Polydispersity of ethylene sequence length in metallocene ethylene/alpha-olefin copolymers. I. Characterized by thermal-fractionation technique

In this article, the polydispersity of the ethylene sequence length (ESL) in ethylene/alpha-olefin copolymers was studied by atomic force microscopy (AFM) and the thermal-fractionation technique. The crystal morphology observation by AFM showed that morphology changed gradually with decreasing average ESL from complete lamellae over shorter and more curved lamellae to a granular-like morphology, and the mixed morphology was observed after stepwise crystallization from phase-separated melt. This result indicated that the ethylene sequence with different lengths crystallized into a crystalline phase with a different size and stability at the copolymer systems. The thermal-fractionation technique was used to characterize the polydispersity of ESL. Three of the following statistical terms were introduced to describe the distribution of ESL and the lamellar thickness: the arithmetic mean (L) over bar (n), the weight mean (L) over bar (w), and the broadness index I = (L) over bar (w)/(L) over bar (n). It was concluded that the polydispersity of ESL could be quantitatively characterized by the thermal-fractionation technique. The effects of temperature range, temperature-dependent specific heat capacity C-p of copolymer, and the molecular weight on the results of thermal fractionation were discussed,

Statistical thermodynamics of polydisperse polymer systems in the framework of lattice fluid model: Effect of molecular weight and its distribution on the spinodal in polymer solution

With the aid of thermodynamics of Gibbs, the expression of the spinodal was derived for the polydisperse polymer-solvent system in the framework of Sanchez-Lacombe Lattice Fluid Theory (SLLFT). For convenience, we considered that a model polydisperse polymer contains three sub-components. According to our calculation, the spinodal depends on both weight-average ((M) over bar (w)) and number-average ((M) over bar (n)) molecular weights of the polydisperse polymer, but the z-average molecular weight ((M) over bar (z)) dependence on the spinodal is invisible. The dependence of free volume on composition, temperature, molecular weight, and its distribution results in the effect of (M) over bar (n) on the spinodal. Moreover, it has been found that the effect of changing (M) over bar (w) on the spinodal is much bigger than that of changing (M) over bar (n) and the extrema of the spinodal increases with the rise of the weight-average molecular weight of the polymer in the solutions with upper critical solution temperature (UCST). However, the effect of polydispersity on the spinodal can be neglected for the polymer with a considerably high weight-average molecular weight. A more simple expression of the spinodal for the polydisperse polymer solution in the framework of SLLFT was also derived under the assumption of upsilon(*)=upsilon(1)(*)=upsilon(2)(*) and (1/r(1)(0))-(1/r(2i)(0))-->(1/r(1)(0)).

Improved thermal fractionation technique for chain structure analysis of ethylene/alpha-olefin copolymers

In this report, we describe an improved thermal fractionation technique used to characterize the polydispersity of crystalline ethylene sequence length (CESL) of ethylene/alpha -olefin copolymers. After stepwise isothermal crystallization, the crystalline ethylene sequences are sorted into groups by their lengths. The CESLs are estimated using melting points of known hydrocarbons. The content of each group is determined using the calibrated peak area. The statistical terms: the arithmetic mean (L) over bar (n), the weighted mean (L) over bar (w) and the broadness index I = (L) over bar (w)/(L) over bar (n) are used to describe the distribution of CESL. Results show that improved thermal fractionation technique can quantitatively characterize the polydispersity of CESL with a high degree of accuracy.

On characterization of organic structures - A highly discriminating molecular topological index

A new molecular topological index, EATI is proposed based on the extended adjacency matrix, It has a hitherto unheard of power of discrimination and can be applied to discriminate various kinds of organic compounds, such as structures containing heteroatoms, etc.. Thus EATI might be possibly used as supplementary reference for CAS Registry Numbers for structure documentation.

On highly discriminating molecular topological index

A highly discriminating molecular topological index, EAID, is proposed based on the extended adjacency matrix. A systematic search for degeneracy was performed for 3 807 434 alkane trees, 202 558 complex cyclic or polycyclic graphs, and 430 472 structures containing heteroatoms. No counterexamples (two or more nonisomorphic structures with the same EAID number) were found. This is a hitherto unheard of power of discrimination. Thus EAID might be possibly used as supplementary reference for CAS Registry Numbers for structure documentation.

