Langmuir Films Research Articles

Tuning Electrostatics to Promote Ordered Monolayers of Phosphole-Lipids.

Heteroatom-doped π-conjugated systems have been exploited for electronic device applications. Phosphole-containing backbones are particularly intriguing with regard to electron delocalization and ultimately control over the photophysical, redox, and charge transfer characteristics. However, practical application of these materials commonly relies on well-structured, thin film architectures. Self-assembly offers a route to generate ordered 2D structures deposited on solid substrates. The orientation of these deposited films can be manipulated by the introduction of alkyl chains of varying length (to form phosphole-based lipids) and chemical modification of the phosphole-derived headgroup. External controls can also be considered to tune these films' properties, e.g., the electrostatic interactions within the film can be controlled by varying the environment with the addition of simple salt counterions. A series of lipids with phosphole-based π-conjugated headgroups have been designed and exhibit intramolecular conformational changes in response to external conditions. Herein the 2D film structure in Langmuir and Langmuir-Blodgett films is reported in the presence and absence of halide salts. The film morphology obtained from Brewster angle and atomic force microscopy shows the formation of a condensed phase but also 3D aggregates, and grazing incidence X-ray diffraction confirmed the presence of untilted, hexagonally packed chains. The size of the counterion influences its ability to intercalate between the phosphole headgroups, which ultimately provides a means to induce the formation of a well-ordered, single monolayer film without aggregates that can be transferred to the solid substrate.

Interfacial insights: [6]-Gingerol monolayers at the air-water interface and beyond

Ginger is a culinary spice with a millennia-old tradition due to its extensive therapeutic applications, recently validated by scientific studies. In particular [6]-Gingerol, a key active molecule in ginger, exhibits extraordinary capabilities in addressing a wide spectrum of health issues. However, its therapeutic potential is limited by its rather low bioavailability. The incorporation of [6]-Gingerol into membrane systems of liposomes, micelles, or exosomes is a promising strategy to overcome this limitation. In this contribution, we report the hitherto unexplored surface properties of [6]-Gingerol at the air-water interface. Our comprehensive study, which includes a detailed analysis of surface pressure and surface potential vs. area per molecule isotherms, surface compression modulus, and Brewster Angle Microscopy, demonstrates the capability of [6]-Gingerol to form Langmuir films. These films can be transferred onto solid substrates, forming remarkably homogeneous Langmuir-Blodgett films which have been characterized by Quartz Crystal Microbalance and Atomic Force Microscopy. This study may be of interest as it paves the way for future research on introducing [6]-Gingerol into membrane systems and transporting it into living cells.

Effect of Hofmeister Anions Series on the Langmuir Film of Tetronic 90R4 and Tetronic 701 Block Copolymers.

The air-water interfacial behavior of Tetronic 90R4 and Tetronic 701 was studied in the presence of sodium salts with different anions namely , , , , Cl-, Br-, , I-, and SCN-. Their presence in the subphase altered the arrangement of both tetronic molecules at the air-water interface. The limiting mean molecular area of the Langmuir film for both tetronics was found to be ion specific; it increased following the series < < < < Cl-< Br-< < I-< SCN-, which was found to be aligned with the Hofmeister series of anions. Furthermore, the study explored the effects of the hydration enthalpy, free energy, viscosity BJD coefficient, and polarizability of these anions on the interfacial behavior of tetronics. The Langmuir-Blodgett film morphology was also examined in the presence of these salt species using SEM. Morphologies were explained considering kosmotropic and chaotropic nature of these anions.

