Chronoamperometry and cyclic voltammetry at conical electrodes, microelectrodes, and electrode arrays: theory

The finite difference method is used to simulate chronoamperometry, linear sweep voltammetry, and cyclic voltammetry at conical electrodes and microelectrodes. Techniques for the numerical simulation of these processes at microdiscs are adapted and extended to accurately model diffusion to the electroactive cone surface. Simulated results are analyzed, and trends are rationalized in terms of the cone apex angle, alpha. The diffusion domain approximation is used to extend the theory to regular and random arrays of conical electrodes.     

Simultaneous measurement of contact angle and surface tension using axisymmetric drop-shape analysis-no apex (ADSA-NA)

Axisymmetric drop-shape analysis-no apex (ADSA-NA) is a recent drop-shape method that allows the simultaneous measurement of contact angles and surface tensions of drop configurations without an apex (i.e., a sessile drop with a capillary protruding into the drop). Although ADSA-NA significantly enhanced the accuracy of contact angle and surface tension measurements compared to that of original ADSA using a drop with an apex, it is still not as accurate as a surface tension measurement using a pendant drop suspended from a holder. In this article, the computational and experimental aspects of ADSA-NA were scrutinized to improve the accuracy of the simultaneous measurement of surface tensions and contact angles. It was found that the results are relatively insensitive to different optimization methods and edge detectors. The precision of contact angle measurement was enhanced by improving the location of the contact points of the liquid meniscus with the solid substrate to subpixel resolution. To optimize the experimental design, the capillary was replaced with an inverted sharp-edged pedestal, or holder, to control the drop height and to ensure the axisymmetry of the drops. It was shown that the drop height is the most important experimental parameter affecting the accuracy of the surface tension measurement, and larger drop heights yield lower surface tension errors. It is suggested that a minimum nondimensional drop height (drop height divided by capillary length) of 1.7 is required to reach an error of less than 0.2 mJ/m(2) for the measured surface tension. As an example, the surface tension of water was measured to be 72.46 ± 0.04 at 24 °C by ADSA-NA, compared to 72.39 ± 0.01 mJ/m(2) obtained with pendant drop experiments.     

Ratcheting motion of liquid drops on gradient surfaces

The motions of liquid drops of various surface tensions and viscosities were investigated on a solid substrate possessing a gradient of wettability. A drop of any size moves spontaneously on such a surface when the contact angle hysteresis is negligible; but it has to be larger than a critical size in order to move on a hysteretic surface. The hysteresis can, however, be reduced or eliminated with vibration that allows the drop to sample various metastable states, thereby setting it to the path of global energy minima. Significant amplification of velocity is observed with the frequency of forcing vibration matching the natural harmonics of drop oscillation. It is suggested that the main cause for velocity amplification is related to resonant shape fluctuation, which can be illustrated by periodically deforming and relaxing the drop at low frequencies.     

Motion of drops on a surface induced by thermal gradient and vibration

It is well known that a liquid drop with a low contact angle (approximately 45 degrees ) and low wetting hysteresis moves toward the colder region of a temperature gradient substrate as a result of the thermal Marangoni force. A moderately sized water drop, however, usually does not move on such a surface because of the overwhelming effect of hysteresis. The water drop can, however, be forced to move when it is vibrated on a temperature gradient surface with its velocity exhibiting maxima at the respective Rayleigh frequencies. A simple model is presented that captures the dependence of drop velocity on hysteresis, vibration amplitude, and the forcing and resonance frequencies of vibration.     

