scholarly journals MONTE CARLO SIMULATIONS OF A POLYMER CHAIN MODEL ON EUCLIDEAN LATTICES

2019 ◽  
Vol 10 (2) ◽  
Author(s):  
Ivan Živić ◽  
Dušanka Marčetić ◽  
Sunčica Elezović Hadžić
Keyword(s):  
Monte Carlo ◽  
Polymer Chain ◽  
Simulation Method ◽  
Two Dimensions ◽  
Polymer Chains ◽  
Three Dimensions ◽  
Chain Model ◽  
Euclidean Lattices ◽  
Spatial Dimensions ◽  
End Distance

We studied the critical properties of flexible polymers, modelled by self-avoiding random walks, in good solvents and homogeneous environments. By applying the PERM Monte Carlo simulation method, we generated the polymer chains on the square and the simplecubic lattice of the maximal length of N=2000 steps.We enumerated approximately the number of different polymer chain configurations of length N,and analysed its asymptotic behaviour (for large N), determined by the connectivity constant μ and the entropic critical exponent γ. Also, we studied the behaviour of the set of effective critical exponents 휈푁, governing the end-to-end distance of a polymer chain of length N. We have established that in two dimensions 휈푁monotonically increases with N, whereas in three dimensions itmonotonically decreases when Nincreases. Values of 휈푁, obtained for both spatial dimensions have been extrapolated in the range of very long chains.In the end, we discuss and compare our results to those obtained previously for polymers on Euclidean lattices.

Monte Carlo studies of polymer-chain dimensions in the melt in two dimensions

1989 ◽  
Vol 22 (7) ◽  
pp. 3120-3124 ◽  
Author(s):  
Johannes Reiter ◽  
Gerhard Zifferer ◽  
Oskar Friedrich Olaj
Keyword(s):  
Monte Carlo ◽  
Polymer Chain ◽  
Two Dimensions ◽  
Monte Carlo Studies

scholarly journals Combined Numerical-Statistical Analyses of Damage and Failure of 2D and 3D Mesoscale Heterogeneous Concrete

2015 ◽  
Vol 2015 ◽  
pp. 1-12
Author(s):  
Xiaofeng Wang ◽  
Andrey P. Jivkov
Keyword(s):  
Cohesive Zone Model ◽  
Volume Fraction ◽  
Simulation Method ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Zone Model ◽  
Generation Process ◽  
Cohesive Elements ◽  
Damage And Failure ◽  
2D And 3D

Generation and packing algorithms are developed to create models of mesoscale heterogeneous concrete with randomly distributed elliptical/polygonal aggregates and circular/elliptical voids in two dimensions (2D) or ellipsoidal/polyhedral aggregates and spherical/ellipsoidal voids in three dimensions (3D). The generation process is based on the Monte Carlo simulation method wherein the aggregates and voids are generated from prescribed distributions of their size, shape, and volume fraction. A combined numerical-statistical method is proposed to investigate damage and failure of mesoscale heterogeneous concrete: the geometrical models are first generated and meshed automatically, simulated by using cohesive zone model, and then results are statistically analysed. Zero-thickness cohesive elements with different traction-separation laws within the mortar, within the aggregates, and at the interfaces between these phases are preinserted inside solid element meshes to represent potential cracks. The proposed methodology provides an effective and efficient tool for damage and failure analysis of mesoscale heterogeneous concrete, and a comprehensive study was conducted for both 2D and 3D concrete in this paper.

Monte Carlo Study on the Statistical Properties of Ising Polymer Chain

2003 ◽  
Vol 17 (22n24) ◽  
pp. 4267-4271 ◽  
Author(s):  
Meng-Bo Luo
Keyword(s):  
Monte Carlo ◽  
Polymer Chain ◽  
Nearest Neighbor ◽  
Spatial Configuration ◽  
Spontaneous Magnetization ◽  
Monte Carlo Study ◽  
Spin Interaction ◽  
Chain Model ◽  
Dynamic Monte Carlo ◽  
Experimental Findings

The configurational and magnetic properties of magnetic polymers are investigated based on an Ising polymer chain model with nearest-neighbor spin-spin interaction on the simple cubic lattice. Dynamic Monte Carlo simulation shows that the model has spontaneous magnetization at low temperature, i.e. the mean-square magnetization <M2> approaches to 1 below the critical temperature Tc. Near Tc, a transition of chain spatial configuration from extended coil to compacted globule is found. A nonlinear magnetization - field curve is observed, in agreement with experimental findings for magnetic polymers.