The Langmuir-Blodgett trough (Langmuir film balance) can be used to understand the stabilizer concentrations in aqueous nano- and microsuspensions

Aqueous suspensions of poorly soluble, crystalline drug particles in the sub-micron range hold the ability to regulate the drug release for a defined period of time after e.g., intramuscular, or subcutaneous administration, working as an eminent formulation strategy for the preparation of long-acting injectables. Aqueous suspensions are typically prepared by top-down approaches, e.g., wet bead media milling or high-pressure homogenization, containing the active pharmaceutical compound and surfactants and/or polymers for stabilization purposes. Currently, the screening of proper stabilizers and adequate stabilizer concentration during formulation investigations is based on a trial-and-error approach with variations in combinations, concentrations, and/or ratios. To obtain a more efficient methodology during formulation screening, the present study investigated the correlation between the surface activity of two different surfactants, i.e., poloxamer 188 and polysorbate 20, by drop profile tensiometry and Langmuir trough monolayer, and the obtained sizes of cinnarizine particles as a tool to predict the optimal surfactant concentration to prepare physical stable nano- and microsuspensions. The obtained results demonstrated that the molecular area determined as the area per surfactant molecule measured in the Langmuir trough combined with the specific surface area of the prepared suspensions could be used to predict the suitable concentration of the surfactant based upon short-term stress stability data. The results further showed that higher concentrations of poloxamer 188 were necessary to stabilize the suspensions when compared to the needed concentration of polysorbate 20. In addition, it was observed that there was a need for a slightly higher surfactant concentration when the suspensions were milled with the smallest bead size of 0.5 mm instead of larger sizes of bead (0.8 and 1.0 mm), which could not be accounted for by differences in specific surface area.

Ultrafine Network-Like Monolayer Structures of Amphiphilic Hyperbranched Copolymers Revealed by the Relative Aggregation Number Method.

The aggregation behavior of two amphiphilic hyperbranched copolymers of poly[oligo(ethylene glycol) methacrylate-co-lauryl methacrylate] (H-[P(OEGMA-co-LMA)]) at the air/water interface was investigated by using the Langmuir film balance technique and atomic force microscopy (AFM). At the air/water interface, H-[P(OEGMA-co-LMA)] copolymers spontaneously form the ultrafine network-like monolayer structures of micelles; each micelle consists of a tiny hydrophobic core of one or two carbon backbones and lauryl side groups and a short hydrophilic shell of oligo(ethylene glycol) (OEG) side groups, and the micellar cores are connected by the branching agent ethylene glycol dimethacrylate (EGDMA). These ultrafine micellar structures are successfully revealed by our relative aggregation number method presented in this work, which is based on our previous relative mass method and methylene number method. The surface pressure-molecular area isotherms of POEGMA29%-PLMA71% (weight percent) and POEGMA69%-PLMA31% are condensed and expanded, respectively, because the density/number of OEG side groups in the former shells is smaller than that in the latter case. Upon monolayer compression, the isotherms of the former are classified into regions I-IV, whereas those of the latter are classified into regions II and III based on their different variation trends of surface pressure. Subphase pH has little influence on the isotherms of the two copolymers because the stretching degrees of hydrophilic OEG side groups in the shells are probably limited by the connected cores, which is different from the large effects in our previous block copolymers containing POEGMA or poly[oligo(ethylene glycol) acrylate] blocks. Under neutral and alkaline conditions, in region III, the mean molecular area (mmA) values of the isotherms of the two copolymers at 20 °C are smaller than those at 10 °C due to the collapse of the OEG side groups above 15 °C. Furthermore, the isotherms of POEGMA69%-PLMA31% move to larger mmA values at 30 °C due to the increased thermal mobility and stretching degrees of more OEG side groups.

Evaluation of the antitumor activity of albendazole using Langmuir-Blodgett monolayers as surface mediated drug delivery system

This study demonstrates the application of Langmuir and Langmuir-Blodgett films as biomimetic drug reservoirs and delivery systems to investigate the effect of an anthelmintic on cancer cell culture. The repurposing of benzimidazole anthelmintics for cancer therapy due to their microtubule-inhibiting properties has gained attention, showing promising anticancer effects and tumor-suppressive properties. Although widely used in medicine, the low aqueous solubility of benzimidazole compounds poses challenges for studying their effects on cancer cells, requiring incorporation into various formulations. Our study demonstrates that incorporating albendazole into stable Palmitic Acid Langmuir monolayers, forming Langmuir-Blodgett films, significantly affects the proliferation of liver carcinoma cells. This report presents the initial findings of the effect of an antitumoral drug on cancer cell culture using a simple and repeatable methodology.

