Qualitative Observations Concerning Packing Densities for Liquids, Solutions, and Random Assemblies of Spheres

Duer, W. C.; Greenstein, J. R.; Oglesby, G. B.; Millero, Frank J.

doi:10.1021/ed054p139

Cited by 6 publications

(3 citation statements)

References 31 publications

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“…A more correct value would be that for the random close packing of spheres, 0.64. 74 In eq 12, a sulfate ) 0.39 nm 2 is the surface area occupied by a sulfate headgroup. 4…”

Section: Discussionmentioning

confidence: 99%

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Effect of the Nature of the Counterion on the Properties of Anionic Surfactants. 3. Self-Association Behavior of Tetrabutylammonium Dodecyl Sulfate and Tetradecyl Sulfate: Clouding and Micellar Growth

2004

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The surfactants tetrabutylammonium dodecyl sulfate (TBADS) and tetradecyl sulfate (TBATS) have been synthesized by ion-exchange, and their self-association behavior has been investigated. The solutions of these surfactants show clouding and phase separation as the temperature is increased. The clouding temperature T C of TBADS solutions has been found to be about 4-5 °C higher than for TBATS solutions in the whole range of composition up to a surfactant content of 64 wt %. The critical micellization concentration (cmc) of TBATS has been determined using the electrical conductivity method. The micelle aggregation numbers (N) have been determined using the time-resolved fluorescence quenching (TRFQ) method, with pyrene/dodecylpyridinium chloride as fluorescent probe/quencher pair. For the two surfactants, N increases with the surfactant concentration and above a threshold concentration with the temperature. This latter increase as well as the phase separation observed for TBADS and TBATS are very unusual features for ionic surfactants. At temperatures approaching T C from below, the TRFQ data show evidence of quencher/probe migration between micelles. This process is shown to occur via collisions between micelles. Approximate calculations indicate that the maximum number of TBA + ions that can be packed at the TBADS micelle surface is smaller than the experimentally determined value of the number of bound TBA + ions. This result suggests that some bound TBA + ions must be located in an outer and probably incomplete second layer of bound TBA + ions. The origin of the attractive intermicellar interaction responsible for the observed phase separation is discussed on the basis of the existence of the second layer of bound TBA + ions and the capacity of TBA + ions to self-associate in water.

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“…A more correct value would be that for the random close packing of spheres, 0.64. 74 In eq 12, a sulfate ) 0.39 nm 2 is the surface area occupied by a sulfate headgroup. 4…”

Section: Discussionmentioning

confidence: 99%

“…Also, the packing factor 0.746 used above represents the maximum possible value. A more correct value would be that for the random close packing of spheres, 0.64 . In eq 12, a sulfate = 0.39 nm 2 is the surface area occupied by a sulfate headgroup …”

Section: Discussionmentioning

confidence: 99%

Effect of the Nature of the Counterion on the Properties of Anionic Surfactants. 3. Self-Association Behavior of Tetrabutylammonium Dodecyl Sulfate and Tetradecyl Sulfate: Clouding and Micellar Growth

2004

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“…Examples of packing spheres in containers include packing reactor beds in nuclear engineering; columns in chemical and petroleum engineering; mortar and concrete; ion‐exchange resins; various mixtures in metallurgy, ceramic engineering and geology; and atoms and molecules in the liquid state (Duer et al, ).…”

Section: Introductionmentioning

confidence: 99%

Packing congruent spheres into a multi‐connected polyhedral domain

Stoyan

Yaskov

2012

Int Trans Operational Res

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In this paper, we have considered a problem of packing the maximal number of congruent spheres into a multi-connected polyhedral domain. A mathematical model of the problem has been formulated on the basis of functions. This paper proposes a special way of constructing starting points. To find local maxima, a modification of the Zoutendijk method of feasible directions and a strategy of active inequalities are used. We developed a special approach to search for an approximation to a global maximum. A number of numerical examples are also provided.

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Physical Properties of Amino Acid Solutions

Lilley¹

1985

Chemistry and Biochemistry of the Amino Acids

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Qualitative Observations Concerning Packing Densities for Liquids, Solutions, and Random Assemblies of Spheres

Cited by 6 publications

References 31 publications

Effect of the Nature of the Counterion on the Properties of Anionic Surfactants. 3. Self-Association Behavior of Tetrabutylammonium Dodecyl Sulfate and Tetradecyl Sulfate: Clouding and Micellar Growth

Effect of the Nature of the Counterion on the Properties of Anionic Surfactants. 3. Self-Association Behavior of Tetrabutylammonium Dodecyl Sulfate and Tetradecyl Sulfate: Clouding and Micellar Growth

Packing congruent spheres into a multi‐connected polyhedral domain

Physical Properties of Amino Acid Solutions

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