Body-centered Cubic Packing Research Articles

Effect of chain architecture on the structure, dynamics, and rheology of thermoresponsive poloxamer hydrogels and associated blends.

Poloxamers, ABA triblock polymers composed of a poly(propylene oxide) (PPO) midblock (B) and poly(ethylene oxide) (PEO) endblocks (A), are widely studied for biomedical applications. Aqueous poloxamer 407 (P407; also referred to as F127) undergoes a solution-to-gel transition with increasing temperature, driven by the formation and ordering of micelles onto periodic lattices; however, the gel temperature and resulting modulus has limited tunability. Here, reverse P407 (RP407), a BAB polymer of the same composition and molar mass but the inverted architecture, is synthesized via anionic polymerization. The micellization and gelation temperatures of RP407 are higher than that of P407 and the PPO endblocks allow for intermicelle bridging; however, both single-component solutions favor body-centered cubic (BCC) packings. Further, aqueous RP407 displays a "soft gel" region with interesting rheological behavior, including viscoelastic aging and thermal hysteresis. Combining P407 and RP407 yields solutions with intermediate transition temperatures and alters the size and micelle packing. While the single-component solutions produce BCC packings, the blends form close-packed structures and larger micelles of higher aggregation numbers. Blends of P407 with an analogous AB diblock (E111P32) display similar behavior, whereas RP407/diblock blends form intermediate-sized BCC-packed micelles. These differences in packing and aggregation alter the local environments within the gels, which could have implications for applications such as drug delivery and protein stabilization.

Determination of the effect of the open cell foam material geometry on the value of energy efficiency

THE PURPOSE. Improving the energy efficiency of open cell foam materials with different geometries (SC, BCC, FCC, DEM) and with different medium porosities (ε=0.7; ε=0.75; ε=0.8; ε=0.85; ε=0.9; ε=0.95) by numerical simulation. To determine the influence of the geometry and porosity of an open cell foam material on the values of pressure drop, heat flux and energy efficiency factor.METHODS .Numerical simulation was carried out using the ANSYS Fluent 19.2 software package. Geometric models of porous structures are sets of intersecting spheres with different packing structures: periodic Simple Cubic packing (SC), Face Centered Cubic packing (FCC), Body Centered Cubic packing (BCC), and random structure generated by the discrete element method (DEM).The calculations were carried out at the following air flow velocities: 0.01; 0.05; 0.25; 0.5; 0.75; 1; 1.25 m/s.RESULTS. Atair flow velocities of 0.01 m/s and 0.05 m/s, all the studied structures show approximately the same heat flux. With porosity values ε=0.75; ε=0.8; ε=0.85 the highest values of heat flow were shown by the FCC structure, with porosity ε=0.7; ε=0.9; ε=0.95 the BCC structure had the highest heat flux. This is explained by the fact that, at the corresponding porosity values, the FCC or BCC structure had the largest surface area, which provided the largest heat flux. With the porosities of media ε=0.7 and ε=0.75, the BCC and FCC cell packages show a high pressure drop. With the porosities of media ε=0.8 and ε=0.85, the highest pressure drop corresponds to FCC cell packing, and for porosities ε=0.9 and ε=0.95, to BCC cell packing.CONCLUSION. With equal high porosity, the BCC cell packing provides a higher value of heat flux than the FCC structure. The SC package has the lowest heat flux values for all studied porosities. The SC package also has the lowest pressure drop values and therefore the highest energy efficiency values.

Biphenyl-Induced Superhelix in l -Phenylalanine-Based Supramolecular Self-Assembly with Dynamic Morphology Transitions

Biphenyl-Induced Superhelix in <scp>l</scp> -Phenylalanine-Based Supramolecular Self-Assembly with Dynamic Morphology Transitions

Emergence of a C15 Laves Phase in Diblock Polymer/Homopolymer Blends.

