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Articles 1 - 27 of 27

Full-Text Articles in Statistical, Nonlinear, and Soft Matter Physics

Analysis Of The Effect Of Different Surface Preparation Methods On Corrosion Resistance And Adhesion Strength Of Astm A36 Steel Substrate With Surface Tolerant Epoxy Paint As Coating Material, Irwan Wijaya Santoso, Daffa Aqila, Rini Riastuti, Rizal Tresna Ramadhani May 2024

Analysis Of The Effect Of Different Surface Preparation Methods On Corrosion Resistance And Adhesion Strength Of Astm A36 Steel Substrate With Surface Tolerant Epoxy Paint As Coating Material, Irwan Wijaya Santoso, Daffa Aqila, Rini Riastuti, Rizal Tresna Ramadhani

Journal of Materials Exploration and Findings

In the industrial world, to extend the service life of materials, protection methods are carried out to slow down the material's corrosion rate. The protection method that is often used is the coating method. The coating method is a protection method by coating the substrate material using a coating material to prevent contact between the substrate material and the environment. In this research, the substrate material used is ASTM A36 steel and the coating material used is Surface Tolerant Epoxy paint. The independent variable used in this study lies in the surface preparation method which consists of: solvent cleaning, hand …


Combined Risk Based Inspection And Fault Tree Analysis For Repetitive 3-Phase Line Piping Leakage At West Java Offshore Topside Facility, Dona Yuliati, Akhmad Herman Yuwono, Datu Rizal Asral, Donanta Dhaneswara Dec 2023

Combined Risk Based Inspection And Fault Tree Analysis For Repetitive 3-Phase Line Piping Leakage At West Java Offshore Topside Facility, Dona Yuliati, Akhmad Herman Yuwono, Datu Rizal Asral, Donanta Dhaneswara

Journal of Materials Exploration and Findings

Hydrocarbon releases might result in serious consequences in various aspects. In addition to the contribution to environmental pollution, repetitive leakages need high repair costs. This study aim is to minimize potential repetitive leakage for other typical 3-phase piping systems. We conducted the risk assessment by adopting Risk Based Inspection (RBI) API 581 to identify risk level, calculating piping lifetime, recommended inspection plan and mitigations. The most relevant root causes can be obtained through quantitative Fault Tree Analysis (FTA). Observation and investigation was taken from eight 3-phase piping systems that experienced repetitive leakages. It has been found that the risk level …


Nitrogen Gas Quenching Pressure Effect On Bs S155 Alloy Steel In Vacuum Furnace, Agus Mulyadi Hasanudin, Eddy Sumarno Siradj Dec 2023

Nitrogen Gas Quenching Pressure Effect On Bs S155 Alloy Steel In Vacuum Furnace, Agus Mulyadi Hasanudin, Eddy Sumarno Siradj

Journal of Materials Exploration and Findings

The production of metal and alloy products requires the use of heat treatment, when during the heat treatment process, quenching is a crucial step. The quenching medium can be anything from water, a salt bath, oil, air and gas. In a vacuum furnace, pressurized gas, most frequently nitrogen (N2) gas, serves as one of the quenching mediums. One of the drawbacks of the quenching process is the distortion and dimensional change of the parts. This paper aims to investigate the influence of nitrogen gas quenching pressure on the distortion and dimensional change of aerospace actuator gear planet parts …


Aspects Of Stochastic Geometric Mechanics In Molecular Biophysics, David Frost Dec 2023

Aspects Of Stochastic Geometric Mechanics In Molecular Biophysics, David Frost

All Dissertations

In confocal single-molecule FRET experiments, the joint distribution of FRET efficiency and donor lifetime distribution can reveal underlying molecular conformational dynamics via deviation from their theoretical Forster relationship. This shift is referred to as a dynamic shift. In this study, we investigate the influence of the free energy landscape in protein conformational dynamics on the dynamic shift by simulation of the associated continuum reaction coordinate Langevin dynamics, yielding a deeper understanding of the dynamic and structural information in the joint FRET efficiency and donor lifetime distribution. We develop novel Langevin models for the dye linker dynamics, including rotational dynamics, based …


Quantifying Temperature-, Pressure-, And Nuclear Quantum Effects On Hydrophobic And Hydrophilic Water-Mediated Interactions, Justin T. Engstler Sep 2023

