Polymer fractionation by continuous chromatography

A review is given of general chromatographic theory, the factors affecting the performance of chromatographi c columns, and aspects of scale-up of the chromatographic process. The theory of gel permeation chromatography (g. p. c.) is received, and the results of an experimental study to optimize the performance of an analytical g.p.c. system are reported. The design and construction of a novel sequential continuous chromatographic refining unit (SCCR3), for continuous liquid-liquid chromatography applications, is described. Counter-current operation is simulated by sequencing a system of inlet and outlet port functions around a connected series of fixed, 5.1 cm internal diameter x 70 cm long, glass columns. The number of columns may be varied, and, during this research, a series of either twenty or ten columns was used. Operation of the unit for continuous fractionation of a dextran polymer (M. W. - 30,000) by g.p.c. is reported using 200-400 µm diameter porous silica beads (Spherosil XOB07S) as packing, and distilled water for the mobile phase. The effects of feed concentration, feed flow rate, and mobile and stationary phase flow rates have been investigated, by means of both product, and on-column, concentrations and molecular weight distributions. The ability to operate the unit successfully at on-column concentrations as high as 20% w/v dextran has been demonstrated, and removal of both high and low molecular weight ends of a polymer feed distribution, to produce products meeting commercial specifications, has been achieved. Equivalent throughputs have been as high as 2.8 tonnes per annum for ten columns, based on continuous operation for 8000 hours per annum. A concentration dependence of the equilibrium distribution coefficient, KD observed during continuous fractionation studies, is related to evidence in the literature and experimental results obtained on a small-scale batch column. Theoretical treatments of the counter-current chromatographic process are outlined, and a preliminary computer simulation of the SCCR3 unit t is presented.

Reactive processing of polyolefins using antioxidant systems

Various monoacrylic compounds containing a hindered phenol function (e.g.3,5-di-tert.-butyl-4-hydroxy benzyl alcohol, DBBA and vinyl-3-[3',5'-di-tert.-butyl-4-hydroxy phenyl] propionate, VDBP), and a benzophenone function (2-hydroxy-4-[beta hydroxy ethoxy] benzophenone, HAEB) were synthesised and used as reactive antioxidants (AO's) for polypropylene (PP). These compounds were reacted with PP melt in the presence of low concentration of a free radical generator such a peroxide (reactive processing) to produce bound-antioxidant concentrates. The binding reaction of these AO's onto PP was found to be low and this was shown to be mainly due to competing reactions such as homopolymerisation of the antioxidant. At high concentrations of peroxide, higher binding efficiency resulted, but, this was accompanied by melt degradation of the polymer. In a special reactive processing procedure, a di- or a trifunctional reactant (referred to as coagent), e.g.tri-methylol propane tri-acrylate, Tris, and Divinyl benzene, DVB, were used with the antioxidant and this has led to an enhanced efficiency of the grating reaction of antioxidants on the polymer in the melt. The evidence suggests that this is due to copolymerisation of the antioxidants with the coagent as well as grafting of the copolymers onto the polymer backbone. Although the 'bound' AO's containing a UV stabilising function showed lower overall stabilisation effect than the unbound analogues before extraction, they were still much more effective when subjected to exhaustive solvent extraction. Furthermore, a very effective synergistic stabilising activity when two reactive AO's containing thermal and UV stabilising functions e.g. DBBA and HAEB, were reactively processed with PP in the presence of a coagent. The stabilising effectiveness of such a synergist was much higher than that of the unbound analogues both before and after extraction. Analysis using the GPC technique of concentrates containing bound-DBBA processed in the presence of Tris coagent showed higher molecular weight (Mn), compared to that of a polymer processed without the coagent, but was still lower than that of the control processed PP with no additives. This indicates that Tris coagent may inhibit further melt degradation of the polymer. Model reactions of DBBA in liquid hydrocarbon (decalin) and analysis of the products using FTIR and NMR spectroscopy showed the formation of grafted DBBA onto decalin molecules as well as homopolymerisation of the AO. In the presence of Tris coagent, copolymerisation of DBBA with the Tris inevitably occured; which was followed by grafting of the copolymer onto the decalin, FTIR and NMR results of the polymer concentrates containing bound-DBBA processed with and without Tris, showed similar behaviour as the above model reactions. This evidence supports the effect of Tris in enhancing the efficiency of the reaction of DBBA in the polymer melt. Reactive procesing of HAEB in polymer melts exhibited crosslinking formation In the early stages of the reaction, however, in the final stage, the crosslinked structure was 'broken down' or rearranged to give an almost gel free polymer with high antioxidant binding efficiency.

