Computer simulation of two-dimensional spherulite growth

The two-dimensional growth of spherulites with impingement was simulated by a computer for athermal, thermal, and combined primary nucleation mechanisms. The simulation provided data on the spherulite size distributions and spherulite shapes. The results of the computer simulation were compared with experimental data on poly(methylene oxide) films.     

Computer simulation of three-dimensional spherulite growth

A computer program for modeling three-dimensional spherulite nucleation, growth, and impingement was elaborated. The Monte Carlo method was used to determine the degree of conversion and calculate the volume of the spherulites. Athermal, thermal, and mixed types of nucleation were tested. The experimental Avrami exponent agrees with the predictions for athermal and thermal nucleation while for mixed nucleation a nonintegral exponent is characteristic. The spherulite size distributions are very different from athermal and thermal nucleations. An intermediate pattern of distribution is proper for the mixed type of nucleation. The boundaries of the largest spherulites from thermal and mixed nucleation are concave while those of the smallest spherulites are convex.     

Measurement of spherulite growth rates using tailored temperature programs

A method recently proposed for measuring spherulite growth rates (G) using temperature programs, tailored for each polymer, is reviewed. This method, compared to the conventional isothermal procedure, permits to expand the temperature range where spherulite growth rates can be measured. Examples of application of this method are reported, in particular, the spherulite growth rates of isotactic polypropylene (iPP) and poly(l-lactic acid) (PLLA) are analyzed. For iPP, growth rates were obtained from 112 to 148 °C using different cooling rates and a self-nucleation procedure. For PLLA, measurements in both isothermal and non-isothermal conditions allowed to overcome the difficulties due to the very high nucleation density that prevent determination of growth rates at low crystallization temperatures. For this polymer the entire curve of G vs. T was obtained.     

Non-isothermal kinetics of melting and nematic to isotropic phase transitions of 5CB liquid crystal

This work reports a non-isothermal kinetics of the melting and the nematic to isotropic (N–I) phase transitions of the pentylcyanobiphenyl (5CB) liquid crystal compared with octylcyanobiphenyl (8CB) liquid crystal using calorimetric technique. Temperature scans and heating rate scans were performed for 5CB and 8CB from 280 to 333 K at various rates using differential scanning calorimetry from 0.5 to 20 K min⁻¹. Double activation was observed for 5CB for two heating rate regimes whereas 8CB indicated single activation only. The 5CB has smaller enthalpy and entropy of the transitions and needs larger activation than 8CB. This kinetic change can be explained in terms of the length scale and mobility of the liquid crystal molecules.     

A statistical model for transitions in nematic liquid crystals

The two-lattice model of Lennard-Jones and Devonshire has been modified and applied to the study of the transition from the nematic to the isotropic phase. We have used the concept of external degrees of freedom for molecules introduced by Prigogine and applied to the case of chain liquids.     

Elastic model for twisted nematic textures in OOBA layers

An elastic model for the twisted nematic texture observed in nematic cells containing octyloxybenzoic acid is proposed. According to the model the twisted textures are due to the presence of cybotactic groups which are responsible for the chirality of the liquid crystal. We show that by assuming for the density of cybotactic groups a critical temperature behaviour close to a special temperature, the experimental data can be well interpreted by our mechanical model.     

Statistical model of polar nematic polymers

The interaction in specially designed polymers may be dominated by the first rank P₁(cos β) type potential instead of the second rank P₂(cos β) type, as in conventional liquid crystal polymers (P₁(cos β) and P₂(cos β) are the first and second Legendre polynomials, respectively of the angle made by the polymer segments with respect to the preferred direction or director). The ordering of the polymers is envisaged in terms of the worm-like theory. The polymers show a polar nematic phase, that is a ferroelectric phase. These polymers have certain interesting properties, such as a second order polar nematic—isotropic transition, and related critical features. These materials are expected to exhibit giant dielectric responses. For more general polymer systems with interactions of both P₁(cos β) and P₂(cos β) types, we predict a peculiar phase behaviour.     