Quantifying Temperature-, Pressure-, And Nuclear Quantum Effects On Hydrophobic And Hydrophilic Water-Mediated Interactions, Justin T. Engstler

Dissertations, Theses, and Capstone Projects

Water-mediated interactions (WMIs) are responsible for diverse processes in aqueous solutions, including protein folding and nanoparticle aggregation. WMI may be affected by changes in temperature and pressure, and hence, they can alter chemical/physical processes that occur in aqueous environments. Traditionally, attention has been focused on hydrophobic interactions while, in comparison, the role of hydrophilic and hybrid (hydrophobic–hydrophilic) interactions have been mostly overlooked. Here, we study the role of T and P on the WMI between nanoscale (i) hydrophobic–hydrophobic, (ii) hydrophilic–hydrophilic, and (iii) hydrophilic–hydrophobic pairs of (hydroxylated/non-hydroxylated) graphene-based surfaces. We find that hydrophobic, hydrophilic, and hybrid interactions are all sensitive to …


Frontiers In The Self-Assembly Of Charged Macromolecules, Khatcher O. Margossian Oct 2022

Frontiers In The Self-Assembly Of Charged Macromolecules, Khatcher O. Margossian

Doctoral Dissertations

The self-assembly of charged macromolecules forms the basis of all life on earth. From the synthesis and replication of nucleic acids, to the association of DNA to chromatin, to the targeting of RNA to various cellular compartments, to the astonishingly consistent folding of proteins, all life depends on the physics of the organization and dynamics of charged polymers. In this dissertation, I address several of the newest challenges in the assembly of these types of materials. First, I describe the exciting new physics of the complexation between polyzwitterions and polyelectrolytes. These materials open new questions and possibilities within the context …


How Dynamic Bond Results In The Unique Viscoelastic Behavior Of The Associating Polymers, Sirui Ge Aug 2022

How Dynamic Bond Results In The Unique Viscoelastic Behavior Of The Associating Polymers, Sirui Ge

Doctoral Dissertations

Associating polymer is a special kind of polymer possessing transient reversible bonds in addition to the conventional covalent bonds. The reversible bonds provide unique dynamics and fascinating viscoelastic properties, resulting in attractive applications for these polymers, such as self-healing and shape memory materials. Despite many years of studies, the understanding of dynamics of polymers with reversible bonds, especially on molecular level, is still in the rudimentary stage, preventing the rational design of the potential novel functional materials based on associating polymers. In this dissertation, we provide a detailed and quantitative understanding of the dynamics and viscoelastic properties of associating polymers. …


A Microfluidic Approach For Synthesis And Kinetic Profiling Of Branched Gold Nanostructures, Qi Cai, Valentina Castagnola, Luca Boselli, Alirio Moura, Hender Lopez, Wei Zhang, João M. De Araújo, Kenneth A. Dawson Feb 2022

A Microfluidic Approach For Synthesis And Kinetic Profiling Of Branched Gold Nanostructures, Qi Cai, Valentina Castagnola, Luca Boselli, Alirio Moura, Hender Lopez, Wei Zhang, João M. De Araújo, Kenneth A. Dawson

Articles

Automatized approaches for nanoparticle synthesis and characterization represent a great asset to their applicability in the biomedical field by improving reproducibility and standardization, which help to meet the selection criteria of regulatory authorities. The scaled-up production of nanoparticles with carefully defined characteristics, including intrinsic morphological features, and minimal intra-batch, batch-to-batch, and operator variability, is an urgent requirement to elevate nanotechnology towards more trustable biological and technological applications. In this work, microfluidic approaches were employed to achieve fast mixing and good reproducibility in synthesizing a variety of gold nanostructures. The microfluidic setup allowed exploiting spatial resolution to investigate the growth evolution …


Manipulating The Properties Of Light-Responsive Active Lipid Bilayer Membranes: Measuring Mechanics And Probing Mechanisms, Arash Manafirad Feb 2022

Manipulating The Properties Of Light-Responsive Active Lipid Bilayer Membranes: Measuring Mechanics And Probing Mechanisms, Arash Manafirad

