Local dynamics and deformation of glass-forming polymers : modelling and atomistic simulations

The research described in the present thesis is about glassy phenomena and mechanical properties in vitrifiable polymer materials. Glasses are solid materials, but, in contrast to crystals, the structure is disordered. Polymers are macromolecular chains formed by covalently linking a very large number of repeating molecular building blocks or monomers. Polymeric materials are easy to reshape and reuse. Also they are lightweight and often transparent. These characteristics make them ideal materials for commodity products such as compact discs, safety helmets, or vandal-proof glazing. Some glassy polymers are also biocompatible, so that they can be used in medical applications. For a successful usage of polymer glasses it is necessary to understand and predict their behaviour under various circumstances. Although many new insights have been acquired over the last decades still a lot of questions remain open. Upon vitrifying a polymer melt the relaxation times and the viscosity increase dramatically. Accompanied with this increase various glassy phenomena are observed — in particular dynamical heterogeneities and non-Gaussian displacements of particles. The comprehension of the striking viscosity increase and the two phenomena mentioned above is still far from complete. During the straining of a polymer glass typical mechanical characteristics are observed, of which the magnitude can vary enormously between different types of polymers. A wellknown example of a polymer glass is atactic polystyrene. In its glassy state polystyrene is usually found to be very brittle. Within a few percent of elongation the material breaks. This behaviour is caused by a relatively high yield tooth in combination with a relatively low strain-hardening modulus. Other polymers, such as bisphenol-A polycarbonate, show a tough response; a test bar can easily be extended to twice its original length. In spite of much study, the physical (molecular) origin of this difference in mechanical behaviour is still not clear. Below the glass transition rubber-elasticity theory appears to be invalid, as it fails to explain the observation that the strain-hardening modulus of polystyrene in its glassy phase is about two orders of magnitude higher than its modulus in the rubbery state. Our main goals are to acquire a better understanding at the molecular scale of heterogeneous and non-Gaussian dynamics and mechanical deformation of glassy polymers and to differentiate chemistry-specific from more universal physical properties. These goals are achieved by carrying out molecular-dynamics simulations on glass-forming systems. In addition, the results are elucidated by the usage of simple physical models. The simulations consist of solving the equations of Newton, a coupled set of differential equations with a given force field and initial conditions. The force field describes the interactions between the various particles. As the main interest is in glassy polymers, most simulations are done for a united-atom model of polystyrene. In the simulation run several characteristics of the glass transition are identified. As is typical for other vitreous systems as well, anomalous, non-Gaussian displacements play an important role near the glass transition for polystyrene; the same observation has been made for a dendritic melt and a colloid-like system. For all these systems of different architecture we have described some essential features of this non-Gaussian behaviour with a simple one-particle model in an effective field. The non-Gaussian behaviour is mainly caused by the cage-to-cage motion of the constituent particles, whereby the cage is formed by interactions with neighbouring particles. By means of the model the height of the so-called non-Gaussian parameter can be interpreted as a measure for the ratio of the root-mean-square displacement within the cage and the effective jump length between cages, without the assumption of any heterogeneity of glassy dynamics in the sense of sitespecific relaxation times. The maximum of the non-Gaussian parameter occurs in each case at the crossover from the cage regime to the (sub)diffusive regime and is connected to the cage-escape time. For the colloid-like system also the shape of the time-dependent non-Gaussian parameter is described well by the model (chapter 3). Dynamical heterogeneity, a phenomenon observed in many experiments on glasses, is also found in the simulation result of the polystyrene phenyl-ring-flip movement (to which the mechanical gamma relaxation is ascribed). This means that some phenyl rings behave very differently than others within a typical simulation run. Different relaxation times and activation enthalpies associated with the flip are determined using various methods. A particular result of the study of the phenyl flip is that an enthalpy barrier determined solely from structural properties is in accordance with an activation enthalpy acquired by analyzing the dynamics of the phenyl rings, even in the presence of dynamical heterogeneity. The heterogeneity arises because of the following mechanism. The conformation of the backbone determines to a large extent the barrier of the phenyl-ring flip. Eventually the relaxation of the backbone is becoming so slow upon cooling down that the phenyl ring is unable to access the conformation-dependent state with the lowest flip barrier within the corresponding barrier-jump time. The phenyl rings are trapped instead in various other states with accompanying different energy barriers. These states are available because of the disordered nature of the material. The mechanism just described for the heterogeneous dynamics in the phenyl-ring flip movement becomes stronger upon cooling down towards the glass transition; eventually the relaxation becomes more Arrhenius-like below the glass transition temperature because only the fastest phenyl flips occur within the accessible observation time (chapter 4). By doing uniaxial-stress extension and compression simulations the stress-strain relation of polystyrene has been measured under various conditions. Although the cooling and deformation velocities in the simulations differ many orders of magnitude from their values in usual experiments, the characteristic features of the experimental stress-strain relation are well reproduced, which allows one to study the origin of the yield tooth and strain hardening. It is observed that the strain-hardening modulus increases with increasing pressure, an effect not described by rubber-elasticity theory. Also it is observed that the thermal history is not completely erased by the mechanical deformation. The picture arising from this study is that the yield peak in polystyrene is mostly mediated by interchain energetic interactions. A net debonding of these interactions is likely causing this yield peak and the subsequent strain softening. The positiveness of the strain-hardening modulus in polystyrene is mainly due to intrachain interactions (chapter 5). From our comparative study of polystyrene and polycarbonate it can be concluded that strain hardening in polymer glasses such as these two polymers is likely caused mainly by the following mechanism. During uniaxial extension a glassy chain adopts a more stretched and hence more inflexible state, also at a local scale. Due to interactions with other particles non-affine displacements take place. The non-affine response is stronger at shorter length scales, but as the deformation proceeds and the effective flexibility decreases also longer length scales are affected. This is accompanied with more bond-altering processes and implies an increase in the rate of energy dissipation, causing in turn an increase in stress upon straining the polymer material further (chapter 6). All these results show that simple physical models supported and tested by results of molecular-dynamics simulations (in which typical physical phenomena observed in real experiments can be reproduced) provide a fruitful approach in understanding glassy material

