Chapter 2 Experimental Methodologyshodhganga.inflibnet.ac.in/bitstream/10603/30557/10/10_chapter2.pdf · based on a common principle of heating a sample with periodical or pulsed

Chapter 2

Experimental Methodology

Abstract

Thermal wave physics has emerged as an effective research and analytic tool

for the accurate evaluation of thermal, optical and transport properties of

matter in its different states. During the last three decades photothermal

techniques which are essentially based on the detection of thermal waves in

the sample after illumination with a pulsed or a chopped optical radiation

finds its applicability as a potential tool for the thermo-optic

characterization of materials both in industry and academic environments.

The experimental methodologies used for the works presented in this thesis

are thermal-lens technique and photoacoustic technique. These techniques

come under the broad field of photothermal techniques. This chapter is

concerned with the discussion of basic principles and characteristics of

photothermal techniques in general and in particular a detailed discussion

on thermal-lens and photoacoustic techniques.

42 Chapter 2

2.1 Introduction

The photothermal (PT) techniques are a group of experimental methods

based on a common principle of heating a sample with periodical or pulsed

radiation and on measuring directly or indirectly the induced change in

temperature. Today a broad range of methods can be subsumed under this

heading, with the common feature that they use light to produce a thermal

excitation. Optical energy is absorbed and eventually converted into thermal

energy by an enormous number of materials–solids, liquids and gases.

Although the initial absorption process in many materials are selective, it is

common for excited electronic states in atoms or molecules to loose their

excitation energy by a series of nonradiative transitions that results in general

heating of the material. Such processes are the origins of the PT effects and

techniques. PT spectroscopy techniques have sensitivities far exceeding

those of conventional absorption spectrophotometry. The reasons for high

sensitivity of PT spectroscopy are that it is an indirect technique for

measuring optical absorption. Light energy absorbed and not lost by

subsequent emission results in sample heating. This heating results in a

temperature change as well as changes in thermodynamic parameters of the

sample which are related to temperature. Measurements of temperature,

pressure, or density changes that occur due to optical absorption are

ultimately the basis for the photothermal spectroscopic methods. PT

spectroscopy is a more direct measure of optical absorption than optical

transmission based spectroscopies. Sample heating is a direct measure of

optical absorption, so PT spectroscopy signals are directly dependent on light

absorption. Scattering and reflection losses do not produce PT signals. The

indirect nature of measurement also results in PT spectroscopy being more

sensitive than optical absorption measured by transmission methods. There

Experimental Methodology 43

are two reasons for this. First, the PT effects can amplify the optical signal

measured. This amplification, referred to as enhancement factor is the ratio

of the signal obtained from the PT spectroscopy to that of the conventional

transmission spectroscopy. Enhancement factors depend on the thermal and

optical properties of the sample, the power or energy of the light source used

to excite the sample and on the optical geometry used to excite the sample.

Since the optical excitation power or energy and the geometry are variable,

the enhancement can be made very large, even with samples with relatively

poor thermal and optical properties. The second reason that PT spectroscopy

is more sensitive than transmission is that the precession of the instrument is

inherently better than that of the direct transmission methods. The

fundamental limitation of the conventional absorption spectroscopy such as

shot noise, may be partially circumvented.

PT spectroscopy is usually performed using laser light sources. The first

reason is the high spectral purity and power. For an excitation of a sample

with a given absorption coefficient, the temperature change will be

proportional to the optical power, in the case of both continuous and pulsed

excitation. The PT signal is generally proportional to the temperature change.

Thus greater the power or energy, the greater the resulting signal. Lasers can

provide high powers or pulse energies over very narrow optical bandwidths,

thereby enhancing photothermal signals. The second reason is the spatial

coherence. The temperature change is not only proportional to the optical

power or energy but is also inversely proportional to the volume over which

the light is absorbed since heat capacity changes with the amount of

substance. The spatial coherence properties of laser sources allow the light to

be focused to small diffraction limited volumes. The small volumes used in

photothermal spectroscopy enhance signal magnitudes, allow PT

44 Chapter 2

spectroscopy to be used in small volume sample analysis and allow for

microscopic analysis of heterogeneous materials.

2.1.1 Basic principle of photothermal techniques

The basic processes responsible for the PT signal generation are shown in

Fig. 2.1.

Fig. 2.1 Basic process involved in photothermal spectroscopy

Optical radiation from a laser is used to excite a sample. The sample absorbs

some of these radiations resulting in an increase in the internal energy. The

internal energy is dispersed in two different modes of hydrodynamic

relaxation, results in a temperature change in the sample or coupling fluid

placed next to the sample. This temperature change results in a change in the

density of the sample or coupling fluid. If the PT induced temperature change

is faster than the time required for the fluid to expand or in a few cases

contract, the rapid temperature change will results in a pressure change. The

Pressure

Change

Temperature Change

(Thermal Diffusion)

Absorption

Optical Excitation

Excited State Relaxation

Density Change

Photothermal

Signal Refractive Index Change Optical Probe

Pressure Change

(Acoustic Wave)


pressure perturbation will disperse in an acoustic wave. In combination,

temperature and density changes affect other properties of the sample. PT

spectroscopy is based on the measurement of these properties. The key to the

success of sensitive PT apparatus lies in measurement of a thermal change,

not of the thermal state itself. Although apparatus could measure directly or

indirectly thermodynamic parameters such as temperature, pressure, density

and energy state, the limiting absorption that could measured would be

imposed by thermodynamic fluctuations. But sensitive PT methods

circumvent direct measurements by measuring refractive index changes due

to a non-equilibrium change in the energy of the sample.

The main excitation schemes can be grouped as pulsed, continuous and

modulated. Pulsed excitation source produce transient signals. These signals

are at a maximum immediately following sample excitation and decay as the

sample approaches equilibrium through thermal diffusion. The transient

signals last for few micro seconds in gas phase to several milliseconds in

condensed phases. The time duration is inversely proportional to the thermal

conductivity of the media since thermal diffusion or conduction removes

energy from the sample and, more important, distributes the energy

throughout the sample. Continuous excitation produces signals that are

initially small but increase in magnitude as the irradiation time progresses.

Initially, thermal diffusion removes heat slower than the heat produced by

optical excitation. As the sample absorbs radiation and converts the energy

to heat, the temperature gradient increases. When the radiative heating flux

equals the energy flux due to thermal conduction, a steady state spatially

dependent thermal change is attained. Thus the PT signal eventually reaches

a steady-state value. The time required to develop thermal-lens signal varies

46 Chapter 2

from milliseconds to seconds which in turn depends on the thermal

conductivity of the medium.

For analytical (e.g., concentration) measurements, both pulsed and

continuous excitation requires estimation of the signal magnitude. Signal

magnitudes are directly proportional to the sample absorbance in a first order

approximation. Signal magnitudes can be measured directly (e.g. using an

oscilloscope), or the signal transient can be recorded and subsequently

processed to enhance measurement precession. Excitation sources may also

be modulated. Chopped or oscillatory excitation produces oscillating signals.

The resulting signals can be processed using lock-in amplifiers. The

magnitude of the oscillating signal depends on sample absorbance, frequency

of excitation and thermal conductivity of the medium. With modulated

excitation, signal amplitude is directly proportional to sample absorbance but

decreases with increasing frequency. In addition to signal amplitude

information, phase sensitive lock-in analyzers also produces signal to

excitation phase shift information. The frequency dependent phase shift

information is essentially equivalent to that contained in the time dependent

signal transients obtained using pulsed excitation.

