Entropy Driven Crystal Formation on Highly Strained Substrates

In heteroepitaxy, lattice mismatch between the deposited material and the underlying surface strongly affects nucleation and growth processes. The effect of mismatch is well studied in atoms with growth kinetics typically dominated by bond formation with interaction lengths on the order of one lattice spacing. In contrast, less is understood about how mismatch affects crystallization of larger particles, such as globular proteins and nanoparticles, where interparticle interaction energies are often comparable to thermal fluctuations and are short ranged, extending only a fraction of the particle size. Here, using colloidal experiments and simulations, we find particles with short-range attractive interactions form crystals on isotropically strained lattices with spacings significantly larger than the interaction length scale. By measuring the free-energy cost of dimer formation on monolayers of increasing uniaxial strain, we show the underlying mismatched substrate mediates an entropy-driven attractive interaction extending well beyond the interaction length scale. Remarkably, because this interaction arises from thermal fluctuations, lowering temperature causes such substrate-mediated attractive crystals to dissolve. Such counterintuitive results underscore the crucial role of entropy in heteroepitaxy in this technologically important regime. Ultimately, this entropic component of lattice mismatched crystal growth could be used to develop unique methods for heterogeneous nucleation and growth of single crystals for applications ranging from protein crystallization to controlling the assembly of nanoparticles into ordered, functional superstructures. In particular, the construction of substrates with spatially modulated strain profiles would exploit this effect to direct self-assembly, whereby nucleation sites and resulting crystal morphology can be controlled directly through modifications of the substrate

