Dynamics of a Spreading Nanodroplet: A Molecular Dynamic Simulation

The spreading of polymer nanodroplets upon a sudden change from partial to complete wetting on an ideally flat and structureless solid substrate has been studied by molecular dynamic simulations using a coarse‐grained bead‐spring model of flexible macromolecules. Tanner's law for the growth of the lateral droplet radius {R(t) ∝ t^0.1} is found to hold as long as the droplet does not disintegrate into individually moving chains. The data for the contact angle θ following from Tanner's law correspond to a dependence on time {θ(t) ∝ t^−0.3}. Our analysis of the mean square displacements of the polymer centers of mass reveals several dynamic regimes during the process of spreading. PACS numbers: 68.10.Gw, 05.70.Ln, 61.20.Ja, 8.45.Gd.

Molecular dynamics results for the average mean square displacement of all polymer chains plotted vs. time for a broad range of values for ε_wall.     

The stability of hydrocarbon oil droplets at the surfactant/oil interface

Summary The effect of the nature of the oil on the coalescence of single oil droplets at the plane aqueous surfactant solution/oil interface has been investigated. The drop rest-times for the first stage coalescence of a range of hydrocarbon oils have been measured with constant drop volume. The apparatus was based on a design byNielsen et al. (13). Variables that affected drop lifetimes such as drop size, apparatus dimensions, saturation of the two phases with the other component, and surfactant concentration and chain length were investigated and a standard technique was developed. For saturated hydrocarbons the droplet stability falls progressively with increase in chain length. Unsaturation or aromatic character brings about a decrease in droplet stability. The results are discussed in terms of the balance between the cohesive forces between oil molecules and the adhesive forces, between the alkyl chain of the surfactant and oil molecules.The addition of small quantities of long chain alcohol brings about a marked increase in stability through the formation of a complex condensed film at the oil/water interface. Attempts to correlate droplet stability data and the stabilities of bulk emulsion systems and spreading coefficient were not successful.

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Zusammenfassung Die Koaleszenz von Öltropfen auf planen Oberflächen von Tensiden wurde untersucht, wozu eine Standardtechnik entwickelt wurde. Bei gesättigten Kohlenwasserstoffn nimmt die Stabilität der Tröpfchen mit zunehmender Kettenlänge ab. Auch ungesättigte Bindungen und aromatische Gruppen erniedrigen die Stabilität.Die Resultate werden diskutiert unter Berücksichtigung der kohäsiven Kräfte zwischen den Molekülen des Kohlenwasserstoffes und den adhäsiven Kräften zwischen den Alkylketten der Tenside und den Kohlenwasserstoffmolekülen.Die Stabilität wird stark erhöht, wenn geringe Mengen langkettigen Alkohols zugesetzt werden, infolge der Bildung eines komplexen kondensierten Films an der Öl/Wasser-Grenzfläche. Versuche, die gewonnenen Stabilitätsdaten mit der Stabilität der Bulkemulsionen und des Spreitungskoeffizienten in Beziehung zu setzen, waren nicht erfolgreich.

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Nomenclature A area per molecule of surfactant at the interface (nm²) - a activity - C concentration (mol dm^–3) - d drop diameter (cm or mm) - d ₀ mean droplet diameter on volume basis at initial storage - d _t mean droplet diameter on volume basis aftert days storage - h film thickness - K Boltzmann's constant - K ₁ coalescence constant - k first order rate constant for coalescence (s^-1) - k ₁ coalescence constant - k ₂ empirical constant - L distance from needle to interface (cm) - M geometric mean rest-time (s) - N number of droplets not coalesced - n exponent - R gas constant - S spreading coefficient (Nm^-1) - T absolute temperature - T1/2 first order half-life for coalescence (s) - t time (s) - t _d drainage time (s) - t1/2 time required for half of droplets to coalesce (s) - ^tmean mean rest-time (s) - V molar volume - v velocity of hole formation - Hv latent heat of vaporization - solubility parameter - interfacial tension (Nm^-1) - ⁰ interfacial tension between pure oil and water - _e viscosity of continuous phase - density - density difference - surface tension - ag geometric standard deviation - T surface excess - T ₀ saturation adsorption     