Polypropylene spherulite morphology and growth rate changes in blends with low-density polyethylene

Morphological studies of isotactic polypropylene/low-density polyethlene blends revealed that the shape, size, and orientation of LDPE occlusions remain undisturbed during the crystallization of IPP spherulites. On the other hand, LDPE occlusions introduce large changes in the internal structure of IPP spherulites. It was found that many new boundaries similar to those between spherulites are fromed when the crystallizing front passes the LDPE occlusion. Dead-ended boundaries with soft LDPE occlusions at the ends give rise to an improvement of the impact properties. It was shown that LDPE obstacles do not influence significantly the IPP spherulite growth rate in thin films or in the bulk.     

Isothermal-crystallization kinetics and spherulite growth of aliphatic polyketone/polyamide-6 blends

In this research,the morphologies,isothermal-crystallization kinetics,and spherulite growth of aliphatic polyketone/polyamide-6 blends were studied.A single glass-transition temperature (Tg) was determined,and the composition dependence of Tg for these blends was well described by the Kwei equation.The strong intermolecular interaction between the two polymer components was confirmed by melting-point depression.The isothermal-crystallization kinetics were analyzed on the basis of the Avrami approach.A linear increase in the radii of the spherulites with time was observed for all compositions.All the spherulites continued to grow at nearly identical growth rates.With increasing polyamide-6 content,the size of the spherulites in the polyketone/polyamide-6 blends gradually decreased,and the number of spherulites in the blends increased.     

A growing 2D spherulite and calculus of variations Part I: A 2D spherulite in a linear field of growth rate

We propose to take the calculus of variations in order to compute the shape of a growing 2D spherulite in an uniaxial field of growth rate. We are concerned with the growth line (a path that is traveled in the shortest possible time from nucleus to a point (x₁, y₁), where a molecule just crystallizes) and the growth front (the times between spherulite and supercooled material). The Euler differential equation—a result of the calculus of variations—is derived for all uniaxial growth ratesv (x). Here we especially investigatev(x)=px+q.     

Anomalous two-stage spherulite growth in poly(aryl ether ketones) during isothermal crystallization

Anomalous two-stage spherulite growth has been observed in poly(aryl ether ketones) during isothermal crystallization. The first stage consists of a conventional growth with Maltesecross pattern at a lower growth rate. The morphology shows a smooth interface, dense structure and negative birefringence. The second stage grows in the form of “aggregate” at a higher rate. The morphology shows an open dendrite structure without preferred optical orientation. The second morphology is also termed the “overgrowth.” The occurrence of overgrowth is favored only near the maximum growth rate region and diminishes in the slow growth region. The transition of the two-stage growth is attributed to the change of growth direction of the constituent lamellae. We have confirmed this by microbeam small-angle light-scattering measurements. The lamellar structures in both growth stages were followed by time-resolved small-angle synchrotron x-ray scattering. It was found that the lamellar structures of the crystals formed at both stages are the same. A possible explanation for the two-stage growth is the interface breakdown caused by large perturbations of local composition and/or stress fields. © 1996 John Wiley & Sons, Inc.     

Luckhurst-Romano model of thermotropic biaxial nematic phase

Recent experiments show that the long looked for thermotropic biaxial nematic phase is finally stabilized in a low mass liquid crystalline system. Inspired by this experimental observation we concentrate on some theoretical issues concerned with this phase. In particular we show that the simplest Lebwohl-Lasher biaxial model, as introduced by Luckhurst and Romano, is consistent with the minimal coupling Landau-de Gennes phenomenological approach. The model shows a rich spectrum of possibilities, in particular a direct isotropic-biaxial nematic phase transition. A possible bridge between molecular and phenomenological approaches, in particular an interpretation of the alignment tensor, is discussed.     

