Monte Carlo Simulation of a Solvated Ionic Polymer with Cluster Morphology

Matthews, Jessica L.; Lada, Emily K.; Weiland, Lisa Mauck; Smith, Ralph C.; Leo, Donald J.

doi:10.21236/ada439431

Cited by 7 publications

(23 citation statements)

References 10 publications

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“…The details of the statistical fitting methods applied to the development of various P (r) expressions for the same distribution of r values are discussed in [31]. Provided here is a brief overview of the cubic spline and Johnson family methods.…”

Section: Discussionmentioning

confidence: 99%

“…To account for this variation, n is sampled from a discrete probability distribution with a minimum of 5, a maximum of 11, and a mean of approximately 7 [31].…”

Section: Simulation Model For Estimating Chain Lengthmentioning

confidence: 99%

“…The grid size is selected to accommodate the longest anticipated, fully extended backbone. Two cluster distribution schemes are considered as detailed in the preliminary work [31].…”

Section: Simulation Model For Estimating Chain Lengthmentioning

confidence: 99%

“…After these matrices have been normalized [31], the orientation of the second bond is dictated by U 2 , the third by U 3 , the last by U N , and all others by U k , with two exceptions. The matrices are overridden when a bond placement coincides with a cluster or when the bond corresponding to a pendant chain attachment point is being placed.…”

Section: Simulation Model For Estimating Chain Lengthmentioning

confidence: 99%

“…It is found that stiffness predictions are sensitive to the choice of statistical methodology and thus represent a tool for expanding the capabilities of this modeling approach to stiffness predictions. Details of the various statistical approaches are discussed in [31]. In this work, the focus is on the impact these various methodologies have on the predicted response.…”

Section: Introductionmentioning

confidence: 99%

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Application of Rotational Isomeric State Theory to Ionic Polymer Stiffness Predictions

et al. 2005

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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 multi-scale 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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Section: Discussionmentioning

confidence: 99%

“…To account for this variation, n is sampled from a discrete probability distribution with a minimum of 5, a maximum of 11, and a mean of approximately 7 [31].…”

Section: Simulation Model For Estimating Chain Lengthmentioning

confidence: 99%

“…The grid size is selected to accommodate the longest anticipated, fully extended backbone. Two cluster distribution schemes are considered as detailed in the preliminary work [31].…”

Section: Simulation Model For Estimating Chain Lengthmentioning

confidence: 99%

Section: Simulation Model For Estimating Chain Lengthmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Application of Rotational Isomeric State Theory to Ionic Polymer Stiffness Predictions

et al. 2005

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Light Activated Shape Memory Polymer Characterization—Part II

Beblo¹,

Weiland

2011

Journal of Applied Mechanics

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Presented are the experimental results of two light activated shape memory polymer (LASMP) formulations. The optical stimulus used to activate the materials is detailed including a mapping of the spatial optical intensity at the .surface of the sample. From this, results of etiergy calculations are presented including the amount of energy available for transitioning from the glassy state to the rubbery state and from the rubbery .•¡täte to the glassy state, highlighting one of the major advantages of LASMP as requiring ¡ess energy to transition than thermally activated shape memory polymers. The mechano-optical e.xperimental setup and procedure is detailed and provides a consistent method for evaluating this relatively new class of shape memory polymer. A chemical kinetic model is used to predict both the theoretical glassy state modulus, as only the sample averaged modulus is experimentally attainable, as well as the through thickness di.itribution of Young's modulus. The experimental and model results for these second generation LASMP fotmtdatiotis are then compared with earlier LASMP generations (detailed previously in Beblo attd Mauck Wetland, 2009, "Light Activated Shape Memoty Polymer Cliaracterization," ASME J. Appl. Mech.. 76, pp. 8) and typical thermally activated shape memory polymer.

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Application of Monte Carlo Simulations to Hydrated Nafion Stiffness Predictions

et al. 2005

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Application of Rotational Isomeric State (RIS) theory to the prediction of Young’s modulus of a solvated ionomer is considered. RIS theory directly addresses polymer chain conformation as it relates to mechanical response trends. Successful adaptation of this methodology to the prediction of elastic moduli would thus provide a powerful tool for guiding ionomer fabrication. The Mark-Curro Monte Carlo methodology is applied to generate a statistically valid number of end-to-end chain lengths via RIS theory for a solvated Nafion case. The distribution of chain lengths is then fitted to a Probability Density Function by the Johnson Bounded distribution method. The fitting parameters, as they relate to the model predictions and physical structure of the polymer, are studied so that a means to extend RIS theory to the reliable prediction of ionomer stiffness may be identified.

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Monte Carlo Simulation of a Solvated Ionic Polymer with Cluster Morphology

Cited by 7 publications

References 10 publications

Application of Rotational Isomeric State Theory to Ionic Polymer Stiffness Predictions

Application of Rotational Isomeric State Theory to Ionic Polymer Stiffness Predictions

Light Activated Shape Memory Polymer Characterization—Part II

Application of Monte Carlo Simulations to Hydrated Nafion Stiffness Predictions

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