The anchoring effect and cooperative interactions in 5CB/CNC molecular films

ABSTRACT The advances in nanotechnology allow for the creation of hybrid materials (HMs) composed of LCs (LC) and cellulose nanocrystals (CNC). Cellulose is a natural polymer whose structural properties are used for designing new LC composite materials. The properties of CNC strongly depend on the origin and technological processes used. The LCs are materials displaying different structural properties in function of temperature or concentration that find applications mainly in electronics. The combination of LC and CNC results in enhanced properties, like an extended temperature range of mesophases, higher stability and mechanical strength of LC films. The CNC obtained through transition metal catalysed oxidative process allows obtaining hydroxyl groups active for interactions with LC molecules. By synergic combination and cooperative interaction between components, we have stabilised the 5CB molecules at the air-water interface by the anchoring effect, creating stable and compressible 5CB/CNC molecular films. The π-A isotherms, compressibility modules, Gibbs free energy of spreading, lift-of area, collapse pressure and surface pressure increment for investigated systems at different stages of the formation process are determined. We have demonstrated that creating a hybrid 5CB/CNC Langmuir film is a two-stage process. Obtained films display enhanced stability, strength and ability to form multilayers.

Line tension and line entropy associated with the monolayer/trilayer boundary of smectic liquid crystal at the air-water interface.

Molecularly thin films of the smectic liquid crystal 4'-octyl-4-biphenylcarbonitrile (8CB) at the air-water interface phase separate into regions with different numbers of layers, in analogy with freestanding smectic liquid crystalline films. This paper reports the line tension associated with the boundary of coexisting trilayer and monolayer phases of in Langmuir films of 8CB at the air-water interface as a function of temperature and humidity and infers information on the boundary profile between the coexisting phases. Two complementary techniques are used to characterize the 8CB thin films: surface pressure-area isotherm and Brewster angle microscopy (BAM). We determine the line tension by stretching isolated domains from their equilibrium circular shape and analyzing the free relaxation with a hydrodynamic model. Then, we interpret the line tension vs temperature data in terms of an excess line entropy for the domain boundary, which requires careful consideration of the thermodynamics of inhomogeneous monolayer systems.

Effects of the ametryn pesticide on biomembrane models based on Langmuir films and giant unilamellar vesicles (GUVs)

The plasma membrane plays a crucial role in regulating various physiological processes within cells, controlling the flow of substances in and out of the cell. It primarily comprises lipids, oligosaccharides, sterols, and proteins, which are responsible for its functionalization. In this study, we utilized 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC) to create mono and bilayers as mimetic systems for the lipid structure of cell plasma membranes. This approach constitutes the initial phase of comprehending the impact of contaminants on in vivo systems. Thus, the impact of the pesticide ametryn (AMT) on DPPC monolayers, which were formed using Langmuir films at the air/water interface, as well as on DPPC bilayers formed by giant unilamellar vesicles (GUVs), was investigated. The use of Brewster Angle Microscopy revealed a significant influence of AMT when in the water subphase on the morphology of DPPC aggregates in Langmuir monolayers, whose surface pressure vs. mean molecular area (π-A) isotherms are shifted to larger areas for higher AMT concentrations. Phase modulation infrared reflection-absorption spectroscopy indicated interactions between AMT and DPPC in Langmuir films, specifically involving the phosphate and choline DPPC head groups. Basically, the negatively charged hydrophilic portion of AMT (SCH3) would be oriented towards the DPPC choline group. At the same time, the AMT triazine ring would be positioned closer to the DPPC phosphate group, leading also to a slight disturb of the vertical orientation of the DPPC alkyl chains. In line with the findings from the monolayer experiments, the confocal microscopy images obtained through phase contrast revealed that the presence of AMT resulted in approximately 85 % of the DPPC GUVs losing their phase contrast. This loss can be attributed to the exchange between the inner and outer contents of the DPPC bilayer.

Assembly Structure Formation in Bulk and Ultrathin Films of Poly(substituted methylene) Having an Azobenzene Side Chain.

