Monte-Carlo chains

A theoretical investigation of the use of NMR lineshape second moments in determining elastomer chain configurations has been undertaken. Monte Carlo chains have been generated by computer using a modified rotational isomeric state (RIS) theory in which parameters have been included which simulate bulk uniaxial deformation. The behavior of the model for a hypothetical poly(methylene) system and for a real poly(p-fluorostyrene) system has been examined. Excluded volume effects are described. Initial experimental approaches are discussed. 

The generator matrix treatment of simple chains with excluded volume described earlier S 010) properly reproduces the known chain length dependence of the mean-square dimensions in the limit of infinite chains. The purpose of this paper is to compare the behaviour of finite generator matrix chains with that of Monte-Carlo chains in which atoms participating in long-range interactions behave as hard spheres. The model for the unperturbed chain is that developed by Flory et at. for PE (S 027). 

Expansion of subchains in a linear PE chain with excluded volume is evaluated by two methods. (1) Monte-Carlo chains with methylene groups participating in long-range interactions behave as impenetrable spheres with a diameter of 300 pm, and (25 generator matrix calculations in which expansion is produced without any effect on the probability of a trans placement in an infinitely long chain. 

Bascle, J., Garel, T., Orland, H. and Velikson, B. (1993). Biasing a Monte Carlo chain growth method with Ramachandran s plot application to twenty-L-alanine. Biopolymers, 33, 1843-1849. 

Fig. 6. A The characteristic ratio as a function of stereoregularity, calculated for a system with R = (CH2)zCH3(z > 1). The parameters used are E /RT = 2.3, E / /RT = 5 1 and A = 20°, respectively. From Ref. 63). B The characteristic ratios for Monte Carlo chains of 100 units each as a function of fj, the fraction of meso dyads in the chain. The curve shown above represents results of calculations carried out with Et"/RT = EW/RT = 5. From Ref. 63). C The characteristic ratios for Monte Carlo chains of 200 units each as a function of fj, the fraction of meso dyads in the chain. The curve shown above represents results of calculations carried out for a temperature of 140 °C with the conformational parameters chosen as indicated, in cal. mol. The experimental values of Bovey and Heatley85) (a) are shown. From Ref.65). D The characteristic ratios for Monte Carlo chains of 200 units each as a function of fj, the fraction of meso dyads in the chain. The values of Ea and Ep in that order, in kcal mol-1, are marked on the curves. The experimental values of Cowie and Bywater81) ( ), and Noda et al.80) (a) are shown. From Ref.6 ). E The characteristic ratios for Monte Carlo chains of 200 units each as a function of fj, the fraction of meso dyads in the chain. Curves are shown for (a) Ea = 1.0, Ep = -0.6, and 6 = 58° (h) Ea= 1.2, Efl= -0.6, and 6 = 58° (c) Ea= 1.2, Ej8= -0.2, and = 56°, energies being in kcal mol-1. The experimental results of various authors are represented by points as follows Katime et al. ( )75), Katime and Roig ( ), Sakurada et ah ( )7°), Fox ( )...

J. Bascle, T. Garel, H. Orland, and B. Velikson, Biopolymers, 33, 1843 (1993). Biasing a Monte Carlo Chain Growth Method with Ramachandran s Plot Application to Twenty-L-Alanine. 

A theory of finite-order walks has been developed which permits the derivation, from data for such walks, of the coefficient y for self-avoiding walks ((r ) N. In three dimensions, y= 1.203, in agreement with other calculations, but the two-dimensional value (1.469) seemed a little low. The idea of thermal blobs , within which ideal statistics apply, derives from the renormalization-group theory of chain statistics. However, expansion within a short segment of a long Monte Carlo chain is partly caused by interactions of the atoms of the segment with the rest of... 

Figure 5 (a) Characteristic ratios calculated for PAVEs having symmetric side chains. Computations were carried out using Monte Carlo chains of 200 units, being kept at 0. (b) Mean-square dipole moments per repeat unit /x calculated for Monte Carlo chains of 100 units. Displacements of rotational states are indicated in the figure for the main chain (A< ) and side chain (about si) conformations (A ), respectively, being kept at 0... 

Figure 7 Fractions of left-handed (fr ) and right-handed helical conformations (/r ). The open (O) and filled circles ( ) indicate the results obtained for R = C HMeC2H5(S), and the open (A) and filled triangles (A) for R = CHjC H MeC2H5(S). All calculations were carried out for Monte Carlo chains of 200 units...

Rosenbluth M N and Rosenbluth A W 1995 Monte Carlo calculation of the average extension of molecular chains J. Ohem. Phys. 23 356-9... 

Siepmann J I and Frenkel D 1992 Configurational bias Monte Carlo—a new sampling scheme for flexible chains Moi. Phys. 75 59-70... 

R N. The exponent v = 0.588 has been calculated using renonnalization group teclmiques [9, 10], enumeration teclmiques for short chain lengths and Monte Carlo simulations [13]. 

The parameter /r tunes the stiffness of the potential. It is chosen such that the repulsive part of the Leimard-Jones potential makes a crossing of bonds highly improbable (e.g., k= 30). This off-lattice model has a rather realistic equation of state and reproduces many experimental features of polymer solutions. Due to the attractive interactions the model exhibits a liquid-vapour coexistence, and an isolated chain undergoes a transition from a self-avoiding walk at high temperatures to a collapsed globule at low temperatures. Since all interactions are continuous, the model is tractable by Monte Carlo simulations as well as by molecular dynamics. Generalizations of the Leimard-Jones potential to anisotropic pair interactions are available e.g., the Gay-Beme potential [29]. This latter potential has been employed to study non-spherical particles that possibly fomi liquid crystalline phases. 

Monte Carlo simulations generate a large number of confonnations of tire microscopic model under study that confonn to tire probability distribution dictated by macroscopic constrains imposed on tire systems. For example, a Monte Carlo simulation of a melt at a given temperature T produces an ensemble of confonnations in which confonnation with energy E. occurs witli a probability proportional to exp (- Ej / kT). An advantage of tire Monte Carlo metliod is tliat, by judicious choice of tire elementary moves, one can circumvent tire limitations of molecular dynamics techniques and effect rapid equilibration of multiple chain systems [65]. Flowever, Monte Carlo... 

L. Holm and C. Sander, Fast and simple Monte Carlo algorithm for side chain optimization in proteins. Proteins 14 (1992), 213-223. 

US model can be combined with the Monte Carlo simulation approach to calculate a r range of properties them is available from the simple matrix multiplication method. 2 RIS Monte Carlo method the statistical weight matrices are used to generate chain irmadons with a probability distribution that is implied in their statistical weights. 

Pablo J J, M Laso, JI Siepmann and U W Suter 1993. Continuum-Configurational Bias Monte Carlo Simulations of Long-chain Alkanes. Molecular Physics 80 55-63. 

Rosenbluth M N and A W Rosenbluth 1955. Monte Carlo Calculation of the Average Extension Molecular Chains. Journal of Chemical Physics 23 356-359. 

Siepmann J I and D Frenkel 1992. Configurational Bias Monte Carlo A New Sampling Scheme f Flexible Chains. Molecular Physics 75 59-70. 

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