Microscopic treatment of a barrel drop on fibers and nanofibers

The microscopic approach of Berim and Ruckenstein (J. Phys. Chem. B 108 (2004) 19330, 19339) regarding the shape and stability of a liquid drop on a planar bare solid surface is extended to a liquid barrel drop on the bare surface of a solid cylinder (fiber) of arbitrary radius. Assuming the interaction potentials of the liquid molecules between themselves and with the molecules of the solid of the London-van der Waals form, the potential energy of a liquid molecule with an infinitely long fiber was calculated analytically. A differential equation for the drop profile was derived by the variational minimization of the total potential energy of the drop by taking into account the structuring of the liquid near the fiber. This equation was solved in quadrature and the shape and stability of the barrel drop were analyzed as functions of the radius of the fiber and the microscopic contact angle theta(0) which the drop profile makes with the surface of the fiber. The latter angle is dependent on the fiber radius and on the microscopic parameters of the model (strength of the intermolecular interactions, densities of the liquid and solid phases, hard core radii, etc.). Expressions for the evaluation of the microcontact angle from experimentally measurable characteristics of the drop profile (height, length, volume, location of inflection point) are obtained. All drop characteristics, such as stability, shape, are functions of theta(0) and a certain parameter a which depends on the model parameters. In particular, the range of drop stability consists of three domains in the plane theta(0)-a, separated by two critical curves a=a(c)(theta(0)) and a=a(c1)(theta(0)) [a(c)(theta(0))h(m1) cannot exist, whereas in the third domain (between those curves) the drop can have values of h(m) either smaller than h(m1) or larger than h(m2), where h(m2)>h(m1) is a second critical height. For sufficiently large fiber radii, R(f)1 >/= microm, the critical curves almost coincide and only two domains, the first and the second, remain. The smaller the radius, the larger is the difference between the critical curves and the larger is the second domain of drop stability. The shape of the drop depends on whether the point (theta(0),a) on the theta(0)-a plane is far from the critical curve or near it. In the first case the drop profile has generally a large circular part, while in the second case the shape is either almost planar or contains a long manchon that is similar to a film on the fiber.     

Wettability and surface free energy of electrolytically oxidized graphite fibers

Wettability of electrolytically oxidized graphite fibers has been investigated by contact angle measurements employing the Wilhelmy method. The atomic ratio of oxygen to carbon, O/C, in the surface layer of the graphite fiber increased with increasing electric specific charge. Contact angle hysteresis was not observed for the untreated graphite fiber (O/C=0.01). The contact angles decreased with increasing O/C, especially for the receding angle, and approached constant for O/C>0.2. The nondispersive and dispersive surface free energies of the oxidized graphite fibers were calculated from the experimentally determined contact angles. The nondispersive surface free energy increased by the oxidation, whereas the dispersive one decreased. From the results of surface analysis, it was found that the changes in the nondispersive and dispersive surface free energies were caused by the increase in O/C ratio and the decrease in surface crystallinity, respectively.     

Self-assembly of hollow cones in a bola-amphiphile/hexadiamine salt solution

Cones are a very rare form of supramolecular self-assembly. It is shown that mixing of an unsymmetrical bola-fatty acid and a diamine (catanionic system) in dilute solutions can produce aggregates having a conical shape. These assemblies are made of frozen unsymmetrical monolayers in which bolas are arranged on a regular hexagonal lattice. Cones are stabilized by the introduction of pentagonal or n-gonal defects in the bola-lattice which yields the quantification of the cone apex angle according to the Euler theorems. The formation of cones represents a novel route for lipid and surfactant systems to minimize the edge energy of a flat membrane.     

Nanodroplets on a planar solid surface: temperature, pressure, and size dependence of their density and contact angles

