High-mode-number limit

The high-mode-number limit, p>NI6n, for the normal mode relaxation time suggests ... 

Fig. 28. Proton spin-lattice relaxation times in the laboratory system (Tj) and in the rotating frame (Tip) of polyisobutylene (PIB) melts as a function of the frequency (v, Lar-mor frequency in the laboratory frame Vi=yBi/(27i), rotating-frame nutation frequency) [125]. The data refer to the molecular weight independent chain-mode regimes I (high-mode-number limit) and II (low-mode-number limit) [49], The arrow indicates the crossover frequency between regions I and II...

Below it will be shown that field-cycling NMR relaxometry studies unambiguously reveal a crossover between high-frequency and low-frequency dispersion regimes that can be identified with the high-mode-number and low-mode-number limits of the renormalized Rouse models. Moreover, the variation of the power law exponents closely corresponds to that predicted by the renormalized Rouse models. These dynamic regimes cannot be ex-... 

High- and Low-Mode-Number Limits (Dispersion Regions I and II)... 

Based on the generalized Langevin equation, the renormalized Rouse models suggest dynamic high- and low-mode-number limits as an implicit structural feature of this equation of motion. This is a stand-alone prediction of paramount importance independent of any absolute values of power law exponents that arise and are measured in the formalism and in experiment, respectively. The two limits manifesting themselves as power law spin-lattice relaxation dispersions were clearly identified in bulk melts of entangled polymers of diverse chemical species. 

The appearance of dispersion regions I and II in experiments is an exultant confirmation of the high- and low-mode-number, short-time limits predicted by the twice renormalized Rouse models (Tables 2 and 3). The exponents of the power laws suggested by the experimental data even match the theoretical predictions almost perfectly [47, 49]. Nevertheless, the good coincidence of the numerical values of these exponents is not considered to be the decisive finding backing up the renormalized Rouse models. The problem is that the theoretical exponents are slightly affected by the renormalization... 

Anions of another group were derivatized with formation of gaseous chemiluminescing species. Chemical reaction - gas extraction has been used with chemiluminescence detection in the stream of canier gas in on-line mode. Rate of a number of reactions has been studied as well as kinetic curves of extraction of gaseous products. Highly sensitive and rapid hybrid procedures have been developed for the determination of lO, BrO, CIO, CIO, NO,, N03, CrO, CIO, Br, T, S, 803 with detection limits at the level of pg/L, duration of analysis 3 min. 

Macrocyclic glycopeptides. The first of these CSPs - based on the cavity of the antibiotic vancomycin bound to silica - was introduced by Armstrong [25]. Two more polycyclic antibiotics teicoplanin and ristocetin A, were also demonstrated later. These selectors are quite rugged and operate adequately in both normal-phase and reversed-phase chromatographic modes. However, only a limited number of such selectors is available, and their cost is rather high. 

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