Expansion of the end-to-end distance and radius of gyration in perturbed polymethylene chains

1984 ◽  
Vol 88 (26) ◽  
pp. 6492-6494 ◽  
Author(s):  
Wayne L. Mattice
Keyword(s):  
Radius Of Gyration ◽  
End Distance ◽  
End To End

Applicability of the Standard Renormalized Field Theory to the Strong Coupling Regime for the Domb–Joyce Model

1998 ◽  
Vol 12 (12n13) ◽  
pp. 1397-1406 ◽  
Author(s):  
P. Sutter ◽  
L. Schäfer ◽  
P. Grassberger
Keyword(s):  
Field Theory ◽  
Strong Coupling ◽  
Excluded Volume ◽  
Radius Of Gyration ◽  
Strong Coupling Regime ◽  
Monte Carlo Data ◽  
End Distance ◽  
End To End ◽  
Standard Formalism ◽  
Self Avoiding Walk

We present a field theoretic analysis of high-precision Monte Carlo data for the Domb–Joyce model. This analysis shows the ability of the standard formalism to describe the data. In the Domb–Joyce model of a polymer chain the repulsion between two segments at the same point is varied between zero (random walk) up to infinity (self avoiding walk). To increase the excluded volume we even include a repulsion between segments at neighbor points. The data for the end-to-end distance, the radius of gyration and the partition function clearly shows the existence of two branches of universal behavior, corresponding to weak or strong excluded volume. The nonuniversal parameters of the renormalized theory have to be considered as fitting parameters to one given quantity (We have chosen the end-to-end distance). Given these nonuniversal parameters, we can predict the variation of all other measured quantities. Good agreement with the MC data is found for all data, including the strong coupling branch. We conclude, in contrast to some claims in the literature, that the standard formalism of the renormalized field theory can be used even for renormalized couplings greater than the fixed point value (strong coupling branch).

scholarly journals Self-Stable Precipitation Polymerization Molecular Entanglement Effect and Molecular Weight Simulations and Experiments

Polymers ◽  
2021 ◽  
Vol 13 (14) ◽  
pp. 2243
Author(s):  
Jiali Qu ◽  
Yi Gao ◽  
Wantai Yang
Keyword(s):  
Molecular Weight ◽  
Maleic Anhydride ◽  
Molecular Conformation ◽  
Average Molecular Weight ◽  
Precipitation Polymerization ◽  
Radius Of Gyration ◽  
Propagation Mechanism ◽  
Reactive Molecular Dynamics ◽  
End Distance ◽  
Good Agreement

In this paper, we developed a reactive molecular dynamics (RMD) scheme to simulate the Self-Stable Precipitation (SP) polymerization of 1-pentene and cyclopentene (C5) with maleic anhydride (MAn) in an all-atom resolution. We studied the chain propagation mechanism by tracking the changes in molecular conformation and analyzing end-to-end distance and radius of gyration. The results show that the main reason of chain termination in the reaction process was due to intramolecular cyclic entanglement, which made the active center wrapped in the center of the globular chain. After conducting the experiment in the same condition with the simulation, we found that the distribution trend and peak value of the molecular-weight-distribution curve in the simulation were consistent with experimental results. The simulated number average molecular weight (Mn) and weight average molecular weight (Mw) were in good agreement with the experiment. Moreover, the simulated molecular polydispersity index (PDI) for cyclopentene reaction with maleic anhydride was accurate, differing by 0.04 from the experimental value. These show that this model is suitable for C5–maleic anhydride self-stable precipitation polymerization and is expected to be used as a molecular weight prediction tool for other maleic anhydride self-stable precipitation polymerization system.

Self‐avoiding walks with span limitations. I. The mean square end‐to‐end distance

1980 ◽  
Vol 72 (4) ◽  
pp. 2702-2707 ◽  
Author(s):  
Ronnie Barr ◽  
Chava Brender ◽  
Melvin Lax
Keyword(s):  
Mean Square ◽  
End Distance ◽  
The Mean ◽  
End To End ◽  
Self Avoiding Walks
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