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.

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

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.

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

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

Effect on Polymer Chain Structure Caused by the Molar Fraction of 4-Hydroxybutyrate in Poly(3-hydroxybutyrate- co -4-hydroxybutyrate)

2012 ◽  
Vol 602-604 ◽  
pp. 776-780
Author(s):  
Zhi Qiang Li ◽  
Mei Li ◽  
Wei Jia Fan
Keyword(s):  
Molecular Weight ◽  
Intrinsic Viscosity ◽  
Polymer Chain ◽  
Molar Fraction ◽  
Chain Structure ◽  
The Other ◽  
Mean Square ◽  
Polarizing Microscope ◽  
Other Hand ◽  
The Mean

Poly(3-hydroxybutyrate-co-4-hydroxybutyrate)copolymer [P(3HB-co-4HB)] is a kind of biodegradable high molecular polymer produced by bioaccumulation. Because of the good biodegradability and biocompatibility, P(3HB-co-4HB)s have attracted wide attention . At first, the intrinsic viscosity[η] in good solvent of P(3HB-co-4HB) s with varying contents of 4HB was investigated in different temperature. Second, observed the changes of crystallization gathered state caused by the varying contents of 4HB by polarizing microscope. The results show that to the P(3HB-co-4HB)s in same molecular weight, the intrinsic viscosity[η] in good solvent barely changes when the mole fractions of 4HB increase. On the other hand, the mean square end to end distances[0] of macromolecular flexible chains increase with the mole fractions of 4HB. At the same time, the states of aggregation change from spherulites to dendrites. In this investigation, we discuss the reasons of the differences in depth.

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
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