Abstract
The study of phase transitions has played a central role in the study of condensed matter. Since the first applications of molecular simulations, which provided some of the first evidence in support of a freezing transition in hardsphere systems, to contemporary research on complex systems, including polymers, proteins, or liquid crystals, to name a few, molecular simulations are increasingly providing a standard against which to measure the validity of theoretical predictions or phenomenological explanations of experimentally observed phenomena.
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References
A. Z. Panagiotopoulos (1992) Direct determination of fluid-phase equilibria by simulation in the gibbs ensemble – A review. Molecular Simulation. 9, pp. 1–23
A. M. Ferrenberg and R. H. Swendsen (1988) New Monte-Carlo technique for studying phase-transitions. Phys. Rev. Lett. 61, pp. 2635–2638
A. M. Ferrenberg and R. H. Swendsen (1989) Optimized Monte-Carlo data-analysis. Phys. Rev. Lett. 63, pp. 1195–1198
B. A. Berg and T. Neuhaus (1992) Multicanonical ensemble – a new approach to simulate 1st-order phase-transitions. Phys. Rev. Lett. 68, pp. 9–12
B. A. Berg and T. Neuhaus (1991) Multicanonical algorithms for 1st order phase-transitions. Phys. Lett. B 267, pp. 249–253
J. Lee (1993) New Monte-Carlo algorithm – entropic sampling. Phys. Rev. Lett. 71, pp. 211–214
F. G. Wang and D. P. Landau (2001) Efficient, multiple-range random walk algorithm to calculate the density of states. Phys. Rev. Lett. 86, pp. 2050–2053
Q. L. Yan, R. Faller, and J. J. de Pablo (2002) Density-of-states Monte Carlo method for simulation of fluids. J. Chem. Phys. 116, pp. 8745–8749
A. P. Lyubartsev, A. A. Martsinovski, S. V. Shevkunov, and P. N. Vorontsovvelyaminov (1992) New approach to Monte-Carlo calculation of the free-energy – method of expanded ensembles. J. Chem. Phys. 96, pp. 1776–1783
B. A. Berg (2003) Multicanonical simulations step by step. Comp. Phys. Comm. 153, pp. 397–406; ibid. (2004) Markov Chain Monte Carlo Simulations and their Statistical Analysis. World Scientific P. 380
P. M. C. de Oliveira, T. J. P. Penna, and H. J. Herrmann (1996) Broad Histogram Method. Braz. J. Phys. 26, pp. 677–683
O. Engkvist and G. Karlstrom (1996) A method to calculate the probability distribution for systems with large energy barriers. Chem. Phys. 213, pp. 63–76
N. Rathore and J. J. de Pablo (2002) Monte Carlo simulation of proteins through a random walk in energy space. J. Chem. Phys. 116, pp. 7225–7230
N. Rathore, T. A. Knotts, and J. J. de Pablo (2003) Configurational temperature density of states simulations of proteins. Biophys. J. 85, pp. 3963–3968
T. S. Jain and J. J. de Pablo (2002) A biased Monte Carlo technique for calculation of the density of states of polymer fllms. J. Chem. Phys. 116, pp. 7238–7243
T. S. Jain and J. J. de Pablo (2003) Calculation of interfacial tension from density of states. J. Chem. Phys. 118, pp. 4226–4229
Q. Yan and J. J. de Pablo (2003) Fast calculation of the density of states of a fluid by Monte Carlo simulations. Phys. Rev. Lett. 90, 035701
N. Rathore, T. A. Knotts, and J. J. de Pablo (2003) Configurational temperature density of states simulations of proteins. Biophys. J. 85, pp. 3963–3968
D. A. McQuarrie (1976) Statistical Mechanics. HarperCollins Publishers Inc., New York
O. G. Jepps, O. Ayton, and D. J. Evans (2000) Microscopic expressions for the thermodynamic temperature. Phys. Rev. E. 62, pp. 4757–4763
B. D. Butler, G. Ayton, O. G. Jepps, and D. J. Evans (1998) Configurational temperature: Verification of Monte Carlo simulations. J. Chem. Phys. 109, pp. 6519–6522
J. R. Ray (1991) Microcanonical ensemble Monte-Carlo method. Phys. Rev. A 44, pp. 4061–4064