Entropy-driven crystal formation on highly strained substrates

In heteroepitaxy, lattice mismatch between the deposited material and the underlying surface strongly affects nucleation and growth processes. The effect of mismatch is well studied in atoms with growth kinetics typically dominated by bond formation with interaction lengths on the order of one lattice spacing. In contrast, less is understood about how mismatch affects crystallization of larger particles, such as globular proteins and nanoparticles, where interparticle interaction energies are often comparable to thermal fluctuations and are short ranged, extending only a fraction of the particle size. Here, using colloidal experiments and simulations, we find particles with short-range attractive interactions form crystals on isotropically strained lattices with spacings significantly larger than the interaction length scale. By measuring the free-energy cost of dimer formation on monolayers of increasing uniaxial strain, we show the underlying mismatched substrate mediates an entropydriven attractive interaction extending well beyond the interaction length scale. Remarkably, because this interaction arises from thermal fluctuations, lowering temperature causes such substratemediated attractive crystals to dissolve. Such counterintuitive results underscore the crucial role of entropy in heteroepitaxy in this technologically important regime. Ultimately, this entropic component of lattice mismatched crystal growth could be used to develop unique methods for heterogeneous nucleation and growth of single crystals for applications ranging from protein crystallization to controlling the assembly of nanoparticles into ordered, functional superstructures. In particular, the construction of substrates with spatially modulated strain profiles would exploit this effect to direct self-assembly, whereby nucleation sites and resulting crystal morphology can be controlled directly through modifications of the substrate. thermodynamics | colloids | tunable depletion interaction C rystal growth typically initiates at surfaces where the barrier for nucleation is significantly lower than in bulk Results Our system consists of 1.30-μm diameter charge stabilized polystyrene spheres in aqueous solution. The solution contains the nonionic surfactant, hexaethylene glycol monodocecyl ether (C 12 E 6 ), which forms micelles in water. The micelles induce an attractive depletion interaction between polystyrene spheres for surface-to-surface distances of approximately one micelle diameter or less. The depth of the interaction potential is proportional to the entropy gained due to the volume liberated to the micelles when the excluded volume around the two particles overlaps with strength of a few k B T, where k B is Boltzmann's constant and T is temperature. This interaction is strongly dependent on both the concentration and the diameter of the micelles. By using the surfactant C 12 E 6 , whose micelle concentration and diameter both increase with increasing temperature, small temperature changes allow the particles to overcome thermal fluctuations and form colloidal crystals To study the role of strain in heterogeneous crystallization, a single layer of particles is first self-assembled in the holes of a lithographically patterned template In the experiments, we use bright-field microscopy to monitor how interparticle spacing in growing crystals varies with the Author contributions: J.R.S., S.F.H., R.G., S.J.G., A.H., and I.C. designed research; J.R.S., S.F.H., and A.H. performed research; S.J.G. contributed new reagents/analytic tools; J.R.S., S.F.H., S.J.G., A.H., and I.C. analyzed data; and J.R.S., S.F.H., S.J.G., A.H., and I.C. wrote the paper. The authors declare no conflict of interest. This article is a PNAS Direct Submission. PHYSICS lattice constant of the underlying substrate. Single-layer crystals were first assembled on a featureless microscope coverslip. The equilibrium lattice constant was obtained by measuring the nearest-neighbor separation probability distribution, P(r). We find P(r) is symmetric, peaks at l 0 ∼ 1.35 μm, and decays to zero within 25 nm. This equilibrium lattice constant l 0 was compared with P(r) for all particles on substrates with square and rectangular lattice symmetries having lattice constants ranging between 1.350 and 1.500 μm. Images and P(r) measurements on substrates with square symmetry and three different lattice parameters are shown in To identify how entropic and energetic contributions to particle interactions vary with substrate strain, we performed Monte Carlo simulations of particle pairs on substrates of both isotropic and uniaxial strains. The depletion interaction is modeled by the temperature-independent Morse potential U(r) = E 0 [1 − exp(−a (r − l 0 ))] 2 − E 0 , where E 0 is the depth of the potential, l 0 = 1.0, and a is inversely proportional to the width of the potential. This interaction is applied to all particles, including both in-plane interactions and particle interactions with the underlying substrate, to faithfully reproduce the experiments. As seen in the experiments, gravity is weak compared with the interaction potential-P(r) particles leave the substrate when the interaction level is too low. Calculations show gravitational effects are more than one order of magnitude smaller. We find the parameters a = 65 and E 0 /k B T = 2.27 reproduce the dependence of ΔF s/us /k B T on uniaxial strain as measured in the experiments The temperature-dependent probability p cryst that neighboring crystallizing particles are bonded can be approximated by reflecting twice the probability distribution P(r/l 0 < 1) about the line r/l 0 = 1, as shown by the blue shaded area in These results reveal a process in which entropy-driven thermal fluctuations stabilize crystal formation on substrates with lattice constants significantly larger than the interaction range. Although previous work has described particle crystallization on strained lattices under the influence of depletion potentials PHYSICS results and calculations have direct bearing on heterogeneous crystallization of globular proteins and nanoparticles (26). Specifically, they clarify how the free energy changes with temperature. As illustrated by Methods Sample Preparation. Samples are prepared by adding NaCl (4 mM) to deionized water, after which the nonionic surfactant C 12 E 6 is added (2 wt%). Once the surfactant has equilibrated, polystyrene particles (3% polydispersity; Molecular Probes) are added to the solution. Templates are fabricated by spinning 500 nm poly(methyl methacrylate) onto a microscope coverslip and using electron beam lithography to pattern holes with a diameter of 1.26 μm. The sample is injected into a sample cell formed between the patterned coverslip and a microscope slide with a 170-μm spacer used to set the gap in height. The sample cell is sealed to prevent flow. Temperature control is accomplished by attaching an objective heater to a 100× (1.4 NA) objective and encasing the inverted microscope in a heated chamber with temperature fluctuations ±0.1°C. All data are acquired after the temperature has equilibrated using bright-field microscopy. Computer Simulations. Monte Carlo simulations using the standard Metropolis criterion were applied. To calculate the probability a dimer arranged parallel or perpendicular to the strained direction in the uniaxially strained case, the Monte Carlo moves also contain rotations of the dimer to generate the large number of transitions between orientations. Free-energy differences are calculated from the Boltzmann probability distribution. Using the Morse potential energy then gives the entropic contribution. We restrict the height of the second-layer particles to (z − z 0 )/l 0 ≤ 0.03 because for larger distances above the bottom layer, particles would start to desorb. ACKNOWLEDGMENTS. The authors thank James Sethna for comments

