Local motion, measurements

Atomistically detailed models account for all atoms. The force field contains additive contributions specified in tenns of bond lengtlis, bond angles, torsional angles and possible crosstenns. It also includes non-bonded contributions as tire sum of van der Waals interactions, often described by Lennard-Jones potentials, and Coulomb interactions. Atomistic simulations are successfully used to predict tire transport properties of small molecules in glassy polymers, to calculate elastic moduli and to study plastic defonnation and local motion in quasi-static simulations [fy7, ( ]. The atomistic models are also useful to interiDret scattering data [fyl] and NMR measurements [70] in tenns of local order. 

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. 

There has been extensive effort in recent years to use coordinated experimental and simulation studies of polymer melts to better understand the connection between polymer motion and conformational dynamics. Although no experimental method directly measures conformational dynamics, several experimental probes of molecular motion are spatially local or are sensitive to local motions in polymers. Coordinated simulation and experimental studies of local motion in polymers have been conducted for dielectric relaxation,152-158 dynamic neutron scattering,157,159-164 and NMR spin-lattice relaxation.17,152,165-168 A particularly important outcome of these studies is the improved understanding of the relationship between the probed motions of the polymer chains and the underlying conformational dynamics that leads to observed motions. In the following discussion, we will focus on the... 

Recent progress in protein dynamics studies by NMR was greatly facilitated by the invention of the model-free formalism [28, 32]. In this approach, the local dynamics of a protein are characterized by an order parameter, S, measuring the amplitude of local motion on a scale from 0 to 1, and the correlation time of the motion, T oc. The model-free expression for the correlation function of local motion reads... 

Of all local motions, v(r), of an interface that pass the same amount of volume from one side to the other, the motion that is normal to the interface with magnitude proportional to the weighted mean curvature, v f) oc /c7n, increases the interfacial energy the fastest. However, fastest depends on how distance is measured. How this distance metric alters the variational principles that generate the kinetic equations is discussed elsewhere [14]. 

The temperature dependencies of the ( 172)0/ 1/2 ratio, where ( 1/2)0 is the 1/2 value measured at room temperature, determined for the CHOH - CH2 - O and CH2 - N units of the hydroxylpropyl ether (HPE) sequence (Fig. 92) in the HMDA network [63] are shown in Fig. 97. It is worth noticing that the 1/2 values of these two types of carbons have the same temperature dependence. Up to 60 °C, the 1/2 values are constant and equal to the rigid-lattice values, indicating that the HPE sequence does not undergo any local motion at a frequency equal to or higher than 105 Hz in this temperature range. Above 60 °C, mobility develops, which leads at 100 °C to motions in the tens of kilohertz for the whole HPE sequence. These results are qualitatively confirmed by data on 13C spin-lattice relaxation time in the rotating frame, Tip(13C). 

Fully deuterated linear poly(ethylene) (PE) has been investigated also via various 2H NMR techniques below Tm, i.e. in the semi crystalline state [83, 84]. The crystallinity ratio was measured as a function of temperature and it was shown that the motions are highly restricted in the amorphous regions of PE. It was shown that the onset of 3 and a transitions (at which mobility appears in the crystalline phase) may be observed by 2H NMR on raising the temperature. This onset of local motions in the crystalline phase is related to the chain relaxation process quoted previously. 

The thickness of the adsorption layer was estimated from the fraction of adsorbed chain units measured by means of h Ty, Tj and H relaxation studies [7, 8, 10, 12]. From the known value of the specific surface of Aerosil, its volume fraction in mixtures and the fraction of low mobile chain units at the Aerosil surface, the thickness of the adsorption layer is estimated assuming imiform coverage of the filler particles by a PDMS layer of constant thickness. This calculation leads to a value of about 0.8 run [7]. This value is increased by a factor 1.5-2, if a part of the filler surface will not be accessible for PDMS chains due to direct contacts between the primarily filler particles in aggregates [27]. Thus, the chain adsorption causes a significant restriction of local motions only in one or two monolayers adjacent to the filler surface. A similar estimation of the adsorption layer thickness has been obtained by other methods such as, e.g. dielectric experiment [27], adsorption study [3], the viscosity of the boundary layer for silicon liquids at the surface of a glass [5], molecular dynamics simulations [6], and C NMR relaxation experiments [22]. 

