Upendra Natarajan

Optimum shapes of convective pin fins with variable heat transfer coefficient

Abstract Principles of variational calculus are used to determine the shapes of convective pin fins that maximize heat dissipation, given the amount of fin material. The analysis considers the convective heat transfer coefficient h to depend on the fin diameter D according to the relationship h ∝ 1/Dn, where n takes on values from 0.2 to 0.5 depending on the type of pin fin configuration and flow condition (1: AIChEJ, Vol. 29, p. 1043, 1983). The Euler equations, which are nonlinear and coupled, are formulated and solved for the cases of both length and weight constraints as well as only weight constraint. The resulting quadrature formulae are represented in the form of a convinient design plot, from which the optimum design parameters may be obtained and used to determine the fin and temperature profiles as well as the cooling performance. The solutions under both constraints yield considerably simple results for the case of only weight constraint, which corresponds to the diameter and excess temperature of the fin tip being zero. An important result is that the Schmidt criterion (2: Z. Verein. Deutsch Ing., Vol. 70, pp. 885, 947, 1926) of a linear temperature profile also holds for pin fins of specified weight with a variable heat transfer coefficient. Finally, by using Pontryagins minimum principle (3: The Mathematical theory of Optimal Processes, Wiley, New York, 1962), it is demonstrated that the problems of maximizing cooling (for a given fin weight) and minimizing weight (for a given fin cooling) are identical as both are governed by the same optimum design equations.

Molecular Dynamics Simulations of Adsorption of Poly(acrylic acid) and Poly(methacrylic acid) on Dodecyltrimethylammonium Chloride Micelle in Water: Effect of Charge Density

We have investigated the interaction of dodecyltrimethylammonium chloride (DoTA) micelle with weak polyelectrolytes, poly(acrylic acid) and poly(methacrylic acid). Anionic as well as un-ionized forms of the polyelectrolytes were studied. Polyelectrolyte-surfactant complexes were formed within 5-11 ns of the simulation time and were found to be stable. Association is driven purely by electrostatic interactions for anionic chains whereas dispersion interactions also play a dominant role in the case of un-ionized chains. Surfactant headgroup nitrogen atoms are in close contact with the carboxylic oxygens of the polyelectrolyte chain at a distance of 0.35 nm. In the complexes, the polyelectrolyte chains are adsorbed on to the hydrophilic micellar surface and do not penetrate into the hydrophobic core of the micelle. Polyacrylate chain shows higher affinity for complex formation with DoTA as compared to polymethacrylate chain. Anionic polyelectrolyte chains show higher interaction strength as compared to corresponding un-ionized chains. Anionic chains act as polymeric counterion in the complexes, resulting in the displacement of counterions (Na(+) and Cl(-)) into the bulk solution. Anionic chains show distinct shrinkage upon adsorption onto the micelle. Detailed information about the microscopic structure and binding characteristics of these complexes is in agreement with available experimental literature.

Conformations and hydration structure of hydrophobic polyelectrolyte atactic poly(ethacrylic acid) in dilute aqueous solution as a function of neutralisation

Chain conformations, counter-ion structure, intermolecular hydrogen bonding structure and dynamics of atactic polyethacrylic acid (PEA) in salt-free aqueous dilute solution at 25°C are studied via molecular dynamics (MD) simulations with explicit-solvent and explicit-ion description for the first time. The intermolecular structure was analysed by the radial distribution functions (RDF) for specific atom types between PEA chain, water molecules and Na+ counter-ions, as well as by the hydration near the PEA chain in the solvated system. An increase in f provides an increase in 〈Rg〉 of the chain, consistent with the existence of the compact form of PEA. The simulations show expansion for radius-of-gyration with increase in f, as expected for flexible polyelectrolytes under salt-free condition. The extent of intermolecular hydrogen bonds (H-bonds) between PEA and water is enhanced by increase in f. Chains having a higher counter-ion density show higher values of 〈Rg〉, influenced by intermolecular interactions between PEA and water. The coordination of Na+ counter ions and water molecules to carboxyl oxygens of polyacrylic acid (PAA) increases with charge density of the chain. A comparison of the structure aspects is made with PAA and PMA polyelectrolytes in dilute solution, which brings out the hydrophobic effect of the ethyl side-groups in PEA on conformational properties and counter-ion condensation structure.

Behaviour of hydrogen bonding and structure of poly(acrylic acid) in water–ethanol solution investigated by explicit ion molecular dynamics simulations

Molecular dynamics simulations of polyelectrolyte poly(acrylic acid) at infinitely dilute conditions in aqueous solutions containing up to 6 vol% ethanol were performed with explicit solvent and counter-ion description for varying degree of neutralisation. In the range of ethanol concentration employed, this study shows a swelling in the case of non-ionised chain, chain collapse for 25% ionised system, minimal swelling for 50% ionised chain and no significant change in conformation for 75–100% ionised chains. Ethanol interacts with non-ionised residues via hydrogen bonding and is found to be dominant in the solvation cage surrounding them, whereas no such interaction is seen with ionised residues. Thus, chains with higher charge densities show a preference for the aqueous environment in comparison to ethanol and hydrogen bonding to water is unaltered. For chains with lower charge density, a reduction in the hydrogen bonding with water is seen with an increase in ethanol concentration.

