Spiral Packing Research Articles

Spiral packing and chiral selectivity in model membranes probed by phase-resolved sum-frequency generation microscopy

Since the lipid raft model was developed at the end of the last century, it became clear that the specific molecular arrangements of phospholipid assemblies within a membrane have profound implications in a vast range of physiological functions. Studies of such condensed lipid islands in model systems using fluorescence and Brewster angle microscopies have shown a wide range of sizes and morphologies, with suggestions of substantial in-plane molecular anisotropy and mesoscopic structural chirality. Whilst these variations can significantly alter many membrane properties including its fluidity, permeability and molecular recognition, the details of the in-plane molecular orientations underlying these traits remain largely unknown. Here, we use phase-resolved sum-frequency generation microscopy on model membranes of mixed chirality phospholipid monolayers to fully determine the three-dimensional molecular structure of the constituent micron-scale condensed domains. We find that the domains possess curved molecular directionality with spiralling mesoscopic packing, where both the molecular and spiral turning directions depend on the lipid chirality, but form structures clearly deviating from mirror symmetry for different enantiomeric mixtures. This demonstrates strong enantioselectivity in the domain growth process and indicates fundamental thermodynamic differences between homo- and heterochiral membranes, which may be relevant in the evolution of homochirality in all living organisms.

Structural Model of Phase Transitions in Manganese Determined by the Closest Spiral Packing of Tetrahedrons

Structural Model of Phase Transitions in Manganese Determined by the Closest Spiral Packing of Tetrahedrons

Aroma absorption in a rotating packed bed with a tailor-made archimedean spiral packing

The high gravity field inside a Rotating Packed Bed (RPB) is a promising approach for the intensification of aroma absorption. Using standard wire mesh packing, the rotation has proven to be an additional degree of freedom for an intensified and more flexible process. Further findings showcase an increase of the absorption efficiency of 9 – 14% using spiral packing, produced by additive manufacturing, compared to a standard wire mesh under equal operating conditions (G ̇ = 100 L/min, ω = 2750 rpm). The spiral packing could be operated at remarkably large gas load factors of up to 15.5 Pa0.5 without any evidence of flooding. All in all, the spiral packing is capable of handling larger liquid flow rates for a given volume and might be in particular beneficial for processing viscous or solid containing media like crude fermentation slurries and is one of the preferable solutions for multirotor RPBs.

Dense Spiral Packing of Circles in the Plane

Dense Spiral Packing of Circles in the Plane

Plastic deformation of tubular crystals by dislocation glide.

Tubular crystals, two-dimensional lattices wrapped into cylindrical topologies, arise in many contexts, including botany and biofilaments, and in physical systems such as carbon nanotubes. The geometrical principles of botanical phyllotaxis, describing the spiral packings on cylinders commonly found in nature, have found application in all these systems. Several recent studies have examined defects in tubular crystals associated with crystalline packings that must accommodate a fixed tube radius. Here we study the mechanics of tubular crystals with variable tube radius, with dislocations interposed between regions of different phyllotactic packings. Unbinding and separation of dislocation pairs with equal and opposite Burgers vectors allow the growth of one phyllotactic domain at the expense of another. In particular, glide separation of dislocations offers a low-energy mode for plastic deformations of solid tubes in response to external stresses, reconfiguring the lattice step by step. Through theory and simulation, we examine how the tube's radius and helicity affects, and is in turn altered by, the mechanics of dislocation glide. We also discuss how a sufficiently strong bending rigidity can alter or arrest the deformations of tubes with small radii.

