Lennard-Jones chains

Simulations of monolayers have focused on internal phase transitions, e.g., between the expanded phase and the condensed phases, between different tilted phases, etc. These phenomena cannot be reproduced by models with purely repulsive interactions. Therefore, Haas et al. [148,149] represent the amphiphiles as stiff Lennard-Jones chains, with one end (the head bead) confined to move in a plane. In later versions of the model [150-152], the head bead interactions differ from those of the tail beads they are taken to be purely repulsive, and the head size is variable. 

FIG. 8 Phase diagram of a Langmuir monolayer in a model of grafted stiff Lennard-Jones chains. LE denotes a disordered expanded phase, LC-U a condensed phase with untilted chains, LC-NN and LC-NNN condensed phases with collective tilt towards nearest neighbors and next-nearest neighbors, respectively, and LC-mod a phase which has a superstructure and an intermediate direction of tilt. (From Stadler and Schmid [151].)... 

Temperature dependence of radius of g> ration in universal form. Upper plot shows Monte-Carlo simulation data on Lennard-Jones chains, with the filled squares from W. W. Graessley et al., Mdcromolecules 32, 3510 (1999) and the tilled circles are courtesy of 1. Withers. Louer plot shows experimental data on... 

Applications of the expanded-ensemble approach have been reported for the partitioning of polymers between a slit pore and the bulk [52,77,79], and for fluid-fluid equilibria [78-80]. Figure 4 shows results of expanded Gibbs ensemble simulations of phase coexistence in a binary system of Lennard-Jones chains dissolved in their own monomer [80] (cross-inter-... 

T. Goel, C.N. Patra, T. Mukheqee, and C. Chakravarty, Excess entropy scaling of transport properties of Lennard-Jones chains. J. Chem. Phys., 129 (2008), 164904-164909. 

Bias FJ, Vega LF (1997) Thermodynamic behaviour of hmnraiuclear Lennard Jones chains with association sites from simulation and theory. Mol Phys 92 135 150... 

In the previous section we have described how to implement TPTl for a mixture of Lennard-Jones chains with a FENE bonding potential. Before considering binary mixtures, however, we shall restrict our attention to the particular case of a one component system of polymers. In order to describe the thermodynamic properties of such a system, we will consider two TPTl implementations, which we denote TPTl-MSA and TPTl-RHNC. In TPTl-MSA, we employ the fiilly analytic equation of state described in the previous section. In TPTl-RHNC, the Lennard-Jones reference system is described by means of the Reference Hypernetted Chain theory (RHNC). This is an integral equation theory which can only be solved numerically. 

Langevin 115, 120 Lennard-Jones beads/sites 73, 76, 78 Lennard-Jones chains 70 Lennard-Jones cluster 167 Lennard-Jones energy 17 Lennard-Jones fluid 21, 69 Lennard-Jones interactions 85 Lennard-Jones liquid 52... 

Johnson JK, Muller EA, Gubbins KE (1994) Equation of state for lennard-jones chains. J Phys Chem 98 6413-6419... 

Duque, D. P mies, J.C. Vega, L.F. (2004). Interfacial properties of Lennard-Jones chains by direct simulation and density gradient theory. J. Chem. Phys. 121,11395-11401. 

The behavior of insoluble monolayers at the hydrocarbon-water interface has been studied to some extent. In general, a values for straight-chain acids and alcohols are greater at a given film pressure than if spread at the water-air interface. This is perhaps to be expected since the nonpolar phase should tend to reduce the cohesion between the hydrocarbon tails. See Ref. 91 for early reviews. Takenaka [92] has reported polarized resonance Raman spectra for an azo dye monolayer at the CCl4-water interface some conclusions as to orientation were possible. A mean-held theory based on Lennard-Jones potentials has been used to model an amphiphile at an oil-water interface one conclusion was that the depth of the interfacial region can be relatively large [93]. 

Concluding this section, one should mention also the method of molecular dynamics (MD) in which one employs again a bead-spring model [33,70,71] of a polymer chain where each monomer is coupled to a heat bath. Monomers which are connected along the backbone of a chain interact via Eq. (8) whereas non-bonded monomers are assumed usually to exert Lennard-Jones forces on each other. Then the time evolution of the system is obtained by integrating numerically the equation of motion for each monomer i... 

A complete set of intermolecular potential functions has been developed for use in computer simulations of proteins in their native environment. Parameters have been reported for 25 peptide residues as well as the common neutral and charged terminal groups. The potential functions have the simple Coulomb plus Lennard-Jones form and are compatible with the widely used models for water, TIP4P, TIP3P and SPC. The parameters were obtained and tested primarily in conjunction with Monte Carlo statistical mechanics simulations of 36 pure organic liquids and numerous aqueous solutions of organic ions representative of subunits in the side chains and backbones of proteins... 

The system used in the simulations usually consists of solid walls and lubricant molecules, but the specific arrangement of the system depends on the problem under investigation. In early studies, hard spherical molecules, interacting with each other through the Lennard-Jones (L-J) potential, were adopted to model the lubricant [27], but recently we tend to take more realistic models for describing the lubricant molecules. The alkane molecules with flexible linear chains [28,29] and bead-spring chains [7,30] are the examples for the most commonly used molecular architectures. The inter- and intra-molecular potentials, as well as the interactions between the lubricant molecule and solid wall, have to be properly defined in order to get reliable results. Readers who intend to learn more about the specific techniques of the simulations are referred to Refs. [27-29]. 

Table 5.1 Parameters of the united atom force field for polyethylene used as the atomistic input for the coarse-graining procedure. The Lennard-Jones parameters pertain to CH2-group interaction, since chain ends were not considered in the coarse-graining. 

Fig. 6.7. Evolution of the sample averaged (R< ) as a function of MC time. The initial value of e(N) = C = 1.0 was changed to the values indicated after 600 MC steps. The indicated melt value corresponds to a comparable system with explicit chains with repulsive Lennard-Jones interactions and a number density of 0.85 cr-3 (from [45])...

Liang, H. J. Chen, H. N., First-order transition of a homopolymer chain with Lennard-Jones potential, J. Chem. Phys. 2000,113, 4469 1471... 

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