## Soret effect and photochemical reaction in liquids with laser-induced local heating |

Optics Express, Vol. 19, Issue 5, pp. 4047-4058 (2011)

http://dx.doi.org/10.1364/OE.19.004047

Acrobat PDF (1116 KB)

### Abstract

We report a theoretical model and experimental results for laser-induced local heating in liquids, and propose a method to detect and quantify the contributions of photochemical and Soret effects in several different situations. The time-dependent thermal and mass diffusion equations in the presence and absence of laser excitation are solved. The two effects can produce similar transients for the laser-on refractive index gradient, but very different laser-off behavior. The Soret effect, also called thermal diffusion, and photochemical reaction contributions in photochemically reacting aqueous Cr(VI)-diphenylcarbazide, Eosin Y, and Eosin Y-doped micellar solutions, are decoupled in this work. The extensive use of lasers in various optical techniques suggests that the results may have significance extending from physical-chemical to biological applications.

© 2011 Optical Society of America

## 1. Introduction

2. B. J. deGans, R. Kita, S. Wiegand, and J. Luettmer-Strathmann, “Unusual thermal diffusion in polymer solutions,” Phys. Rev. Lett. **91**, 245501 (2003). [CrossRef]

3. A. Würger, “Molecular-weight dependent thermal diffusion in dilute polymer solutions,” Phys. Rev. Lett. **102**, 078302 (2009). [CrossRef] [PubMed]

4. R. Piazza and A. Guarino, “Soret effect in interacting micellar solutions,” Phys. Rev. Lett. **88**, 208302 (2002). [CrossRef] [PubMed]

6. S. N. Rasuli and R. Golestanian, “Soret motion of a charged spherical colloid,” Phys. Rev. Lett. **101**, 108301 (2008). [CrossRef] [PubMed]

7. J. Lenglet, A. Bourdon, J. C. Bacri, and G. Demouchy, “Thermodiffusion in magnetic colloids evidenced and studied by forced Rayleigh scattering experiments,” Phys. Rev. E **65**, 031408 (2002). [CrossRef]

8. B. Hoffmann, W. Köhler, and M. Krekhova, “On the mechanism of transient bleaching of the optical absorption of ferrofluids and dyed liquids,” J. Chem. Phys. **118**, 3237–3242 (2003). [CrossRef]

10. F. Huang, P. Chakraborty, C. C. Lundstrom, C. Holmden, J. J. G. Glessner, S. W. Kieffer, and C. E. Lesher, “Isotope fractionation in silicate melts by thermal diffusion,” Nature (London) **464**, 396–400 (2010). [CrossRef]

22. D. Vigolo, S. Buzzaccaro, and R. Piazza, “Thermophoresis and thermoelectricity in surfactant solutions,” Langmuir **26**, 7792–7801 (2010). [CrossRef] [PubMed]

27. P. R. B. Pedreira, L. R. Hirsch, J. R. D. Pereira, A. N. Medina, A. C. Bento, M. L. Baesso, M. C. Rollemberg, M. Franko, and J. Shen, “Real-time quantitative investigation of photochemical reaction using thermal lens measurements: theory and experiment,” J. Appl. Phys. **100**, 044906 (2006). [CrossRef]

29. N. G. C. Astrath, F. B. G. Astrath, J. Shen, J. Zhou, K. H. Michaelian, C. Fairbridge, L. C. Malacarne, P. R. B. Pedreira, P. A. Santoro, and M. L. Baesso, “Arrhenius behavior of hydrocarbon fuel photochemical reaction rates by thermal lens spectroscopy,” Appl. Phys. Lett. **95**, 191902 (2009). [CrossRef]

## 2. Thermal Lens theory in the presence of PCR and Soret effects

28. N. G. C. Astrath, F. B. G. Astrath, J. Shen, J. Zhou, K. H. Michaelian, C. Fairbridge, L. C. Malacarne, P. R. B. Pedreira, A. N. Medina, and M. L. Baesso, “Thermal-lens study of photochemical reaction kinetics,” Opt. Lett. **34**, 3460–3462 (2009). [CrossRef] [PubMed]

