139

Luminescence Spectroscopy • Excitation is very rapid (10 - 15s).

• Vibrational relaxation is a non-radiational process. It involves vibrational levels of the same electronic state. The excess of vibrational energy is released by the excited molecule in the form of thermal or vibrational motion to the solvent molecules. It takes between 10-11 and 10-10s.

• Internal conversion is a non-radiational process. It is the crossover between states of the same multiplicity. It occurs when the high vibrational levels of the lower electronic state overlap with the low vibrational levels of the high electronic state. It can occur between excited states (S2 and S1) or between excited and ground states (S1 and S0). Between excited states is rapid (10-12s).

• Fluorescence is a radiational transition between S1 and S0. It occurs from the ground vibrational level of S1 to various vibrational levels in S0. It requires 10-10 to 10-6 s to occur.

• External conversion is a nonradiative process in which excited states transfer their excess energy to other species, such as solvent or solute molecules.

• Intersystem crossing is a non-radiative process between electronic states of different multiplicities. It requires a change in electronic spin and, therefore, it has a much lower probability to occur than spin-allowed transitions. Because the time scale is similar to the one for fluorescence (10-8 - 10-7s), it competes with fluorescence for the deactivation of the S1 state

• Phosphorescence is a radiational deactivation process between electronic states of different multiplicity, i.e. T1 to S0. It usually takes between 10-4 to 10s to occur because the process is spin forbidden.

140

Intensity of fluorescence (or phosphorescence) emission as a function of

fluorophor (or phosphor) concentration

• The power of fluorescence (or phosphorescence) radiation (F or P) is proportional to the radiant power of the excitation beam that is absorbed by the system:

F = K’(P0 – P) (1)

• The transmittance of the sample is given by Beer’s law:

P/P0 = 10-ebc (2)

• Re-arranging Eq. 1:

F = K’ P0 (1 – P / P0)

• Substituting Eq. 2 above:

F = K’ (1 –10-ebc) (3)

• The exponential term in Eq. 3 can be expanded as a Maclaurin series to:

F = K’.P0.[2.303ebc – (2.303ebc)2 + (2.303ebc)3 - …] (4)

2! 3!

• For diluted solutions, i.e. 2.303ebc < 0.05, all of the subsequent terms in the brackets become negligible with respect to the first, so:

F = K’.P0.2.303ebc or F = 2.303.P0.K’.ebc (5)

• A plot of fluorescence (or phosphorescence) intensity as a function of concentration should be linear up to a certain concentration.

• Three are the main reasons for lack of linearity at high concentrations:

a) 2.303ebc > 0.05

b) self-quenching

c) self-absorption

P0 P

LDR

In

tensity

Concentration

Detector

F

141

Fluorescence quantum yield • The slope of the calibration curve is equal to

2.303.P0.K’.ebc.

• K’ is also known as the fluorescence quantum yield (fF).

• The fluorescence quantum yield is the ratio between the number of photons emitted as fluorescence and the number of photons absorbed:

fF = # of fluorescence photons

# of absorbed photons

• Fluorescence quantum yields may vary between zero and unity:

0 < fF< 1

The higher the quantum yield, the stronger the fluorescence emission.

• In terms of rate constants, the fluorescence quantum yield is expressed as follows:

fF = kf

kf + ki + kec + kic + kpd +kd

kf

ki

kec

kic

• Consider a dilute solution of a fluorescent species A whose concentration is [A] (in mol.L-1). A

very short pulse of light at time 0 will bring a certain number of molecules A to the S1 excited

state by absorption of photons:

A + hν → A*

• The excited molecules then return to S0, either radiatively or non-radiatively, or undergo

intersystem crossing. As in classical kinetics, the rate of disappearance of excited molecules is

expressed by the following differential equation:

-d[A*] / dt = (kf + knr) [A*]

knr = ki + kec + kic + kpd + kd are the rate constants of competing processes that ultimately

reduce the intensity of fluorescence. k units = s-1.

142

Fluorescence lifetime

• Integration of equation:

-d[A*] / dt = (kf + knr) [A*]

yields the time evolution of the concentration of excited molecules [A*].

• Let [A*]0 be the concentration of excited molecules at time 0 resulting from the pulse light excitation. Integration leads to:

[A*] = [A*]0 exp(-t / t)

where t is the lifetime of the excited state S1.