Two sensitive PT techniques ― dual-beam thermal-lens technique and laser

induced photoacoustic technique are employed for the works presented in

this thesis. The following section gives a brief description of basic principles

and theory of these techniques.

2.2 Thermal-lens technique

2.2.1 History of thermal-lens effect

The thermal-lens is a commonly employed experimental approach for the

accurate evaluation of various thermo-optic properties of samples. The


thermal-lens effect was first reported in 1964 by Gordon et al. [1-2]. In an

attempt to study Raman spectra, they placed cuvetts containing various

liquids inside the cavity of a He-Ne laser. Power transients, mode changes

and relaxation-type oscillations with time constants on the order of seconds

were observed. These phenomena have been explained in terms of the

formation of a thermal-lens in the liquid. Solimini measured the absorptivity

of a number of organic liquids at 632.8 nm and later reported an extensive

study of the accuracy and sensitivity of the intracavity thermal-lens for

measuring sample absorptivity [3]. He was also the first to postulate that the

absorptivity in organic liquids might arise from transitions between vibration

energy sates in the molecule. Carmen and Kelley studied the time evolution

of the thermal-lens created in 4CCl solutions of iodine [3]. These authors

recorded the growth of the thermal-lens by the use of a moving camera and

measured the size of the beam image frame by frame.

The important advance in thermal-lens technique was introduced by Hu and

Whinnery [4]. The authors demonstrated that maximum divergence of the

laser beam could be obtained for a given sample by positioning the sample at a

distance of one confocal length from the minimum beam waist of the laser,

which results in sensitive absorbance measurements. Most importantly, Hu

and Whinnery demonstrated that a sensitive detection of thermal-lens

formation can be achieved for samples placed outside the laser cavity by use

of an auxiliary lens to form a beam waist at a distance of one confocal length

before the sample cell. The change in the laser beam size is monitored in the

far field.

The most refinement of the thermal-lens technique was given by Dovichi and

Harris [5]. They introduced procedures needed for reliable and reproducible

measurements of thermal-lens signal. The authors constructed a differential

48 Chapter 2

thermal-lens spectrophotometer for canceling the back absorbance of the

sample matrix or the solvent. When the sample, with negative thermal

coefficient of refractive index, is placed beyond the beam waist, a diverging

beam is created and when it is placed at an equal distance before the beam

waist, a converging beam is resulted. Therefore, when two cuvetts filled with

identical samples are placed symmetrically about a beam waist, a

cancellation of about 99% of thermal-lens signal is observed. Hence, signal

due to the matrix or solvent can be optically subtracted from that of the

sample automatically, if blank sample is placed √3 time’s confocal distance

before and after the beam waist. Using this procedure, an improved

sensitivity was reported.

The experiments described above used a single laser source to provide both

the sample excitation and the means for probing the heat produced by the

absorption process. But there are several advantages by using separate laser

sources for the pump and probe beams. The small intensity modulation that

can be repetitively imposed on a well behaved continuous laser beam by the

creation of a thermal-lens can be sensitively monitored by signal averaging

devices such as lock-in amplifiers and transient recorders. In addition,

detection optics and detectors can be optimized for a single, convenient

probe laser wavelength. The first report of dual-beam thermal-lens

measurements was reported by Grabiner et al. who used a He-Ne laser to

probe the time resolved formation of thermal-lens.

The first application of the dual-beam thermal-lens technique to

spectroscopic absorption measurements was reported by Long et al. They

used a repetitively chopped continuous wave dye laser to provide the pump

beam and a He-Ne laser for the probe. Rojas et al. fabricated a dual-beam

thermal-lens optical fiber spectrometer which is capable of measuring


sensitive thermal-lens spectra at a location remote from the pump laser such

as remote environmental analysis [6]. Franko and Tran [7] constructed a CW

dual-wavelength pump-probe configuration thermal-lens spectrometer that

was capable of measuring thermal-lens signal at two different wavelengths.

The advantage of this dual-wavelength setup included the correction for

solvent background absorption and its improved selectivity. Swofford et al.

[8-9] described the dependence of the magnitude of thermal-lens on the

parameters of the experimental design in a dual-beam thermal-lens setup.

They observed good agreement between measured and calculated thermal-

lens signal. Franko and Tran fabricated various analytical thermal-lens

instruments such as differential thermal-lens, multiwavelength and spectral

tunable instruments, circular dichroism spectropolarimeters and miniaturized

instruments. Leach and Harris [10-11] demonstrated sensitivity of three

orders of magnitude in supercritical fluids [12-13], which opened new

possibilities for using thermal-lens spectroscopy in combination with

supercritical fluid extraction or chromatography.

Experimentally, recent advances in optics, electronics and quantum

electronics have been exploited to develop novel instruments which have

lower background noise, higher sensitivity and selectivity and wider

applications (by expanding its measurement capability from the conventional

visible region to the ultraviolet, near-infrared and infrared regions). The

unique characteristics of a laser, namely its low beam divergence, pure

polarization, high spectral and spatial resolution and its ability to be focused

on a diffraction-limited spot, have been fully exploited to develop novel

thermal-lens instruments which are particularly suited for small volume ( lµ )

and low concentration samples. As a consequence of these developments, the

thermal-lens technique has been established as a highly sensitive technique

50 Chapter 2

not only for chemical and stereochemical analyses but also for the detection

in chromatography and electrophoresis. Furthermore, different from

conventional techniques, in addition to the sample concentration and

excitation laser power, the thermal-lens signal is also dependent on the

position and thermo-physical properties of the sample.

2.2.2 Theory of thermal-lens effect

Assumptions

(1) The laser beam is in the TEM00 mode so that the beam cross-section is

Gaussian.

(2) The spot of the laser beam remains constant over the length of the

sample cell.

(3) The sample is homogeneous and satisfies Beer’s law.

(4) The thermal conduction is the main mechanism of heat transfer and the

temperature rise produced within the sample does not induce

convection.

(5) Refractive index change of the sample with temperature, is constant

over the temperature rise induced by the laser.

(6) The strength of the thermal-lens is not sufficient to induce a change in

the beam profile within the sample

The various processes responsible for the thermal-lens formation are given in

the following sections.

(i) Heat generation

In the thermal-lens technique the sample is illuminated using radiation from

a TEM00 or Gaussian intensity profile laser beam. Some of the radiation is


absorbed by the sample. Excited states formed in this way may either lose

energy radiatively, e.g., fluorescence or phosphorescence or by nonradiative

routes, e.g., internal conversion or by interaction with other molecules in the

sample which results in the generation of heat. These are often competing

mechanisms. However, in nearly all situations where the quantum efficiency

of fluorescence is less than, for e.g. 0.95, some heat is evolved. Even if the

quantum efficiency for fluorescence was unity, some heat would be evolved

as a consequence of the Stokes’ shift. The flow of heat from the region

illuminated by the laser results in a thermal gradient proportional to the beam

intensity profile in the sample which may be a solution, solid or gas. Heating

is stronger at the center of the beam profile than in the wings and hence the

thermal gradient in turn establishes a refractive index gradient and a thermal-

lens is said to be created. For most liquids, the temperature coefficient of

refractive index, dTdn , is negative. Gaussian-shaped beam incident on the

liquid sample produces a concave lens and the beam diverges, or “blooms”.

Thus, the thermal-lens phenomenon is sometimes referred to as “thermal

blooming”. One can observe thermal-lensing quite readily. First, a sample is

placed beyond the focal point of a lens which focuses the laser. The resulting

thermal-lens causes the beam to become more divergent after passing

through the sample. Next, a pinhole is placed some distance away from the

sample and positioned so that the center part of the beam passes through it.

