Simulated Materials have Finite Molecular Weight

Peer Review of...

Simulated materials have finite molecular weight

Peter H. Nelson

Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge Massachusetts 02139

(submitted to the Journal of Chemical Physics, May 1996)

SUMMARY

One referee suggested that:

"The text, perhaps in a somewhat shorter form, might be very appropriate as an example in an advanced undergraduate or graduate physical chemistry textbook."

The same referee also indicated that the conclusons of the paper were:

"[not] in my opinion particularly new, they largely put into words aspects of what is fairly obvious to most researcher using simulation techniques that make use of periodic boundary conditions"

It was also indicated that:

"If the literature were full of examples of the gross mis-use use of periodic boundary conditions that led to seriously erroneous interpretations of polymer properties, one might be concerned. But this is not the case. ... The author uses examples in which the periodic box contains only a few repeat units [where the finite molecular weight effect is large] ... typical modern day simulations of polymeric systems (even the "crystalline" work of Boyd and other) uses much larger systems with 100's or 1000's or repeat units. [where the finite molecular weight effect is smaller] "

Finally, the manuscript was considered to be of little practical value as it merely provides a warning as to the effect of low molecular weight in simulations. The replication mechanism can not be usefully applied to realistic polymer systems because of the rigid contraints.

As a result, the manuscript was not accepted for publication in the Journal of Chemical Physics.

AUTHOR'S COMMENTS

The main point of the manuscript is to present the fact that there is a significant finite-size (finite molecular weight) effect in the simulation of "endless" polymeric materials (and other materials such as graphite).

As far as I am aware, these finite-molecular-weight effects are not specifically mentioned in the published literature. The only references that I could find on this issue indicate a lack of awareness e.g. Allen and Tildesley (ref. 4) (p. 26) say:

"...the common experience in simulation work is that periodic boundary conditions have little effect on the equilibrium properties and structures of fluids away from phase transitions and where the interactions are short-ranged."

I agree that the rigid approximation implied by the replication index is a bad one for real polymers, but it is the only way to modify the phase behavior without going to very large systems. To put it another way, the main point is that to realistically model polyethylene you have to go to very long chains. Periodic boundaries don't help out at all in this regard -- even if you remove the chain ends.

A related issue, of some practical importance, is that the approach of ref. 3 has the significant advantage that it does not suffer from these finite-size effects. This does not seem to have been stated in the literature either.

The statement that the manuscript has conclusions which are "fairly obvious to most researchers" seems a little strong. During preparation of the manuscript I discussed the conclusions with a number of researchers, none of whom were previously aware of the conclusions. One researcher, who has worked on simulations of many different materials, was unaware of the effect of molecular weight on simulations of materials such as polymers or graphite. Another, who has worked on simulations of polymers for some years, did not agree with the conclusions when they were originally put to him. The discussion of the (rather unrealistic) rigid rod model for polyethylene was included in the manuscript to provide the required support for the conclusion that simulated materials do in fact have finite molecular weight.

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