The observation of complex, Frank-Kasper (FK) particle packings in diblock polymer melts has until recently been limited to low molecular weight, conformationally asymmetric polymers. We report temperature-dependent small-angle X-ray scattering (SAXS) studies of blends of a sphere-forming poly(styrene-block-1,4-butadiene) (SB) diblock polymer (Mn = 33.3 kg/mol, Đ = Mw/Mn = 1.08, fB = 0.18) with two different poly(1,4-butadiene) (B) homopolymer additives. When the B additive Mn is the same as that of the diblock core-forming B segment, these blends remarkably form tetrahedrally close-packed FK σ and Laves C14 and C15 phases with increasing B content. However, binary blends in which the B additive Mn is 60% of that of the diblock B segment form only the canonical body-centered cubic (BCC) particle packing and hexagonally-packed cylinders (HEXc). The observed phase behavior is rationalized in terms of "wet" and "dry" brush blending, whereby higher B Mn drives stronger localization of the homopolymer in the particle cores while preserving the interfacial area per SB diblock chain. The consequent packing constraints in these blends destabilize the BCC packing, and FK phases emerge as optimal minimal surface solutions to filling space at constant density while maximizing local particle sphericity.

Assessment of flow pattern and temperature profiles by residence time distribution in typical structured packed beds

The flow and temperature fields in packed beds are rather complex but are of great importance since they will influence macroscopic parameters and the overall performance of the packed bed system. Regions with either too high or too low velocity are not preferred since they will decrease the heat and mass transfer characteristics of packed beds. The residence time distribution (RTD) is a way to assess the characteristics of the flow maldistribution, where a narrower distribution is closer to the ideal plug flow with less dispersion. In this article, the RTD in three typical structured packed beds, namely, the simple cubic (SC) packing, the body-centered cubic (BCC) packing and the face-centered cubic (FCC) packing, are studied by using ANSYS FLUENT. Results show that, firstly, the RTD curve can be used to diagnose the flow pattern in packed beds where the skewed peak indicates the channeling effect and a long tail relates to recirculation. It is revealed secondly that, FCC packing has the narrowest RTD curve in the studied structures, BCC packing comes second and SC packing has the flattest RTD curve, which demonstrates that the flow uniformity in FCC packing is the best. For the same packing form, the flow is less maldistributed at higher velocity. Finally, it is shown that the packing form with less dispersion, which behaves more like the ideal plug flow, has a more uniform distribution of the particle-to-fluid heat transfer coefficient near the particle surface.

Rectangular Body-centered Cuboid Packing Lattices and Their Possible Applications

We first introduce several sphere packing ways such as simple cubic packing (SC), face-centered cubic packing (FCC), body-centered cubic packing (BCC), and rectangular body-centered cuboid packing (recBCC), where the rectangular body-centered cuboid packing means the packing method based on a rectangular cuboid whose base is square and whose height is times the length of one side of its square base such that the congruent spheres are centered at the 8 vertices and the centroid of the cuboid. The corresponding lattices are denoted as SCL, FCCL, BCCL, and recBCCL, respectively. Then we consider properties of those lattices, and show that FCCL and recBCCL are the same. Finally we point out some possible applications of the recBCC lattices.

Particle filtration characteristics of typical packing granular filters used in hot gas clean-up

Granular filter is a promising method in hot gas clean-up for advanced coal gasification technologies. Numerical simulations were performed in this paper for the particle filtration characteristics of granular filters with two typical packings: body centered cubic (BCC) and face centered cubic (FCC) packings. Fluid flow characteristics were investigated and pressure drop correlations for the two granular packings were obtained. The pressure drop of both packings increases linearly with the increase of velocity, and the pressure drop of the FCC packing is significantly higher than that of BCC. The discrete phase model (DPM) was employed to trace fly ash particle motion during the filtration process, and particle deposition characteristics on the granular surface, including the particle penetration, deposition distribution of different particle sizes, and deposition distribution along filter layers were determined. The deposition fraction of particles on each layer of granules decreases with the increase of row number, and the maximum deposition location is different for BCC and FCC packings. Large particles mainly deposit on the first four layers of granules, while small particles deposit over all layers. The collection efficiency of BCC and FCC packings increases with the increase of velocity, and they decrease first and then increase with particle diameter. Correlations of collection efficiency for the two granular packings are presented and they have good prediction accuracy.