• The fluorescence lifetime is then given by:

t = 1 / kf + knr

• Typical fluorescence lifetimes are in the ns range.

• Typical phosphorescence lifetimes are in the ms to s range.

• The fluorescence (or phosphorescence lifetime) is the time needed for the concentration of excited molecules to decrease to 1/e of its original value.

• The fluorescence lifetime correlates to the fluorescence quantum yield as follows:

ff = kf. t

143

Excitation and emission spectra

• Excitation spectra appear in the same wavelength

region as absorption spectra.

• However, it is important to keep in mind that

absorption spectra are not the same as excitation

spectra.

• Fluorescence and phosphorescence spectra

appear at longer wavelength regions than

excitation spectra.

• Phosphorescence spectra appear at longer

wavelength regions than fluorescence spectra.

• In some cases, it is possible to observe vibrational

transitions in room-temperature fluorescence

spectra.

There are several parameters (many wavelengths and two lifetimes) for compound identification.

144

Fluorescence and Structure

• General rule: Most fluorescent compounds are

aromatic. An increase in the extent of the p-electron

system (i.e. the degree of conjugation) leads to a shift

of the absorption and fluorescence spectra to longer

wavelengths and an increase in the fluorescence

quantum yield.

• Example:

Aromatic hydrocarbon Fluorescence

Naphthalene ultraviolet

Anthracene blue

Naphthacene green

Pentacene red

• The lowest-lying transitions of aromatic hydrocarbons

are of the p→p* type, which are characterized by high

molar absorption coefficients and relatively high

quantum fluorescence quantum yields.

No fluorescence

Fluorescence

145

• The effect of substituents on the fluorescence characteristics of aromatic hydrocarbons varies with the type of substituent.

• Heavy atoms: the presence of heavy atoms (e.g. Br, I, etc.) results in fluorescence quenching (internal heavy atom effect) because of the increase probability of intersystem crossing (ISC).

• Electron- donating :

-OH, -OR, -NH2, -NHR, -NR2

This type of substituent generally induces and increase in the molar absorption coefficient and a shift in both absorption and fluorescence spectra.

• Electron-withdrawing substituents:

carbonyl and nitro-compounds

Carbonyl groups: There is no “general rule”. Their effect depends on the position of the substituent group in the aromatic ring.

Nitro groups: No detectable fluorescence.

Substituted Aromatic Hydrocarbons

146

pH of solution

Additional resonance

forms lead to a more

stable first excited state

Rigidity

Rigidity usually

enhances

fluorescence emission

147

Quenching

• Quenching: nonradiative energy transfer from an excited species to other molecules.

• Quenching results in deactivation of S1 without the emission of radiation causing a decrease in fluorescence intensity.

• Types of quenching: dynamic, static and others.

• Dynamic quenching: or collisional quenching requires contact between the excited species and the quenching agent.

• Dynamic quenching is a diffusion controlled process. As such, its rate depends on the temperature and viscosity of the sample.

• High temperatures and low viscosity promote dynamic quenching.

• For dynamic quenching with a single quencher, the Stern-Volmer expression is valid:

F0/F = 1 + Kq[Q]

Where F0 and F are the fluorescence intensities in the absence and the presence of quencher, respectively. [Q] is the concentration of quencher (mols.L-1) and Kq is the Stern-Volmer quenching constant.

• The Stern-Volmer constant is defined as:

Kq = kq / kf + ki + kic

where kq is the rate constant for the quenching process (diffusion controlled).

• Static Quenching: the quencher and the fluorophor in the ground state form a complex. The complex is no fluorescent (dark complex).

• The Stern-Volmer equation is still valid but Kq in this case is the equilibrium constant for complex formation: A + Q <=> AQ.

• In static quenching, the fluorescence lifetime of the fluorophor is not affected. In dynamic quenching, the fluorescence lifetime of the fluorophor is affected. So, lifetime can be used to distinguish between dynamic and static quenching.

Fluorescence

quenching of quinine

sulfate as a function of

chloride concentration

Oxygen sensors

O2 is paramagnetic, i.e.

its natural electronic

configuration is the

triplet state.

