IPC Friedrich-Schiller-Universität Jena 1 6. Fluorescence Spectroscopy

IPC Friedrich-Schiller-Universität Jena 2 J = 0 J = 1 J = 2 J = 3 J = 4 Rotational levels v = 0 v = 1 v = 0 v = 1 v = 3 v = 4 Vibrational levels Excitation [ s] Internal conversion [ s] Fluorescence [10 -9 s] Intersystem crossing Phosphorescence [10 -3 s] S0S0 S1S1 S2S2 S3S3 S4S4 T1T1 TnTn IR- & NIR- spectroscopy UV-VIS-spectroscopy Microwave- spectroscopy 6. Basic concepts in fluorescence spectroscopy

IPC Friedrich-Schiller-Universität Jena 3 C. A. Parker „Photoluminescence of Solutions with Applications to Photochemistry and Analytical Chemistry” Elsevier 1968, Page 26: Estimating the extent of the first absorption band

IPC Friedrich-Schiller-Universität Jena 4 C. A. Parker „Photoluminescence of Solutions with Applications to Photochemistry and Analytical Chemistry” Elsevier 1968, Page 8: Basic principles and definitions

IPC Friedrich-Schiller-Universität Jena 5  Energy differences between vibrational states which determine vibronic band intensities are very often the same for ground and electronic excited state  Emission spectrum = mirror image of absorption spectrum  Emission bands are shifted bathochromically i.e. to higher wavelengths = Stokes-Shift due to vibrational energy relaxation within electronic excited state 6.1 Stokes-Shift 6. Basic concepts in fluorescence spectroscopy

IPC Friedrich-Schiller-Universität Jena 6 The following transitions will be considered: S0S0 S1S1 T1T1 : rate constant for radiative S 1  S 0 decay via fluorescence; : rate constant for internal conversion (S 1  S 0 ); : rate constant for intersystem crossing; : rate constant for radiative decay via phosphorescence (T 1  S 0 ); : rate constant for non-radiative decay (T 1  S 0 ). Non radiative transitions originating from S 1 are combined in: 6.2 Fluorescence life-time 6. Basic concepts in fluorescence spectroscopy

IPC Friedrich-Schiller-Universität Jena 7  Dilute solution of fluorescent species A.  Short  -laser pulse excites certain fraction of molecules A at t = 0.  Decay rate of excited molecules A*:  Integration: together with: number of molecules A promoted in the excited state at t = 0 and life-time of excited state S 1 :  Fluorescence intensity is number of photons emitted per time and volume: 1 A* 1 A + Photon 6. Basic concepts in fluorescence spectroscopy 6.2 Fluorescence life-time

IPC Friedrich-Schiller-Universität Jena 8  Fluorescence intensity I F at time t after excitation by a short light pulse:  Part of molecules can end up in triplet state.  Life-time of triplet state is defined as: in analogy to 6. Basic concepts in fluorescence spectroscopy 6.2 Fluorescence life-time

IPC Friedrich-Schiller-Universität Jena Fluorescence quantum yield  Fluorescence quantum yield: Emitted Photons per Excitation events  It follows:  The quantum yields for ISC and phosphorescence can be expressed in analogy: Integration over complete decay bzw. 6. Basic concepts in fluorescence spectroscopy

IPC Friedrich-Schiller-Universität Jena 10 Life-times & quantum yields Attention: Quantum yield is proportional to life-time but other non-radiative decay processes change lifetime radiative rate depends on refractive index of medium 6. Basic concepts in fluorescence spectroscopy 6.3 Fluorescence quantum yield

IPC Friedrich-Schiller-Universität Jena Basic concepts in fluorescence spectroscopy Complication 1: Timescale of photon absorption process? Rate of absorption is proportional to Intensity Vibrational depopulation vs Phase decoherence time vs. Rabi Oscillations For practical purposes (in Water): Absorbtion is faster than decoherence Typical timescale: fs = s

IPC Friedrich-Schiller-Universität Jena Basic concepts in fluorescence spectroscopy Blackboard exercise: Cross section  and absorption coefficient 

IPC Friedrich-Schiller-Universität Jena Basic concepts in fluorescence spectroscopy Blackboard exercise: Steady State Fluorescence Saturation

IPC Friedrich-Schiller-Universität Jena Basic concepts in fluorescence spectroscopy Complication 2: Plotting "intensity": A Mess should be called irradiance: intensity is irradiance per unit angle Units of irradiance are W/cm 2 =J/(s cm 2 ) Photon number is proportional to irradiance !? But conversion depends on energy, wavelength: I( ) = (photons/Area/Time) h = (photons/Area/Time) hc/ When plotting I( ) : measured energy flux per unit energy range  E? measured energy flux per unit slit width? measured energy flux per constant wavelength range? counted photons per unit energy range? counted photons per unit slit width? counted photons per unit wavelength range?

IPC Friedrich-Schiller-Universität Jena 15  It is advantageous to define the steady-state fluorescence per absorbed photon as photon flux in dependence of wavelength (Photon spectrum) :  Emission photon spectrum expresses the probability distribution of the different transitions from the vibrational ground state of S 1 down to the various vibrational states of S 0.  The normalized steady-state fluorescence I F ( F ), recorded for the wavelength F is proportional to as well as to the number of absorbed photons at the excitation wavelength E.  Number of absorbed photons is given by: irradiated transmitted Intensity 6. Basic concepts in fluorescence spectroscopy 6.4 Steady-State fluorescence emission

IPC Friedrich-Schiller-Universität Jena 16  Fluorescence intensity can be expressed as follows:  Considering the intensity of the transmitted light by Lambert-Beer‘s law yields:  Recording the intensity I F as function of the wavelength F for a fixed excitation wavelength E yields fluorescence spectrum.  For low concentrations it follows:  Higher terms can be neglected for diluted solutions.  Thus it follows: A( E ) = absorbance at E  Proportionality between fluorescence intensity and concentration for diluted solutions only with k = proportionality constant dependent on numerous experimental values like e.g. collection angle, band width of monochromator, slid width, etc. 6. Basic concepts in fluorescence spectroscopy 6.4 Steady-State fluorescence emission

IPC Friedrich-Schiller-Universität Jena Fluorescence excitation spectroscopy  Recording fluorescence intensity as function of excitation wavelength E for a fixed observation wavelength  F yields fluorescence excitation spectrum.  According to: the fluorescence intensity recorded as a function of the excitation wavelength reflects the product  In case the wavelength dependency of the incoming light can be compensated the fluorescence excitation spectrum depends only on what corresponds to the absorption spectrum.  As long as only one ground state species exists the corrected excitation spectrum is identical to the absorption spectrum. Otherwise a comparison between fluorescence excitation and absorption spectrum yields valuable information about the sample species present. 6. Basic concepts in fluorescence spectroscopy

IPC Friedrich-Schiller-Universität Jena 18 Cinoxacin in H 2 O 6. Basic concepts in fluorescence spectroscopy 6.4 Fluorescence excitation spectroscopy