Correlation time of molecular motion

Various models have been proposed relating quadrupolar relaxation times to the correlation times of molecular motions, (lc) The more sophisticated the model considered the greater the number of parameters involved and thus the necessity for more independent NMR measurements. These may be obtained from a consideration of both14N and 2H relaxation data on a series of closely related molecules. Ordinary and... 

Heterogeneous soft matter, in particular polymer materials, are often characterized by distributions of correlation times of molecular motion. For relaxation studies of polymers, sophisticated filters have been developed which fit the classification of combination filters because they combine Tj and Tip relaxation [Gotl, Gbt2, G6t3]. These filters can be used... 

Despite the inhomogeneous B field of the siuface coil, spin-lock experiments can also be performed to interrogate 7 ip relaxation (cf. Sections 3.5 and 7.2.3) [Blii2]. If Tc denotes the correlation time of molecular motion then, from eqn (3.5.7) Tip can be expressed in the weak collision limit as... 

In this chapter, NMR studies for four ILs having a common anion bis(fluoromethylsulfonyl)amine (TFSA) will be described. The cations are N-ethyl-N-methylimidazolium (EMIm), N,2-dimethyl-N-propylimidazolium (DMPIm), N-methyl-N-propylpyrrolidinium (F 13), and N,N-diethyl-N-methyl-N-(2-methoxylethyl)ammonium (DEME). These ILs are important candidates to use as electrolytes in various batteries or cells. The basic properties of molecular weight (MW), viscosity (q) and cation and TFSA diffusion coefficients (Dcaiion and ZTtfsa) measured at 30°C are given in Table 1 for the four ILs. The experimental data have been published in our previous papers for individual ILs.i-4 In the present chapter, the individual experimental data for the four ILs are plotted on a sheet to clarify the cation properties. In addition, newly derived plots of Dcaaon versus correlation times of molecular motion are included. The chemical structures of the ions are shown. 

The C Ti values were plotted against inverse absolute-temperature in Fig. 9. 17 together with those of the amorphous region for MQPESL (melt-quenched polyethylene (single C-labeled)) which was melted at 150°C and quenched to -70°C and PESL (polyethylene single C-labeled) which was dissolved at 130°C in xylene at a concentration of 0.03% and crystallized. The Ti curves for these three samples have the minimum at different temperatures. The Ti minimum for polyethylene adsorbed on the surface of silica gel appears at the highest temperature compared with other samples. According to the BPP theory, the correlation time for molecular motion at the Ti minimum corresponds to the resonance frequency. 

Fig. 9.18. Plots of correlation times in molecular motion for the methylene carbons in the region B for C-labeled polyethylene adsorbed on the surface of silica gel against the inverse absolute temperature [23].

From the Ti minimum, the correlation time for molecular motion at megahertz frequencies is obtained. The plot of log (tc) vs. 1/T for the DMS moiety in Fig. 17.31 shows a good linear relationship. The temperature dependence of the correlation time Tc usually obeys the Arrhenius form [39] as Tc = To exp(-AE/RT), where Tq is the prefactor, R is the gas constant and T is the absolute temperature. The activation energy AE, which is considered to correspond to the barrier height for the potential hindering rotation, can... 

The quantity (e2 qQ) is the known quadrupole coupling constant and is made up of the electronic charge e, electric field gradient q and nuclear quadrupole moment Q. ra is a correlation time for molecular motion, rj is an asymmetry parameter and I is the nuclear spin quantum number. 

One characteristic of in situ NMR experiments is that there is typically a wide range of correlation times characterizing molecular motion. Some species will be essentially immobile as a result of strong chemisorption to the catalyst surface or physical entrapment, as in the case of a coke molecule. Other species may reside exclusively in the gas phase or else be partitioned into adsorbed and gas phase populations in slow exchange on the NMR time scale owing to diffusional constraints. Figure 7 shows an example. At high temperatures, methanol and dimethyl ether are partitioned between the gas phase and adsorbed phase on zeolite HZSM-5 [31 ]. For many adsorbates on zeolites, especially at reaction... 

Evaluation of Correlation Time for Molecular Motion from ESR Spectra... 

Fig. 10 Correlation time in molecular motion, tg, of pure water and water in 200 wt/wt% aqueous solution calculated from T as a function of temperature. Mobile water squares), immobile water triangles) and pure water circles)...

When a macromolecule adsorbs at a solid-liquid interface, the molecular motion of the polymer s backbone becomes slower, and the longer correlation time of the motion is reflected in the relaxation times of protons ( H NMR) or free electrons (electron paramagnetic resonance, EPR) that are attached closely to the backbone. Provided there is slow exchange between segments associated with the surface (trains) and those in loops or tails, the spectrum of the whole molecule will be resolvable into the fraction of the chain in each state. As discussed in more detail later, these fractions obtained by EPR and NMR may well be quite different from, but complementary to, those obtained by IR measurements. 

Figure 23 illustrates the dependence of T2, and 7 ip on the frequencies of molecular motion. values show minima where the correlation times for molecular motion are comparable to the resonance frequency. T2 processes show no minima. Ti, shows a minimum when motions occur at frequencies near the resonant frequency corresponding to the field. Thus, a complete description of molecular motion is obtained by a combination of the Tj, T2, and Ti, methods. 

In Eq. (4-62) Wq is the Larmor precessional frequency, and Tc is the correlation time, a measure of the rate of molecular motion. The reciprocal of the correlation time is a frequency, and 1/Tc may receive additive contributions from several sources, in particular I/t, where t, is the rotational correlation time, t, is, approximately, the time taken for the molecule to rotate through one radian. Only a rigid molecule is characterized by a single correlation time, and the value of Tc for different atoms or groups in a complex molecule may provide interesting chemical information. 

Turning from chemical exchange to nuclear relaxation time measurements, the field of NMR offers many good examples of chemical information from T, measurements. Recall from Fig. 4-7 that Ti is reciprocally related to Tc, the correlation time, for high-frequency relaxation modes. For small- to medium-size molecules in the liquid phase, T, lies to the left side of the minimum in Fig. 4-7. A larger value of T, is, therefore, associated with a smaller Tc, hence, with a more rapid rate of molecular motion. It is possible to measure Ti for individual carbon atoms in a molecule, and such results provide detailed information on the local motion of atoms or groups of atoms. Levy and Nelson " have reviewed these observations. A few examples are shown here. T, values (in seconds) are noted for individual carbon atoms. 

In presence of molecular motion the NMR line shape will change. A particularly simple situation arises, if the motion is rapid on timescale defined by the inverse width of the spectrum in absence of motion 6 1. In this fast exchange limit, which in 2H NMR is reached for correlation times tc < 1CT7 s, the motion leads to a partially averaged quadrupole coupling and valuable information about the type of motion can directly be obtained from analysis of the resulting line shapes. The NMR frequency is then given by... 

This connection between the correlation time of perturbation and that of response is a very general result independent of a model of molecular motion. It is valid not only when a molecule is perturbed by a sequence of instantaneous collisions (as in a gas), but also when it is subjected to perturbations that are continuous in time (caused by the nearest... 

---