Week 1-Lecture 1

Frequency Domain Spectroscopy Overview

Introduction to Frequency Domain Spectroscopy

• The session introduces frequency domain spectroscopy, explaining that a spectrum is a plot of intensity against energy measures such as electron volts, kilocalories, wavelength, or wave number.

• The speaker hints at the existence of time domain spectroscopy and mentions that both frequency and time are interconvertible concepts.

Types of Spectroscopy

• Two primary types of spectroscopy are discussed: absorption spectroscopy and emission spectroscopy.

• In absorption spectroscopy, light interacts with a sample to determine which energies are absorbed versus transmitted, influencing the observed color.

Understanding Absorption and Emission

• The concept of color in relation to absorption is explained; for example, a red solution absorbs blue wavelengths while transmitting red.

• Emission spectroscopy is described as producing different colors based on emitted light from materials exposed to UV light.

Key Parameters in Spectroscopy

Absorbance and Molar Absorption Coefficient

• Absorbance is defined using the formula log(I0/IT), where I0 is incident light intensity and IT is transmitted light intensity.

• This leads to the molar absorption coefficient (ε), indicating how probable a transition is within the material.

Emission Quantum Yield

• For emission measurements, quantum yield becomes crucial; it’s defined as the ratio of emitted radiation intensity to absorbed radiation intensity.

• The emission quantum yield can be expressed as photons emitted per unit time divided by photons absorbed per unit time.

Absorption Spectroscopy Mechanics

Lambert-Beer Law Fundamentals

• The relationship between incident (I0) and transmitted (IT) light intensities during absorption through a sample length (L).

• Lambert's law states that changes in intensity (dI) depend on concentration (C), path length (DL), and initial intensity (I).

Mathematical Formulation

• A proportionality equation emerges: -dI = A * I * C * dL, where A represents a constant proportionality factor.

Integration of Absorbance and Lambert-Beer's Law

Understanding the Integration Limits

• The integration limits for absorbance are defined as going from I_0 to I_T on the left side, and from 0 to L on the right side. This is a fundamental concept in spectrophotometry.

• By eliminating the minus sign, we can express the relationship as ln(I_0/I_T) = A cdot C cdot L , where A represents absorbance.

Transitioning from Natural Logarithm to Base 10

• To convert from natural logarithm (ln) to log base 10, multiply by 2.303, leading to the equation: log(I_0/I_T) = epsilon C L . Here, epsilon ( epsilon ) denotes molar absorptivity.

• The left-hand side of this equation is referred to as absorbance (A), which is crucial for understanding Lambert-Beer’s law.

Units in Spectrophotometric Measurements

• Concentration (C) is measured in moles per liter (molar), while path length (L) should be expressed in centimeters rather than decimeters for practical reasons. This reflects common usage in laboratory settings.

• Absorbance has no units; it is a dimensionless quantity that simplifies calculations in spectrophotometry. Epsilon ( epsilon ) has units of molar per centimeter, which can also be expressed differently based on conversion factors between units.

Limitations of Linearity in Absorbance

• The linearity of absorbance being proportional to concentration holds true only for dilute solutions; high concentrations may lead to deviations from this relationship due to saturation effects.

• For example, if absorbance (A) equals 1, then only 10% of incident light passes through; at an absorbance of 5, nearly all light is absorbed indicating opacity at that wavelength. Thus, high values complicate measurements due to increased noise levels in spectra.

Strategies for High Absorbance Solutions

Managing High Absorbances

• To accurately determine concentration when faced with high absorbances (e.g., A = 2), performing precise dilutions using micropipettes can yield valid results through back-calculation methods after dilution measurements are taken.

Alternative Approaches

• An alternative method involves utilizing shorter path lengths during measurement; instead of a standard path length of 1 cm, one could use a cuvette with a path length of 0.1 cm to reduce effective absorbance levels and improve measurement accuracy under challenging conditions.

Emission Quantification Techniques

Emission Quantum Yield

• In emission studies, quantifying emitted light intensity relative to absorbed light intensity provides better insights into sample behavior; this ratio defines emission quantum yield ( Φ_em = I_em/I_abs ). Here I_abs refers specifically to absorbed intensity rather than total incident intensity ( I_0).

Relationship Between Intensities

• The relationship between transmitted intensity ( I_T), incident intensity ( I_0), and absorbed intensity ( I_abs = I_0 - I_T) allows further exploration into absorption spectroscopy principles and their applications within emission contexts for more comprehensive analysis methodologies.

Quantum Yield Measurement Techniques

Understanding the Mathematical Relationships

• The relationship between intensity and absorbance is established by raising both sides to a power, leading to the equation I_0 - I_APS divided by I_APS = 10^-A . This allows for the derivation of I_APS .

• Simplifying further, the expression becomes I_0(1 - 10^-A) . This expression can be substituted into other equations to analyze emission intensity ratios.

Experimental Measurement of Quantum Yield

• To measure quantum yield experimentally, ideally all photons should be captured for an absolute measurement. However, using a reference with a known quantum yield (denoted as Phi_EMR ) is more common.

• Maintaining identical conditions during measurements is crucial. This means ensuring that parameters like initial intensity ( I_0 ) and temperature remain constant when comparing sample and reference emissions.

Key Steps in Determining Emission Quantum Yield

• The ratio of emission intensities from the sample and reference under identical conditions provides a method to determine the unknown sample's quantum yield. Consistency in measurement settings is emphasized.

Importance of Absorption Measurements

• It’s essential to perform absorption measurements before emission measurements when determining quantum yield. Skipping this step can lead to inaccurate results, particularly in laboratory settings where fluorescence spectra are recorded.