32. N. G. C. Astrath, J. H. Rohling, A. N. Medina, A. C. Bento, M. L. Baesso, C. Jacinto, T. Catunda, S. M. Lima, F. G. Gandra, M. J. V. Bell, and V. Anjos, “Time-resolved thermal lens measurements of the thermo-optical properties of glasses at low temperature down to 20K,” Phys. Rev. B **71**, 214202 (2005). [CrossRef]

27. P. R. B. Pedreira, L. R. Hirsch, J. R. D. Pereira, A. N. Medina, A. C. Bento, M. L. Baesso, M. C. Rollemberg, M. Franko, and J. Shen, “Real-time quantitative investigation of photochemical reaction using thermal lens measurements: theory and experiment,” J. Appl. Phys. **100**, 044906 (2006). [CrossRef]

29. N. G. C. Astrath, F. B. G. Astrath, J. Shen, J. Zhou, K. H. Michaelian, C. Fairbridge, L. C. Malacarne, P. R. B. Pedreira, P. A. Santoro, and M. L. Baesso, “Arrhenius behavior of hydrocarbon fuel photochemical reaction rates by thermal lens spectroscopy,” Appl. Phys. Lett. **95**, 191902 (2009). [CrossRef]

*A*(

_{e}*t*) =

*C*(

*t*)

*ɛ*, where

*ɛ*is the molar optical absorption coefficient of the sample and

*C*(

*t*) [29

29. N. G. C. Astrath, F. B. G. Astrath, J. Shen, J. Zhou, K. H. Michaelian, C. Fairbridge, L. C. Malacarne, P. R. B. Pedreira, P. A. Santoro, and M. L. Baesso, “Arrhenius behavior of hydrocarbon fuel photochemical reaction rates by thermal lens spectroscopy,” Appl. Phys. Lett. **95**, 191902 (2009). [CrossRef]

27. P. R. B. Pedreira, L. R. Hirsch, J. R. D. Pereira, A. N. Medina, A. C. Bento, M. L. Baesso, M. C. Rollemberg, M. Franko, and J. Shen, “Real-time quantitative investigation of photochemical reaction using thermal lens measurements: theory and experiment,” J. Appl. Phys. **100**, 044906 (2006). [CrossRef]

**95**, 191902 (2009). [CrossRef]

### 2.1. Temperature and concentration gradients

_{00}laser excites the sample at 0 <

*t*≤

*ξ*(laser-on). No excitation exists when

*t*>

*ξ*(laser-off). It will be shown later that the laser-off TL transient is required to distinguish between Soret and PCR effects in the TL transient signal. For an isotropic, weakly absorbing material, the temperature rise distribution in a sample is described by the heat conduction differential equation where

*D*=

*k*/(

*ρc*) is the thermal diffusivity,

*k*is thermal conductivity,

*ρ*is mass density and

*c*is the specific heat of the sample. The source term

*Q*(

*r*,

*t*), described for on-off excitation under the assumption that the sample exhibits a photochemical reaction [28

28. N. G. C. Astrath, F. B. G. Astrath, J. Shen, J. Zhou, K. H. Michaelian, C. Fairbridge, L. C. Malacarne, P. R. B. Pedreira, A. N. Medina, and M. L. Baesso, “Thermal-lens study of photochemical reaction kinetics,” Opt. Lett. **34**, 3460–3462 (2009). [CrossRef] [PubMed]

*C*(

*t*) = (

*C*

_{0}−

*C*) exp(−

_{eq}*K*) +

_{T}t*C*is the concentration of absorbing species,

_{eq}*C*

_{0}denotes the initial concentration, and

*C*is the equilibrium concentration in the illuminated area. The total reaction rate constant

_{eq}*K*is given by

_{T}*K*=

_{T}*k*+

_{r}*k*, where

_{d}*k*and

_{r}*k*represent the reaction and species diffusion rates, respectively.

_{d}*Q*

_{0}= 2

*P*/(

_{e}φ*ρcπω*

^{2}), where

*ω*and

*P*are the radius and power of the excitation laser, respectively.

