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PRISM theory function, polyethylene

It is possible to empirically modify PRISM theory for polyethylene [59] by making the direct correlation longer range by simply adding a power law tail to C(r) beyond some hard core diameter. The power law exponent can then be adjusted to force the theory to yield the correct compressibility. This procedure led [59] to almost quantitative agreement of the theoretical g r) with MD for polyethylene. Unfortunately, this modification to PRISM theory is not useful for atomistic polymer models involving more than a single site since constraints, in addition to the compressibility, are needed to fix the exponents of the various direct correlation functions. [Pg.230]

The outline of the paper is as follows. In Sect. 2 we describe the basic RISM and PRISM formalisms, and the fundamental approximations invoked that render the polymer problem tractable. The predicticms of PRISM theory for the structure of polymer melts are described in Sect. 3 for a variety of single chain models, including a comparison of atomistic calculations for polyethylene melt with diffraction experiments. The general problem of calculating thermodynamic properties, and particularly the equation-of-state, within the PRISM formalism is described in Sect. 4. A detailed application to polyethylene fluids is summarized and compared with experiment. The develojanent of a density functional theory to treat polymer crystallization is briefly discussed in Sect. 5, and numerical predictions for polyethylene and polytetrafluoroethylene are summarized. [Pg.322]

Fig. 5. Structure factor S(k) for polyethylene melt (N — 6429) as a function of wavevector k at T = 430 K. The points are experimental results [32,33] of Narten and Habenschuss from X-ray scattering (the k a 0 data is inaccurate due to sample preparation related scattering). The soiid curve is the PRISM theory with the hard core diameter d = 3.90 A. Use of a value of d = 3.7 A results in roughly a 10% underestimate of the intensity rf the amorphous halo feature. Disagreement between experiment and theory at large k is eliminated if thermal broadening, due to vibrational and torsional oscillations, is taken into account [33,34]... Fig. 5. Structure factor S(k) for polyethylene melt (N — 6429) as a function of wavevector k at T = 430 K. The points are experimental results [32,33] of Narten and Habenschuss from X-ray scattering (the k a 0 data is inaccurate due to sample preparation related scattering). The soiid curve is the PRISM theory with the hard core diameter d = 3.90 A. Use of a value of d = 3.7 A results in roughly a 10% underestimate of the intensity rf the amorphous halo feature. Disagreement between experiment and theory at large k is eliminated if thermal broadening, due to vibrational and torsional oscillations, is taken into account [33,34]...
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]

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...
The basic approximation in the Percus-Yevick closure is that the direct correlation function is short range. In Fig. 7 we can observe that indeed C(r) for both the bead-spring model and polyethylene are short range approaching zero on a scale of 5 A. However, C(r) from self-consistent PRISM theory is even shorter range and... [Pg.229]


See other pages where PRISM theory function, polyethylene is mentioned: [Pg.319]    [Pg.336]    [Pg.336]    [Pg.340]    [Pg.23]    [Pg.27]    [Pg.36]    [Pg.60]    [Pg.432]    [Pg.228]    [Pg.232]   
See also in sourсe #XX -- [ Pg.23 ]




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