Numerical Study on the Elastic Properties of Perforated Hollow Spheres Structure in Body-Centered Cubic Pattern

This paper investigates the elastic properties of a new type of hollow spheres structure numerically. In the new structure, hollow spheres perforated regularly with several holes, which are to open the inner sphere volume and surface, are bonded in the body-centered cubic (BCC) pattern. A 5×5 cells finite element model under the uniaxial load is established by Abaqus for the simulation. By changing the wall thickness, hole diameter and the bonding radius in the finite element model, the Young’s modulus and Poisson’s ratio of the BCC packing perforated hollow spheres structure (PHSS) as functions of these geometrical properties are shown, and the influence of these parameters on the structural elastic properties is analyzed.

Effective elastic moduli of core-shell-matrix composites

The effective Young’s modulus and Poisson’s ratio of spherical monodisperse and polydisperse core-shell particles ordered or randomly distributed in a continuous matrix were predicted using detailed three-dimensional numerical simulations of elastic deformation. The effective elastic moduli of body-centered cubic (BCC) and face-centered cubic (FCC) packing arrangements of monodisperse microcapsules and those of randomly distributed monodisperse or polydisperse microcapsules were identical. The numerical results were also compared with predictions of various effective medium approximations (EMAs) proposed in the literature. The upper bound of the EMA developed by Qiu and Weng (1991) was in good agreement with the numerically predicted effective Young’s modulus for BCC and FCC packings and for randomly distributed microcapsules. The EMA developed by Hobbs (1971) could also be used to estimate the effective Young’s modulus when the shell Young’s modulus was similar to that of the matrix. The EMA developed by Garboczi and Berryman (2001) could predict the effective Poisson’s ratio, as well as the effective Young’s modulus when the Young’s modulus of the core was smaller than that of the matrix. These results can find applications in the design of self-healing polymers, composite concrete, and building materials with microencapsulated phase change materials, for example.

Predicting the Crystal Structure and Phase Transitions in High-Entropy Alloys

High-entropy alloys (HEAs) have advantageous properties compared with other systems as a result of their chemistry and crystal structure. The transition between a face-centered cubic (FCC) and body-centered cubic (BCC) structure in the Al x CoCrFeNi high-entropy alloy system has been investigated on the atomic scale in this work. The Al x CoCrFeNi system, as well as being a useful system itself, can also be considered a model HEA material. Ordering in the FCC structure was investigated, and an order–disorder transition was predicted at ~600 K. It was found that, at low temperatures, an ordered lattice is favored over a truly random lattice. The fully disordered BCC structure was found to be unstable. When partial ordering was imposed (lowering the symmetry), with Al and Ni limited specific sites of the BCC system, the BCC packing was stabilized. Decomposition of the ordered BCC single phase into a dual phase (Al-Ni rich and Fe-Cr rich) is also considered.

Micellar packing of pluronic block copolymer solutions: Polymeric impurity effects

Small angle X-ray scattering (SAXS), dynamic light scattering (DLS), and high performance liquid chromatography (HPLC) experiments are performed to support that the inter-micellar distance of Pluronic cubic structures in aqueous solutions is governed by the poly(ethylene oxide) (PEO)-poly(propylene oxide) (PPO)-PEO triblock copolymer concentration (not the overall polymer concentration) in the solutions. The “as-received (AR)” and “purified (Pure)” F108 solutions show a separate concentration dependence of body-centered cubic (BCC) lattice spacing, when the overall polymer concentration is used as a micellar packing parameter in aqueous solution. When the 22 wt% of non-micellizable polymeric impurities in the AR Pluronic F108 is taken into account, however, a universal concentration dependence of the BCC lattice spacing is observed, unifying results from both AR and Pure F108 solutions. When the PEO-PPO-PEO triblock copolymer concentration from the HPLC analysis is employed as an effective polymer concentration parameter, the universal relationship is observed to provide strong evidence that the polymeric impurities in AR F108 locate themselves in the less dense parts of the interstitial regions on the BCC lattice points, where were occupied by the triblock copolymer micelles. Although the polymeric impurities in AR F108 do not affect the actual triblock concentration dependence of the lattice spacing, they do shift the onset concentration of BCC micellar ordering. In the Pure F108, the onset of BCC packing occurs at the point where the nearest-neighbor radius (Rnn) in the BCC lattice is approximately equal to the hydrodynamic radius (Rh), indicating that lattice formation begins upon “hydrodynamic contact” between micelles. In the AR F108, the onset of packing occurs when Rnn/Rh is approximately 0.9, indicating that, in the presence of the polymeric impurities, micelles must be forced together beyond the point of hydrodynamic contact for the BCC packing. Open image in new window