When the thermal-lens forms, the resulting divergence causes decrease of the

light passing through the pinhole. The creation of thermal-lens is

schematically shown in Fig. 2.2.

52 Chapter 2

Optical lens

Fig. 2.2 Creation of thermal-lens (Refractive index distribution caused by

the pump beam in the medium makes a probe beam to get diverged

like a concave lens)

(ii) Heat conduction

The classic work on heat conduction by Carslaw and Jaeger derives the

propagation function describing the temperature rise in an infinite

cylindrically symmetric medium at radius r and time t due to an

instantaneous cylindrical heat pulse of strength per unit length 'Q applied to

the medium at radius 'r and time 0 as [3]

+−=

tD

rrI

tD

)rr(exp

tD

Q)t,r,r(G

''''

2440

22

π (2.1)

where pC/kD ρ= , with D the thermal diffusivity )sec(12 −

cm , k the

thermal conductivity )Kcmseccal(111 −−− , ρ the sample density ),cmg(

3−

pC the heat capacity )Kgcal(11 −− and 0I a modified Bessel function. The

strength )( 3Kcm of a heat pulse is defined by Carslaw and Jaeger as the

Probe beam

Sample


temperature to which the amount of heat liberated would raise unit volume of

the sample. Thus the quantity of heat instantaneously generated per unit

length of the cylinder is '

p QCρ )cmcal(1− . We can insert the rate of

continuous heat generation per unit length of the cylinder )cmseccal(Q.

11 −−

for the instantaneous heat pulse per unit length given by '

p QCρ . Thus Eq.

2.1 can be written as

+−=

'

'

'

'

'

p

.'

',,.

tD

rrI

tD

)rr(exp

tD

CQrdt)t,r,r(G

244

20

22

π

ρπ (2.2)

For a distributed heat source ''.

)( drrQ ),cmseccal(21 −− which specifies the

rate of heat generation per unit length of the sample, per unit thickness of

cylinder between radius 'r and ,''

drr + the temperature rise at r is calculated

by integrating over all 'r in the cylindrically symmetric medium. Thus for a

distributed and continues heat source, the temperature rise is given by

)t,r,r(Gdrdt)t,r(T ''.

''

∫∫∞

=0

(2.3)

In the limit of low absorptivity, the rate of heat generation between 'r and

'' drr + per unit length of the sample as a result of absorption of a Gaussian

laser beam is given by

''

'.

drr

expJ

P)r(Q

−=

2

2

2

22

ωωπ

α (2.4)

where 1184

−= calJ.J , )(1−α cm is the absorptivity of the sample, P is the

incident laser power and ω is the "e"2

1 beam radius of the laser in the

54 Chapter 2

sample cell, i.e., the radius which encompasses 8601 2 .e =− − of the total

beam power,

( )2''

2

2'

02

''

0

' 122

exp2

2)( −−=

−= ∫∫ ePdrr

rPdrrrI π

ωωππ

ωω

(2.5)

In Eq. 2.4, it has been implicitly assumed that the laser beam size ω is

constant along the cell length.

We can calculate the temperature rise in the medium and can evaluate its

second derivative at r = 0. The integral over 'r in Eq. 2.3 is evaluated to give

+

−

+=∫

∞

''

'''.

tD

rexp

tD

D

kJ

Pdr)t,r,r(G

8

2

8

22

2

2

0ωωπ

α (2.6)

We can evaluate second derivative with respect to r at r=0 before performing

the time integral in Eq. 2.3. Thus

( )22

00

2

2

8

8

)tD(kJ

DPdr)t,r,r(G

r'

r

.

'''.

+

−=

∂

∂

=

∞

∫ ωπ

α (2.7)

The integral over 't in Eq. 2.3 is evaluated to give

∫ +

−=

∂

∂

=

t

'

'

r)tD(

dtD

kJ

P

r

T

0

22

0

2

2

8

8

ωπ

α (2.8)

= ( )∫

+

−t

'

'

tD

dtD

kJ

P

0

22

2

281

8

ω

ω

ωπ

α (2.9)

=

t

'/tDkJ

P

0

2281

1

+

−

ωωπ

α (2.10)


=

+ωπ

α−

t2/t1

1

kJ

P

c

2 (2.11)

The characteristic time D

tc4

2ω= , is the response time of the medium to the

heat input.

(iii) Thermal effect on index of refraction

When a laser radiation having a Gaussian profile is incident on the sample,

by absorbing some of the incident energy, the molecules get excited to higher

energy states. Nonradiative de-excitation of these excited molecules

generates a temperature rise which in turn produces density variation in the

medium which creates a refractive index variation given by [3]

∂

∂

∂

∂+

∂

∂=

T

n

T

n

dT

dn ρ

ρρ

(2.12)

is determined primarily by changes in the sample density (second term).

Most liquids expands when heated, resulting in a negative value of dT

dn. The

change in the index of refraction of the illuminated liquid is given by

TdT

dnn ∆=∆ (2.13)

(iv) Focal length of thermal-lens

The formation of an inhomogeneous spatial profile of the refractive index is

nothing but an optical lens. For most liquids the lens formed is a divergent

one and the effective focal length of the lens is calculated by Born and Wolf

[14]. We can write the index of refraction of the cylindrically symmetric

56 Chapter 2

distribution as a Maclaurin series in the radial displacement from the center

of the distribution [3]

( ) ( ) .....r

nr

r

nrnrn

rr

+

∂

∂

+

∂

∂+=

== 0

2

22

02

10 (2.14)

Such distribution has a vanishing first derivative at 0=r .

Fig. 2.3 Diagram for calculation of the focal length of the thermal-lens

Referring to Fig. 2.3, consider the path of ray AB incident parallel to central

axis HM but displaced by a distance rKB = . The ray follows the circular

path BC with radius of curvature R, given by Born and Wolf as

( )nlngrad.vR

1= (2.15)

where v is the unit principal normal at a typical point along BC.

Since we assume that the gradient is only in the radial direction and that the

sample cell is thin (so that point O is fixed), then Eq. 2.15 reduces to


0r

2

2

r

n

n

r

r

n

n

1

R

1

=

∂

∂

=

∂

∂

= (2.16)

The ray would normally depart along CE, but refraction at the glass air

interface sends it along CD instead. By construction, DCFBJK =<< and

ECFBHK =<< .

Without refraction, the ray departing along CE would have a virtual image at

H, resulting in a focal length of fHK −=− . Instead the ray departs along

CD and has a virtual image at J, or a focal length 'fKJ −=− .

Snells law of refraction gives

1

2

1

2

)sin(

)sin(

φ

φ≈=

φ

φn (2.17)

since ,1=airn and both 1φ and 2φ are small.

We also have from geometric construction,

( ) 11tan φ≈=φf

r, (2.18)

( ) ,tan 2'2 φ≈=φf

r (2.19)

and hence

nf

f==

φ

φ'

1

2 (2.20)

From ∆ COG,

11)sin( φ≈=φR

l (2.21)

58 Chapter 2

and thus, f

r=φ1 =

R

l (2.22)

Finally,

0

2

2

=

∂

∂=

rr

nl

rR

nl (2.23)

Giving the focal length of the distribution in Eq. 2.14 as

=−= 'fF

1

0

2

2−

=

∂

∂−

rr

nl (2.24)

The radial distribution of the index of refraction in terms of the radial

temperature distribution is given by repeated use of chain rule. Since

0r

T

0r

2

2

=

∂

∂

=

, Eq. 2.24 becomes

=F

1

0

2

2−

=

∂

∂

−

rr

T

dT

dnl (2.25)

We can see in Eq. 2.25 how the strength of the thermal-lens depends on the

temperature distribution in the sample. Both dTdn / and

0

2

2

=

∂

∂

rr

Tare

negative and hence the thermal-lens is divergent )0F( < . Putting the value of

0

2

2

=

∂

∂

rr

Tfrom Eq. 2.11 in Eq. 2.25, the focal length F of the resulting

thermal-lens is obtained as

+=

t

t

)dT/dn(lP

kJ)t(F c

21

2

α

ωπ (2.26)


Eq. 2.26 assumes that conduction is the dominant mechanism of heat

dissipation.

