Fluid-Fluid and Fluid-Solid transitions in the Kern-Frenkel model from Barker-Henderson thermodynamic perturbation theory

We study the Kern-Frenkel model for patchy colloids using Barker-Henderson second-order thermodynamic perturbation theory. The model describes a fluid where hard sphere particles are decorated with one patch, so that they interact via a square-well (SW) potential if they are sufficiently close one another, and if patches on each particle are properly aligned. Both the gas-liquid and fluid-solid phase coexistences are computed and contrasted against corresponding Monte-Carlo simulations results. We find that the perturbation theory describes rather accurately numerical simulations all the way from a fully covered square-well potential down to the Janus limit (half coverage). In the region where numerical data are not available (from Janus to hard-spheres), the method provides estimates of the location of the critical lines that could serve as a guideline for further efficient numerical work at these low coverages. A comparison with other techniques, such as integral equation theory, highlights the important aspect of this methodology in the present context.Comment: Accepted for publication in The Journal of Chemical Physics (2012

A simple patchy colloid model for the phase behavior of lysozyme dispersions

We propose a minimal model for spherical proteins with aeolotopic pair interactions to describe the equilibrium phase behavior of lysozyme. The repulsive screened Coulomb interactions between the particles are taken into account assuming that the net charges are smeared out homogeneously over the spherical protein surfaces. We incorporate attractive surface patches, with the interactions between patches on different spheres modeled by an attractive Yukawa potential. The parameters entering the attractive Yukawa potential part are determined using information on the experimentally accessed gas-liquid-like critical point. The Helmholtz free energy of the fluid and solid phases is calculated using second-order thermodynamic perturbation theory. Our predictions for the solubility curve are in fair agreement with experimental data. In addition, we present new experimental data for the gas-liquid coexistence curves at various salt concentrations and compare these with our model calculations. In agreement with earlier findings, we observe that the strength and the range of the attractive potential part only weakly depend on the salt content

Effect of glycerol and dimethyl sulfoxide on the phase behavior of lysozyme: Theory and experiments

Salt, glycerol and dimethyl sulfoxide (DMSO) are used to modify the properties of protein solutions. We experimentally determined the effect of these additives on the phase behavior of lysozyme solutions. Upon the addition of glycerol and DMSO, the fluid-solid transition and the gas-liquid coexistence curve (binodal) shift to lower temperatures and the gap between them increases. The experimentally observed trends are consistent with our theoretical predictions based on the thermodynamic perturbation theory (TPT) and the Derjaguin-Landau-Verwey-Overbeek (DLVO) model for the lysozyme-lysozyme pair interactions. The values of the parameters describing the interactions, namely the refractive indices, dielectric constants, Hamaker constant and cut-off length, are extracted from literature or are experimentally determined by independent experiments, including static light scattering to determine the second virial coefficient. We observe that both, glycerol and DMSO, render the potential more repulsive, while sodium chloride reduces the repulsion.Comment: Manuscript accepted for publication in The Journal of Chemical Physic

Structure, processing and performance of ultra-high molecular weight polyethylene (IUPAC Technical Report). Part 2: crystallinity and supra molecular structure

Test methods including OM, SEM, TEM, DSC, SAXS, WAXS, and IR were used to characterise supra-molecular structure in three batches of polyethylene (PE), which had weight-average relative molar masses ¯¯¯¯ M w of approximately 0.6 × 106, 5 × 106, and 9 × 106. They were applied to compression mouldings made by the polymer manufacturer. Electron microscopy showed that powders formed in the polymerization reactor consisted of irregularly shaped grains between 50 and 250 μm in diameter. Higher magnification revealed that each grain was an aggregate, composed of particles between 0.4 and 0.8 μm in diameter, which were connected by long, thin fibrils. In compression mouldings, lamellar thicknesses ranged from 7 to 23 nm. Crystallinity varied between 70 and 75 % in reactor powder, but was lower in compression mouldings. Melting peak temperatures ranged from 138 to 145 °C, depending on processing history. DMTA showed that the glass transition temperature θg was −120 °C for all three grades of polyethylene. IR spectroscopy found negligibly small levels of oxidation and thermal degradation in mouldings. Optical microscopy revealed the presence of visible fusion defects at grain boundaries. It is concluded that relatively weak defects can be characterized using optical microscopy, but there is a need for improved methods that can detect less obvious fusion defects

