Wetting transitions of asymmetric binary polymer mixtures

We examine the effect on surface-wetting phase transitions in polymer mixtures when the degrees of polymerization of the two components are different. It has been demonstrated by Schmidt and Binder (J. Phys. (Paris) 46 , 1631 (1985)) that in a symmetric polymer mixture a second-order wetting transition occurs if the wall-polymer interaction f(ϕ₀) has a negative curvature f″(ϕ₀), where ϕ₀ is the surface volume fraction of the polymer component preferred by the wall. We found that in an asymmetric mixture this is not necessarily the case.     

Spinodal decomposition in asymmetric polymer mixtures

We present a preliminary numerical study of spinodal decomposition in an asymmetric polymer mixture, i.e., of polymer with different chain lengths, in three dimensions with full Flory-Huggins-de Gennes free energy, numerically integrating the time evolution equations for the conserved order parameter. For the sake of comparison, we also present a numerical study of the symmetric polymer mixture. The results indicate that the scaled structure factor for the asymmetric polymer mixture is much broader than that of a symmetric polymer mixture. It is interesting that the growth exponents are not symmetric around the critical quench, i.e., growth exponents on the two sides of the critical composition are different. In addition to that, the magnitudes of the pair correlation functions of asymmetric mixtures are very small for x larger than the characteristic domain size r_g and the oscillations seen in the symmetric mixture are almost absent. We have attributed this finding to the rough interfaces and broader domain size distribution in the phase separated asymmetric polymer mixtures. Therefore, the simulation reveals that the asymmetry plays an important role for the spinodal decomposition dynamics of polymer mixtures.     

Coupling of the phase and relaxation transitions in polymer mixtures

The coupling and the competition of two phase transitions (demixing and crystallization) and the coupling of both demixing and vitrification are investigated during phase transformations under far-from-equilibrium conditions. The coupling leads to formation of the different non-equilibrium morphologies and to kinetic pecularities of phase transformations.     

Multiple glass transitions and local composition effects on polymer solvent mixtures

Recent differential scanning calorimetry (DSC) results on polystyrene–solvent mixtures show two distinct glass transitions whose positions and widths vary with composition. Parallel work on the dynamic response in polymer blends has focused on how segmental mobilities are controlled by local composition variations within a “cooperative volume” containing the segment. Such variations arise from both chain connectivity and composition fluctuations. We account for both using a lattice model for polymer–solvent mixtures that yields the composition distribution around polymer and solvent segments. Insights from our lattice model lead us to simplified calculations of the mean and variance of local composition, both in good agreement with lattice results. Applying our model to compute DSC traces leads to an estimate of the cooperative volume, since a larger cooperative volume both reduces the biasing effect of connectivity, and narrows the composition distribution. Comparing our results to data, we are able to account for the composition-dependent broadening with a cooperative length scale of about 2.5 nm. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 3528–3545, 2006     

Kalman filtering of data from first- and second-order kinetics

The Kalman filter algorithm was used to process data obtained in the simultaneous determination of species following first- and second-order kinetics. The performance of the algorithm in the quantification of chemical components from simulated data was assessed, and the influence of various parameters involved was estimated. The algorithm was applied to the resolution of cysteine-ascorbic acid and glutathione-ascorbic acid mixtures where the ascorbic acid followed pseudo first-order kinetics and the amino acids second-order kinetics in the reaction with the copper(II)-neocuproine system. Some features of the determinations (namely, afforded concentration ratios, accuracy and precision) are discussed.     

Studies of first- and second-order phase transitions in LC methacrylic monomers based on the ω-hexyloxysalicylaldimine group

The synthesis and phase characterization of two liquid crystalline methacrylic monomers based on the ω-hexyloxysalicylaldimine group with octyl and decyloxy chain substitutions is presented. The liquid crystalline materials were characterized by polarizing optical microscopy, differential thermal analysis and X-ray diffractometry. Nematic and tilted smectic C phases were observed in the compounds. Their liquid crystalline properties where compared with previously studied samples of homologous compounds. In contrast to previous results, this structural modification induces pronounced enantiotropic first-order phase transitions between nematic and smectic C mesophases. A correlation between the phase transition behaviour and structural features of the sample is included.     

