Local motions in polymers

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... 

I. Bahar and B. Erman, Macromolecules, 20, 1368 (1987). Investigation of Local Motions in Polymers by the Dynamic Rotational Isomeric State Model. 

Two broad generalisations may be drawn from these studies and applied to local motions in polymers. The first is that, in the absence of unusual steric restrictions, the atoms of a side-chain will increase in both their extent and rate of motion as the number of bonds from the main-chain increases. This will result in a lengthening of T, and in most (but not all) cases an increase of NOE, for both carbons and comparable protons, e.g. in a methylene chain. However, the underlying motions will usually not have the extent anticipated for free rotation at each bond. This generalisation will hold true for both the solution state and the bulk polymer above Tg, where the local motions are similar. 

In addition to the levels of stmctural and performance characterisation described above, there is also some interest in measurement of the dynamics of local motions in polymer chains. Techniques such as NMR have the capability to generate this type of information through the measurement of relaxation times. The results can be useful in, for example, morphological studies of polymer blends. 

K. Ono, K. Ueda,T. Sasaki, S.Murase, andM. Yamamoto. Fluorescence depolarization study of local motions in polymers at the temperature. Macromolecules, 29 (1996), 1584-1588. 

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. 

A given type of local motion in the glassy state must be responsible for a characteristic transition. This transition will be arbitrarily called (3, y, 8, etc., in the order of decreasing temperatures or increasing frequencies a is reserved in amorphous polymers to the transition between glass (local motions) and rubbery (cooperative motions) domains. 

There is a number of literature data on the motions of y and P types in glassy polymers50). However, it is not clear whether this picture is applicable to densely crosslinked polymers. The study of local motions in the networks under consideration has been performed using mainly the TSD technique 51) because of its high resolution and sensitivity. 

The still faster ( nsec) dynamics of local motions of polymer molecules in dilute solutions have been investigated by Ediger and coworkers (Zhu and Ediger 1995, 1997). They find that the rates of these local motions of a few bonds are not proportional to the solvent viscosity, unless the solvent reorientation rate is fast compared to the polymer local motion. Thus, for local motions (such as bond reorientations) of polymer molecules, Stokes law of drag does not always hold. 

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. 

In this paper, we have shown the utility of time-resolved optical techniques for the investigation of local segmental motions in polymer chains on a sub-nanosecond time scale. Detailed information about chain motions is contained in the time dependence of the orientation autocorrelation function of a backbone bond. 

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. 

The C-Ti values of CH2 group of the PDES moiety, in the range of —30 to 120°C are similarly small compared to those of the disordered phases for the PDES and PEMS (see below) comonomers. The C-Ti values of the two Me(l) and Me(2) groups for the PDMS moiety are almost similar although a little larger when compared with that for the CH3 group of the PDES moiety. The data may reflect some increased local motion in the backbones of PM-co-ES, but more likely the shorter Ti s are the result of the substantially increased motion of the side chains. Side-chain motions are particularly important in this polymer since it is primarily the dipolar interaction with the side-chain protons that causes the relaxation of the silicon nuclei. 

Obviously, if found experimentally, the exponent -2 is only a sign of reptation motion but not a sufficient condition for it. Thus, in order to prove that reptation is a really dominant mode of chain motion in polymer concentrates, we have to test it not only with self-diffusion but also with other physical properties which reflect the local motion of polymer chains. One such property is the (coherent) dynamic structure factor 5(fc, r) (see Section 3.2 of Chapter 4 for its definition). In fact, it was predicted theoretically [45-47] that the k dependence of its decay with r in the range of k defined by... 

The viscoelastic and dielectric data in the segmental relaxation process are insensitive to the molecular weight M and the molecular weight distribution (either in the monodisperse systems or blends). In fact, the viscoelastic and dielectric data for this process are indistinguishable for PS samples with M W (cf. Matsumiya et al., 2011 Uno, 2(X)9). This insensitivity naturally emerges because the mechanism of the local motion of polymer chains is independent of M. The M-insensitive viscoelastic and dielectric data for the... 

The characterization of the segmental motions of polymers is difficult, especially in concentrated solutions. One technique that is well suited to study polymer segmental motions is NMR relaxation measurement.(i, Studies have mostly focussed on the carbon or proton relaxation behavior at lower concentrations. Dipolar interactions among protons, or protons and tie the relaxation phenomena to local motions of polymer segments. Proton and techniques have been of limited use in more concentrated solutions, which to some extent is the most important regime for the development of many polymer properties. In more concentrated solutions, the overlap of spectral features and/or the complexity of the interactions make extracting motional information difficult, even if the relaxation measurements can be made. 

All the above theory also applies to flexible molecules, except for the assumption that G(t) decays exponentially. Let us now consider a somewhat more sophisticated motional model in which the relevant internuclear vector, e.g. the C-H bond, jumps freely within a cone [6] of semi-angle X, but is prevented from further movement either by other parts of the molecule, or by, for example, neighbouring polymer chains. This will turn out to be a surprisingly good approximation for local motions in a dissolved or molten polymer. The added motion fairly rapidly reduces G(t) from 1 to... 

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