Novel packing‐enhanced distillation separation of isoamyl alcohol isomer: Experimental and pilot scale study

AbstractSeparation of isoamyl isomers by means of internally enhanced ordinary distillation was investigated in this work. Because of very close boiling points between the target components of the mixture, a novel paralleling spiral packing of extremely low HEPT was experimentally developed with success for this purpose. A coupled scheme of pilot scale was subsequently setup separating 2‐methyl‐butanol and 3‐methyl‐butanol from fusel oil, usually low‐class byproduct of fuel bioethanol manufactures. Basically, batch distillation is used to remove light ends and the continuous partner to separate 2‐methyl‐butanol and 3‐methyl‐butanol. Operating results satisfactorily suggested that the concentration of 2‐methyl‐butanol was over 99 wt % with the yield over 80%. Computational flowsheet simulation was also done with the outcome in good agreement with the tested onsite to facilitate industrial design. © 2011 American Institute of Chemical Engineers AIChE J, 2011

Packing configurations for methane storage in carbon nanotubes

In this paper we investigate methane packing in single-walled carbon nanotubes. We employ classical applied mathematical modelling using the basic principles of mechanics to exploit the Lennard-Jones potential function and the continuous approximation, which assumes that intermolecular interactions can be approximated by average atomic surface densities. We consider both zigzag and spiral configurations formed by packing methane molecules into (9, 5), (8, 8) and (10, 10) carbon nanotubes, and we derive analytical expressions for the interaction potential energy of these configurations. Our findings indicate that for the zigzag configuration for a (9, 5) tube, the potential energy of the system is minimized when the methane molecules simply form a linear chain along the tube axis, but genuine zigzag patterns are found as the tube size increases such as for the (8, 8) and (10, 10) tubes. For the spiral configuration, the potential energy of the system is minimized when the angular spacing is approximately equal to π for the (9, 5) and (8, 8) tubes, and π/2 for the (10, 10) tube. Overall, our results are in good agreement with molecular dynamics simulations in the literature and show that the most energetically efficient packing configuration of the three tubes studied, occurs for a (10, 10) tube with a zigzag packing, while a (10, 10) tube with a spiral packing configuration has the largest free-cavity volume for methane adsorption at higher temperatures.

Spiral packing

We present a simple method for creating artistic space-filling designs based on spiral packings. Connected spiral sets are generated by successively branching child spirals from parent spirals, constrained to fit nearby neighbors in their environment. The underlying geometry is discussed in detail and a number of color examples generated by the algorithm are given.

Hydraulic Resistance of a Random Spiral Packing for Regenerators

Results of an experimental investigation of two types of metallic spiral packings for regenerative heat exchangers are considered. They are compared to packings of other types used in regenerators; a method of calculation of the hydraulic resistance of the packings investigated is proposed.

The phenomenon of conglomerate crystallization: Part 52. Stereochemical control of the crystallization pathway by small alterations of ligands

The X-ray structure analysis of mer- trans-[Co(aepn)Cl 2(OH 2)](ClO 4)·H 2O ( 1) (aepn= N-(2-aminoethyl)-1,3-propanediamine) reveals that the compound crystallizes in an enantiomorphic space group P2 12 12 1 implying a spontaneous resolution of its racemic solution, known as conglomerate crystallization. Substitutions of the two chloride ligands with bromides result in the isostructural compound mer- trans-[Co(aepn)Br 2(OH 2)](ClO 4)·H 2O ( 2), which also crystallizes as a conglomerate in the space group P2 12 12 1. Meanwhile, a substitution of the coordinated OH 2 of 1 with NH 3 gives mer- trans-[Co(aepn)Cl 2(NH 3)](ClO 4) ( 3), which crystallizes as a simple racemate in P2 1/ n space group. When N-(3-aminopropyl)-1,3-propanediamine (dpt) is used instead of aepn in the preparation of 1, it gives racemic crystals of mer- trans-[Co(dpt)Cl 2(OH 2)](ClO 4) ( 4) whose molecular packing pattern is identical to that of 3. In the conglomerate structures, the protons of coordinated water ligand are strongly hydrogen-bonded to the oxygen of a water of crystallization to form a spiral packing structures. In the packing structures of 3 and 4, two molecules of opposite chirality are brought together around a crystallographic center of inversion by hydrogen bonds of the protons of the corresponding tridentate amine ligand with oxygens of perchlorate anion.