Static and dynamic first- and second-order properties by variational wave functions

The problem of the evaluation of first- and second-order energies by the use of arbitrary variational wave functions is examined in detail for time-independent perturbations as well as for time-dependent perturbations. By using a compact formalism the general formulae to be used for the case of a fully optimized set of variational parameters are readily obtained and the most prominent features are examined. The generality of the approach is tested by showing how some widely used methods are obtained by using particular types of variational wave functions. The case of incompletely optimized sets of variational parameters is examined examined extensively and several approaches at different levels of approximation are proposed. Emphasis is put upon the importance of considering, in the calculation of higher-order energies, the variational parameters which may be of negligible importance, and thus often neglected, in the absence of perturbations.     

Analogues in clusters of second-order transitions?

The question of existence and nature of a finitesystem analogue of a second-order phase transition in molecular clusters is discussed. By means of constant-energy molecular dynamics, we have simulated the phase transitions of various free clusters of TeF₆6 during cooling and heating. Structural changes have been recognized by changes of slope of the caloric curve and by the distributions of the molecular axes of symmetry. The structure seen at about 160K is an orientationally disordered phase. It transforms in two steps to an orientationally ordered structure as cluster cools: 1) an intermediate structure with partial alignment of the molecular axes of symmetry is formed at about 80 K; 2) almost all molecules align their axes of symmetry. We interpret the appearance of the intermediate phase to be a result of an ordering-displacement coupling. In addition, a size-dependent Coriolis force has been identified as another cause generating a metastable phase. As the number N of molecules in a cluster increases, this force decreases as 1/N. We associate the hysteresis of the caloric curve with the finite-size effects and critical slowing down, typical of second order transitions.     

From Langmuir kinetics to first- and second-order rate equations for adsorption

So far, the first- and second-order kinetic equations have been most frequently employed to interpret adsorption data obtained under various conditions, whereas the theoretical origins of these two equations still remain unknown. Using the Langmuir kinetics as a theoretical basis, this study showed that the Langmuir kinetics can be transformed to a polynomial expression of dtheta t /d t = k 1(theta e - theta t ) + k 2(theta e - theta t ) (2), a varying-order rate equation. The sufficient and necessary conditions for simplification of the Langmuir kinetics to the first- and second-order rate equations were put forward, which suggested that the relative magnitude of theta e over k 1/ k 2 governs the simplification of the Langmuir kinetics. In cases where k 1/ k 2 is greater than theta e or k 1/ k 2 is very close to theta e, adsorption kinetics would be reasonably described by the first-order rate equation, whereas the Langmuir kinetics would be reduced to the second-order equation only at k 1/ k 2 < theta e. It was further demonstrated that both theta e and k 1/ k 2 are the function of initial adsorbate concentration ( C 0) at a given dosage of adsorbent, indicating that simplification of the Langmuir kinetics indeed is determined by C 0. Detailed C 0-depedent boundary conditions for simplifying the Langmuir kinetics were also established and were verified by experimental data.     

Phase transitions in chlorobenzene-cis-decalin mixtures

The dielectric constant ?' and loss tangent tan δ of chlorobenzene-cis-decalin mixtures have been measured in the temperature range 77 K to 330 K and frequency range 0.1 to 100 kHz. On cooling, ?' increases with decreasing temperature upto about 135 K, after which it drops rapidly with decreasing T followed by a slow decrease. This indicates that the liquid mixture goes to an amorphous phase which transforms to a glass phase of restricted dipole rotation below T_g; however, the peak in ?' is due to relaxation in the amorphous phase (α relaxation) and does not give an exact T_g. On heating, the behaviour of the cooling curve is retraced upto 160 K, after which ?' drops suddenly to a value lower than that at 77 K in the glass phase. This indicates the transition to a crystalline phase in which dipole rotational freedom is completely lost. The crystalline phase changes to a eutectic liquid phase of high ?' at a temperature (200 K) lower than the melting point of chlorobenzene and cis-decalin. Dielectric dispersion is observed only in the glass and amorphous phases. The dielectric relaxation time is independent of the concentration of chlorobenzene.     