R. Lustig (1998) Microcanonical Monte Carlo simulation of thermodynamic properties. J. Chem. Phys. 109, pp. 8816–8828
P. Dayal, S. Trebst, S. Wessel, D. Wurtz, M. Troyer, S. Sabhapandit, and S. N. Coppersmith (2004) Performance limitations of flat-histogram methods. Phys. Rev. Lett. 92, 097201
T. Lazaridis and M. Karplus (1999) Effective energy function for proteins in solution. Proteins 35, pp. 133–152
P. Ferrara, J. Apostolakiz, and A. Caflisch (2002) Evaluation of a fast implicit solvent model for molecular dynamics simulations. Proteins 46, pp. 24–33
Q. L. Yan and J. J. de Pablo (1999) Hyper-parallel tempering Monte Carlo: Application to the Lennard-Jones fluid and the restricted primitive model. J. Chem. Phys. 111, pp. 9509–9515
E. B. Kim, R. Faller, Q. Yan, N. L. Abbott, and J. J. de Pablo (2002) Potential of mean force between a spherical particle suspended in a nematic liquid crystal and a substrate. J. Chem. Phys. 117, pp. 7781–7787
N. Rathore, Q. L. Yan and J. J. de Pablo (2004) Molecular simulation of the reversible mechanical unfolding of proteins. J. Chem. Phys. 120, pp. 5781–5788
M. Doxastakis, Y. L. Chen, and J. J. de Pablo (2005) Potential of mean force between two nanometer-scale particles in a polymer solution. J. Chem. Phys. 123, 034901
T. A. Knotts, N. Rathore, and J. J. de Pablo (2005) Structure and stability of a model three-helix-bundle protein on tailored surfaces. Proteins-Structure Function and bioinformatics 61, pp. 385–397
N. Rathore, Q. L. Yan, and J. J. de Pablo (2004) Molecular simulation of the reversible mechanical unfolding of proteins. J. Chem. Phys. 120, pp. 5781–5788
M. Chopra, M. Müller, and J. J. de Pablo (2006) Order-parameter-based Monte Carlo simulation of crystallization. J. Chem. Phys. 124 p. 134102
J. Valleau (1999) Thermodynamic-scaling methods in Monte Carlo and their application to phase equilibria. Adv. Chem. Phys. 105, pp. 369–404
P. Virnau and M. Müller (2004) Calculation of free energy through successive umbrella sampling. J. Chem. Phys. 120, pp. 10925–10930
B. J. Schulz, K. Binder, M. Müller, and D. P. Landau (2003) Avoiding boundary effects in Wang-Landau sampling. Phys. Rev. E 67, 067102
Certainly, restricting the window size limits order parameter fluctuations to far less than those explored in a grandcanonical simulation and each subsimulations resembles more closely a simulation in the canonical ensemble than in the grandcanonical ensemble.We emphasize, however, that local density (order parameter) fluctuations are not restricted and that, ideally, configurations with a fixed order parameter have identical statistical weight in the canonical ensemble, in the ensemble used in our simulation and in the grandcanonical ensemble.
D. Chandler (1987) Introduction to Modern Statistical Mechanics. Oxford University Press, New York
D. Frenkel and B. Smith (1996) Understanding Molecular Simulation. Academic, Boston
P. Virnau, M. Müller, L. G. MacDowell, and K. Binder (2004) Phase behavior of n-alkanes in supercritical solution: A Monte Carlo study. J. Chem. Phys. 121, pp. 2169–2179
K. Binder, M. Müller, P. Virnau, and L. G. MacDowell (2005) Polymer plus solvent systems: Phase diagrams, interface free energies, and nucleation. Adv. Polym. Sci. 173, pp. 1–104
R. L. C. Vink and J. Horbach (2004) Grand canonical Monte Carlo simulation of a model colloid-polymer mixture: Coexistence line, critical behavior, and interfacial tension. J. Chem. Phys. 121, pp. 3253–3258
R. L. C. Vink, J. Horbach, and K. Binder (2005) Capillary waves in a colloid polymer interface. J. Chem. Phys. 122, p. 134905
R. L. C. Vink, J. Horbach, and K. Binder (2005) Critical phenomena in colloid polymer mixtures: Interfacial tension, order parameter, susceptibility, and coexistence diameter. Phys. Rev. E 71, 011401