Currently available data for the flow properties of the fluidized catalyst bed are fragmentary, since the local motion of the emulsion phase is diflicult to measure experimentally. Therefore, it is useful to clarify the flow properties of the bed in terms of our knowledge of bubble columns. First, the fluid-dynamic properties of the bubble columns will be explained then, the available data will be adapted to apply to fluid catalyst beds. The reader will be able to picture an emulsion phase of carefully prepared catalyst particles operating in intense turbulence for fluidized beds under conditions of practical interest. This turbulence distinguishes the flow properties of fluid catalyst beds from those of widely studied teeter beds. 

Local motions of a, a)-bis( 1-pyrene) alkanes and pyrene -labelled poly(methyl methacrylate) in solution have been measured by pico-second excimer fluorescence spectroscopy In this study the formation of the polymers during polymerisation could be accurately maintained by measuring excimer fluorescence lifetime. The photophysical properties of poly (N-vinylcarbazole) have been interpreted on the basis of a study in diastereoisomers of 2,4-di(N-carbazolyl)t In this work it is concluded that 95% of the excitation energy occurs with chromophores associated with specific excimer sites. Excimer formation in various polyvinyl carbazole... 

The main interest of C NMR spectroscopy is that it allows one to investigate the local motions performed by the various groups of the polymer chain. Thus, it yields more detailed information than other techniques. On the other hand, to derive the correlation times of the motions from the T. measurements, it is necessary to use an "a priori" expression of the OACF, M2(t). 

The transient absorption method utilized in the experiments reported here is the transient holographic grating technique(7,10). In the transient grating experiment, a pair of polarized excitation pulses is used to create the anisotropic distribution of excited state transition dipoles. The motions of the polymer backbone are monitored by a probe pulse which enters the sample at some chosen time interval after the excitation pulses and probes the orientational distribution of the transition dipoles at that time. By changing the time delay between the excitation and probe pulses, the orientation autocorrelation function of a transition dipole rigidly associated with a backbone bond can be determined. In the present context, the major advantage of the transient grating measurement in relation to typical fluorescence measurements is the fast time resolution (- 50 psec in these experiments). In transient absorption techniques the time resolution is limited by laser pulse widths and not by the speed of electronic detectors. Fast time resolution is necessary for the experiments reported here because of the sub-nanosecond time scales for local motions in very flexible polymers such as polyisoprene. 

Viovy, Monnerie, and Brochon have performed fluorescence anisotropy decay measurements on the nanosecond time scale on dilute solutions of anthracene-labeled polystyrene( ). In contrast to our results on labeled polyisoprene, Viovy, et al. reported that their Generalized Diffusion and Loss model (see Table I) fit their results better than the Hall-Helfand or Bendler-Yaris models. This conclusion is similar to that recently reached by Sasaki, Yamamoto, and Nishijima 3 ) after performing fluorescence measurements on anthracene-labeled polyCmethyl methacrylate). These differences in the observed correlation function shapes could be taken either to reflect the non-universal character of local motions, or to indicate a significant difference between chains of moderate flexibility and high flexibility. Further investigations will shed light on this point. 

In experiments currently in progress, the techniques used in this paper are being applied to the observation of local polymer dynamics in concentrated solutions and in the bulk. Measurements can be made on time scales as long as several triplet lifetimes ( 100 msec) because the transient grating technique utilizes absorption and not fluorescence. This long time window will allow the investigation of local motions in the bulk as a function of temperature from the rubbery state to the glass transition. 

Above the polymer concentration of 707., starts to Increase due to increased friction of rotation or reduced available free volume. The value of Ej increases by a factor of three over the concentration range from 707. to 1007. as shown in Figure 5, whereas the local viscosity measured by Nishijima Increased ten times above 607.. As a result of extensive overlap of polymer chains in this concentration region, the rotational motion of the chromophores is highly restricted and subject to a high energy barrier to be crossed over to the a state. 

The results of QENS measurements for TaV2H [76] are consistent with this microscopic picture of H motion. First, on the frequency scale of tf the measured QENS spectra S(Q, co) are well described by the sum of a narrow elastic line and a broader quasielastic line having Q-dependent intensity, but Q-independent width. These features are typical of the case of spatially-confined (localized) motion [14]. 

---