Folding kinetics of a polymer [corrigendum]

In our original article (Phys. Chem. Chem. Phys., 2012, 14, 60446053) a convergence problem resulted in an averaging error in computing the entropy from a set of Wang-Landau Monte-Carlo simulations. Here we report corrected results for the freezing temperature of the homopolymer chain as a function of the range of the non-bonded interaction. We find that the previously reported forward-flux sampling (FFS) and brute-force (BF) simulation results are in agreement with the revised Wang-Landau (WL) calculations. This confirms the utility of FFS for computing crystallisation rates in systems of this kind.Comment: 2 pages, 4 figure

Efficient Langevin and Monte Carlo sampling algorithms: the case of field-theoretic simulations

We introduce Langevin sampling algorithms to field-theoretic simulations (FTSs) of polymers that, for the same accuracy, are ∼10× more efficient than a previously used Brownian dynamics algorithm that used predictor corrector for such simulations, over 10× more efficient than the smart Monte Carlo (SMC) algorithm, and typically over 1000× more efficient than a simple Monte Carlo (MC) algorithm. These algorithms are known as the Leimkuhler–Matthews (the BAOAB-limited) method and the BAOAB method. Furthermore, the FTS allows for an improved MC algorithm based on the Ornstein–Uhlenbeck process (OU MC), which is 2× more efficient than SMC. The system-size dependence of the efficiency for the sampling algorithms is presented, and it is shown that the aforementioned MC algorithms do not scale well with system sizes. Hence, for larger sizes, the efficiency difference between the Langevin and MC algorithms is even greater, although, for SMC and OU MC, the scaling is less unfavorable than for the simple MC