Self-association behaviour of atactic polymethacrylic acid in aqueous solution investigated by atomistic molecular dynamics simulations

The self-association behaviour of atactic poly(methacrylic acid) (a-PMA) in water was investigated by atomistic molecular dynamics (MD) simulations. Simulations show that interchain association of a-PMA occurs only in its un-neutralised form, by hydrogen bonding between –COOH groups, which is in agreement with the experimental observation. Chain conformations, dihedral angle distributions, hydration behaviour, scattering structure factor and enthalpy-of-hydration (i.e. aqueous solvation) were analysed as a function of concentration for un-neutralised PMA, across dilute to concentrated regimes. The average 〈Rg〉 of the chain remains unaffected in solution and also for amorphous undissolved a-PMA phase, confirming the occurrence of the approximate theta-solution condition for the first time, as revealed by simulations, in a polar hydrogen-bonding polymer aqueous solution. Chain hydration behaviour and scattering structure factor show significant changes in concentrated regime. Scattering intensity collapse occurs in concentrated PMA solution, due to the existence of the swollen regime captured for the first time by explicit-MD-simulations. The hydration of PMA is driven by H-bonding, specifically between H atoms of the COOH groups and O atoms of water molecules in the closest coordination shell. The enthalpy of hydration of PMA is dominated by PMA–water interactions (charges and H-bonding). The thermodynamic contributions of PMA–PMA and PMA–water interactions towards the electrostatics as well as the dispersion components of the total solvation-enthalpy become more favourable than water–water interactions.

Conformational analysis, RIS models and single-chain properties of structurally modified polycarbonates, 1. Effect of cyclohexyl and phenyl ring substitutions

Conformational properties of segments and chains of structurally different polycarbonates are investigated in detail. Conformational analysis and rotational isomeric state (RIS) models for some of the polycarbonates and single-chain properties of all the polycarbonates are reported here for the first time. Substitution of the methyl group on the bisphenol phenyl rings results in increased energy barriers to rotations as well as changes in positions of local minima, compared to the case without substitutions. Conformational structure about the isopropylidene linkage C α atom is not altered by ortho methyl substitutions on the rings. Substitution by a cyclohexyl ring rigidly attached to the C α atom restricts conformational mobility within the bisphenol unit. Rotational flexibility of the phenyl-oxygen bond is hindered by additional substitutions on the cyclohexyl ring. The carbonate group prefers the trans-trans conformation in all the polycarbonates. The energy difference between the cis-trans and trans-trans states of the carbonate group is lowered by the ortho methyl substituent on the phenyl rings. There is a reduction in 2 >, 2 >, and C n accompanying the substitutions. The introduction of other substituents on a cyclohexyl polycarbonate results in an increase in all chain dimensions including the persistence length. Also, the cyclohexyl or trimethylcyclohexyl substituents do not significantly alter the overall average shape of the chains. Substitutions both on the phenyl rings and at the isopropylidene linkage lead to a compaction of the polymer chain, but the effect is more pronounced when due to substituents on phenyl rings.

Dynamics of conformations, hydrogen bonds and translational diffusion of poly(methacrylic acid) in aqueous solution and the concentration transition in MD simulations

The dynamic behaviour of chain conformations, hydrogen bonds and translational diffusion of aqueous poly(methacrylic acid) (PMA) solution as a function of polymer volume fraction Φp across dilute to concentrated regimes inclusive of the pure polymer amorphous state was studied by molecular dynamics simulations. The behaviour of the relaxation time (τ) of the backbone dihedral angle auto-correlation function (ACF) reveals slower relaxation at higher level of polymer concentration and the existence of a concentration-driven relaxation transition for the aqueous polymer solution which occurs in the polymer volume fraction range, specifically 54% < Φp < 82% for this system. The relaxation constant τ for backbone dihedral angle exhibits a linear variation with Φp, indicating a first-order kinetic transition. The intermittent ACF for decay of the H-bond correlation shows that H-bonds among water molecules relax faster than those of the PMA–PMA and PMA–water type. The relaxation rate of PMA–water H-bonds shows a decrease up to Φp = 72% and becomes faster at Φp = 82% due to the confining influence of neighbouring PMA chains. PMA–water and water–water H-bond dynamics show transitions around Φp = 72% PMA. With increase in Φp PMA diffusion coefficient decreases exponentially and water diffusion coefficient decreases linearly, in agreement with experimental observations using fluorescence and nuclear magnetic resonance (NMR) spectroscopic studies.

