Measurements of the Rayleigh ratio of some pure liquids at several laser light wavelengths

Bayesian analysis of static light scattering data for globular proteins

Static light scattering is a popular physical chemistry technique that enables calculation of physical attributes such as the radius of gyration and the second virial coefficient for a macromolecule (e.g., a polymer or a protein) in solution. The second virial coefficient is a physical quantity that characterizes the magnitude and sign of pairwise interactions between particles, and hence is related to aggregation propensity, a property of considerable scientific and practical interest. Estimating the second virial coefficient from experimental data is challenging due both to the degree of precision required and the complexity of the error structure involved. In contrast to conventional approaches based on heuristic ordinary least squares estimates, Bayesian inference for the second virial coefficient allows explicit modeling of error processes, incorporation of prior information, and the ability to directly test competing physical models. Here, we introduce a fully Bayesian model for static light scattering experiments on small-particle systems, with joint inference for concentration, index of refraction, oligomer size, and the second virial coefficient. We apply our proposed model to study the aggregation behavior of hen egg-white lysozyme and human γS-crystallin using in-house experimental data. Based on these observations, we also perform a simulation study on the primary drivers of uncertainty in this family of experiments, showing in particular the potential for improved monitoring and control of concentration to aid inference.

Static laser speckle suppression using liquid light guides

Static laser speckle suppression using multimode fibers has practical limitations as the technique requires an extremely long fiber to achieve an acceptable speckle contrast. An effective method based on liquid light guides was developed in this study to suppress laser speckle. In this study, a speckle simulation model of the liquid light guide was established for numerically calculating the speckle contrast without solving the analytical solution of the photon diffusion equation. The obtained simulation results were compared with the experimental results for the dependence of speckle contrast on the required length and numerical aperture with different liquid core types of liquid light guides. A speckle contrast of 12% and a speckle suppression efficiency of 5 was achieved at the end of a 2.4 m long liquid light guide. For the same fiber length, liquid light guides were found to suppress speckle more efficiently when compared to multimode fibers.

Determination of the Rayleigh Ratio with an Uncertainty Analysis by Static Light-Scattering Measurements of Certified Reference Materials for Molecular Weight

The most important parameter for light-scattering measurements in the Rayleigh scattering region is the Rayleigh ratio, which is necessary to obtain the absolute scattered light intensity from the relative scattered light intensity. The absolute scattered light intensity is directly related to the molar masses of polymers, colloids, biomolecules, and the like. A new Rayleigh ratio was determined by measuring static light scattering from certified reference materials with highly accurate certified values of the molecular weight determined by several other techniques, such as MALDI-TOF mass spectrometry or size-exclusion chromatography. The new Rayleigh ratio can be used for evaluating the uncertainty of the molecular weight of polymers and macromolecules, as measured by light scattering.

Third harmonic scattering in liquids

Third harmonic scattering (THS) from liquids has been observed and analyzed in several recent papers. It is considered to be analogous to second harmonic scattering (hyper-Rayleigh scattering) and to provide a means for measuring the second hyperpolarizability tensor of molecules in a liquid. However, the observed signal for a pure solvent is in fact mainly due to coherent third harmonic generation followed by Rayleigh scattering and direct incoherent THS (direct THS) makes only a small contribution (<2% for parallel polarized THS). This invalidates the internal reference method and the polarization analysis that has been applied for pure liquids. Theoretical comparison for the two processes, extensive experimental measurements for CCl₄ liquid, SiO₂ glass, and CCl₂F₂ gas and survey measurements for D₂O, CDCl₃, CD₃CN, and (CD₃)₂SO liquid, are presented.

Exploiting Complex Formation between Polysaccharides and Protein Microgels To Influence Particle Stabilization of W/W Emulsions

Protein particles were complexed with polysaccharides, and the effect on their capacity to stabilize water-in-water (W/W) emulsions was investigated. Protein microgels were formed by heating aqueous solutions of whey protein isolate. The microgels were subsequently mixed with anionic or cationic polysaccharides: κ-carrageenan (κ-car) or chitosan, respectively. The molar mass and radius of the complexes formed in dilute microgel suspensions (40 mg/L) were characterized by light scattering techniques as a function of the pH and the composition. The structure and stability of complexes formed at a higher microgel concentration (3 g/L) were studied by confocal laser scanning microscopy. It was found that small stable complexes can be formed with κ-car between pH 4.3 and pH 5.5 and with chitosan between pH 4.1 and pH 6.5, that is, both below and above the isoionic point of the microgels (pI = 5.0). Complexation with polysaccharides stabilized aqueous suspensions of microgels in the pH range where they flocculated in the absence of polysaccharides (4.3-5.5). W/W emulsions were produced by mixing dextran and poly(ethylene oxide) solutions. Microgels added to these emulsions spontaneously form a layer around the dispersed droplets, which inhibits coalescence to different extents depending on the conditions. The effect of complexation on the structure of the emulsions was investigated as a function of the pH. It is shown that stable liquid-like emulsions can be obtained in the pH range where emulsions containing only microgels flocculate.

