Flux and storage of energy in non-equilibrium, stationary states

Systems kept out of equilibrium in stationary states by an external source of energy store an energy $\Delta U=U-U_0$. $U_0$ is the internal energy at equilibrium state, obtained after the shutdown of energy input. We determine $\Delta U$ for two model systems: ideal gas and Lennard-Jones fluid. $\Delta U$ depends not only on the total energy flux, $J_U$, but also on the mode of energy transfer into the system. We use three different modes of energy transfer where: the energy flux per unit volume is (i) constant; (ii) proportional to the local temperature (iii) proportional to the local density. We show that $\Delta U /J_U=\tau$ is minimized in the stationary states formed in these systems, irrespective of the mode of energy transfer. $\tau$ is the characteristic time scale of energy outflow from the system immediately after the shutdown of energy flux. We prove that $\tau$ is minimized in stable states of the Rayleigh-Benard cell

Communication: Molecular-level insights into asymmetric triblock copolymers: Network and phase development

Copyright (2014) AIP Publishing. This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. The following article appeared in Journal of Chemical Physics (Communication) 141 and may be found at http://dx.doi.org/10.1063/1.4896612Molecularly asymmetric triblock copolymers progressively grown from a parent diblock copolymer can be used to elucidate the phase and property transformation from diblock to network-forming triblock copolymer. In this study, we use several theoretical formalisms and simulation methods to examine the molecular-level characteristics accompanying this transformation, and show that reported macroscopic-level transitions correspond to the onset of an equilibrium network. Midblock conformational fractions and copolymer morphologies are provided as functions of copolymer composition and temperature.Nonwovens Institute at North Carolina State University and the Polish Ministry of Science and Higher Education (Grant No. N204 125039)

Microphase and macrophase separation in binary and ternary block copolymer blends

In this thesis we investigate some properties of microphase separated copolymer blends by means of the theory of polymer mixtures developed by K. M. Hong and J. Noolandi, carrying out numerical self-consistent calculations for copolymer solvent blends and modifying a fourth order expansion of the free energy for copolymer/homopolymer blends. In all cases we restrict attention to the lamellar structure. -- Using the numerical self-consistent calculations we carry out systematic studies for copolymer/selective solvent blends in both the weak and strong segregation regimes. Comparison with earlier results of Whitmore and Noolandi for copolymer/neutral solvent blends is provided. -- We also study the lamellar structure of binary A-b-B/A and ternary A-b-B/A/B copolymer/homopolymer blends near the microphase separation transition. The approach we have developed in this case combines perturbative solutions to the modified diffusion equation with a model for the total A and B polymer density profiles. As test of this procedure we have compared numerical self-consistent calculations for binary copolymer/selective solvent blends with the modification of fourth order expansion introduced in this thesis. We have used the procedure to calculate the domain and subdomain thicknesses, the interfacial width, swelling of the copolymers by the homopolymers, and individual polymer density profiles, and their dependence on the copolymer and homopolymer degrees of polymerization, overall composition, and Flory interaction parameter. The results are compared with three sets of experiments on copolymer/homopolymer blends. They are consistent with the picture that added homopolymers tend to penetrate within the copolymers and swell them laterally, and that the degree to which this occurs depends on the relative molecular weights of the copolymers and homopolymers, as indicated in experiments of Hashimoto and coworkers and others. The tendency of added homopolymers to cause an increase or decrease in the domain thickness correlates with their tendency to stabilize or destabilize the microphase. -- Finally we construct phase diagrams of ternary, A-b-B/A/B, copolymer/homopolymer blends. This work is an extension of earlier research by Whitmore and Noolandi for binary and ternary blends. The approach, again, uses a perturbative solution to the modified diffusion equation to calculate the polymer distribution functions, but it employs only one wavenumber in the fourth order expansion of the free energy, significantly simplifying the numerical calculations. The main results of these calculations are phase diagrams for a variety of model systems containing symmetric and asymmetric copolymers mixed with homopolymers of varying molecular weights, and for a PS-b-PI/PS/PI mixture. We also compare induced microphase formation in ternary and binary blend

The scaling of <i>μ</i>_<i>c</i> corresponding to the onset of chaos with respect to <i>L</i> and m¯.

<p>The scaling of <i>μ</i>_<i>c</i> corresponding to the onset of chaos with respect to <i>L</i> and <math><mi>m</mi><mo>¯</mo></math>.</p