The beta effect in alkylsilanes

It was suggested to us that compounds of the type XCH2SiR2CH2CH2Y might show interesting chemical and biological activity due to them possessing both an alpha group and a beta group. The aim of this research was to discover whether or not the alpha and beta effects interact with each other, and if so whether interaction is via steric or electronic effects. A series of compounds were made with a constant chloromethyl alpha function and varying beta functions (hydroxy, methoxy and chloro groups); plus a second series of trimethylsilyl substituted silanes with the same variety of beta functions were synthesised. The stereochemistry of the products was investigated by analysis of NMR spectra and of dipole moment data. It was found that the β-chloro-substituted compounds possessed restricted rotation. The methoxy- and hydroxy-substituted compounds which displayed more or less simple triplets, appear to possess free rotation; the smaller sized hydroxy and methoxy groups seemingly no great barrier to rotation. Similarly, compounds possessing larger alpha alkyl groups appeared also to possess restricted rotation, it was concluded that for the compounds possessing large alpha or a large beta function steric effects dominate. The kinetics of the solvolysis reaction were studied. β-functional alkylsilanes commonly undergo solvolysis by unimolecular elimination at remarkably enhanced rates. The β-hydroxy- and β-methoxy-substituted chloroethyl derivatives reacted substantially slower that their trimethylsilyl analogues, due to the electronegative chlorine pulling electrons into the Si-C bond. For compounds possessing an electronegative substituent alpha to silicon it seems it is the electronic effects that act to inhibit the beta effect. 2-Chloroethylchloromethyldimethylsilane initially appeared not to react solvolytically, however NMR analysis of the solvolysis products indicated that a reaction did occur but by an as yet unknown mechanism. For compounds with an a α-electronegative substituent in conjunction with a large β-function it was concluded both steric and electronic effects are important.

Improvements to the arc-spraying process

After a brief review of the various forms of thermal spraying equipment and processes, descriptions of the basic principles involved and the general functions for which thermally sprayed coatings are used are given. The background of the collaborating company, Metallisation, is described and their position in the overall market discussed, providing a backdrop against which the appropriateness of various project options might be judged. Current arc-spraying equipment is then examined, firstly in terms of the workings of their constituent parts and subsequently by examining the effects of changes in design and in operating parameters both upon equipment operation and the coatings produced. Published literature relating to these matters is reviewed. Literature relating to the production, comminution and propulsion of the particles which form the spray is discussed as are the mechanisms involved at impact with the substrate. Literature on the use of rockets for thermal spraying and induction heating as a process for feedstock melting are also reviewed. Three distinct options for further study are derived and preliminary tests and costings made to allow one option alone, the use of rocket acceleration, to go forward to the experimental phase. A suitable rocket burner was developed, tested and incorporated into an arc-spray system so that the sprayability of the whole could be assessed. Coatings were made using various parameters and these are compared with coatings produced by a standard system. Coatings were examined for macro and micro hardness, cohesive strength, porosity and by microstructural examination. The results indicate a high degree of similarity between the coatings produced by the standard system and the high velocity system. This was surprising in view of the very different atomising media and velocities. Possible causes for this similarity and the general behaviour of this new system and the standard system are discussed before the study reaches its conclusions in not proving the hypothesis that an increase in particle velocity would improve the mechanical properties of arc-sprayed steel coatings. KEY WORDS: Sprayed metal coatings, Electric arc spraying, High velocity flame spraying, Sprayed coating properties

An overview of Total Factor Productivity estimations adjusted for pollutant outputs:an application to sugarcane farming

The conventional Total Factor Productivity (TFP) measurement does not incorporate the effects of undesirable outputs, which are harmful to the environment. Using sugarcane farming in Kenya, this paper illustrates the differences between the conventional Malmquist index measures where the environment variable is not adjusted and environment-adjusted measures using both hyperbolic and directional distance functions. The mean TFP change estimates for the conventional Malmquist index, adjusted hyperbolic index and Luenberger indicator were 3.13%, 0.11% and 2.21%, respectively. The conventional non-adjusted measure lies between the two adjusted measures of hyperbolic index and Luenberger indicator. © 2012 Inderscience Enterprises Ltd.

