Modeling Polyethylene

Very recently. LET effects on fluorescence lifetimes of low molecular polyethylene model compounds (n-alkane) have been studied by many kinds of pulse radiolysis - methods such as electron beam, ion beam and synchrotron radiation (SR) [40] pulse radiolysis techniques [41]. Figure 10 shows time profiles of the fluorescence from neat n-dodecane liquids irradiated many kinds of radiation with different LET. The fluorescence lifetimes from irradiated neat... 

Very recently LET effects of ion beams on both standard polymers such as polystyrene and low molecular polyethylene model compounds (n-alkanes) have been studied by time-resolved spectroscopic methods, that is, ion beam pulse radiolysis techniques. Further basic studies are necessary so that the detailed mechanisms of ion beams on polymers can be clarified, especially LET effects and high density excitation effects. 

Polyethylene modeling using ADMET step-polymerization began with the production of strictly linear polyethylene by polymerization of 1,9-decadiene followed by exhaustive hydrogenation (Scheme 3) [68,69]. 

De Pablo, Laso, and Suter studied the behavior of polyethylene above and below the melting point." A variation of the MC technique was used to study polyethylene and to sample its configuration space. The technique is suitable for the study of long chains at high densities. The simulations were carried out in an isobaric—isothermal statistical mechanical ensemble, which allows the calculation of density at a given pressure and temperature. A series of simulations at different temperatures indicated a phase transition. The polyethylene model employed in the simulations crystallizes spontaneously at low temperatures. At temperature higher than the melting point, the simulated melt is described accurately by the model. 

Figure 2. ADMET functionalized polyethylene model polymers.

The polymerization mechanism and conditions used to make polyethylene markedly affect the quantity and occasionally the identity of the branches that are present. Figure 4 shows quantitatively just how different the thermal properties can be for a number of different types of polyethylene. The polyethylenes are listed in descending order from theoretical polyethylene, with an infinitely long chain and no branches, to those with increasing degrees of branching. Included in this list are our linear and branched ADMET polyethylene models. 

The four-body potential term [Eq. (5)] has two parameters (a and p) that can be fitted to give a desired barrier height and rotational isomer energy difference (for example, in the paraffins and polyethylene models discussed here, a cis barrier of... 

Values of the parameter used are listed in Table 1. For comparison purposes we have also investigated, to a limited extent, a so-called freely-rotating chain model, which is identical to the above polyethylene model except that k,j, is set equal to zero, i.e., the torsional barrier to conformational transitions is eliminated. 

Recently Cartier and Pfluger [27] reported that hot electrons with a threshold energy of about 4 e " induce a radiation damage in a polyethylene model substance. This means that there exists a coupling of local electronic states with quasi mobile states, as supposed by Zakrevskii and Pakhotin. 

Figure 4. General synthetic scheme for synthesis of symmetrical methyl-branched polyethylene models by ADMET.

Fig. 5.3 Density as a function of temperature at 1 bar pressure, averaged over five sampies of polyethylene model PE I, with a degree of polymerization of 1000. The cooling rate was about K ps but at each temperature the samples were relaxed for about a further 1 ns. The Lennard-Jones potential parameters for the van der Waals interactions were adjusted to give a density at SOO K which agreed with a linear extrapolation of experimental data (see text for further details). Also shown are data reported for a sample of model PE III polyethylene cooled at a comparable rate. ...

Fig. 5.4 Variation with temperature of the percentage of trans conformers in the cooling simulation of polyethylene model PE I. The theoretical equilibrium curve was calculated according to equation (5.14) in the text.

Fig. 5.8 The measured tension —Pyy) as a function of percentage extension (7 100) for tension applied at 5 bar ps for polyethylene model PE I with N = 1000. The data at each temperature represent the average behavior over five independent samples.

Fig. 5.10 Tension at 20% extension ( yield stress ) as a function of temperature or polyethylene model PE I with N = 1000. Squares and circles refer to tension application rates of 5 W ps and 1 bar ps respectively. Open symbols indicate data for which no discernible yield was observed these points are excluded from the curve fits and extrapolations to zero tension. The error bars shown are the standard deviations in the results for the five independent samples.

The persistence length a measures the correlation in the orientation of successive monomers as we move along a polymer chain. One useful definition which is easily apphed to the polyethylene model used here is ... 

Fig. 5.13 Measured load plotted as a function of extension for the four sets of samples of the model linear polymer subjected to uniaxial tension increasing at a rate of 5 bar ps"f Data for each set are averaged over five samples, the four sets are based on polyethylene model PE I. The samples were prepared directly in the glassy state and sets A-D have different configurational properties (see Table 5.1) as a result of different preparation procedures.

Molecular dynamics studies of penetrant diffusion have so far been performed for polyethylene, polyisobutylene and polydimethylsiloxane. Calculated diffusion coefficients have not been in particularly good agreement with experiment. In the case of polyethylene, modeled using the united atom approximation, diffusion coefficients were much higher than expected and the activation energies too small although much better results have been obtained using PE IV. Reliable comparisons with experimental data are made difficult by uncertainties as to the true diffusion coefficients... 

It is likely that local motions of the polymer chain are also important to penetrant diffusion. Removal of the torsional potential in polyethylene considerably increases the chain mobility and gave an increase of about a factor of two in the diffusion coefficient of 02. Conversely, decreasing the magnitude of the torsion angle fluctuations in the polyethylene model PE IV drastically reduces the diffusion coefficient of methane. ... 

Simulation studies are not limited in the above way and one can study the reorientational motions directly and in great detail by determining the full probability distribution function W(6, t) for bond reorientation through an angle 0 in a time t. This has been obtained for polyethylene model PE in. As a result of recent developments in multidimensional NMR techniques it should be possible to study this function experimentally in favorable cases although no relevant data are yet available in the case of polyethylene. 

Foteinopoulou, K., Karayiaimis, N.C., Mavrantzas, V.G., and Kroger, M. (2006) Primitive path identification and entanglement statistics in polymer melts results from direct topological analysis on atomistic polyethylene models. 

To isolate the source of this discrepancy we also performed theoretical calculations and MD simulations for a hypothetical FJC polyethylene model for which both the bond angle and torsional constraints are turned off. Therefore, the only difference between this FJC polyethylene model and the bead-spring model is the overlapping site aspect. It should be pointed out that this is a somewhat artificial model since... 

The fact that the agreement is somewhat better in this FJC polyethylene model indicates that internal constraints cause some difficulty in SC/PRISM theory. As seen in the semiflexible chain model, the bending and torsion constraints probably cause some local nematic ordering in the melt which cannot be captured in the present theory [59]. 

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