The thermal-lens develops over a period of tenths of milliseconds. During

that time, the laser beam may be observed as a spot on a plane located a few

meters past the sample. The spot “blooms” or increases in size. It is not

actually necessary to measure the size of the spot; a tiny photodiode detector

positioned carefully at the center of the spot produces a photocurrent which

is proportional to the laser intensity on axis and thus inversely proportional

to the beam area. As the area blooms, the photocurrent diminishes according

to the expression [15]

( ) ( ) ( )1

221

0 212

1211

−

−−

+++−= ttttItI cc θθ (2.27)

Here the parameter θ is proportional to the power degraded as heat thP ,

laser wavelength λ and the other thermo optic parameters of the material as

( ) ,kdTdnPth λ=θ where )/( dTdn is the temperature dependence of the

refractive index.

(v) Sensitivity of the thermal-lens measurement

The sensitivity of thermal-lens signal can be understood by comparing it

with conventional UV/Vis spectrophotometry. In UV/Vis spectrometry the

absorbance, A, of a solution is given by Beer’s Law

AeII −= 0 (2.28)

where 0I is the initial intensity and ,lcA α= where α is the molar

absorption coefficient, c is the concentration of the solution and l is the

60 Chapter 2

length of the medium. For a weakly absorbing solution the relative change in

the signal, I∆ , can be written as

AII 0=∆ (2.29)

Hence

AI

IS A =

∆

∆=

0

(2.30)

In thermal-lens technique the thermal gradient established after optical

absorption and thermal relaxation of the sample results in a change in

intensity at the beam center owing to the induced beam divergence. The

thermal-lens signal is expressed as the relative change in power

λ=

∆=

−=

dT

dn

k

AP

I

I

I

IIS

303.20 (2.31)

where 0I and I are the transmitted power before and after the formation of

the thermal-lens respectively, A is the absorbance, P is the excitation laser

power and λ is the laser wavelength. Eq. 2.31 can be written as [16]

AEI

I303.2=

∆ (2.32)

where k

dTdnPE

λ=

)/( (2.33)

Comparing Eqs. 2.30 and 2.32 for the same absorbance, it is clear that the

thermal-lens signal is increased by a factor E, called the enhancement factor.

The enhancement factor is a function of the thermodynamic and optical

properties of the medium and on the power used to excite the sample. Thus

the sensitivity of the photothermal method can be increased by using


solvents with high refractive index gradient and low thermal conductivity for

a given power. The thermal-lens signal is inversely proportional to the square

of the excitation beam waist, while the sensitivity is independent of the beam

size. The selectivity of thermal-lens technique is hindered by the limited

wavelength range of available lasers and is most frequently confined to

single wavelength only.

(vi) Restrictions imposed on the thermal-lens model

There are several important restrictions implicit in the development of the

thin lens approximation, the most crucial being on the path length of the

sample cell. The model described earlier, assumed an index of refraction

distribution which remains constant along the beam path through the cell,

requiring that the laser beam remains reasonably well collimated over this

distance. The depth of focus, or Rayleigh length, of a laser beam is related to

focal spot size 0ω and the wavelength λ by λ

ωπ=

2

0b . The parameter

( )cmb , also called the confocal length, is the distance which the beam

expands from its minimum size to a radius 02 ω . The analysis of Gordon et

al. assumes a sample length which is a fraction of confocal length of the

incident beam. An additional restriction is that the cell edge should be short

compared with the focal length of the thermal-lens. The third restriction is

that the absorbed power must be limited to avoid full wave shifts in the phase

front of the laser beam which would otherwise lead to interference fringes in

the transmitted beam, a phenomenon known as spherical aberration. Such

strong aberration must be avoided under normal circumstances, either by use

of lower laser power, shorter path lengths, or more dilute samples. Finally it

62 Chapter 2

is implicitly assumed that heat travels out of the illuminated region of the

sample by conduction.

2.2.3 Measurement approach

According to the principle of operation, thermal-lens instruments can be

classified into two basic categories, namely single-beam and dual-beam

(pump/probe) configuration.

(i) Single-beam setup

Single-beam thermal-lens spectrometers are unique among the thermal-lens

instruments because the same laser beam is used to excite the sample and to

simultaneously probe the thermal-lens generated. Single-beam instruments

were widely used in the early stages of the thermal-lens technique. This setup

was applied to study the dependence of the thermal-lens effect on parameters

such as laser power, beam divergence, sample length, concentration,

convection and flow [17-19]. A schematic of a single-beam thermal-lens

spectrometer is shown in Fig. 2.4.

Fig. 2.4 Schematic of a single-beam thermal-lens spectrometer


Application of the thermal-lens technique in chemical analysis has not been

realized until 1979 when Dovichi and Harris [5] used the technique to detect

Cu (11) as EDTA complexed at ppm levels. The use of single-beam

experiment, in general, is due to the relative simplicity of such an instrument

and ease of operation compared to dual-beam instruments, i.e., only one laser

is used to generate and to detect the thermal-lens. In a single-beam thermal-

lens instrument the laser beam is focused with a lens and modulated by a

chopper or a shutter. After passing through the sample, the beam center

intensity is usually measured in the far field with a photodiode placed behind

a pinhole. The photodiode output is amplified and fed into a digital storage

oscilloscope which facilitates the recording of transient changes in the beam

center intensity.

(ii) Dual-beam setup

In single-beam configuration we use a single laser source to provide both

sample excitation and the means of probing the heat produced by the absorption

process. In many cases the use of separate laser sources for the ‘pump’ and

‘probe’ beams can provide significant benefits in performance. In the case of

experiments where we have to change the excitation wavelength, the detector

should be carefully chosen and corrected taking into account its wavelength

response. This problem can be overcome by the dual-beam technique [20-25]. In

a dual-beam setup the generation and detection of the thermal-lens are achieved

separately by a modulated pump beam and an unmodulated probe beam,

respectively. Good spatial overlapping of both beams inside the sample is

necessary for optimal sensitivity. The alignment and combining of the two

beams is facilitated by a beam splitter or a dichroic mirror. A schematic of dual-

beam thermal-lens spectrometer is shown in Fig. 2.5.

64 Chapter 2

Fig. 2.5 Schematic of a dual-beam thermal-lens spectrometer

2.2.4 Instrumentation

The essential components of the apparatus used for dual-beam experimental

setup are: (i) pump (modulated continuous wave or pulsed) and probe lasers

(low power, intensity stabilised) (ii) chopper (iii) a sample cell (iv) a means of

detecting the thermal-lens signal and (v) signal processing unit.

(i) Pump and probe lasers

A diode pumped solid state (DPSS) laser (Coherent Inc., mW20 ) operating at

532 nm wavelength is used as the pump laser for the works presented in the

thesis. This creates thermal-lens in the medium and thermal-lens is probed by

the probe beam. A low power, intensity stabilized He–Ne laser (Melles

Griot, mW1 ) is used to probe the thermal-lens generated in the sample.