Determination of molar masses of macromolecules by size exclusion chromatography-light scattering not requiring knowledge of refractive index increments

A new approach for the calibration of SEC-light scattering (SEC-LS) setups is proposed, which requires solely the molar mass of a reference polymer. Neither the specific refractive index increment of the calibrant nor of the analyte is required. Comparison of the molar masses derived in different solvents for a large number of chemically different polymers shows that the new approach yields the same molar masses as if molar masses were derived using dn/dc to calibrate the light scattering setup. The approach therefore allows easier determination of molar masses by SEC-LS.

Polymorphic Protein Crystal Growth: Influence of Hydration and Ions in Glucose Isomerase

Crystal polymorphs of glucose isomerase were examined to characterize the properties and to quantify the energetics of protein crystal growth. Transitions of polymorph stability were measured in poly(ethylene glycol)/NaCl solutions, and one transition point was singled out for more detailed quantitative analysis. Single crystal x-ray diffraction was used to confirm space groups and identify complementary crystal structures. Crystal polymorph stability was found to depend on the NaCl concentration, with stability transitions requiring > 1 M NaCl combined with a low concentration of PEG. Both salting-in and salting-out behavior was observed and was found to differ for the two polymorphs. For NaCl concentrations above the observed polymorph transition, the increase in solubility of the less stable polymorph together with an increase in the osmotic second virial coefficient suggests that changes in protein hydration upon addition of salt may explain the experimental trends. A combination of atomistic and continuum models was employed to dissect this behavior. Molecular dynamics simulations of the solvent environment were interpreted using quasi-chemical theory to understand changes in protein hydration as a function of NaCl concentration. The results suggest that protein surface hydration and Na+ binding may introduce steric barriers to contact formation, resulting in polymorph selection.

Determining the optical properties of a gelatin‑TiO(2) phantom at 780 nm

Tissue phantoms play a central role in validating biomedical imaging techniques. Here we employ a series of methods that aim to fully determine the optical properties, i.e., the refractive index n, absorption coefficient μ(a), transport mean free path [Formula: see text], and scattering coefficient μ(s) of a TiO(2) in gelatin phantom intended for use in optoacoustic imaging. For the determination of the key parameters μ(a) and [Formula: see text], we employ a variant of time of flight measurements, where fiber optodes are immersed into the phantom to minimize the influence of boundaries. The robustness of the method was verified with Monte Carlo simulations, where the experimentally obtained values served as input parameters for the simulations. The excellent agreement between simulations and experiments confirmed the reliability of the results. The parameters determined at 780 nm are [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text]The asymmetry parameter g obtained from the parameters [Formula: see text] and [Formula: see text] is 0.93, which indicates that the scattering entities are not bare TiO(2) particles but large sparse clusters. The interaction between the scattering particles and the gelatin matrix should be taken into account when developing such phantoms.

Reexamining protein-protein and protein-solvent interactions from Kirkwood-Buff analysis of light scattering in multi-component solutions

The classic analysis of Rayleigh light scattering (LS) is re-examined for multi-component protein solutions, within the context of Kirkwood-Buff (KB) theory as well as a more generalized canonical treatment. Significant differences arise when traditional treatments that approximate constant pressure and neglect concentration fluctuations in one or more (co)solvent/co-solute species are compared with more rigorous treatments at constant volume and with all species free to fluctuate. For dilute solutions, it is shown that LS can be used to rigorously and unambiguously obtain values for the osmotic second virial coefficient (B(22)), in contrast with recent arguments regarding protein interactions deduced from LS experiments. For more concentrated solutions, it is shown that conventional analysis over(under)-estimates the magnitude of B(22) for significantly repulsive(attractive) conditions, and that protein-protein KB integrals (G(22)) are the more relevant quantity obtainable from LS. Published data for α-chymotrypsinogen A and a series of monoclonal antibodies at different pH and salt concentrations are re-analyzed using traditional and new treatments. The results illustrate that while traditional analysis may be sufficient if one is interested in only the sign of B(22) or G(22), the quantitative values can be significantly in error. A simple approach is illustrated for determining whether protein concentration (c(2)) is sufficiently dilute for B(22) to apply, and for correcting B(22) values from traditional LS regression at higher c(2) values. The apparent molecular weight M(2, app) obtained from LS is shown to generally not be equal to the true molecular weight, with the differences arising from a combination of protein-solute and protein-cosolute interactions that may, in principle, also be determined from LS.

