Steric interactions between finite objects and end-grafted polymer chains: a two-dimensional mean-field analysis

We examine the usefulness of a two-dimensional self-consistent mean-field theory for predicting polymer-induced forces between a finite object and a surface. The predictions are compared with scaling results for the compression of a single, end-grafted chain by a disk and for the compression of a brush with an athermal wall. For the former, the mean-field predictions agree with scaling theory and, in addition, provide the necessary prefactor in the scaling expressions for the Helmholtz potential and force of compression. For the brush, the mean-field results agree with the Alexander-de Gennes scaling result at moderate compressions and also provide an analytical expression for the force without any unknown parameters. We also use the mean-field theory to examine the interaction of a model bacterium with a planar substrate and show that steric interactions due to a single polymer chain alone can dominate van der Waals attraction under typical practical conditions and thus prevent bacterial adhesion to the surface.     

Nonisothermal decomposition of methyl nitrate: Anomalous reaction order and activation energies and their correction

Methyl nitrate decomposition is accompanied by self-heating. Using very fine thermocouples, direct measurements of excess temperatures have been made to establish the intensity and extent of self-heating in nonisothermal reaction. The measurements are displayed as contourlines of equal degrees of temperature excess on the pressure–temperature ignition diagram. A twofold kinetic investigation has been made of the overall reaction. One part concentrates on achieving isothermal conditions and full characterization of intermediate products. It uses mass-spectrometric analyses both to establish stoichiometry throughout decomposition and to validate velocity constant measurements derived from continuous pressure–time records. The best value for E = 151 ± 3 kJ/mol is about 10 kJ/mol less than previously. The other part deliberately invades the nonisothermal region to test the qualitative and quantitative predictions of theory (1) that uncorrected reaction orders and activation energies will exceed their isothermal values, (2) that their relative excess (δn/n, δE/E) will be about the same, and (3) that they will be dependent in a simple and predictable way on the reduced excess central temperature.     

Study of the binary mixtures of {monoglyme + (hexane,cyclohexane, octane,dodecane)} by ECM-average and PFP models

Excess molar volumes and excess permittivity of binary mixtures involving monoglyme and alkanes, such as n-hexane, cyclohexane, n-octane and n-dodecane, were calculated from density and relative permittivity measurements for the entire composition range at several temperatures (288.15, 298.15 and 308.15) K and atmospheric pressure. The excess permittivity was calculated on the basis of a recent definition considering the ideal volume fraction. Empirical equations for describing the experimental data in terms of temperature and concentration are given. The experimental values of permittivity have been compared with those estimated by well-known models from literature. The results have indicated that better predictions are obtained when the volume change on mixing is incorporated in these calculations. The contribution of interactions to the excess permittivity was analysed by means of the ECM-average model. The Prigogine–Flory–Patterson (PFP) theory of the thermodynamics of solutions was used to shed light on the contribution of interactions to the excess molar volume. The work concludes with an interpretation of the information given by the theoretical models and the behaviour of both excess magnitudes.     

Modeling spreading-pressure-dependent binary gas coadsorption equilibria using gravimetric data

The present work proposes an approach to building nonideal coadsorption models in a thermodynamically consistent fashion, including the effects of pressure and spreading pressure, from simple gravimetric measurements. This is an "inverse problem" of parameter determination from appropriate and limited experimental data.The approach relies on the nonideal adsorbed solution theory, which includes activity coefficients and their dependence on spreading pressure, and on an original form of the excess Gibbs energy of mixing. A fully analytical development leads to explicit relations between the infinite dilution activity coefficients and three sets of independent information: the parameters of this excess Gibbs function, the limiting slopes of measured binary gravimetric curves at two different total pressures, and the properties of the single-component isotherms. From there, the four parameters of the model may be determined quasi-analytically and uniquely. The method is exemplified with the coadsorption of CO(2) and CH(4) on activated carbon, and a heterogeneous set of data. On one hand, the total adsorbed mass of the two components is measured at 1 bar by "incremental gravimetry." On the other hand, data obtained from independent batch-type equilibration measurements at 2 bar allow a comparison of calculated and measured data for the individual component concentrations. It is emphasized, however, that only total adsorbed mass data are needed for application of the method.     