NOx storage-reduction characteristics of Ba-based lean NOx trap catalysts subjected to simulated road aging

In order to study the effect of washcoat composition on lean NOx trap (LNT) aging characteristics, fully formulated monolithic LNT catalysts containing varying amounts of La-stabilized CeO2 (5 wt% La2O3) or CeO2-ZrO2 (Ce:Zr = 70:30) were subjected to accelerated aging on a bench reactor. Subsequent catalyst evaluation revealed that aging resulted in deterioration of the NOx storage, NOx release and NOx reduction functions, whereas the observation of lean phase NO2 slip for all of the aged catalysts indicated that LNT performance was not limited by the kinetics of NO oxidation. After aging, all of the catalysts showed increased selectivity to NH3 in the temperature range 250–450 °C. TEM, H2 chemisorption, XPS and elemental analysis data revealed two main changes which can explain the degradation in LNT performance. First, residual sulfur in the catalysts, present as BaSO4, decreased catalyst NOx storage capacity. Second, sintering of the precious metals in the washcoat was observed, which can be expected to decrease the rate of NOx reduction. Additionally, sintering is hypothesized to result in segregation of the precious metal and Ba phases, resulting in less efficient NOx spillover from Pt to Ba during NOx adsorption, as well as decreased rates of reductant spillover from Pt to Ba and reverse NOx spillover during catalyst regeneration. Spectacular improvement in LNT durability was observed for catalysts containing CeO2 or CeO2-ZrO2 relative to their non-ceria containing analog. This was attributed to (i) the ability of ceria to participate in NOx storage/reduction as a supplement to the main Ba NOx storage component; (ii) the fact that Pt and CeO2(-ZrO2) are not subject to phase segregation; and (iii) the ability of ceria to trap sulfur, resulting in decreased sulfur accumulation on the Ba component.

Polynomial function intervals for floating-point software verification

The focus of our work is the verification of tight functional properties of numerical programs, such as showing that a floating-point implementation of Riemann integration computes a close approximation of the exact integral. Programmers and engineers writing such programs will benefit from verification tools that support an expressive specification language and that are highly automated. Our work provides a new method for verification of numerical software, supporting a substantially more expressive language for specifications than other publicly available automated tools. The additional expressivity in the specification language is provided by two constructs. First, the specification can feature inclusions between interval arithmetic expressions. Second, the integral operator from classical analysis can be used in the specifications, where the integration bounds can be arbitrary expressions over real variables. To support our claim of expressivity, we outline the verification of four example programs, including the integration example mentioned earlier. A key component of our method is an algorithm for proving numerical theorems. This algorithm is based on automatic polynomial approximation of non-linear real and real-interval functions defined by expressions. The PolyPaver tool is our implementation of the algorithm and its source code is publicly available. In this paper we report on experiments using PolyPaver that indicate that the additional expressivity does not come at a performance cost when comparing with other publicly available state-of-the-art provers. We also include a scalability study that explores the limits of PolyPaver in proving tight functional specifications of progressively larger randomly generated programs. © 2014 Springer International Publishing Switzerland.

Atmospheric plasma treatment of porous polymer constructs for tissue engineering applications

Porous 3D polymer scaffolds prepared by TIPS from PLGA (53:47) and PS are intrinsically hydrophobic which prohibits the wetting of such porous media by water. This limits the application of these materials for the fabrication of scaffolds as supports for cell adhesion/spreading. Here we demonstrate that the interior surfaces of polymer scaffolds can be effectively modified using atmospheric air plasma (AP). Polymer films (2D) were also modified as control. The surface properties of wet 2D and 3D scaffolds were characterised using zeta-potential and wettability measurements. These techniques were used as the primary screening methods to assess surface chemistry and the wettability of wet polymer constructs prior and after the surface treatment. The surfaces of the original polymers are rather hydrophobic as highlighted but contain acidic functional groups. Increased exposure to AP improved the water wetting of the treated surfaces because of the formation of a variety of oxygen and nitrogen containing functions. The morphology and pore structure was assessed using SEM and a liquid displacement test. The PLGA and PS foam samples have central regions which are open porous interconnected networks with maximum pore diameters of 49 μm for PLGA and 73 μm for PS foams. (Figure Presented) © 2007 Wiley-VCH Verlag GmbH & Co. KGaA.

