Grating relaxation

To extract a value of the step-mobility h from the grating relaxation experiments [12], we must evaluate the strength of the step-step interaction y. Computational work suggests that ydue to elastic interactions between Si(OOl) steps is 0.2 eV run [29], while, we estimate that the entropic interaction is 10 times larger. (We use a step stiffness P calculated from the geometric mean of P for Sa and Sb steps given in Ref [30] P, 0.03 eV mn-. ) Therefore, entropic repulsion should dominate, and... 

Keefe et al. [12] observed that the relaxation of micron-sized 1-D gratings on Si(OOl) is consistent with Eq. 1. But as discussed above, the derivation of Eq. 1 is not strictly valid at r < Tr. We show here that these experiments are also in agreement with dynamics of the conserved, step-mobility-limited model derived by Nozieres [21] ... 

Data for step-mobilities shown in Fig. 6 span an impressively large range a factor of 10 " separates step-mobilities measured by STM from the step-mobilities extracted from the relaxation of micron-sized gratings. Some discrepancies exist, but most of the step-mobilities are consistent with a single activation energy of 1.8 eV and an attempt rate given by the frequency of atomic vibrations. We hope that this initial comparison of step-mobility data will help motivate more detailed theoretical analysis and experiments on the coimections between step-mobility and the evolution of surface morphology. 

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). 

The response time, r, is typically determined by measuring the grating build-up time or erasure rate. For large grating spacings, the response time is the inverse dielectric relaxation rate ... 

Charge transport is one of the important processes that control the speed of the PR index grating formation and the PR sensitivity. According to the standard theory of photorefraction [21], the response time for the formation and erasure of the space-charge field [xr in Eq. (21)] is proportional to the dielectric relaxation... 

Finally, we note that the time scale for the PE experiment is determined by the dephasing times, which are very short in proteins ( 300 fs) (41). Other complementary 2D techniques were proposed in Ref. 17. In particular, energy relaxation, which occurs in proteins and polypeptides on a large time scale ( 2-15 ps) (15,41), can be studied by utilizing the transient grating and the three pulse PE techniques. These can be calculated as well using the third-order response function presented here. 

Saphiannikova M, Geue T M, Hennenberg O, Morawetz K, Pietsch U. (2004) Linear viscoelastic analysis of formation and relaxation of azobenzene polymer gratings. J Chem Phys 120 4039 045... 

The authors are grateful to Prof. F. Hirata of Kyoto University, Prof. S. Kinoshita of Osaka University, and Dr. A. Yoshimoii of Nagoya University for fmitful discussion on the relaxation processes of solution. The present work was partly supported by a Grant-in-Aid (06NP301 and 06239240) to T.O. from the Ministry of Education, Science, and Qilture of Japan. 

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