A new topological index for the Changchun institute of applied chemistry C-13 NMR information system

A method to assign a single number representation for each atom (node) in a molecular graph, Atomic IDentification (AID) number, is proposed based on the counts of weighted paths terminated on that atom. Then, a new topological index, Molecular IDentification (MID) number is developed from AID. The MID is tested systematically, over half a million of structures are examined, and MID shows high discrimination for various structural isomers. Thus it can be used for documentation in the Changchun Institute of Chemistry C-13 NMR information system.

NEW TOPOLOGICAL INDEX AND PREDICTION OF PHASE-TRANSFER ENERGY FOR PROTONATED AMINES AND TETRAALKYLAMINES IONS

The applications of new topological indices A(x1)-A(x3) suggested in our laboratory for the prediction of Gibbs energy values of phase transfer (water to nitrobenzene) of amine ions are described with satisfactory results. Multiple regression analysis and neural network were employed simultaneously in this study.

ON HALL AND KIERS TOPOLOGICAL STATE AND TOTAL TOPOLOGICAL INDEX

The topological state and the total topological index, tau, have been tested systematically. Counterexamples are provided proving that the topological state method cannot determine classes of symmetrically equivalent atoms in a molecule fully correct. The

STATISTICAL THERMODYNAMICS IN THE FRAMEWORK OF THE LATTICE FLUID MODEL .1. POLYDISPERSE POLYMERS OF SPECIAL DISTRIBUTION

The Gibbs free energies and equations of state of polymers with special molar mass distributions, e.g., Flory distribution, uniform distribution and Schulz distribution, are derived based on a lattice fluid model. The influence of the polydispersity (or t

STATISTICAL THERMODYNAMICS IN THE FRAMEWORK OF THE LATTICE FLUID MODEL .2. BINARY MIXTURE OF POLYDISPERSE POLYMERS OF SPECIAL DISTRIBUTION

In this paper, the Gibbs free energy, the equation of state and the chemical potentials of polydisperse multicomponent polymer mixtures are derived. For general binary mixtures of polydisperse polymers, we also give the Gibbs free energy, the equation of

STATISTICAL THERMODYNAMICS IN THE FRAMEWORK OF THE LATTICE FLUID MODEL .3. BINARY MIXTURE OF POLYDISPERSE POLYMERS OF SPECIAL DISTRIBUTION WITH STRONG-INTERACTIONS

For a binary mixture of polydisperse polymers with strong interactions, the free energy, the equation of state, the chemical potentials and the spinodal are formulated on the basis of the lattice fluid model. Further, the spinodal curves for the system wi

STATISTICAL THERMODYNAMICS OF POLYDISPERSE POLYMER MIXTURES

A statistical thermodynamics theory of polydisperse polymer blends based on a lattice model description of a fluid is formulated. Characterization of a binary polydisperse polymer mixture requires a knowledge of the pure polymer system and the interaction energy. It is assumed that the intrinsic and interactive properties of polymer (for example, T*, P*, rho*, and epsilon(ij)*) are independent of molecular size. Thermodynamic properties of ternary and higher order mixtures are completely defined in terms of the pure fluid polymer parameters and the binary interaction energies. Thermodynamic stability criteria for the phase transitions of a binary mixture are shown. The binodal and spinodal of general binary systems and of special binary systems are discussed.

A NEW TOPOLOGICAL INDEX FOR RESEARCH ON STRUCTURE-PROPERTY RELATIONSHIPS OF ALKANES

in this Raper, based on distance matrix and branch vertex of atomes in a molecule, a new topological index (Y(x)) has been developed to be used in research on physical and chemical properties of alkanes. It is concluded that this index bears good structure selectivity and relativity when the results from index were compared with that of other ones.

STATISTICAL THERMODYNAMICS OF POLYDISPERSE POLYMER BLENDS WITH STRONG INTERACTION

A statistical thermodynamics theory of polydisperse polymer mixtures with strong interaction between dissimilar components based on a lattice fluid model is formulated. Expressions for the free energy, equation of state, phase stability and spinodal for a polydisperse, binary polymer mixture with strong interaction are derived.

STATISTICAL THERMODYNAMICS OF POLYDISPERSE POLYMERS

A statistical thermodynamics theory of polydisperse polymers based on a lattice model of fluids is formulated. Pure polydisperse polymer can be completely characterized by three scale factors and the molecular weight distribution of the system. The equation of state does not satisfy a simple corresponding-states principle, except for a polymer fluid of sufficiently high molecular weight. The relationships between thermal expansion coefficient alpha and isothermal compressibility beta with reduced variables are also predicted.