Polymer-grafted surfaces and channels are increasingly used for the design of responsive materials and sensors due to robust performance and ease of use. Various strategies for the control of the ...nanoscale morphologies of such materials and devices are being tested. Entropic repulsion between the polymer chains in a grafted brush of sufficient density causes the chains to extend in the direction perpendicular to the grafting surface in comparison to the position of unattached polymers. When nanoparticles having attractive interactions with the polymers are introduced into the solvent, these nanoparticles tend to infiltrate into the brush and reduce its extension. Under certain conditions, a sharp reduction in brush height extension can occur over a narrow range of nanoparticle concentrations in solution. We describe a way of controlling transport through polymer-functionalized nanochannels with nanoparticle additives, relying on the physics of nanoparticles and polymer brushes under confinement, and we suggest a blueprint for the creation of a tunable nanovalve. The nanovalve is modeled as a cylinder with a polymer brush grafted on its inside surface. Brush properties such as the chain length and the grafting density are chosen so that the brush chains extend into the center of the cylinder in the absence of nanoparticles, occluding the flux of analyte molecules through the pore. When nanoparticles that are attracted to the polymers are introduced into solution, they infiltrate into the brush and partially collapse it against the cylindrical grafting surface, opening space in the center of the cylinder through which analyte molecules can flow. The operation of such a nanovalve is analyzed via self-consistent field theory calculations in the strong-stretching approximation. Self-consistent field analysis is supported by Langevin dynamics simulations of the underlying coarse-grained model of the polymer–nanoparticle system.
We study the role of temperature on the structure of pure polymer brushes and their mixture with attractive nanoparticles in flat and cylindrical geometries. It has previously been established that ...the addition of such nanoparticles causes the polymer brush to collapse and the intensity of the collapse depends on the attraction strength, the nanoparticle diameter, and the grafting density. In this work, we carry out molecular dynamics simulation under good solvent conditions to show how the collapse transition is affected by the temperature, for both plane grafted and inside-cylinder grafted brushes. We first examine the pure brush morphology and verify that the brush height is insensitive to temperature changes in both planar and cylindrical geometries, as expected for a polymer brush in a good solvent. On the other hand, for both system geometries, the brush structure in the presence of attractive nanoparticles is quite responsive to temperature changes. Generally speaking, for a given nanoparticle concentration, increasing the temperature causes the brush height to increase. A brush which contracts when nanoparticles are added eventually swells beyond its pure brush height as the system temperature is increased. The combination of two easily controlled external parameters, namely, concentration of nanoparticles in solution and temperature, allows for sensitive and reversible adjustment of the polymer brush height, a feature which could be exploited in designing smart polymer devices.
In this paper, we apply the Matteoli−Mansoori empirical formula for the pair correlation function of simple fluids obeying the Lennard-Jones potential to calculate reduced self-diffusion coefficients ...on the basis of the modified free volume theory. The self-diffusion coefficient thus computed as functions of temperature and density is compared with the molecular dynamics simulation data and the self-diffusion coefficient obtained by the modified free volume theory implemented with the Monte Carlo simulation method for the pair correlation function. We show that the Matteoli−Mansoori empirical formula yields sufficiently accurate self-diffusion coefficients in the supercritical regime, provided that the minimum free volume activating diffusion is estimated with the classical turning point of binary collision at the mean relative kinetic energy 3k B T/2, where k B is the Boltzmann constant and T is the temperature. In the subcritical regime, the empirical formula yields qualitatively correct, but lower values for the self-diffusion coefficients compared with computer simulation values and those from the modified free volume theory implemented with the Monte Carlo simulations for the pair correlation function. However, with a slightly modified critical free volume, the results can be made quite acceptable.
The shear viscosity formula derived by the density fluctuation theory in previous papers is computed for argon, krypton, and methane by using the self-diffusion coefficients derived in the modified ...free volume theory with the help of the generic van der Waals equation of state. In the temperature regime near or above the critical temperature, the density dependence of the shear viscosity can be accounted for by ab initio calculations with the self-diffusion coefficients provided by the modified free volume theory if the minimum (critical) free volume is set equal to the molecular volume and the volume overlap parameter (α) is taken about unity in the expression for the self-diffusion coefficient. In the subcritical temperature regime, if the density fluctuation range parameter is chosen appropriately at a temperature, then the resulting expression for the shear viscosity can well account for its density and temperature dependence over the ranges of density and temperature experimentally studied. In the sense that once the density fluctuation range is fixed at a temperature, the theory can account for the experimental data at other subcritical temperatures on the basis of the intermolecular force only; the theory is predictive even in the subcritical regime of temperature. Theory is successfully tested in comparison with experimental data for self-diffusion coefficients and shear viscosity for argon, krypton, and methane.
In previous work on the density fluctuation theory of transport coefficients of liquids, it was necessary to use empirical self-diffusion coefficients to calculate the transport coefficients (e.g., ...shear viscosity of carbon dioxide). In this work, the necessity of empirical input of the self-diffusion coefficients in the calculation of shear viscosity is removed, and the theory is thus made a self-contained molecular theory of transport coefficients of liquids, albeit it contains an empirical parameter in the subcritical regime. The required self-diffusion coefficients of liquid carbon dioxide are calculated by using the modified free volume theory for which the generic van der Waals equation of state and Monte Carlo simulations are combined to accurately compute the mean free volume by means of statistical mechanics. They have been computed as a function of density along four different isotherms and isobars. A Lennard-Jones site−site interaction potential was used to model the molecular carbon dioxide interaction. The density and temperature dependence of the theoretical self-diffusion coefficients are shown to be in excellent agreement with experimental data when the minimum critical free volume is identified with the molecular volume. The self-diffusion coefficients thus computed are then used to compute the density and temperature dependence of the shear viscosity of liquid carbon dioxide by employing the density fluctuation theory formula for shear viscosity as reported in an earlier paper (J. Chem. Phys. 2000, 112, 7118). The theoretical shear viscosity is shown to be robust and yields excellent density and temperature dependence for carbon dioxide. The pair correlation function appearing in the theory has been computed by Monte Carlo simulations.
