Chapter 5Photometry

5.1 Instrumentation

The simplest device to measure interaction of a sample with light is the absorbancespectrophotometer. Monochromatic light is passed through the sample (or, in somecases, reflected from it). If absorption occurs, the light intensity that arrives at adetector is lower than what would arrive in the absence of the sample.

Better instruments use a beam splitter after the monochromator to create twolight beams: one passes through the sample and one through a reference cuvettefilled with pure solvent or reagent blank (see Fig. 5.1). Thus any artifact causedby variations in light intensity or by absorbtion by the solvent are automaticallyeliminated (double beam spectrophotometer).

In modern instruments, the signal from the detector is usually digitalised, whichallows convenient data handling by a computer.

A key part of a photometer is the monochromator, because measurements needto be taken with monochromatic light. This can be either a filter, a prism, or a grat-ing, the latter being most common.

Some light will be scattered on the grating, depending on the shape of the groves.The groves need to be as flat as possible, they are optimised for low scattering ata particular wavelength and angle of incident (blaze angle). Modern gratings aremade by laser holography, their groves have a concave cross-section to reduce straylight further.

Cuvettes should have high optical quality. For visible light they can be madeof normal laboratory glass, for UV-light cuvettes need to be made of fused silica,usable down to about 180 nm. To reduce cross-contamination disposable cuvettesmade of plastic may be used. Polystyrene is cheapest, but absorbs UV-light stronglybelow 320 nm. Polymetacrylate can be used down to about 280 nm, certain propri-etary plastics to about 230 nm (all wavelengths for 50 % transmission).

5.2 LAMBERT–BEER’s Law

What influence will the sample have on the intensity of light reaching thedetector?

E. Buxbaum, Biophysical Chemistry of Proteins: An Introductionto Laboratory Methods, DOI 10.1007/978-1-4419-7251-4 5,© Springer Science+Business Media, LLC 2011

33

34 5 Photometry

2-beam spectral photometer

Samplelog(I)

log(I0)

I0−log

Sample

Reference

Reference

Diode-array detector

+

+

+

−

−

−

Fig. 5.1 Top: Principle of an absorbtion spectrophotometer. Light is passed through a monochro-mator (prism, grid, or filter) and a beam splitter. The resulting two monochromatic light beamspass through a sample or reference cuvette, respectively, onto detectors. Their relative intensity isconverted into an electrical signal. Light source can be a tungsten filament lamp for visible andnear-IR light, UV light is usually produced by a deuterium-lamp. Most research photometers haveboth, you need to select the one appropriate for your measurements. Bottom: The light may bepassed through the sample directly, and then through a grid or prism which projects the spectrumonto an array of (usually 256 or 512) light sensitive diodes. This way an entire absorbtion spectrumcan be determined in one go (about 0:1 s per spectrum, but averaging over several spectra is oftenrequired for better S/N ratio), albeit with lower sensitivity and resolution. Such instruments tend tobe used as chromatographic detectors, where different peaks may absorb at different wavelengths

Assume that a sample absorbs just half of the light that passes through it.Then a second, identical sample will absorb half of the light that passed throughthe first, and the detector will see only 1/4 of the light generated by the source.Thus doubling the thickness of the sample (d) results in doubling of absorbance(E D � log.I=I0/). Thickness is usually measured in cm, because standard cuvettesused in spectroscopy have d D 1 cm.

By the same reasoning, if the amount of absorbing substance in the second sam-ple were dissolved in the first sample, doubling its concentration (c), we would alsoexpect doubling of the absorbance.

We also know that there are substances that cause strong absorbtion at a certainwavelength even in minute concentration, while other substances do not absorb thesame wavelength at all (but may cause absorption at a different wavelength). Thisproperty can be expressed mathematically as a wavelength dependent constant, themolar absorbtion coefficient �(�), which has the unit l mol�1 cm�1.

5.2 LAMBERT–BEER’s Law 35

These considerations lead directly to LAMBERT–BEER’s law:

E D � log

�I

I0

�D �.�/ � c � d (5.1)

the absorbance E caused by the sample, defined as the negative logarithm of thequotient of outgoing (I ) and incoming (I0) light intensity, is proportional to itsconcentration (c, measured in mol/l) and its thickness (d , measured in cm). The pro-portionality constant is the wavelength dependent molar absorption coefficient, �.