(ii) Chopper

For dual-beam CW thermal-lens measurements, the pump laser beam was

modulated using a mechanical chopper (SR 540, Stanford Research Systems).


Mechanical chopper is the simplest form of a modulator consisting of a

rotating slotted disk placed in the path of light beam. It offers 100%

modulation depths for frequencies from a few Hz to 5-8 KHz.

(iii) Sample cell

The sample is most often taken in a standard square cuvette. Quartz cuvette of

path length 1cm is used for the present studies.

(iv) Detection of thermal-lens

The changes in laser beam intensity which result from the thermal-lens effect

are most frequently monitored by a monochromator-PMT assembly but a

photovoltaic detector such as silicon photodiode can also be used. A

monochromator is a spectrometer capable of measuring a single wavelength

which can be scanned through a wide wavelength range. Monochromator

consists of fixed entrance and exit slits, fixed focusing mirrors and a rotatable

diffraction grating. As the grating rotates different wavelength is focused onto

the exit slit. The spectral resolution depends on the widths of the slits, the

choice of grating and focal length. Grating monochromators may have planar

or concave gratings. Planar gratings are produced mechanically and may

contain imperfections in some of the grooves. Concave gratings are usually

produced by holographic methods and imperfections are usually rare. PMT

consist of a photocathode and a series of dynodes in an evacuated glass

enclosure. Photons that strikes the photoemissive cathode emits electrons due

to the photoelectric effect. Instead of collecting these few electrons at an anode

like in the phototubes, the electrons are accelerated towards a series of

additional electrodes called dynodes. These electrodes are each maintained at a

more positive potential. Additional electrons are generated at each dynode.

This cascading effect creates 105 to 10

7 electrons for each photon hitting the

66 Chapter 2

first cathode depending on the number of dynodes and the accelerating

voltage. This amplified signal is finally collected at the anode where it can be

measured. The monochromator-PMT assembly, Monora 201, Dongwoo

Optron Co. Ltd, is used for the thermal-lens studies.

(v) Thermal-lens signal analysis

The thermal-lens strength is most frequently measured as a relative change in

the beam center intensity. Only two values of the beam center intensity, initial

intensity I0 and intensity at some later time during the excitation )t(I are, in

principle, needed to calculate the thermal-lens strength. A digital storage

oscilloscope can be conveniently used to record the thermal-lens signal and

hence to find 0I and ).t(I The digital storage oscilloscope used for the present

study is APLAB (D36200CA, 200 MHZ). Digital oscilloscopes sample signals

using a fast analog-to-digital converter (ADC). At evenly spaced intervals, the

ADC measures the voltage level and stores the digitized value in high-speed

dedicated memory. The shorter the intervals, the faster the digitizing rate, and

the higher the signal frequency which can be recorded. The greater the

resolution of the ADC, the better the sensitivity to small voltage changes.

Captured waveforms can be expanded to reveal minute details.

A very efficient and rapid approach to eliminate signal noise is the use of lock-

in amplifier, which is suitable for the dual-beam thermal-lens configuration.

Lock-in amplifier is used to detect and measure very small AC signals. Lock-

in amplifiers use phase-sensitive detection to single out the component of the

signal at a specific reference frequency and phase. Noise signals at frequencies

other than the reference frequency are rejected and do not affect the

measurement. Stanford research systems (SR 830) Lock-in amplifier is used

for the works presented in this thesis.


2.2.5 Applications of thermal-lens technique

The sensitive thermal-lens technique can be used for a wide variety of

applications. Some of the important applications are listed below.

(i) Determination of fluorescence quantum yield

Fluorescence quantum yield is one of the key photophysical quantities that are

amenable to direct experimental determination. The quantum yield of

fluorescence is a measure of the rate of nonradiative transitions that compete

with the emission of light. The knowledge of fluorescence quantum efficiency

of organic dyes and its concentration dependence are essential for selecting

efficient laser media. Conventional measurements require the use of accurate

luminescence standard samples and comparison of the given sample with a

standard for which the fluorescence yield is known. The reliability of such

relative determinations is then limited by both the accuracy of the standard yield

value and by the confidence that can be placed on the comparison technique.

Even after making various corrections for system geometry, re-absorption,

polarization, etc., the accuracy of the quantum yield values obtained from

photometric measurements is rather poor. In order to evaluate absolute quantum

efficiency, we have to consider both the radiative and nonradiative processes

taking place in the medium. As the contribution from nonradiative processes is

not directly measurable using the traditional optical detection methods, thermo-

optic techniques such as photoacoustic and thermal-lens methods have been

adopted recently for this purpose. Measurements based on photothermal effects

are capable of giving fluorescence yields of fluorescent solutions with high

accuracy and reproducibility.

68 Chapter 2

(ii) Determination of metal ions

The determination of chromium, especially Cr (III) and Cr (VI) in

environmental and biological systems, is currently of considerable interest

because the essentiality or the toxicity of chromium compounds, including

humans, depends on its oxidation state. Cr (III) is considered as essential in

mammals and Cr (VI) is toxic because of its oxidizing capability and adverse

impact on lung, liver and kidney. The applicability of thermal-lens

spectrometry for quantification and routine determination of hexavalent

chromium was investigated by Sikovec et al. using a collinear dual-beam

thermal-lens spectrometer [26]. The authors have validated the technique by

comparison between thermal-lens technique results on realistic samples with

results obtained by atomic absorption spectrometry (AAS) and by the

determination of Cr (VI) in standard reference materials (SRM). The results

have demonstrated that the thermal-lens technique is a reliable and accurate for

the determination of Cr (VI) with a detection limit of 0.1 µg l–1

, confirming its

high degree of sensitivity.

The determination of iron is very important for environmental and biological

studies because of the influence of its chemical forms on the bioavailability of

iron and physicochemical and toxicological properties of the other trace

elements. The low concentration of iron present in a natural medium

necessitates the use of a sensitive procedure for its determination. Natural iron

concentrations in real water samples have been determined by thermal-lensing

by Seibel and Faubel [27]. Thermal-lens spectrometry has been used for the

determination of iron in calf serum by Legeai and Georges [28]. There is a

continuing interest toward developing and evaluating highly sensitive analytical

techniques for determining the concentration of trace of heavy metals in

environmental and biological samples.


(iii) Heat of reactions, energetics and kinetic studies

Suzuki et al. successfully employed thermal-lens technique to study heats of

reaction, energetics and reactivity of photocyclisation of diphenylamine which

highlights the potential for thermal-lens in fundamental studies of reaction

kinetics and energetics [29]. In this study a pulsed XeCl excimer laser as a

light source and an IR diode laser as a probe laser. Since the time resolved

method detects time dependent heat emitted through radiationless transitions,

metastable and excited state information can be obtained which is not

obtainable by other techniques such as flash photolysis. This twice–resolved

thermal-lens signal in the 1-10 sµ regions yielded a time profile from which

the rate constants for the decay of diphenylamine and the growth of ground

state dihydrocarbazole could be determined. The heat emitted was also

quantitatively determined by comparing the ratio of energy released as heat to

absorbed photon energy. The authors were able to determine the required

values of H∆ and the relative energetics of the triplet and singlet states of

dihydrocarbazole.