Doctoral Dissertations

This thesis explores an experimental system probing the effect of energy input (in light-responsive bilayers) on membrane physicomechanical properties and dynamics of response to a trigger. We were inspired by the ability of cell membranes to alter their elastic and permeability properties and shape in response to energy input, change in lipid chemistry, or bilayer composition. Our work demonstrates and sheds new light on the roles of lipid chemical character, light-responsive moieties' incorporation in the membrane, and the lipid bilayer's mechanical properties on membrane response to chemical tuning or energy input. To observe how lipid chemistry affects membrane physical properties …


A Nanoscale Shape-Discovery Framework Supporting Systematic Investigations Of Shape-Dependent Biological Effects And Immunomodulation, Wei Zhang, Hender Lopez, Luca Boselli, Paolo Bigini, André Perez-Potti, Zengchun Xie, Valentina Castagnola, Qi Cai, Camila P. Silveira, Joao M. De Araujo, Laura Talamini, Nicolò Panini, Giuseppe Ristagno, Martina B. Violatto, Stéphanie Devineau, Marco P. Monopoli, Mario Salmona, Valeria A. Giannone, Sandra Lara, Kenneth A. Dawson, Yan Yan Dec 2021

A Nanoscale Shape-Discovery Framework Supporting Systematic Investigations Of Shape-Dependent Biological Effects And Immunomodulation, Wei Zhang, Hender Lopez, Luca Boselli, Paolo Bigini, André Perez-Potti, Zengchun Xie, Valentina Castagnola, Qi Cai, Camila P. Silveira, Joao M. De Araujo, Laura Talamini, Nicolò Panini, Giuseppe Ristagno, Martina B. Violatto, Stéphanie Devineau, Marco P. Monopoli, Mario Salmona, Valeria A. Giannone, Sandra Lara, Kenneth A. Dawson, Yan Yan

Articles

Since it is now possible to make, in a controlled fashion, an almost unlimited variety of nanostructure shapes, it is of increasing interest to understand the forms of biological control that nanoscale shape allows. However, a priori rational investigation of such a vast universe of shapes appears to present intractable fundamental and practical challenges. This has limited the useful systematic investigation of their biological interactions and the development of innovative nanoscale shape-dependent therapies. Here, we introduce a concept of biologically relevant inductive nanoscale shape discovery and evaluation that is ideally suited to, and will ultimately become, a vehicle for machine …


Characterization Of Lamellar Liquid Crystal Emulsifiers In Topical Creams Containing A Novel Solvent, Melinda Joanna Sutton Aug 2021

Characterization Of Lamellar Liquid Crystal Emulsifiers In Topical Creams Containing A Novel Solvent, Melinda Joanna Sutton

MSU Graduate Theses

Diethylene glycol monoethyl ether (DEGEE) is a promising solvent component in topical cream formulations due to its superior solubilizing abilities with certain active pharmaceutical ingredients. One of the goals of this study is to characterize the effects of pH on the physical and chemical stabilities of topical cream formulations containing particularly high concentrations of DEGEE by characterizing a full topical pH profile of 3.5 – 9.0. The second goal is to evaluate the presence, amount, and characteristics of lyotropic liquid crystals (LLCs), molecularly structured in a lamellar phase, in a model cream emulsion utilizing polarized light microscopy (PLM). The presence …


Establishing Independent Tunability Of The Mechanical And Transport Properties Of Polymer Gels, Lucas Rankin Jan 2021

Establishing Independent Tunability Of The Mechanical And Transport Properties Of Polymer Gels, Lucas Rankin

Master’s Theses

Polymer gels can be used in the fabrication of materials for filtering liquid and gaseous media, solid-state electrolytes, and transdermal medical patches. This diverse range of applications primarily relies on the transport and mechanical properties of polymer gels. Both sets of properties have shown excellent tunability, but typically in a coupled fashion. Establishing the independent tunability of the transport and mechanical properties of polymer gels (using simple, cost-effective methods) is paramount if polymer gels are to be used to their full potential. Specifically, block copolymer gels self-assemble into organized nanoscale networks within the gel solvent, which allows for facile control …


Quantifying Confinement Of Chain Dynamics For Chains Tethered To Self-Assembling Crystalline Nanodomains Using Neutron Spin Echo Spectroscopy, Logan Benninghoff Jan 2021

Quantifying Confinement Of Chain Dynamics For Chains Tethered To Self-Assembling Crystalline Nanodomains Using Neutron Spin Echo Spectroscopy, Logan Benninghoff

