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Polyethylene radial distribution functions

If go(r), g CrX and g (r) are known exactly, then all three routes should yield the same pressure. Since liquid state integral equation theories are approximate descriptions of pair correlation functions, and not of the effective Hamiltonian or partition function, it is well known that they are thermodynamically inconsistent [5]. This is understandable since each route is sensitive to different parts of the radial distribution function. In particular, g(r) in polymer fluids is controlled at large distance by the correlation hole which scales with the radius of gyration or /N. Thus it is perhaps surprising that the hard core equation-of-state computed from PRISM theory was recently found by Yethiraj et aL [38,39] to become more thermodynamically inconsistent as N increases from the diatomic to polyethylene. The uncertainty in the pressure is manifested in Fig. 7 where the insert shows the equation-of-state of polyethylene computed [38] from PRISM theory for hard core interactions between sites. In this calculation, the hard core diameter d was fixed at 3.90 A in order to maintain agreement with the experimental structure factor in Fig. 5. [Pg.339]

The above considerations suggest that the hard core radial distribution function obtained for polyethylene was sufficiently accurate on short length scales to predict the perturbative contribution (Eq. (4.9)) to the attractive branch... [Pg.340]

Plot the radial distribution function 47ir P(r)against r/p fora linear polyethylene molecule of RMM = 63 000. taking / = 381 pm, and n = j (number of C-C bonds). Hence find the value of i- (r > p)at which the distribution function falls to a tenth of its maximum value. [Pg.65]

Fig. 1.28. Comparisons among the rotational isomeric (RIS) radial distribution functions at 413 K for polyethylene (o) and PDMS ( ) chains having n — 20 skeletal bonds, and the Gaussian approximation ( — ) to the distribution for PDMS [45]. The RIS curves represent cubic-spline fits to the discrete Monte Carlo data, for 80 000 chains, and each curve is normalized with respect to an area of unity (with / being the skeletal bond length). Fig. 1.28. Comparisons among the rotational isomeric (RIS) radial distribution functions at 413 K for polyethylene (o) and PDMS ( ) chains having n — 20 skeletal bonds, and the Gaussian approximation ( — ) to the distribution for PDMS [45]. The RIS curves represent cubic-spline fits to the discrete Monte Carlo data, for 80 000 chains, and each curve is normalized with respect to an area of unity (with / being the skeletal bond length).
Figure 6. Predicted interchain radial distribution function for a hard-core polyethylene melt described by three single-chain models atomistic RIS at 430 K, overlapping (lid = 0.5) SFC model with appropriately chosen aspect ratio and site number density (see text), and the Gaussian thread model (shifted horizontally to align the hard core diameter with the value of rld = l). Figure 6. Predicted interchain radial distribution function for a hard-core polyethylene melt described by three single-chain models atomistic RIS at 430 K, overlapping (lid = 0.5) SFC model with appropriately chosen aspect ratio and site number density (see text), and the Gaussian thread model (shifted horizontally to align the hard core diameter with the value of rld = l).
Figure II. PRISM predictions for hard-core atomistic RIS models of polyolefins, (a) The three diagonal radial distribution functions of isotactic polypropylene. (b) A com parison of chain averaged site-site radial distribution functions at 473 K for = 400 models of polyethylene, isotactic polypropylene, and syndiotactic polypropylene. The charactcris tic ratio. C, of the RIS models employed for PP arc shown in parentheses. Figure II. PRISM predictions for hard-core atomistic RIS models of polyolefins, (a) The three diagonal radial distribution functions of isotactic polypropylene. (b) A com parison of chain averaged site-site radial distribution functions at 473 K for = 400 models of polyethylene, isotactic polypropylene, and syndiotactic polypropylene. The charactcris tic ratio. C, of the RIS models employed for PP arc shown in parentheses.
Figure 16. The radial distribution functions for a blend of polyethylene and isotactic polypropylene = N = 200) at a volume fraction of polyethylene of /= 0.5. The four diagonal correlations are shown. Figure 16. The radial distribution functions for a blend of polyethylene and isotactic polypropylene = N = 200) at a volume fraction of polyethylene of /= 0.5. The four diagonal correlations are shown.
Fig. 5. The intemiolecular radial distribution functions obtained from SC/PRISM theory (lines) and MD simulations (points) for a system of 3200 united atom polyethylene chains with 48 CHx sites per chain at a density 0.03282 at the temperatures indicated. All results are for a repulsive Lennard-Jones nonbond potential with the TraPPE parameters in Table 1. The curves were displaced vertically for clarity... Fig. 5. The intemiolecular radial distribution functions obtained from SC/PRISM theory (lines) and MD simulations (points) for a system of 3200 united atom polyethylene chains with 48 CHx sites per chain at a density 0.03282 at the temperatures indicated. All results are for a repulsive Lennard-Jones nonbond potential with the TraPPE parameters in Table 1. The curves were displaced vertically for clarity...

See other pages where Polyethylene radial distribution functions is mentioned: [Pg.448]    [Pg.283]    [Pg.336]    [Pg.336]    [Pg.340]    [Pg.4829]    [Pg.27]    [Pg.34]    [Pg.228]    [Pg.114]   
See also in sourсe #XX -- [ Pg.47 ]




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