R. L. C. Vink, M. Schmidt (2005) Simulation and theory of fluid demixing and interfacial tension of mixtures of colloids and nonideal polymers. Phys. Rev. E 71, 051406
R. L. C. Vink, and T. Schilling (2005) Interfacial tension of the isotropicnematic interface in suspensions of soft spherocylinders. Phys. Rev. E 71, 051716
R. L. C. Vink, S. Wolfsheimer, and T. Schilling (2005) Isotropic-nematic interfacial tension of hard and soft rods: Application of advanced grand canonical biased-sampling techniques. J. Chem. Phys. 123, 074901
J. E. Mayer and W. W. Wood (1965) Interfacial Tension effects in Finite, Periodic, Two-Dimensional Systems. J. Chem. Phys. 42, pp. 4268–4274
K. Binder and M. H. Kalos (1980) Critical clusters in a supersaturated vapor - theory and Monte-Carlo simulation. J. Stat. Phys. 22, pp. 363–396
H. Furukawa and K. Binder (1982) 2-phase equilibria and nucleation barriers near a critical-point. Phys. Rev. A 26, pp. 556–566
B. A. Berg, U. Hansmann, and T. Neuhaus (1993) Properties of interfaces in the 2 and 3-dimensional ising-model. Z. Phys. B 90, pp. 229–239
J. E. Hunter and W. P. Reinhardt (1995) Finite-size-scaling behavior of the free-energy barrier between coexisting phases – determination of the critical temperature and interfacial-tension of the Lennard-Jones fluid. J. Chem. Phys. 103, pp. 8627–8637
M. Biskup, L. Chyes, and R. Kotecky (2002) On the formation/dissolution of equilibrium droplets. Europhys. Lett. 60, pp. 21–27
K. Binder (2003) Theory of the evaporation /condensation transition of equilibrium droplets in finite volumes. Physica A 319, pp. 99–114
L. G. MacDowell, P. Virnau, M. Müller, and K. Binder (2004) The evaporation/ condensation transition of liquid droplets. J. Chem. Phys. 120, pp. 5293–5308
Generally, the density of the liquid inside the drop will also deviate from the coexistence density of the liquid. Since the compressibility of the liquid phase, however, is much smaller than that of the vapor the deviation of the density inside the drop from the coexistence value will be much smaller than the deviation in the vapor phase.
F. H. Stillinger Jr. (1963) Rigorous Basis of the Frenkel-Band Theory of Association Equilibrium. J. Chem. Phys. 38, pp. 1486–1494
T. Neuhaus and J. S. Hager (2003) 2D crystal shapes, droplet condensation, and exponential slowing down in simulations of first-order phase transitions. J. Stat. Phys. 113, pp. 47–83
K. Leung and R. K. P. Zia (1990) Geometrically induced transitions between equilibrium crystal shapes. J. Phys. A 23, pp. 4593–4602
L. G. MacDowell, M. Müller, C. Vega, and K. Binder (2000) Equation of state and critical behavior of polymer models: A quantitative comparison between Wertheim’s thermodynamic perturbation theory and computer simulations. J. Chem. Phys. 113, pp. 419–433
J. I. Siepmann (1990) A method for the direct calculation of chemical-potentials for dense chain systems. Mol. Phys., 70, pp. 1145–1158; D. Frenkel, G. C. A. M. Mooij, and B. Smit (1992) Novel scheme to study structural and thermal properties of continuously deformable molecules. J. Phys. Condens. Matter 4, pp. 3053–3076; M. Laso, J. J. dePablo, U. W. Suter (1992) Simulation of phase-equilibria for chain molecules. J. Chem. Phys. 97, pp. 2817–2819
M. Müller and L. G. MacDowell (2000) Interface and surface properties of short polymers in solution: Monte Carlo simulations and self-consistent field theory. Macromolecules 33, pp. 3902–3923
C. Borgs and R. Kotecky (1990) A rigorous theory of finite-size scaling at 1st-order phase-transitions. J. Stat. Phys. 61, pp. 79–119; ibid. (1992) Finite size effects at asymmetric 1st-order phase-transitions. Phys. Rev. Lett. 68, pp. 1734–1737