Formation and stability of water-soluble, molecular polyelectrolyte complexes: effects of charge density, mixing ratio, and polyelectrolyte concentration

The formation of complexes with stoichiometric (1:1) as well as nonstoichiometric (2:1) and (1:2) compositions between oppositely charged synthetic polyelectrolytes carrying strong ionic groups and significantly different molecular weights is reported in this contribution. Poly(sodium styrenesulfonate) (NaPSS) was used as polyanion, and a range of copolymers with various molar ratios of the poly(methacryloxyethyltrimethylammonium) chloride, poly(METAC), and the nonionic poly(ethylene oxide) ether methacrylate, poly(PEO45MEMA), were used as polycations. Formation and stability of PECs have been investigated by dynamic and static light scattering (LS), turbidity, and electrophoretic mobility measurements as a function of polyelectrolyte solution concentration, charge density of the cationic polyelectrolyte, and mixing ratio. The data obtained demonstrate that in the absence of PEO45 side chains the 100% charged polymer (polyMETAC) formed insoluble PECs with PSS that precipitate from solution when exact stoichiometry is achieved. In nonstoichiometric complexes (1:2) and (2:1) large colloidally stable aggregates were formed. The presence of even a relatively small amount of PEO45 side chains (25%) in the cationic copolymer was sufficient for preventing precipitation of the formed stoichiometric and nonstoichiometric complexes. These PEC's are sterically stabilized by the PEO45 chains. By further increasing the PEO45 side-chain content (50 and 75%) of the cationic copolymer, small, water-soluble molecular complexes could be formed. The data suggest that PSS molecules and the charged backbone of the cationic brush form a compact core, and with sufficiently high PEO45 chain density (above 25%) molecular complexes are formed that are stable over prolonged times.

Molar mass, radius of gyration and second virial coefficient from new static light scattering equations for dilute solutions: application to 21 (macro)molecules

New static light scattering (SLS) equations for dilute binary solutions are derived. Contrarily to the usual SLS equations [Carr-Zimm (CZ)], the new equations have no need for the experimental absolute Rayleigh ratio of a reference liquid and solely rely on the ratio of scattered intensities of solutions and solvent. The new equations, which are based on polarizability equations, take into account the usual refractive index increment partial differential n/partial differential rho(2) complemented by the solvent specific polarizability and a term proportional to the slope of the solution density rho versus the solute mass concentration rho(2) (density increment). Then all the equations are applied to 21 (macro)molecules with a wide range of molar mass (0.2<M<8000 kg mol(-1)). On the studied dataset with M<200 kg mol(-1), the new equations clearly achieve a better agreement with supplier M values. For macromolecules (M>500 kg mol(-1)), for which the scattered intensity is no longer independent of the scattering angle, the new equations give the same value of the radius of gyration as the CZ equation and consistent values of the second virial coefficient.

Surface properties of bottle-brush polyelectrolytes on mica: effects of side chain and charge densities

Surface properties of a series of cationic bottle-brush polyelectrolytes with 45-unit-long poly(ethylene oxide) side chains were investigated by phase modulated ellipsometry and surface force measurements. The evaluation of the adsorbed mass of polymer on mica by means of ellipsometry is complex due to the transparency of mica and its birefringence and low dielectric constant. We therefore employed a new method to overcome these difficulties. The charge and the poly(ethylene oxide) side chain density of the bottle-brush polymers were varied from zero charge density and one side chain per segment to one charge per segment and no side chains, thus spanning the realm from a neutral bottle-brush polymer, via a partly charged brush polyelectrolyte, to a linear fully charged polyelectrolyte. The adsorption properties depend crucially on the polymer architecture. A minimum charge density of the polymer is required to facilitate adsorption to the oppositely charged surface. The maximum adsorbed amount and the maximum side chain density at the surface are obtained for the polymer with 50% charged segments and the remaining 50% of the segments carrying poly(ethylene oxide) side chains. It is found that brushlike layers are formed when 25-50% of the segments carry poly(ethylene oxide) side chains. In this paper, we argue that the repulsion between the side chains results in an adsorbed layer that is non-homogeneous on the molecular level. As a result, not all side chains will contribute equally to the steric repulsion but some will be stretched along the surface rather than perpendicular to it. By comparison with linear polyelectrolytes, it will be shown that the presence of the side chains counteracts adsorption. This is due to the entropic penalty of confining the side chains to the surface region.

