Continuum Theory of Polymer Crystallization

We present a kinetic model of crystal growth of polymers of finite molecular weight. Experiments help to classify polymer crystallization broadly into two kinetic regimes. One is observed in melts or in high molar mass polymer solutions and is dominated by nucleation control with $G \sim \exp(1/T \Delta T)$, where $G$ is the growth rate and $\Delta T$ is the super-cooling. The other is observed in low molar mass solutions (as well as for small molecules) and is diffusion controlled with $G \sim \Delta T$, for small $\Delta T$. Our model unifies these two regimes in a single formalism. The model accounts for the accumulation of polymer chains near the growth front and invokes an entropic barrier theory to recover both limits of nucleation and diffusion control. The basic theory applies to both melts and solutions, and we numerically calculate the growth details of a single crystal in a dilute solution. The effects of molecular weight and concentration are also determined considering conventional polymer dynamics. Our theory shows that entropic considerations, in addition to the traditional energetic arguments, can capture general trends of a vast range of phenomenology. Unifying ideas on crystallization from small molecules and from flexible polymer chains emerge from our theory.Comment: 37 double-spaced pages including 8 figures, submitted to the Journal of Chemical Physic

The Structure of TGBC_C Phases

We study the transition from the cholesteric phase to two TGB$_C$ phases near the upper critical twist $k_{c2}$: the Renn-Lubensky TGB$_C$ phase, with layer normal rotating in a plane perpendicular to the pitch axis, and the Bordeaux TGB$_C$ phase, with the layer normal rotating on a cone parallel to the pitch axis. We calculate properties, including order-parameter profiles, of both phases.Comment: 4 pages, 4 figures, Submitted to Physical Review E, Rapid Communications, September 5, 2003; Revised manuscript (to the paper submitted on March 18, 2003, cond-mat/0303365)that includes an important missing reference and presents an improved analysis of a generalized mode

Growth Models and Models of Turbulence : A Stochastic Quantization Perspective

We consider a class of growth models and models of turbulence based on the randomly stirred fluid. The similarity between the predictions of these models, noted a decade earlier, is understood on the basis of a stochastic quantization scheme.Comment: 3 page

Heterosis, Potence Ratio and Genetic Distance for yield and yield contributing traits in single cross maize hybrids

The study is concerned with the development of single cross heterotic hybrids and to understand the underlying genetic principle for heterosis as well as to establish its relation with parental genetic divergence to formulate a breeding strategy for maize improvement. Heterosis was trait dependent exhibiting high level for plant height, cob characters and grain yield/plant. Two hybrids were better than standard checks, but only DMR QPM 103 x CML 539 recorded 26-28% heterosis over both checks and also displayed positive heterosis for cob characters as well for grain weight. Significanly it was almost seven days earlier in floweringwhich favoured pollination advantage with better floweringsynchrony. Cob characters were positively correlated with yield heterosis’s cob diameter was positively correlated with all cob characters. Cob diameter heterosis could be effective predictor for grain yield heterosis. Majority of the traits were controlled by over dominance gene effect, where more than 80% of hybrids recorded over dominance gene effect for plant height and cob characters. The breeding strategy has to be adopted to maximize heterosis. In this context it appears that inbred tester would improve the population more than the population tester because in an inbred, alleles are fixed whereas in population they are intermediate in frequency. As many as 34 hybrids recorded mid parent heterosis of 100% or above. Of them 25 (74%) belonged to the medium parental divergence group having parental grain yield of 50 g or above. It was observed that parents with high per se performance and intermediate genetic divergence produced highly heterotic and high yielding hybrids

Extended Self-similarity in Kinetic Surface Roughening

We show from numerical simulations that a limited mobility solid-on-solid model of kinetically rough surface growth exhibits extended self-similarity analogous to that found in fluid turbulence. The range over which scale-independent power-law behavior is observed is significantly enhanced if two correlation functions of different order, such as those representing two different moments of the difference in height between two points, are plotted against each other. This behavior, found in both one and two dimensions, suggests that the `relative' exponents may be more fundamental than the `absolute' ones.Comment: 4 pages, 4 postscript figures included (some changes made according to referees' comments. accepted for publication in PRE Rapid Communication

Counterion adsorption on flexible polyelectrolytes: comparison of theories

Counterion adsorption on a flexible polyelectrolyte chain in a spherical cavity is considered by taking a "permuted" charge distribution on the chain so that the "adsorbed" counterions are allowed to move along the backbone. We compute the degree of ionization by using self-consistent field theory (SCFT) and compare with the previously developed variational theory. Analysis of various contributions to the free energy in both theories reveals that the equilibrium degree of ionization is attained mainly as an interplay of the adsorption energy of counterions on the backbone, the translational entropy of the small ions, and their correlated density fluctuations. Degree of ionization computed from SCFT is significantly lower than that from the variational formalism. The difference is entirely due to the density fluctuations of the small ions in the system, which are accounted for in the variational procedure. When these fluctuations are deliberately suppressed in the truncated variational procedure, there emerges a remarkable quantitative agreement in the various contributing factors to the equilibrium degree of ionization, in spite of the fundamental differences in the approximations and computational procedures used in these two schemes. Nevertheless, since the significant effects from density fluctuations of small ions are not captured by the SCFT, and due to the close agreement between SCFT and the other contributing factors in the more transparent variational procedure, the latter is a better computational tool for obtaining the degree of ionization