(iv) Thermal-lens effect in glass

Sampaio et al. applied thermal-lens spectrometry to study fluoride glasses as a

function of temperature [30]. The experiments, in the temperature range

between 20 and 300 0C, were performed to determine how the thermal-lens

technique can be compared with conventional differential thermal analyses

(DTA) method. Their results showed that the temperature dependence of the

thermal-lens signal amplitude provided a better definition in locating the glass

transition as compared to the DTA data. Lima et al. applied thermal-lens

technique to determine the thermal diffusivites, temperature coefficient of

optical path length changes, dT/ds and the fluorescence quantum efficiencies

70 Chapter 2

of several glasses such as fluorides, chalcogenides, chalcohalides, soda lime

and low silica calcium aluminosilicate [31].

2.3 Photoacoustic technique

2.3.1 Introduction to photoacoustic technique

Photoacoustic (PA) spectroscopy, also known as opto-acoustic spectroscopy,

is one of the families of photothermal techniques, which are based on the

conversion of light into thermal energy. Photoacoustic spectroscopy deals with

the generation of acoustic waves by any type of incident energetic beam

ranging from radio frequency to X-ray.

The PA effect was discovered by Alexander Graham Bell in 1880 while

experimenting on the transmission of sound via a beam of collimated sunlight

[32]. Bell discovered that modulated light can directly generate sound when

absorbed by solid or gaseous samples. In a series of experiments, he found out

most of the basics of PA spectroscopy and correctly interpreted his findings as

thermal expansion of matter due to the warming following the absorption of

light. He described the correlation between the absorbance of material exposed

to light and the generated acoustical signal and proposed that the effect can be

employed to investigate the optical properties of materials in the invisible part

of the optical spectrum. Bell [33] and, at the same time, Tyndall [34] and

Roentgen [35] performed several experiments with intense beams of sunlight

and arc lamps, modulated by rotating slotted disks and directed onto

transparent solid and gas samples, which generated intense acoustical signals.

Viengerov was able to measure CO2 concentrations down to ~ 0.2 vol % in N2,

using a Nernst glower as IR light source and an electrostatic microphone as

detector, thus presenting the first application of PA spectroscopy for

quantitative analysis [36]. Rosencwaig and Gersho laid the theoretical


foundation of all further works on PA spectroscopy, formulating the famous

Rosencwaig–Gersho (R-G) theory [37].

2.3.2 Fundamental principle of photoacoustic technique

The underlying principle of PA is the thermal waves produced in a sample due

to the absorption of incident energetic beam. The different stages in PA signal

generation is shown in Fig. 2.6.

Fig. 2.6 Different stages in PA signal generation

The absorption of incident beam and the subsequent nonradiative de-excitation

―relaxation process give rise to a heat source in the sample, which may be

distributed throughout its volume or confined to its surface. This heat source

Modulated Laser

beam

Local Absorption

Local Temperature

Increase

Adiabatic Expansion

Pressure Wave

Generation

Acoustic Resonance

Amplification

Modulated

Photoacoustic Signal

72 Chapter 2

give rise to pressure fluctuations, which is coupled to air in contact with the

surface and thus acoustic waves are produced. Physically, nonradiative de-

excitation in the sample by the incident beam depends not only on light to heat

conversion efficiency, but also on how the heat diffuses through the sample. The

detected PA signal strongly depends on the interplay of these three factors and

this dependence is the main reason underlying the versatility of PA technique.

The fact that the PA signal strongly depends on how the heat diffuses through

the sample allows us to perform not only thermal characterization of the sample

(i. e., measurement of its thermal properties like thermal diffusivity and

conductivity) but also to conduct thermal imaging. This is due to the fact that the

thermal wave generated by the absorption of an incident energetic pulse may be

reflected and scattered as it encounters cracks, defects and so on, thereby

affecting the detected signal. One of the principal advantages of photoacoustic

spectroscopy is that it enables one to obtain spectra similar to optical absorption

spectra on any type of solid or semisolid material, whether it be crystalline,

powder, amorphous, smear, gel, etc. This capability is based on the fact that only

the absorbed light is converted to sound. Scattered light, which presents a

serious problem when dealing with many solid materials by conventional

spectroscopic techniques, produces no difficulties in photoacoustic

spectroscopy.

2.3.3 Theory of photoacoustic technique

According to R-G theory, which is based on the one dimensional heat flow

model, the sound waves detected by the microphone depends on the acoustic

pressure disturbance at the sample-gas interface. The generation of surface

pressure disturbance, in turn, depends on the periodic temperature fluctuations

at the sample gas interface. Rosencwaig and Gersho developed an exact


expression for the temperature fluctuations by treating the acoustic disturbance

in the gas in an approximate heuristic manner.

The theoretical formulation of the R-G model [37] is based on the light

absorption and the thermal wave propagation in an experimental configuration

as shown in Fig. 2.7. Here, the sample, which is in the form a disc having a

thickness, l is in contact with backing material of low thermal conductivity

and of thickness bl . The front surface of the sample is in contact with a gas

column of length gl . The backing and the gas are considered to be non-

absorbing at the incident wavelength. Following are the parameters used in the

theoretical explanation of R-G model.

The thermal conductivity k , the density ρ , the specific heat capacity C , the

thermal diffusivity CkD ρ= , the thermal diffusion coefficient Da 2ω=

where ,fπω 2= with f modulation frequency of the incident light beam,

and the thermal diffusion length a/1=µ .

Fig. 2.7 Schematic representation of PA experimental configuration

The thermal diffusion equation in the three regions by taking into account of

the heat diffusion equation can be written as [37]

Incident light

gπµ2 gl

Boundary

layer of gas Gas Backing

material Sample

Xl− )ll( b+− 0

74 Chapter 2

( )tixee

k

I

tDx

ωβηβθθ+−

∂

∂=

∂

∂1

2

1 0

2

2

for 0≤≤− xl (2.34)

tD

1

x b

2

2

∂

θ∂=

∂

θ∂ for ( ) lxll b −≤≤+− (2.35)

tD

1

x g

2

2

∂

θ∂=

∂

θ∂ for glx ≤≤0 (2.36)

where θ is the temperature and η is the light to heat conversion efficiency

respectively. Here the subscripts b and g represent the backing medium and

gas respectively. The real part of the complex valued solution )t,x(θ of

these equations has physical significance and it represents the temperature

fluctuations in the gas cell as a function of position and time.

After imposing appropriate boundary conditions for the temperature and heat

flux continuity, and neglecting convective heat flow in the gas at steady-state

conditions, the explicit solution for the complex amplitude of the periodic

temperature at the solid-gas boundary can be obtained as

−−−++

−+−+−+−

−=

−

−−

ll

lll

e)b)(g(e)b)(g(

e)rb(e)b)(r(e)b)(r(

)(k

I

σσ

βσσ

σβ

βθ

1111

21111

2 22

00 (2.37)

where ka

akb bb= ,

ka

akg

gg= , ( ) air 21 β−= and ( ) ai+=σ 1

The periodic thermal waves, which are rapidly attenuating, damped

completely as it travels a distance equal to gµπ2 , where gµ is the thermal

diffusion length in gas. Thus the gas column within this distance expands

and contracts periodically so that it acts as an acoustic piston for the

remaining gas in the PA cell. Assuming that the rest of the gas responds


adiabatically to the action of acoustic piston, the adiabatic gas law can be

used to derive an expression for the complex envelope of the sinusoidal for

the pressure variation Q as

gg alT

PQ

0

00

2

θγ= (2.38)

where ,γ 0P and 0T are the ratio of heat capacities of air, ambient pressure

and temperature respectively. Eq. 2.38 can be used to evaluate the magnitude

and phase of the acoustic pressure wave in the cell due to PA effect. This

expression takes a simple form in special cases.

