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Results for “Rouse model”

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At least 19 records

Two-population Rouse models for polymer segmental dynamics in nanocomposites

Segmental dynamics of polymer chains in a model nanocomposite of poly(ethylene oxide) and silica nanoparticles (NPs) was investigated using quasielastic neutron scattering. The dynamics can be accurately described with the Rouse model. The bulklike polymer far from the NP surface behaves as the neat polymer. However, the slower polymer in the interface close to the NP surface is described either with a second Rouse population with different relaxation time or using the suppressed Rouse model. These simple two-population models accurately reproduce the experimental data, with the suppressed Rouse model describing topological constraints, on average, every 12 beads with an interfacial thickness up to 13.5 beads, and the effect of the interface extending to a layer of thickness comparable to the end-to-end distance of the polymer. This modeling provides an explanation for the observed reinforcement in PNC even at low loadings, consistent with current understanding of the relevance of the interphase.

Composite materials↗

Quantifying molecular deformation in polymer melts by a generalized Zimm plot approach

The Zimm plot has been widely used to characterize the molecular dimensions of polymers from small-angle scattering experiments, where the reciprocal intensity is analyzed as a function of the square of the magnitude of the scattering wavevector Q. Here, this work explores the benefits of analyzing the reciprocal scattering intensity from deformed polymers, extending the original Zimm plot to anisotropic materials. In the small-angle limit, a tensorial extension of the Guinier law is found for the gyration tensor and the reciprocal single-chain structure factor. In the high-Q limit, application of the spherical harmonic expansion technique to the reciprocal structure factor permits direct model-independent analysis of spatially dependent molecular deformation of polymers. Additionally, the contributions from high-order spherical harmonics become insignificant in the reciprocal-intensity representation. The proposed generalized Zimm plot approach is demonstrated computationally with the affine deformation model and the Rouse model, and experimentally with small-angle neutron scattering measurements of deformed polystyrene melts.

36 MATERIALS SCIENCE↗

Dynamics of a single polyampholyte chain

Polymers that feature both positive and negative charges along chains, known as polyampholytes, represent a class of materials that hold promise for a new generation of energy storage devices, the design of which will require knowledge of the underlying structure and dynamics. Here, we develop a theory based on the Rouse model for the dynamic structure factor of a single polyampholyte chain in the weak coupling regime (negligible intramolecular electrostatics) or subjected to weak external electric fields (governed by linear response). Neglecting effects of small ions, we find deviations in scaling from the classic Rouse theory and make predictions for scattering experiments performed on polyampholytes. We find that, under weak coupling with arbitrarily strong fields, the dynamics are highly dependent on the charge distribution and consequently look at two representative examples—random charge densities and periodic charge densities—with different scaling properties. Additionally, under weak fields, the dynamics are largely independent of charge distribution. Finally, we investigate the influence of hydrodynamic effects and the implications of including inertial effects in the model.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Associative polymers with controlled sticker placement: How reversible bond distribution and density govern polymer dynamics

Associative polymers with precisely arranged stickers offer opportunities to program material properties with molecular precision. Yet, it remains unclear how the placement and fraction of stickers dictate structure, dynamics, and macroscopic properties. By developing a model unentangled polymer system with hydrogen-bonding stickers, we show that randomly distributed stickers neither form clusters nor change flow properties, whereas stickers placed at chain ends drive nanocluster formation even at low concentrations. Adding more end stickers produces a rubbery plateau spanning eight decades in frequency with two distinct relaxation timescales, in contrast to the single plateau predicted by the classic sticky Rouse model. These results demonstrate that sticker distribution dictates whether associative polymers undergo nanocluster formation or microphase separation, while substantial alterations in dynamics and viscoelasticity require both sticker aggregation and thermomechanical stability of associated domains. Our findings resolve a longstanding debate on associative polymer dynamics and provide molecular design rules for programmable soft materials.

36 MATERIALS SCIENCE↗

End block dynamics in unentangled polymers by dielectric spectroscopy

Dielectric spectroscopy measures the dynamics of polymer melts over a broad frequency range. Developing a theory for the spectral shape can extend the analysis of dielectric spectra beyond determining relaxation times from the peak maxima and adds physical meaning to shape parameters determined with empirical fit functions. Toward this goal, we use the experimental results on unentangled poly(isoprene), and unentangled poly(butylene oxide), polymer melts, to test whether the concept of end blocks could be one reason for the Rouse model deviating from experimental data. These end blocks have been suggested by simulations and neutron spin echo spectroscopy and are a consequence of the monomeric friction coefficient depending on the position of the bead in the chain. The concept of an end block is an approximation which partitions the chain in a middle and two end blocks to avoid overparameterization by a continuous position dependent change of the friction parameter. Analysis of dielectric spectra shows that the deviations of the calculated from the experimental normal mode cannot be related to the end block relaxation. However, the results do not contradict an end block hiding below the segmental relaxation peak. Finally, it seems that the results are compatible with an end block being the specific part of the sub-Rouse chain interpretation close to the chain ends.