Evaluation of the relaxation modules from the response to a constant rate of strain followed by a constant strain

The stress response σ(t) to a constant rate of strain $ \dot \varepsilon $ ε during the period 0 < t ≤ t^* and to the constant strain ε^* $ ( = \dot \varepsilon t*) $ thereafter is considered in terms of the Boltzmann superposition principle. When t ≤ t^*, the data directly give the constant-rate modulus F (t) ≡ σ(t)/ε(t), which can be converted straightforwardly into the relaxation modulus E(t). Results from illustrative calculations show that a reduction in the relaxation rate effects a decrease in [σ(t^*)/ε^*]/E(t^*) and also in the time at which [σ(t)/ε^*]/E(t) becomes essentially unity. To evaluate E(t) at t > t^*, F(t) is first obtained from σ(t) and F(t ? t^*) by using a derived equation similar to that presented by Meissner. Thereafter, F(t) is transformed into E(t). For illustration, E(t) for a rubbery solid is evaluated over some 2.5 decades of time from its response to a strain rate of 0.25 min^?1 for 0.40 min and thereafter to the attained strain of 0.10 for 5.4 min.     

Approximate relations among compliance functions of linear viscoelasticity for amorphous polymers

In the glass–rubber transition region of viscoelastic behavior of amorphous polymers, it is found that is a good first approximation. Here J(t) is the value of the shear creep compliance at time t and J″(1/t) is the value of the shear loss compliance at an angular frequency of 1/t. Previous approximations related the creep compliance to the storage compliance. When J(t) is proportional to t^m, where m is a positive constant, J″(1/t) is within 30% of J(t) for m > 0.6. Over the entire range, is a better approximation than either of the other two. The relaxation modulus G(t) is hardly ever a good approximation for the loss modulus G″(1/t).     

Reaction of Iron Phthalocyanine with Oxygen: Critical Survey and New Data on the Structure of the Forming PcFe(II) μ-Oxo Dimer

Reaction of iron tetra-4-tert-butylphthalocyanine (Pc ^t Fe) with oxygen in noncoordinating solvents at Pc ^t Fe concentrations within (0.63-10.71) × 10^-2 M was studied. The uptake of oxygen (moles per mole of iron phthalocyanine taken into reaction) depends on the concentration of the complex, varying in the examined concentration range from 1/5 to 1/2.7, and thus can significantly differ from the value implied by the stoichiometry of the Pc^tFe -oxo dimer. This fact is due to consumption of the reactants in side processes, including oxidative degradation of the macroring. Indeed, the -oxo dimer is the major but not the only product of reaction of Pc^tFe with oxygen: Up to 20% of the initial complex undergoes oxidative degradation. These data, in combination with the spectral and chemical properties of the Pc^tFe -oxo dimer, suggest that this compound is an Fe(2+) derivative.     

Salen Supported Molecular Borosilicates

Various Salen ligands (Salen( ^t Bu)H₂=N, N-ethylenebis(3,5-di-tertbutyl(2-hydroxy)benzylidenimine) were used to prepare borosilyl and -O bridged borosilyl compounds having the formula, L{B(OSiMe₃)₂}₂ (L=Salen( ^t Bu) (1), Salpen( ^t Bu) (2), Salben( ^t Bu) (3), Salhen( ^t Bu) (4) and L(BOSiMe₃)₂(-O) (L=Salen( ^t Bu) (5) and Salben( ^t Bu) (6)). In the case of 5 and 6 the formation of the B–O–B linkage takes precedence over the formation of a B–O–Si linkage. All of the compounds were characterized by Mp, elemental analysis, ¹H and ¹¹B NMR, IR, MS and in the case of 1, 2, and6 by X-ray crystallography.     