_{e}*φ*is the fraction of the absorbed energy available for conversion to heat. The heat produced by absorbed excitation beam is treated as a line heat source, and the sample as an infinite medium with respect to the excitation beam radius

*ω*. The heat conduction equation is solved using integral transform methods (Laplace, Fourier cosine, and Hankel transform methods) and Eq. (2), yielding with

*t*

_{0}= 0 for

*t*≤

*ξ*and

*t*

_{0}=

*t*−

*ξ*for

*t*>

*ξ*. Eq. (3) describes the temperature rise in a photo-reacting sample during laser-on and laser-off periods. The characteristic heat diffusion time constant is

*t*=

_{c}*ω*

^{2}/(4

*D*).

5. R. Rusconi, L. Isa, and R. Piazza, “Thermal-lensing measurement of particle thermophoresis in aqueous dispersions,” J. Opt. Soc. Am. B **21**, 605–616 (2004). [CrossRef]

*D*is the mass diffusion coefficient,

_{m}*c̄*is the initial average concentration and

*S*=

_{T}*D*/

_{T}*D*is the Soret coefficient.

_{m}*D*denotes the coefficient of thermal diffusion. Writing the characteristic mass diffusion time as

_{T}*t*=

_{m}*ω*

^{2}/(4

*D*) ≫

_{m}*t*, for

_{c}*t*≫

*t*[5

_{c}5. R. Rusconi, L. Isa, and R. Piazza, “Thermal-lensing measurement of particle thermophoresis in aqueous dispersions,” J. Opt. Soc. Am. B **21**, 605–616 (2004). [CrossRef]

^{2}

*T*(

*r*,

*t*) in Eq. (4) with the stationary solution of the heat conduction equation, Eq. (1). Within this approximation, the mass diffusion equation is formally the same as the heat conduction equation. We assume that the sample is sufficiently thick that the axial null thermal flux approximation can be applied as shown in Ref. [28

28. N. G. C. Astrath, F. B. G. Astrath, J. Shen, J. Zhou, K. H. Michaelian, C. Fairbridge, L. C. Malacarne, P. R. B. Pedreira, A. N. Medina, and M. L. Baesso, “Thermal-lens study of photochemical reaction kinetics,” Opt. Lett. **34**, 3460–3462 (2009). [CrossRef] [PubMed]

### 2.2. Probe beam phase shifts

_{00}Gaussian probe laser beam propagates through the illuminated volume of the liquid sample, its wave front is slightly distorted, and the distortion can be expressed as an additional phase shift, which can be calculated by considering the problem from the point of view of optical path length variation regarding the axis as

*n*is the refractive index,

*L*is the sample thickness, and

*λ*the probe beam wavelength. The total additional phase shift on the probe beam when both the PCR and Soret effects occur is the superposition of the phase shifts,

_{p}*ϕ*and

_{PCR}*ϕ*, caused by the temperature gradient [28

_{Soret}**34**, 3460–3462 (2009). [CrossRef] [PubMed]

5. R. Rusconi, L. Isa, and R. Piazza, “Thermal-lensing measurement of particle thermophoresis in aqueous dispersions,” J. Opt. Soc. Am. B **21**, 605–616 (2004). [CrossRef]

*z*-independent refractive index gradients that act as optical elements in the sample. The phase shifts are given by and The temperature and concentration coefficients of the refractive index at the probe beam wavelength

*λ*are

_{p}*dn*/

*dT*and

*dn*/

*dc*, respectively. In other words, the phase shift describes the distortions of the probe beam caused by the temperature and concentration changes in the medium. From Eq. (6) using Eq. (3),

*ϕ*can be calculated as From Eq. (7) using Eq. (5) the phase shift produced by the Soret effect can be written In Eqs. (8) and (9), the variables

_{PCR}*m*= (

*ω*

_{1}

*/*

_{P}*ω*)

^{2}, and

*c*=

_{r}*C*/

_{eq}*C*

_{0}have been introduced. In addition,

*θ*is defined as and

_{th}*θ*is

_{m}*ω*

_{1P}is the radius of the probe laser beam in the sample. When a PCR and the Soret effect both occur, the total phase shift is

### 2.3. Thermal lens intensity at the detector plane

30. J. Shen, R. D. Lowe, and R. D. Snook, “A model for cw laser-induced mode-mismatched dual-beam thermal lens spectrometry,” Chem. Phys. **165**, 385–396 (1992). [CrossRef]

