The Configuration Partition Function, a priori Probabilities, and Conditional Probabilities for Branched Macromolecules Subject to the Rotational Isomeric State Approximation

1975 ◽  
Vol 8 (5) ◽  
pp. 644-651 ◽  
Author(s):  
Wayne L. Mattice
Keyword(s):  
Partition Function ◽  
Isomeric State ◽  
A Priori ◽  
Conditional Probabilities ◽  
Rotational Isomeric State ◽  
State Approximation

n-Hexane proton dipolar couplings and the rotational isomeric state approximation

1991 ◽  
Vol 72 (2) ◽  
pp. 333-344 ◽  
Author(s):  
D.J. Photinos ◽  
B. Janik Poliks ◽  
E.T. Samulski ◽  
A.F. Terzis ◽  
H. Toriumi
Keyword(s):  
Isomeric State ◽  
Dipolar Couplings ◽  
Rotational Isomeric State ◽  
State Approximation

scholarly journals On the use of the rotational isomeric state approximation in studies of internal rotation

1983 ◽  
Vol 61 (1) ◽  
pp. 163-170 ◽  
Author(s):  
Victor M. S. Gil ◽  
Antonio J. C. Varandas ◽  
John N. Murrell
Keyword(s):  
Potential Energy ◽  
Internal Rotation ◽  
Isomeric State ◽  
Model Potential ◽  
Energy Curve ◽  
Energy Functions ◽  
Potential Energy Functions ◽  
Rotational Isomeric State ◽  
State Approximation

A critical appraisal is made of the validity of the rotational isomeric state (RIS) approximation in studies of rotational isomerism, especially as far as the determination of energy differences for the stable conformers is concerned. By using simple model potential energy functions for internal rotation appropriate to some ethane derivatives, a comparison is made between the thermodynamic parameters that can be extracted from such potential functions and those obtained by applying the RIS method to continuum averaged values of conformation dependent properties. The effects due to the form of this conformation dependence, to the features of the potential energy curve, and to the temperature are discussed. The errors can be very large for realistic situations, and variable with temperature and with the property being studied; cases for which the errors are small are usually accidental.

scholarly journals Application of Rotational Isomeric State Theory to Ionic Polymer Stiffness Predictions

2005 ◽  
Vol 20 (9) ◽  
pp. 2443-2455 ◽  
Author(s):  
Lisa Mauck Weiland ◽  
Emily K. Lada ◽  
Ralph C. Smith ◽  
Donald J. Leo
Keyword(s):  
Isomeric State ◽  
Mechanical Response ◽  
Physical Structure ◽  
State Theory ◽  
Chain Conformation ◽  
Ionic Polymer ◽  
Polymer Morphology ◽  
Rotational Isomeric State ◽  
Material Stiffness ◽  
Chain Lengths

Presently, rotational isomeric state (RIS) theory directly addresses polymer chain conformation as it relates to mechanical response trends. The primary goal of this work is to explore the adaptation of this methodology to the prediction of material stiffness. This multiscale modeling approach relies on ionomer chain conformation and polymer morphology and thus has potential as both a predictive modeling tool and a synthesis guide. The Mark–Curro Monte Carlo methodology is applied to generate a statistically valid number of end-to-end chain lengths via RIS theory for four solvated Nafion® cases. For each case, a probability density function for chain length is estimated using various statistical techniques, including the classically applied cubic spline approach. It is found that the stiffness prediction is sensitive to the fitting strategy. The significance of various fitting strategies, as they relate to the physical structure of the polymer, are explored so that a method suitable for stiffness prediction may be identified.

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