The shape and the density of a liquid drop on a planar solid surface, embedded in an inert gas at constant temperature and pressure, were examined on the basis of a microscopic density functional approach that accounts for the entropic (temperature-dependent) and energetic contributions to the free energy of the system. Integro-differential equations describing the profile and the density of a cylindrical (2D) drop were derived by the variational minimization of the Gibbs free energy with respect to both the drop profile and density under the assumption of uniform density. The equations were solved numerically using the constraint of a constant number of molecules N(l) per unit length of the drop. It was shown that for temperatures lower than a certain temperature Tw the free energy against density has generally two minima, representing a stable equilibrium state and a metastable one. One of those minima is located at a density corresponding to the density of a normal liquid, whereas the other one is located at a density comparable to the density of the surrounding inert gas. For this reason, the latter state of the drop cannot be stable. For T > Tw, the minimum corresponding to the liquid state disappears, and no drop can be formed on the surface. The temperature Tw depends on N(l) and the external pressure p and increases when N(l) and p increase. The true wetting angle theta0 that the drop profile makes with the solid surface depends on the parameters characterizing the microscopic interactions, the density, and the surface densities. If in the thermodynamically stable state absolute value(cos theta0) > 1, then no drop is formed on the surface. If in that state absolute value(cos theta0) < 1, then at any pressure the true contact angle decreases when the temperature increases and approaches Tw. However, theta0 does not reach a zero value for T < or = Tw but has for T = Tw a discontinuity from a finite to a zero value. The true contact angle also depends on the number of molecules in the drop and on the external pressure. For all considered values of N(l), p, and microscopic parameters of the intermolecular interactions, the density of the drop decreases with increasing temperature. The rate of decrease is constant for temperatures sufficiently far from Tw and increases when T approaches Tw. At a given temperature and pressure, the density of the drop decreases with decreasing N(l). For relatively large drops (N(l) approximately = 10(14)-10(20)), the rate of decrease is very small, whereas for small droplets (N(l) approximately = 10(12)) it becomes much larger.     

Influence of drawing and heat treatment on surface free energies of polyethylene terephthalate fibers

The surface free energies of polyethylene terepthalate fibers with different draw ratios were experimentally determined by contact angle measurements inn-alkane/water systems. The dispersive component of the surface free energy increased with increasing draw ratio, whereas the nondispersive one remained almost constant. After heat treatment, the dispersive surface free energy increased, but was reduced above 140°C. The nondispersive component increased by heat treatment at 190°C. The increases in the density and birefringence of the fibres due to the drawing and heat treatment suggested that the increase in the dispersive surface free energy was caused by the increase in the atomic density at the fiber surface due to drawing and heat treatment. ESCA results indicated that the increment in the nondispersive surface free energy due to heat treatment was caused by the addition of functional groups to the fiber surface due to heat treatment.     

Motion of liquid drops on surfaces induced by asymmetric vibration: role of contact angle hysteresis

Hysteresis of wetting, like the Coulombic friction at solid/solid interface, impedes the motion of a liquid drop on a surface when subjected to an external field. Here, we present a counterintuitive example, where some amount of hysteresis enables a drop to move on a surface when it is subjected to a periodic but asymmetric vibration. Experiments show that a surface either with a negligible or high hysteresis is not conducive to any drop motion. Some finite hysteresis of contact angle is needed to break the periodic symmetry of the forcing function for the drift to occur. These experimental results are consistent with simulations, in which a drop is approximated as a linear harmonic oscillator. The experiment also sheds light on the effect of the drop size on flow reversal, where drops of different sizes move in opposite directions due to the difference in the phase of the oscillation of their center of mass.     

Evaluation of the surface free energy of spin‐coated photodefinable epoxy

The surface free energy of crosslinked photodefinable epoxy (PDE) was evaluated from the advancing contact angles measured by the sessile drop method. Poly(tetrafluoroethylene) (PTFE) was used as a reference material in the evaluation of the surface free energies by various models. Pure water, diiodomethane, formamide, ethylene glycol, diethylene glycol, glycerol, 1‐bromonaphthalene, decane, and tetradecane were used as the probing liquids. The surface free energies for PDE and PTFE were calculated to be 43.6 and 21.2 mJ/m², respectively. The contact‐angle measurements indicated the isotropy of the PDE surface with respect to the surface free energy. The PDE coating was further characterized with scanning electron microscopy and atomic force microscopy. The PDE surface was treated chemically and by reactive ion etching (RIE) to determine their impact on the wettability and adhesion. The treatments resulted in decreased contact angles between the crosslinked PDE surface and water as the polarity of the surface increased from about 9% to 18 and 43% by the chemical and RIE treatments, respectively. On the contrary, the surface free energy of the treated PDEs, as calculated by the geometric mean model, did not change markedly (to 47.4 and 41.8 mJ/m² by the chemical and RIE treatments, respectively). Consequently, the contact angles of diiodomethane and the PDE solution on the treated surfaces did not decrease noticeably. The stud‐pull test showed improved adhesion strength for PDE that was left less crosslinked and, therefore, had residual affinity against the sequential PDE layer. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 2137–2149, 2002     