Determination of tube theory parameters using a simple grid model as an example

Although the tube theory is successful in describing entangled polymers qualitatively, a more quantitative description requires precise and consistent definitions of its parameters. Here we investigate the simplest model of entangled polymers, namely a single Rouse chain in a cubic lattice of line obstacles, and illustrate the typical problems and uncertainties of the tube theory. In particular we show that in general one needs 3 entanglement related parameters, but only 2 combinations of them are relevant for the long-time dynamics. Conversely, the plateau modulus can not be determined from these two parameters and requires a more detailed model of entanglements with explicit entanglement forces, such as the slipsprings model. It is shown that for the grid model the Rouse time within the tube is larger than the Rouse time of the free chain, in contrast to what the standard tube theory assumes

Instability of the Microemulsion Channel in Block Copolymer-Homopolymer Blends

Field theoretic simulations are used to predict the equilibrium phase diagram of symmetric blends of AB diblock copolymer with A- and B-type homopolymers. Experiments generally observe a channel of bicontinuous microemulsion (BμE) separating the ordered lamellar (LAM) phase from coexisting homopolymer-rich (A+B) phases. However, our simulations find that the channel is unstable with respect to macrophase separation, in particular, A+B+BμE coexistence at high T and A+B+LAM coexistence at low T. The preference for three-phase coexistence is attributed to a weak attractive interaction between diblock monolayers

Home monitoring of coronavirus disease 2019 patients in different phases of disease

Purpose of reviewVarious home monitoring programs have emerged through the COVID-19 pandemic in different phases of COVID-19 disease.Recent findingsThe prehospital monitoring of COVID-19-positive patients detects early deterioration. Hospital care at home provides early discharge with oxygen to empty hospital beds for other patients. Home monitoring during recovery can be used for rehabilitation and detection of potential relapses. General goals of home monitoring in COVID-19 are early detection of deterioration and prompt escalation of care such as emergency department presentation, medical advice, medication prescription and mental support. Due to the innovations of vaccination and treatment changes, such as dexamethasone and tocilizumab, the challenge for the healthcare system has shifted from large numbers of admitted COVID-19 patients to lower numbers of admitted patients with specific risk profiles (such as immunocompromised). This also changes the field of home monitoring in COVID-19. Efficacy and cost-effectiveness of home monitoring interventions depend on the costs of the intervention (use of devices, apps and medical staff) and the proposed patient group (depending on risk factors and disease severity).SummaryPatient satisfaction of COVID-19 home monitoring programs was mostly high. Home monitoring programs for COVID-19 should be ready to be re-escalated in case of a new global pandemic

Solid–liquid interfacial free energy of ice Ih, ice Ic, and ice 0 within a mono-atomic model of water via the capillary wave method

We apply the capillarywave method, based on measurements of fluctuations in a ribbon-like interfacial geometry, to determine the solid–liquid interfacial free energy for both polytypes of ice I and the recently proposed ice 0 within a mono-atomic model of water. We discuss various choices for the molecular order parameter, which distinguishes solid from liquid, and demonstrate the influence of this choice on the interfacial stiffness. We quantify the influence of discretisation error when sampling the interfacial profile and the limits on accuracy imposed by the assumption of quasi onedimensional geometry. The interfacial free energies of the two ice I polytypes are indistinguishable to within achievable statistical error and the small ambiguity which arises from the choice of order parameter. In the case of ice 0, we find that the large surface unit cell for low index interfaces constrains the width of the interfacial ribbon such that the accuracy of results is reduced. Nevertheless, we establish that the interfacial free energy of ice 0 at its melting temperature is similar to that of ice I under the same conditions. The rationality of a core–shell model for the nucleation of ice I within ice 0 is questioned within the context of our results. © 2017 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/). [http://dx.doi.org/10.1063/1.4975776

