What is Spectroscopy? --- makes use of the absorption, emission, or scattering of electromagnetic radiation by atoms or molecules (or atomic or molecular ions) to study various physical and chemical properties of atoms and molecules. 3-Main Ways That Light Interacts With Matter 1. Absorption of Radiation 2. Emission of Radiation 3. Scattering of Radiation What is Spectroscopy? In practice: Design experiments around an atomic or molecular probe that can give information of interest in biological molecules. Choose some independent variable that may/may not uncover a hint about a molecular area of interest. Probe energy levels (electronic, vibrational, rotational, nuclear, etc). Challenges: Difficult as unless pure there is convolution of spectra with other molecules. Broadest sense: the study of interaction of light with matter. Light Can Interact With Matter in Different Ways 1. Scattering --light interacts with matter (no absorption) creating an oscillating dipole that emits electromagnetic radiation (per Maxwellʼs Equations). Refraction, diffraction, Rayleigh, Mie scattering can be described as scattering processes. 2. Absorption Processes 1. UV-Vis Spectroscopy: absorption of photon from ground to excited electronic states. 2. Infrared Spectroscopy: absorption of photon from ground to excited vibrational state (Raman too can give vibrational information). 3. Microwave Spectroscopy: absorption of photon from ground to excited rotational state 3. Emission: 1. Fluorescence--emission of photon from an excited singlet state to ground state 2. Phosphorence--emission of a photon from an excited triplet state to the ground state. Electromagnetic Radiation and Molecular Processes Scattering from Solutions of Macromolecules • Molecular mass • Size • Shape • Interaction • Intensity • Polarization • Angular distribution • Fluctuations Molecular properties that can be determined Physical properties that are observed
Transcript
What is Spectroscopy? --- makes use of the absorption, emission, or scattering of electromagnetic radiation by atoms or molecules (or atomic or molecular ions) to study various physical and chemical properties of atoms and molecules.
3-Main Ways That Light Interacts With Matter
1. Absorption of Radiation
2. Emission of Radiation
3. Scattering of Radiation
What is Spectroscopy?
In practice: Design experiments around an atomic or molecular probe that can give information of interest in biological molecules. Choose some independent variable that may/may not uncover a hint about a molecular area of interest.
Probe energy levels (electronic, vibrational, rotational, nuclear, etc).
Challenges: Difficult as unless pure there is convolution of spectra with other molecules.
Broadest sense: the study of interaction of light with matter.
Light Can Interact With Matter in Different Ways1. Scattering--light interacts with matter (no absorption) creating an oscillating dipole that emits electromagnetic radiation (per Maxwellʼs Equations). Refraction, diffraction, Rayleigh, Mie scattering can be described as scattering processes.
2. Absorption Processes1. UV-Vis Spectroscopy: absorption of photon from ground to excited electronic states.2. Infrared Spectroscopy: absorption of photon from ground to excited vibrational state (Raman too can give vibrational information).3. Microwave Spectroscopy: absorption of photon from ground to excited rotational state 3. Emission:1. Fluorescence--emission of photon from an excited singlet state to ground state2. Phosphorence--emission of a photon from an excited triplet state to the ground state.
The wavelength, λ, is the crest-to-crest-distance. The frequency ν, is the number of times per second that a crest passes a given point on the x-axis. c is the speed of light (In vacuum = 2.99 x 108 m s-1).
!
Symbolizing Electromagnetic Radiation
E
A traveling wave
Since a sample is located at some fixed position and not moving then the sample’s point of view only an oscillating electric field disturbance is present.
Oscillating electric field at a point x interacts with matter
Two-headed vector oscillating at a frequency " = c/!
c = λv
Ex = E0 cos(ωt)Ex = E0 cos(2πνt)
Ex = E0 cos 2π(x
λ− νt)
If the electric field vector vibrates then it considered polarized.
All EM-waves travel at the speed of light and are characterized by a specific wavelength and frequency.
Frequency (#) and wavelength (!) are related by the speed of light.
where c = 2.99 x 108 m s-1 " is the frequency in Hz (s-1) and ! is the wavelength of light.
Frequency (#) and wavelength (!) can be related to units of energy (J) of a photon through Plank’s equation of quantization, where h is Plank’s constant = 6.63 x 10-34 J s.
E = hν = hc
λ
All electromagnetic radiationc = ! x "
EM-Radiation Are Also Photons of Light with an energy given by Plank’s LawBecause expression of frequency can be very large number chemists and physicists will specify the properties of a wave in reciprocal wavelength or wave-numbers with units of cm-1.