A more formal way to derive this equation starts with the assumption that a givenvolume of solution V contains a certain number of molecules n with a certain prob-ability P to absorb a light quantum of a given wavelength. Then the cross-sectionfor absorption k D P n=V and I D I0eknd D I0e��cd . The absorption probabilityis k D3:28 � 10�21�.

LAMBERT–BEER’s law is, however, valid only under certain conditions:

� The light must be (as nearly as practical) monochromatic. Since absorbtion oflight is wavelength dependent, polychromatic light results in a non-linear rela-tionship between concentration and absorbance.

� The sample must be free of dust particles, gas bubbles, or other objects that causelight scattering. Vacuum filtration of all samples is a good way to achieve this.

� The sample must be so dilute that interactions between molecules do not influ-ence the absorbance. Additionally, as absorbance increases the light sensor seesless and less light, until measurements become influenced by noise. The noiselevel depends on the quality of the photometer. As a rule of thumb, E > 1 (90 %light absorbed) will cause non-linear E vs c plots in most cases but problemscan occur earlier with some substances (see Fig. 5.2). Before establishing a new

0

0.1

0.2

0.3

0.4

0.5

0 3 6 9 12 15

Immunoglobulin G (mg)

Bradford protein determination

linear regressionparabolic regression

Data

E595

Fig. 5.2 LAMBERT–BEER’s law is valid only for small concentrations. Here, different amountsof Immunoglobulin G were used to establish a standard curve for protein determination accordingto BRADFORD [36]. The last point clearly deviates from the linear regression line. For such highconcentrations, either the sample would have to be diluted, or a parabolic regression curve used

36 5 Photometry

Bradford Protein Assay: Spectrum

Wavelength (nm)400

300

200

100

0

−100

−200500 600 700

Abs

orba

nce

(aga

inst

rea

gent

bla

nk)

1 µg/ml2 µg/ml3 µg/ml4 µg/ml6 µg/ml

Fig. 5.3 Spectrum of the BRADFORD protein assay [36]. Maximum sensitivity is obtained at590 nm, the isosbestic point is at about 535 nm

assay, the concentration range where LAMBERT-BEER’s law is valid must bechecked. Higher concentrations may however be used if a parabolic standardcurve is established.

5.2.1 The Isosbestic Point

Figure 5.3 shows the spectrum of BRADFORD’s protein assay for different pro-tein concentrations. Maximum difference between the samples is at 590 nm, thisis the wavelength one would select to measure protein concentrations. There isan isosbestic point at 535 nm, where the absorbance is independent of the proteinconcentration. Differences between samples at this wavelength are caused by experi-mental artifacts, for example inhomogeneities in the bottom of 96-well plates. Platereaders therefore measure the ratio of absorbance at two wavelengths, the secondwavelength should be at the isosbestic point; in the case of the BRADFORD assay,one would measure the ratio of A590=A535. If the spectrum has several isosbesticpoints, select the one closest to the measurement wavelength so that scattering issimilar at both wavelengths.

5.3 Environmental Effects on a Spectrum

The absorbtion spectrum of a substance depends on the polarity of its solvent.If a change from a less to a more polar solvent leads to a shift of the ab-sorbance maximum toward red (longer wavelengths, lower energy), we speak

5.3 Environmental Effects on a Spectrum 37

of a bathochromic effect; a shift towards blue (shorter wavelengths, higher energy)is called a hypsochromic effect. Bathochromic effects are usually seen in   !  �-transitions, hypsochromic in n !  �-transitions. Higher solvent polarity stabilisesthe more polar, that is excited, state of an orbital, which explains the bathochromiceffect of high polarity solvents on the   !  �-transition. At the same time, polarsolvents will form hydrogen bonds with n-orbitals, which need to be broken for an !  �-transition. This requires energy, explaining the hypsochromic effect.

Interactions between chromophores in highly organised macromolecules can re-duce (hypochromic effect) or increase (hyperchromic effect) the molar absorbtioncoefficient at a particular wavelength. Thus the absorbtion of a DNA-solution at260 nm will increase sharply with temperature around the melting point of DNA.This has to do with interactions between dipole moments of the chromophores(attraction and repulsion of partial charges, which stabilise or destabilise a partic-ular state). According to the KUHN–THOMAS-rule a hyperchromic effect needs tobe compensated by a hypochromic effect at a different wavelength, that is, the in-tegral under the absorbtion curve is constant. In case of DNA, hypochromic effectsare observed in the far UV region, which is not accessible with normal laboratoryequipment.