A. Sariban and K. Binder (1988) Phase-Separation of polymer mixtures in the presence of solvent. Macromolecules 21, pp. 711–726; ibid. (1991) Spinodal decomposition of polymer mixtures – a Monte-Carlo simulation. 24, pp. 578–592; ibid. (1987) Critical properties of the Flory-Huggins lattice model of polymer mixtures. J. Chem. Phys. 86, pp. 5859–5873; ibid. (1988) Interaction effects on linear dimensions of polymer-chains in polymer mixtures. Makromol. Chem. 189, pp. 2357–2365
M. Müller (1999) Miscibility behavior and single chain properties in polymer blends: a bond fluctuation model study. Macromol. Theory Simul. 8, pp. 343–374; M. Müller and K. Binder (1995) Computer-simulation of asymmetric polymer mixtures. Macromolecules 28, pp. 1825–1834; ibid. (1994) An algorithm for the semi-grand-canonical simulation of asymmetric polymer mixtures. Computer Phys. Comm. 84, pp. 173–185
R. D. Kaminski (1994) Monte-Carlo evaluation of ensemble averages involving particle number variations in dense fluid systems. J. Chem. Phys. 101, pp. 4986–4994
I. Carmesin and K. Kremer (1988) The bond fluctuation method – a new e.ective algorithm for the dynamics of polymers in all spatial dimensions. Macromolecules 21, pp. 2819–2823; H.-P. Deutsch and K. Binder (1991) Interdiffusion and self-diffusion in polymer mixtures – a monte-carlo study. J. Chem. Phys. 94, pp. 2294–2304
M. L. Huggins (1941) Solutions of Long Chain Compounds. J. Chem. Phys. 9, p. 440; P. J. Flory (1941) Thermodynamics of High Polymer Solutions. J. Chem. Phys. 9, pp. 660–661
K. S. Schweizer and J. G. Curro (1997) Integral equation theories of the structure, thermodynamics, and phase transitions of polymer fluids. Adv. Chem. Phys. 98, pp. 1–142.
K. W. Foreman and K. F. Freed (1998) Lattice cluster theory of multicomponent polymer systems: Chain semiflexibility and specific interactions. Advances in Chemical Physics 103, pp. 335–390; K. F. Freed and J. Dudowicz (1998) Lattice cluster theory for pedestrians: The incompressible limit and the miscibility of polyolefin blends. Macromolecules 31, pp. 6681–6690
E. Helfand and Y. Tagami (1972) Theory of interface between immiscible polymers .2. J. Chem. Phys. 56, p. 3592; E. Helfand (1975) Theory of inhomogeneous polymers – fundamentals of Gaussian random-walk model. J. Chem. Phys. 62, pp. 999–1005
K. M. Hong and J. Noolandi (1981) Theory of inhomogeneous multicomponent polymer systems. Macromolecules 14, pp. 727–736; ibid., (1982) Interfacial properties of immiscible homopolymer blends in the presence of block copolymers. 15, pp. 482–492
K. R. Shull (1993) Interfacial phase-transitions in block copolymer homopolymer blends. Macromolecules 26, pp. 2346–2360
J. M. H. M. Scheutjens and G. J. Fleer (1979) Statistical-theory of the adsorption of interacting chain molecules .1. Partition-function, segment density distribution, and adsorption-isotherms. J. Phys. Chem. 83, pp. 1619–1635; ibid. (1980) Statistical-theory of the adsorption of interacting chain molecules .2. Train, loop, and tail size distribution. 84, pp. 178–190; ibid. (1985) Interaction between 2 adsorbed polymer layers. Macromolecules 18, pp. 1882–1900
M. W. Matsen (1995) Stabilizing new morphologies by blending homopolymer with block-copolymer. Phys. Rev. Lett. 74, pp. 4225–4228
G. H. Fredrickson, V. Ganesan, and F. Drolet (2002) Field-theoretic computer simulation methods for polymers and complex fluids. Macromolecules 35, pp. 16–39
M. Müller and F. Schmid (2005) Incorporating fluctuations and dynamics in self-consistent field theories for polymer blends. Adv. Polym. Sci. 185, pp. 1–58
M. Müller (2005) Monte Carlo Simulations of Binary Polymer Liquids. In Molecular Simulation Methods for Predicting Polymer Properties, V. Galiatsatos (ed), pp. 95–152, Wiley Hoboken, NJ.
