11/23/2009. v Solve for Flight Time t d t. 2 d. 2 t. v m. t And the derivative is: 2. tdt. R m. Time-of-Flight (TOF) Time-of-Flight (TOF)

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1 /3/009

2 /3/009 Tie-f-Flight (TOF Suce Regin (Acceleatin Regin E = V/ Detect E s Dift Regin E = 0 = ift length ev ev Kinetic Enegy gien t the In in the Suce Regin Sling f Velcity Tie-f-Flight (TOF Sle f Flight Tie t t ev S, with a cnstant acceleatin ltage an a knwn ift length, the ift tie is pptinal t the squae t f the ass t chage ati (/e. Mass spectetists efine eslutin as: In TOF we stat f the ift tie equatin: S, ev Tie-f-Flight (TOF ev t An the eiatie is: tt t t S tie-f-flight eslutin is efine by: R t t t is usually efine a peak with at half height. R E z

3 /3/009 Why is eslutin s iptant? Vyage Spec #[BP = 395.8, 5907] % Intensity Mass (/z Tie-ag Fcusing The Quauple Fiel Detect The ptential at any pint (x,y,z is efine as: ( x y z E=0 Fiel Fee Dift Regin Whee, the applie fiel ae weighing cnstants f thei cinate E s E a = cnstant f the eice Acceleatin egin w aw ut ltage T cect f an Distibutin f in enegy. Ex. ~300V The applie fiel is the cbinatin f a RF an DC (U fiel: U V cs( t V= 0 t Peak (a/s = f(hz ( x y z We eebe the cnstaints f the aplace eq.: 0 inea Quas inea Quas If we ae nly inteeste in quauple MS (x,y then: 0 If we set =, then: ( x y The equiptential fiel plt 8eU ax ay 4eV qx qy. 48 R Ez 3

4 /3/009 0 ( x y z Tansf int cylinical cinates: Qua In Taps ( cs sin (cs sin z ( z Geetical cnstaints: z R ttap # RFcycles z Qua In Taps a a z q q 6eU 8eV Cylinical In Taps V V V cs t c ac VT R ttap # RFcycles In Mtin in a Static Magnetic Fiel: entzian Fce: F q( B a q( B The css puct states that the paticles acceleatin is always thnal t the iectin f the agnetic fiel. This will be tue een if B aies with psitin (, but will change if B aies with tie (t. ets take a cnstant agnetic fiel in the iectin z: B k B Unit ect in the z-iectin (k. a q( k B qb x y z 0 0 i j k (. (. (.3 (.4 Cycltn Mtin: xy Substitute angula elcity: Angula elcity qb Siplify int the celebate in cycltn equatin : qb This equatin is the heat f ICR. It tells us that the cycltn fequency is inepenent f the ins initial elcity, an all ins with the sae ass/chage (/q will hae the sae fequency. (.5 (.6 (.7 4

5 /3/009 Cycltn Mtin: Y We can see f u equatins that catins will cycltn cunte-clckwise t the in-the-plane agnetic fiel iectin, while anins will cycltn clckwise B O + X Z (Hz /z Cycltn Mtin: Othe Useful Equatins f Cycltn Mtin: F Eq..4, we can set up the elatinship between cycltn aius an angula elcity: xy (.8 qb useful equatins can be eie f.8;. Calculate elcity f a in with a specific aius: qb xy (.9. Calculate tanslatinal enegy f an in with a specific aius: E xy E tans (.0 q B Cycltn Mtin: Othe Useful Equatins f Cycltn Mtin: Tanslatinal enegy f the in as 0000 a functin f cycltn aius at 000 iffeing agnet fiels (Eq with a ass f 00u z B 9.4 E tans F the siplifie equatin aius( abe, E(eV,B(T,(, (g/l. Tanslatinal enegy f the in at iffeing asses as a functin f aius in a 7.0 Tesla fiel. KE(eV KE(e V u 00u 000u 0000u Cycltn Mtin: Othe Useful Equatins f Cycltn Mtin: One f the st useful eiatins f cycltn tin is fining the aius at specific tepeatues. T this we use the Bltzan equatin an sle: We assue: xy kt kt qb (. aius( 5

6 /3/009 Cycltn Mtin: Othe Useful Equatins f Cycltn Mtin: Hee we isplaye the cycltn aius f the cnentinal cyagnets as a functin f /z at tepeatue. (Eq zb aius( T /z (g/l q F the abe siplifie equatin; (, (g/le, B(T, T(K. aius( /z (g/l q Mass Resling Pwe in FT-ICR MS: Stat with the cycltn equatin: qb Take the fist eiatie with espect t ass (: Reaange t the eslutin equatin: qb qb Thugh f fist glance the fiel has a iect effect n eslutin, eebe that in elcity will als incease as a functin f B, s cllisin fequency (theefe will incease aking eslutin inepenent f B. Uppe Mass iit in FT-ICR MS: Rewiting the cycltn equatin: qb c F thealize ins the cycltn elcity beces the s aeage elcity: kt c ( theal Substituting in we get: q B ( theal kt S in a 7T fiel with a c aius cell the ax ass will be 94 kd. Hwee thee is n t excite an agnetn an axial tin is nt inclue int this equatin. Uppe Mass iit in FT-ICR MS: Nte: Magnetn tin an cell shapes: a B q 4V T S in a 7T fiel in a cylinical tap f c aius the ass liit will be abut 50 kd. Cllisin Css Sectin: Ieal elastic ha sphee cllisin: ( Whee is the cllisin css-sectin ( Mean Fee Path (: #cllisins pe unit tie: Z N Mean fee path (length b/w cllisins Whee is the cllisin istance These equatins negate ptential inteactins between the tw lecules (ats, attactie an epulsie, an assue spheical geety. Z ( ( N N 6