30. J. Shen, R. D. Lowe, and R. D. Snook, “A model for cw laser-induced mode-mismatched dual-beam thermal lens spectrometry,” Chem. Phys. **165**, 385–396 (1992). [CrossRef]

*Z*

_{1}and

*Z*

_{2}are the distances from the probe beam waist to the sample and the sample to the detector plane, respectively. In Eq. (13),

*V*=

*Z*

_{1}/

*Z*,

_{C}*Z*is the confocal distance of the probe beam, and

_{C}*C*is a constant [27

**100**, 044906 (2006). [CrossRef]

*I*(

*t*) at the detector plane can be calculated as As special cases, pure Soret or PCR effects are obtained in this model by taking

*K*= 0 or

_{T}*θ*= 0, respectively, in Eq. (12).

_{m}*I*(

*t*) with Eq. (12) is used to fit the experimental data, where

*m*,

*V*,

*ω*,

*P*,

_{e}*L*and

*λ*are experimental setup parameters previously determined and

_{p}*θ*,

_{th}*θ*,

_{m}*t*,

_{c}*t*,

_{m}*c*and

_{r}*K*are obtained from the fits.

_{T}## 3. Experimental results and discussion

*P*

_{1}triggered the digital oscilloscope that recorded the TL signal. Converging lens

*L*

_{1}focused the excitation beams, with the sample placed at its focal plane. The probe beams were focused by lens

*L*

_{2}, and the sample was positioned near its confocal plane. A small angle

*γ*< 1.5° existed between the excitation and probe beams. After passing through the TL the probe beam propagated to photodiode

*P*

_{2}, positioned in the far field (

*Z*

_{2}≈ 5m). A pinhole was placed in front of photodiode

*P*

_{2}, such that only the central part of the probe beam was detected and recorded by the oscilloscope. The probe-beam power absorbed by the sample was assumed to be negligible as compared to the power of the excitation beam in both cases. Sample temperatures were maintained at 28°C. For setup B,

*ω*= 55

*μm*was measured while

*m*= 23.6 and

*V*= 3.05 were calculated using the relations presented above. Setup A was used for the Cr(VI) solution with

*ω*= 72

*μm*,

*m*= 45.2 and

*V*= 8.3. These geometrical parameters, which were constant during the measurements, were determined as described in Ref. [30

30. J. Shen, R. D. Lowe, and R. D. Snook, “A model for cw laser-induced mode-mismatched dual-beam thermal lens spectrometry,” Chem. Phys. **165**, 385–396 (1992). [CrossRef]

**100**, 044906 (2006). [CrossRef]

33. S. Hazebroucq, F. Labat, D. Lincot, and C. Adamo, “Theoretical insights on the electronic properties of eosin Y, an organic dye for photovoltaic applications,” J. Phys. Chem. A **112**, 7264–7270 (2008). [CrossRef] [PubMed]

_{3}(CH

_{2})

_{11}(OCH

_{2}CH

_{2})

_{23}OH, polyoxyethylene 23 lauryl ether] in cobalt nitrate (absorbance 0.04) [34

34. N. Arnaud and J. Georges, “On the analytical use of the Soret-enhanced thermal lens signal in aqueous solutions,” Anal. Chim. Acta **445**, 239–244 (2001). [CrossRef]

**100**, 044906 (2006). [CrossRef]

33. S. Hazebroucq, F. Labat, D. Lincot, and C. Adamo, “Theoretical insights on the electronic properties of eosin Y, an organic dye for photovoltaic applications,” J. Phys. Chem. A **112**, 7264–7270 (2008). [CrossRef] [PubMed]

34. N. Arnaud and J. Georges, “On the analytical use of the Soret-enhanced thermal lens signal in aqueous solutions,” Anal. Chim. Acta **445**, 239–244 (2001). [CrossRef]

*L*= 0.5cm quartz cuvettes. Photo-reactive dyes such as Cr(VI) and Eosin as well as micellar Brij solutions are commonly used to improve spectroscopic sensitivity [33

33. S. Hazebroucq, F. Labat, D. Lincot, and C. Adamo, “Theoretical insights on the electronic properties of eosin Y, an organic dye for photovoltaic applications,” J. Phys. Chem. A **112**, 7264–7270 (2008). [CrossRef] [PubMed]