Phase Behaviour of Proteins and Colloid-Polymer Mixtures

In this thesis, we present a theoretical and experimental study of the equilibrium phase behaviour of colloidal dispersions and protein solutions. The thesis consists of two theoretical parts on the phase diagram of lysozyme solutions, and mixtures of charge-stabilised colloids and neutral polymers, respectively, and an experimental part on the stability of mixtures of charged colloids and non-adsorbing polymers, including a theoretical model of the aggregation kinetics. In the first part, the phase behaviour of lysozyme solutions is calculated using thermodynamic perturbation theory applied to a patchy colloidal model with an anisotropic interaction part that incorporates screened Coulomb repulsions. The interaction parameters in this model are obtained from experimental data sets. The experimental phases are consistently described by our model of protein interactions, and nearly quantitative agreement is found for the metastable gasliquid and the fluid-solid coexistence lines. We show that the phase behaviour of lysozyme strongly depends on the anisotropic hydrophobic interactions. The range of attraction obtained with our model is in excellent agreement with previous surface force measurements. In addition, a consistent description is obtained for the structure factor at small wave numbers. The second part addresses the depletion interaction and the phase behaviour of mixtures of charged spherical colloids and neutral polymer chains under good and θ-solvent conditions. To predict the phase behaviour, we have derived a generalised free-volume theory, which is in good agreement with computer simulation data of the binodal for polymer-to-colloid size ratios q ≤ 1. For q > 1, our theory captures the qualitative trends. We study the effect of weak electrostatic repulsions and the influence of the solvent quality, and show that the colloid charge stabilises the homogeneous phase against demixing. The phase stability is enhanced with increasing q and solvent quality. Our theory predicts that the solvent quality strongly affects the location of the gas-liquid coexistence curve in case of weakly charged colloids. For a θ-solvent and q > 1, the gas-liquid coexistence curve is almost unaffected by electrostatic repulsions. In the third part, the stability and phase behaviour of an aqueous mixture of charged, nanosized spheres and polysaccharide chains of roughly equal sizes is investigated by visual inspection and photon correlation spectroscopy. We explore the interplay between charge-induced repulsion and polymer-induced colloid attraction. We find that even weak electrostatic screening, or small amounts of polymers enhance colloid aggregation. Good agreement is observed between the experimental cluster growth rates and the predictions of doublet formation theory with hydrodynamic interactions, where the polymer-induced attractions are well described by the Asakura-Oosawa-Vrij potential. We compare the non-equilibrium phases caused by macroscopic phase separation, with predictions from a generalised free-volume theory on equilibrium phases, and observe similar trends regarding the salt influence

From square-well to Janus: Improved algorithm for integral equation theory and comparison with thermodynamic perturbation theory within the Kern-Frenkel model

Building upon past work on the phase diagram of Janus fluids [F. Sciortino, A. Giacometti, and G. Pastore, Phys. Rev. Lett. 103, 237801 (2009)], we perform a detailed study of integral equation theory of the Kern-Frenkel potential with coverage that is tuned from the isotropic square-well fluid to the Janus limit. An improved algorithm for the reference hypernetted-chain (RHNC) equation for this problem is implemented that significantly extends the range of applicability of RHNC. Results for both structure and thermodynamics are presented and compared with numerical simulations. Unlike previous attempts, this algorithm is shown to be stable down to the Janus limit, thus paving the way for analyzing the frustration mechanism characteristic of the gas-liquid transition in the Janus system. The results are also compared with Barker-Henderson thermodynamic perturbation theory on the same model. We then discuss the pros and cons of both approaches within a unified treatment. On balance, RHNC integral equation theory, even with an isotropic hard-sphere reference system, is found to be a good compromise between accuracy of the results, computational effort, and uniform quality to tackle self-assembly processes in patchy colloids of complex nature. Further improvement in RHNC however clearly requires an anisotropic reference bridge function

X-ray diffraction study of strain-induced crystallization of hydrogenated nitrile-butadiene rubbers: Effect of crosslink density

International audienc

Structure, processing and performance of ultra-high molecular weight polyethylene (IUPAC Technical Report). Part 3: deformation, wear and fracture