Hydrodebromination of bromobenzene over Pt(111)

The surface chemistry of benzene and bromobenzene over Pt(111) has been studied by temperature-programmed XPS/MS and NEXAFS. Time-resolved XPS shows that benzene adopts a single chemically distinguishable environment during low-temperature adsorption within the monolayer, with a saturation coverage at θC6H6 = 0.2 ML. Around 20% of a benzene monolayer desorbs molecularly, while the remainder dehydrogenates to surface carbon. Bromobenzene likewise adsorbs molecularly at 90 K, giving rise to two C 1s environments at 284.4 and 285.3 eV corresponding to the C−H and C−Br functions, respectively. The saturation C6H5Br monolayer coverage is 0.11 ML. NEXAFS reveals that bromobenzene adopts a tilted geometry, with the ring plane at 60 ± 5° to the surface. Bromobenzene multilayers desorb at ∼180 K, with higher temperatures promoting competitive molecular desorption versus C−Br scission within the monolayer. Approximately 30% of a saturated bromobenzene monolayer either desorbs reversibly or as reactively formed hydrocarbons. Debromination yields a stable (phenyl) surface intermediate and atomic bromine at 300 K. Further heating results in desorption of reactively formed H2, C6H6, and HBr; however, there was no evidence for either biphenyl or Br2 formation. Pt(111) is an efficient surface for low-temperature bromobenzene hydrodebromination to benzene and HBr. © 2007 American Chemical Society.

Probabilistic control for uncertain systems

In this paper a new framework has been applied to the design of controllers which encompasses nonlinearity, hysteresis and arbitrary density functions of forward models and inverse controllers. Using mixture density networks, the probabilistic models of both the forward and inverse dynamics are estimated such that they are dependent on the state and the control input. The optimal control strategy is then derived which minimizes uncertainty of the closed loop system. In the absence of reliable plant models, the proposed control algorithm incorporates uncertainties in model parameters, observations, and latent processes. The local stability of the closed loop system has been established. The efficacy of the control algorithm is demonstrated on two nonlinear stochastic control examples with additive and multiplicative noise.

Boundary-Value Problems for almost Nonlinear Singularly Perturbed Systems of Ordinary Differential Equations

A boundary-value problems for almost nonlinear singularly perturbed systems of ordinary differential equations are considered. An asymptotic solution is constructed under some assumption and using boundary functions and generalized inverse matrix and projectors.

Обобщенные Интервальные Оценки в Сценарном Анализе

Показано, что метод обобщенных интервальных оценок (ОИО), первоначально предназначавшийся для выявления и формализованного представления экспертных знаний об известных с неопределенностью количественных исходных данных моделей интеллектуальных систем поддержки экспертных решений (СПЭР), можно рассматривать как развитие сценарного подхода в теории принятия решений. Предложены процедуры исследования методом ОИО задач с зависимыми параметрами, таких как задача прогнозирования объемов извлекаемых запасов месторождений в зависимости от уровней цены на углеводороды. Установлены аналитические соотношения для функций распределения вероятностей обобщенных равномерных распределений, используемых в сценарном анализе и анализе результирующих показателей моделей включенных в базу моделей СПЭР.

Fractional Calculus of the Generalized Wright Function

Mathematics Subject Classification: 26A33, 33C20.

A Brief Story about the Operators of the Generalized Fractional Calculus

2000 Mathematics Subject Classification: 26A33, 33C60, 44A20

Teaching University-Level Mathematics Using Mathematica

This paper considers the use of the computer algebra system Mathematica for teaching university-level mathematics subjects. Outlined are basic Mathematica concepts, connected with different mathematics areas: algebra, linear algebra, geometry, calculus and analysis, complex functions, numerical analysis and scientific computing, probability and statistics. The course “Information technologies in mathematics”, which involves the use of Mathematica, is also presented - discussed are the syllabus, aims, approaches and outcomes.