A P P L I C A T I O N N O T E
ATR – Theory and Applications
Attenuated Total Reflectance (ATR) is today the most widely used
FTIR sampling tool. ATR generally allows qualitative or quantitative
analysis of samples with little or no sample preparation, which
greatly speeds sample analysis. The main benefit of ATR sampling
comes from the very thin sampling pathlength and depth of
penetration of the IR beam into the sample. This is in contrast to
traditional FTIR sampling by transmission where the sample must
be diluted with IR transparent salt, pressed into a pellet or pressed to
a thin film, prior to analysis to prevent totally absorbing bands in
the infrared spectrum.
A comparison of transmission versus ATR sampling results for
a thick polymer sample is shown below where the sample is too
thick for high quality transmission analysis (shown in the lower
blue spectrum). In transmission spectroscopy, the IR beam passes
through the sample and the effective pathlength is determined by
the thickness of the sample and its orientation to the directional
plane of the IR beam. Clearly in the example below the sample is
too thick for transmission analysis because most of the IR bands
are totally absorbing.
However, simply placing the thick sample on the ATR crystal
(Diamond MIRacle) and applying pressure generates a nearly
perfect result (upper red spectrum) – identified by library search
as a polybutylene terephthalate. The total analysis time for the
thick polymer by ATR was less than 1 minute.
How ATR Works
With ATR sampling we direct the IR beam into a crystal of relatively
higher refractive index. The IR beam reflects from the internal
surface of the crystal and creates an evanescent wave, which
projects orthogonally into the sample in intimate contact with
the ATR crystal. Some of the energy of the evanescent wave is
absorbed by the sample and the reflected radiation (some now
absorbed by the sample) is returned to the detector. This ATR
phenomenon is shown graphically in the following representation
of a single reflection ATR;
While the analysis of samples by ATR is easy, it is interesting
and useful to be aware of each of the following experimental
factors and how they affect the final spectrum:
• Refractive indices of the ATR crystal and the sample
• Angle of incidence of the IR beam
• Critical angle
• Depth of penetration
• Wavelength of the IR beam
• Effective pathlength
• Number of reflections
• Quality of the sample contact with ATR crystal
• ATR crystal characteristics
The refractive indices of the crystal and sample are important
considerations in the ATR sampling technique by virtue of the
following equation,
where n2 is the refractive index of the sample, n1 is the refractive
index of the crystal and θc is the critical angle.
When we exceed the critical angle, we will observe a purely
ATR spectral result. If the critical angle is not met, we will observe
a combined ATR and external reflectance result. This occurs if the
angle of incidence of the IR beam is too low, if the refractive
index of the crystal is too low, if the refractive index of the sample
is too high or a combination of these 3 factors. In most cases this
problem is not observed, however, an example of this is shown in
the following spectral data for your reference. The sample is a
high refractive index liquid (n=1.8) run on a 45 degree accessory
using diamond and Ge crystal plates. The spectrum run on the
Ge crystal plate exhibits a normal baseline and symmetric
absorbance bands – critical angle is met. The spectrum run on
the diamond crystal plate has a baseline shifted and asymmetric
absorbance bands due to non-adherence to the critical angle
requirements for this set of analysis parameters.
Another way to correct the spectral artifacts observed (above) in
the high refractive index sample spectrum would be to increase
the angle of incidence in the ATR accessory to a value above the
critical angle. Adjustment or selection of the angle of incidence is
available in several of the PIKE Technologies ATR accessories.
0
10
20
30
40
50
60
70
80
90
100
%Transmittance
100020003000
Wavenumbers (cm-1)
ATR and Transmission Spectra of a Thick Polymer Sample
Graphical Representation of a Single Reflection ATR
20
30
40
50
60
70
80
90
100
%Transmittance
100020003000
Wavenumbers (cm-1)
Spectra of High Refractive Index Liquid using Ge (upper red) and
Diamond (lower blue) ATR Crystals
Further useful consideration for ATR analysis is the depth of
penetration (dp) of the IR beam into the sample. Technically, this
is defined as the distance required for the electric field amplitude
to fall to e-1
of its value at the surface and is further defined by:
where λ is the wavelength of light and θ is the angle of incidence
of the IR beam relative to a perpendicular from the surface of the
crystal. Typical depth of penetration in ATR ranges from about 0.5
microns up to about 5 microns depending upon these experimental
conditions. Shown in the graphical representation of the ATR
phenomenon, the strength of the evanescent wave decays rapidly
as we progress from the surface of the ATR crystal. If we wish to
compare the sample absorbance of the ATR measurement with
that of a transmission measurement, we need to calculate the
volume of the evanescent wave, known as the effective penetration
of the IR beam. The effective penetration (de), is unique for parallel
polarization (deII) and perpendicular polarization (d⊥) and these
are defined by:
The effective penetration for an unpolarized IR beam is the
average of the parallel and perpendicular penetration.
