Sphericity and Symmetry Breaking in Asymmetric Diblock Copolymer Melts

Block polymers have captured the interest of scientists and engineers for more than half a century. In general, the phase behavior of A-B diblock copolymers, the simplest category of such self-assembling macromolecules, has been accepted as thoroughly understood. Experiments and theory conducted over the past decade have revealed remarkable phase complexity in the limit of asymmetric compositions, where the A block is considerably shorter than the B block, resulting in the formation of nanoscale micelles. Small-angle x-ray scattering (SAXS) measurements have revealed the formation of various low symmetry Frank-Kasper phases and a dodecagonal quasicrystal, reflecting fascinating analogies with the phase behavior of metal alloys. These findings will be discussed in the context of a competition between the tendency to form spherical particles and the constraints associated with filing space at uniform density

Molecular Weight Dependence of Polymersome Membrane Elasticity and Stability

Vesicles prepared in water from a series of diblock copolymers and termed "polymersomes" are physically characterized. With increasing molecular weight $\bar{M}_n$, the hydrophobic core thickness $d$ for the self-assembled bilayers of polyethyleneoxide - polybutadiene (PEO-PBD) increases up to 20 $nm$ - considerably greater than any previously studied lipid system. The mechanical responses of these membranes, specifically, the area elastic modulus $K_a$ and maximal areal strain $\alpha_c$ are measured by micromanipulation. As expected for interface-dominated elasticity, $K_a$ ($\simeq$ 100 $pN/nm$) is found to be independent of $\bar{M}_n$. Related mean-field ideas also predict a limiting value for $\alpha_c$ which is universal and about 10-fold above that typical of lipids. Experiments indeed show $\alpha_c$ generally increases with $\bar{M}_n$, coming close to the theoretical limit before stress relaxation is opposed by what might be chain entanglements at the highest $\bar{M}_n$. The results highlight the interfacial limits of self-assemblies at the nano-scale.Comment: 16 pages, 5 figures, and 1 tabl

Stable Frank-Kasper phases of self-assembled, soft matter spheres

Single molecular species can self-assemble into Frank Kasper (FK) phases, finite approximants of dodecagonal quasicrystals, defying intuitive notions that thermodynamic ground states are maximally symmetric. FK phases are speculated to emerge as the minimal-distortional packings of space-filling spherical domains, but a precise quantitation of this distortion and how it affects assembly thermodynamics remains ambiguous. We use two complementary approaches to demonstrate that the principles driving FK lattice formation in diblock copolymers emerge directly from the strong-stretching theory of spherical domains, in which minimal inter-block area competes with minimal stretching of space-filling chains. The relative stability of FK lattices is studied first using a diblock foam model with unconstrained particle volumes and shapes, which correctly predicts not only the equilibrium {\sigma} lattice, but also the unequal volumes of the equilibrium domains. We then provide a molecular interpretation for these results via self-consistent field theory, illuminating how molecular stiffness regulates the coupling between intra-domain chain configurations and the asymmetry of local packing. These findings shed new light on the role of volume exchange on the formation of distinct FK phases in copolymers, and suggest a paradigm for formation of FK phases in soft matter systems in which unequal domain volumes are selected by the thermodynamic competition between distinct measures of shape asymmetry.Comment: 40 pages, 22 figure

Electromechanical Limits of Polymersomes

Self-assembled membranes of amphiphilic diblock copolymers enable comparisons of cohesiveness with lipid membranes over the range of hydrophobic thicknesses d = 3-15 nm. At zero mechanical tension the breakdown potential Vc for polymersomes with d = 15 nm is 9 V, compared to 1 V for liposomes with d = 3 nm. Nonetheless, electromechanical stresses at breakdown universally exhibit a V2 c dependence, and membrane capacitance shows the expected strong d dependence, conforming to simple thermodynamic models. The viscous nature of the diblock membranes is apparent in the protracted postporation dynamics