Effect of the ionic surfactant concentration on the stabilization/destabilization of polystyrene colloidal particles

One of the most interesting properties of the surfactants is that they are able to alter the stability of colloidal dispersions. Despite its great industrial relevance, only a few works analyze the colloidal stability of these systems at high surfactant concentrations (well above the critical micelle concentration (CMC)). In the present work, the colloidal stability of polystyrene particles is studied under a wide range of ionic surfactant concentrations. The effects of the surface charge of the latex particles (evaluating both sign and value), and surfactant type (cationic or anionic) have been examined. Colloidal stability data have been gathered by monitoring aggregation using a nephelometric technique. As will be shown, it is possible to reach different stability regimes using the same colloidal system just by changing the surfactant concentration. Independently of the sign of both the surfactant and the surface, the destabilization of the system consistently takes place above certain surfactant concentration due to a depletion effect from non-adsorbed micelles. This destabilization can be predicted by adding to the DLVO interaction energy a new contribution addressing the force between two spherical particles in the presence of non-adsorbing spherical macromolecules.

Aggregation and gelation of micellar casein particles

Micellar casein particles (submicelles) are formed by removing calcium phosphate from native casein. The submicelles aggregate and eventually form a gel with a rate that increases strongly with increasing temperature and casein concentration. At low casein concentrations the gel is very weak and collapses under its own weight so that a precipitate is formed. The structure of the aggregates is studied using light scattering and cryo-electron microscopy. It is found that the aggregates have a self-similar structure with fractal dimension 2. The viscoelastic properties of the gel are studied by frequency scans of the loss and storage moduli during the gelation process. The bonds between the submicelles probably involve calcium phosphate complexes.

Experimental test of the Rayleigh-Debye-Gans theory for light scattering by fractal aggregates

Calibrated measurements of optical (lambda = 488-nm) scattering cross sections, in the form of Rayleigh ratios, are presented for two fractal aggregate aerosols. The aggregates have radii of gyration of approximately 280 nm, fractal dimensions of approximately 1.75, and monomer sizes of approximately 20 nm with approximately 150 monomers per cluster. One aerosol was composed of vitreous SiO2 with a refractive index of 1.46, the other of anatase TiO2 with a refractive index of 2.61. We found good agreement with the Rayleigh-Debye-Gans prediction for the scattering cross section of fractal aggregates.

Adsorption of an amphiphilic penicillin onto human serum albumin: characterisation of the complex

The complex formed by the interaction of the amphiphilic penicillin drug nafcillin and human serum albumin (HSA) in water at 25 degrees C has been characterised using a range of physicochemical techniques. Measurements of the solution conductivity and the electrophoretic mobility of the complexes have shown an ionic adsorption of the drug on the protein surface leading to a surface saturation at a nafcillin concentration of 0.012 mmol kg(-1) and subsequent formation of drug micelles in solutions of higher nafcillin concentration. Measurements of the size of the complex and the thickness of the adsorbed layer by static and dynamic light scattering have shown a gradual change in hydrodynamic radius of the complex with increasing drug concentration typical of a saturation rather than a denaturation process, the magnitude of the change being insufficient to account for any appreciable extension or unfolding of the HSA molecule. The interaction potential between the HSA/nafcillin complexes, and the stability of the complexes were determined from the dependence of diffusion coefficients on protein concentration by application of the DLVO colloidal stability theory. The results indicate decreasing stability of the colloidal dispersion of the drug/protein complexes with an increase in the concentration of added drug.

Structure of aggregating kappa-carrageenan fractions studied by light scattering

We have studied kappa-carrageenan fractions with varying molar mass, obtained by sonication, using static and dynamic light scattering and polarimetry. The samples were characterised in 0.1 M NaCl and 0.1 M NaI, i.e. in the coil and helix conformation, respectively. We find that the molar mass and size of the untreated sample are the same in the coil and helix conformation. For the sonicated samples, we find larger average molar masses and sizes in the helix conformation. The critical temperature, T(c), below which the coil-helix transition sets in, decreases with decreasing molar mass. Aggregation is induced by lowering the temperature in the presence of 0.01 M KCl, which leads to the formation of locally rigid bundles of kappa-carrageenan chains. The thickness of the bundles increases slowly with time and we have not observed stabilisation, even after 24 h at 10 degrees C below T(c). The local structure of the aggregates is the same for all fractions, but at a given temperature, the rate of aggregation decreases with decreasing molar mass.