Beautiful, simple, exact, crazy

This is a review of the book “Beautiful, Simple, Exact, Crazy” written by Apoorva Khare and Anna Lachowska. The authors write in the preface that this book arose out of an introductory course called Mathematics in the Real World which they co-designed (and taught at Stanford and Yale University, respectively). The target audience of that course consisted mainly of undergraduates of humanities and social sciences – students whose principal interests lay outside of mathematics and the sciences

Structures of some surfactant-polyelectrolyte complexes

Structures of complexes formed in aqueous solutions by some anionic polyelectrolytes (double and single stranded (ds and ss) DNA, poly(vinyl sulfonate) (PVS), and poly(styrene sulfonate) (PSS)) with a cationic surfactant system consisting of cetyltrimethylammonium bromide (CTAB) and sodium 3-hydroxy-2-naphthoate (SHN) have been determined using small angle X-ray diffraction. All complexes are found to have a two-dimensional (2-D) hexagonal structure at low SHN concentrations. Analysis of the diffraction data shows that the ds DNA-CTAB complex has an intercalated structure, with each DNA strand surrounded by three cylindrical micelles. On increasing SHN concentration, DNA-CTAB-SHN complexes exhibit a hexagonal-to-lamellar transition, whereas PVS complexes show a hexagonal → centered rectangular → lamellar transition. PSS complexes show yet another sequence of structures. These results indicate the significant influence of the chemical nature of the polyelectrolyte on the structure of the complexes

Reentrant phase transitions of DNA-surfactant complexes

Complexes of double-stranded DNA with the cationic surfactant cetyltrimethylammonium bromide have been studied using small angle X-ray diffraction at varying concentrations of DNA and the cosurfactant hexanol. At low DNA concentrations, an intercalated hexagonal (HIc)→lamellar (Lαc)→inverted hexagonal (HIIc) transformation is found on increasing hexanol content. The HIIc structure is converted into Lαc on adding more DNA. Further increase in hexanol content leads to a phase separation in the surfactant solution, and a reentrant Lαc→HIIc→Lαc transition is observed as DNA concentration is increased. Such structural transformations of DNA-surfactant complexes, driven by DNA concentration, have not been reported until now

Shear-induced ordering of nano-pores and instabilities in surfactant mesh phases

Mixed surfactant systems show many interesting phases such as the random mesh phase con sisting of a disordered array of defects (water-filled nano-pores in the bilayers). The present study addresses the non-equilibrium phase transition of the random mesh phase under shear to an ordered mesh phase with high degree of coherence between defects in three dimensions. In-situ small-angle synchrotron X-ray diffraction under different shear stress conditions shows sharp Bragg peaks in X-ray diffraction, successfully indexed to the rhombohedral lattice with the R¯3m space group sym metry. The ordered mesh phase shows isomorphic twinning and buckling at higher shear stress. Our experimental studies bring out rich phase transitions in concentrated mixed surfactant systems hitherto not well explored and provide motivation for a quantitative understanding

Grazing incidence x-ray diffraction studies of lipid-peptide mixed monolayers during shear flow

Grazing Incidence X-ray Diffraction (GIXD) studies of monolayers of biomolecules at the air-water interface give quantitative information of in-plane packing, coherence lengths of the ordered diffracting crystalline domains and the orientation of hydrocarbon chains. Rheo-GIXD measurements revel quantitative changes in the monolayer under shear. Here we report GIXD studies of monolayers of Alamethicin peptide, DPPC lipid and their mixtures at the air-water interface under the application of steady shear stresses. The Alamethicin monolayer and the mixed monolayer show flow jamming transition. On the other hand, pure DPPC monolayer under the constant stress flows steadily with a notable enhancement of area/molecule, coherence length, and the tilt angle with increasing stress, suggesting fusion of nanocrystallites during flow. The DPPC-Alamethicin mixed monolayer shows no significant change in the area/DPPC molecule or in the DPPC chain tilt but the coherence length of both phases (DPPC and Alamethicin) increases suggesting that the crystallites of individual phases are merging to bigger size promoting more separation of phases in the system during flow. Our results show that Rheo-GIXD has the potential to explore in-situ molecular structural changes under rheological conditions for a diverse range of confined biomolecules at the interfaces.Comment: 21 pages, 11 figures, 2 table