Adhesion of Polymer Vesicles

The adhesion and bending modulus of polybutadiene-poly(ethylene oxide) block copolymer vesicles made from a bidisperse mixture of polymers is measured using micropipette aspiration. The adhesion energy between biotinylated vesicles and avidin beads is modeled by incorporating the extension of the adhesive ligands above the surface brush of the vesicle according to the blob model of bidisperse polymer mixtures of Komura and Safran assuming the polymer brush at the surface of the vesicle is compact. The same model accurately reproduces the scaling of the bending modulus with polymer composition

VisiCalc program for calculating nutrient requirements for beef cattle

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A simple non-linear analytical relationship between aerosol accumulation number and sub-micron volume, explaining their observed ratio in the clean and polluted marine boundary layer

We propose an analytical expression for the relation between aerosol accumulation number and sub-micron volume over the marine boundary layer (MBL), based on a simple balance equation. By providing appropriate source and sink terms which account for entrainment, coagulation, in-cloud scavenging and condensational growth, the model is able to reproduce the observed ratio between MBL particles larger than 80 nm diameter (as a proxy for accumulation mode number) and submicron aerosol volume, from freshly polluted to background conditions. Entrainment and coagulation are essential in predicting the observed ratio. Budget and lifetime calculations show that, due to relatively low source rates of oceanic non-sea-salt-sulfate and sea-salt, the anthropogenic signature in aerosol volume remains significant even after 8 days of MBL transport

The growth of ZnO crystals from the melt

The peculiar properties of zinc oxide (ZnO) make this material interesting for very different applications like light emitting diodes, lasers, and piezoelectric transducers. Most of these applications are based on epitaxial ZnO layers grown on suitable substrates, preferably bulk ZnO. Unfortunately the thermochemical properties of ZnO make the growth of single crystals difficult: the triple point 1975 deg C., 1.06 bar and the high oxygen fugacity at the melting point p_O2 = 0.35 bar lead to the prevailing opinion that ZnO crystals for technical applications can only be grown either by a hydrothermal method or from "cold crucibles" of solid ZnO. Both methods are known to have significant drawbacks. Our thermodynamic calculations and crystal growth experiments show, that in contrast to widely accepted assumptions, ZnO can be molten in metallic crucibles, if an atmosphere with "self adjusting" p_O2 is used. This new result is believed to offer new perspectives for ZnO crystal growth by established standard techniques like the Bridgman method.Comment: 6 pages, 6 figures, accepted for J. Crystal Growt

Quantitative Membrane Loading of Polymer Vesicles

We utilize a series of structurally homologous, multi-porphyrin-based, fluorophores (PBFs) in order to explore the capacity of polymer vesicles (polymersomes) to stably incorporate large hydrophobic molecules, non-covalently within their thick lamellar membranes. Through aqueous hydration of dry, uniform thin-films of amphiphilic polymer and PBF species deposited on Teflon, self-assembled polymersomes are readily generated incorporating the hydrophobic fluorophores in prescribed molar ratios within their membranes. The size-dependent spectral properties of the PBFs allow for ready optical verification (via steady-state absorption and emission spectroscopy) of the extent of vesicle membrane loading and enable delineation of intermembranous molecular interactions. The resultant effects of PBF membrane-loading on polymersome thermodynamic and mechanical stability are further assessed by cryogenic transmission electron microscopy (cryo-TEM) and micropipet aspiration, respectively. We demonstrate that polymersomes can be loaded at up to 10 mol/wt% concentrations, with hydrophobic molecules that possess sizes comparable to those of large pharmaceutical conjugates (e.g. ranging 1.4–5.4 nm in length and Mw = 0.7–5.4 kg mol–1), without significantly compromising the robust thermodynamic and mechanical stabilities of these synthetic vesicle assemblies. Due to membrane incorporation, hydrophobic encapsulants are effectively prevented from self-aggregation, able to be highly concentrated in aqueous solution, and successfully shielded from deleterious environmental interactions. Together, these studies present a generalized paradigm for the generation of complex multi-functional materials that combine both hydrophilic and hydrophobic agents, in mesoscopic dimensions, through cooperative self-assembly