2001 # Adsorption of surfactants at air/solution interfaces: theoretical description of adsorption equilibrium based on a model of clustering of the surfactant molecules at the air/solution interface

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“…To explain these observations and account for the small A pm , a surface micelle conjecture is appealing. Surface micelles are commonly formed in diblock copolymer films and at solid surfaces and have been treated theoretically . If one supposes that the adsorbed film is composed of hemispherical micelles, the curved area available to the headgroups is roughly twice the flat area projected on the planar surface.…”

confidence: 99%

“…To explain these observations and account for the small A pm , a surface micelle conjecture is appealing. Surface micelles are commonly formed in diblock copolymer films and at solid surfaces and have been treated theoretically . If one supposes that the adsorbed film is composed of hemispherical micelles, the curved area available to the headgroups is roughly twice the flat area projected on the planar surface.…”

confidence: 99%

“…where i y is the measured surface tension, ˆi y is the maximum likelihood estimation of surface tension from the models and n is the number of total data sets. The alternative form of the sum of squares, which has also been widely used [74,75], is the root-mean-square deviation (RMSD, RMSE):…”

confidence: 99%

“…Wustneck [102] reached a similar conclusion that their model fitting is realistic because the standard deviations from predicted parameters were within 0.2 mN and the accuracy was comparable to that of the direct measurement. Other researchers [74] have used similar methods but given fewer details. Evaluating fitting quality by objective functions, although seemingly straightforward, may be vulnerable to the potential heteroscedasticity problem [70]; i.e., in the presence of heteroscedasticity, the smallest objective function is always the one chosen for minimization.…”

confidence: 99%

“…RegressiondataofisothermsbydoubleLangmuirequation intheinsetofFig.1Dindicatesadramaticchangeinthead鄄 sorptionmechanismwhichisduetotheformationofsmallclus鄄 terofNPEO鄄10moleculesontothesurfaceuntilthesurfaceis saturatedwiththehemimicelles [24][25][26] .Inregion3,formationofnew surfaceclusterslowsdown;hencethereisadecreaseintheslope ofisotherm.Athigherconcentrations,theslopeofisothermde鄄 creases,andaplateauforms(region4),wheretheadsorption amountsremainconstant.NPEO鄄10mayalsoadsorbontothe surfacescontainingoxygenbyelectrostaticinteractionbetween theoxyethylenicgroupsandthesurfaces.Theadsorbedphaseis assumedtobeatwo鄄dimensionalmixtureconsistingofsingly dispersedsurfactantmolecules,monolayeredandbilayeredag鄄 gregatesofvarioussizes,andemptysites [27][28] .Theexplanations forthenatureofadsorptioncurveinthethreeregionsarede鄄 pictedinFig.2.…”

confidence: 99%