Beautiful, simple, exact, crazy

This is a review of the book “Beautiful, Simple, Exact, Crazy” written by Apoorva Khare and Anna Lachowska. The authors write in the preface that this book arose out of an introductory course called Mathematics in the Real World which they co-designed (and taught at Stanford and Yale University, respectively). The target audience of that course consisted mainly of undergraduates of humanities and social sciences – students whose principal interests lay outside of mathematics and the sciences

Growth, self-assembly and dynamics of nano-scale films at fluid interfaces

Ultrathin films at fluid interfaces are important not only from a fundamental point of view as 2D complex fluids but have also become increasingly relevant in the development of novel functional materials. There has been an explosion in the synthesis work in this area over the last decade, giving rise to many exotic nanostructures at fluid interfaces. However, the factors controlling particle nucleation, growth and self-assembly at interfaces are poorly understood on a quantitative level. We will outline some of the recent attempts in this direction. Some of the selected investigations examining the macroscopic mechanical properties of molecular and particulate films at fluid interfaces will be reviewed. We conclude with a discussion of the electronic properties of these films that have potential technological and biological applications

Shear banding in a yield stress bearing Langmuir monolayer

We examine the shear-thinning behaviour of a two dimensional yield stress bearing monolayer of sorbitan tristearate at air/water interface. The flow curve consists of a linear region at low shear stresses/shear rates, followed by a stress plateau at higher values. The velocity profile obtained from particle imaging velocimetry indicates that shear banding occurs, showing coexistence of the fluidized region near the rotor and solid region with vanishing shear-rate away from the rotor. In the fluidized region, the velocity profile, which is linear at low shear rates, becomes exponential at the onset of shear-thinning, followed by a time varying velocity profile in the plateau region. At low values of constant applied shear rates, the viscosity of the film increases with time, thus showing aging behaviour like in soft glassy three-dimensional (3D) systems. Further, at the low values of the applied stress in the yield stress regime, the shear-rate fluctuations in time show both positive and negative values, similar to that observed in sheared 3D jammed systems. By carrying out a statistical analysis of these shear-rate fluctuations, we estimate the effective temperature of the soft glassy monolayer using the Galavatti-Cohen steady state fluctuation relation

Aggregation of a Peptide Antibiotic Alamethicin at the Air#Water Interface and Its Influence on the Viscoelasticity of Phospholipid Monolayers

The aggregation properties of an antibiotic membrane-active peptide alamethicin at the air-water interface have been studied using interfacial rheology and fluorescence microscopy techniques. Fluorescence microscopy of alamethicin monolayers revealed a coexistence of liquid expanded (LE) and solid phases at the surface concentrations studied. Interfacial oscillatory shear measurements on alamethicin monolayers indicate that its viscoelastic properties are determined by the area fraction of the solid domains. The role of zwitterionic phospholipids dioleoylphosphatidyl choline (DOPC) and dioleoylphosphatidyl ethanolamine (DOPE) on the peptide aggregation behavior was also investigated. Fluorescence microscopy of alamethicin/phospholipid monolayers revealed an intermediate phase (I) in addition to the solid and LE phase. In mixed monolayers of phospholipid (L)/alamethicin (P), with increase in L/P, the monolayer transforms from a viscoelastic to a viscous fluid with the increase in area fraction of the intermediate phase. Further, a homogeneous mixing of alamethicin/lipid molecules is observed at L/P > 4. Our studies also confirm that the viscoelasticity of alamethicin/phospholipid monolayers is closely related to the alamethicin/phospholipid interactions at the air-water interface