Entropy-driven crystal formation on highly strained substrates

In heteroepitaxy, lattice mismatch between the deposited material and the underlying surface strongly affects nucleation and growth processes. The effect of mismatch is well studied in atoms with growth kinetics typically dominated by bond formation with interaction lengths on the order of one lattice spacing. In contrast, less is understood about how mismatch affects crystallization of larger particles, such as globular proteins and nanoparticles, where interparticle interaction energies are often comparable to thermal fluctuations and are short ranged, extending only a fraction of the particle size. Here, using colloidal experiments and simulations, we find particles with short-range attractive interactions form crystals on isotropically strained lattices with spacings significantly larger than the interaction length scale. By measuring the free-energy cost of dimer formation on monolayers of increasing uniaxial strain, we show the underlying mismatched substrate mediates an entropydriven attractive interaction extending well beyond the interaction length scale. Remarkably, because this interaction arises from thermal fluctuations, lowering temperature causes such substratemediated attractive crystals to dissolve. Such counterintuitive results underscore the crucial role of entropy in heteroepitaxy in this technologically important regime. Ultimately, this entropic component of lattice mismatched crystal growth could be used to develop unique methods for heterogeneous nucleation and growth of single crystals for applications ranging from protein crystallization to controlling the assembly of nanoparticles into ordered, functional superstructures. In particular, the construction of substrates with spatially modulated strain profiles would exploit this effect to direct self-assembly, whereby nucleation sites and resulting crystal morphology can be controlled directly through modifications of the substrate. thermodynamics | colloids | tunable depletion interaction C rystal growth typically initiates at surfaces where the barrier for nucleation is significantly lower than in bulk Results Our system consists of 1.30-μm diameter charge stabilized polystyrene spheres in aqueous solution. The solution contains the nonionic surfactant, hexaethylene glycol monodocecyl ether (C 12 E 6 ), which forms micelles in water. The micelles induce an attractive depletion interaction between polystyrene spheres for surface-to-surface distances of approximately one micelle diameter or less. The depth of the interaction potential is proportional to the entropy gained due to the volume liberated to the micelles when the excluded volume around the two particles overlaps with strength of a few k B T, where k B is Boltzmann's constant and T is temperature. This interaction is strongly dependent on both the concentration and the diameter of the micelles. By using the surfactant C 12 E 6 , whose micelle concentration and diameter both increase with increasing temperature, small temperature changes allow the particles to overcome thermal fluctuations and form colloidal crystals To study the role of strain in heterogeneous crystallization, a single layer of particles is first self-assembled in the holes of a lithographically patterned template In the experiments, we use bright-field microscopy to monitor how interparticle spacing in growing crystals varies with the Author contributions: J.R.S., S.F.H., R.G., S.J.G., A.H., and I.C. designed research; J.R.S., S.F.H., and A.H. performed research; S.J.G. contributed new reagents/analytic tools; J.R.S., S.F.H., S.J.G., A.H., and I.C. analyzed data; and J.R.S., S.F.H., S.J.G., A.H., and I.C. wrote the paper. The authors declare no conflict of interest. This article is a PNAS Direct Submission. PHYSICS lattice constant of the underlying substrate. Single-layer crystals were first assembled on a featureless microscope coverslip. The equilibrium lattice constant was obtained by measuring the nearest-neighbor separation probability distribution, P(r). We find P(r) is symmetric, peaks at l 0 ∼ 1.35 μm, and decays to zero within 25 nm. This equilibrium lattice constant l 0 was compared with P(r) for all particles on substrates with square and rectangular lattice symmetries having lattice constants ranging between 1.350 and 1.500 μm. Images and P(r) measurements on substrates with square symmetry and three different lattice parameters are shown in To identify how entropic and energetic contributions to particle interactions vary with substrate strain, we performed Monte Carlo simulations of particle pairs on substrates of both isotropic and uniaxial strains. The depletion interaction is modeled by the temperature-independent Morse potential U(r) = E 0 [1 − exp(−a (r − l 0 ))] 2 − E 0 , where E 0 is the depth of the potential, l 0 = 1.0, and a is inversely proportional to the width of the potential. This interaction is applied to all particles, including both in-plane interactions and particle interactions with the underlying substrate, to faithfully reproduce the experiments. As seen in the experiments, gravity is weak compared with the interaction potential-P(r) particles leave the substrate when the interaction level is too low. Calculations show gravitational effects are more than one order of magnitude smaller. We find the parameters a = 65 and E 0 /k B T = 2.27 reproduce the dependence of ΔF s/us /k B T on uniaxial strain as measured in the experiments The temperature-dependent probability p cryst that neighboring crystallizing particles are bonded can be approximated by reflecting twice the probability distribution P(r/l 0 < 1) about the line r/l 0 = 1, as shown by the blue shaded area in These results reveal a process in which entropy-driven thermal fluctuations stabilize crystal formation on substrates with lattice constants significantly larger than the interaction range. Although previous work has described particle crystallization on strained lattices under the influence of depletion potentials PHYSICS results and calculations have direct bearing on heterogeneous crystallization of globular proteins and nanoparticles (26). Specifically, they clarify how the free energy changes with temperature. As illustrated by Methods Sample Preparation. Samples are prepared by adding NaCl (4 mM) to deionized water, after which the nonionic surfactant C 12 E 6 is added (2 wt%). Once the surfactant has equilibrated, polystyrene particles (3% polydispersity; Molecular Probes) are added to the solution. Templates are fabricated by spinning 500 nm poly(methyl methacrylate) onto a microscope coverslip and using electron beam lithography to pattern holes with a diameter of 1.26 μm. The sample is injected into a sample cell formed between the patterned coverslip and a microscope slide with a 170-μm spacer used to set the gap in height. The sample cell is sealed to prevent flow. Temperature control is accomplished by attaching an objective heater to a 100× (1.4 NA) objective and encasing the inverted microscope in a heated chamber with temperature fluctuations ±0.1°C. All data are acquired after the temperature has equilibrated using bright-field microscopy. Computer Simulations. Monte Carlo simulations using the standard Metropolis criterion were applied. To calculate the probability a dimer arranged parallel or perpendicular to the strained direction in the uniaxially strained case, the Monte Carlo moves also contain rotations of the dimer to generate the large number of transitions between orientations. Free-energy differences are calculated from the Boltzmann probability distribution. Using the Morse potential energy then gives the entropic contribution. We restrict the height of the second-layer particles to (z − z 0 )/l 0 ≤ 0.03 because for larger distances above the bottom layer, particles would start to desorb. ACKNOWLEDGMENTS. The authors thank James Sethna for comments