The density of the side chain introduced to a polymer main chain greatly influences the properties and functions of the polymer. This work first reports on the packing structure and properties at an interface of a poly(substituted methylene) where an azobenzene side chain is introduced at every carbon atom in the main chain (C1PAz). The structure and properties are compared with those of a conventional vinyl polymer [poly(methacrylate)] possessing an identical side-chain structure (C2PAz). The packing structure in the bulk state analyzed by X-ray measurements revealed that C1PAz adopts a highly ordered rectangular unit cell structure, whereas C2PAz shows a less ordered lamellar one. Langmuir film balance experiments indicated that both polymers with the trans-azobenzene give essentially the identical 2D side-chain occupying area on water, which agrees well with the smectic B (hexatic packing) model based on the X-ray data. Upon transfer onto a solid substrate, only C1PAz shows a conformational transformation to a spread bilayer-type layer, most probably due to conformational frustration stemming from the crowding of the side chains. This study proposes new insights into the effects of side-chain density on the self-assembly and photoreaction of azobenzene-containing polymers, which are expected to expand the possibilities of polymer design for various applications.

Physicochemical control of solvation and molecular assembly of charged amphiphilic oligomers at air-aqueous interfaces

Hypothesis: Understanding the rules that control the assembly of nanostructured soft materials at interfaces is central to many applications. We hypothesize that electrolytes can be used to alter the hydration shell of amphiphilic oligomers at the air-aqueous interface of Langmuir films, thereby providing a means to control the formation of emergent nanostructures.Experiments: Three representative salts – (NaF, NaCl, NaSCN) were studied for mediating the self-assembly of oligodimethylsiloxane methylimidazolium (ODMS-MIM+) amphiphiles in Langmuir films. The effects of the different salts on the nanostructure assembly of these films were probed using vibrational sum frequency generation (SFG) spectroscopy and Langmuir trough techniques. Experimental data were supported by atomistic molecular dynamic simulations.Findings: Langmuir trough surface pressure – area isotherms suggested a surprising effect on oligomer assembly, whereby the presence of anions affects the stability of the interfacial layer irrespective of their surface propensities. In contrast, SFG results implied a strong anion effect that parallels the surface activity of anions. These seemingly contradictory trends are explained by anion driven tail dehydration resulting in increasingly heterogeneous systems with entangled ODMS tails and appreciable anion penetration into the complex interfacial layer comprised of headgroups, tails, and interfacial water molecules. These findings provide physical and chemical insight for tuning a wide range of interfacial assemblies.

Unveiling Texture and Topography of Fatty Acid Langmuir Films: Domain Stability and Isotherm Analysis.

3D texturing by self-assembly at the air-water interface has recently been proposed. The hypothesis of this work is that, if this is true, such domain formation should be inferable directly from pressure-area isotherms and be thermodynamically stable. Monolayers of branched fatty acid mixtures with straight chain analogues and their stability are thus studied using a combination of pressure-area isotherms, thermodynamic analysis, in situ Brewster angle microscopy, and atomic force microscopy of both LB-deposited and drop-cast films on silicon wafers. Isotherms reflecting the behavior of monodisperse 3D domains are shown to be independent of compression rate and display long-term stability. Gibbs analysis further confirms the thermodynamic rather than kinetic origin of such novel species by revealing that deviations from ideal mixing can be explained only a priori by differences in the topography of the water surface, thus also indirectly confirming the self-assembly deformation of the water interface. The intrinsic self-assembly curvature and miscibility of the two fatty acids is confirmed by drop-casting, which also provides a rapid, tunable thin-film preparation approach. Finally, the longevity of the nanostructured films is extraordinary, the long-range order of the deposited films increases with equilibration time at the water interface, and the integrity of the nanopatterns remains intact on the scale of years.

Closely Packed Core-Shell Micelle Structures of Double Hydrophilic Miktoarm Star Copolymers at the Air-Water Interface.

