Stochastic TDFRS

In the previous sections it has been shown that there are similarities between TDFRS and PCS, and that the main advantage of TDFRS stems from the possi- 

Of course, there is a major drawback of short excitation pulses. Since, due to sample heating, the laser intensity cannot be increased in the same way as the pulses are shortened, the product I Tp decreases, and, as a consequence, the signal vanishes in the baseline noise. When viewed from the frequency domain, this is a direct consequence of the low spectral power density of short excitation pulses. The decrease of the concentration signal is already obvious for the short excitation times in Fig. 13. 

In this section, more general excitation patterns will be discussed, which allow for tailored deconvolutable excitations with high spectral power densities. Periodic amplitude modulation with a single frequency has been proposed in the literature [73]. It is well suited for noise suppression by lock-in detection, but in practice it suffers from stability problems during the slow frequency sweep. 

Pseudostochastic random binary sequences in combination with fast Fourier transform and correlation techniques avoid these problems and allow for a direct measurement of g(t) with high spectral power density and frequency multiplexing (stochastic TDFRS). Tailoring of the pseudostochastic sequences even allows for a selective enhancement and suppression of certain frequencies and, hence, of certain molecular species [74]. 

Pseudostochastic random binary sequences are noise-like time patterns. They are defined at times n A t and assume only two different values, corresponding to the grating amplitudes -1 and +1, if 180°-phase modulation is used for switching off the optical grating. Only software modifications, and no changes in the hardware of the TDFRS setup, are necessary in order to utilize pseudostochastic excitation sequences. The timing for heterodyne/homodyne separation is identical to the one already described for pulsed excitation. 

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Before stochastic TDFRS is treated in detail, periodic amplitude modulation of the grating in combination with phase-sensitive lock-in detection, similar to the procedure proposed by Bloisi [73], will be briefly discussed. With periodic amplitude modulation with a single frequency, which is slowly scanned through the frequency range of interest, the Fourier transform of the TDFRS response function, G([Pg.40]

Figure 26 shows a stochastic TDFRS measurement. The system is PS (M = 250 kg/mol, c = 0.0205) in toluene. The upper half of the insert shows a short sequence of the pseudostochastic binary excitation sequence of length 211 [75]. The sampling time At is 140 /us. How the sequence has been generated will be discussed in the next section. 

Fig. 26. Memory function g(t) as obtained from stochastic TDFRS with an optimized random binary sequence. The inserts show a short sequence of the excitation and the corresponding heterodyne response. From Ref. [75]...

Fig. 33. Rate distribution of the PCS and the stochastic TDFRS (g(t)) measurement in Fig. 32. The arrow marks the fast diffusion of the component with M=0.895 kg/mol. From Ref. [75]...

Fig. 33 shows in a more quantitative analysis the rate distributions as obtained by a CONTIN analysis of the PCS and the stochastic TDFRS measurement. 

The ratio of 6.8 for the two peak areas from stochastic TDFRS is close to the value of 5.9 as expected from the concentration ratio and the refractive index increments of the two PS, which depends on molar mass due to end-group effects. The thermal diffusion coefficient DT= 1.12 x 10 7 cm2 (sK) l is in excellent agreement with the value found previously in our laboratory [36]. 

Fig. 36. Differential and integral rate distributions as obtained from a CONTIN analysis of the measurements in Fig. 35. The central peak is enhanced in the filtered stochastic TDFRS experiment...

Figures 35 to 37 show an experiment in which digital filtering has been utilized to enhance a certain species and to suppress others. The sample is a trimo-dal mixture of PS (5,50,2000 kg/mol) in toluene. It has been measured by PCS and stochastic TDFRS, with and without digital filtering.

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