Cylindrical droplet on nanofibers: a step toward the clam-shell drop description

The existence and shape of a cylindrical (infinitely long) liquid drop on a fiber of arbitrary radius are examined using a microscopic approach based on the interaction potentials between the molecules of the system. A differential equation for the drop profile was derived by the variational minimization of the total potential energy by taking into account the structuring of the liquid near the fiber. This equation was solved by quadrature, and the existence conditions and the shape of the drop were examined as functions of the radius of the fiber, microscopic contact angle theta(0), which the actual drop profile makes with the fiber, and a certain parameter, a, which depends on the interaction potential parameters. Angle theta(0) is defined in the nanoscale range near the leading edge where the interactions between the liquid and solid are strong. It differs from the macroscopically measured wetting angle (theta(m)) that represents the extrapolation of the profile outside the range of liquid-solid interaction to the solid surface. Expressions for both theta(0) and theta(m) are established in the paper. For any given fiber radius, the range of drop existence involves two domains in the plane theta(0) - a, separated by a critical curve a = a(c)(theta(0)). In the first domain, below the curve a = a(c)(theta(0)), the drop always exists and can have any height, h(m). In the second domain, above the curve a = a(c)(theta(0)), there is an upper limit of h, h(m1), such that drops with h(m) > h(m1) cannot exist. The shape of the drop depends on whether the point (theta(0), a) on the theta(0) - a plane is far from the critical curve or near to it. In the first case, the drop profile has generally a circular shape, with the center of the circle not located on the fiber axis, whereas in the second case the shape is "quasi planar", that is, most of the drop profile lies on a circle concentric with the fiber profile. Comparing the potential energies of a cylindrical drop on a fiber and a film of uniform thickness covering the fiber and having the same volume as the drop, the energetically preferred configuration was determined for various conditions. Considering the cylindrical drop as a limiting case of a clam-shell one, and the film as a limiting case of a barrel drop, the obtained analytical results could be employed to examine the barrel-drop-clam-shell-drop transformation (roll-up transition).     

Contact angle hysteresis of cylindrical drops on chemically heterogeneous striped surfaces

Contact angle hysteresis of a macroscopic droplet on a heterogeneous but flat substrate is studied using the interface displacement model. First, the apparent contact angle of a droplet on a heterogeneous surface under the condition of constant volume is considered. By assuming a cylindrical liquid-vapor surface (meniscus) and minimizing the total free energy, we derive an equation for the apparent contact angle, which is similar but different from the well-known Cassie's law. Next, using this modified Cassie's law as a guide to predict the behavior of a droplet on a heterogeneous striped surface, we examine several scenarios of contact angle hysteresis using a periodically striped surface model. By changing the volume of the droplet, we predict a sudden jump of the droplet edge, and a continuous change of the apparent contact angle at the edge of two stripes. Our results suggest that as drop volume is increased (advancing contact lines), the predominant drop configuration observed is the one whose contact angle is large; whereas, decreasing drop volume from a large value (receding contact lines) yields drop configuration that predominantly exhibit the smaller contact angle.     

Efficiency of sildenafil encapsulation in poloxamer micelles

Abstract

The purpose of this study is to prepare and investigate the physicochemical and thermodynamic evidence of sildenafil (SIL) encapsulated poloxamer 188 (P188) micelles. The micelles were prepared by the thin-film hydration technique and investigated by pendant drop tensiometry and dynamic light scattering techniques. The closed association model was used to determine the micelle-monomer equilibrium parameters. The standard Gibbs free energy of the micelle formation was calculated from the partition coefficient. The change in the pattern of the surface tension, particle count rate, and particle size of the SIL encapsulated P188 micelles was observed. The corresponding critical micelle concentration (CMC) was approximately 0.04?mM. The hydrodynamic Z-average size of the micelles ranged from 6 to 9 d. nm. The encapsulation efficiency (EE) of SIL in the micelles was up to 54.3?±?0.2%. The obtained equilibrium constant was 0.67. The standard Gibbs free energy of the formation of SIL encapsulated micelles at 25?°C was ?32.9?kJ/mol. The formation of SIL encapsulated P188 micelles was confirmed by the change in the pattern of the surface tension, particle count rate and size of the micellar solution. The standard Gibbs free energy of the formation indicated the spontaneous partition process in the micellar systems.     

