Nonequilibrium Thermodynamics of Polymeric Liquids via Atomistic Simulation

The challenge of calculating nonequilibrium entropy in polymeric liquids undergoing flow was addressed from the perspective of extending equilibrium thermodynamics to include internal variables that quantify the internal microstructure of chain-like macromolecules and then applying these principles to nonequilibrium conditions under the presumption of an evolution of quasie equilibrium states in which the requisite internal variables relax on different time scales. The nonequilibrium entropy can be determined at various levels of coarse-graining of the polymer chains by statistical expressions involving nonequilibrium distribution functions that depend on the type of flow and the flow strength. Using nonequilibrium molecular dynamics simulations of a linear, monodisperse, entangled C₁₀₀₀H₂₀₀₂ polyethylene melt, nonequilibrium entropy was calculated directly from the nonequilibrium distribution functions, as well as from their second moments, and also using the radial distribution function at various levels of coarse-graining of the constituent macromolecular chains. Surprisingly, all these different methods of calculating the nonequilibrium entropy provide consistent values under both planar Couette and planar elongational flows. Combining the nonequilibrium entropy with the internal energy allows determination of the Helmholtz free energy, which is used as a generating function of flow dynamics in nonequilibrium thermodynamic theory.     

Purely elastic interfacial instabilities in superposed flow of polymeric fluids

Purely elastic interfacial stability of superposed plane Poiseuille flow of polymeric liquids has been investigated utilizing both asymptotic and numerical techniques. It is shown that these instabilities are caused by an unfavorable jump in the first normal stress difference across the fluid interface. To determine the significance of these instabilities in finite experimental geometries, a comparison between the maximum growth rates of purely elastic instabilities with instabilities driven primarily by a viscosity or a combined viscosity and elasticity difference is made. Based on this comparison, it is shown that purely elastic interfacial instabilities can play a major role in superposed flow of polymeric liquids in finite experimental geometries.     

Modulation of cyanobacterial photosystem I deposition properties on alkanethiolate Au substrate by various experimental conditions

We present results from atomic force microscopy (AFM) images indicating various experimental conditions, which alter the morphological characteristics of self-assembled cyanobacterial PS I on hydroxyl-terminated self-assembled alkanethiolate monolayers (SAM/Au) substrates. AFM topographical images of SAM/Au substrates incubated in solutions containing different PS I concentrations solubilized with Triton X-100 as the detergent reveal large columnar aggregates (～100 nm and hence, much taller than a single PS I trimer) at high PS I concentrations. Depositions from dilute PS I suspensions reveal fewer aggregates and relatively uniform surface topography (～10 nm). Confocal fluorescence microscopy analysis of fluorescently tagged PS I deposited on to SAM/Au substrates using electric field and gravity driven techniques reveal preliminary indications of directionally aligned PS I attachments, besides corroborating a uniform monolayer formation, for the former deposition method. The complex attachment dynamics of PS I onto SAM substrates are further investigated from the AFM images of PS I/SAM/Au substrates prepared under different experimental conditions using: 1) PS I isolated as monomers and trimers 2) adsorption at elevated temperatures, and 3) different detergents with varying pH values. In each of the cases, the surface topology indicated distinct yet complex morphological and phase characteristics. These observations provide useful insight into the use of experimental parameters to alter the morphological assembly of PS I on to SAM substrates en route to successful fabrication of PS I based biohybrid photoelectrochemical devices.     

A note on start-up and large amplitude oscillatory shear flow of multimode viscoelastic fluids

Start up of plane Couette flow and large amplitude oscillatory shear flow of single and multimode Maxwell fluids as well as Oldroyd-B fluids have been analyzed by analytical or semi-analytical procedures. The result of our analysis indicates that if a single or a multimode Maxwell fluid has a relaxation time comparable or smaller than the rate of change of force imparted on the fluid, then the fluid response is not singular as Elasticity Number (E ). However, if this is not the case, as E , perturbations of single and multimode Maxwell fluids give rise to highly oscillatory velocity and stress fields. Hence, their behavior is singular in this limit. Moreover, we have observed that transients in velocity and stresses that are caused by propagation of shear waves in Maxwell fluids are damped much more quickly in the presence of faster and faster relaxing modes. In addition, we have shown that the Oldroyd-B model gives rise to results quantitatively similar to multimode Maxwell fluids at times larger than the fastest relaxation time of the multimode Maxwell fluid. This suggests that the effect of fast relaxing modes is equivalent to viscous effects at times larger than the fastest relaxation time of the fluid. Moreover, the analysis of shear wave propagation in multimode Maxwell fluids clearly show that the dynamics of wave propagation are governed by an effective relaxation and viscosity spectra. Finally, no quasi-periodic or chaotic flows were observed as a result of interaction of shear waves in large amplitude oscillatory shear flows for any combination of frequency and amplitudes.     

A computational study of the influence of viscoelasticity on the interfacial dynamics of dip coating flow

The effect of viscoelasticity on the interfacial dynamics of air displacing a viscoelastic fluid under the presence of gravity, i.e., the dip coating flows is examined. A stabilized finite element method coupled with a pseudo-solid domain mapping technique is used to carry out the computations. The fluid is modeled by the Finitely Extensible Non-linear Elastic Chilton–Ralison (FENE-CR) constitutive equation. Simulations at various Ca and Bo are performed in order to determine the limiting condition for dip coating where the flow characteristics become independent of Bo. For all values of Ca and Bo studied, the flow is characterized by recirculation near the interface. To this end the film thickness scaled with the capillary length, as a function of Wi, at low Ca and high Bo collapses onto a single curve, and agrees with the analytical expression for the film thickness in the low Wi limit. As the value of Ca is increased, the corresponding value of Bo that is required to collapse the results onto a single curve, i.e., the dip coating flow limit, is correspondingly higher. For a fixed Ca and Wi, increasing Bo results in a decrease in the film thickness, an increase in the size of the recirculation region and an increase in the strain rates subsequently leading to an increase in the normal stresses. We show that the interfacial dynamics in the dip coating flow are qualitatively similar to those observed in the Hele-Shaw flow. Specifically, at low Wi, film thinning occurs and as the value of Wi is increased, the formation of normal elastic stress boundary layers in the capillary transition region is observed. This is accompanied by a sharp increase in the film thickness and a compression of the air–liquid interface in the capillary transition region.     

Quaternary (liquid + liquid) equilibria of aqueous two-phase poly (ethylene glycol), poly (DMAM–TBAM), and KH2PO4: Experimental and generalized Flory–Huggins theory

Quaternary (liquid + liquid) equilibrium (LLE) data of the aqueous two-phase poly (ethylene glycol), poly (N,N-dimethylacrylamide-t-butylacrylamide) with abbreviation name poly (DMAM–TBAM) as a hydrophobic association water-soluble copolymer and KH₂PO₄ has been determined experimentally at T = 338.15 K. Furthermore, the generalized Flory–Huggins theory with two electrostatic terms (the Debye–Hückel and Pitzer–Debye–Hückel) was used for correlation of the phase behavior of the quaternary system and the interaction parameters between all species were calculated.It was found that addition of poly (DMAM–TBAM) copolymer as well as changing the temperature can shift the binodal curves of aqueous two-phase systems containing polyethylene glycol (PEG) and salt. Also, the phase behavior of the DMAM–TBAM copolymer with some salts containing sodium chloride, ammonium hydrogen phosphate, potassium hydrogen phosphate, and sodium carbonate were studied experimentally at T = 338.15 K and the effect of the salt type on the their binodal curves was determined.