26. N. Arnaud and J. Georges, “Thermal lens spectrometry in aqueous solutions of Brij 35: investigation of micelle effects on the time-resolved and steady-state signals,” Spectrochim. Acta A **57**, 1085–1092 (2001). [CrossRef]

*g*/

*dm*

^{3}. The geometry of the micelles is ambiguous, although their structures have recently been modelled using spherical and/or ellipsoidal cores. The radius of the micelles is about 40

*Å*. As mentioned above, the Cr(VI) and EY samples analyzed here are expected to display only a PCR while the Brij solution exhibit only the Soret effect. Accordingly, when EY and Brij solutions are mixed, both PCR and Soret effects should be observable.

**34**, 3460–3462 (2009). [CrossRef] [PubMed]

*K*= 0, which actually pertains to the Soret effect. It should be noted that this use of Eq. (12) with

_{T}*K*= 0 is effected only to show that the PCR and Soret contributions to the TL on-signal can have similar trends. The dotted line in the Fig. 2(a) on-transient thus represents either the Soret (Eq. (12) with

_{T}*K*= 0) or PCR (Eq. (12) with

_{T}*θ*= 0) fit. In other words, both mass diffusion and PCR effects would give similar trends in the TL on-transient signal. Further experimental evidence is therefore required to ascertain whether the Soret or PCR effect is responsible for the transient TL signal.

_{m}*K*= 0 (Soret) and the parameters obtained from the on-transient does not yield a satisfactory fit of the experimental data. On the other hand, the parameters derived from the PCR model, Eq. (12) with

_{T}*θ*= 0, produce very good agreement between the calculated curve (off-transient dotted line) and the experimental data. This shows that the off-transient signal must be taken into account when processing the experimental data if the effect taking place in the sample is to be correctly identified. The fitted parameters obtained using Eq. (12) with

_{m}*θ*= 0 (estimated uncertainty ±5%) are as follow:

_{m}*θ*/

_{th}*P*= 18.1

_{e}L*W*

^{−1}

*cm*

^{−1};

*c*= 0.59; and

_{r}*K*= 2

_{T}*s*

^{−1}. The thermal diffusivity is

*D*= 1.45 × 10

^{−3}

*cm*

^{2}

*s*

^{−1}.

*t*< 200

*ms*, corresponds to a the thermally induced refractive index gradient with a time constant of approximately 5.3ms. The Soret effect then occurs under the influence of the temperature gradient, causing species to migrate and establish a concentration gradient. The on/off-transient was fitted to Eq. (14) using Eq. (12) with

*K*= 0 (Soret), yielding the results listed in Table 1. The agreement between theory and experimental results is very good and the obtained parameters agree well with the expected values for this sample [34

_{T}34. N. Arnaud and J. Georges, “On the analytical use of the Soret-enhanced thermal lens signal in aqueous solutions,” Anal. Chim. Acta **445**, 239–244 (2001). [CrossRef]

**112**, 7264–7270 (2008). [CrossRef] [PubMed]

*K*= 0; the dotted line in the Fig. 3(a) on-transient represents either the Soret or the PCR fit. As noted for Cr(VI), both PCR and mass diffusion yield similar trends in the TL on-transient signal. However, use of the parameters obtained with the Soret equation for the laser-off transient produces a curve that does not fit the experimental data. By contrast, the parameters obtained from the PCR model, Eq. (14) using Eq. (12) with

_{T}*θ*= 0, provide very good agreement between the calculated curve and the experimental off-transient data (dotted line).

_{m}*θ*= 0 (PCR) and

_{m}*K*= 0 (Soret) and the resulting parameters were used to generate off-transient curves for the PCR (dotted line) and Soret (dashed line) contributions. As might be expected, the PCR contribution alone does not fit the experimental data well; this suggests that the off-transient may incorporate both PCR and Soret components. In fact, the use of Eq. (14) and Eq. (12) makes it possible to fit all of the data (both on- and off-transients). The result (continuous line) agrees very well with experiment, again indicating that - although the on-transient appears to be due to either the PCR or Soret effects - the off-transient must be taken into consideration to arrive at a correct interpretation of the results.