When O2 interacts with

the fluorophor, it

promotes conversion

and deactivation of

excited fluorophor

molecules.

Upon interaction, O2

goes into the singlet

state (diamagnetic).

148

Instrumentation

Typical spectrofluorometer

(or spectrofluuorimeter)

configuration

Recording

excitation and

emission spectra

Recording

synchronous

fluorescence

spectra

149

Spectrofluorimeter capable to correct for

source wavelength dependence

Spectrofluorimeter with the ability to

record total luminescence

150

Measuring phosphorescence

• Using a spectrofluorimeter with a continuous

excitation source: be careful with fluorescence and

second order emission!

• Rotating-can phosphoroscope: “good-old” approach

to discriminate against fluorescence.

A. True representation

B. Approximate representation

te = exposure time; td = shutter delay time; tt =

shutter transit time; tC = time for one cycle of

excitation and observation; tE = te + tt; tD = td + tt

• Spectrofluorimeters with a pulsed source: employ a gated PMT for

fluorescence discrimination.

Excitation source on => PMT off = fluorescence decays

Excitation source off => PMT on – phosphorescence measurement

151

Introduction to Chromatographic Separations

• Analysis of complex samples usually involves previous separation prior to compound determination.

• Two main separation methods based on instrumentation are available:

Chromatography

Electrophoresis

• Chromatography is based on the interaction of chemical species with a mobile phase (MP) and a stationary phase (SP).

• The MP and the SP are immiscible.

• The sample is transported by the MP. The interaction of species with the MP and the SP separates chemical species in zones or bands.

• The relative chemical affinity of chemical species with the MP and the SP dictates the time the species remain in the SP.

• Two general types of chromatographic techniques exist:

• Planar: flat SP, MP moves through capillary action or gravity

• Column: tube of SP, MP moves through gravity or pressure.

SP Detector MP + sample

152

Classification of Chromatographic Methods

• Chromatographic methods can be classified on the type of MP and SP and the kinds of equilibrium involved in the transfer of solutes between phases:

Column 1: Type of MP

Column 2: Type of MP and SP

Column 3: SP

Column 4: Type of equilibrium

Concentration profiles of solute bands A and B at

two different times in their migration down the

column.

153

Migration Rates of Solutes

• Two-component chromatogram illustrating two methods for improving separation:

• (a) Original chromatogram with overlapping peaks; (b) improvement brought about an increase in band separation; (c) improvement brought about by a decrease in the widths.

Distribution constant or partition ratio or partition coefficient:

It describes the partition equilibrium of an analyte between the

SP and the MP.

If K = Kc and SP = S and MP = M

Kc = cS / CM = nS / VS

nM / VM

Where VS and VM are the

volumes of the two phases and

nS and nM are the moles of A in

SP and MP, respectively.

154

Retention Time

• Retention time is a measured quantity.

• From the figure:

tM = time it takes a non-retained species (MP) to travel through the column = dead or void time.

tR = retention time of analyte. The analyte has been retained because it spends a time tS in the SP. The retention time is then given by:

tR = tS + tM

• The average migration rate (cm/s) of the solute through the column is:

Where L is the length of the column.

• The average linear velocity of the MP molecules is:

155

Relationship Between Retention Time and

Distribution Constant

The Rate of Solute Migration: The Retention Factor

Where VS and VM are the volumes of SP and MP in the column. Knowing that:

An equation can be derived to obtain KC of A (KA) as a function of experimental parameters.

=>

Retention factor = capacity factor = kA = k’A.

However: k’A ≠ KC or k’A ≠ KA

=>

156

• The selectivity factor can be measured from the chromatogram.

• Selectivity factors are always greater than unity, so B should be always the compound with higher affinity by the SP.

• Selectivity factors are useful parameters to calculate the resolving power of a column.

Band Broadening and Column Efficiency

• The “shape” of an analyte zone eluting from a chromatographic column follows a Gaussian profile.

• Some molecules travel faster than the average. The time it takes them to reach the detector is: tR – Dt.

• Some molecules travel slower than the average molecule. The time it takes them to reach the detector is: tR + Dt

• So, the Gaussian provides an average retention time (most frequent time) and a time interval for the total elution of an analyte from the column.

• The magnitude of Dt depends on the width of the peak.