Thermal transitions and polymer/polymer miscibility

Poly(vinyl chloride) was blended with ethylene-vinyl acetate copolymer containing 70 wt% of vinyl acetate. The system shows a single glass transition temperature for all compositions, indicating their miscibility. TheT _g vs. composition curves display an inflection, which changes with the chemical environment of the initial solution. The best fit to the shape of the curve was well reproduced by the Kovacs-Braun equation. The T _g values reveal local heterogeneity, which means no total miscibility at a molecular level. Negative values of the Flory-Huggins interaction parameter were obtained from the calorimetric data.Support for this research by CNP_q, FINEP and CAPES is appreciated.     

Simultaneous determination of manganese and zinc in mixtures using first- and second-derivative spectrophotometry

A new direct spectrophotometric determination of manganese with 5,8-dihydroxy-1,4-naphthoquinone (naphthazarin,NAZA) is reported. Absorption maximum, molar absorptivity and Sandell's sensitivity of 1:2 (M:L) complex are 695 nm, 1.88x10(4) l mol(-1) cm(-1) and 2.92 ng cm(-2), respectively. A linear calibration graph is obtained up to a concentration of 7.2 mug ml(-1) of manganese. The optimum range for determination (Ringbom) is between 0.20 and 6.8 mug ml(-1). A rapid method for simultaneous determination of manganese and zinc in their mixture using derivative spectra is described. The range 0.28-5.6 mug ml(-1) manganese could be determined in the presence of 0.33-6.8 mug ml(-1) zinc and vice versa. The developed method was applied to the simultaneous spectrophotometric determination of manganese and zinc in some synthetic mixtures and was found to give satisfactory results.     

A method for computer analysis of kinetics of competing first- and second-order reactions

Competing first- and second-order reactions of transient molecular species (e.g., triplet states and free radicals) are a common occurrence in kinetic studies such as flash photolysis and pulse radiolysis. We have developed a method for analyzing the decay kinetics of any species (Y) whose disappearance is described by ?dY/dt = k₁Y + k₂Y². The computer program (written in time-sharing BASIC) employs an iterative technique to obtain the least-squares estimates of the three parameters in the integrated rate equation.     

Phase transitions in mixtures of a side-on-side chain liquid crystalline polymer and low molar mass nematic liquid crystals

Miscibility phase diagrams of mixtures of side-on side chain liquid crystalline polymers (s-SCLCP) and low molar mass liquid crystals (E48 and E44) have been established by means of polarized optical microscopy and light scattering. E48 and E44 are cyanobiphenyl-based eutectic nematic liquid crystal (LC) mixtures with nematic-isotropic transition temperatures of 93 and 105 C, respectively. The phase diagram of the s-SCLCP/E48 system reveals the coexistence of an isotropic nematic region and a single nematic phase in order of descending temperature. The single nematic phase suggests that the pair is miscible in the nematic region. On the other hand, the s-SCLCP/E44 mixture shows liquid liquid and nematic nematic coexistence phases, suggestive of the immiscibility character of the pair. These nematic phase diagrams of the s-SCLCP/E48 and s-SCLCP/E44 have been analysed in the context of the combined Flory-Huggins (FH) free energy for isotropic mixing and the Maier-Saupe (MS) free energy for nematic ordering of the mesogens. This combined FH/MS theory is capable of predicting the observed nematic phase diagrams consisting of liquid liquid, liquid nematic, nematic nematic, and the pure nematic regions. The change of colour accompanying the appearance and disappearance of the inversion walls may be attributed to the temperature dependence of birefringence.     