_{T}**112**, 7264–7270 (2008). [CrossRef] [PubMed]

*s*(on-transient). The solid line in Fig. 4 displays the least-squares on/off curve fit obtained with Eq. (14) using Eq. (12). Several transients were recorded at different excitation powers; the resulting parameters are plotted in Fig. 5. Reasonably, the thermal diffusivities (

*D*) for the samples are very close to the accepted value of 1.45 × 10

^{−3}

*cm*

^{2}

*s*

^{−1}for pure water. The mass diffusion coefficients (

*D*) of the samples are listed in Table 1. These values were calculated using the relations

_{m}*D*=

*ω*

^{2}/4

*t*and

_{c}*D*=

_{m}*ω*

^{2}/4

*t*, respectively. Dotted and dashed lines in Fig. 4 represent the on/off calculated contributions of the PCR and Soret effects using the same equations with

_{m}*θ*= 0 and

_{m}*k*= 0, respectively, and parameters obtained for the on- and off-transient curves.

_{T}## 4. Conclusions

## Acknowledgments

## References and links

1. | C. Soret, “Concentrations differentes d’une dissolution dont deux parties sont a’ des temperatures differentes,” Arch. Sci. Phys. Nat. |

2. | B. J. deGans, R. Kita, S. Wiegand, and J. Luettmer-Strathmann, “Unusual thermal diffusion in polymer solutions,” Phys. Rev. Lett. |

3. | A. Würger, “Molecular-weight dependent thermal diffusion in dilute polymer solutions,” Phys. Rev. Lett. |

4. | R. Piazza and A. Guarino, “Soret effect in interacting micellar solutions,” Phys. Rev. Lett. |

5. | R. Rusconi, L. Isa, and R. Piazza, “Thermal-lensing measurement of particle thermophoresis in aqueous dispersions,” J. Opt. Soc. Am. B |

6. | S. N. Rasuli and R. Golestanian, “Soret motion of a charged spherical colloid,” Phys. Rev. Lett. |

7. | J. Lenglet, A. Bourdon, J. C. Bacri, and G. Demouchy, “Thermodiffusion in magnetic colloids evidenced and studied by forced Rayleigh scattering experiments,” Phys. Rev. E |

8. | B. Hoffmann, W. Köhler, and M. Krekhova, “On the mechanism of transient bleaching of the optical absorption of ferrofluids and dyed liquids,” J. Chem. Phys. |

9. | S. R. De Groot and P. Mazur, |

10. | F. Huang, P. Chakraborty, C. C. Lundstrom, C. Holmden, J. J. G. Glessner, S. W. Kieffer, and C. E. Lesher, “Isotope fractionation in silicate melts by thermal diffusion,” Nature (London) |

11. | M. Giglio and A. Vendramini, “Thermal-diffusion measurements near a consolute critical-point,” Phys. Rev. Lett. |

12. | C. Debuschewitz and W. Köhler, “Molecular origin of thermal diffusion in benzene plus cyclohexane mixtures,” Phys. Rev. Lett. |

13. | P. A. Artola and B. Rousseau, “Microscopic interpretation of a pure chemical contribution to the Soret effect,” Phys. Rev. Lett. |

14. | D. Jung and M. Lücke, “Localized waves without the existence of extended waves: oscillatory convection of binary mixtures with strong Soret effect,” Phys. Rev. Lett. |

15. | K. I. Morozov, “Soret effect in molecular mixtures,” Phys. Rev. E |

16. | A. Parola and R. Piazza, “Particle thermophoresis in liquids,” Eur. Phys. J. E |

17. | N. Ghofraniha, C. Conti, G. Ruocco, and F. Zamponi, “Time-dependent nonlinear optical susceptibility of an out-of-equilibrium soft material,” Phys. Rev. Lett. |

18. | S. Fayolle, T. Bickel, S. LeBoiteux, and A. Würger, “Thermodiffusion of charged micelles,” Phys. Rev. Lett. |

19. | S. Duhr and D. Braun, “Thermophoretic depletion follows Boltzmann distribution,” Phys. Rev. Lett. |

