Polymer motion

The topic of molecular motion is an active one in experimental and theoretical polymer physics, and we may expect that in time the simple reptation model will be superseded by more sophisticated models. However, in the form presented here, reptation is likely to remain important as a semi-quantitative model of polymer motion, showing as it does the essential similarity of phenomena which have their origin in the flow of polymer molecules. 

Hybrid MPC-MD schemes are an appropriate way to describe bead-spring polymer motions in solution because they combine a mesoscopic treatment of the polymer chain with a mesoscopic treatment of the solvent in a way that accounts for all hydrodynamic effects. These methods also allow one to treat polymer dynamics in fluid flows. 

In this review we consider large-scale polymer motions which naturally occur on mesoscopic time scales. In order to access such times by neutron scattering a very high resolution technique is needed in order to obtain times of several tens of nanoseconds. Such a technique is neutron spin echo (NSE), which can directly measure energy changes in the neutron during scattering [32,33]. 

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... 

In a mode coupling approach, a microscopic theory describing the polymer motion in entangled melts has recently been developed. While these theories describe well the different time regimes for segmental motion, unfortunately as a consequence of the necessary approximations a dynamic structure factor has not yet been derived [67,68]. 

NMR is the most fundamental molecular specific probe of diffusion. Polymer motions and the spectroscopic signature of a given nucleus can be unambiguously related to a particular morphological domain. The size and time scale of the experiments are such that the fundamental hopping events of diffusing molecules can be sampled. 

Nuclear magnetic resonance spectroscopy of dilute polymer solutions is utilized routinely for analysis of tacticlty, of copolymer sequence distribution, and of polymerization mechanisms. The dynamics of polymer motion in dilute solution has been investigated also by protoni - and by carbon-13 NMR spectroscopy. To a lesser extent the solvent dynamics in the presence of polymer has been studied.Little systematic work has been carried out on the dynamics of both solvent and polymer in the same systan. 

T] is in general greater than T2. This difference can in part be a consequence of the slower modes of polymer motion, which are characterized by correlation times sufficiently long that they do not contribute significantly to T] but do to T2. It is therefore important, in terms of describing the fine structure of the non-crystalline regions, to understand the type motions which contribute to T2 and to develop a rationale for the relatively broad lines that are observed for most crystalline polymers. 

Although the above work was serendipitous, the study of concentration fluctuations in bulk polymers should be a fruitful area of research. Intentional polymer mixtures could be prepared which would allow the mutual diffusion of polymers in polymers to be obtained. Although the molecular weights might need to be kept low, the measurement of polymer motions in the bulk state would be very valuable. 

The molecular theory of Pace and Datyner (12) predicts that the frequency of polymer motions important to diffusion of CO and H2 in PVC is in the range of 105-108 Hz. We can expect RiP(C) measurements performed between 104 to 105 Hz to be sensitive to alterations in v by additives. The dependence of on the rotating-frame Larmor frequency observed for the PVC-TCP system (28) means that a general change in main-chain motions (restriction or enhancement) will result in a change (decrease or increase, respectively) in measured at 34 kHz (29). 

In Section IB we presented experimental evidence that diffusion coefficients correlate with PVC main-chain polymer motions. This relationship has also been justified theoretically (12). In the previous section we demonstrated that the presence of CO2 effects the cooperative main-chain motions of the polymer. The increase in with increasing gas concentration means that the real diffusion coefficient [D in eq. (11)] must also increase with concentration. The nmr results reflect the real diffusion coefficients, since the gas concentration is uniform throughout the polymer sample under the static gas pressures and equilibrium conditions of the nmr measurements. Unfortunately, the real diffusion coefficient, the diffusion coefficient in the absence of a concentration gradient, cannot be determined from classical sorption and transport data without the aid of a transport model. Without prejustice to any particular model, we can only use the relative change in the real diffusion coefficient to indicate the relative change in the apparent diffusion coefficient. 

As indicated earlier, these relaxation results are only preliminary more extensive measurements are in progress aimed at fully explaining the relaxation behavior and deriving information on the polymer motions, including activation energies. 

Fillers such as silica In silicone rubber have the same effect as crystallinity, reducing polymer motion by physical crosslinking and increasing the tortuosity of the diffusion path (14,15). 

The dynamical trajectory generated by such a process can be visualized as a movie showing the polymer motion. Figure 1 presents a frame of an = 20, N = 5 system. The duplicated chains are a consequence of the periodic boundary conditions. When part of a chain sticks out of the fundamental box, its image enters the opposite face. Rather than showing pieces of chains we have drawn complete chains for both the original and image chain. 

Figure 2 Properties in polyphosphazenes are determined hy (1) the backbone bonds that control the inherent flexibility of the polymer via their influence on bond torsional freedom, and also provide photo-and thermo-oxidative stahihty (2) the side groups control polymer solubility, reactivity, thermal stability, crystallinity, cross-linking, and (indirectly) polymer flexibility (3) free volume between the side groups affects polymer motion, solvent penetration, membrane behavior, and density (4) functional groups (usually introduced hy secondary reactions) affect soluhihty, biological behavior, proton conduction, cross-hnking, and many other properties...

J. L. Viovy, Polymer Motions in Dense Systems, Springer Proceedings in... 

D. B. Adolf and M. D. Ediger, in Computer Simulation of Polymers, R. J. Roe, Ed., Prentice Hall, New York, 1991, pp. 154-166. Brownian Dynamics Simulations of Local Polymer Motions in Polyisoprene Comparison to NMR Experiments. 

A comment must be made about the cis— trans thermal isomerization rate at pressure. At room temperature, the thermal back reaction of DRl-PMMA follows a complex, nonexponential recovery, most of which is completed after a few seconds with a rate of 0.25 s" and deviates from a single exponential decay after the first 10 seconds.Larger relaxation times at Tg -98°C include slow polymer motion coupled with the chromophores rotational diffusion. We confirmed that this behavior is true in the polymer... 

Topological constraints do not influence polymer motion on length scales smaller than the size of an entanglement strand. In entangled polymer solutions, chain sections with end-to-end distance shorter than the tube... 

On length scales larger than the correlation length but smaller than the tube diameter a, hydrodynamic interactions are screened, and topological interactions are unimportant. Polymer motion on these length scales is described by the Rouse model. The relaxation time Tg of an entanglement strand of monomers is that of a Rouse chain of N jg correlation volumes [Eg. (8.76)] ... 

Time-Resolved Optical Spectroscopy as a Probe of Local Polymer Motions... 

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