Equation of state of poly(dimethylsiloxane) melts

The pressure–volume–temperature (PVT) properties of three commercial samples of poly(dimethylsiloxane) are studied experimentally and theoretically in the temperature range 25–150°C and for pressure to ∼ 3 kbar. The Tait equation is employed to represent the data at elevated pressure. Isothermal compressibilities are computed for the three samples. The melt data are analyzed in terms of the Simha–Somcynsky hole theory, and scaling parameters of pressure, volume, and temperature are obtained. Satisfactory agreement between theory and experiment is found over the entire range of experimental pressures. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 841–850, 1998     

A scaling theory for number-flux distributions generated during steady-state coagulation and settling and application to particles in Lake Zurich,Switzerland

In this study, we extend the established scaling theory for cluster size distributions generated during unsteady coagulation to number-flux distributions that arise during steady-state coagulation and settling in an unmixed water mass. The scaling theory predicts self-similar number-flux distributions and power-law decay of total number flux with depth. The shape of the number-flux distributions and the power-law exponent describing the decay of the total number flux are shown to depend on the homogeneity and small i/j limit of the coagulation kernel and the exponent kappa, which describes the variation in settling velocity with cluster volume. Particle field measurements from Lake Zurich, collected by U. Weilenmann and co-workers (Limnol. Oceanogr.34, 1 (1989)), are used to illustrate how the scaling predictions can be applied to a natural system. This effort indicates that within the mid-depth region of Lake Zurich, clusters of the same size preferentially interact and large clusters react with one another more quickly than small ones, indicative of clusters coagulating in a reaction-limited regime.     

Spreading of liquid drops over dry surfaces

Spreading of thin, axisymmetric, non-volatile, Newtonian liquid drops over a dry, smooth, flat solid surface is considered both theoretically and experimentally in the case of complete wetting. The drop profile is solved analytically by matching the “outer” solution for large film thicknesses, where only the capillary effects are important, with the “inner” solution for small film thicknesses, where the viscous and disjoining pressure effects are comparable to capillary effects. It is shown that the apparent radius of the wetted spot, the apex height of the drop, and the apparent advancing dynamic contact angle follow different power laws in time and the advancing dynamic contact angle follows a power law in capillary number. Both the prefactor and the exponent of each power law are derived theoretically. Good agreement between the theory predictions and experimental measurements is shown for both the prefactor and exponent of each power law. It is necessary to emphasize that the theory suggested does not include any fitting parameters.     

The inflection point in the pressure dependence of viscosity under high pressure: a comprehensive study of the temperature and pressure dependence of the viscosity of propylene carbonate

The pressure dependence of the prototypical glass-former propylene carbonate has been investigated over a broad range of temperature and pressure that were inaccessible in previous investigations using dielectric spectroscopy. We find that the viscosity measurements validate the scaling relation, eta(T,V)=J(TV gamma), with a scaling parameter gamma close to that found from dielectric relaxation measurements. In the pressure dependence of the viscosity, we observe an inflection point in the log eta versus P response, similar to that found previously for other materials. However, this inflection has never been observed in dielectric relaxation measurements. Using the scaling property above, it is possible to determine the behavior of the dielectric relaxation time in this otherwise inaccessible experimental range and compare it with the viscosity measurements. We find that the behaviors of eta and tau are very similar, and a very good agreement between the function phi P calculated for these two quantities is found. Starting from the validity of the scaling properties, we show that the inflection point in the pressure dependence of the viscosity can be attributed to the convolution of the pressure dependences of the compressibility kappa T and the apparent activation energy at constant volume EV.     

Thermodynamic properties of binary mixtures containing aldehydes. II. Liquid-vapor equilibria in normal or branched alkanal + normal alkane mixtures: Analysis in terms of a quasichemical group-contribution model

Recent liquid-vapor equilibrium data for three alkanal + n-alkane mixtures are examined on the basis of the surface-interaction version of the quasichemical group-contribution theory used in Part I to correlate and predict excess enthalpies and excess Gibbs energies for such mixtures. The predictions prove to be accurate to better than 10%. Using the new data, revised interaction parameters are proposed for the estimation of liquid-vapor equilibrium for normal or branched alkanal + normal alkane mixtures.     

A Corresponding-state Model for Predicting Surface Tension

A generalized corresponding-state model based on two reference fluids was developed for the prediction of surface tensions for non-polar and weakly polar pure fluids and their binary mixtures. Four parameters,po, Tc, Vc and ω, were used in this model, and the acentric factor ω was used as a scaling parameter. This model has been tested for 69 pure substances and 20 binary mixtures; the average absolute deviations are 0. 28 and 0. 20 mN/m, respectively. The results indicate that the predictions by means of this model were in good agreement with experimental data. In addition, the calculated deviation would increase with the excess surface tension rising, and if the excess surface tension is less than 3 mN/m, the prediction will be good and credible.     