Uncommon acquired Gerbode defect following extensive bicuspid aortic valve endocarditis

Gerbode defect is a rare type of left ventricle to right atrium shunt. It is usually congenital in origin, but acquired cases are also described, mainly following infective endocarditis, valve replacement, trauma or acute myocardial infarction. We report a case of a 50-year-old man who suffered an extensive and complex infective endocarditis involving a bicuspid aortic valve, the mitral-aortic intervalvular fibrosa and the anterior leaflet of the mitral valve. After dual valve replacement and annular reconstruction, a shunt between the left ventricle and the right atrium - Gerbode defect, and a severe leak of the mitral prosthesis were detected. Reintervention was performed with successful shunt closure with an autologous pericardial patch and paravalvular leak correction. No major complications occurred denying the immediate post-surgery period and the follow-up at the first year was uneventful

Der Konflikt in Afghanistan : Historischer und gesellschaftlicher Hintergrund, Evolution und Lageentwicklung – ein Positionspapier

This study is part of a larger project, the aim of which is to elucidate “mental health nurses” attitudes towards their patients'. In this study, nurses' and patients' attitudes are described from the perspective of both parties using a qualitative approach. The informants were selected from a rehabilitation unit for young adults, below 40, suffering from psychosis at a psychiatric clinic that provides acute psychiatric care. The informant group consisted of three dyads: three patients with various diagnoses and three nurses with primary responsibility for the patients' daily care. The aim of this particular study was to extend our preliminary understanding of nurses' attitudes towards psychiatric patients in the context of psychiatric in-patient care, by elucidating the patient's “inner” picture of her/his past, present and future and the nurse's picture of the same patient's past, present and future. Data were collected and analysed using a phenomenological-hermeneutic approach and the narrative picturing technique. For each picture and group, 15 related sub-themes emerged, on the basis of which six themes were formulated. The findings show that the nurses overrate their own importance when it comes to the patient's well-being on the ward. All the nurses emphasize confirmation and safety as the basis of their nursing care, while in the patient's picture the nurses represent a replication of childhood demands, which probably means that nursing care risks becoming a continuation of the patient's childhood estrangement

Slab melting as a barrier to deep carbon subduction

Interactions between crustal and mantle reservoirs dominate the surface inventory of volatile elements over geological time, moderating atmospheric composition and maintaining a lifesupporting planet1. While volcanoes expel volatile components into surface reservoirs, subduction of oceanic crust is responsible for replenishment of mantle reservoirs2,3. Many natural, ‘superdeep’ diamonds originating in the deep upper mantle and transition zone host mineral inclusions, indicating an affinity to subducted oceanic crust4–7. Here we show that the majority of slab geotherms will intersect a deep depression along the melting curve of carbonated oceanic crust at depths of approximately 300 to 700 kilometres, creating a barrier to direct carbonate recycling into the deep mantle. Low-degree partial melts are alkaline carbonatites that are highly reactive with reduced ambient mantle, producing diamond. Many inclusions in superdeep diamonds are best explained by carbonate melt–peridotite reaction. A deep carbon barrier may dominate the recycling of carbon in the mantle and contribute to chemical and isotopic heterogeneity of the mantle reservoir