Rotational isomeric state chain

The dimensionless ratios of the form (s2p)q/ s2)pq are easily evaluated from a theoretical model for the distribution function, P(s2), using Equation (1.22). For small p, they can also be calculated for unperturbed rotational isomeric state chains by efficient generator matrix methods... 

Figure 4 Cartoon for hidden liquid-liquid spinodal in a polymer melt, calculated for a Flory Rotational Isomeric State chain with a simple coupling between density and conformational order A is the trans-gauche energy gap and a dimensionless density. Shown is the path of an isochoric quence into the unstable regime. r, is the spinodal temperature, T the melting temperature, T the liquid-liquid critical point, and Tp the temperature at which the harrier between dense liquid and crystal is of order ksT ...

A comparison has been made of rotational isomeric state chains modelled by matrix multiplication methods, as in most of the papers mentioned in this section, with lattice and off-lattice chains obtained by Monte Carlo techniques. excluded volume effects than or Rotational angle flexibility has been expressed in the co-ordinates transform motion matrix, and its influence examined upon , the distribution function for r, and the correlation of the relative orientation of the end bonds of the polymer. ... 

The structurally simplest polymer, and one of the most commercially important, is polyethylene. It consists of a linear chain of CH2 units, which we model as single spherical sites in the single-site homopolymer spirit. There exist well-developed ideal rotational isomeric state chain models where the bond rotational degrees of freedom are represented as discrete trans and gauche isomers. Numerical calculation of the required single-chain structure factor can be achieved via Monte Carlo simulation or using the recently developed computationally convenient approximate methods of McCoy and co-workers. ... 

Assuming that the intramolecular structure of the chains in the athermal blend is independent of composition, then the elements of the 4x4 Cl y(k) intramolecular matrix for the blend are already available from the corresponding one-component melt Intramolecular structure functions. The noy(k) for a, -y = A, B, C were obtained from Monte Carlo simulations of a single, rotational isomeric state chain using the parameterization of Suter and Flory discussed in Section III.B. Likewise, dd( ) was obtained from the RIS calculations of Honnell and coworkers for polyethylene... 

Chain models capture the basic elements of the amphiphilic behaviour by retaining details of the molecular architecture. Ben-Shaul et aJ [ ] and others [ ] explored the organization of tlie hydrophobic portion in lipid micelles and bilayers by retaining the confonuational statistics of the hydrocarbon tail withm the RIS (rotational isomeric state) model [4, 5] while representing the hydrophilic/liydrophobic mterface merely by an... 

The conformational characteristics of PVF are the subject of several studies (53,65). The rotational isomeric state (RIS) model has been used to calculate mean square end-to-end distance, dipole moments, and conformational entropies. C-nmr chemical shifts are in agreement with these predictions (66). The stiffness parameter (5) has been calculated (67) using the relationship between chain stiffness and cross-sectional area (68). In comparison to polyethylene, PVF has greater chain stiffness which decreases melting entropy, ie, (AS ) = 8.58 J/(molK) [2.05 cal/(molK)] versus... 

Moller,M. Cross Polarization — Magie Angle Sample Spinning NMR Studies. With Respect to the Rotational Isomeric States of Saturated Chain Molecules. Vol. 66, pp. 59 — 80. 

With Respect to the Rotational Isomeric States of Saturated Chain Molecules... 

A suitable approach to the equilibration of an amorphous polymer system at bulk density becomes much more likely when the fully atomistic model in continuous space is replaced by an equivalent coarse-grained model on a lattice with sufficient conformational flexibility. Different strategies, which seek results at different levels of detail, can be employed to create an appropriate coarse-grained model. Section 4 (Doruker, Mattice) describes an approach which attempts to retain a connection with the covalent bonds in the polymer. The rotational isomeric state (RIS) [35,36] model for the chain is mapped into... 

Muller et al. focused on polybead molecules in the united atom approximation as a test system these are chains formed by spherical methylene beads connected by rigid bonds of length 1.53 A. The angle between successive bonds of a chain is also fixed at 112°. The torsion angles around the chain backbone are restricted to three rotational isomeric states, the trans (t) and gauche states (g+ and g ). The three-fold torsional potential energy function introduced [142] in a study of butane was used to calculate the RIS correlation matrix. Second order interactions , reflected in the so-called pentane effect, which almost excludes the consecutive combination of g+g- states (and vice-versa) are taken into account. In analogy to the polyethylene molecule, a standard RIS-model [143] was used to account for the pentane effect. 

Monte Carlo computer simulations were also carried out on filled networks [50,61-63] in an attempt to obtain a better molecular interpretation of how such dispersed fillers reinforce elastomeric materials. The approach taken enabled estimation of the effect of the excluded volume of the filler particles on the network chains and on the elastic properties of the networks. In the first step, distribution functions for the end-to-end vectors of the chains were obtained by applying Monte Carlo methods to rotational isomeric state representations of the chains [64], Conformations of chains that overlapped with any filler particle during the simulation were rejected. The resulting perturbed distributions were then used in the three-chain elasticity model [16] to obtain the desired stress-strain isotherms in elongation. 

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. 

In a real chain segment-segment correlations extend beyond nearest neighbour distances. The standard model to treat the local statistics of a chain, which includes the local stiffness, would be the rotational isomeric state (RIS) [211] formalism. For a mode description as required for an evaluation of the chain motion it is more appropriate to consider the so-called all-rotational state (ARS) model [212], which describes the chain statistics in terms of orthogonal Rouse modes. It can be shown that both approaches are formally equivalent and only differ in the choice of the orthonormal basis for the representation of statistical weights. In the ARS approach the characteristic ratio of the RIS-model becomes mode dependent. 

A general theory is presented on the effect of elongation of a polymer chain on the apportionment of its bonds and bond sequences among various rotational Isomeric states. Numerical calculations are presented for PE chains and for syndiotactlc vinyl polymers. 

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