Effect of organic modification on the intercalation and the properties of poly(phenylene oxide)/ polystyrene blend-clay nanocomposites

Nanocomposites prepared by the dispersion of unmodified and organically modified montmorillonite (MMT) clay into poly(2,6-dimethyl phenylene oxide)/polystyrene miscible blend in the range of 2–10 wt% clay were investigated by wide-angle x-ray diffraction, transmission electron microscopy, differential scanning calorimetry, thermogravimetric analysis and tensile mechanical tests. The systems based on unmodified sodium MMT (Na+MMT) as well as Cloisite 20A, Cloisite 30B and Cloisite 10A organically modified clays showed polymer intercalation. The glass transition temperature (T g) value was not affected by the volume fraction of clay and chemical nature of the organoclay. The thermal degradation stability of nanocomposites is found to be only slightly better than that of the blend matrix. A percolation threshold of around 4 wt% organoclay loading is observed. An improvement of 35% relative to unfilled polymer blend matrix is observed for the modulus, for Cloisite 20A nanocomposite containing 2 wt% organoclay. The observed modulus improvement with significant retention of elongational tensile strength and tensile ductility in case of unmodified Na-MMT and Cloisite 30B nanocomposites appears promising. The modulus prediction using Halpin-Tsai model is found to be closer to the experimental data when MMT volume fraction rather than the organoclay volume fraction is used.

Anionic polyelectrolyte poly(acrylic acid) (PAA) chain shrinkage in water–ethanol solution in presence of Li+ and Cs+ metal ions studied by molecular dynamics simulations

Abstract Molecular dynamic simulations of anionic polyelectrolyte poly(acrylic acid) (PAA) in water–ethanol solution, specifically Li+-PAA and Cs+-PAA, were carried out across the solvent composition range 0 ≤ фeth ≤ 0.9. Chain collapse (i.e. shrinkage) occurs with increase in фeth for both types of counter-ion systems and in agreement with the experiments. The qualitative difference in the collapse point is in agreement with experimental results, with counter-ion specific chain collapse of PAA following the order Li+ > Cs+. With increase in фeth the number of hydrogen-bonds between PAA and water decreases while that between PAA and ethanol increases. At higher level of ethanol content in solution, ethanol molecules displace water molecules from the vicinity of the chain. The analysis of the radial distribution functions shows that counter-ion binding distance of Li+ to chain is lesser as compared to that of Cs+, as well as a higher coordination number exhibited by Li+. Thus, as compared to Cs+-PAA, greater number of contact ion pairs formed between Li+ and PAA induce chain collapse more easily. The coordination of Li+ to PAA is better than that of Cs+ throughout the фeth range, which could be the reason for the greater extent of PAA chain shrinkage observed in the case of Li+. Binding of water molecule to PAA units is stronger in the case of Cs+. The backbone dihedral trans probability of both systems displayed a decrease with фeth indicating chain shrinkage. The relaxation time of H-bonds between PAA and EtOH is greater for Li+-PAA as compared to Cs+-PAA system. The enhancement of counter-ion pairs formation is found to be directly responsible for the solvent composition at which chain collapse occurs in the particular system.

Polyelectrolyte conformational transition in aqueous solvent mixture influenced by hydrophobic interactions and hydrogen bonding effects: PAA-water-ethanol.

Molecular dynamics simulations of poly(acrylic acid) PAA chain in water-ethanol mixture were performed for un-ionized and ionized cases at different degree-of-ionization 0%, 80% and 100% of PAA chain by Na(+) counter-ions and co-solvent (ethanol) concentration in the range 0-90vol% ethanol. Aspects of structure and dynamics were investigated via atom pair correlation functions, number and relaxation of hydrogen bonds, nearest-neighbor coordination numbers, and dihedral angle distribution function for back-bone and side-groups of the chain. With increase in ethanol concentration, chain swelling is observed for un-ionized chain (f=0) and on the contrary chain shrinkage is observed for partially and fully ionized cases (i.e., f=0.8 and 1). For un-ionized PAA, with increase in ethanol fraction ϕeth the number of PAA-ethanol hydrogen bonds increases while PAA-water decreases. Increase in ϕeth leads to PAA chain expansion for un-ionized case and chain shrinkage for ionized case, in agreement with experimental observations on this system. For ionized-PAA case, chain shrinkage is found to be influenced by intermolecular hydrogen bonding with water as well as ethanol. The localization of ethanol molecules near the un-ionized PAA backbone at higher levels of ethanol is facilitated by a displacement of water molecules indicating presence of specific ethanol hydration shell, as confirmed by results of the RDF curves and coordination number calculations. This behavior, controlled by hydrogen bonding provides a significant contribution to such a conformational transition behavior of the polyelectrolyte chain. The interactions between counter-ions and charges on the PAA chain also influence chain collapse. The underlying origins of polyelectrolyte chain collapse in water-alcohol mixtures are brought out for the first time via explicit MD simulations by this study.