The size distribution for theA g RB f−g Model of polymerization

This paper gives the equilibrium distribution of polymer sizes for Flory'sA _g RB _f–g model of polymerization. In this model, the polymers are composed of structural units withg functional groups of the typeA and (f-g) functional groups of the typeB. Reaction is subject to three conditions: (1) Functional groups of the typeA react only with those of typeB, and vice versa. (2) Intramolecular reactions do not occur [and therefore only branched-chain (noncyclic) polymers and formed]. (3) Subject to conditions (1) and (2), all functional groups are equally reactive. The derivation employs Stockmayer's statistical mechanical method (first used on Flory'sRA _f model), coupled with a recursion giving the number of distinct polymers which may be assembled fromk units of theA _g RB _f–g type. We also give distributions for a limiting case of theA _g RB _f–g model, the so-calledA _g RB model. This paper completes the solution of the Smoluchowski coagulation equation (monodisperse case) for the kernelsa _ij =A + B(i +j)+ Cij. The proof will be given in another publication.     

A generalization of the Rouse-Zimm model

The idea of consistently averaging the hydrodynamic interaction and its various consequences for Hookean dumbbells are reviewed. For long chains this idea can be used to generalize the Rouse-Zimm model for polymer solutions. Unlike the usual Rouse-Zimm model, the new model for steady shear flow predicts a nonzero second normal stress coefficient and shear rate dependent material functions. In the limit of long chains, the viscosity and the normal stress coefficients are universal functions of the reduced shear rate.This paper was presented at the Frühjahrstagung des Fachausschusses Polymerphysik der Deutschen Physikalischen Gesellschaft at Kaiserslautern (West Germany), March 12–14, 1986.     

Inverse relaxation-model and relation to recovery internal friction

Inverse relaxation is studied for hard elastic polypropylene (HEPP), rubber and non-elastic polypropylene. The results show that contractive stress, stress, and internal friction are three essential factors related to the phenomenon. A three-element model in which each element has a definite meaning is proposed to describe this phenomenon. The results also show that, in the first cyclic deformation, relaxation time increases with the increase of recovery for all the materials, which indicates that recovery viscosity increases with the increase of recovery, but the stress rising amplitude (SRA) of inverse relaxation has a maximum in the recovery range. Analysis indicates that SRA equals recovery internal friction (RIF) for ideal material in which stress is solely a function of strain, independent of paths, and approximately equals RIF for non-ideal material at a given strain. From this principle it is found that the order of the work counteracted by RIF for the four materials is the same as that of their second hysteresis loop, and the RIF of HEPP has a sudden increase at the later recovery range.     

Studies on the properties of ionic liquid EMIInCl4

This paper reports that an ionic liquid (IL) has been prepared by directly mixing InCl₃ and 1-methyl-3-ethylimidazolium chloride (EMIC) with molar ratio 1/1 under dry argon atmosphere. The densities, and surface tension of the pure IL were determined at temperature range of 293.15 to 343.15 ± 0.1 K. The volumetric properties and the properties of surface for ionic liquid based on group III were discussed by Glasser's theory and Yang's interstice model.     

Cellulose: the structure slowly unravels

This article attempts to bring together basic and complex information which has been gathered on cellulose structure, principally that of native cellulose, over the last few decades. Even though advances have been made in the field of crystallography, powder crystallography cannot yield a definitive cellulose structure and single crystal diffraction is not possible due to the lack of suitable crystals. Knowledge obtained on the biosynthesis of native cellulose and on the polymorphy of cellulose and its derivatives help our understanding of ultrastructure. Many inconsistencies between early crystallographic studies of native cellulose have been clarified by the discovery that two polymorphs (α and β) of cellulose I exist. Models of the possible ultrastructural arrangements within native cellulose have been put forward over the decades; with advancement in technology, computer simulations of small and large systems are being created to test the viability of these ultrastructural models. It is hoped that this review will aid in the understanding of the complexity and uncertainties that still exist in this subject. This revised version was published online in August 2006 with corrections to the Cover Date.     