Synthesis of natural rubber-based telechelic cis-1,4-polyisoprenes and their use to prepare block copolymers via RAFT polymerization

A new trithiocarbonate functionalized cis-1,4-polyisoprene was obtained from oxidative degradation of natural rubber followed by reductive amination and amidation. The structure of the resulting functionalized cis-1,4-polyisoprene was confirmed by a combination of ¹H NMR spectroscopy, ¹³C NMR spectroscopy, MALDI-TOF mass spectrometry and FTIR spectroscopy. ¹H NMR spectroscopy showed that the trithiocarbonate functionality was equal to one. The well-defined trithiocarbonyl-end functionalized cis-1,4-polyisoprene was used as a macromolecular chain transfer agent (macroCTA) to mediate the RAFT polymerization of t-BA using AIBN as the initiator ([t-BA]₀/[macroCTA]₀/[AIBN]₀ = 250/1/0.2) in toluene at 60 °C. The resulting PI-b-P(t-BA) diblock copolymer presents an unimodal SEC trace shifted toward higher molecular weight in comparison with the SEC trace of the macroCTA, indicating that the polymerization of the second block is effective. The characteristics of the copolymer were determined by SEC = 26,000 g mol⁻¹, PDI = 1.76) and ¹H NMR spectroscopy ( (PI) = 62 and (P(t-BA)) = 87).     

Homo- and heterometallic trinuclear nickel(ii) and cobalt(ii) pivalate complexes

The reaction of the dinuclear complex Co₂(bpy)₂(OOCBu^t)₄ with the tetranuclear complex Ni₄(₃-OH)₂(OOCBu^t)₆(EtOH)₆ afforded the trinuclear heterometallic complex M₃(bpy)₂(₃-OH)(-OOCBu^t)₄(OOCBu^t) (6) (M = Ni, Co; Ni : Co = 1.2 : 1) in which two metal atoms are in an octahedral environment and one metal atom is in a tetrahedral environment. The reaction of 2,2"-bipyridine with Co₄(₃-OH)₂(OOCBu^t)₆(HOEt)₆ (reagent ratio was 2 : 1) or the reaction of bpy with Co₈(₄-O)₂( _n -OOCBu^t)₁₂ (reagent ratio was 4 : 1) produced a homometallic analog of 6, viz., the trinuclear cluster Co₃(bpy)₂(₃-OH)(-OOCBu^t)₄(OOCBu^t) (8). The reaction of 1,10-phenanthroline (phen) with the [Co(OH) _n (OOCBu^t)_2–n ] _x polymer gave the analogous trinuclear cluster (phen)₂Co₃(₃-OH)(₂-OOCBu^t)₄(¹-OOCBu^t). Compounds 6 and 8 exhibit antiferromagnetic spin-spin exchange interactions.     

Heats of solution of 1:1 electrolytes in 1,2- and 1,1-dichloroethane and derived enthalpies and entropies of transfer of electrolytes from water to these solvents

Heats of solution of nine electrolytes in 1,2-dichloroethane and of three electrolytes in 1,1-dichloroethane have been determined calorimetrically at various electrolyte concentrations and extrapolated to zero concentration to yield H _s ^o values for these electrolytes. It is shown that values of H _t ^o for transfer from water to the dichloroethanes of 11 electrolytes are often negative, so that these electrolytes can be more stable enthalpically in the less polar solvents. Combinations of the H _t ^o values with previously determined G _t ^o values yield values of S _t ^o for transfer of 11 electrolytes from water to the dichloroethanes. These S _t ^o values are mostly very negative; they can be correlated very well by the method of Abraham, and in this way S _t ^o values for transfer of numerous other anions and cations have been predicted. The Ph₄As⁺/Ph₄B^– convention yields single-ion entropies of transfer from water to the dichloroethanes in reasonable agreement with values calculated by the correspondence-plot method.     