36 MATERIALS SCIENCE↗

A model of the human in a cognitive prediction task.

The human decision maker's behavior when predicting future states of discrete linear dynamic systems driven by zero-mean Gaussian processes is modeled. The task is on a slow enough time scale that physiological constraints are insignificant compared with cognitive limitations. The model is basically a linear regression system identifier with a limited memory and noisy observations. Experimental data are presented and compared to the model.

Rouse, W. B.↗

Spatial correlations of entangled polymer dynamics

The spatial correlations of entangled polymer dynamics are examined by molecular dynamics simulations and neutron spin-echo spectroscopy. Due to the soft nature of topological constraints, the initial spatial decays of intermediate scattering functions of entangled chains are, to the first approximation, surprisingly similar to those of an unentangled system in the functional forms. However, entanglements reveal themselves as a long tail in the reciprocal-space correlations, implying a weak but persistent dynamic localization in real space. Furthermore, comparison with a number of existing theoretical models of entangled polymers suggests that they cannot fully describe the spatial correlations revealed by simulations and experiments. In particular, the strict one-dimensional diffusion idea of the original tube model is shown to be flawed. The dynamic spatial correlation analysis demonstrated in this work provides a useful tool for interrogating the dynamics of entangled polymers. Lastly, the failure of the investigated models to even qualitatively predict the spatial correlations of collective single-chain density fluctuations points to a possible critical role of incompressibility in polymer melt dynamics.

74 ATOMIC AND MOLECULAR PHYSICS↗

Models of human problem solving - Detection, diagnosis, and compensation for system failures

The role of the human operator as a problem solver in man-machine systems such as vehicles, process plants, transportation networks, etc. is considered. Problem solving is discussed in terms of detection, diagnosis, and compensation. A wide variety of models of these phases of problem solving are reviewed and specifications for an overall model outlined.

Rouse, W. B.↗

Viscoelastic Properties of Polymer Blends

Viscosity, shear modulus and other viscoelastic properties of multicomponent polymer blends are predicted from behavior of individual components, using a mathematical model. Model is extension of two-component-blend model based on Rouse-Bueche-Zimm theory of polymer viscoelasticity. Extension assumes that probabilities of forming various possible intracomponent and intercomponent entanglements among polymer molecules are proportional to relative abundances of components.

Hong, S. D.↗

Nonlocal Effect of Percolated Particle Networks on Viscoelasticity of Polymer–Filler Nanocomposites: A Mesoscale Simulation Study

With nanoparticles (NPs) as fillers, polymer nanocomposites (PNCs) usually exhibit enhanced mechanical properties. However, a direct connection between the microscopic structural relaxation and macroscopic mechanical properties of PNCs remains to be established. To investigate the micro-to-macro connection, we develop a mesoscale model, in which the NPbridging polymer chains are represented by a dynamic bonded interaction between NPs, and the bulk polymer matrix is implicitly modeled by overdamped Langevin dynamics. Extensive equilibrium simulations are performed to quantify the microscopic dynamics of model PNCs. Systematic analyses of modified Rouse dynamics, dynamic structure factor, and relaxation modulus uncover that the microscopic relaxation dynamics of PNCs are significantly decelerated across different length scales because of nonlocal effects of percolated particle networks a phenomenon that has not been adequately captured in prior simulation studies. We find that NPvolume- fraction and NP-bonding-energy barrier are the two critical variables that affect bulk viscoelasticity the most. The proposed mesoscale model is versatile and provides a powerful framework for studying structure−property relations of different PNCs.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Three-Dimensional Settling Dynamics of Environmental Microplastics

Resolving the three-dimensional settling dynamics of microplastic (MP) particles is essential for developing comprehensive models of MP transport in rivers-both vertically within the water column and laterally across the channel. While previous research has largely examined one-dimensional vertical settling velocities, little is known about the lateral drifting, settling paths, and horizontal velocities of MPs. To address this, we investigated the full three-dimensional settling behavior of environmental MPs collected from rivers and ocean water, as well as from estuarine and ocean sediment. Geometric properties of 127 environmental MPs were quantified by a dynamic particle image analyzer, and their settling trajectories were recorded and reconstructed via a multicamera tracking algorithm. This enabled quantification of a particle's horizontal drift, tortuosity, amplitude and settling pattern, as well as vertical and horizontal velocities. Results showed that spherical MPs settled with minimal lateral displacement, whereas elongated particles, such as rod- and blade-shaped MPs, displayed pronounced lateral movements, reaching up to 65 times their equivalent diameter and averaging more than twice that of spheres. These dynamics suggest that elongated MPs may have a greater probability for wider lateral dispersion in rivers, increasing their likelihood for interactions with riverbanks and channel boundaries compared to more spherical shaped MPs.