157

• Considering that:

v_ = L / tR

=> L = v_ x

or

L ± DL = v_ x [tR ± Dt]

• The equation above correlates chromatographic peaks with Gaussian profiles to the length of the column.

• Both Dt and DL correspond to the standard deviation of a Gaussian peak:

Dt ≡ DL ≡ s

• If s = Dt, s units are in minutes. If s = DL, s units are in cm.

• The width of a peak is a measure of the efficiency of a column. The narrower the peak, the more efficient is the column.

=>

• The efficiencies of chromatographic columns can be compared in terms of number of theoretical plates .

158

The Plate Theory

• The plate theory supposes that the chromatographic column contains a large number of separate layers, called theoretical plates.

• Separate equilibrations of the sample between the

stationary and mobile phase occur in these "plates". • The analyte moves down the column by transfer of

equilibrated mobile phase from one plate to the next.

• It is important to remember that theoretical plates do not really exist. They are a figment of the imagination that helps us to understand the processes at work in the column.

• As previously mentioned, theoretical plates also serve as a figure of merit to measuring column efficiency, either by stating the number of theoretical plates in a column (N) or by stating the plate height (H); i.e. the Height Equivalent to a Theoretical Plate.

• The number of theoretical plates is given by:

N = L / H

• If the length of the column is L, then the HETP is:

H = s2 / L

• Note:

• For columns with the same length (same L):

The smaller the H, the narrower the peak.

The smaller the H, the larger the number of plates.

=> column efficiency is favored by small H and large N.

• It is always possible to using a longer column to improve separation efficiency.

159

Experimental Evaluation of H and N

• Calling s in time units (minutes or seconds) as t:

=> s / t = cm / s

• Considering that: v_ = L / tR = cm /s

• We can write:

L / tR = s / t

or

t = s = s

L / tR v_

• If the chromatographic peak is Gaussian,

approximately 96% of its area is included within

± 2s. This area corresponds to the area between

the two tangents on the two sides of the

chromatographic peak.

• The width of the peak at its base (W) is then

equal to:

W = 4t in time units

or

W = 4s in length units.

• Substituting t = W / 4 in the equation above we obtain:

s = LW / 4tR

• Substituting s = W / 4 in the same equation we obtain:

t = WtR / 4L

• Substituting s = LW / 4tR in the HEPT equation:

H = LW2 / 16tR2

• Substitution of this equation in N gives:

N = 16 (tR / W)2

• These two equations allow one to estimate H and N

from experimental parameters.

• If one considers the peak of the width at the half

maximum (W1/2):

N = 5.54 (tR / W1/2)2

In comparing columns, N and H should be obtained with the same compound!

160

Kinetic Variables Affecting Column Efficiency • The plate theory provides two figures of merit

(N and H) for comparing column efficiency but it does not explain band broadening.

• Table 26-2 provides the variables that affect band broadening in a chromatographic column and, therefore, affect column efficiency.

• The effect of these variables in column efficiency is best explained by the theory of band broadening. This theory is best represented by the van Deemter equation:

H = A + B / u+ CS . u + CM . U

where H is in cm and u is the velocity of the mobile phase in cm.s-1. The other terms are explained in Table 26-3.

• Table 26-3:

f(k) and f’(k) are functions of k

l and g are constants that depend on the quality of the packing.

B is the coefficient of longitudinal diffusion.

CS and CM are coefficients of mass transfer in stationary and mobile phase, respectively.

• Before we try to understand the meaning of the van Deemter equation, a better understanding of chromatographic columns is needed.

161

Some Characteristics of Gas Chromatography

(GC) Columns

• Two general types

=> Open Tubular Columns (OTC) or Capillary Columns

=> Packed Columns

• OTC:

=> Wall Coated Open Tubular (WCOT) Columns

=> Support Coated Open Tubular (SCOT) Columns

=> The most common inner diameters for capillary tubes are 0.32 and 0.25mm.

• Packed Columns:

=> Glass tubes with 2 to 4mm inner diameter.

=> Packed with a uniform, finely divided packing material of solid support, coated with a thin layer (005 to 1mm) of liquid stationary phase.

• Solid Support Material in OTC and Packed Columns

Diatomaceous Earth: “skeletons of species of single-celled plants that once inhabited ancient lakes and seas”.

