PVC autoclave model

The batch reaction of polyvinyl chloride (PVC) in a pressure autoclave is modelled by considering the various mechanisms for conversion from vinyl chloride monomer (VCM) to the polymer during the middle phase of the industrial process. A key step is to determine at what stage the droplets of VCM stop contracting because of the density difference between VCM and PVC - this is known as the 'freeze point'. A model is proposed that locates the freeze point as that point where the unfavourable energy due to wetting of the PVC by water is dominated by the energy required to compress the gel network inside the droplets. Preliminary investigations support this explanation and suggest avenues for further work. A corollary of this model is an explanation of the role of 'secondary granulating agents' in controlling the porosity of the final product

Manning condensation in two dimensions

We consider a macroion confined to a cylindrical cell and neutralized by oppositely charged counterions. Exact results are obtained for the two-dimensional version of this problem, in which ion-ion and ion-macroion interactions are logarithmic. In particular, the threshold for counterion condensation is found to be the same as predicted by mean-field theory. With further increase of the macroion charge, a series of single-ion condensation transitions takes place. Our analytical results are expected to be exact in the vicinity of these transitions and are in very good agreement with recent Monte-Carlo simulation data.Comment: 4 pages, 4 figure

Many-body interactions and melting of colloidal crystals

We study the melting behavior of charged colloidal crystals, using a simulation technique that combines a continuous mean-field Poisson-Boltzmann description for the microscopic electrolyte ions with a Brownian-dynamics simulation for the mesoscopic colloids. This technique ensures that many-body interactions between the colloids are fully taken into account, and thus allows us to investigate how many-body interactions affect the solid-liquid phase behavior of charged colloids. Using the Lindemann criterion, we determine the melting line in a phase-diagram spanned by the colloidal charge and the salt concentration. We compare our results to predictions based on the established description of colloidal suspensions in terms of pairwise additive Yukawa potentials, and find good agreement at high-salt, but not at low-salt concentration. Analyzing the effective pair-interaction between two colloids in a crystalline environment, we demonstrate that the difference in the melting behavior observed at low salt is due to many-body interactions

Effect of many-body interactions on the solid-liquid phase-behavior of charge-stabilized colloidal suspensions

The solid-liquid phase-diagram of charge-stabilized colloidal suspensions is calculated using a technique that combines a continuous Poisson-Boltzmann description for the microscopic electrolyte ions with a molecular-dynamics simulation for the macroionic colloidal spheres. While correlations between the microions are neglected in this approach, many-body interactions between the colloids are fully included. The solid-liquid transition is determined at a high colloid volume fraction where many-body interactions are expected to be strong. With a view to the Derjaguin-Landau-Verwey-Overbeek theory predicting that colloids interact via Yukawa pair-potentials, we compare our results with the phase diagram of a simple Yukawa liquid. Good agreement is found at high salt conditions, while at low ionic strength considerable deviations are observed. By calculating effective colloid-colloid pair-interactions it is demonstrated that these differences are due to many-body interactions. We suggest a density-dependent pair-potential in the form of a truncated Yukawa potential, and show that it offers a considerably improved description of the solid-liquid phase-behavior of concentrated colloidal suspensions

Classical Coulomb Systems:Screening and Correlations Revisited

From the laws of macroscopic electrostatics of conductors (in particular the existence of screening) taken for granted, one can deduce universal properties for the thermal fluctuations in a classical Coulomb system at equilibrium. The universality is especially apparent in the long-range correlations of the electrical potentials and fields. The charge fluctuations are derived from the field fluctuations. This is a convenient way for studying the surface charge fluctuations on a conductor with boundaries. Explicit results are given for simple geometries. The potentials and the fields have Gaussian fluctuations, except for a short-distance cutoff.Comment: 17 pages,TE