A population distribution model for the alignment of nematic liquid crystals

In polymer aligned liquid crystal cells, a surface layer exists. In this surface layer the in-plane distribution of the mesogens, the shape of the mesogens, and their average angle with the surface determine the pretilt angle in the bulk of the sample. A model to incorporate those effects has been proposed. This model gives quantitative agreement with a number of experiments for thick cells, where the optical effects of the surface layer can be neglected. By introducing a linear variation of the optical axis through the surface layer we get qualitative agreement between the model and the pretilt found in thin cells. The thickness of the surface layer is of the order 0·1-1·0 μm.     

A mathematical model for blade coating of a nematic liquid crystal

The standard industrial process of blade-coating is now being used to produce new liquid crystal displays (LCDs) in which a liquid crystal and optical layers are coated onto a substrate. Motivated by this new LCD manufacturing process, we use the Ericksen-Leslie equations to develop a simple mathematical model for blade coating of a nematic liquid crystal. The direction and uniformity of the director are important factors for the performance of the displays, particularly when this alignment is 'frozen in' within optical layers. For this reason we investigate the flow and director within a liquid crystal film both after emerging from the region under a blade (the so-called 'drag-out' problem) and before entering the region under a blade (the so-called 'drag-in' problem). We restrict our attention to thin films and small director angles, and we study two particular cases in which either orientational elasticity effects or flow effects dominate the alignment of the liquid crystal. We find that there is a unique solution of the drag-out problem, whereas there may be multiple solutions of the drag-in problem. When orientational elasticity effects dominate we obtain a simple analytical solution for the director. When flow effects dominate we find that the director is uniform in the bulk of the liquid crystal, which exhibits thin orientational boundary layers near the substrate and the free surface, within which the director orientation changes rapidly from its prescribed boundary value to the flow alignment angle. These boundary layers may be potential locations for the nucleation of defects.     

Solution of a molecular statistical model for chiral nematic liquid crystals

A molecular statistical model for the chiral nematic phase of liquid crystals is investigated. The model is treated in the molecular field approximation. The resulting set of coupled integral equations for the order parameters and the pitch determining equation are solved numerically. The model hamiltonian consists of a nematic and a twist producing term. If only the nematic term is present, the model is known to have a first order phase transition. The model containing only the twist producing term is shown to exhibit a second order phase transition. The order parameters and wave length are presented for three ratios of the coupling constants in the case that both interactions are present.     

Anisotropy of domain growth in nematic liquid crystals

We have studied domain growth in nematic liquid crystals using a lattice Boltzmann algorithm to solve the full, three-dimensional equations of hydrodynamics. An initially cylindrical V (bend) domain in an H (splay) state grows or shrinks anisotropically in agreement with experiment. A disclination loop forms at the mid-point of the wall surrounding the domain. We argue that different director configurations at different points on the loop lead to velocity anisotropy and show that both elastic effects and backflow are relevant. We discuss the dependence of the domain wall velocity on surface tilt and on the magnitude of an applied electric field.     

Anisotropy of domain growth in nematic liquid crystals

We have studied domain growth in nematic liquid crystals using a lattice Boltzmann algorithm to solve the full, three-dimensional equations of hydrodynamics. An initially cylindrical V (bend) domain in an H (splay) state grows or shrinks anisotropically in agreement with experiment. A disclination loop forms at the mid-point of the wall surrounding the domain. We argue that different director configurations at different points on the loop lead to velocity anisotropy and show that both elastic effects and backflow are relevant. We discuss the dependence of the domain wall velocity on surface tilt and on the magnitude of an applied electric field.     

Real-time image analysis and numerical simulation of isothermal spherulite nucleation and growth in polyoxymethylene

A method of analysing nucleation and crystallization kinetics, based on real time image analysis and hot stage optical microscopy, has been used to investigate the isothermal crystallization of different grades polyoxymethylene. The data were compared with results from differential scanning calorimetry (DSC), using a simple numerical simulation to model the effects of finite smaple thickness on the form of the isothermal DSC curves. This simulation was then used to predict the microstructural development in a bulk sample for different boundary conditions, taking into account latent heat evolution and diffusion during crystallization.