The aggregation behavior of amphiphilic block copolymers at the air-water interface has been extensively studied, but less attention was given to that of star copolymers. In this work, we studied the interfacial aggregation behavior of two double hydrophilic pH- and temperature-responsive miktoarm star copolymers of poly[di(ethylene glycol) methyl ether methacrylate]-poly[2-(dimethylamino)ethyl methacrylate] (PDEGMA3-PDMAEMA3 and PDEGMA4-PDMAEMA7, the subscripts denote arm numbers) with different molecular weights. The effects of subphase pH and temperature on the monolayer isotherms and hysteresis curves of the two star copolymers and the morphologies of their Langmuir-Blodgett (LB) films were studied by the Langmuir film balance technique and atomic force microscopy, respectively. At the air-water interface, the two star copolymers tend to form closely packed micelles. These micelles exhibit a core-shell structure, where the small hydrophobic core consists of cross-linker of ethylene glycol dimethacrylate (EGDMA) and the carbon backbones of PDEGMA and PDMAEMA arms and the short hydrophilic shell is composed of di(ethylene glycol) and tertiary amine side groups. With increasing subphase pH, the surface pressure versus molecular area isotherms shift toward larger mean molecular areas as a result of the enhanced interface adsorption of nonprotonated tertiary amine groups. The isotherm shift of PDEGMA3-PDMAEMA3 monolayers is primarily attributed to high density of tertiary amine groups in the shells, while that of PDEGMA4-PDMAEMA7 is mainly attributed to high density of di(ethylene glycol) groups in the shells. The hysteresis degrees in the monolayers of the two copolymers under alkaline and neutral conditions are greater than those under acidic conditions due to the decreased protonation degree of the tertiary amine groups. At 10 °C, the mobility of the shells is poor and the isotherms are located on the right. Above the lower critical solution temperature, di(ethylene glycol) groups contract, which causes a slight shift of the isotherms toward smaller mean molecular areas.

Molecular Templates on Surfaces by Exploiting Supramolecular Chemistry in Langmuir–Blodgett Monolayers

AbstractAttaining precise control over molecular arrangements is of paramount importance for numerous applications in nanotechnology, particularly in constructing molecular templates to accurately immobilize target materials on surfaces. A strategic combination of supramolecular and interfacial chemistry may serve to build a well‐organized molecular network, enabling the subsequent location of target molecules on specific positions of a surface. A supramolecular complex (compound 1) comprised of a melamine unit forming hydrogen bonds with dendritic arms terminated in a coumarin unit is utilized, which readily undergoes photodimerization. The research demonstrates the formation of well‐organized Langmuir films of compound 1 which can be transferred on substrates at low surface pressures adopting a lying‐flat orientation. Upon irradiation of the pristine films at 365 nm the coumarin units undergo photo‐cross linking, leading to the formation of a compact photo‐crosslinked film. Incubation of these photo‐crosslinked films in a solution containing 1‐hexanethiol results in the withdrawal of the melamine and the chemisorption of two thiol molecules per each melamine unit. The nanopores created by the removal of the melamine core are attributed to the disruption of hydrogen bonds in compound 1 by the thiols. This precisely defined molecular network holds significant promise as a template for orchestrating the arrangement of functional materials on surfaces.

Assessing the negative impact of chlorantraniliprole, isoxaflutole, and simazine pesticides on phospholipid membrane models and tilapia gill tissues