1. Optically transparent solids ( )ll >β

Case1 (a): Thermally thin solids ( )βµµ l;l >>>

We can set lel ββ −≅− 1 , 1≅± l

eσ and 1>r in Eq. 2.38 and we obtain

( )Y

ka

liQ

b

b

g

−=

µβ

2

1 (2.39)

with

glT

IPY

0

00

22

γ=

Now the acoustic signal is proportional to lβ and varies as 1−f . Moreover,

the signal is now determined by thermal properties of the backing material

Case 1(b): Thermally thin solids ( )βµµ l;l <>

We can set lel β−≅β− 1 , ( )le

l σσ +≅± 1 and 1<r in Eq. 2.38 and we obtain

( )Y

ka

liQ

b

b

g

−≅

µβ

2

1 (2.40)

76 Chapter 2

The acoustic signal now behaves in the same fashion as in the previous case.

Case l(c): Thermally thick solids ( )βµµ l;l <<<

lel ββ −≅− 1 , 0≅− l

eσ and 1<<r , in Eq. 2.38 and we obtain

Yka

iQg

−≅

µβµ

2 (2.41)

Now, only the light absorbed within the first thermal diffusion length

contributes to the signal in spite of the fact that light is being absorbed

throughout the length of the sample. Also since ( )l<µ , the backing material

does not have any contribution to the signal. Interestingly, the signal now

varies as .5.1−

f

2. Optically opaque solids ( )ll <<β

Case 2(a): Thermally thin solids ( )βµµ l;l >>>>

We can set 0≅− le

β , 0≅σ± le and 1>>r , in Eq. 2.38 and we obtain

Yka

iQ

b

b

g

µ−≅

2

)1( (2.42)

Now the signal is independent of β , which is valid for a perfect black

absorber such as carbon black. The signal will be much stronger compared to

the case 1(a) and varies as 1−f , but still depends on the properties of backing

material.

Case 2 (b): Thermally thick solids ( )βµµ l;l ><

We can set 0≅β− le , 0≅σ− l

e and ;r 1> in Eq. 2.38 and we obtain


( )Y

ka

iQ

g

µ−≅

2

1 (2.43)

Equation 2.43 is analogous to Eq. 2.42, but the thermal properties of backing

material are now replaced with those of the sample. Again the signal is

independent of β and varies as 1−f .

Case 2 (c): Thermally thick solids ( )βµµ l;l <<<

We can set 0≅− le

β , 0≅− le

σ and 1<r in, Eq. 2.38 and we obtain

Yka

iQg

−≅

µµβ

2 (2.44)

This is very interesting and important case. Even though the solid is optically

opaque, the photoacoustic signal is proportional to β as long as 1<µβ . As

in case 1 (c), the signal is independent of the thermal properties of the

backing material and varies as 51.f

− . The R-G theory also predicts the linear

dependence of PA signal to light intensity.

The one dimensional R-G theory of PA effect is quite successful in that, its

variation can be successfully applied to evaluate thermophysical parameters

such as thermal effusivity of solid and liquid samples, with high accuracy [38].

2.3.4 Instrumentation

The essential components of the apparatus used for photoacoustic

spectroscopy are: (1) a source of periodic radiation (i.e., modulated

continuous wave or pulsed) in the spectral region of interest; (2) a PA cell;

(3) a means of detecting the acoustic signal and (4) signal processing equipment.

78 Chapter 2

A schematic of the experimental arrangement of PA spectroscopy is shown

in Fig. 2.8.

Fig. 2.8 Basic experimental arrangement of PA spectroscopy

Various modifications of this fundamental instrumentation have been used to

perform a wide variety of PA experiments. In all cases, however, the

modulated light from the source is used to repetitively excite one species in the

sample cell. This periodic excitation is transformed by radiationless relaxation

processes into a periodic variation in the sample temperature. Because of

pressure variation a periodic acoustic disturbance in the sample is produced,

which can be monitored by an appropriate acoustic detector. The signal from

the acoustic detector can be amplified, averaged and further manipulated to

provide valuable information regarding sample composition, kinetics of

energy transfer processes and a wide variety of other phenomena. The major

apparatus employed for the instrumentation of photoacoustic technique are

described below.

Light Source

Modulator

Sample Cell

Signal Processing

Microphone


(i) Light sources

The classical lamp/monochromator and the laser are two types of light

sources currently in use for PA spectroscopy. The lamp/monochromator

combination can provide continuous tunability from the infrared to

ultraviolet. A major limitation of this source is the modest bandwidth-

throughput product. The lamp/monochromator combination is generally used

with strongly absorbing samples or where low resolution suffices. But lasers,

with their nearly monochromatic high spectral brightness, have significant

advantages over lamp/monochromator combinations which account for their

wider acceptance as PA spectroscopy light sources. A laser output is highly

collimated, with cylindrical beam symmetry being ideal for exciting radial

resonances in a PA cell.

(ii) Modulation techniques

Several devices such as optical choppers, electronic shutters and acousto-

optic (AO) modulators are available for efficient and accurate modulation of

CW laser beams. Choppers are more appropriate, particularly when high

excitation powers are used (several hundred mW ). This is because heating

of the chopper blade is minimized due to its constant motion.

(iii) Cell design

Most common acoustic cell designs adopt the basic symmetry of the exciting

light source and are cylindrically shaped sample containers. The excitation

source is a smaller diameter light beam centered along the cylinder axis.

Local heating caused by light absorption and subsequent relaxation generates

a local pressure increase which propagates radially outward perpendicular to

the exciting beam.

80 Chapter 2

The cross-sectional view of some of the important cell designs are shown in

Fig. 2.9.

(a) Variable temperature PA cell (b) OPC cell

(c) Resonance PA cell (d) Liquid PA cell

Fig. 2.9 Different PA cell design

The open photoacoustic cell (OPC) configuration shown in Fig. 2.9(b) is a

modified and more convenient form of conventional photoacoustic

configuration. In OPC sample will be mounted directly on top of the

microphone, leaving a small volume of air in between the sample and the

microphone. It is an open cell detection configuration in the sense that the

sample is placed on top of the detection system itself. Consequently, this

configuration is a minimum volume PA detection scheme and hence the

signal strength will be much greater than the conventional PA configurations.

The major advantage of this configuration is that samples having large area

can be studied, whereas in conventional PA cells sample size should be small

enough to be contained inside the PA cavity.


(iv) Acoustic detectors

Several devices exist for detecting the acoustic disturbance generated by

sample absorption. They can be broadly classified into three groups: pressure

sensors, refractive index sensors and temperature sensors. Most PA

experiments utilize pressure sensors, the most common of which are

microphones.

A condenser microphone produces an electrical signal when a pressure wave

impinging on the diaphragm pushes the diaphragm closer to a fixed metal

plate, thereby increasing the capacitance between these two surfaces. The

capacitance change leads to a voltage signal Vs which increases with bias

voltage VB and diaphragm area Am. Condenser microphones generally have

flat frequency response to 15 kHz, have low distortion, are generally not

sensitive to mechanical vibrations and respond well to pressure, impulses,

which enable their use in pulsed applications. The dielectric material

between the condenser plates in this type of microphone is air. In contrast to

condenser microphones, electret microphones [37] are constructed using

solid materials of high dielectric constant which are electrically polarized.

One side of the electret foil is metallized and the insulating side is placed on

a fixed back plate. A sound wave impinging on the metallized side causes a

change in the polarization characteristics of the electret material which in

turn produces a small voltage between the metallized front electret surface

and the back plate of the microphone. Thus, an electret microphone requires

no bias voltage, which affords a simplification of the apparatus needed.

