OU NanoLab/NSF NUE/Bumm & Johnson Spectrophotometry Key Concepts Lambert’s Law of Absorption Beer’s Law Beer-Lambert Law Absorption Cross-Sections Photometric quantities Spectrophotometer The Cary 50 Spectrophotometer

OU NanoLab/NSF NUE/Bumm & Johnson Lambert’s Law of Absorption The intensity I 0 if a beam of light decreases exponentially as it passes though a uniform absorbing medium with the linear decay constant α. Restatement: In a uniform absorbing medium, the intensity of a beam of light decreases by the same proportion for equal path lengths traveled. The linear decay constant α is a characteristic of the medium. It has units of reciprocal length. α is the path length over which the intensity is attenuated to 1/e. Photo: α I0I0 I(x)I(x) x Lambert described how intensity changes with distance in an absorbing medium. I l Johann Heinrich Lambert The distance traveled through the medium is called the path length.

OU NanoLab/NSF NUE/Bumm & Johnson Lambert’s Law of Absorption (base 10) Typically base 10 is used in photometry. k is the path length over which the intensity is attenuated to 1/10.

OU NanoLab/NSF NUE/Bumm & Johnson Lambert’s Law Example If one slab of absorbing material of thickness l reduces the intensity of a beam of light to half. α I0I0 I l And three slabs will reduce the intensity of a beam of light to one eight. Then two slabs of the same absorbing material will then reduce the intensity of a beam of light to one quarter. α I0I0 I l α l α I l α l α I0I0 l

OU NanoLab/NSF NUE/Bumm & Johnson Beer’s Law Beer found that Lambert’s linear decay constant k for a solution of an absorbing substance is linearly related to its concentration c by a constant, the absorptivity ε, a characteristic of the absorbing substance. Restatement: The linear decay constant k is linear in concentration c with a constant of proportionality ε. (August Beer, ) A colored absorber has an absorptivity that is dependent on wavelength of the light ε(λ). The absorptivity is the fundamental property of a substance. This is the property that contains the observable spectroscopic information that can be linked to quantum mechanics (also see absorption cross section.) Typical units are: k cm −1 ; c M (moles/liter); ε M −1 cm −1

OU NanoLab/NSF NUE/Bumm & Johnson Photometric Quantities Transmittance (T) Absorbance (A) (AKA optical density, O.D.) usually given in percent by convention, base 10 logs are used In photometry we measure the intensity of light and characterize its change by and object or substance. This change is typically expresses as percent transmittance or absorbance. Frequently when your primary interest is the light beam Used almost exclusively when your interest concerns the properties of the material

OU NanoLab/NSF NUE/Bumm & Johnson Beer-Lambert Law Lambert’s and Beer’s Laws are combined to describe the attenuation of light by a solution. It is easy to see how the two standard photometric quantities can be written in terms of this law. TransmittanceAbsorbance

OU NanoLab/NSF NUE/Bumm & Johnson Cross-Sections and Absorptivity the connection to single particles and molecules The absorption of light by particles (and single molecules) is characterized by an absorption cross section C. In this model the particle is replaced by a perfectly absorbing sphere with a cross sectional area C. This cross section is a property of the particle and is not related to its geometric cross sectional area. The concentration of particles per unit volume is N. typical units are: C cm 2 ; N cm −3 The cross section can be directly related to the molar absorptivity. N A is Avagadro’s number. units are: C cm 2 ; N cm −3 ; N A mole −1 ; ε M −1 cm −1

OU NanoLab/NSF NUE/Bumm & Johnson Efficiency The absorption efficiency Q of a particle is the ratio of its absorption cross section C to its geometric cross section C geo. Absorption efficiency is dimensionless.

OU NanoLab/NSF NUE/Bumm & Johnson Extension to Scattering and Extinction Attenuation of light by absorption and scattering both obey Lambert’s Law. Thus we can extend our treatment of absorption to scattering and extinction. (Recall that extinction is the effect of absorption + scattering.) The scattering efficiency can be much larger than unity. Extinction paradox: Q ext = 2 (Q abs = 1; Q sca = 1) for an perfectly absorbing particle very large compared to the wavelength of light. Note: All of these quantities are in general wavelength dependent. Our discussion has not included the mechanism (cause) of absorption and scattering. There are many different mechanisms that cause of absorption and scattering.

OU NanoLab/NSF NUE/Bumm & Johnson Instrumentation Spectrometer: measures I vs λ. Simply measures the spectrum of the light (e.g. emission spectroscopy). Spectrophotometer: measures I/I 0 vs λ. Measures how the sample changes the spectrum of the light (e.g. transmission, reflection, scattering, fluorescence). All spectrophotometers contain a spectrometer. -meter: the detector is electronic -graph: light intensity recorded on film photometer: measures I/I 0 without λ selection.

OU NanoLab/NSF NUE/Bumm & Johnson The Spectrophotometer Measures absorbance as a function of wavelength Components: light source, monochromator, sample cell, detector, optical system. monochromator sample cell detector light source slit diffraction grating

OU NanoLab/NSF NUE/Bumm & Johnson balance the forces: Computer controlled acquisition of absorption spectra Cary 50 UV-Vis Spectrophotometer sample detector light source monochromator Can you find the diffraction grating and the slit?

OU NanoLab/NSF NUE/Bumm & Johnson Making a Measurement with the Cary 50 First, measure the baseline using a blank sample. This is raw I 0. The blank sample is the cuvette with deionized water (everything but your nanoparticles). This corrects for any absorption due to the cuvette, water, and variations of the light intensity of the light source, monochromator, etc. Second, measure the zero by inserting the beam block. This corrects the instrument for the detector background. Third, measure your sample. This is the raw I. The Cary 50 automatically calculates the corrected intensities (I and I 0 ) by subtracting the zero from each of the raw intensities. Subsequent measurements do not require re-measuring the blank and zero, simply repeat step 3.

OU NanoLab/NSF NUE/Bumm & Johnson Applications of Spectrophotometry Spectroscopy Chemical Analysis: trace analysis, pH, forensic, in situ monitoring, remote monitoring, geology, astronomy,.... Particle size Thin film characterization Color matching Optics