Modelling the precipitation of copper oxalate aggregates

The precipitation of copper oxalate has been studied in a batch reactor. Like many other systems, the morphology of these particles suggests that they were formed by an aggregation mechanism. A mathematical model has been developed to predict particle-size distributions grown in a batch reactor, which accounts for growth by two competing mechanisms, i.e., atomistic growth and particle aggregation. The results of this model are in good agreement with experimental observations for the precipitation of copper oxalate aggregates and other spherical aggregation systems cited in the literature.     

Micelle aggregation numbers from colligative properties

An equilibrium model has been developed to derive micelle aggregation numbers n from colligative properties of surfactant solutions, with special regard to freezing point depression. The introduction of a mass action approach in the solute activity equation allows to get aggregation numbers close to those obtained from light scattering. The model can be applied with small formal changes to ionic and nonionic surfactants.     

Overall crystallization kinetics of thin polymer films. General theoretical approach. I. Volume nucleation

A general theoretical approach of the overall crystallization kinetics of thin polymer films is developed. This new model makes it possible to calculate the evolution of the transformed volume fraction anywhere in the film, whatever the cooling conditions are. In its isothermal limit this model is equivalent to previous approaches which have been well verified by a computer simulation. In conclusion, it is pointed out that both isothermal and anisothermal determinations of crystallization kinetic parameters are greatly dependent on the sample thickness.     

The theory of flexoelectric effect of polymer glasses

Electric polarization induced by a nonhomogenous deformation flied — flexo-electricity — has has been studied on a model of polymer in the glassy state. The results are expressed in terms of phenomenological coefficients, which are analogical to the electric polarizability. It is found that a gradient of the tensor of small rotation, and not just that of small deformation contributes to the polarization. Dedicated to Prof. Dr. W. Pechhold on the occasion of his 60th birthday     

X-ray investigations of the formation of core-fibrils crystallized out of the oriented melt

Crystallization models for the formation of core-fibrils crystallized from the oriented melt are discussed by comparing results from X-ray experiments with theoretical predictions. Two sets of polymer blends, the systems iPP/PB-1 and iPP/aPP have been measured. From wide angle X-ray scattering, the thicknesses of the core-fibrils, lattice distortions, and unit-cell parameters have been determined. Interface distribution functions have been used to evaluate the axial morphology of the fibers from meridional small angle X-ray scattering curves. It appears that the morphological predictions made by the crystallization models of Pennings and of Hoffman cannot be confirmed by the experimental findings. The diffusion model proposed by Petermann partially describes the morphological properties of the core-fibrils.     

Mathematical model of suspension flocculation kinetics

A mathematical model of suspension flocculation kinetics which describes its evolution in a wide time interval, and later stages is presented. The rate constant of floc formation has been found. The calculated dependence of particle number in volume unit on time correlates well with experimental data.     

A phenomenological model of photoprecipitation in a-Se colloid solutions

An attempt has been made in this study to develop a physical model for the photoprecipitation and photoaggregation effects in amorphous Se (a-Se) colloids. The theory explains in basic terms the experimental time dependence of the precipitated elemental Se concentration. Several kinetic parameters were evaluated by correlating the experiment to theory, subject to strong light intensity and narrow beam approximations. The results were used to quantify and clarify several further features of photoprecipitation in a phenomenological way.     

Diffusion of single elements and steric limitations in kinetic theory of nucleation and crystallization

Translational and rotational diffusion equation of single elements in solution in the external orienting potential forces has been formulated. The equation should govern long-range diffusion effects in the kinetics of nucleation and crystal growth. Boundary conditions, adequate to the reversible reaction of cluster growth typical for kinetic model of nucleation and accounting for steric limitations, has been proposed. Uniaxial single elements in uniaxial orienting force field are considered.Depression of the concentration of single elements at the cluster boundary as controlled by kinetic factors, is predicted i. e., chemical rate constants, finite translational and rotational diffusion, supercolling, and steric limitations. Effective rate constants, controlled by long-range diffusion of single elements at steric limitations present, have been used. Two dimensionless kinetic factors (i. e., reduced addition-reaction rate constant and reduced rotational diffusion constant), supercooling, and steric tolerance anlge range, control process kinetics and distribution of single elements in the cluster's surroundings. Rate reduction factor responsible for the effects of long-range diffusion at steric limitations present is defined and applied for kinetic models of nucleation and crystal growth in unoriented and oriented systems.Computation examples are performed for a wide range of the model variables, and rate reduction effects of several orders of magnitude are predicted. The dominating role ranges of particular model variables, i. e., kinetic, thermodynamic, or steric variables, are discussed.     