New ruthenium–tin clusters with bulky ligands. Crystal and molecular structures of [Ru2(CO)6(µ-SnR2)(µ-Ph2PCH2PPh2)], [Ru3(CO)9(µ-SnR′2)3], [Ru3(CO)9(µ-SnR2)(µ-SnR′2)2] and [Ru3(CO)9(µ-SnR2)2(µ-SnR′2)][R = CH(SiMe3)2, R′= C6H2Pri3-2,4,6

The first heterometallic clusters containing the SnR′2(R′= 2,4,6-triisopropylphenyl) moiety have been prepared. Triruthenium dodecacarbonyl reacted at low temperatures with SnR′2 or, at higher temperatures, with its trimer (SnR′2)3 to give both [Ru3(CO)10(µ-SnR′2)2]1 and [Ru3(CO)9(µ-SnR′2)3]2. Reaction of the pentametallic species [Ru3(CO)10(µ-SnL2)2][L = R = CH(SiMe3)23 or R′] with SnR′2 or SnR2 respectively afforded the hexametallic clusters [Ru3(CO)9(µ-SnR2)(µ-SnR′2)2]4 and [Ru3(CO)9(µ-SnR2)2(µ-SnR′2)]5. In the reaction of [Ru3(CO)12] with SnR2 the hexametallic cluster [Ru3(CO)9(µ-SnR2)3]6 has now been isolated in addition to the previously reported Ru3Sn2 cluster. The trimer (SnR′2)3 also reacted with [Ru3(CO)10(dppm)](dppm = Ph2PCH2PPh2) to give [Ru3(CO)8(µ-SnR′2)2(dppm)]7, whereas with SnR2 the product was [Ru2(CO)6(µ-SnR2)(µ-dppm)]8. Compound 7 can also be obtained by the reaction of 2 with dppm, using sodium–benzophenone to activate the cluster. Reaction of the dodecacarbonyl with Sn[CH(PPh2)2]2 or its lead analogue surprisingly did not yield a mixed cluster, but afforded a rapid and quantitative route to [Ru3(CO)10(dppm)]. Compound 2 behaves similarly, yielding 7 again in high yield. The crystal and molecular structures of 2, 4, 5 and 8 have been determined. In compounds 2, 4 and 5, the ruthenium triangle and the three tin atoms form a planar array. A detailed comparison of ligand steric effects is made. In 8 the metal atoms and the two P atoms are coplanar, with a long Ru–Ru vector bridged by the R2Sn group and the diphosphine [2.954(2)A]. The structure of 4 is unusual, the characteristic aryltin twist on only two of the three tin atoms generating chirality, resulting in a spiral packing in space group P65. This structure was determined both diffractometrically and using two different image-plate systems, and the results are remarkably consistent in all three cases.

CLOSE-PACKING OF GROWING DISCS

Spiral lattices are derived by allowing growing discs to aggregate under a close-packing rule. Both Fibonacci and Lucas numbers of visible spirals arise naturally, dependent only on the choice of growth centre. Both the rate of convergence towards an ideal spiral, and chirality, are determined by the initial placement of the first few discs (initial conditions). Thus the appearance of spiral packings is no more or less mysterious than the appearance of hexagonal packed arrays of equal discs.

Order and deterministic chaos in hard-disk arrays

Order in computer-generated binary arrays of hard disks grown from a seed cluster is studied. As the composition and ratio of disk diameters are varied, we find both crystalline and amorphous samples, as well as "hexatic" configurations with short-range translational order but extended orientational correlations. A single impurity disk placed at the center of an otherwise homogeneous array traps dislocations and disclinations when its diameter deviates sufficiently from that of the disks packed deterministically around it. For still larger deviations, the impurity disk gives rise to chaotic arrays of stacking faults and grain boundaries. An alternative spiral packing algorithm leads to a particularly simple transition from order to deterministic chaos. The ratio of disk diameters plays the role of a control parameter.

Heat teansfer between a surface and a fluidized bed with packing

Heat transfer coefficients were measured under the following conditions: a fluidized bed with a spiral packing and a vertically immersed cylinder; a fluidized bed with a bundle of smooth tubes and with a bundle of lengthwise finned tubes.

Mass transfer between phases in a fluidized bed and in a layer with a cylindrical spiral filling

It has been shown by experiment that the mass transfer between phases in a fluidized bed with cylindrical spiral packing is improved on account of improvement in the rate constant for the process with fixed values for the proportion of gas passing through the layer in bubbles and the linear velocity for the phases.