Synthesis and properties of a new AB-cross-linked copolymer membrane system

The alcohol permeability and permselectivity properties as well as the morphology of membranes made of a newly developed AB-cross-linked copolymer system composed of elastomeric and glassy components were investigated. The copolymer was synthesized by a hydrosilylation reaction between poly(styrene-stat-isoprenes) (Mn from 40,000 to 100,000 g/mol) with high content in unsaturated side groups (≈ 60% of entire isoprene content) and polyhydrogen polysiloxanes with varying SiH content (0.75 10.7 mol %) and molecular mass, Mn, from 2,500 to 36,000 g/mol. A two-track approach was taken to determine the morphology of the copolymer system. The first employed the usual polymer characterization methods such as electron microscopy, DSC, IR spectroscopy, the density gradient method, and mechanical measurements. For the second approach, different copolymer permeability models were tested so as to give an insight into the copolymer morphology. As a final step, the permeability and permselectivity properties were correlated with the morphological structure of the copolymer system. It was observed that the respective continuous microphase dominated the copolymer's physical properties, as, e.g., permeability, permselectivity, and mechanical properties. The microphase inversion in the copolymer system was proved by the permeability/permselectivity as well as by the mechanical measurements

Recent advances in the formation of phase inversion membranes made from amorphous or semi-crystalline polymers

Structural characteristics in membranes formed by diffusion induced phase separation processes are discussed. Established theories on membrane formation from ternary systems can be extended to describe the effects of high or low molecular weight additives. A mechanism for the formation of nodular structures in the top layer of ultrafiltration membranes is presented. In the last part structures arising from polymer crystallization during immersion precipitation are discussed

A Kernel Test of Goodness of Fit

We propose a nonparametric statistical test for goodness-of-fit: given a set of samples, the test determines how likely it is that these were generated from a target density function. The measure of goodness-of-fit is a divergence constructed via Stein's method using functions from a Reproducing Kernel Hilbert Space. Our test statistic is based on an empirical estimate of this divergence, taking the form of a V-statistic in terms of the log gradients of the target density and the kernel. We derive a statistical test, both for i.i.d. and non-i.i.d. samples, where we estimate the null distribution quantiles using a wild bootstrap procedure. We apply our test to quantifying convergence of approximate Markov Chain Monte Carlo methods, statistical model criticism, and evaluating quality of fit vs model complexity in nonparametric density estimation

Characterization of morphology controlled polyethersulfone hollow fiber membranes by the addition of polyethylene glycol to the dope and bore liquid solution

The preparation of polyethersulfone (PES) hollow fiber membranes has been studied using N-methylpyrrolidone (NMP) as solvent, polyethylene glycol 400 (PEG 400) as weak nonsolvent and water as strong nonsolvent. When PEG 400 is used as polymeric additive to the spinning dope the viscosity of the PES solution is strongly enhanced. Furthermore, it was observed that PEG 400 could be added to the solution in large amounts without causing phase separation (NMP/PEG ratio 1:9, PES concentration approximately 11 wt.%). Membranes prepared from a solution containing a NMP/PEG ratio of 1:1 results in higher fluxes than when a ratio of 1:4 is used. Similar fluxes were obtained for PES concentrations of 16 and 20 wt.%. Looking at the fiber cross-section it became clear that macrovoid formation could not be suppressed by the addition of PEG 400 alone, not even at concentrations as high as 38 wt.%. Only when relatively large amounts of water were added to the dope solution macrovoids disappeared and nice spongy structures were obtained. Variation of the bore liquid composition using the components NMP, PEG 400 and water showed to be a powerful method to control the pore size of the bore surface. Pores of 5–28 nm were obtained in combination with high pure water fluxes; e.g. a membrane with pores of 7 nm had a pure water flux of 940 l/(m2 h bar) and showed 100% BSA retention. When an air gap larger than 10 mm was applied the shell surface contained relatively large pores. Spinning directly in water (airgap=0) resulted in shell side pores of 8–10 nm, while an air gap of 10 mm resulted in pore sizes of 40–54 nm

Non-aqueous retention measurements: ultrafiltration behaviour of polystyrene solutions and colloidal silver particles

The retention behaviour of polyimide ultrafiltration membranes was investigated using dilute solutions of polystyrene in ethyl acetate as test solutions. It is shown that flow-induced deformation of the polystyrene chains highly affects the membrane retention. This coil-stretch transition is not instantaneous, but gradual. The concept of a deformation resistance has been ontroduced to explain this behaviour. This concept can be applied to describe the flux behaviour of the membranes during the tests as well. Solute deformation allows comparison of the pore size distributions of the membranes qualitatively. Retention measurements were also performed with silver sol particles that were prepared in mixtures of ethanol and water; these sols remain stable as long as the ethanol concentration does not exceed 57 vol%. The sols were completely retained by the membranes, which is probably caused by the fact that the effective diameter of the particles is much larger than that observed by transmission electron microscopy

Learning deep kernels for exponential family densities

The kernel exponential family is a rich class of distributions, which can be fit efficiently and with statistical guarantees by score matching. Being required to choose a priori a simple kernel such as the Gaussian, however, limits its practical applicability. We provide a scheme for learning a kernel parameterized by a deep network, which can find complex location-dependent features of the local data geometry. This gives a very rich class of density models, capable of fitting complex structures on moderate-dimensional problems. Compared to deep density models fit via maximum likelihood, our approach provides a complementary set of strengths and tradeoffs: in empirical studies, deep maximum-likelihood models can yield higher likelihoods, while our approach gives better estimates of the gradient of the log density, the score, which describes the distribution's shape

Kernel Sequential Monte Carlo

We propose kernel sequential Monte Carlo (KSMC), a framework for sampling from static target densities. KSMC is a family of sequential Monte Carlo algorithms that are based on building emulator models of the current particle system in a reproducing kernel Hilbert space. We here focus on modelling nonlinear covariance structure and gradients of the target. The emulator's geometry is adaptively updated and subsequently used to inform local proposals. Unlike in adaptive Markov chain Monte Carlo, continuous adaptation does not compromise convergence of the sampler. KSMC combines the strengths of sequental Monte Carlo and kernel methods: superior performance for multimodal targets and the ability to estimate model evidence as compared to Markov chain Monte Carlo, and the emulator's ability to represent targets that exhibit high degrees of nonlinearity. As KSMC does not require access to target gradients, it is particularly applicable on targets whose gradients are unknown or prohibitively expensive. We describe necessary tuning details and demonstrate the benefits of the the proposed methodology on a series of challenging synthetic and real-world examples

Characterization of polyacrylonitrile ultrafiltration membranes

Various methods have been used to characterize ultrafiltration membranes, such as gas flux measurements, (field emission) scanning electron microscopy, permporometry and liquid-liquid displacement. Significant differences in the pore size distributions determined from permporometry and liquid-liquid displacement were found