20. | S. A. Putnam, D. G. Cahil, and G. C. L. Wong, “Temperature dependence of thermodiffusion in aqueous suspensions of charged nanoparticles,” Langmuir |

21. | R. Piazza, “Thermophoresis: moving particles with thermal gradients,” Soft Matter |

22. | D. Vigolo, S. Buzzaccaro, and R. Piazza, “Thermophoresis and thermoelectricity in surfactant solutions,” Langmuir |

23. | D. Braun and A. Libchaber, “Trapping of DNA by thermophoretic depletion and convection,” Phys. Rev. Lett. |

24. | S. Duhr and D. Braun, “Optothermal molecule trapping by opposing fluid flow with thermophoretic drift,” Phys. Rev. Lett. |

25. | M. Ichikawa, H. Ichikawa, K. Yoshikawa, and Y. Kimura, “Extension of a DNA molecule by local heating with a laser,” Phys. Rev. Lett. |

26. | N. Arnaud and J. Georges, “Thermal lens spectrometry in aqueous solutions of Brij 35: investigation of micelle effects on the time-resolved and steady-state signals,” Spectrochim. Acta A |

27. | P. R. B. Pedreira, L. R. Hirsch, J. R. D. Pereira, A. N. Medina, A. C. Bento, M. L. Baesso, M. C. Rollemberg, M. Franko, and J. Shen, “Real-time quantitative investigation of photochemical reaction using thermal lens measurements: theory and experiment,” J. Appl. Phys. |

28. | N. G. C. Astrath, F. B. G. Astrath, J. Shen, J. Zhou, K. H. Michaelian, C. Fairbridge, L. C. Malacarne, P. R. B. Pedreira, A. N. Medina, and M. L. Baesso, “Thermal-lens study of photochemical reaction kinetics,” Opt. Lett. |

29. | N. G. C. Astrath, F. B. G. Astrath, J. Shen, J. Zhou, K. H. Michaelian, C. Fairbridge, L. C. Malacarne, P. R. B. Pedreira, P. A. Santoro, and M. L. Baesso, “Arrhenius behavior of hydrocarbon fuel photochemical reaction rates by thermal lens spectroscopy,” Appl. Phys. Lett. |

30. | J. Shen, R. D. Lowe, and R. D. Snook, “A model for cw laser-induced mode-mismatched dual-beam thermal lens spectrometry,” Chem. Phys. |

31. | M. L. Baesso, J. Shen, and R. D. Snook, “Mode-mismatched thermal lens determination of temperature-coefficient of optical-path length in soda lime glass at different wavelengths,” J. Appl. Phys. |

32. | N. G. C. Astrath, J. H. Rohling, A. N. Medina, A. C. Bento, M. L. Baesso, C. Jacinto, T. Catunda, S. M. Lima, F. G. Gandra, M. J. V. Bell, and V. Anjos, “Time-resolved thermal lens measurements of the thermo-optical properties of glasses at low temperature down to 20K,” Phys. Rev. B |

33. | S. Hazebroucq, F. Labat, D. Lincot, and C. Adamo, “Theoretical insights on the electronic properties of eosin Y, an organic dye for photovoltaic applications,” J. Phys. Chem. A |

34. | N. Arnaud and J. Georges, “On the analytical use of the Soret-enhanced thermal lens signal in aqueous solutions,” Anal. Chim. Acta |

**OCIS Codes**

(350.5340) Other areas of optics : Photothermal effects

(350.6830) Other areas of optics : Thermal lensing

**ToC Category:**

Materials

**History**

Original Manuscript: January 13, 2011

Revised Manuscript: February 2, 2011

Manuscript Accepted: February 3, 2011

Published: February 15, 2011

**Virtual Issues**

Vol. 6, Iss. 3 *Virtual Journal for Biomedical Optics*

**Citation**

L. C. Malacarne, N. G. C. Astrath, A. N. Medina, L. S. Herculano, M. L. Baesso, P. R. B. Pedreira, J. Shen, Q. Wen, K. H. Michaelian, and C. Fairbridge, "Soret effect and photochemical reaction in liquids with laser-induced local heating," Opt. Express **19**, 4047-4058 (2011)

http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-19-5-4047

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### References

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