The structure of TGB(C) phases near the upper critical twist k(c2)

The analogy between superconductors and smectic liquid crystals leads to the prediction of the intriguing twist-grain-boundary (TGB) phase, the liquid crystal analog of the Abrikosov vortex lattice phase in type-II superconductors. Motivated by the idea proposed by de Gennes, Renn and Lubensky constructed a detailed description of the TGB phase in smectic-A systems and the theory for the transition to it from the cholesteric phase. They determined, in mean field theory, that the TGB state, which appears between the disordered cholesteric phase and the ordered smectic phase, consists of uniformly spaced grain boundaries composed of equally spaced parallel screw dislocations. The analogous critical fields were calculated and the most favourable lattice structure for the TGBA phase was also determined following the Abrikosov theory for the vortex lattice system. In the present work, we investigate the transition from the cholesteric to TGB C phases near the upper critical twist field h c2. Analyzing the chiral version of a generalized phenomenological De Gennes free energy used in the Chen-Lubensky model, we find the differential equations for the smectic order parameter near the proposed transition. From the stability analysis of the cholesteric phase within the harmonic theory, two different configurations are found to be stable. In one the layer normal to the smectic slabs is on the plane perpendicular to the pitch-axis (the Renn-Lubensky phase), and in the other the layers tilt toward the pitch-axis and their normals rotate on a cone coaxial to it (the Bordeaux phase). We analyze the order paramater equations using both variational and numerical methods, and we introduce an analytical interpolation formula that closely tracks the numerical solution and that can be used to calculate nonlinear terms. We calculate the upper critical field hc2 for both phases and analyze the stability for a given set of parameters in the phenomenological free energy. We minimize the free energy with respect to the dislocation lattice parameters and determine the ratio of the distance between the grain boundaries ( lb) to the distance between the dislocations within a grain boundary (ld) and their dependence on cholesteric pitch P and smectic layer spacing d. We find that both the order parameter profile and the grain boundary structure for these phases are similar to that of the TGBA phase. We have found no sign of a melted grain boundary phase suggested by Dozov in which the smectic order collapses not only at the dislocations but actually throughout the plane of the grain boundary. In contrast, we find that the smectic order parameter, having a robust value at the grain boundaries, is nearly constant along the pitch axis

The structure of TGB(C) phases near the upper critical twist k(c2)

The analogy between superconductors and smectic liquid crystals leads to the prediction of the intriguing twist-grain-boundary (TGB) phase, the liquid crystal analog of the Abrikosov vortex lattice phase in type-II superconductors. Motivated by the idea proposed by de Gennes, Renn and Lubensky constructed a detailed description of the TGB phase in smectic-A systems and the theory for the transition to it from the cholesteric phase. They determined, in mean field theory, that the TGB state, which appears between the disordered cholesteric phase and the ordered smectic phase, consists of uniformly spaced grain boundaries composed of equally spaced parallel screw dislocations. The analogous critical fields were calculated and the most favourable lattice structure for the TGBA phase was also determined following the Abrikosov theory for the vortex lattice system. In the present work, we investigate the transition from the cholesteric to TGB C phases near the upper critical twist field h c2. Analyzing the chiral version of a generalized phenomenological De Gennes free energy used in the Chen-Lubensky model, we find the differential equations for the smectic order parameter near the proposed transition. From the stability analysis of the cholesteric phase within the harmonic theory, two different configurations are found to be stable. In one the layer normal to the smectic slabs is on the plane perpendicular to the pitch-axis (the Renn-Lubensky phase), and in the other the layers tilt toward the pitch-axis and their normals rotate on a cone coaxial to it (the Bordeaux phase). We analyze the order paramater equations using both variational and numerical methods, and we introduce an analytical interpolation formula that closely tracks the numerical solution and that can be used to calculate nonlinear terms. We calculate the upper critical field hc2 for both phases and analyze the stability for a given set of parameters in the phenomenological free energy. We minimize the free energy with respect to the dislocation lattice parameters and determine the ratio of the distance between the grain boundaries ( lb) to the distance between the dislocations within a grain boundary (ld) and their dependence on cholesteric pitch P and smectic layer spacing d. We find that both the order parameter profile and the grain boundary structure for these phases are similar to that of the TGBA phase. We have found no sign of a melted grain boundary phase suggested by Dozov in which the smectic order collapses not only at the dislocations but actually throughout the plane of the grain boundary. In contrast, we find that the smectic order parameter, having a robust value at the grain boundaries, is nearly constant along the pitch axis