Williams Honors College, Honors Research Projects

Polyisobutylene (PIB) rubbers can be reinforced with crystalline β-alanine nanodomains. Progress has been made in understanding the morphology of the nanodomains, but the dynamics of the PIB molecule chains attached to the surface of the nanodomains and in the matrix are not well understood. It is possible to observe the motion of these PIB chains using Neutron Spin Echo (NSE) experiments, since the experimental technique can give data for smaller timescales. Data collection for reinforced rubber samples has already been performed, but the data still need to be analyzed. For my honors project I will be comparing the data to …


Theory And Improved Methods For Probing The Cavitation To Fracture Transition, Christopher Barney Dec 2020

Theory And Improved Methods For Probing The Cavitation To Fracture Transition, Christopher Barney

Doctoral Dissertations

A material is considered soft when its bulk modulus is significantly greater than its shear modulus. Rubbery polymers are a class of soft materials where resistance to extension is mainly entropic in nature. Polymeric soft solids differ from liquids due to the presence of a percolated network of strong bonds that resist deformation and flow on a given time scale. The incompressible nature, entropically driven elasticity, and molecular scale network structure of soft polymeric solids combine to impart unique mechanical behavior that often results in complex material responses to simple loading situations. An important example of this is cavitation in …


Predicting The Hydration Free Energy Of Small Alkanes And Alcohols From Custom, Electronic Structure-Based Force Fields, T. Ryan Rogers Dec 2020

Predicting The Hydration Free Energy Of Small Alkanes And Alcohols From Custom, Electronic Structure-Based Force Fields, T. Ryan Rogers

Graduate Theses and Dissertations

Mathematical theories reveal the fundamental physics involved in experimentalphenomena. Computer models of such theories are routinely used to corroborate or explain experiments and predict properties of chemical systems. Therefore, an important effort in computational chemistry is the development of more accurate and efficient chemical models. Current-generation models are only beginning to approach experimental-quality predictions of hydration free energies (HFEs).Using computations of quantum mechanical (QM) forces and classical simulations based on these forces, I investigate models to predict several properties of solutes and solutions. This dissertation is a collection of projects exemplifying methods used to gain insight into chemical systems.

Simulations …


Adsorption And Reconfiguration Of Amphiphiles At Silica-Water Interfaces: Role Of Electrostatic Interactions, Van Der Waals Forces And Hydrogen Bonds, Yao Wu Nov 2020

Adsorption And Reconfiguration Of Amphiphiles At Silica-Water Interfaces: Role Of Electrostatic Interactions, Van Der Waals Forces And Hydrogen Bonds, Yao Wu

LSU Doctoral Dissertations

The ability to explore and predict metastable structures of hybrid self-assemblies is of central importance for the next generation of advanced materials with novel properties. As compared to their thermodynamically stable forms, the kinetically stabilized materials show improved functionality potentially over their stable counterparts. The self-assembly processes usually originate from weak intermolecular interactions, involving a dynamic competition between attractive and repulsive interactions. These weak forces, including van der Waals (vdW), electrostatic interaction and the hydrogen bonding (H-bonding), can be tuned by external stimuli, e.g., confinement, temperature and ionization, and consequently driving hybrid materials into different configurations. It is challenging to …


Reactive And Stimuli-Responsive Sulfonium-Based Polymer Zwitterions, Cristiam Santa Chalarca Jul 2019

Reactive And Stimuli-Responsive Sulfonium-Based Polymer Zwitterions, Cristiam Santa Chalarca

Doctoral Dissertations

This dissertation describes the synthesis and characterization of novel monomers and (co)polymer zwitterions that incorporate trialkylsulfonium cations. The novel materials presented herein constitute a unique type of polymer zwitterions that exhibit salt- and temperature-dependent water solubility as well as inherent reactivity. The behavior of these polymers in aqueous solutions, as nanostructures, and at liquid-liquid interfaces was studied; in all cases, the inherent reactivity of the polymers was harnessed towards the fabrication of novel polymers and soft materials. Following an introductory chapter, Chapter 2 describes the synthesis of sulfonium sulfonate monomers and polymer zwitterions. Both styrenic and methacrylic monomers were synthesized …


