Collision Cross Section: Ideal elastic hard sphere collision:
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1 Collision Cross Section: Ideal elastic hard sphere collision: ( r r 1 ) Where is the collision cross-section r 1 r ) ( 1 Where is the collision distance r 1 r These equations negate potential interactions between the two molecules (atoms), attractive and repulsive, and assume spherical geometry.
2 Motion in an Applied Field (Maxwellian ions) KE v d K v d =drift velocity(cm/sec) K=mobility(cm /Vsec) E=applied field (V/cm) Langevin Equation: e m e=ionic charge(volts) =mean free path(m) Assumptions: ignoring coulombic interaction, Low field limit, close to thermal equilibrium.
3 We then arrive at the Nernst-Townsend-Einstein Equation, sometimes referred to as the Einstein relation: K qd The main assumption of the Einstein relation is that mobility theory (motion acting on one species, but not the other) and diffusion theory are at equilibrium. Wannier no longer assumed that the applied field was weak and the ion mass was small. k b T D K kbt q m m M 3 m 1.908M E K q 3 D K kbt q m m 3.7M 3 m 1.908M E K q 3
4 At this point we can solve the resolution using either the Einstein relation or Wannier s relation. We will see from some of the future results that the maximum resolution is attained from systems that fit the Einstein relation. So, if we solve the resolution equation in terms of the Nernst- Townsend-Einstein equation: R Simplifies to for single charges ions: R L KkbT q LE T L KE o o (.8) (.9)
5 Taking Wannier s relation in the z direction: D z K kbt q m m 3.7M 3 m 1.908M E K q 3 Simplify the mass term in the relation: w m m 3.M 3 m 1.908M Resolution for a broader range of fields: R E qkt 3.3 k T E K b w d
6 Wannier Relation, 15cm Drift Cell 1 Torr Diffusion (m /s) Nernst-Einstein Relation E=50V/cm E=0V/cm 0.05 E=10V/cm K O (cm /Vs)
7 60 Comparison of Reduced Mobility vs. Resolution 1 Torr, 15cm Drift Cell E=50V/cm Resolution 30 0 E=0V/cm 10 E=10V/cm K O (m /Vs)
8 Liq. Flow Collar Channeltron Detector EI Source Drift Cell TOF Detector 4 Element Electrostatic Lens
9 peptide line m/z carbon cluster line Arrival Time (Ion Mobility) us
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21 Time-of-Flight (TOF) Source Region (Acceleration Region) E = V/d Detector E s Drift Region E = 0 d = drift length
22 Time-of-Flight (TOF) ev 1 mv Kinetic Energy given to the Ion in the Source Region v ev m 1 Solving for Velocity d v Solve for Flight Time t d t ev m 1 So, with a constant acceleration voltage and a known drift length, the drift time is proportional to the square root of the mass to charge ratio (m/e).
23 Time-of-Flight (TOF) Mass spectrometrists define resolution as: In TOF we start from the drift time equation: m m m ev d t And the derivative is: dm tdt ev d So, m dm t dt R So time-of-flight resolution is defined by: m m t t R L E z t is usually defined a peak width at half height.
24 Why is resolution so important?
25 Voyager Spec #1[BP = , 5907] % Intensity Mass (m/z)
26 Time-Lag Focusing Detector E=0 Field Free Drift Region E s E a Low draw out voltage To correct for random Distribution of ion energy. Ex. ~300V Acceleration region
27 Linear Quads a q x x a q y y 8eU mro 4eV mr o r r o R r r o 1 E L z r o
28 Quad Ion Traps 0 1 ( x y z r o o Transform into cylindrical coordinates: ( r cos r sin z r o o ( r z r o o ) ) ) (cos sin Geometrical constraints: r o z o 1)
29 Quad Ion Traps a z q z a r q r 16eU mr o 8eV mr o R ttrap # RFcycles
30 Ion Motion in a Static Magnetic Field: Lorentzian Force: F m a q( v B) q( v B) The cross product states that the particles acceleration is always orthonormal to the direction of the magnetic field. This will be true even if B varies with position (r), but will change if B varies with time (t). Lets take a constant magnetic field in the direction z: m a B k B o Unit vector in the z-direction (k). q( v k Bo ) qb vx vy vz i j k (1.1) (1.) (1.3) (1.4)
31 Cyclotron Motion: v xy r Substitute angular velocity: m r qb Angular velocity o r (.5) (.6) Simplify into the celebrated ion cyclotron equation : qb o m This equation is the heart of ICR. It tells us that the cyclotron frequency is independent of the ions initial velocity, and all ions with the same mass/charge (m/q) will have the same frequency. (.7)
32 Cyclotron Motion: Y We can see from our equations that cations will cyclotron counter-clockwise to the in-the-plane magnetic field direction, while anions will cyclotron clockwise B O + X Z v(hz) m/z
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35 Upper Mass Limit in FT-ICR MS: Note: Magnetron motion and cell shapes: m q a 4 B V T So in a 7T field in a cylindrical trap of cm radius the mass limit will be about 50 kd.