F. S. Bates, M. F. Schultz, J. H. Rosedale, and K. Almdal (1992) Order and Disorder in symmetrical diblock copolymer melts. Macromolecules 25, p. 5547; M. D. Gehlsen and F. S. Bates (1994) Macromolecules 27, p. 3611; F. S. Bates and G. H. Fredrickson (1994) Macromolecules 27, p. 1065
D. Schwahn, G. Meier, K. Mortensen, and S. Janssen (1994) On the N-scaling of the ginzburg number and the critical amplitudes in various compatible polymer blends. J. Phys. II (France) 4, pp. 837–848; H. Frielinghaus, D. Schwahn, L. Willner, and T. Springer (1997) Thermal composition fluctuations in binary homopolymer mixtures as a function of pressure and temperature. Physica B 241, pp. 1022–1024
P. Van Konynenburg and R. L. Scott (1980) Critical lines and phase-equilibria in binary vanderwaals mixtures. Philos. Trans. Soc. London Series A 298, pp. 495–540
H. A. Lorentz (1881) Annalen Phys. 12, p. 127
D. C. Berthelot (1898) r. hebd. Seanc. Acad Sci. Paris 126, p. 1703
G. Schneider, Z. Alwani, W. Heim, E. Horvath, and E. U. Franck (1967) Phase equilibria and critical phenomena in binary mixtures (CO2 with N-octane Nundecane N-tridecane and N-hexadecane up to 1500 bar). Chem. Ing. Techn. 39, p. 649
T. Charoensombut-Amon, R. J. Martin, and R. Kobayashi (1986) Application of a generalized multiproperty apparatus to measure phase-equilibrium and vapor-phase densities of supercritical carbon-dioxide in normal-hexadecane systems up to 26 mpa. Fluid Phase Equilibria 31, pp. 89–104
C. Menduina, C. McBride, and C. Vega (2001) Correctly averaged Non-Gaussian theory of rubber-like elasticity – application to the description of the behavior of poly(dimethylsiloxane) bimodal networks. Phys. Chem. Chem. Phys. 3, p. 1289
P. G. de Gennes and J. Prost (1993) The Physics of Liquid Crystals. Clarendon Press, Oxford
L. Leibler (1980) Theory of microphase separation in block co-polymers. Macromolecules 13, pp. 1602–1617
P. J. Steinhardt, D. R. Nelson, and M. Ronchetti (1983) Bond-orientational order in liquids and glasses. Phys. Rev. B 28, pp. 784–805
L. D. Landau and E. M. Lifshitz (1980) Statistical Physics, 3rd, Pergamon, London
K. Binder (1982) Monte-Carlo calculation of the surface-tension for twodimensional and 3-dimensional lattice-gas models. Phys. Rev. A 25, pp. 1699–1709
P. R. Ten Wolde, M. J. Ruiz-Montero, and D. Frenkel (1995) Numerical evidence for BCC ordering at the surface of a critical fcc nucleus. Phys. Rev. Lett. 75, pp. 2714–2717
M. J. Mandell, J. P. McTaque, and A. Rahman (1976) Crystal nucleation in a 3-dimensional lennard-jones system – molecular-dynamics study. J. Chem. Phys. 64, pp. 3699–3702
C. S. Hsu and A. Rahman (1979) Crystal nucleation and growth in liquid rubidium. J. Chem. Phys. 71, p. 4974
W. C. Swope and H. C. Andersen (1990) 10(6)-Particle molecular-dynamics study of homogeneous nucleation of crystals in a supercooled atomic liquid. Phys. Rev. B 41, pp. 7042–7054
J. S. van Duijneveldt and D. Frenkel (1992) Computer-simulation study of free-energy barriers in crystal nucleation. J. Chem. Phys. 96, pp. 4655–4668
E. B. Kim, R. Faller, Q. Yan, N. L. Abbott, and J. J. de Pablo (2002) Potential of mean force between a spherical particle suspended in a nematic liquid crystal and a substrate. J. Chem. Phys. 117, pp. 7781–7787
N. B. Wilding and A. D. Bruce (2000) Freezing by Monte Carlo phase switch. Phys. Rev. Lett. 85, pp. 5138–5141
M. B. Sweatman (2005) Self-referential Monte Carlo method for calculating the free energy of crystalline solids. Phys. Rev. E 72, 016711
D. M. Eike, J. F. Brennecke, and E. J. Maginn (2005) Toward a robust and general molecular simulation method for computing solid-liquid coexistence. J. Chem. Phys. 122, 014115
D. Moroni, P. Rein ten Wolde, and P. G. Bolhuis (2005) Interplay between structure and size in a critical crystal nucleus. Phys. Rev. Lett. 94, p. 235703