Hydration interactions: aqueous solvent effects in electric double layers

A model for ionic solutions with an attractive short-range pair interaction between the ions is presented. The short-range interaction is accounted for by adding a quadratic non-local term to the Poisson-Boltzmann free energy. The model is used to study solvent effects in a planar electric double layer. The counter-ion density is found to increase near the charged surface, as compared with the Poisson-Boltzmann theory, and to decrease at larger distances. The ion density profile is studied analytically in the case where the ion distribution near the plate is dominated only by counter-ions. Further away from the plate the density distribution can be described using a Poisson-Boltzmann theory with an effective surface charge that is smaller than the actual one.Comment: 11 Figures in 13 files + LaTex file. 20 pages. Accepted to Phys. Rev. E. Corrected typos and reference

Casimir forces in binary liquid mixtures

If two ore more bodies are immersed in a critical fluid critical fluctuations of the order parameter generate long ranged forces between these bodies. Due to the underlying mechanism these forces are close analogues of the well known Casimir forces in electromagnetism. For the special case of a binary liquid mixture near its critical demixing transition confined to a simple parallel plate geometry it is shown that the corresponding critical Casimir forces can be of the same order of magnitude as the dispersion (van der Waals) forces between the plates. In wetting experiments or by direct measurements with an atomic force microscope the resulting modification of the usual dispersion forces in the critical regime should therefore be easily detectable. Analytical estimates for the Casimir amplitudes Delta in d=4-epsilon are compared with corresponding Monte-Carlo results in d=3 and their quantitative effect on the thickness of critical wetting layers and on force measurements is discussed.Comment: 34 pages LaTeX with revtex and epsf style, to appear in Phys. Rev.

Microscopic Analysis For Water Stressed By High Electric Fields In The Prebreakdown Regime

Analysis of the electrical double layer at the electrode-water interface for voltages close to the breakdown point has been carried out based on a static, Monte Carlo approach. It is shown that strong dipole realignment, ion-ion correlation, and finite-size effects can greatly modify the electric fields and local permittivity (hence, leading to optical structure) at the electrode interface. Dramatic enhancements of Schottky injection, providing a source for electronic controlled breakdown, are possible. It is also shown that large pressures associated with the Maxwell stress tensor would be created at the electrode boundaries. Our results depend on the ionic density, and are in keeping with recent observations. A simple, perturbative analysis shows that high field regions with a sharp variation in permittivity can potentially be critical spots for instability initiation. This suggests that the use of polished electrodes, or composite materials, or alternative nonpolar liquids might help enhance high-voltage operation

Recursion and Ambiguity: a Linguistic and Computational Perspective

In this chapter I will be concerned with what characterizes human language and the parser that computes it in real communicative situations. I will start by discussing and dismissing Hauser, Chomsky and Fitch's(2002) (HC&F) disputed claim that the "only uniquely human component of the faculty of language" be "recursion". I will substantiate my rejection of HC&F's claims, with the fact that recursion only appears in mature and literate language - an opinion also shared by some papers in a book on recursion by Harry van der Hulst (2010). I will then present in detail Chomsky's proposal - now part of the Minimalist Theory (MT) - of the architecture of the human parser as being based on Phases. I will accept this part of the theory and compare it with the computational architecture contained in a system for deep text understanding called Getaruns (Delmonte,2007;2009). I will then argue in favour of what I regard the peculiar component of human language faculty that is "the ability to associate meaning to deficient propositions and generic linguistic expressions, which are highly ambiguous in their structure”. And this is also due to the presence of recursion (but not only). I will then speak in favour of a parser that takes "context" into account and strives for a "complete" syntactic representation. As to the problem of ambiguity, I will introduce the use of a computational device, a lookahead mechanism, which is presented in association with the need to specify UG parameters characterizing a given language. I will discuss the use of psychologically viable Parsing Strategies implemented in the parser to overcome ambiguity and prevent Garden Path, whenever possible. This will be highlighted by reference to peculiar features associated to different languages, Italian and English. Eventually, I will present a theory that encompasses all my previous proposals and is called LSLT