Directional Self‐Assembly of Fluorinated Star Block Polymer Thin Films Using Mixed Solvent Vapor Annealing

We demonstrate the directional alignment of perpendicular‐lamellae domains in fluorinated three‐armed star block polymer (BP) thin films using solvent vapor annealing with shear stress. The control of orientation and alignment was accomplished without any substrate surface modification. Additionally, three‐armed star poly(methyl methacrylate‐block‐styrene) [PMMA‐PS] and poly(octafluoropentyl methacrylate‐block‐styrene) were compared to their linear analogues to examine the impact of fluorine content and star architecture on self‐assembled BP feature sizes and interdomain density profiles. X‐ray reflectometry results indicated that the star BP molecular architecture increased the effective polymer segregation strength and could possibly facilitate reduced polymer domain spacings, which are useful in next‐generation nanolithographic applications. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019 , 57, 1663–1672     

Density fluctuations and the structure of a nonuniform hard sphere fluid

We derive an exact equation for density changes induced by a general external field that corrects the hydrostatic approximation where the local value of the field is adsorbed into a modified chemical potential. Using linear response theory to relate density changes self-consistently in different regions of space, we arrive at an integral equation for a hard sphere fluid that is exact in the limit of a slowly varying field or at low density and reduces to the accurate Percus-Yevick equation for a hard core field. This and related equations give accurate results for a wide variety of fields.     

Toward Homological Characterization of Semirings: Serre’s Conjecture and Bass’s Perfectness in a Semiring Context

Among other results on homological characterization of semirings, we prove that the classes of projective and free right (left) semimodules over the polynomial semiring R[x₁, x₂,..., x_n] over an additively regular division semiring R coincide iff R is a field. Also it is shown that an additively regular commutative semiring R is perfect (in H. Basss sense) iff R is a perfect ring.In Celebration of the Sixtieth Birthday of Ralph N. McKenzieReceived July 27, 2003; accepted in final form April 2, 2004.     

Determining Liquid Structure from the Tail of the Direct Correlation Function

In important early work, Stell showed that one can determine the pair correlation function h(r) of the hard-sphere fluid for all distances r by specifying only the tail of the direct correlation function c(r) at separations greater than the hard-core diameter. We extend this idea in a very natural way to potentials with a soft repulsive core of finite extent and a weaker and longer ranged tail. We introduce a new continuous function T(r) which reduces exactly to the tail of c(r) outside the (soft) core region and show that both h(r) and c(r) depend only on the out projection of T(r): i.e., the product of the Boltzmann factor of the repulsive core potential times T(r). Standard integral equation closures can thus be reinterpreted and assessed in terms of their predictions for the tail of c(r) and simple approximations for its form suggest new closures. A new and very efficient variational method is proposed for solving the Ornstein–Zernike equation given an approximation for the tail of c. Initial applications of these ideas to the Lennard-Jones and the hard-core Yukawa fluid are discussed.     

On V-semirings and Semirings All of Whose Cyclic Semimodules Are Injective

In this article, we introduce and study V- and CI-semirings—semirings all of whose simple and cyclic, respectively, semimodules are injective. We describe V-semirings for some classes of semirings and establish some fundamental properties of V-semirings. We show that all Jacobson-semisimple V-semirings are V-rings. We also completely describe the bounded distributive lattices, Gelfand, subtractive, semisimple, and antibounded, semirings that are CI-semirings. Applying these results, we give complete characterizations of congruence-simple subtractive and congruence-simple antibounded CI-semirings which solve two earlier open problems for these classes of CI-semirings.     

Defects and their removal in block copolymer thin film simulations

In recent years, there has been increased interest in using microphase-separated block copolymer thin films as submicrometer/suboptical masks in next generation semiconductor and magnetic media fabrication. With the goals of removing metastable defects in block copolymer thin film simulations and potentially examining equilibrium defect populations, we report on two new numerical techniques that can be used in field-theoretic computer simulations: (1) a spectral amplitude filter (SF) that encourages the simulation to relax into high symmetry states (representing zero defect states), and (2) different variants of force-biased, partial saddle point Monte Carlo algorithms that allow for barrier crossing toward lower energy defect-free states. Beyond their use for removing defects, the force-biased Monte Carlo algorithms will be seen to provide a promising tool for studying equilibrium defect populations. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 2495–2511, 2006     

Symmetry breaking of in-plane order in confined copolymer mesophases

Packing of spherical-domain block copolymer mesophases confined to a thin film is investigated as a function of the number of layers n. We find an abrupt transition from hexagonal to orthorhombic in-plane ordering of domains when n is increased from 4 to 5. As n increases further (up to 23 in this study), the symmetry of the orthorhombic phase asymptotically approaches that of the body-centered cubic (110) plane. These results are interpreted in terms of the energetics of competing packings in the bulk and at the film interfaces. Detailed structural and thermodynamic properties are obtained with self-consistent field theory.     

Exact communication costs for consensus and leader in a tree

We continue the study of communication costs of Consensus and Leader initiated in a previous paper. We deal with all scenarios with linear complexity in a tree topology, and prove exact (as opposed to asymptotic) tight bounds for the bit and message complexities. A particular scenario depends on whether the tree size or the size parity is known to the processors.     

Low-Light Trees, and Tight Lower Bounds for Euclidean Spanners

We show that for every n-point metric space M and positive integer k, there exists a spanning tree T with unweighted diameter O(k) and weight w(T)=O(k⋅n ^1/k )⋅w(MST(M)), and a spanning tree T′ with weight w(T′)=O(k)⋅w(MST(M)) and unweighted diameter O(k⋅n ^1/k ). These trees also achieve an optimal maximum degree. Furthermore, we demonstrate that these trees can be constructed efficiently.