A comparison of the strength of autohesion of plasma treated amorphous and semi‐crystalline PEEK films

Polyether ether ketone (PEEK) is a promising material for the encapsulation of electronic components for medical implants but a strong and hermetic joining technology is required. Autohesion is a self‐bonding method that avoids the need for adhesives. The strengths of autohesive joins using amorphous and semi‐crystalline PEEK films after surface activation using RF plasma were compared. Both types of PEEK films showed successful autohesion after activation with the bond strength of the amorphous sample being twice as high as the bond strength of the semi‐crystalline sample. Plasma treatment increased the autohesion strength of PEEK with no observed change in surface roughness (as measured by profilometer). The water contact angle was reduced by the treatment. X‐ray photoelectron spectroscopy (XPS) was carried out to determine surface chemistry. In the case of the semi‐crystalline surface, plasma treatment increased the relative percentage of C? O functional groups compared to the untreated surface. For treated surfaces nitrogen concentration correlated positively with bond strength while oxygen concentration correlated negatively with the semi‐crystalline PEEK samples and positively with the amorphous PEEK samples. The oxygen groups most likely are formed after the treatment by ambient oxidation are not conducive to bond formation, possibly because of the quenching of radicals that would otherwise form links. Copyright © 2010 John Wiley & Sons, Ltd.     

Quenched Free Energy and Large Deviations for Random Walks in Random Potentials

We study quenched distributions on random walks in a random potential on integer lattices of arbitrary dimension and with an arbitrary finite set of admissible steps. The potential can be unbounded and can depend on a few steps of the walk. Directed, undirected, and stretched polymers, as well as random walk in random environment, are covered. The restriction needed is on the moment of the potential, in relation to the degree of mixing of the ergodic environment. We derive two variational formulas for the limiting quenched free energy and prove a process‐level quenched large deviation principle (LDP) for the empirical measure. As a corollary we obtain LDPs for types of random walks in random environments not covered by earlier results. © 2012 Wiley Periodicals, Inc.     

Variational Formulas and Cocycle solutions for Directed Polymer and Percolation Models

We discuss variational formulas for the law of large numbers limits of certain models of motion in a random medium: namely, the limiting time constant for last-passage percolation and the limiting free energy for directed polymers. The results are valid for models in arbitrary dimension, steps of the admissible paths can be general, the environment process is ergodic under spatial translations, and the potential accumulated along a path can depend on the environment and the next step of the path. The variational formulas come in two types: one minimizes over gradient-like cocycles, and another one maximizes over invariant measures on the space of environments and paths. Minimizing cocycles can be obtained from Busemann functions when these can be proved to exist. The results are illustrated through 1+1 dimensional exactly solvable examples, periodic examples, and polymers in weak disorder.     

An almost sure invariance principle for random walks in a space-time random environment

We consider a discrete time random walk in a space-time i.i.d. random environment. We use a martingale approach to show that the walk is diffusive in almost every fixed environment. We improve on existing results by proving an invariance principle and considering environments with an L² averaged drift. We also state an a.s. invariance principle for random walks in general random environments whose hypothesis requires a subdiffusive bound on the variance of the quenched mean, under an ergodic invariant measure for the environment chain. T. Sepp?l?inen was partially supported by National Science Foundation grant DMS-0402231.     

Statistical models for optimisation of properties of bottles produced using blends of reactive extruded recycled PET and virgin PET

Blends of chain-extended reactive extruded recycled PET (RER-PET) and virgin PET were fed in injection stretch blow moulding (ISBM) process. The RER-PET blends have different RER-PET concentrations and RER-PET have different pyromellitic dianhydride (PMDA) chain extender concentrations. RER-PET composition and percentage in the blend were used as process variables. The resulted ISBM bottles were tested for burst pressure, top load, liquid permeation and carbonation loss. The experimental results were used in an optimisation process aiming to identify the best blend composition that produces best bottles properties. Models were fitted and statistically analysed to represent the bottles properties in the optimisation calculations. Two optimum points were found in which highest chain extender concentration in RER-PET were favoured. The optimum points showed different optimum RER-PET concentrations in the blend. The first optimum concentration is 20% RER-PET which resulted in best burst pressure and top load resistance. The second optimum point with RER-PET concentration of 29% produced minimum liquid permeation and carbonation loss. The results of the optimisation procedure are beneficial in identifying the possibility of the use of RER-PET for bottling application.     

Parameter identification in periodic delay differential equations with distributed delay

In this study, a parameter identification approach for identifying the parameters of a periodic delayed system with distributed delay is introduced based on time series analysis and spectral element analysis. Using this approach the parameters of the distributed delayed system can be identified from the time series of the response of the system. The experimental or numerical data of the response is examined with Floquet theory and time series analysis techniques to estimate a reduced order dynamics, or truncated state space to identify the Floquet multipliers. Parameter identification is then completed using a dynamic map developed for the assumed model of the system which can relate the Floquet multipliers to the unknown parameters in the model. The parameter identification technique is validated numerically for first and second order delay differential equations with distributed delay.     

Surface properties of polypropylene following a novel industrial surface‐treatment process

Polypropylene (PP) is used in many automotive applications where good paint adhesion is of primary importance. PP is widely known for its low surface energy which impacts negatively on its adhesion strength. PP surfaces were modified using a new industrial surface‐treatment process known as the Accelerated Thermo‐molecular adhesion Process (ATmaP). ATmaP grafts functional groups to the polymer surface derived from an atomised and vapourised nitrogen‐containing coupling agent. The surface properties and adhesion performance of PP samples treated using the ATmaP process and two different flame processes were compared using XPS, time‐of‐flight secondary ion mass spectrometry (ToF‐SIMS) and mechanical testing (pull‐up tests). The latter showed that ATmaP improved adhesion strength significantly in comparison with conventional flame treatments. XPS showed an increase in oxygen and nitrogen concentration on the surface of ATmaP‐treated samples compared with untreated and flame‐treated samples. Principal components analysis (PCA) of the ToF‐SIMS data revealed the major phenomena occurring during the surface treatment of PP samples. Early stage events, including the chain scission of the PP backbone chain and the subsequent reaction of these chains with the surrounding air, are captured by the first principal component (PC1). The increase in the concentration of NO surface functional groups resulting from ATmaP treatment is captured by the second principal component (PC2). Copyright © 2008 John Wiley & Sons, Ltd.