Thermodynamics and partitioning of homopolymers into a slit-A grand canonical Monte Carlo simulation study

Grand canonical ensemble Monte Carlo simulation (GCMC) combined with the histogram reweighting technique was used to study the thermodynamic equilibrium of a homopolymer solution between a bulk and a slit pore. GCMC gives the partition coefficients that agree with those from canonical ensemble Monte Carlo simulations in a twin box, and it also gives results that are not accessible through the regular canonical ensemble simulation such as the osmotic pressure of the solution. In a bulk polymer solution, the calculated osmotic pressure agrees very well with the scaling theory predictions both for the athermal polymer solution and the theta solution. However, one cannot obtain the osmotic pressure of the confined solution in the same way since the osmotic pressure of the confined solution is anisotropic. The chemical potentials in GCMC simulations were found to differ by a translational term from the chemical potentials obtained from canonical ensemble Monte Carlo simulations with the chain insertion method. This confirms the equilibrium condition of a polymer solution partition between the bulk and a slit pore: the chemical potentials of the polymer chain including the translational term are equal at equilibrium. The histogram reweighting method enables us to obtain the partition coefficients in the whole range of concentrations based on a limited set of simulations. Those predicted bulk-pore partition coefficient data enable us to perform further theoretical analysis. Scaling predictions of the partition coefficient at different regimes were given and were confirmed by the simulation data.     

Equilibrium conformational dynamics of a polymer in a solvent

Molecular dynamics simulations were used to study the conformational dynamics of a bead-spring model polymer in an explicit solvent under good solvent conditions. The dynamics of the polymer chain were investigated using an analysis of the time autocorrelation functions of the Rouse coordinates of the polymer chain. We have investigated the variation of the correlation functions with polymer chain length N, solvent density rho, and system size. The measured initial decay rates gamma(p) of the correlation functions were compared with the predictions from a theory of polymer dynamics which uses the Oseen tensor to describe hydrodynamic interactions between monomers. Over the range of chain lengths considered (N = 30-60 monomers), the predicted scaling of gamma(p) proportional to N(-3nu) was observed at high rho, where nu is the polymer scaling exponent. The predicted gamma(p) are generally higher than the measured values. This discrepancy increases with decreasing rho, as a result in the breakdown in the conditions required for the Oseen approximation. The agreement between theory and simulation at high rho improves considerably if the theoretical expression for gamma(p) is modified to avoid sum-to-integral approximations, and if the values of (R(p)2), which are used in the theory, are taken directly from the simulation rather than being calculated using approximate scaling relations. The observed finite-size scaling of gamma(p) is not quantitatively consistent with the theoretical predictions.     

Thermodynamics of the xenon + methyl chloride system

The total vapour pressure of the xenon + methyl chloride system has been measured as a function of composition at 175.44 and 182.32 K. The resulting data have been used to evaluate the excess Gibbs functions G^E at the same temperatures. The excess enthalpy and excess molar volume have also been measured at 182.32 K. The system shows large positive deviations from Raoult's law but negative volumes on mixing. These results are compared with theoretical predictions of a recent molecular theory and of standard engineering methods. The calculations show the superiority of the molecular theory over more empirical procedures such as those based on the Redlich-Kwong equation of state or the regular-solution model.     

Experimental and theoretical study of excess molar volumes and enthalpies for the ternary mixture butyl butyrate + 1-octanol + decane at 308.15 K

This paper reports measurements on excess thermodynamic properties for the ternary system: butyl butyrate+1-octanol+decane at the temperature 308.15 K and atmospheric pressure.The binary and ternary experimental data were correlated using the Redlich-Kister and Cibulka equation, respectively. Experimental values were compared with the predictions obtained by several contribution models and several empirical equations.     

Onset of slow dynamics in difluorotetrachloroethane glassy crystal

Complementary neutron spin-echo and x-ray experiments and molecular-dynamics simulations have been performed on difluorotetrachloroethane (CFCl2-CFCl2) glassy crystal. Static, single-molecule reorientational dynamics and collective dynamics properties are investigated. Our results confirm the strong analogy between molecular liquids and plastic crystals. The orientational disorder is characterized at different temperatures and a change in the nature of rotational dynamics is observed. A careful check of the rotational diffusion model is performed using self-angular correlation functions Cl with high l values and compared to results obtained on molecular liquids composed of A-B dumbbells. Below the crossover temperature at which slow dynamics emerge, we show that some scaling predictions of the mode coupling theory hold and that alpha-relaxation times and nonergodicity parameters are controlled by the nontrivial static correlations.     