Rates of Dissociative Ionic Reactions in Aqueous Mixtures Correlated with Opposing Gibbs Energies of Transfer of Single Ions: Solvolysis of Chloropentacyanocobaltate(III) Anions in Water + Ethanol and Water + Urea

The kinetics of the solvolysis of Co(CN)₅Cl^3– have been investigated in water with an added structure former, ethanol, and with added urea, which has only a weak effect on the solvent structure. As this solvolysis involves a rate-determining dissociative step corresponding closely to a 100%; separation, Co³⁺ Cl^-, in the transition state, a Gibbs energy cycle relating Gibbs energies of activation in water and in the mixtures to Gibbs energies of transfer of individual ionic species between water and the mixtures, G _t ^o (i), can be applied. The acceleration of the reaction found with both these cosolvents results from the compensation of the retarding positive G _t ^o (Cl^- by the negative term [G _t ^o [Co(CN) ₅ ^2- ]-G _t ^o [Co(CN)₅Cl^3- arising from G _t ^o [Co(CN)₅Cl^3-]> G _t ^o [Co(CN) ₅ ^2- ]. Moreover, only a small tendency to extrema in the enthalpies and entropies of activation is found with both these cosolvents, as was also found with added methanol or ethane-1,2-diol, but unlike the extrema found when hydrophobic alcohols are added to water. With the latter, much greater negative values for G _t ^o [Co(CN) ₅ ^2- ]- _t ^o [Co(CN)₅Cl^3-] are found. When G G _t ^o [Co(CN) ₅ ^2- ]-G G _t ^o [CO(CN)₅Cl^3-] becomes low enough not to compensate for the positive G _t ^o (Cl^-), as with added hydrophilic glucose, the reaction is retarded. Compensating contributions of the various G _t ^o (i) involved in the Gibbs energy cycle with added methanol or ethane-1, 2-diol allow log (rate constant) to vary linearly with the reciprocal of the relative permittivity of the medium.     

Kinetic role of t-amines in the ligand inhibited osmium tetraoxide catalyzed trimethylamine-N-oxide dihydroxylation of alkenes

Kinetic studies on the t-amine inhibited catalytic OsO₄ dihydroxylation of cyclooctene, octene, styrene and 4-methyl-, 4-methoxy-, 4-chloro-, 4-(chloromethyl), 4-(trifluoromethyl) and 3-chloro-derivatives of styrene with Me₃NO in t-BuOH have been carried out at 50 °C. The reactions follow identical kinetics: first order in total osmium species, first order in Me₃NO and zero order in alkene. All t-amines have been found to retard the catalysis and the reaction order in t-amine changes from inverse first order to zero. The involvement of dioxomonoglycolataosmium(VI) esters and their monoamine adducts in the rate-determining oxidation step was established by the linear plots of 1/k ₂ versus. 1/[L] where k ₂ is the decrease in second order rate constant in the presence of [L] concentration of t-amine ligand. Beyond a definite concentration of t-amine, the rate reaches a minimum and remains constant. Activation parameters were evaluated for catalytic OsO₄ dihydroxylation of 4-(chloromethyl)styrene at different t-amine concentrations. The values of H and S are consistent with the proposed mechanism.     

Analysis of kinetic data by Johnson-Mehl equation

Johnson-Mehl equation is written as d/dt=k ⁿ t ^n–1 (1–) where is the degree of reaction,t time andn a constant. Use of this equation in kinetic analysis present problems because of the presence of a t term on the right hand side. The equation is not a true kinetic equation andk is not a true rate constant.This paper presents a brief discussion on the use of this equation as such or in a modified form and also indicates the proper procedure for evaluating kinetic parameters correctly. Some experimental data on the reduction of Fe₂O₃ to Fe₃O₄ have been used to test the mathematical procedure proposed. This reaction is known to follow the typical trend described by Johnson-Mehl equation.