Small angle neutron scattering studies on micellar systems part 1. Ammonium octanoate,ammonium decanoate and ammonium perfluoroocatanoate

Small angle neutron scattering has been used to examine the size and shape of micelles of ammonium octanoate, ammonium decanoate and ammonium perfluoro-octanoate. Ammonium octanoate was found to form micelles with a micellar weight of 1640 and ammonium decanoate with a micellar weight of 12,576; both materials appeared to form spherical micelles. Ammonium perfluoro-octanoate formed micelles with a micellar weight of 17,610. Evidence from the scattering experiments suggested that the micelles were cylindrical and a model for the micelle is proposed.     

Shear field modification of strongly flocculated suspensions — Aggregate morphology

Rheological and microscopical studies have been made to elucidate the effects of shear fields on the morphology of concentrated, aggregated model colloids. The models employed are well-characterised, predominantly chargestabilised polymer latices, coagulated by the addition of excess electrolyte. Continuous shear rheological and viscoelastic measurements indicate a very significant decrease in shear yield stress, apparent viscosity and shear modulus following prolonged shearing.Electron microscopy reveals the source of these changes. Freshly coagulated suspensions form networks that are porous, strong and qualitatively similar to simulated structures for diffusion limited aggregation. Following protracted shearing, the network structure is rearranged to yield discrete, tightly packed aggregates with a characteristic size, which is principally a function of the primary particle size.     

Effects of thermal history on the rigid amorphous phase in poly(phenylene sulfide)

The rigid amorphous phase of semicrystalline poly(phenylene sulfide) (PPS) has been studied as a function of thermal history using scanning calorimetry, dielectric relaxation, density, and small-angle x-ray scattering (SAXS). Based on the new heat of fusion of perfect crystalline PPS, which is 26.7±0.8 cal/gram, the weight fraction of rigid amorphous phase is shown to be nearly twice as large as previously reported [1]. The mass fraction of the rigid amorphous phase ranges from 0.24 to 0.42 and is dependent upon thermal treatment. We have taken the approach of assuming a three-phase model for the morphology of semicrystalline PPS consisting of crystalline lamellae, mobile amorphous, and rigid amorphous components. Using this three-phase model, we determine that the average density of the rigid amorphous fraction is 1.325 g/cc, which is slightly larger than the density of the mobile amorphous phase fraction and was insensitive to thermal history. From the SAXS long period, the layer thicknesses of the mobile amorphous phase, rigid amorphous phase, and crystal lamellae were estimated. Only the lamellar thickness shows a systematic variation with thermal history, increasing with melt or cold crystallization temperature, or with decreasing cooling rate.     

The thermorheological complexity of photoelastic behaviour of 2-hydroxyethyl methacrylate — dodecyl methacrylate copolymers

The viscoelastic photoelastic behaviour of networks of 2-hydroxyethyl methacrylate — dodecyl methacrylate (DMA) copolymers in the main transition and rubberlike region was investigated. With increasing DMA content, photoelastic functions are quickly shifted to lower temperatures or shorter times; a detailed course of the functions suggests heterogeneity of the copolymers. Due to the existence of long side chains, optical function of all samples change the sign from positive to negative with increasing temperature. While the temperature dependences of the moduli of copolymers can be described by the two-phase Takayanagi model, the temperature dependences of optical functions cannot be described by using this model. It has been found, however, that the tempeature and time dependences of photoelastic functions can be described semiquantitatively by a three-phase model with a hypothetical statistical copolymer as the third component. The high values of the volume fraction of the hypothetical statistical copolymer found for the individual samples, suggest a considerable miscibility and a strong influence of the interphase boundary on the photoelastic behaviour of the copolymers.     

The exact shear modulus of particulates based on the concept of mesophase

An accurate relationship for the shear modulus of particulates is derived based on the Kerner model, but not using its approximate relations. Furthermore, the model takes into account the existence of the mesophase layer between the inclusions and the matrix, which acts as a smooth transition boundary layer between constituent materials. By applying Christensen's field to the Kerner model, modified by introducing the mesophase, the new model is liberated from any inconsistencies. Experimental evidence and application to a glass particle-epoxy resin-matrix composite indicated the superiority of the model over previous ones.     

Adsorption of polar substances from binary and ternary mixtures on silica gel

The adsorption isotherms of acetone and methyl ethyl ketone from binary and ternary mixtures in benzene and n-heptane on silica gel were measured. The experimental adsorption data are discussed on the basis of changes of the composition of mixed solvent (benzene + n-heptane) in ternary mixtures. It has been found that the different structures of the surface phase correspond to the system investigated. The marked dependence of the adsorption on the solvent character is demonstrated. For benzene and ternary (ketone + benzene + n-heptane) mixtures a mixed character of the surface phase is observed whose composition is determined by competition of liquid components for silica surface as well as its tendency to complex. Bilayer model of the surface phase gives a good representation of the experimental data for binary systems benzene + ketone.     