Thermodynamic studies of molecular interactions in aqueous alpha-cyclodextrin solutions: application of McMillan-Mayer and Kirkwood-Buff theories

Osmotic vapor pressure and density measurements were made for aqueous alpha-cyclodextrin (alpha-CD) solutions in the temperature range between 293.15 and 313.15 K. The experimental osmotic coefficient data were used to determine the corresponding activity coefficients and the excess Gibbs free energy of solutions. Further, the activity data obtained at different temperatures along with the enthalpies of dissolution (reported in the literature) were processed to obtain the excess enthalpy and excess entropy values for the solution process. The partial molar entropies of water and of alpha-cyclodextrin were calculated at different temperatures and also at different concentrations of alpha-CD. Using the partial molar volume data at infinite dilution, the solute-solvent cluster integrals were evaluated which yielded information about solute-solvent interactions. The application of McMillan-Mayer theory of solutions was made to obtain osmotic second and third virial coefficients which were decomposed into attractive and repulsive contributions to solute-solute interactions. The second and third osmotic virial coefficients are positive and show minimum at 303.15 K. The Kirkwood-Buff (KB) integrals G(ij), defined by the equation G(ij) = f(infinity)0 (g(ij)- 1)4pir(2) dr, have been evaluated using the experimental osmotic coefficient (and hence activity coefficient) and partial molar volume data. The limiting values of KB integrals, G(ij)(0) are compared with molecular interaction parameters (solute-solute i.e., osmotic second virial coefficient) obtained using McMillan-Mayer theory of solutions. We found an excellent agreement between the two approaches.     

内压与非电解质溶液理论

本文用热学方法,为非电解质溶液建立了一个无热溶液理论.这个理论不包含任何可调参数,完全可由纯组分的性质来预测液体混合物的过量Gibbs自由能, 倘若以知混合物的体积,还可预测其过量焓和过量熵.而这些纯组分的性质, 都与液体的内压有关, 对37 个二元系统预测结果表明, 实验值的一致性大多优于Scatchrd-Hilderand正规溶液理论及其修正型式SHFH理论.     

Scaling behavior of a brush-homopolymer interface in the limit of high grafting density

The interface between a polymer brush and a chemically equivalent homopolymer is examined using self-consistent field theory (SCFT). Focusing on ultrahigh grafting densities, we extract how the properties scale with the brush thickness, L, and compare with predictions based on strong-stretching theory (SST). Although the scaling exponents are consistent, the overall agreement is poor. We attribute this to the inaccurate way the SST-based calculation treats chain fluctuations at the extremity of the brush. This accounts for a previous disagreement between SCFT and SST in regards to autophobic dewetting, and brings into question a number of other SST predictions. Our conclusion is that SST requires a more sophisticated treatment of finite-stretching corrections, along the lines of that proposed by Likhtman and Semenov [Europhys. Lett. 51, 307 (2000)].     

Molecular interactions of cationic and anionic surfactants in mixed monolayers and aggregates

The properties of anionic-rich and cationic-rich mixtures of CTAB (cetyltrimethylammonium bromide) and SDS (sodium dodecyl sulfate) were investigated with conductometry and surface tension measurements and by determining the surfactant NMR self-diffusion coefficients. The critical aggregate concentration (CAC), surface tension reduction effectiveness(gamma(CAC)), surface excess(Gamma(max)), and mean molecular surface area (A(min)) were determined from plots of the surface tension (gamma) as a function of the total surfactant concentration. The compositions of the adsorbed films (Z) and aggregates (chi) were estimated by using regular solution theory, and then the interaction parameters in the aggregates (beta) and the adsorbed film phases (beta(sigma)) were calculated. The results showed that the synergism between the surfactants enhances the formation of mixed aggregates and reduces the surface tension. Further, the nature and strength of the interaction between the surfactants in the mixtures were obtained by calculating the values of the following parameters: the interaction parameter, beta, the size parameter, rho, and the nonrandom mixing parameter, P*. These results indicate that in ionic surfactant mixtures the optimized packing parameter has the highest value and that the size parameter can be used to account for deviations from the predictions of regular solution theory. It was concluded that, for planar air/aqueous interfaces and aggregation systems, this nonideality increases as the temperature increases. This trend is attributed to the increased dehydration of the surfactant head groups that results from increases in temperature. Further, our conductometry measurements show that the counterion binding number of mixed micelles formed in mixtures with a high CTAB content is different to those with a high SDS content. This difference is due to either their different aggregation sizes or the different interactions between the head groups and the counterions.