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Zusammenfassung Die Johnson-Mehl-Beziehung lautet:d/dt=k ⁿ t ^n–1(1–) mit der Reaktionskoordinate, der Zeitt und der Konstanten. Eine Anwendung dieser Gleichung in der kinetischen Analyse verursacht Probleme, da auf der rechten Seite der Gleichung ein t-haltiger Ausdruck steht. Die Gleichung ist keine wirkliche kinetische Gleichung undk ist keine wahre Geschwindigkeitskonstante.Diese Arbeit beschreibt eine kurze Diskussion der Anwendung dieser Gleichung in dieser oder einer modifizierten Form und beschreibt, wie korrekte kinetische Parameter erhalten werden können. Zum Testen des vorgeschlagenen mathematischen Verfahrens wurden einige experimentelle Daten der Reduktion von Fe₂O₃ zu Fe₃O₄ benutz. Diese Reaktion ist bekannt, dem typischen, durch die Johnson-Mehl-Gleichung beschriebenem Trend zu folgen.

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Dr. S. B. Sarkar wishes to acknowledge the financial support of the Commonwealth Commission (U.K.) and the experimental facilities provided by the Imperial College of Science and Technology, London U.K.     

Synthesis and Structure of Two Isomers of Re2Os2(CO)14(CNBu t )4: Clusters with Linear ReOs2Re Chains

The complexes (OC)₄(CNBu ^t )ReOs(CO)₃(CNBu ^t )Os(CO)₃(CNBu ^t )Re(CNBu ^t )(CO)₄ (A) and (OC)₃(CNBu ^t )₂ReOs(CO)₄Os(CO)₃(CNBu ^t )Re(CNBu ^t )(CO)₄ (B) have been isolated in low yield from the reaction of Os(CO)₃(CNBu ^t )₂ with Re₂(-H)(--C₂H₃)(CO)₈ in hexane at room temperature. Both compounds have approximately linear ReOs₂Re chains. The Re–Os lengths are in the range 2.9311(7)–2.952(1) Å the Os–Os lengths are 2.875(1) (A) and 2.8759(7) Å (B).     

Synthesis and Study of Ruthenium Phthalocyanine Complexes

Methods of synthesis of ruthenium tetra-tert-butylphthalocyaninate (Pc ^t Ru) were developed. The synthesis performed in both autoclave and in open system (in isoamyl alcohol in the presence (1,8-diazabicyclo[5,4,0]undecene) resulted in Pc ^t Ru() containing CO as axial ligand. When quinoline was used in the synthesis of Pc ^t Ru, the Pc ^t Ru(Iqnl)₂ complex was obtained with two isoquinoline molecules (Iqnl) as axial ligands, which were detached consecutively in the course of thermogravimetric analysis. The compounds formed were studied by different physicochemical methods: electron, IR, and ¹H NMR spectroscopies, MALDI-TOF mass spectroscopy, thermogravimetric and elemental analyses.     

Kinetics of the droplet formation at the early and intermediate stages of the spinodal decomposition in homopolymer blends

The kinetics of the droplet formation during the spinodal decomposition (SD) of the homopolymer blends has been studied by numerical integration of the Cahn‐Hilliard‐Cook equation. We have found that the droplet formation and growth occurs when the minority phase volume fraction, f_m , approaches the percolation threshold value, f_thr = 0.3 ± 0.01. The time for the formation of the disperse droplet morphology (coarsening time) depends only on the equilibrium minority phase volume fraction, f_m . f_m approaches its equilibrium value logarithmically at the late SD stages, and, therefore, the coarsening time decreases exponentially as the average volume fraction or the quench depth decrease. Since the temporal evolution of the total interfacial area does not depend on the quench conditions and blend morphology, the average droplet size and the droplet number density is determined by the coarsening time. Within the time scale studied, the droplet number density decreases with time as t ^{–0.63±0.03}; the average mean curvature decreases as t ^{–0.35±0.05}; the average Gaussian curvature decreases as t ^{–0.42±0.03}, and the average droplet compactness ˜V/S^3/2 where S is the surface area and V is the volume) approaches a spherical limit logarithmically with time. The droplets with larger area have lower compactness and in the low compactness limit their area is a parabolic function of compactness. The size and shape distribution functions have been also investigated.     