Ionic conductivity of poly[N-(3,6,9-trioxadecyl)-4-vinylpyridinium)] salts with univalent counter-ions in aqueous solutions

In order to determine the counter-anion effect on conductivity of poly[N-(3,6,9-trioxadecyl)-4-vinylpyridinium)] backbone in aqueous solutions, a set of three polyelectrolytes with three different counter-ions: poly[N-(3,6,9-trioxadecyl)-4-vinylpyridinium]bromide P4VP164Br and its chlorate and tosylate derivatives P4VP164ClO₄ and P4VP164Ts respectively, were prepared by spontaneous polymerization of 4-vinylpyridine. This method gives a grafted polyelectrolyte having a positive charge on each pyridinic moiety on the backbone. The conductivities of cationic polyelectrolyte aqueous solution were determined in the concentration range from 10⁻⁴ to 10⁻² M at 25 °C. The variation of the conductivity versus concentration of the investigated system exhibits a typical polyelectrolyte behavior. The polycation mobility was found to be dependent on the counter-anion nature. Thus, the polyelectrolyte conductivity increases with the ion size. This shows that big ions are weakly or not associated to the backbone.In order to confirm this steric hindrance, we have considered the conductivities of these three anions Br⁻, ClO₄⁻ and Ts⁻ in their sodium salts, both alone and in the presence of 3,6,9-trioxadecanol (PEO164) free chains. In the two cases, the conductivities decrease in the order Λ_Br>Λ_ClO4>Λ_Ts.These results suggest that counter-ion mobility is mainly influenced by steric effect PEO164 grafted chains.Values of the conductivity predicted from Manning rod-like polyelectrolyte model were compared with our experimental results.     

Effect of Neck Formation on the Measurement of Dynamic Interfacial Tension in a Drop Volume Tensiometer

Dynamic interfacial tension values obtained by drop volume tensiometry will be affected under certain experimental conditions by the formation of a neck between the drop and the capillary tip. This phenomenon must be accounted for to obtain accurate values of interfacial tension. In this work, neck formation for a water–mineral oil system is studied under conditions where hydrodynamic effects can be neglected. A model originally developed for the determination of the surface tension of a suspended drop is modified for application to dynamic interfacial tensions of surfactant-containing liquids. The model relates apparent values of interfacial tension calculated from drops possessing necks to actual values. Experiments with Span 80 (sorbitan monooleate) and sodium dodecyl sulfate (SDS) surfactants in a mineral oil–water system are used to test the validity of the developed model. For the small tip diameter used, good agreement is obtained for Span 80 up to the critical micelle concentration, and for low concentrations of SDS, when the surfactant adsorption is diffusion-limited. In both cases, the neck diameter of the growing drop can be considered constant over the range of dynamic interfacial tensions tested.     

Symmetries and correlation inequalities for classicaln-vector models

We describe a new class of single spin measures on then-dimensional sphereS _r ⁿ of radiusr (n 4) for which Lebowitz-type [J. Lebowitz,J. Stat. Phys. 16:463 (1977)] inequalities hold. This is achieved by an appropriate parametrization ofS _r ⁿ . The above class includes the uniform measures onxs Rⁿ ¦x¦ r for any 0 p r. The second topic of this paper is an abstract formulation of the first Griffiths inequality [R. B. Griffiths,J. Math. Phys. 8:478 (1967)] and the underlying symmetry property.     

Ising-like field theory

A field theory model onR ² in which the basic fields are Ising spins instead of Gaussian spins is examined. Using statistical mechanics techniques we discuss the ultraviolet and the infrared problems. In particular we discuss a technique yielding the asymptotic expansion in of the ground state energy, as 0, without using the cluster expansion.Supported in part by Consiglio Nazionale delle Ricerche.     

Objective Information Theory Exemplified in Air Traffic Control System

Information is the core of Air traffic con-trol system (ATCS).In this paper,objective information theory is extended to depict,model and measure the information exemplified in ATCS.The sextuple model is presented with information ontology,state occurrence time,state set,carrier,reflection time,and reflection set.The metric system is given to quantitively measure the information with extensity,detailedness,continuity,richness,containability,delay,pervasiveness,authenticity,and adaptability.The results show that the proposed method is potential to find out actual indexes in ATCS for flight safety.