OPTIma:simplifying calorimetry for proton computed tomography in high proton flux environments

Objective. Proton computed tomography (pCT) offers a potential route to reducing range uncertainties for proton therapy treatment planning, however the current trend towards high current spot scanning treatment systems leads to high proton fluxes which are challenging for existing systems. Here we demonstrate a novel approach to energy reconstruction, referred to as ‘de-averaging’, which allows individual proton energies to be recovered using only a measurement of their integrated energy without the need for spatial information from the calorimeter. Approach. The method is evaluated in the context of the Optimising Proton Therapy through Imaging (OPTIma) system which uses a simple, relatively inexpensive, scintillator-based calorimeter that reports only the integrated energy deposited by all protons within a cyclotron period, alongside a silicon strip based tracking system capable of reconstructing individual protons in a high flux environment. GEANT4 simulations have been performed to examine the performance of such a system at a modern commercial cyclotron facility using a σ ≈ 10 mm beam for currents in the range 10–50 pA at the nozzle. Main results. Apart from low-density lung tissue, a discrepancy of less than 1% on the Relative Stopping Power is found for all other considered tissues when embedded within a 150 mm spherical Perspex phantom in the 10–30 pA current range, and for some tissues even up to 50 pA. Significance. By removing the need for the calorimeter system to provide spatial information, it is hoped that the de-averaging approach can facilitate clinically relevant, cost effective and less complex calorimeter systems for performing high current pCTs

Nucleation of NaCl from aqueous solution: critical sizes, ion-attachment kinetics, and rates

Nucleation and crystal growth are important in material synthesis, climate modeling, biomineralization, and pharmaceutical formulation. Despite tremendous efforts, the mechanisms and kinetics of nucleation remain elusive to both theory and experiment. Here we investigate sodium chloride (NaCl) nucleation from supersaturated brines using seeded atomistic simulations, polymorph-specific order parameters, and elements of classical nucleation theory. We find that NaCl nucleates via the common rock salt structure. Ion desolvation - not diffusion - is identified as the limiting resistance to attachment. Two different analyses give approximately consistent attachment kinetics: diffusion along the nucleus size coordinate and reaction-diffusion analysis of approach-to-coexistence simulation data from Aragones et al. [J. Chem. Phys., 2012, 136, 244508]. Our simulations were performed at realistic supersaturations to enable the first direct comparison to experimental nucleation rates for this system. The computed and measured rates converge to a common upper limit at extremely high supersaturation. However, our rate predictions are between 15 and 30 orders of magnitude too fast. We comment on possible origins of the large discrepancies

Hit-hard and early versus step-up treatment in severe sarcoidosis

Purpose of reviewThe treatment of sarcoidosis remains uncertain, despite 70 years of study. The conventional approach is to initiate corticosteroids in individuals who require treatment. The position of more aggressive regimes is unknown.Recent findingsRecent recognition that many patients will require prolonged therapy, and the observation that corticosteroids lead to overt and insidious toxicities, have led to suggestions that steroid-sparing medications be used earlier in the management of sarcoidosis. Individuals with poor prognostic features, designated as 'high-risk' sarcoidosis may, especially benefit from a broader palette of therapeutic options in the initial treatment regimen. An even more aggressive approach, known as 'top-down' or 'hit-hard and early' therapy has emerged in the fields of gastroenterology and rheumatology in the past 15 years, on the premise that highly effective early control of inflammation leads to better outcomes. These regimens typically involve early initiation of biologic therapies.SummaryFor certain subpopulations of sarcoidosis patients, 'top-down' therapy could be helpful. Severe pulmonary sarcoidosis, neurosarcoidosis, cardiac sarcoidosis and multiorgan sarcoidosis are phenotypes that may be most relevant for revised therapeutic algorithms. Precision medicine approaches and randomized trials will be necessary to confirm a role for top-down therapy in the routine management of sarcoidosis