Diffusive thermal grating

After the thermal grating signal, the signal rose again and finally it decayed to the baseline. This rise-decay component depended on q2 (Fig. 8.6a) and this q2 dependence is a clear indication that these components represent the diffusion processes. On the basis of considerations similar to the previous PYP case, it was concluded that this rise-decay feature of the diffusion signal... 

Frez C, Diebold GJ, Tran C et al. (2006) Determination of thermal diffusivities, thermal conductivities, and sound speeds of room temperature ionic liquids by the transient grating technique. J Chem Eng Data 51 1250-1255... 

This technique was applied to study the photophysical processes involved in the excited triplet states [87-89], After the photoexcitation of a photo-chemically stable organic molecule in solution under air saturated condition, generally a strong thermal grating signal, which decays to the baseline with the thermal diffusion time, was observed. Initially, the signal rise can be analyzed by... 

The relaxation processes of Br2 from the photoexcited state in carbon tetrachloride (CC14) was investigated by the diffusive component of the thermal grating [95]. A long-lived component (18 ns) and a fast-rising component were observed in the TG signal. The slower dynamics was assigned to the decay from the lowest excited state A ( n2u). From the amplitude of these components, the quantum yield of the A state formation was estimated to be 0.50 + 0.08. 

The thermal grating method was applied to a free ion yield measurement after a photoinduced electron-transfer reaction [98], The principle was similar to the measurement of (j)isc by the diffusive component of the Dens.G. The free ion yields in the photoinduced electron transfer from various donors to 9,10-dicyanoanthracene were determined from the ratio of the fast and slow rising intensities. The later one came from the released energy by the recombination reaction of the free ions and the former one came from the other processes (energy diagram Fig. 11). The quantum yield decreased from 0.5 to about 0 by changing the donor from biphenyl to N,N-dimethylaniline [different ox(Z))]. The determined [Pg.290]

The quantum yield of photodissociated diphenyldisulfide was measured in various solvents from the rise part of the diffusive thermal (Dens.G) grating and also from the PA signal intensity [115] (Scheme 6). 

Figure 14. Diffusive TG signal after photodissociation of DPCP (solid line) and the fitted lines by two exponential decays (dotted line). The strong signal represents the thermal grating signal and the two exponential decays are due to the species grating. The inlet is the plot of the decay rate constant versus q2. The diffusion constant of each species can be determined from the slopes [120].

For transient wave mixings, the detailed calculations for the three-dimensional thermal grating buildup and temperature distribution and dissipation are obviously very complex, and are further complicated by the anisotropic thermal diffusion constants of the liquid crystals, as well as the enclosing glass slides. In the simplest case where the thermal grating is reducible to a one-dimensional problem [14] (e.g., the case of very small grating constant A compared to the cell thickness /), the thermal decay time constants for heat dissipation along and per-... 

Figure 9.6. Interference of the propagative index gratings (arising from electrostrictive density changes) with the diffusive 9 (but not propagative) thermal grating.

The spatially periodic temperature distribution produces the corresponding relxactive index distribution, which acts as an optical phase grating for the low-power probing laser beam of the nonabsorbed wavelength in the sample. The thermal diffusivity is determined by detecting the temporal decay of the first-order diffracted probing beam [°o exp(-2t/x)] expressed by... 

The thermal healing has been studied most extensively for one-dimensional gratings. Above roughening, the gratings acquire, for small amplitude to wavelength ratios, a sinusoidal form, as predicted by the classical continuum theory of Mullins and confirmed by experimenf-s and Monte Carlo simulations. - The decay of the amplitude is, asymptotically, exponential in time. This is true for both evaporation dynamics and (experimentally more relevant) surface diffusion. 

One of the widely used methods of analysis of kinetic data is based on extraction of the distribution of relaxation times or, equivalently, enthalpic barrier heights. In this section, we show that this may be done easily by using the distribution function introduced by Raicu (1999 see Equation [1.16] above). To this end, we use the data reported by Walther and coworkers (Walther et al. 2005) from pump-probe as well as the transient phase grating measurements on trehalose-embedded MbCO. Their pump-probe data have been used without modification herein, while the phase grating data (also reproduced in Figure 1.12) have been corrected for thermal diffusion of the grating using the relaxation time reported above, r,, and Equation (1.25). 

Some constraints apply for the measurement of mass and thermal diffusion by TDFRS, which originate from excessive sample heating at high laser powers, the resulting onset of convection, and the need to avoid boundary effects at the cuvette windows when the grating constant becomes comparable to the sample thickness. The problem of optimization of the experimental boundary condi-... 

Since the length scales associated with the thermal lens are on the order of 10 to 1000 times the grating constant, their characteristic time scale interferes with polymer diffusion within the grating. Such thermal lensing has been ignored in many FRS experiments with pulsed laser excitation [27,46] and requires a rather complicated treatment. A detailed discussion of transient heating and finite size effects for the measurement of thermal diffusivities of liquids can be found in Ref. [47]. 

Concentration grating Due to the Ludwig-Soret effect, the temperature grating is the driving force for a secondary concentration grating, which starts to build up and is superimposed upon the thermal one. Its temporal and spatial evolution is obtained from the one-dimensional form of the extended diffusion equation... 

T = (Dq2) 1 is the collective diffusion time constant, DT the thermal diffusion coefficient. In Eq. (18), the low modulation depth approximation c( M c0, resulting in c(x,t)(l-c(x,t)) c0(l-c0)y has been made, which is valid for experiments not too close to phase transitions. Eqs. (16) and (20) provide the framework for the computation of the temperature and concentration grating following an arbitrary optical excitation. 

The transport coefficients have been measured by the transient holographic grating technique of Thermal Diffusion Forced Rayleigh Scattering (TDFRS) that has already been described in more detail in previous works [85-87] and will only be briefly sketched in the following (Fig. 1). 

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