7 /3/009 Mtin in an Applie Fiel (Maxwellian ins KE =ift elcity(c/sec K=bility(c /Vsec E=applie fiel (V/c angein Equatin: e K e=inic chage(vlts =ean fee path( Assuptins: igning culbic inteactin, w fiel liit, clse t theal equilibiu. Deiing the Nenst-Twnsen-Einstein Relatin (Einstein Relatin: At equilibiu, the space istibutins f ins is gien by the Bltzan istibutin: ee n n e kt Diffeentiating yiels: n n ee kt Substitutin int the linea tanspt equatin an setting J=0 gies the Einstein elatin: ed K kt Paticle Paaetes: B = Mechanical bility D = Diffusin cefficent K = Electic bility Relatin: D = ktb K = qb Nenst-Twnsen-Einstein Relatin: K=eD/kT Once again, this nly hls tue at lw fiels. We ake the assuptin that in s tepeatue is theal. Nube Density (N an Applie Fiel (E Depenency: Bth K an D ae inesely pptinal t N at these lw fiels. Hwee, at highe applie fiels, E is nw a fact. E N E N Aies at the buffe gas faste with e cllisin enegy E N Nw aies at the buffe gas at half the istance with the sae spee an cllisin enegy as the fist E/N. At all fiels, we can see that ift elcity, bility, an iffusin ae bette chaacteize with the E/N ati. Mentu: p (kg/s M el cs( Whee, is the entu tansfee, el is the elatie elcity b/w cllisin bies, an θ is eflectin angle. M M Whee, μ is the euce ass. Cllisin Fequency: Spheical: Z =b ax< >N Aing Mentu Tansfe: Z =Q D (ε < >N At lw fiels this is an easy calculatin because the elcity f the in ( an the bath gas (V ae theal. Hwee, the fiel cntibutes t the elcity f the in at highe fiels. 7

8 /3/009 Wannie equatins f Diffusin in high E/N: Weak Fiel D(0: Einstein Relatin: ed K kt Mbility Equatin: KE Wannie equatins f Diffusin in high E/N: High Fiel D: D M ( E D ( 0 T, M T, T 3 ( M ( M ee 3 S, D ( 0 kt ee 3 ( M ( M ( M 4 KE Mbility is Define As: 3kT el What happens when the elatie elcity is geate than theal? p 73.5 K K 760 T K e N 3kbT Whee the euce bility is: The celebate bility Equatin: ee el N K Fiel inuce elatie elcity. Whee λ is the elatie enegy lss f the cllisin eent. e M EN M High fiel bility equatin: S the aiance is: Dt HWHM (half with at half ax is.7σ, an FWHM (full with at half ax is.35σ. FWHM W / Reslutin is efine as the ati f the taele istance ( t the peak with at half height (W /. R W / Dt Using the ift elcity equatin: KE t Substituting in the eslutin equatin f : An siplify: t KE R 3.3 Dt KE R t 3.3D 8

9 /3/009 We then aie at the Nenst-Twnsen-Einstein Equatin, seties efee t as the Einstein elatin: qd K k T The ain assuptin f the Einstein elatin is that bility they (tin acting n ne species, but nt the the an iffusin they ae at equilibiu. Wannie n lnge assue that the applie fiel was weak an the in ass was sall. 3 kbt M E K D K q 3.908M q kbt 3.7M E K D K q 3.908M q b 3 At this pint we can sle the eslutin using eithe the Einstein elatin Wannie s elatin. We will see f se f the futue esults that the axiu eslutin is attaine f systes that fit the Einstein elatin. S, if we sle the eslutin equatin in tes f the Nenst- Twnsen-Einstein equatin: R 3.3 Siplifies t f single chages ins: R 3.33 KkbT q E T KE (.8 (.9 Taking Wannie s elatin in the z iectin: Siplify the ass te in the elatin: Reslutin f a bae ange f fiels: 3 kbt 3.7M E K Dz K q 3.908M q 3.M w M R E qkt 3.3 kbt we K /s Diffusin ( Wannie Relatin, 5c Dift Cell T Nenst-Einstein Relatin E=50V/c K O (c /Vs E=0V/c E=0V/c 60 Cpaisn f Reuce Mbility s. Reslutin T, 5c Dift Cell iq. Flw Clla E=50V/c Reslutin E=0V/c E=0V/c Channeltn Detect EI Suce K O ( /Vs TOF Detect 4 Eleent Electstatic ens Dift Cell 9

10 /3/ peptie line /z cabn cluste line Aial Tie (In Mbility us Hitachi M8000 C/MSn QSta SID ESI 0

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