Adhesion At Solid/Liquid Interfaces, Neda Ojaghlou Jan 2019

Adhesion At Solid/Liquid Interfaces, Neda Ojaghlou

Theses and Dissertations

The adhesion at solid/liquid interface plays a fundamental role in diverse fields and helps explain the structure and physical properties of interfaces, at the atomic scale, for example in catalysis, crystal growth, lubrication, electrochemistry, colloidal system, and in many biological reactions. Unraveling the atomic structure at the solid/liquid interface is, therefore, one of the major challenges facing the surface science today to understand the physical processes in the phenomena such as surface coating, self-cleaning, and oil recovery applications. In this thesis, a variety of theory/computational methods in statistical physics and statistical mechanics are used to improve understanding of water adhesion …


Analyses Of Densely Crosslinked Phenolic Systems Using Low Field Nmr, Jigneshkumar Patel Nov 2017

Analyses Of Densely Crosslinked Phenolic Systems Using Low Field Nmr, Jigneshkumar Patel

Doctoral Dissertations

A uniform dispersion of reactants is necessary to achieve a complete reaction involving multi-components, especially for the crosslinking of rigid high-performance materials. In these reactions, miscibility is crucial for curing efficiency. This miscibility is typically enhanced by adding a third component, a plasticizer. For the reaction of the highly crystalline crosslinking agent hexamethylenetetramine (HMTA) with a strongly hydrogen-bonded phenol formaldehyde resin, furfural has been traditionally used as the plasticizer. However, the reason for its effectiveness is not clear. In this doctoral thesis work, miscibility and crosslinking efficiency of plasticizers in phenolic curing reactions are studied by thermal analysis and spectroscopic …


The Effect Of Composition And Architecture On Polymer Behavior In Homopolymer Blends And Inter-Filament Bonding In 3d Printed Models, Edward Roy Duranty Dec 2015

The Effect Of Composition And Architecture On Polymer Behavior In Homopolymer Blends And Inter-Filament Bonding In 3d Printed Models, Edward Roy Duranty

Doctoral Dissertations

This dissertation presents work that increases our understanding of the effects of composition and architecture on copolymer structure and dynamics and how they affect material diffusion between filaments in a 3D printed model. Copolymers are polymer chains made up of at least two different monomers. The ordering and arrangement of the two monomer species within a copolymer can have drastic effects on the behavior and properties of the copolymer.

The first chapter of this dissertation examines how the copolymer composition affects the structure and dynamics of the chain in a homopolymer blend. This study used a modified Monte Carlo BFM …


Contact Angles And Contact Lines Around Particles At Isotropic And Anisotropic Liquid Interfaces, Nesrin Senbil Nov 2015

Contact Angles And Contact Lines Around Particles At Isotropic And Anisotropic Liquid Interfaces, Nesrin Senbil

Doctoral Dissertations

Liquid interfaces, capillarity and self-assembly of particles at interfaces are important in nature and technology. When a particle is adsorbed to a liquid interface, the contact line of the particle with the liquid interface and the associated contact angle are the crucial parameters that drive assembly of the particles. We looked at how the shape of the liquid interface and the shape of the particle affect the contact angle and the shape of the contact line. We used millimeter-sized PDMS-coated glass spheres and measured the contact angles at isotropic (planar) and anisotropic interfaces (saddle and cylindrical in shape). Anisotropy of …


Sucralose Destabilization Of Protein Structure, Christina M. Othon Mar 2015

Sucralose Destabilization Of Protein Structure, Christina M. Othon

Christina M Othon

Sucralose is a commonly employed artificial sweetener that behaves very differently than its natural disaccharide counterpart, sucrose, in terms of its interaction with biomolecules. The presence of sucralose in solution is found to destabilize the native structure of two model protein systems: the globular protein bovine serum albumin and an enzyme staphylococcal nuclease. The melting temperature of these proteins decreases as a linear function of sucralose concentration. We correlate this destabilization to the increased polarity of the molecule. The strongly polar nature is manifested as a large dielectric friction exerted on the excited-state rotational diffusion of tryptophan using time-resolved fluorescence …


Morphology Characterization Of Low Band Gap Polymer-Based Organic Photovoltaics, Feng Liu Aug 2014

Morphology Characterization Of Low Band Gap Polymer-Based Organic Photovoltaics, Feng Liu

