Self‐avoiding walks with span limitations. II. The mean square radius of gyration

1981 ◽  
Vol 75 (1) ◽  
pp. 453-459 ◽  
Author(s):  
Ronnie Barr ◽  
Chava Brender ◽  
Melvin Lax
Keyword(s):  
Radius Of Gyration ◽  
Mean Square ◽  
The Mean ◽  
Self Avoiding Walks

Statistical properties of a polymer chain in the two-parametor approximation

1981 ◽  
Vol 376 (1766) ◽  
pp. 361-375 ◽  
Keyword(s):  
Polymer Chain ◽  
Numerical Data ◽  
Ring Closure ◽  
Radius Of Gyration ◽  
Mean Square ◽  
Virial Series ◽  
The Mean ◽  
Diagrammatic Method ◽  
Mean Square Distance ◽  
Self Avoiding Walks

The diagrammatic method developed in a previous paper is used to derive two terms of the virial expansion for the mean square distance from the origin, the mean square radius of gyration, and the probability of ring closure for a lattice model of a simple polymer chain. It is found that the logarithmic terms in the partition function cancel in the virial series for these universal quantities. The universality hypothesis is tested with the numerical data for self-avoiding walks (s.a.w.) for different lattices. The virial series is combined with the s.a.w. results to provide formulae for the expansion factor as a function of the excluded volume.

SELF-AVOIDING WALKS ON THE 4–8 LATTICE

2002 ◽  
Vol 16 (08) ◽  
pp. 1241-1246 ◽  
Author(s):  
KEH YING LIN ◽  
CHI CHEN CHANG
Keyword(s):  
Theoretical Prediction ◽  
Radius Of Gyration ◽  
Mean Square ◽  
Amplitude Ratios ◽  
Connective Constant ◽  
End Distance ◽  
The Mean ◽  
Critical Amplitudes ◽  
Mean Square Distance ◽  
Self Avoiding Walks

We have calculated exactly the number, the mean-square end-to-end distance, the mean-square radius of gyration, and the mean-square distance of a monomer from the origin for self-avoiding walks on the 4–8 lattice up to 42 steps by computer. We estimated the connective constant and the critical amplitudes. Our numerical results are consistent with the theoretical prediction by Cardy and Saleur on the universality for certain amplitude ratios.

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

Calculation of the mean-square radius of gyration for polymer chains with side-groups

1992 ◽  
Vol 28 (11) ◽  
pp. 1339-1343 ◽  
Author(s):  
Zhou Zhiping ◽  
Xu Jianmin ◽  
Song Xubing ◽  
Yan Deyue
Keyword(s):  
Polymer Chains ◽  
Radius Of Gyration ◽  
Mean Square ◽  
The Mean

Computer Simulation on Conformation Properties of Polymer Chain

2013 ◽  
Vol 341-342 ◽  
pp. 195-198
Author(s):  
Lin Lin Cui ◽  
Hua Nan Guan
Keyword(s):  
Polymer Chain ◽  
Volume Fraction ◽  
Solvent Molecule ◽  
Radius Of Gyration ◽  
Mean Square ◽  
Chain Segment ◽  
End Distance ◽  
The Mean ◽  
Multiple Chain ◽  
Linear Polymer Chain

The author adopts Monte Carlo compute method to simulate the linear polymer chain lattice model in multiple chain systems of chain lengthn=20, 50, 100 while the volume fraction Φ=0.125, and makes a research on the variational situation of the size (measured with the mean-square end-to-end distance <R2> and the mean-square radius of gyration <S2>), shape (measured with the mean asphericity factor <A>) with changing of the interaction energy between solvent molecule and polymer chain segment molecule εPS. Results indicate <R2>, <S2> and <A> have the changing rules that they become small with the increase of the εPS

Excluded-volume effects on the mean-square radius of gyration of oligo- and polystyrenes in dilute solutions

1993 ◽  
Vol 26 (8) ◽  
pp. 1884-1890 ◽  
Author(s):  
Fumiaki Abe ◽  
Yoshiyuki Einaga ◽  
Takenao Yoshizaki ◽  
Hiromi Yamakawa
Keyword(s):  
Excluded Volume ◽  
Radius Of Gyration ◽  
Mean Square ◽  
Dilute Solutions ◽  
Excluded Volume Effects ◽  
The Mean ◽  
Volume Effects

Monte Carlo Simulation on Conformation Properties of Polymer Multiple Chain System

2013 ◽  
Vol 734-737 ◽  
pp. 3141-3144
Author(s):  
Lin Lin Cui ◽  
Hua Nan Guan
Keyword(s):  
Monte Carlo ◽  
Polymer Chain ◽  
Volume Fraction ◽  
Solvent Molecule ◽  
Radius Of Gyration ◽  
Mean Square ◽  
End Distance ◽  
The Mean ◽  
Multiple Chain ◽  
Linear Polymer Chain

The author adopts Monte Carlo compute method to simulate the linear polymer chain lattice model in multiple chain systems of different volume fraction Φ while chain lengthn=50, and makes a research on the variational situation of the size (measured with the mean-square end-to-end distance <R2> and the mean-square radius of gyration <S2>), shape (measured with the mean asphericity factor ) with changing of the interaction energy between solvent molecule and polymer chain segment moleculeεPS. Results indicate <R2>, <S2> and have the changing rules that they become small with the increase of theεPS.

scholarly journals The Effect of Grafting Density on the Crystallization Behaviors of Polymer Chains Grafted onto One-Dimensional Nanorod

2019 ◽  
Vol 2019 ◽  
pp. 1-10 ◽  
Author(s):  
Tongfan Hao ◽  
Yongqiang Ming ◽  
Shuihua Zhang ◽  
Ding Xu ◽  
Zhiping Zhou ◽  
...  
Keyword(s):  
Polymer Nanocomposites ◽  
Polymer Chains ◽  
Radius Of Gyration ◽  
Mean Square ◽  
Crystalline Morphology ◽  
One Dimensional ◽  
Crystallization Behaviors ◽  
Grafting Density ◽  
Dynamic Monte Carlo ◽  
The Mean

The crystallization behaviors of five polymer chain systems grafted on a nanorod and the corresponding effect of grafting density were investigated by dynamic Monte Carlo simulations. The segment density near the interfacial regions, the number of crystallites, and the mean square radius of gyration (<Rg2>) increase with increasing grafting density, which are beneficial to the enhancement of crystallizability. Meanwhile, the crystalline morphology is greatly influenced by grafting density and polymer-nanorod interaction. For the grafted system with 52 chains, a nanohybrid shish-kebab (NHSK) structure is formed, when the polymer-nanorod interaction (Eb/Ec) is -0.4. For the system with 128 chains, a NHSK structure is formed, when Eb/Ec is -1.0. For the system with 252 chains, NHSK structure cannot be formed. The findings in this work can supply important theoretical reference for the design, preparation, and application of polymer nanocomposites.

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