Pore Space Microstructure Evolution of Regular Sphere Packings Undergoing Compaction and Cementation

We examine the pore space structure evolution of ordered uniform sphere packs: simple cubic (SC), body centered cubic (BCC), and face centered cubic (FCC), undergoing simple diagenetic processes that reduce their pore spaces. Focus is on the occurrence of pore space microstructure changes or transitions, which are followed through their characteristic or critical pore lengths (lc). For almost all the cubic packings undergoing either compaction or cementation there are no singularities in lc. This is a consequence of having a single pore shape controlling flow at all stages of the process. However, this is not so for the BCC packing under cementation, for which lc is non-monotonic exhibiting a kink at \({\phi \approx 0.1452}\) , the porosity at which the pore shape controlling flow switches to a different form and position. These results for uniform compaction/cementation complement our previous works on pore networks under random shrinkage. Kinks in lc as porosity decreases signal pore space microstructure transitions that anticipate sudden changes in the permeability–porosity relation as porosity decreases. The consequences are great; clearly lc is not a constant unless the diagenetic process is mild. A lc function of compaction/cementation advancement should be used above a transition and a different lc function below. For the sphere packs here, once the diagenetic process has reduced the pore space substantially, a lc function of compaction/cementation advancement is mandatory if we are to capture all significant flow features.

Simulation of electric double layer capacitors with mesoporous electrodes: Effects of morphology and electrolyte permittivity

Abstract This paper aims to numerically predict the capacitance of electric double layer capacitors (EDLCs) made of mesoporous electrodes consisting of closely packed monodispersed mesoporous carbon spheres in (C 2H 5) 4NBF 4/propylene carbonate electrolyte. The model faithfully accounts for the electrode packing morphology and the dependency of electrolyte dielectric permittivity on local electric field. Three sphere packing morphologies were investigated, namely, simple cubic (SC), body-centered cubic (BCC), and face-centered cubic (FCC). A cylindrical mesopore in a mesoporous carbon sphere was also simulated. This study demonstrates that the field-dependent electrolyte dielectric permittivity significantly affects the predicted capacitance of EDLCs. Moreover, the Stern layer needs to be accounted for in order to match predicted specific area capacitance with experimental data. This study also establishes that, for all packing structures, larger sphere diameter results in larger electric field at the electrode surface and thus larger diffuse layer specific area capacitance. For sphere diameter less than 40 nm, SC packing had the largest electrolyte volume fraction. This provided more space for the electric potential to decrease resulting in larger electric field at the electrode surface and diffuse layer specific area capacitance compared with BCC and FCC packings. On the contrary, FCC features the smallest volume fraction resulting in the lowest surface electric field and diffuse layer specific area capacitance. The packing morphologies of electrode spheres were found to have no significant effect on the diffuse layer specific area capacitance for sphere diameter larger than 40 nm.

A body centred cubic phase of elemental yttrium prepared by the rapid solidification of yttrium-iron alloys

A body centred cubic (BCC) form of elemental yttrium has been observed in rapidly quenched Y-Fe alloys. X-ray diffraction, 57Fe Mossbauer effect and scanning electron microscopy measurements are reported. The lattice parameter of this previously unobserved form of yttrium (a0=4.12+or-0.02 AA) is in good agreement with measurements on Y-Th solid solutions and the value calculated assuming an ideal BCC packing.