The indiscriminate and, very often, incorrect use of pesticides in Brazil, as well as in other countries, results in severe levels of environmental pollution and intoxication of human life. Herein, we studied plasma membrane models (monolayer and bilayer) of the phospholipid Dioleoyl-sn-glycerol-3-phosphocholine (DOPC) using Langmuir films, and large (LUVs) and giant (GUVs) unilamellar vesicles, to determine the effect of the pesticides chlorantraniliprole (CLTP), isoxaflutole (ISF), and simazine (SMZ), used in sugarcane. CLTP affects the lipid organization of the bioinspired models of DOPC π-A isotherms, while ISF and SMZ pesticides significantly affect the LUVs and GUVs. Furthermore, the in vivo study of the gill tissue in fish in the presence of pesticides (2.0 × 10−10 mol/L for CLTP, 8.3 × 10−9 mol/L for ISF, and SMZ at 9.9 × 10−9 mol/L) was performed using optical and fluorescence images. This investigation was motivated by the gill lipid membranes, which are vital for regulating transporter activity through transmembrane proteins, crucial for maintaining ionic balance in fish gills. In this way, the presence of phospholipids in gills offers a model for understanding their effects on fish health. Histological results show that exposure to CLTP, ISF, and SMZ may interfere with vital gill functions, leading to respiratory disorders and osmoregulation dysfunction. The results indicate that exposure to pesticides caused severe morphological alterations in fish, which could be correlated with their impact on the bioinspired membrane models. Moreover, the effect does not depend on the exposure period (24h and 96h), showing that animals exposed to pesticides for a short period suffer irreparable damage to gill tissue. In summary, we can conclude that the harm caused by pesticides, both in membrane models and in fish gills, occurs due to contamination of the aquatic system with pesticides. Therefore, water quality is vital for the preservation of ecosystems.

Mesoscale self-organization of polydisperse magnetic nanoparticles at the water surface.

In this study, we investigated the self-ordering process in Langmuir films of polydisperse iron oxide nanoparticles on a water surface, employing in situ x-ray scattering, surface pressure-area isotherm analysis, and Brewster angle microscopy. X-ray reflectometry confirmed the formation of a monolayer, while grazing incidence small-angle x-ray scattering revealed short-range lateral correlations with a characteristic length equal to the mean particle size. Remarkably, our findings indicated that at zero surface pressure, the particles organized into submicrometer clusters, merging upon compression to form a homogeneous layer. These layers were subsequently transferred to a solid substrate using the Langmuir-Schaefer technique and further characterized via scanning electron microscopy and polarized neutron reflectometry. Notably, our measurements revealed a second characteristic length in the lateral correlations, orders of magnitude longer than the mean particle diameter, with polydisperse particles forming circular clusters densely packed in a hexagonal lattice. Furthermore, our evidence suggests that the lattice constant of this mesocrystal depends on the characteristics of the particle size distribution, specifically the mean particle size and the width of the size distribution. In addition, we observed internal size separation within these clusters, where larger particles were positioned closer to the center of the cluster. Finally, polarized neutron reflectometry measurements provided valuable insights into the magnetization profile across the layer.

The effect of structural changes on the self-assembly of novel green pyridinium-carboxylate gemini surfactants in Langmuir and Langmuir-Blodgett films.

Engineered molecules with tailored molecular structures have the potential to advance various disciplines by enhancing the properties of biological membranes. In this study, we investigated the fundamental interfacial behavior of newly synthesized, water insoluble, cationic pyridinium-carboxylate based gemini surfactants (GSs) using picolinic acid (PA), nicotinic acid (NA), and isonicotinic acid (INA) and their interactions with dipalmitoylphosphatidylcholine (DPPC) in Langmuir and Langmuir-Blodgett (LB) films. Two synthetic methodologies were employed: (a) connecting two alkyl pyridinecarboxylates through the nitrogen atoms with a xylenyl spacer, namely, PAGS, NAGS1, and INAGS; and (b) dimerizing two nicotinic acid molecules through ester linkages with 1,4-benzenedimethanol, and then quaternizing the pyridine nitrogens with hexadecyl chains to yield NAGS2. A combination of Brewster angle microscopy (BAM) and atomic force microscopy (AFM) imaging techniques yielded valuable insights into the morphology of the GS films and their mixtures with DPPC. Density functional theory (DFT) calculations were used to gain further information on the GSs structures and understand their assembly. The results indicate that the film of INAGS is the most hydrophobic film, and its monolayer is the least compressible. When the nitrogen atom and a carboxylate group of the headgroup are positioned closer to each other, the GS molecules tend to form aggregates instead of a continuous film which is observed for the INAGS surfactant. This observation is consistent with the DFT energy values of pair interactions, indicating that both PAGS and NAGS1 have closely packed conformations with high stabilization energy.

