Instrumentation J. M. Harris and N. J. Dovichi Dept. of Chemistry University of Utah Salt Lake City, Utah 8 4 1 1 2
THERMAL LENS CALORIME TRY Figure 1.
T h e incorporation of laser light sources into instrumentation for mo lecular fluorescence spectroscopy has produced outstanding advances in sensitivity and detection limit (7, 2). This improvement over conventional excitation sources arises from the in crease in emitted radiation from the sample, due to the larger incident light flux from the laser. T o improve the limit of detection of molecules whose fluorescence q u a n t u m yield is insignificant, one may obtain a similar sensitivity advantage with laser exci tation by observing the heat given off by the sample, arising from the pre dominantly nonradiative relaxation of the excited states produced. T h i s calorimetric approach to deter mining small absorbances in con densed phase samples forms a general class of techniques (3, 4), the differ ences among which depend mainly on the method of measuring the tempera ture increase in the sample. Thermo couple calorimetry involves a direct measurement of the temperature change using a thermocouple, general ly by comparison to a nonilluminated reference sample. Photoacoustic spec troscopy involves either the measure
m e n t of a pressure change in a gas above the sample due to the tempera t u r e rise, or a direct measurement of the expansion of the condensed sam ple. With interferometry, one places the sample in one arm of a Michelson or Zehnder-Mach interferometer such t h a t the t e m p e r a t u r e rise is observed as a change in the refractive index of t h e sample. Although the above meth ods benefit from the high power of laser excitation, they can be carried out with conventional light sources. This is in contrast to thermal lens cal orimetry, which relies on the unique spatial coherence of the laser. T h e r m a l blooming or thermal lens effect, first reported by Gordon et al. (5), is similar to interferometry since the temperature rise associated with absorption of radiation is detected as a refractive index change. By using a TEMoo laser beam having a radially symmetric, Gaussian intensity distri bution for excitation, the sample is most strongly heated at the center of the beam where the intensity is great est. As a result, a lens-like optical ele ment is formed in the sample due to the temperature gradient between the center of the beam and the bulk sam-
Figure 1. Photograph of a thermal lens A 1.5 W argon ion laser beam, λ = 488 nm, spot size, ω = 1.75 mm, has been used to illuminate a 0.65-cm-thick piece of yellow polymethylmethacrylate, A = 0.58, for about 20 s. The plastic was placed quickly between the camera and grid pattern to show the diverging lens formed (left). After sev eral minutes, a second photograph (right) was taken to record the disappearance of the lens with cooling
0003-2700/80/0351-695AS01.00/0 © 1980 American Chemical Society
pie. For most materials, the increase in temperature produces a lowering of t h e refractive index such t h a t the op tical p a t h is shorter at the beam cen ter, equivalent to a diverging lens as pictured in Figure 1. T h e thermal lens is an unusual opti cal element since its effect on the beam is time dependent. If the path between a continuous wave laser and the sample is initially blocked and then opened with a shutter, the lens requires a finite time to develop with in the sample. A steady-state condi tion results when the rate of laser heating, which depends on laser power density and sample absorbance, equals the rate of heat loss, which de pends on the thermal conductivity of the solvent and the temperature change produced. T h e steady state focal length, /(°°), of a thermal lens produced by a Gaussian laser beam of spot size, ω, has been derived (5, 6): (
f{) =
ττλιω 2
2.303P(dn/dT)A
l
(1)
'
where k is the thermal conductivity in W cm*1 K~x, Ρ is the laser power in watts, (dn/dT) is the variation in re fractive index with temperature (usu ally negative) and A is the absorbance of the sample. This expression as sumes all of the absorbed radiation is converted to heat; if the fluorescence q u a n t u m yield is finite, a correction term may be applied (7). T h e ap proach of the thermal lens to steady
ANALYTICAL CHEMISTRY, VOL. 52, NO. 6, MAY 1980 • 695 A
Fill a Staff Position on Capitol Hill Two ACS Congressional Fellowships Available To Begin Fall 1981 Figure 2. Gaussian laser beam propagation
The objectives of the fellowship program are: • To provide an opportunity for scientists to gain firsthand knowledge of the op erations of the legislative branch of the federal government, • To make available to the government an increasing amount of scientific and technical expertise, and • To broaden the perspective of both the scientific and governmental com munities regarding the value of such scientific-governmental interaction.
Applications should be submit ted by January 30, 1981 to: Dr. Annette T. Rosenblum Department of Public Affairs American Chemical Society 1155— 16th St., N.W. Washington, D.C. 20036
Applications consist of a letter of intent, resume, and two letters of reference. The letter of intent should include a description of the applicant's experience in publicoriented projects in which scientific or technical knowledge was used as a basis for interaction and a statement that tells why they have applied for the Fellowship and what they hope to accomplish as an ACS Congressional Fellow. The resume should describe the candidate's educa tion and professional experience and in clude other pertinent personal informa tion. Letters of reference should be so licited from people who can discuss not only the candidate's competence but also the applicant's experience in publicoriented projects. Arrangements should be made to send the letters of reference directly to ACS. For further information call (202) 872-4383.
The heavy solid curves indicate the spot size at any point, z. The radial amplitude distribution, shown for the waist of the beam on the left, is a Gaussian function. The dashed lines indicate the spherical sur faces of constant phase
state is characterized (5) by the fol lowing expression: f(t) « /(«,)(1 + te/2t)
(2)
where tc is a time constant given by:
where ρ is the density of the sample in g cm~:i and Cp is the specific heat in Jg~l K~l. Characteristic time con s t a n t s in the range of tens of microsec onds to several seconds may be ob served, depending on the spot size of the laser beam and the thermal prop erties of the sample. T h e presence of a thermal lens in the sample is conveniently detected by its effect on the propagation of the laser beam which produced the lens. Alternatively, one may align a second laser beam with the center of the lens and observe the effect on this probe beam. Regardless of the method, in order to quantitatively describe the effect of the lens and how it will vary depending on the design of the optical system, one must first consider the propagation of Gaussian laser beams through common optical elements.
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696 A • ANALYTICAL CHEMISTRY, VOL. 52, NO. 6, MAY 1980
φ\
TS""5j
(5)
where Zc (the confocal distance) = πα>ο2/λ. T h e third term in the expo nential expresses the radial amplitude profile, which is a Gaussian of spot size, ω. (Note, the amplitude a t r = ω is smaller relative to the center by a factor e _ 1 , whereas the intensity is re duced by e~ 2 .) ω2
= ω 2 [1 + (Ζ/Ζ,.)2]
(6)
T h e origin of the wavefront, Ζ = 0, is the waist of the beam where the spot size is a minimum, o, and the radius of curvature, R =