超疏水表面微纳二级结构对冷凝液滴最终状态的影响

从超疏水表面(SHS)上初始冷凝液核长大、合并、形成初始液斑开始,分析计算了冷凝液斑变形成为Wenzel或Cassie液滴过程中界面能量的变化,并以界面能曲线降低、是否取最小值为判据,确定冷凝液滴的最终稳定状态.计算结果表明:在只有微米尺度的粗糙结构表面上,冷凝液滴的界面能曲线一般都是先降低再升高,呈现Wenzel状态;而当表面具有微纳米二级粗糙结构,且纳米结构的表面空气面积分率较高时,冷凝液滴的能量曲线持续降低,直至界面能最小的Cassie状态,因此可以自发地形成Cassie液滴.还计算了文献中具有不同结构参数的SHS上冷凝液滴的状态和接触角,并与实验结果进行了比较,结果表明,计算的冷凝液滴状态与实验观察结果完全吻合.因此,微纳二级结构是保持冷凝液滴在SHS上呈现Cassie状态的重要因素.     

Conical intersections in solution: formulation, algorithm, and implementation with combined quantum mechanics/molecular mechanics method

The significance of conical intersections in photophysics, photochemistry, and photodissociation of polyatomic molecules in gas phase has been demonstrated by numerous experimental and theoretical studies. Optimization of conical intersections of small- and medium-size molecules in gas phase has currently become a routine optimization process, as it has been implemented in many electronic structure packages. However, optimization of conical intersections of small- and medium-size molecules in solution or macromolecules remains inefficient, even poorly defined, due to large number of degrees of freedom and costly evaluations of gradient difference and nonadiabatic coupling vectors. In this work, based on the sequential quantum mechanics and molecular mechanics (QM/MM) and QM/MM-minimum free energy path methods, we have designed two conical intersection optimization methods for small- and medium-size molecules in solution or macromolecules. The first one is sequential QM conical intersection optimization and MM minimization for potential energy surfaces; the second one is sequential QM conical intersection optimization and MM sampling for potential of mean force surfaces, i.e., free energy surfaces. In such methods, the region where electronic structures change remarkably is placed into the QM subsystem, while the rest of the system is placed into the MM subsystem; thus, dimensionalities of gradient difference and nonadiabatic coupling vectors are decreased due to the relatively small QM subsystem. Furthermore, in comparison with the concurrent optimization scheme, sequential QM conical intersection optimization and MM minimization or sampling reduce the number of evaluations of gradient difference and nonadiabatic coupling vectors because these vectors need to be calculated only when the QM subsystem moves, independent of the MM minimization or sampling. Taken together, costly evaluations of gradient difference and nonadiabatic coupling vectors in solution or macromolecules can be reduced significantly. Test optimizations of conical intersections of cyclopropanone and acetaldehyde in aqueous solution have been carried out successfully.     

Accurate predictions of water cluster formation, (H₂O)(n=2-10)

An efficient mixed molecular dynamics/quantum mechanics model has been applied to the water cluster system. The use of the MP2 method and correlation consistent basis sets, with appropriate correction for BSSE, allows for the accurate calculation of electronic and free energies for the formation of clusters of 2-10 water molecules. This approach reveals new low energy conformers for (H(2)O)(n=7,9,10). The water heptamer conformers comprise five different structural motifs ranging from a three-dimensional prism to a quasi-planar book structure. A prism-like structure is favored energetically at low temperatures, but a chair-like structure is the global Gibbs free energy minimum past 200 K. The water nonamers exhibit less complexity with all the low energy structures shaped like a prism. The decamer has 30 conformers that are within 2 kcal/mol of the Gibbs free energy minimum structure at 298 K. These structures are categorized into four conformer classes, and a pentagonal prism is the most stable structure from 0 to 320 K. Results can be used as benchmark values for empirical water models and density functionals, and the method can be applied to larger water clusters.     