Elimination of an isolated pore: Effect of grain size

1995 ◽  
Vol 10 (4) ◽  
pp. 1000-1015 ◽  
Author(s):  
Wan Y. Shih ◽  
Wei-Heng Shih ◽  
Ilhan A. Aksay
Keyword(s):  
Grain Size ◽  
Monte Carlo ◽  
Sample Size ◽  
Scaling Laws ◽  
Pore Diameter ◽  
Scaling Law ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Scaling Analysis ◽  
Scaling Relationships

The effect of grain size on the elimination of an isolated pore was investigated both by the Monte Carlo simulations and by a scaling analysis. The Monte Carlo statistical mechanics model for sintering was constructed by mapping microstructures onto domains of vectors of different orientations as grains and domains of vacancies as pores. The most distinctive feature of the simulations is that we allow the vacancies to move. By incorporating the outer surfaces of the sample in the simulations, sintering takes place via vacancy diffusion from the pores to the outer sample surfaces. The simulations were performed in two dimensions. The results showed that the model is capable of displaying various sintering phenomena such as evaporation and condensation, rounding of a sharp corner, pore coalescence, thermal etching, neck formation, grain growth, and growth of large pores. For the elimination of an isolated pore, the most salient result is that the scaling law of the pore elimination time tp with respect to the pore diameter dp changes as pore size changes from larger than the grains to smaller than the grains. For example, in sample-size-fixed simulations, tp ∼ d3p for dp < G and tp ∼ d2p for dp > G with the crossover pore diameter dc increasing linearly with G where G is the average grain diameter. For sample-size-scaled simulations, tp ∼ d4p for dp < G and tp ∼ d3p for dp > G. That tp has different scaling laws in different grain-size regimes is a result of grain boundaries serving as diffusion channels in a fine-grain microstructure such as those considered in the simulations. A scaling analysis is provided to explain the scaling relationships among tp, dp, and G obtained in the simulations. The scaling analysis also shows that these scaling relationships are independent of the dimensionality. Thus, the results of the two-dimensional simulations should also apply in three dimensions.

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.

Fractional Brownian modeled linear polymer chains with one dimensional Metropolis Monte Carlo simulation

2015 ◽  
Vol 36 ◽  
pp. 1560017
Author(s):  
J. P. B. Sambo ◽  
B. V. Gemao ◽  
J. B. Bornales
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Probability Distribution ◽  
Numerical Data ◽  
Polymer Chains ◽  
Linear Polymer ◽  
Hurst Parameter ◽  
Metropolis Monte Carlo ◽  
End Distance ◽  
Good Agreement

The scaling expression for fractional Brownian modeled linear polymer chains was obtained both theoretically and numerically. Through the probability distribution of fractional Brownian paths, the scaling was found out to be 〈R2〉 ~ N2H, where R is the end-to-end distance of the polymer chain, N is the number of monomer units and H is the Hurst parameter. Numerical data was generated through the use of Monte Carlo simulation implementing the Metropolis algorithm. Results show good agreement between numerical and theoretical scaling constants after some parameter optimization. The probability distribution confirmed the Gaussian nature of fractional Brownian motion and the behavior is not affected by varying values of the Hurst parameter and of the number of monomer units.

Effect of Structural Features on the Statistical Correlation of Dipole Moments on the End-to-End Distance of Polymer Chains

1992 ◽  
Vol 278 ◽  
Author(s):  
Vassilios Galiatsatos
Keyword(s):  
Dipole Moment ◽  
Polymer Chain ◽  
Structural Characteristics ◽  
Dipole Moments ◽  
Structural Features ◽  
Statistical Correlation ◽  
Polymer Chains ◽  
Moment Vector ◽  
End Distance ◽  
End To End

AbstractA recently developed computational methodology allows the quantitative study of the correlation between the end-to-end distance of a polymer chain and its dipole moment. This paper focuses on the further analysis of this correlation and aims in identifying the structural characteristics of the polymer chain that are responsible for the observed behavior of the correlation. We study chains in the independent rotation approximation with symmetric rotational potentials. We focus on two different orientations of the bond dipole moment vector : 010 and 001 (the bond length vector's orientation is [100]).

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