1λ
=ν
c= wavenumber
E = hν = hc
λEnergy of a single photon is proportional to wavenumber
E� = NA hν = NA hc
λ= NA hν̄
Energy of one mole of photons, E’ is called an “einstein”
Light Scattering In A Nutshell
Electromagnetic radiation is classified as wave phenomenon or particle-photon (DeBroglie’s Wave-Particle Duality)
In 1873, James Clerk Maxwell: light consists of electro-magnetic waves. DeBroglie’s work connecting EM theory to photons follows in 1926. Maxwell found that:
• EM waves are travel in a straight line with an oscillating electric field perpendicular to direction and an oscillating magnetic field;
• both fields are perpendicular to the direction of propagation, i.e. EM’s waves are transverse waves).
• EM Wave travels through a vacuum at velocity, c = 3.00 x 108 m/s.
• EM waves have a wavelength, !, and a frequency, ".
Light scattering is result of concentration fluctuations that occurs in solution that then gives rise to local fluctuations in refractive index (which we can see).
--Rate of the macromolecule fluctuations is determined by the diffusion of solute macromolecules.
--The scattered light looks like “noise” but its not! There information that we can relate to molecular parameters.
!0
Raman-StokesBrillouinBrillouinRaman-
Anti-Stokes
Rayleigh
Wavelength
Frequency shifts in scattered light. The Rayleigh line is broadened due to motion of molecules. The extent of the broadened lines can tell us about diffusion. The Raman shifts are associated with photon-vibrational level shifts.
Scattering Polarized
Light
Scattering Unpolarized
Light
Diffusion is the net transfer of matter from an area of high concentration to one of lower concentration due to random thermal motion.
• Concentration Differences (chemical potential)
• Potential Difference (Flow of Charged Matter)
• Temperature Gradients (Heat Flow)
• Centripetal Force (sedimentation)• Pressure Differences (mass flow)
Transport Processes requires a “Force” C2 C1
t1 >> t0
t0
Einstein and Stokes derived expressions relating the diffusion coefficient, D to temperature and the friction coefficient of the diffusing molecule.
Stoke’s Law: “the frictional coefficient of a unsolvated spherical molecule varies linearly with its radius”.
f0 = 6πηr
Frictional Coefficient (molecules/cm2 sec)
Solvent Viscosity
Sphere Radiusmolecules/cm3
D =kBT
f0Diffusion
Coefficient(cm2/s) Frictional Coefficient
(molecules/cm2 sec)
Einstein’s Ph.D thesis work Boltzmann Constant
1.38× 10−16g cm2s−2K−1
The Autocorrelation Function Summarizes the Dynamic Properties of a Fluctuating Scattering System
Zimm Plot
Absorption Spectroscopy
Light Can Interact With Matter in Different Ways1. Scattering--light interacts with matter (no absorption) creating an oscillating dipole that emits electromagnetic radiation (per Maxwellʼs Equations). Refraction, diffraction, Rayleigh, Mie scattering can be described as scattering processes.
2. Absorption Processes1. UV-Vis Spectroscopy: absorption of photon from ground to excited electronic states.2. Infrared Spectroscopy: absorption of photon from ground to excited vibrational state (Raman too can give vibrational information).3. Microwave Spectroscopy: absorption of photon from ground to excited rotational state 3. Emission:1. Fluorescence--emission of photon from an excited singlet state to ground state2. Phosphorence--emission of a photon from an excited triplet state to the ground state.
Quantum Mechanics Describes how Light Interacts with Matter
Two results of Quantum mechanics that can help us conceptualize how light and matter interact:
1. The spatial distribution of a particle is given by the square of a wave function.
2. Energy states of interest (rotational, vibrational, electronic) in matter are quantized.
3. If the frequency of light is of a resonance frequency of an electronic transition that the light may be absorbed.
Energy Is Distributed In Molecules In Many Ways
--Atoms and molecules exist in a limited number of discrete or “quantized” energy levels (nothing in between).
--Each molecule or atom has a unique set of energy levels that depend on the structure and arrangement of atoms in the molecule.
--The potential energy of a other states can be viewed relative to the ground state and is made up of electronic, vibration, rotation, nuclear and translational energies: Etotal = Etranslational + Erotation + Evibration + Eelectronic + Ee-Spin + Enuclear + Eother
--The lowest energy state is called the “ground state” and states with higher energy called “excited state”.