Charging and Release Mechanisms of Flexible Macromolecules in Droplets

We study systematically the charging and release mechanisms of a flexible macromolecule, modeled by poly(ethylene glycol) (PEG), in a droplet by using molecular dynamics simulations. We compare how PEG is solvated and charged by sodium Na⁺ ions in a droplet of water (H₂O), acetonitrile (MeCN), and their mixtures. Initially, we examine the location and the conformation of the macromolecule in a droplet bearing no net charge. It is revealed that the presence of charge carriers do not affect the location of PEG in aqueous and MeCN droplets compared with that in the neutral droplets, but the location of the macromolecule and the droplet size do affect the PEG conformation. PEG is charged on the surface of a sodiated aqueous droplet that is found close to the Rayleigh limit. Its charging is coupled to the extrusion mechanism, where PEG segments leave the droplet once they coordinate a Na⁺ ion or in a correlated motion with Na⁺ ions. In contrast, as PEG resides in the interior of a MeCN droplet, it is sodiated inside the droplet. The compact macro-ion transitions through partially unwound states to an extended conformation, a process occurring during the final stage of desolvation and in the presence of only a handful of MeCN molecules. For charged H₂O/MeCN droplets, the sodiation of PEG is determined by the H₂O component, reflecting its slower evaporation and preference over MeCN for solvating Na⁺ ions. We use the simulation data to construct an analytical model that suggests that the droplet surface electric field may play a role in the macro-ion–droplet interactions that lead to the extrusion of the macro-ion. This study provides the first evidence of the effect of the surface electric field by using atomistic simulations.

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Graphical Abstract ?

     

The reaction of atomic oxygen O(3P) with isobutane

The reaction of O(³P) atoms with isobutane has been studied by using the discharge-flow system described previously [1]. The rate constant was measured from determinations of the isobutane concentration in the presence of an excess of O atoms and is given by k₁ = (7.9 ± 1.4) × 10⁷ dm³/mol·s at 307 K. In order to explain the observed reaction products, the mechanism requires that the principal process be the successive abstraction of H atoms from isobutane and from the t-butyl radical to give isobutene. A minor part of the reaction between O(³P) and the t-butyl radical gives the t-butoxy radical, which decomposes to acetone. The branching ratios are .     

Asymptotic Behavior of the t Expansion

The asymptotic behavior of a system's ground-state energy from the t expansion of Horn and Weinstein has been suggested to have the form E ₁(t)=E ₁+exp(–a _n t+b _n ). In the limit of very large t, this becomes E ₁(t)=E ₁+exp(–a ₁ t+b ₁). A simple analysis shows that the parameters are a ₁=E ₂–E ₁ and b ₁=ln[(E ₂–E ₁)|c ₂|²/|c ₁|²]. Functions are introduced which allow determination of a ₁, b ₁ and lower bounds to E ₁.     

Silver Electrodeposition from Cyanide Solutions: Effect of Lead Ions

Effect of lead hydroxy compounds on the process of electrodeposition of silver from cyanide electrolytes is studied on an electrode whose surface is renewed in solution by cutting off a thin layer of metal. This permitted to perform the study on both the freshly renewed electrode and at controlled values of the time of the electrode contact with solution t. Shown is that on the freshly renewed electrode (t<1 s) the presence in the solution of lead ions in concentrations c ₁ on the order of 10^–5 M leads to the process depolarization only in the initial portion of a polarization curve. With c ₁ increased to 10^–4 M the effect of depolarization extends on the entire polarization curve. Keeping the electrode in solution after the renewal of the metal surface magnifies depolarization, and the greater the concentration c ₁, the shorter the time period t required to achieve the same effect. These regularities are attributed to catalytic influence of lead adatoms, whose surface concentration depends on c ₁ and t, as well as on the intensity of their incorporation in the silver deposit.