Another striking difference between air spaced condenser microphones and

electret microphones is physical size. Due to the large capacitance per unit

area possible from electret materials, they can be made into miniaturized

microphones.

82 Chapter 2

(iv) Photoacoustic signal processing

Signal processing in photoacoustic experiments entails three stages:

amplification, filtering and signal averaging. Amplifiers should be very low-

noise, broad-banded (~MHz) devices in order to prepare the signal for the

averager. Depending on the information desired, filtering might involve the

use of a high-Q filter to select the dominant frequency component in the

complex acoustic signal, the use of band pass filtering to discriminate

especially against 1−f noise, or the use of no filtering at all to accurately

reproduce the time evolution of the acoustic signal. The amplified and

filtered signal is then processed by lock-in amplifiers.

2.3.5 Applications of photoacoustic technique

(i) Depth profile analysis and microscopy

One of the important features of the PA technique is the potentiality of this

technique to detect subsurface variations in both optical and thermal

properties of the sample. The studies are called PA imaging and are

essentially classified in to two categories. PA imaging is mainly concerned

with the variations of the sample properties along its thickness, the technique

is called PA depth profiling. The depth profile analysis is performed by

measuring the PA signal amplitude and phase as a function of modulation

frequency. The PA signal is sensitive to the heat generated within one

thermal diffusion length ( ) 21 /f/D πµ = beneath the sample surface. Here

D , is the sample thermal diffusivity and f is the modulation frequency.

Thus, at high modulation frequency the PA signal comes deeper within the

sample. If however high lateral resolution is required, the PA imaging is

called PA microscopy. The potentialities of PA depth profile analysis were

originally demonstrated by Adans and kirkbright [39] for the simple case of


two layer sample consisting of a top transparent layer of thickness l on an

optically thick substrate. The specific example used by these authors to

illustrate PA depth profile capability was that of a polymer coating on a

copper substrate. The PA depth profile technique can provide not only

information about the thickness of a surface layer, the thermal diffusivity of a

coating, or irregularities below the surface, but also about depth dependent

spectral features.

(ii) Thermal diffusivity measurements

The quantity which measures the rate of heat diffusion in the sample is the

thermal diffusivity ‘ D ’. Apart from its own intrinsic importance, its

determination gives the value of thermal conductivity k , if the density ρ and

the thermal capacity at constant pressure are known, since

ckD ρ= (2.45)

The importance of D as a physical parameter to be monitored is due to the

fact that, it is unique for each material. Furthermore, thermal diffusivity is

known to be extremely dependent upon the effect of compositional and

microstructural variables [40], processing conditions, as in the case of

polymers [41-43], Glasses [44] and ceramics [40]. Thermal diffusivity of

many materials can be accurately measured by PA technique. This was first

demonstrated by Adams and kirkbrigt [45]. The authors have used PA

method to obtain thermal diffusivity values of copper and glass by plotting

the phase angle φ of the PA signal as a function of the square root of the

chopping frequency ω .

84 Chapter 2

(iii) Biological applications

In many cases PA technique is an alternative method for studying biological

materials not suitable for conventional spectroscopic techniques such as

transmission or reflectance, due to scattering properties. The capability of PA

technique for obtaining biological spectra of samples of different types has

been illustrated by Rosencwaig [46]. Balasubramanian et al. used this

technique to monitor the malaria parasite in order to establish the nature of

this pigment, provide direct evidence of drug interaction in the parasite and

distinguish drug sensitive strains of resistant microorganism [47].

Various examples of the use of PA technique on intact green leaf have been

reported. For example, Lima et al. [48] presented evidence that PA technique

can be very useful complementary tool in assessing plant productivity at

some stage of its development. In addition to the usual spectroscopic

information such as band position and relative intensities, PA spectroscopy

can offer new information that arises uniquely from the combination of the

spectroscopic and calorimetric phenomena that comprise the PA Effect. This

information includes quantum yield, life times from various metastable

excited states and the kinetics of relaxation pathways of photobiological

systems [49].

The frequency dependence of the PA signal can give information on the

amounts of energy stored in the intermediates of biologial photoprocesses

[50-55]. Cahen et al. [50-51] studied photosynthesis of lettuce chloroplasts.

Carpentier et al. [52-54] reported the use of PA spectroscopy to study the

photosynthesis of algaue and leaves. The same group used the technique to

monitor the photosynthetic energy storage in hetrosystems. In the area of

dermatology, PA spectroscopy has been used particularly for studying the


effects of active drugs in the skin. This was first demonstrated by Campbell

et al. [55] by carrying out drug detection and determination of drug diffusion

rate in the human skin. Using an open ended cell, Giese et al. [56] reported

measurements on human skin treated with sunscreens. Poulet and chambron

[57] described an open ended cell for in-vivo PA spectroscopy of the skin.

As demonstrated by the authors a satisfactory signal to noise ratio can be

obtained by using a differential microphone. In the area of food stuff quality

control many applications of PA technique on the monitoring of food stuffs

adulterants have also appeared in the literature [58].

(iv) Photoacoustic spectroscopy for aerosol characterization

Aerosols are fine particles in a size range between a few nanometers to

several micrometers suspended in gases. The first diode-laser based

instrument for atmospheric soot measurements was presented by Petzold

et al. in 1993 [59-60]. As opposed to most other analytical problems, the aim

of optical measurements on aerosols is the optical properties itself rather than

concentration of analyte. The optical properties are highly relevant for the

calculation of radiation balance in the context of global climate modeling.

Most PA systems developed for aerosol measurements are meant for the

characterization of their optical properties. Typical applications of PA-based

atmospheric aerosol measurements are demonstrated in many large-scale field

studies regarding aerosol distribution and their climate relevance [61-62].

(v) Industrial process analysis

PA spectroscopy can be employed for the analysis of food stuff. However, the

limited selectivity of optical absorption measurements restricts this field of

application to cases where the optical properties themselves are the target of the

analysis. Examples are the quantification of carotene in margarine [63] or the

86 Chapter 2

determination of colorant additives in different types of food [64-66]. Yang et al.

tested FTIR/PA for application in food analysis, e.g. for the quantification of

proteins, fats, water and carbohydrates in meat [67-69]. The same group

compared the capabilities of FTIR/PA with conventional attenuated total

reflection (ATR) and diffuse reflectance-FTIR and with NIR spectroscopy. PA-

induced ultrasound was also developed for the analysis of pulp in the process of

paper manufacture [70].

Conclusions

To conclude photothermal techniques are an ultrasensitive means to measure

optical absorbance. The field of photothermal science has partially fulfilled

some of its promises since its rediscovery, almost fifteen years ago, by

Rosencwaig. Yet its potential as a research and analytical tool seems to be

not fully explored and each year new routes for developments are being

opened up. Its ease of operation and versatility, together with the wealth of

information contained in the photothermal signal, warrants us that further

areas of applied research will adapt these techniques to their own uses. This

chapter described a survey about the state-of-the-art of two photothermal

techniques ― Thermal-lens technique and laser induced photoacoustic

technique. Both these techniques are nondestructive and noncontacting

measuring methods correlating the thermal and optical properties of

materials. They have gained a substantial progress during the last 10 years,

due to intensive research work. It is hoped that these systematic

measurement methods will a play a major role in the industrial applications

of the coming future.


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Chapter 2 Experimental Methodologyshodhganga.inflibnet.ac.in/bitstream/10603/30557/10/10_chapter2.pdf · based on a common principle of heating a sample with periodical or pulsed