36 Hitachi M8000 LC/MSn QStar
37 ESI
38 Multidimensional Analyses m/z response m/z m/z chromatogram time 38
39 Collision induced dissociation Argon gas CH 3 O CH 3 CH 3 O O CH CH 3 H 3 C CH O Precursor ion CH 3 Product ions In the collision cell, the TRANSLATIONAL ENERGY of the ions is converted to INTERNAL ENERGY. Collision conditions (FRAGMENTATION) is controlled by altering: The collision energy (speed of the ions as they enter the cell) Number of collisions undertaken (collision gas pressure) 39
40 collision energy > fragmentation Product ion scanning 100 % 5eV % % % 0 10 ev 0 ev 30 ev ev % m/z
41 Product Ion Spectrum: Progesterone Product ion scanning 100 % O CH CH 3 CH 3 Mass Spectrum from MS1 O Precursor ion m/z 100 % O O CH CH 3 H 3 C CH CH 3 Product ions Product ion spectrum from MS m/z 41
42 Full Scan Acquisition Mode 100 % Sirolimus: MS Spectrum [M+H] + [M+Li] [M+NH 4 ] [M+Na] [M+K] m/z 4
43 Single ion monitoring (MS) HPLC MS HPLC UV Sirolimus: LC-MS (SIM) vs LC-UV SIR m/z % 0 30µg / L 1.5 min 43
44 Full Scan Acquisition Mode 100 % Sirolimus: MS Spectrum [M+H] + [M+Li] [M+NH 4 ] [M+Na] [M+K] m/z 44
45 Product ion scanning MS1 Precursor Static (m/z 81.5) Collision Cell Ar (.5 3.0e -3 mbar) MS Products Scanning The first quadrupole mass analyzer is fixed, or Static, at the mass-to-charge ratio (m/z) of the precursor ion to be interrogated while the second quadrupole is Scanning over a user-defined mass range. 45
46 NH 4 + Product ion scanning 100 % Mass spectrum from MS m/z 100 % Product ion spectrum from MS m/z
47 Multiple Reaction Monitoring MS1 Precursor(s) Collision Cell Ar (.5 3.0e -3 mbar) MS Product(s) Static (m/z 81.5) Static (m/z 768.5) MS/MS : Compound Specific Monitoring 47
48 Multiple Reaction Monitoring Sirolimus LC-MS(SIM) vs LC-MS/MS (MRM) SIR m/z 81 MRM m/z 81> % % Time 100 3µg / L 30µg / L % % Time 48
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50 Amino Acid 3 Letter Code Single Letter Code Residue Mass Monoisotopic Average Glycine Gly G Alanine Ala A Serine Ser S Proline Pro P Valine Val V Threonine Thr T Cysteine Cys C Isoleucine Ile I Leucine Leu L Asparagine Asn N Aspartic Acid Asp D Glutamine Gln Q Lysine Lys K Glutamic Acid Glu E Methionine Met M Histidine His H Phenylalanine Phe F Arginine Arg R Tyrosine Tyr Y Tryptophan Try W Homoserine Lactone Homoserine Pyroglutamic acid Carboxyamidomethyl Cysteine Carboxymethylcysteine Pyridylethylcysteine
51 Peptide Fragmentation
52 Peptide Fragmentation
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