Collapse transitions in a flexible homopolymer chain: application of the Wang-Landau algorithm.

The thermodynamic behavior of a continuous homopolymer is described using the Wang-Landau algorithm for chain lengths up to N=561. The coil-globule and liquid-solid transitions are analyzed in detail with traditional thermodynamic and structural quantities. The behavior of the coil-globule transition is well within theoretical and computational predictions for all chain lengths, while the behavior of the liquid-solid transition is much more susceptible to finite-size effects. Certain "magic number" lengths (N=13,55,147,309,561) , whose minimal energy states offer unique icosahedral geometries, are discussed along with chains residing between these special cases. The low temperature behavior near the liquid-solid transition is rich in structural transformations for certain chain lengths, showing many similarities to the behavior of classical clusters with similar interaction potentials. General comments are made on this size dependent behavior and how it affects transition behavior in this model.

[1]  K. Binder,et al.  Molecular-dynamics simulations of the thermal glass transition in polymer melts: α-relaxation behavior , 1997, cond-mat/9710132.

[2]  A. Khokhlov,et al.  Some problems of the statistical physics of polymer chains with volume interaction , 1978 .

[3]  J. Northby.  Structure and binding of Lennard‐Jones clusters: 13≤N≤147 , 1987 .

[4]  Wolfhard Janke,et al.  Surface effects in the crystallization process of elastic flexible polymers , 2009, 1002.2118.

[5]  Globule transitions of a single homopolymer: a Wang-Landau Monte Carlo study. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[6]  J. Doye,et al.  Collapse of Lennard-Jones homopolymers: Size effects and energy landscapes , 2002 .

[7]  Vladimir A Mandelshtam,et al.  Low-temperature structural transitions: circumventing the broken-ergodicity problem. , 2007, Physical review letters.

[8]  An off-lattice Wang-Landau study of the coil-globule and melting transitions of a flexible homopolymer. , 2006, The Journal of chemical physics.

[9]  David P. Landau,et al.  A Wang-Landau study of the phase transitions in a flexible homopolymer , 2009, Comput. Phys. Commun..

[10]  Thomas Wüst,et al.  Versatile approach to access the low temperature thermodynamics of lattice polymers and proteins. , 2009, Physical review letters.

[11]  D. D. Frantz.  Magic number behavior for heat capacities of medium-sized classical Lennard-Jones clusters , 2001, physics/0107013.

[12]  David P. Landau,et al.  Monte Carlo simulations of systems with complex energy landscapes , 2009, Comput. Phys. Commun..

[13]  Vladimir A Mandelshtam,et al.  Multiple structural transformations in Lennard-Jones clusters: generic versus size-specific behavior. , 2006, The Journal of chemical physics.

[14]  Kurt Binder,et al.  All-or-none proteinlike folding transition of a flexible homopolymer chain. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[15]  Kurt Binder,et al.  Formation of Block Copolymer Micelles in Solution: A Monte Carlo Study of Chain Length Dependence , 2001 .

[16]  P. Frantsuzov,et al.  Size-temperature phase diagram for small Lennard-Jones clusters. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[17]  A. Mackay.  A dense non-crystallographic packing of equal spheres , 1962 .

[18]  Magic numbers for classical Lennard‐Jones cluster heat capacities , 1995, chem-ph/9406001.

[19]  D. Landau,et al.  Wang-Landau algorithm for continuous models and joint density of states. , 2005, Physical review letters.

[20]  G. Grest,et al.  Dynamics of entangled linear polymer melts: A molecular‐dynamics simulation , 1990 .

[21]  Athanassios Z Panagiotopoulos,et al.  Generalization of the Wang-Landau method for off-lattice simulations. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[22]  D. Landau,et al.  Developments in Wang-Landau Simulations of a Simple Continuous Homopolymer , 2008 .

[23]  George Marsaglia,et al.  Random Number Generators , 2003 .

[24]  Jun Wang,et al.  Collapse of homopolymer chains with two fixed terminals , 2003 .

[25]  Wolfhard Janke,et al.  Freezing and collapse of flexible polymers on regular lattices in three dimensions. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[26]  Wolfhard Janke,et al.  Elastic Lennard-Jones polymers meet clusters: differences and similarities. , 2009, The Journal of chemical physics.

[27]  D. Landau,et al.  Application of the Wang-Landau algorithm to the dimerization of glycophorin A. , 2009, The Journal of chemical physics.

[28]  K. Binder,et al.  The phase diagram of a single polymer chain: New insights from a new simulation method , 2006 .

[29]  D. Landau,et al.  A new approach to Monte Carlo simulations in statistical physics: Wang-Landau sampling , 2004 .

[30]  David P. Landau,et al.  The HP model of protein folding: A challenging testing ground for Wang-Landau sampling , 2008, Comput. Phys. Commun..

[31]  Jonathan P. K. Doye,et al.  Entropic effects on the structure of Lennard-Jones clusters , 2001 .

[32]  Kurt Binder,et al.  On the first-order collapse transition of a three-dimensional, flexible homopolymer chain model , 2005 .

[33]  Jonathan P K Doye,et al.  Structural transitions in the 309-atom magic number Lennard-Jones cluster. , 2006, The Journal of chemical physics.

[34]  David P. Landau,et al.  A new approach to Monte Carlo simulations in statistical physics , 2002 .

[35]  K. Binder,et al.  Unexpectedly normal phase behavior of single homopolymer chains. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[36]  Wang-Landau algorithm: a theoretical analysis of the saturation of the error. , 2007, The Journal of chemical physics.

[37]  R. Belardinelli,et al.  Analysis of the convergence of the 1t and Wang-Landau algorithms in the calculation of multidimensional integrals. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.