162

Some Characteristics of HPLC Columns

• Only packed columns are used in HPLC.

• Current packing consists of porous micro-particles with diameters ranging from 3 to 10mm.

• The particles are composed of silica, alumina, or an ion-exchange resin.

• Silica particles are the most common.

• Thin organic films are chemically or physically bonded to the silica particles.

• The chemical nature of the thin organic film determines the type of chromatography.

SP for normal-phase chromatography

SP for partition chromatography Typical

micro-

particle

163

Another Look at the van Deemter Equation

• H = A + B/u + CSu + CMu

• The multi-path term A or Eddy-Diffusion:

=> This term accounts for the multitude of pathways by which a molecule (or ion) can find its way through a packed column.

• A = 2ldp

where: l is a geometrical factor that depends on the shape of the particle: 1 ≤ l ≤ 2.

dp is the diameter of the particle.

Using packing with spherical particles of small diameters should reduce eddy -diffusion.

Injection Detector

164

• The Longitudinal Diffusion Term B/u:

• Longitudinal diffusion is the migration of solute from

the concentrated center of the band to the more

diluted regions on either side of the analyte zone.

• B/u = 2gDM/u

where: g is a constant that depends on the nature

of the packing and it varies from 0.6 ≤ g ≤

0.8.

DM is the diffusion coefficient in the mobile

phase. DM a T / m, where T is the

temperature and m is the viscosity of the

mobile phase.

• As u → infinite, B/u → zero. So, the contribution of

longitudinal diffusion in the total plate height is only

significant at low MP flow rates.

• Its contribution is potentially more significant in GC

than HPLC because of the relatively high column

temperatures and low MP viscosity (gas).

Initial band

Diffusion of the band with time

The initial part of the curve is

predominantly due to the B/u term.

Because the term B/u in GC is larger

than HPLC, the overall H in GC is

about 10x the overall H in HPLC.

165

• The Stationary-Phase Mass Transfer Term CSu:

• CS = mass transfer coefficient in the SP.

CS a df2 / DS

where df is the thickness of the SP film and DS is the

diffusion coefficient in the SP.

=> Thin-film SP and low viscosity SP (large DS) provide low

mass transfer coefficients in the SP and improve column

efficiency.

• The Mobile-Phase Mass Transfer Term CMu:

• CM = mass transfer coefficient in the MP.

CM a dp2 / DM

where dp is the diameter of packing particles and DM is the

diffusion coefficient in the MP.

• The contribution of mass transfer in the SP and MP on the

overall late height depends on the flow velocity of the mobile

phase. Both phenomena play a predominant role at high MP

flow rates.

Liquid SP

coated on

solid

support

Cartoon with example of SP mass-transfer in

a liquid SP: different degrees of penetration

of analyte molecules in the liquid layer of SP

lead to band-broadening

Porous in

silica

particle

Cartoon with example of MP mass-transfer: stagnant pools of MP retained in the porous of silica particles lead to band-

broadening.

166

Summary of Methods for Reducing Band Broadening

• Packed Columns:

• Most important parameter that affects band broadening is the particle diameter.

• If the SP is liquid, the thickness of the SP is the most important parameter.

• Capillary Columns:

• No packing, so there is no Eddy-diffusion term. Most important parameter that affects band broadening is the diameter of the capillary.

• Gaseous MP (GC):

The rate of longitudinal diffusion can be reduced by lowering the temperature and thus the diffusion coefficient.

• The effect of temperature is mainly noted at low flow rate velocities where the term B/u is significant.

• Temperature has little effect on HPLC.

Effect of particle

diameter in GC

Effect of particle

diameter in HPLC

Note: m = mm

167

Optimization of Column Performance

• Optimization experiments are aimed at either reducing zone broadening or altering relative migration rates of components.

• The time it takes for chromatographic analysis is also an important parameter that should be optimized without compromising chromatographic resolution.

• Column Resolution:

• It is a quantitative measure of the ability of the column to separate two analytes.

• It can be obtained from the chromatogram with the equation:

• In terms of retention factors kA and kB for the two solutes, the selectivity factor and the number of theoretical plates of the column:

• From the last equation we can obtain the number of theoretical plates needed to achieve a given resolution:

168

• For compounds with similar capacity factors,

i.e. kA ≈ kB:

• The time it takes to achieve a separation

can be predicted with the formula:

Where k = kA + kB / 2

169

The General Elution Problem

• The general elution problem occurs in the

separation of mixtures containing compounds

with widely different distribution constants.