Electromagnetic Radiation and Molecular Processes
Wavenumber ν
Wavelength λ
Transition Energies Vs 1/2 kT at 300K
Quantum mechanics yields the expressions for the electronic, vibrational, rotational and nuclear energy levels in molecules: The energies associated with various spectroscopic transitions can be summarized as follows: Note Elec > Vib > Rot > Trans
Electronic
Vibrational
Rotational
1/2 kT
cm-1 kcal/molSpectral Transition
20,000
2,000
10
100
60
6
0.029
0.3
This tells us about the spacing of transitions and the populations
IntersystemCrossing
InternalConversion
TripletState
SingletStateManifold
Red-shiftedfluorescence
Absorptionof radiation
Jablonski Diagram
depicts variousradiative and non-radiative processesthat can take placebetween electronicstates.
Ground ElectronicState, S0
Radiative and Non-Radiative Processes and Lifetimes
1. Internal Conversion: excitation energy in S1 is lost by collision of excited state molecules with the solvent or by dissipation of energy by vibrational modes.
2. Quenching: De-excitation resulting from collisions with “quenching” solutes in solution or through resonance energy transfer or excitation coupling.
3.Intersystem Crossing: small degree of forbidden spin exchange converts excited state singlet to triplet state which can convert to ground state by phosphoresance or by internal conversion.
Non-Radiative Processes Alter S1 Population Levels and the efficiency of Fluorescence.
UV-Visible Transitions Occur Between Electronic States
Discrete roto-vibronic modes within the electronic transition are smeared out due to collisions giving the appearance of a band.
Sub-levels are vibrational levelswithin an electronic state.
E = h"
Rotation-Vibrational Energies Make Broad Absorption Bands
Transitions of electrons between molecular or atomic orbitals give rise to absorption spectrum
Boltzman Distribution Determines the Population of Energy Levels
nupper
nlower= exp(
−∆E
k T)
The relative population of molecules in either state is described by the Boltzmann equation.
E is the energy in Joules, k is Boltzman constant = 1.38 x 10-21 J K-1 and T is the temperature in Kelvin.
Consider two-state system, N1 molecules per unit volume in State 1, S1 and N2 molecules per unit volume in excited state, S2. Let’s analyze the change of number of molecules per unit volume in each state considering only absorption, emission and thermal decay processes only and light of energy density ρ(ν) with units of energy per volume per sec.
Rate of N1 absorption = dN12
dt= B12 N1 ρ(ν)
Rate of N2 emission = dN21
dt= B21 N2 ρ(ν)
Rate of N2 spontaneous emission = dN21
dt= A21 N2
ρ(ν)
h" sample State 1
State 2
B12 B21 A21 Energy
N1
N2 Under steady-state or equilibrium conditions there will (no net change in numbers of molecules occupying each state). We can sum and set them equal to each other.
dN21
dt=
dN12
dt
B21 N2 ρ(ν) + A21 N2 = B12 N1 ρ(ν)
N2(B21 ρ(ν) + A21) = B12 N1 ρ(ν)
This is Plank’s Radiation Law for a Blackbody at temperature T. It is key expression for radiation density.
N2
N1=
B12 N1 ρ(ν)B21 ρ(ν) + A21
A21 N2 = B12 N1 ρ(ν)−B21 N2 ρ(ν)
A21 N2 = ρ(ν)[B12 N1 −B21 N2]
ρ(ν) =A21 N2
B12 N1 −B21 N2
ρ(ν) =A21 N2
B12 N1 −B21 N2=
8πhν3
c3(e(hv/kT ) − 1)
1ρ(ν)
=B12 N1 −B21 N2
A21 N2=
c3(e(hv/kT ) − 1)8πhν3
1ρ(ν)
=B12 N1
A21 N2− B21
A21=
c3(e(hv/kT ) − 1)8πhν3
1ρ(ν)
=B12 N1
A21 N2− B21
A21=
c3(e(hv/kT ) − 1)8πhν3
N2
N1= exp(−∆E/kT )
N1
N2= exp(∆E/kT )
e(∆E/kT ) B12
A21− B21
A21=
(e(∆E/kT ) − 1)8π hν3 c−3
e(∆E/kT ) B12
A21− B21
A21= (e(∆E/kT ) c3
8π hν3− c3
8π hν3
B12
A21=
c3
8π hν3=
B21
A21B12 = B21
A21 =8π hν3
c3B(ν)
Rate of spontaneous emission is proportional to ν3. At short wavelength spontaneous emission dominates!
Rate of stimulated emission is equal to rate of stimulated absorption (but there are no excited state molecules).