Liquid-liquid phase equilibria in polymer solutions and polymer mixtures

The pressure dependence of liquid-liquid equilibria in weakly interacting binary macromolecular systems (homopolymer solutions and blends) will be discussed. The common origin of the separate high-temperature/low-temperature and high-pressure/low-pressure branches of demixing curves will be demonstrated by extending the study into the region of metastable liquid states including the undercooled, overheated and stretched states (i.e. states at negative pressures). The seemingly different response of the UCST-branch of solutions and blends when pressurized (pressure induced mixing for most polymer solutions, pressure induced demixing for most blends) will be explained in terms of the location of a hypercritical point found either at positive (most solutions) or negative pressure (most blends). Further, it is shown that the pressure dependence of demixing of homopolymer solutions and blends may be described using a ‘master-curve’ which, however, is sometimes partly masked by degradation or by vapour-liquid and/or solid-liquid phase transitions. Experimental results demonstrating the extension of liquid-liquid phase boundary curves into the metastable regions will be presented, and the existence of solubility islands in the vicinity of the hypercritical points discussed.     

Phase transitions in polymer brushes

Liquid crystalline ordering in planar polymer brushes is investigated theoretically by numerical calculations within a self-consistent field approximation. The brushes are formed by macromolecules with mesogenic groups in main chain and immersed in a solvent. Existence of a microphase segregated brush (MSB) regime with a collapsed orientationally ordered intrinsic sublayer and a swollen external sublayer is shown. At small grafting density, the transition from a conventional brush state to the microphase segregated state is a jump-wise first order phase transition for a finite chain length (N). The magnitudes of the jumps in the average characteristics of the brush tend to zero in the limit N → ∞ since this transition occurs only in a vanishingly small part (∝ N^−1/2) of the brush. High compressibility of MSB brush is demonstrated. The origin of phase transition in planar brushes is discussed.     

Hydrogen bonding in polymer mixtures

The enthalpy–infrared frequency shift correlation for simple acids and bases is extended to study hydrogen bonding in polymer systems. The acidity of a polymer is calibrated by comparing the shifts in hydroxyl absorption frequency of the acidic polymer when mixed with a series of bases with the corresponding spectral shifts of known acids with the same bases. The basicity of a polymer is calibrated by measuring the hydroxyl frequency shifts of known acids when mixed with the basic polymer. For polymers containing carbonyl groups, the shift in carbonyl absorption is also a measure of basicity. The acidity and basicity constants obtained for polymers are in good agreement with the values for small-molecule analogs. The enthalpies of hydrogen bond formation in polymer mixtures are calculated from the acidity or basicity constants.     

Analysis of mixtures of purines and pyrimidines by first- and second-derivative ultraviolet spectrometry

Zero-order, first-derivative and second-derivative ultraviolet absorption spectra of a series of purines, pyrimidines and their binary mixtures in aqueous solution have been recorded at 298 K. It is shown that second-derivative spectra can be used for the identification of eight mixtures of purines and pyrimidines. Several graphical procedures are tested for evaluating derivative spectra in quantitative measurements of single compounds and mixtures. Linear log-log calibration plots are obtained with correlation coefficients generally larger than 0.99. Second-derivative spectra appear to provide a precise and simple method for determination of purines and pyrimidines, at concentrations ranging between 5 x 10(-6) and 5 x 10(-4)M.     

Structural ordering transitions in ionic liquids mixtures

Differential capacitance curves for the electrical double layer (EDL) of mixtures of imidazolium-based ionic liquids (ILs) with a common cation (1-ethyl-3-methylimidazolium, [C₂MIM]⁺) and two different anions (bis(trifuoromethylsulfonyl)imide, [Tf₂N]⁻) and tris(pentafluoroethyl)trifluorophosphate [FAP]⁻) were obtained. Sharp peaks in the differential capacitance curves were observed for a small range of mixtures compositions at positive charge densities. The appearance and position on the potential scale of the peaks were found to be dependent on the mixture composition and temperature. The occurrence of these phenomena is interpreted as corresponding to an abrupt change in the EDL structure arrangement as a result of a complex interplay of electrostatic interactions and steric effects. The use of the non-structured mercury electrode allowed to decouple the eventual potential induced restructuring occurring at the double layer from the well-known surface reconstruction effects often reported for ionic liquids in contact with single crystal face electrodes.