Generally, a single reflection ATR is ideal for qualitative analysis,
“What is my sample?” When we need to look at minor components
of a sample for qualitative or quantitative analysis, then we need
to increase the effective path length (EPL) by increasing the number
of reflections (N) within the ATR crystal. The effective pathlength
in ATR is derived by the following equation:
An example of the benefit of increased number of reflections
is shown in the following spectral data for the analysis of carbohydrate
content in a soft drink sample. The upper red spectrum is
run using a 10 reflection HATR accessory. The lower blue spectrum
is run using a single reflection ATR using an identical scaling
factor. Clearly the minor carbohydrate bands are more readily
apparent in the multi-reflection ATR accessory.
For your convenience we have calculated theoretical values
of depth of penetration, effective penetration, and effective path
length for typical combinations of crystal materials, angles of
incidence, and number of reflections shown in Table 1.
With the thin penetration of the evanescent wave into the
sample, it is obvious that intimate contact of the sample be made
onto the surface of the ATR crystal. For liquid or pliable samples,
quality of sample contact with the ATR crystal is generally not
a problem. For rigid, irregular shaped or porous samples, high
pressure sufficient to deform the sample will increase the extent
of sample contact and thereby increase sample absorbance. This
is shown in the following spectral data collected for a porous
foam polymer using a MIRacle ATR with ZnSe crystal.
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Absorbance
10001200140016001800
Wavenumbers (cm-1)
Soft Drink Sample using 10 Reflection and 1 Reflection ATR
ATR Sampling ZnSe, Diamond AMTIR Ge
for n2 = 1.5 n1 = 2.4 n1 = 2.5 n1 = 4.0
λ = 1000 cm-1
θc = 38.7 θc = 36.9 θc = 22.0
θ N dp de EPL dp de EPL dp de EPL
45 1 2.0 4.36 4.36 1.7 3.38 3.38 0.66 0.61 0.61
45 3 2.0 4.36 13.08 1.7 3.38 10.15 0.66 0.61 1.84
45 10 2.0 4.36 43.60 1.7 3.38 33.84 0.66 0.61 6.14
30 1 N/A N/A N/A N/A N/A N/A 1.2 1.59 1.59
30 3 N/A N/A N/A N/A N/A N/A 1.2 1.59 4.76
30 10 N/A N/A N/A N/A N/A N/A 1.2 1.59 15.85
60 1 1.11 1.53 1.53 1.02 1.30 1.30 0.51 0.32 0.32
60 3 1.11 1.53 4.59 1.02 1.30 3.91 0.51 0.32 0.97
60 10 1.11 1.53 15.32 1.02 1.30 13.03 0.51 0.32 3.23
Table 1: Pathlengths (stated in microns) of ATR Crystals at Various Angles of Incidence and Numbers of Reflections
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The lower blue spectrum was collected with low pressure
applied to the foam sample, whereas the upper red spectrum is
produced with high pressure. The ATR absorbance using high
pressure is about 10 times greater than with low pressure – all
other sampling factors are identical. For rigid, crystalline, or hard,
irregular surface samples we recommend a single reflection
Diamond MIRacle ATR because it is relatively easy to apply high
pressure onto the small crystal (1.8 mm diameter) with the highpressure
clamp, producing over 10,000 PSI.
The selection of the ATR crystal characteristics should be
matched to the type of samples we run. Selection can be made to
control depth of penetration of the IR beam, for hardness to prevent
crystal damage, for desired spectral range and for acceptable pH
range for acid or caustic samples. No individual crystal type will
solve all problems, so PIKE Technologies offers a broad range of
choices for ATR. Table 2 will give you some guidelines for selection
of your ATR crystal.
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
0.50
Absorbance
1000200030004000
Wavenumbers (cm-1)
Porous Foam Sample with High Pressure (upper red) and Low Pressure
(lower blue)
dp, for n2 = 1.5 Water Solubility, Hardness,
n1 λ = 1000 cm-1
, 45 deg, microns g/100g pH Range Kg/mm
AMTIR 2.5 1.70 Insoluble 1-9 170
Diamond/ZnSe 2.4 2.01 Insoluble 1-14 5,700
Germanium 4.0 0.66 Insoluble 1-14 550
KRS-5 2.37 2.13 0.05 5-8 40
Silicon 3.4 0.85 Insoluble 1-12 1150
ZnS 2.2 3.86 Insoluble 5-9 240
ZnSe 2.4 2.01 Insoluble 5-9 120
Table 2: ATR Crystal Characteristics for FTIR Sampling