54 ENVIRONMENTAL SCIENCES↗

Effects of local order parameter dependent transport coefficient in diblock copolymers under applied electric fields

In this work, we present an approach for constructing thermodynamically consistent time-dependent models relevant to thin films of diblock copolymers in applied electric fields. The approach is based on the principles of linear irreversible thermodynamics, and, in this work, it is applied to study the effects of electric fields on thin films of incompressible diblock copolymers. Enforcement of local incompressibility constraint at all times leads to a local order parameter dependent transport coefficient in the model for the diblock copolymers. The dependence of the transport coefficient on the local order parameter is used to relate it with the diffusion constant of Rouse chains and leads to sensitivity of the model to initial conditions. In addition, transient behavior is found to be affected when compared with an ad hoc model assuming a constant transport coefficient. Numerical results such as electric field induced alignment of lamellae domains due to the field are found to be in qualitative agreement with experiments. This approach opens up a systematic way of developing kinetic models for simulating effects of electrolytes added to thin films containing diblock copolymers in the presence of applied electric fields.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

A queueing model of pilot decision making in a multi-task flight management situation

Allocation of decision making responsibility between pilot and computer is considered and a flight management task, designed for the study of pilot-computer interaction, is discussed. A queueing theory model of pilot decision making in this multi-task, control and monitoring situation is presented. An experimental investigation of pilot decision making and the resulting model parameters are discussed.

Walden, R. S.↗

Modeling the human as a controller in a multitask environment

Modeling the human as a controller of slowly responding systems with preview is considered. Along with control tasks, discrete noncontrol tasks occur at irregular intervals. In multitask situations such as these, it has been observed that humans tend to apply piecewise constant controls. It is believed that the magnitude of controls and the durations for which they remain constant are dependent directly on the system bandwidth, preview distance, complexity of the trajectory to be followed, and nature of the noncontrol tasks. A simple heuristic model of human control behavior in this situation is presented. The results of a simulation study, whose purpose was determination of the sensitivity of the model to its parameters, are discussed.

Govindaraj, T.↗

Human controller modeling in environments that include non-control tasks

In complex environments where the human operator is a supervisor, he must allocate his attention between different kinds of tasks for optimum overall performance. When a portion of the future reference trajectory for the control task is available for preview, scheduling various activities is possible. A model has been developed for this situation using dynamic programming to solve an optimal control problem. An experiment was conducted where subjects controlled an airplane symbol over a map, shown a fixed distance into the future. Discrete, non-control tasks were introduced as number entry tasks. Results from the model are compared with experimental results.

Govindaraj, T.↗

Modeling the human controller in environments that include continuous and discrete tasks

In complex environments where the human operator is a supervisor, he must allocate his attention between different kinds of tasks for satisfactory overall performance. When a portion of the future reference trajectory for a continuous control task is available for preview, scheduling various other discrete activities is possible. A model has been developed for this situation using dynamic programming to solve an optimal control problem. An experiment was conducted where subjects controlled an airplane symbol over a map, shown a fixed distance into the future. Discrete tasks were introduced as data entry tasks. Results showed that the model compared favorably with experimental results.

Govindaraj, T.↗

Viscoelastic properties of entangled polymers - Ternary blends of monodisperse homopolymers

In a previous publication from this laboratory, the Rouse-Bueche-Zimm molecular theory of viscoelasticity has been extended by using a transient network model to apply to binary blends of monodisperse polymers with chain entanglements. The dynamics of the entanglements were modeled both by the enhanced frictional coefficients and by the additional elastic couplings. It was recognized that entanglements not only may form between chains of the same lengths (intracomponent entanglements) but also between those of different lengths (intercomponent entanglements). At a given intercomponent entanglement, the longer chain was assumed to have the frictional coefficient of the shorter chain. Similarly, for blends consisting of several monodisperse components with different molecular weights, such modifications are also required to predict their linear viscoelastic behavior. The frequency of these interactions is assumed to be proportional to the weight ratio of the respective component chains in the blend. Equations of motion are formulated for each component and solved numerically for the relaxation time spectra. Linear viscoelastic properties such as the dynamic mechanical moduli, stress relaxation moduli, and zero-shear viscosity can then be computed for these systems by linear summation of those of the components.

Soong, D.↗