P. R. ten Wolde, M. J. Ruiz-Montero, and D. Frenkel (1996) Numerical calculation of the rate of crystal nucleation in a Lennard-Jones system at moderate undercooling. J. Chem. Phys. 104, pp. 9932–9947
B. B. Laird and R. L. Davidchack (2005) Direct calculation of the crystal-melt interfacial free energy via molecular dynamics computer simulation. J. Phys. Chem. B 109, pp. 17802–17812
M. Müller, K. Binder, and W. Oed (1995) Structural and thermodynamic properties of interfaces between coexisting phases in polymer blends – a monte-carlo simulation. J. Chem. Soc. Faraday Trans. 91, pp. 2369–2379
M. Müller and M. Schick (1996) Bulk and interfacial thermodynamics of a symmetric, ternary homopolymer-copolymer mixture: A Monte Carlo study. J. Chem. Phys. 105, pp. 8885–8901
B. Grossmann and M. L. Laursen (1993) The confined deconfined interface tension in quenched qcd using the histogram method. Nuc. Phys. B 408, pp. 637–656
F. Schmid and M. Müller (1995) Quantitative comparison of self-consistent-field theories for polymers near interfaces with monte-carlo simulations. Macromolecules 28, pp. 8639–8645
A. Werner, F. Schmid, M. Müller, and K. Binder (1999) “Intrinsic” profiles and capillary waves at homopolymer interfaces: A Monte Carlo study. Phys. Rev. E 59, pp. 728–738
M. Müller (2006) Soft Matter vol. 1, Chap. 3, pp. 179–283 edited by G. Gompper and M. Schick, Wiley-VCH, Weinheim
A. N. Semenov (1996) Theory of long-range interactions in polymer systems. J. Phys. (France) II, 6, pp. 1759–1780
A. Werner, F. Schmid, and M. Müller (1999) Monte Carlo simulations of copolymers at homopolymer interfaces: Interfacial structure as a function of the copolymer density. J. Chem. Phys. 110, pp. 5370–5379
H. Lu, B. Isralewitz, A. Krammer, V. Vogel, and K. Schulten (1998) Unfolding of titin immunoglobulin domains by steered molecular dynamics simulation. Biophys. J. 75, pp. 662–671
C. Jarzynski (2001) How does a system respond when driven away from thermal equilibrium? Proc. Nat. Acad. Sci. 98, pp. 3636–3638
H.C. Öttinger (2005) Beyond Equilibrium Thermodynamics. Wiley Interscience, New Jersey
J. Baschnagel, K. Binder, P. Doruker, A. A. Gusev, O. Hahn, K. Kremer, W. L. Mattice, F. Muller-Plathe, M. Murat, W. Paul, S. Santos, U. W. Suter, and V. Tries (2000) Bridging the gap between atomistic and coarse-grained models of polymers: Status and perspectives. Adv. Polym. Sci. 152, pp. 41–156
J. C. Shelley, M. Y. Shelley, R. C. Reeder, S. Bandyopadhyay, P. B. Moore, and M. L. Klein (2001) Simulations of phospholipids using a coarse grain model. J. Phys. Chem. B 105, pp. 9785–9752
M. Müller, K. Katsov, and M. Schick (2003) Coarse-grained models and collective phenomena in membranes: Computer simulation of membrane fusion. J. Polym. Sci. B 41, pp. 1441–1450
S. O. Nielsen, C. F. Lopez, G. Srinivas, and M. L. Klein (2004) Coarse grain models and the computer simulation of soft materials. J. Phys.: Condens. Matter 16, pp. R481–R512
F. Müller-Plathe (2002) Chem. Phys. Chem. 3, p. 754
R. Faller, H. Schmitz, O. Biermann and F. Müller-Plathe (1999) Molecular mobility in cyclic hydrocarbons: A simulation study. J. Comput. Chem. 20, p. 1009; ibid. (2004) Polymer 45, p. 3869
L. Delle Site, C. F. Abrams, A. Alavi, and K. Kremer (2002) Polymers near metal surfaces: Selective adsorption and global conformations. Phys. Rev. Lett. 89, p. 156103; M. Praprotnik, L. Delle Site, and K. Kremer (2005) J. Chem. Phys. 123, p. 224106
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Müller, M., de Pablo, J. (2006). Simulation Techniques for Calculating Free Energies. In: Ferrario, M., Ciccotti, G., Binder, K. (eds) Computer Simulations in Condensed Matter Systems: From Materials to Chemical Biology Volume 1. Lecture Notes in Physics, vol 703. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-35273-2_3
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