Three grades of polyethylene, with weight-average relative molar masses, ¯¯¯¯ M W , of approximately 0.6 × 106, 5 × 106, and 9 × 106, were supplied as compression mouldings by a leading manufacturer of ultra-high molecular weight polyethylene (UHMWPE). They were code-named PE06, PE5, and PE9, respectively. Specimens cut from these mouldings were subjected to a wide range of mechanical tests at 23 °C. In tensile tests, deformation was initially elastic and dominated by crystallinity, which was highest in PE06. Beyond the yield point, entanglement density became the dominant factor, and at 40 % strain, the rising stress–strain curves for PE5 and PE9 crossed the falling PE06 curve. Fracture occurred at strains above 150 %. Differences in stress–strain behaviour between PE5 and PE9 were relatively small. A similar pattern of behaviour was observed in wear tests; wear resistance showed a marked increase when ¯¯¯¯ M W was raised from 0.6 × 106 to 5 × 106, but there was no further increase when it was raised to 9 × 106. It is concluded that the unexpected similarity in behaviour between PE5 and PE9 was due to incomplete consolidation during moulding, which led to deficiencies in entanglement at grain boundaries; they were clearly visible on the surfaces of both tensile and wear specimens. Fatigue crack growth in 10 mm thick specimens was so severely affected by inadequate consolidation that it forms the basis for a separate report – Part 4 in this series

Structure, processing and performance of ultra-high molecular weight polyethylene (IUPAC Technical Report). Part 1: characterizing molecular weight

The aim of this project was to study the efficacy of current methods of quality control and quality assurance for ultra-high molecular weight polyethylene (UHMWPE) products, and find improvements where possible. Intrinsic viscosity (IV) tests were performed on three grades of polyethylene with weight average relative molar masses ̅ M w of about 6 × 105, 5.0 × 106 and 9.0 × 106. Results from three laboratories showed substantial scatter, probably because different methods were used to make and test solutions. Tensile tests were carried out to 600 % extension at 150 °C under both constant applied load and constant Hencky strain rate, on compression mouldings made by a leading manufacturer of ultra-high molecular weight polyethylene. They gave low values of ̅ M w, suggesting incomplete entanglement at ‘grain boundaries’ between powder particles. Results from conventional melt-rheology tests are presented, and their relevance to quality control and assurance is discussed. Attempts to calculate molecular weights from these data met with limited success because of extended relaxation times. Suggestions are made for improving international standards for IV testing of UHMWPE, by investigating the various factors that can cause significant errors, and by introducing methods for checking the homogeneity (and hence validity) of the solutions tested. Part 2 addresses characterization of crystallinity and structure. Part 3 covers mechanical properties, and Part 4 focuses on the sporadic crack propagation behaviour exhibited by all three grades of UHMWPE in fatigue tests on 10 mm thick compact tension specimens

Structure, processing and performance of ultra-high molecular weight polyethylene (IUPAC Technical Report). Part 4: sporadic fatigue crack propagation

Fatigue tests were carried out on compression mouldings supplied by a leading polymer manufacturer. They were made from three batches of ultra-high molecular weight polyethylene (UHMWPE) with weight-average relative molar masses, ¯¯¯¯ M W, of about 0.6 × 106, 5 × 106 and 9 × 106. In 10 mm thick compact tension specimens, crack propagation was so erratic that it was impossible to follow standard procedure, where crack-tip stress intensity amplitude, ΔK, is raised incrementally, and the resulting crack propagation rate, da/dN, increases, following the Paris equation, where a is crack length and N is number of cycles. Instead, most of the tests were conducted at fixed high values of ΔK. Typically, da/dN then started at a high level, but decreased irregularly during the test. Micrographs of fracture surfaces showed that crack propagation was sporadic in these specimens. In one test, at ΔK = 2.3 MPa m0.5, there were crack-arrest marks at intervals Δa of about 2 μm, while the number of cycles between individual growth steps increased from 1 to more than 1000 and the fracture surface showed increasing evidence of plastic deformation. It is concluded that sporadic crack propagation was caused by energy-dissipating crazing, which was initiated close to the crack tip under plane strain conditions in mouldings that were not fully consolidated. By contrast, fatigue crack propagation in 4 mm thick specimens followed the Paris equation approximately. The results from all four reports on this project are reviewed, and the possibility of using fatigue testing as a quality assurance procedure for melt-processed UHMWPE is discussed