Doctoral Dissertations

In bulk heterojunction (BHJ) thin film organic photovoltaics (OPV), morphology control is critical to obtain good device efficiency. Nanoscale phase separation that creates bicontinuous interpenetrating structure on a size scale commensurate with exciton diffusion length (~10 nm) is thought to be the ideal morphology. Results obtained from this work indicate that morphology can be affected by chemical structure of the polymer, processing conditions, blending ratio and post treatments. Physical properties of the material, such as crystallinity, crystal orientation, material interactions and miscibility, surface energy and particle aggregations are critical for determining the morphology and thus the device performance. Previous investigations …


Creasing Instability Of Hydrogels And Elastomers, Dayong Chen Aug 2014

Creasing Instability Of Hydrogels And Elastomers, Dayong Chen

Doctoral Dissertations

CREASING INSTABILITY OF HYDROGELS AND ELASTOMERS MAY 2014 DAYONG CHEN, B.S., TIANJIN UNIVERISTY M.S., TIANJIN UNIVERSITY M.S., UNIVERSITY OF MASSACHUSETTS AMHERST Ph.D., UNIVERSITY OF MASSACHUSETTS AMHERST Directed by: Professor Ryan C. Hayward Soft polymers placed under compressive stress can undergo an elastic creasing instability in which sharp folds spontaneously form on the free surfaces. This process may play an important role in contexts as diverse as brain morphogenesis, failure of tires, and electrical breakdown of soft polymer actuators. While the creasing instability has been used for collotype printing since as early as the 1850s, the scientific appreciation of this instability …


Composition Dependence Of The Flory-Huggins Interaction Parameter In Polymer Blends: Structural And Thermodynamic Calculations, Travis H. Russell Aug 2014

Composition Dependence Of The Flory-Huggins Interaction Parameter In Polymer Blends: Structural And Thermodynamic Calculations, Travis H. Russell

Doctoral Dissertations

Flory-Huggins Theory has been the basis for understanding polymer solvent and blended polymer thermodynamics for much of the last 60 years. Within this theory, a parameter (χ) [chi] was included to quantify the enthalpic energy of dispersion between distinct components. Thin film self-assembly of polymer melts and block copolymers depends critically on this parameter, and in application, χ has generally been assumed to be independent of the concentrations of the individual components of the system. However, Small-Angle Neutron Scattering data on isotopic polymer blends, such as polyethylene and deuterated polyethylene, have shown a roughly parabolic concentration dependency for …


Structural Dynamics And Charge Transport In Room Temperature Ionic Liquids, Philip James Griffin Aug 2014

Structural Dynamics And Charge Transport In Room Temperature Ionic Liquids, Philip James Griffin

Doctoral Dissertations

Room temperature ionic liquids are an important class of materials due to their chemical tunability and numerous advantageous physicochemical properties. As a result, ionic liquids are currently being investigated for use in a wide array of chemical and electrochemical applications. Despite their great potential, however, the relationship between the chemical structure and physicochemical properties of ionic liquids is not well understood.

To this end, this dissertation presents experimental studies of the reorientational structural dynamics and charge transport properties of a variety of room temperature ionic liquids using quasielastic light scattering spectroscopy and broadband dielectric spectroscopy.

Studies of a series of …


Systematic Approach To Electrostatically Induced 2d Crystallization Of Nanoparticles At Liquid Interfaces, Sumit Kewalramani, Suntao Wang, Yuan Lin, Huong Giang Nguyen, Qian Wang, Masafumi Fukuto, Lin Yang Nov 2010

Systematic Approach To Electrostatically Induced 2d Crystallization Of Nanoparticles At Liquid Interfaces, Sumit Kewalramani, Suntao Wang, Yuan Lin, Huong Giang Nguyen, Qian Wang, Masafumi Fukuto, Lin Yang

Faculty Publications

We report an experimental demonstration of a strategy for inducing two-dimensional (2D)crystallization of charged nanoparticles on oppositely charged fluid interfaces. This strategy aims to maximize the interfacial adsorption of nanoparticles, and hence their lateral packing density, by utilizing a combination of weakly charged particles and a high surface charge density on the planar interface. In order to test this approach, we investigated the assembly of cowpea mosaic virus (CPMV) on positively charged lipid monolayers at the aqueous solution surface, by means of in situX-ray scattering measurements at the liquid–vapor interface. Theassembly was studied as a function of the solution …