Synthesis, mixed-spin-state structure and Langmuir-Blodgett deposition of amphiphilic Fe(iii) quinolylsalicylaldiminate complexes.

Designing and integrating Fe(iii)-based spin crossover (SCO) complexes onto substrates remains a challenging goal with only a handful of examples reported. In this work, we successfully synthesized and characterized three [Fe(qsal-OR)2]NO3 (qsal-OR = 5-alkoxy-2-[(8-quinolylimino)methyl]phenolate) complexes, in which R = C12H251, C16H332, and C22H453 to explore the impact of alkyl chain on the modulation of SCO activity and potential for self-assembly on a glass surface. The SCO is found to be gradual and incomplete in all cases, with the LS state more stabilised as the alkyl group shortens. We also demonstrate that all complexes form stable Langmuir films and achieve good transfer ratios to the glass surface, with 2 being the best in terms of stability. This paves the way for the SCO modulation of complexes in this class and the development of SCO devices.

Motion of a disk embedded in a nearly inviscid Langmuir film. Part 1. Translation

The motion of a disk in a Langmuir film bounding a liquid substrate is a classical hydrodynamic problem, dating back to Saffman (J. Fluid Mech., vol. 73, 1976, p. 593) who focused upon the singular problem of translation at large Boussinesq number, ${\textit {Bq}}\gg 1$ . A semianalytic solution of the dual integral equations governing the flow at arbitrary ${\textit {Bq}}$ was devised by Hughes et al. (J. Fluid Mech., vol. 110, 1981, p. 349). When degenerated to the inviscid-film limit ${\textit {Bq}}\to 0$ , it produces the value $8$ for the dimensionless translational drag, which is $50\,\%$ larger than the classical $16/3$ -value corresponding to a free surface. While that enhancement has been attributed to surface incompressibility, the mathematical reasoning underlying the anomaly has never been fully elucidated. Here we address the inviscid limit ${\textit {Bq}}\to 0$ from the outset, revealing a singular mechanism where half of the drag is contributed by the surface pressure. We proceed beyond that limit, considering a nearly inviscid film. A naïve attempt to calculate the drag correction using the reciprocal theorem fails due to an edge singularity of the leading-order flow. We identify the formation of a boundary layer about the edge of the disk, where the flow is primarily in the azimuthal direction with surface and substrate stresses being asymptotically comparable. Utilising the reciprocal theorem in a fluid domain tailored to the asymptotic topology of the problem produces the drag correction $(8\,{\textit {Bq}}/{\rm \pi} ) [ \ln (2/{\textit {Bq}}) + \gamma _E+1]$ , $\gamma _E$ being the Euler–Mascheroni constant.

Dense Monolayer Network Structures of Double Hydrophilic Hyperbranched Copolymers at the Air/Water Interface.

Influences of subphase pH and temperature on the interfacial aggregation behavior of two double hydrophilic hyperbranched copolymers of poly[oligo(ethylene glycol) methacrylate-co-(2-diisopropylamino)ethyl methacrylate] (P(OEGMA-co-DIPAEMA)) at the air/water interface are studied by the Langmuir film balance technique. Morphologies of their Langmuir-Blodgett (LB) films are characterized by atomic force microscopy (AFM). At the interface, P(OEGMA-co-DIPAEMA) copolymers tend to form a dense network structure of circular micelles composed of branching agent-connected carbon backbone cores and mixed shells of OEGMA and DIPAEMA segments (pendant groups). This network structure containing many honeycomb-like holes with diameters of 6-8nm is identified for the first time and clearly observed in the enlarged AFM images of their LB films. Under acidic conditions, surface pressure versus molecular area isotherms of the two copolymers in the low-pressure region show larger mean molecular area than those under neutral and alkaline conditions due to the lack of impediment from DIPAEMA segments. Upon further compression, each isotherm exhibits a wide pseudo-plateau, which corresponds to OEGMA segments being pressed into the subphase. Furthermore, the isotherms under neutral and alkaline conditions exhibit the lower critical solution temperature behavior of OEGMA segments, and the critical temperature is lower when the hyperbranched copolymer contains higher OEGMA content.