tehniqes) In the se of wepons-gde nthx, the potent ibone is teted with bentonite o sili to dy the sfes nd ede ptile dhesion This enbles the spoes to be dispesed finely in i Anothe impotnt qestion tht needs to be ddessed ding the molel simltions phse is elted to the nte of the long-nge nd shot-nge foes At lge septions between the svenge ptiles nd the biologil ptiles (moe thn tens of Angstoms), only long-nge eletostti foes between the ptiles hve to be onsideed The potentil behves (t fist ode) s q q / fo net hges, q i, on eh ptile nd seption distne, It is le tht the eltive ontibtion of eletostti intetions depends on the hges of the inteting ptiles Likehges will led to eplsive tems tht might inese (see Fige ) Opposite hges old inese the tttion between the svenge nd the biologil ptiles to sh n extent tht old beome zeo o negtive In ddition, it is qite possible tht t lest one of the ptiles is eletilly netl In these ses, the intetion of highe moments (eg, dipoles, qdpoles, nd so foth) with hges might be impotnt elevnt to the oet simltion of the eletosttis of the system is the ssignment of the imm hge tht might be impted to ptile Althogh thee e instnes whee sh ssignment is not le, eletophoesis expeiments povide vlble tool to hieve this tsk As the ptiles ppoh eh othe, vn de Wls intetions beome signifint In these ses, the potentil is popotionl to 6 s, whee s is the distne between individl ptiles on the sfe This step might eqie ppopite methodologies to obtin intetion pmetes fo vn de Wls potentils bsed on sond qntm hemil simltions intetion between svenges nd biologil ptiles eqies the tetment of the bonding, eletosttis, nd vn de Wls intetions, given tht the enegy of the system wold most likely be the eslt of the enegetis of smll nmbe of hemil bonds, n intemedite nmbe of eletostti intetions, nd lge nmbe of vn de Wls intetions 5 CONCLUSION Designing sfe hemisty to stengthen the bondy intetions is il to imizing svenge pbility Wek vn de Wls nd pi-wise eletostti intetions my not be sffiient to pte ptiles with n ppe nge of kineti enegy Sbseqent models fo svenging ibone btei will lso inlde moe peise vles fo the modls of ompessibility, eltive veloity, povision fo non-hedon ollisions, nd othe-thn-spheil shpes 6 ACNOWLDGMNT The thos wold like to thnk Ds Anne Chk nd Clos Gonzlez of the Ntionl Institte fo Stndds nd Tehnology (NIST) fo mny helpfl disssions nd insights egding sfe intetions FNCS [] G Boeze, M Smith, nd I ohlbeg, Applition of Atmosphei Svenging poesses fo the emovl of Colltel Biologil nd Chemil Agents, Poeedings of the 000 AIAA Missile Sienes Confeene, Monteey, Clifoni, 35 Novembe 000 [] I ohlbeg, I Sykes, nd G Boeze, Dimensionl Anlysis Applied to Svenging of Biologil nd Chemil Agents, Poeedings of the AIAA nd Biennil Ntionl Fom on Wepon System ffetiveness, Johns Hopkins Univesity, Lel, Mylnd, 7 9 Mh 00 [3] S Timoshenko nd JN Goodie, Theoy of lstiity, nd dition, MGw-Hill, New Yok, 95 [4] JN Iselhvili, Intemolel nd Sfe Foes, nd dition, Ademi Pess, New Yok, 99 Bonding if it os is vey stong A hemil bond is to odes of mgnitde stonge thn hydogen bond, whih is n ode of mgnitde stonge thn vn de Wls intetion A eltively te desiption of the bonding is itil nd mst be teted with te qntm hemil methods In the end, esonble simltion of the