Diffuse spectrum

By comparison wifh diafomics, polyatomic molecules are more likely fo show diffuseness in fhe rofafional, and even fhe vibrational, sfmcfure of elecfronic fransifions. There is also a 

The line widfh Av of a rofafional fransifion accompanying an elecfronic or vibronic fransifion is related to fhe lifetime t of fhe excited sfafe and fhe firsf-order rate consfanf k for decay by 

In a large molecule fhe vibrational and rofafional levels associated wifh any elecfronic sfafe become so exfremely congested af high vibrational energies fhaf fhey form a pseudo-continuum. This is illusfrafed for Sq, Si and fhe lowesf excited friplef sfafe T, lying below Sj, 

For some — Sq transitions, Pp is so low that fluorescence has not been detected. 

The fluorescence lifetime tp can be measured directly and is the lifetime of the state, taking into account all decay processes. It is related to and by 

By comparison with diatomics, polyatomic molecules are more likely to show diffuseness in the rotational, and even the vibrational, structure of electronic transitions. There is also a 

The line width Av of a rotational transition accompanying an electronic or vibronic transition is related to the lifetime r of the excited state and the first-order rate constant k for decay by 

In a large molecule the vibrational and rotational levels associated with any electronic state become so extremely congested at high vibrational energies that they form a pseudocontinuum. This is illustrated for S0,5) and the lowest excited triplet state 7), lying below Sh 

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The diffused spectra were recorded under these conditions for all zeolites. Figure 1 shows the spectra obtained for sample 3. Conclusions based on the spectra are listed in Table I. 

Fig. 85. Two-dimensional, 3C spin diffusion spectra of mixtures of adamantane and 2,2,3,3-tetramethylbutane at 75.4 MHz (424) (a) Mixture of powders (b) mixture by melt. Note the absence of cross-peaks between signals belonging to different species in the heterogeneous sample in (a).

This technique measures the optical spectrum of light which is diffusely scattered off the catalyst sample. Absorption frequencies are characteristic of certain arrangements of molecules and their environment. Even pure compounds give rather broad diffuse spectra, and catalysts show even broader spectra. Hence, results are only semiquantitative at best. In regards to molybdena catalysts, the information derived with this technique is the coordination environments of Mo and Co in the catalyst. 

The corresponding band systems have approximately the same separation (ca. 5000 cm-1) as observed between the 2IIj and 2I1 components of the ground state of CH3I+. Similar effects appear in the more diffuse spectra of CH3Br and CH3I (Herzberg and Scheibe, 1930 Price, 1936). 

It has long been recognized that both the diffuse spectra and quenching problems can be alleviated by performing the fluorescence measurement in a low-temperature solid matrix, rather than in a fluid solution. The most common low-temperature matrices used in molecular fluorometric analysis are frozen liquid solutions the analytical characteristics of frozen-solution luminescence spectrometry have been discussed extensively in the literature (2-10). Obviously, MI represents an alternative technique to use of frozen liquid solutions for low-temperature fluorometric analysis. There are two principal advantages of MI over frozen-solution fluorometry. First, in MI, any material which has an appreciable vapor pressure at room temperature can be used as a matrix one is not limited by the... 

We now consider two special cases in which the diffusion spectra are nontrivial and Eq. (66) may be used to evaluate the result of a modulated spin-echo experiment. The first case concerns slow molecular collision rates. As pointed out by Einstein (1956), the result... 

Fig. 5. Diffusion spectra for water traveling through close-packed ion-exchange resin beads (50-100 mesh) at flow rates of 13 ml hr" (solid circles), 25 ml hr" (open squares), 50 ml hr" (open circles), and 100 ml hr" (solid squares). The crosses represent the measured spectrum for stationary water. The lines are to guide the eye. The pronounced peak is believed to arise from the oscillatory motion of water around the beads, while the low-frequency plateau is due to perfusive spreading of the flow. [Reproduced by permission from Callaghan and Stepisnik, 1995a.]...

Fig. 4.11. Proton driven spin-diffusion spectra of l- C glycine and alanine-labeled Nephila madagascariensis dragline silk at T = 150 K. A mixing time of 10 s was used. The spectrum was acquired with 128 transients per data point in ti, 96 spectra have been recorded in the Fi domain. The data matrix of 96 x 128 points was zero-filled to 256 x 256. As inset, the contour plot of the same data is shown. (Figure adapted from Ref. [63]).

Fig. 10.20. Spin-diffusion spectra taken after the indicated spin-diffusion times for PS(OH)/PBMA = 60/40 the Mo spectrum is given as a reference lineshape corresponding to full internal spin equilibrium. (Reprinted with permission from Ref. [116]. 1992 American Chemical Society, Washington, DC.)...

Figure 9 Experimental 2D "P NMR spin-diffusion spectra of hydrated VPI-5 recorded with 3-s mixing time at various MAS speeds 77 (a) 4.9 kHz (b) 6.5 kHz and (c) 10.1 kHz. The three spectra are not on the same intensity scale, so only the relative intensities within each can be compared.

Fig. 7. Experimental 2D P spin diffusion spectra of hydrated VPl-5 recorded with the mixing time of 3 s and MAS speeds of 4.9 kHz (top), 6.5 kHz (middle) and 10.1 kHz (bottom), respectively (used from Koiodziejski et with permission).

Pulsed-Field Gradient Spin-Echo NMR Diffusion NMR experiments resolve different compounds in a mixture based on their diffusion coefficients, depending on physical parameters such as size and shape of the molecules, temperature, and viscosity. The diffusion NMR technique is often referred to as diffusion-ordered spectroscopy (DOSY) or pulsed-field gradient spin-echo (PGSE) NMR. A series of NMR diffusion spectra are acquired as a function of the gradient strength G (Fig. 2.19) [56], and the slope of the peak decay is used to obtain the diffusion coefficient D. Furthermore, the hydrodynamic radius can be obtained from the Stokes-Einstein equation (Eq. 2.3). 

Figure 20 Comparison of proton-driven spin diffusion spectra obtained using...

Ngai and Phillies(61) extend the Ngai-Rendell coupling model(62) to treat probe diffusion and polymer dynamics in polymer solutions. This is not an experimental paper it forces extant experimental data to confront a particular theoretical model, which in the paper was extensively reconstructed to treat the particular experimental methods under consideration. Ngai and Phillies consider zero-shear viscosities and optical probe diffusion spectra for HPC solutions, extracting from them the Ngai-Rendell model relaxation time tq and coupling exponent n. Optical probe spectra and other measurements were used to obtain n in four independent ways, namely from r](c) and from the concentration, time, and wave-vector dependences of g q,t). The four paths from t] and lead to consis-... 

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