Numerical analysis of density gradient centrifugation profiles from eukaryotic DNA

A numerical method for the deconvolution of superimposed Gaussian distributions with a unique solution has been proposed by Medgyessy [10]. We have tested the usefulness of this method for the analysis of density gradient centrifugation profiles from eukaryotic DNA, which are normally composed from overlapping Gaussian distributed profiles of several subcomponents with different mean buoyant densities. From the analysis of human DNA and from model calculations we conclude that major subcomponents can be identified by this method, if they differ in their buoyant density by approximatly 0.005 g/ml. Minor components can only be identified if the total DNA has been fractionated according to buoyant density and the analysis is performed on the density profiles of the subfractions. This procedure represents a quick method to determine a reliable minimum number of subcomponents of DNA.This paper was presented at the VI. Symposium on Analytical Ultracentrifugation, Marburg, FRG, February 16–17, 1989.     

A model of flocculation by very-high-molecular-weight polymers

A simple model is proposed to describe flocculation of fine particles by high polymers. The model is based on the assumption that the number of colloid particles attached to a single polymer molecule is a random quantity, and that a minimum number of particles must be attached to a polymer molecule to trigger its removal from the system. The predictions of the model are confronted with experimental data concerning the stability of the system polyacrylamide-sol AgJ.     

Charge-transfer interaction of some pyridinium salts with hen egg-white lysozyme

The charge-transfer interaction of pyridinium salts with lysozyme and L-tryptophan has been investigated by visible absorption, circular dichroism and fluorescence spectroscopy. Four quaternized and substituted pyridinium salts were used as electron acceptors. L-tryptophan was used as a model compound of electron donor for the purpose of the comparison with lysozyme. The binding constants obtained from absorption and circular dichroism spectra were 2.0–13 M^–1 and the sequence of the magnitude was found as EPCl(1-ethylpyridinium chloride) < MPCl(1-methylpyridinium chloride) < MNCl(1-methylnicotinamide chloride) < MNMCl(1-methyl-3-carbomethoxypyridinium chloride), which could be explained by the electron affinity of the pyridinium salt. The fluorescence spectra of lysozyme and L-tryptophan in the absence and presence of pyridinium salts were interpreted by Stern-Volmer plot. The static constants thus determined were in agreement with the binding constants obtained by other methods.     

The orientational state of uniaxially stretched PMMA

Uniaxially stretched samples of PMMA were investigated by Brillouin Spectroscopy (BS). From the velocity of hypersound we could determine most of the elastic constants. Using a recently developed analysis [1] it is demonstrated that the properties of this polymer can be well described by the aggregate model. This result offers the possibility of mapping the mechanical properties by birefringence measurements. The dependence of the fourth momentP ₄ on the second momentP ₂ is identical with that determined for PC [2] and follows, in the measured range, that of an affine orientational state. Nevertheless, the dependence on the stretching ratio differs for different molecular weights. Thus the partition of the deformation into an orientational and an elongational contribution, as has been proposed [3], seems to be well founded.The partition depends on the stretching conditions.     

Dielectric relaxation in polymeric solids Part 1. A new model for the interpretation of the shape of the dielectric relaxation function

A model is proposed which explains the shape of the dielectric relaxation function at the glass transition of polymers. The model is based on the idea that the molecular mobility at the glass transition is controlled by intra- and intermolecular interaction. In addition, a specific model for the local chain dynamics in amorphous polymer systems is used. According to the scaling hypothesis of molecular dynamics the model relates the high frequency dependence of the dielectric loss curve to the local chain dynamics and the low frequency dependence to the intermolecular correlation.     

Isothermal crystallization kinetics in a limited volume. A geometrical approach based on Evans' theory

A new theoretical approach of the isothermal crystallization of a thin polymer film is proposed. This model, derived from Evans' theory, is in very good agreement with a previous one, but is much more interesting because it makes it possible to calculate the transformed volume fraction anywhere in the film. The main effects of decreasing thickness are a slower average crystallization of the film and a decrease in the Avrami exponent caused by a slower crystallization of the polymer close to the surfaces.A slight modification of the model allows us to calculate the isothermal crystallization kinetics at any point of the film when it contains two identical transcrystalline regions on its surfaces.All the models are well verified by computer simulations.