• The best solution to the general elution

problem is to optimize eluting conditions for

each compound during the chromatographic

run.

• In HPLC, this is best accomplished by

changing the composition of the mobile phase

(Gradient Elution Chromatography).

• In GC, this is best accomplished by changing

the temperature of the column during the

chromatographic run.

170

Qualitative and Quantitative Analysis in GC and HPLC

• Both are done with the help of standards.

• Qualitative analysis, i.e. compound identification is done via retention time. The retention time from the pure standard is compared to the retention time of the analyte in the sample.

Note: retention times are experimental parameters and as such are prone to standard deviation.

• Quantitative analysis is done via the calibration curve method (or external standard method) or the internal standard method.

• Calibration curve or external standard method: the procedure is the same as usual. The calibration curve can be built plotting the peak height or the peak area versus standard concentration.

The same volume of sample was injected in each case, but

“Sample B ” has a much smaller peak. Since the tR at the

apex of both peaks is 2.85 minutes, this indicates that they

are both the same compound, (in this example, acrylamide

(ID)). The “Area” under the peak (“ Peak Area Count ”)

indicates the concentration of the compound. This area value

is calculated by the Computer Data Station. Notice the area

under the “Sample A” peak is much larger. In this example,

“Sample A” has 10 times the area of “Sample B”. Therefore,

“Sample A” has 10 times the concentration, (10 picograms)

as much acrylamide as “Sample B”, (1 picogram). Note, there

is another peak, (not identified), that comes out at 1.8 min. in

both samples. Since the area counts for both “samples” are

about the same, it has the same concentration in both

samples.

171

Internal Standards

• An internal standard is a known amount of a compound that is added to the unknown.

• The signal from analyte is compared to the signal from the standard to find out how much analyte is present.

• This method compensates for instrumental response that varies slightly from run to run and deteriorates reproducibility considerably.

• This is the case of mobile phase flow rate variations in chromatographic analysis.

• Internal standards are also desirable in cases where the possibility of loosing sample during analysis exists. This is the case of sample separation in the chromatographic column.

• The internal standard should be chosen according to the analyte. Their chemical behavior with regards to the SP and MP should be similar.

• How to use an internal standard?: a mixture with the same known amount of standard and analyte is prepared to measure the relative response of the detector for the two species.

• The factor (F) is obtained from the relative response of the detector.

• Once the relative response of the detector has been found, the analyte concentration is calculated according to the formula:

Area of analyte signal = F x Area of standard signal

Concentration of analyte Concentration of standard

A known amount of standard is added to the unknown

X. The relative response is measured to obtain the

detector’s response factor “F”.

172

Example of Internal Standards

• In a preliminary experiment, a solution containing 0.0837M X and 0.066M S gave peak areas of AX = 423 and AS = 347. Note that areas are measured in arbitrary units by the instrument’s computer. To analyze the unknown, 10.0mL of 0.146M S were added to 10.0mL of unknown, and the mixture was diluted to 25.0mL in a volumetric flask. This mixture gave a chromatogram with peak areas AX = 553 and AS = 582. Find the concentration of X in the unknown.

• First use the standard mixture to find the response factor:

AX / [x] = F x {AS / [S]}

Standard mixture:

423 / 0.0837 = F {347 / 0.0666}

=> F = 0.9700

• In the mixture of unknown plus standard, the concentration of S is:

[S] = (0.146M)(10.0mL / 25.0mL) = 0.0584M

where: 10.0mL / 25.0mL is the dilution factor

• Using the known response factor and S concentration of the diluted sample in the equation above:

553 / [X] = 0.9700 (582 / 0.0584)

=>[X] = 0.05721M

173

Liquid Chromatography

Size exclusion or gel:

polystyrene-divinylbenzene

Silica with various porous sizes

174

Instrumentation

175

Pumping Systems

• Pumping systems that allow to change the

MP composition during the chromatographic

run provide better separation of compounds

with wide range of k’ factors.

176

Detectors

UV-VIS absorption cell for HPLC