Effect of Cationic and Zwitterionic Surfactants on Contact Angle of Quartz–Water–Crude Oil System

The influences of four cationic surfactants hexadecyl glycidyl ether ammonium chloride and four zwitterionic surfactants hexadecyl glycidyl ether glycine Betaine solutions on contact angle of crude oil on a quartz surface were investigated using a captive drop method. The effects of surfactant type, structure, and concentration on contact angle were expounded. From obtained results it appears that the adsorbed surfactant at oil–water interface reduces the interfacial tension and the adsorption at quartz–water interface improves interfacial free energy, which results in reducing the stable value of contact angle and weakening dynamic behavior. At high concentration, the zwitterionic surfactant with branched-chain may form semi-micelle at quartz surface. As a result, the stable value of contact angle passes through a sharp minimum with the increasing concentration.     

Density Functional Theory Study of Reaction Equilibria in Signal Amplification by Reversible Exchange

An in-depth theoretical analysis of key chemical equilibria in Signal Amplification by Reversible Exchange (SABRE) is provided, employing density functional theory calculations to characterize the likely reaction network. For all reactions in the network, the potential energy surface is probed to identify minimum energy pathways. Energy barriers and transition states are calculated, and harmonic transition state theory is applied to calculate exchange rates that approximate experimental values. The reaction network energy surface can be modulated by chemical potentials that account for the dependence on concentration, temperature, and partial pressure of molecular constituents (hydrogen, methanol, pyridine) supplied to the experiment under equilibrium conditions. We show that, under typical experimental conditions, the Gibbs free energies of the two key states involved in pyridine-hydrogen exchange at the common Ir-IMes catalyst system in methanol are essentially the same, i. e., nearly optimal for SABRE. We also show that a methanol-containing intermediate is plausible as a transient species in the process.     

Radiationless decay mechanism of cytosine: an ab initio study with comparisons to the fluorescent analogue 5-methyl-2-pyrimidinone

The ultrafast radiationless decay mechanism of photoexcited cytosine has been theoretically supported by exploring the important potential energy surfaces using multireference configuration-interaction ab initio methods for the gas-phase keto-tautomer free base. At vertical excitation, the bright state is S1 (pipi*) at 5.14 eV, with S2 (nNpi*) and S3 (nOpi*) being dark states at 5.29 and 5.93 eV, respectively. Minimum energy paths connect the Franck-Condon region to a shallow minimum on the pipi* surface at 4.31 eV. Two different energetically accessible conical intersections with the ground state surface are shown to be connected to this minimum. One pathway involves N3 distorting out of plane in a sofa conformation, and the other pathway involves a dihedral twist about the C5-C6 bond. Each of these pathways from the minimum contains a low barrier of 0.14 eV, easily accessed by low vibronic levels. The path involving the N3 sofa distortion leads to a conical intersection with the ground state at 4.27 eV. The other pathway leads to an intersection with the ground state at 3.98 eV, lower than the minimum by about 0.3 eV. Comparisons with our previously reported study of the fluorescent cytosine analogue 5-methyl-2-pyrimidinone (5M2P) reveal remarkably similar conformational distortions throughout the decay pathways of both bases. The different photophysical behavior between the two molecules is attributed to energetic differences. Vertical excitation in cytosine occurs at a much higher energy initially, creating more vibrational energy than 5M2P in the Franck-Condon region, and the minimum S1 energy for 5M2P is too low to access an intersection with the ground state, causing population trapping and fluorescence. Calculations of vertical excitation energies of 5-amino-2-pyrimidinone and 2-pyrimidinone reveal that the higher excitation energy of cytosine is likely due to the presence of the amino group at the 4-position.