Molecular weight determination from light scattering and refraction in solutions. A new and coherent theoretical equation

The classical theoretical equation allowing for the determination of the solute's molecular weight (M₂) from light scattering (LS) and refractive measurements in diluted solutions is reexamined. Serious theoretical and practical defects in its derivation and application are pointed out, especially about the refraction increment dn/dc. A new theoretical equation is deduced from a more consistent application of the basic molecular orientation formulae to binary liquid mixtures. More adequate additive molecular properties, the specific mean polarizability and the specific square of the mean polarizability instead of ga and , are considered with respect to refraction and LS, respectively. Inadequate approximations are avoided and a corrected LS intensity expression is used. The new equation is tested upon several typical mixtures of small molecules from measurements either performed in this work or collected in the literature (for LS perpendicular to the incident beam) to ensure objectivity. Examples of measurements in macromolecule solutions from other authors are also analysed. The new equation is suitable for practical applications, because it is based upon easy relative measurements only, and allows for a reliable determination of the M₂ values in macromolecules. The reasons for which the classic equation leads to realistic values, in spite of its theoretical inconsistency, are also explained.     

Molecular weights of polystyrenes in toluene solutions by light scattering. Comparison between classical values and values deduced from a new method

Light scattering measurements in toluene solutions are performed for a series of monodisperse polystyrenes with a molecular weight M_w range from 4×10³ to 8×10⁶. The scattered polarized intensities I_v and the natural depolarization ratios ρ_n are registered with different apparatus at λ=633 or 488 nm and the M_w values are deduced through different formulae. The complete Carr and Zimm formula (CL_a), from I_v and ρ_n, and the usual simplified formula (CL_b), from I_v, are considered for the classical method. An already demonstrated formula is considered for the new method (New). Values of M_w and related parameters do not depend on the experimental systems used but deviations appear when using different formulae. The deviations are generally low (about 10%) but often systematic: M_w(CL_a)<M_w(CL_b)<M_w(New). The most important difference concerns the effect of destructive interferences for M_w>5×10⁵: the new formula leads to a lower increase from θ=90° to θ→0 for M_w values (θ is the observation angle). For instance, in the 8×10⁶ sample, M_w(θ→0)/M_w(θ=90°)=3.6 instead of 6.1, which implies a revision of the usual determination of the radius of gyration, R_g.     

Polymer analysis by fractionation with on-line light scattering detectors

Summary The classical method for the determination of the molecular weight distribution (MWD) curve of a polymer requires fractionation according to the molecular weight and prior calibration of the separator. It is shown that the use of a dual detection system which includes a molecular mass sensitive detector eliminates the need for prior calibration. The principles of operation of a low-angle light scattering photometer, working as such a detector, are presented, as well as the basic equations for determination of the MWD curve from the elution curve and of the average molecular weights. Then the performances of the light scattering photometer are discussed with special emphasis on the various sources of errors and unaccuracies in these determinations.     

香菇多糖的成分及其分子量研究

从香菇子实体中用0.9%NaCl水溶液、85%乙醇、热水、1%草酸铵、5%NaOH/0.05%NaBH₄和2%NaOH/2%尿素分别提取出四种杂多糖(L-FⅠ-L-FⅣn)和两种葡聚糖(L-FⅤ和L-FⅥn).红外光谱和高效液相色谱分析结果表明杂多糖主要由葡萄糖、葡萄糖醛酸、木糖、甘露糖、半乳糖和鼠李糖组成,而且按照分离过程的进行多糖中葡萄糖含量递增.由光散射和膜渗透压法研究了多糖的重均分子量Mw、均方根旋转半径2>^1/2、第二维利系数A₂及数均分子量M_n.L-FⅡ、L-FⅢ、L-FⅤ及L-FⅥn的M_w值依次为19.7×10⁴、192.3×10⁴、136.4×10⁴和136.7×10⁴,它们的多分散系数-Mw/-Mn在3～5范围.     

Temperature depending light scattering measurements of aqueous gelatin and alginate solutions and their mixtures

Highly diluted solutions of an alkaline treated pig bone gelatin and a seaweed alginate of Macrocystis pyrifera have been investigated by means of static light scattering at various temperatures. With these results the thermodynamic properties found by other authors and us before can be verified. Furthermore, diluted mixtures of both polymers with different ratios of composition have been investigated. These measurements show that both polymers in all mixtures behave quasi-binarily in the investigated temperature range. They maintain their association phenomena of the pure polymer solutions.     

Influence of light scattering particles in the TiO2 photoelectrode for solid-state dye-sensitized solar cell

A TiO₂ film was modified by adding light scattering particles and applied to an anode electrode in solid-state dye-sensitized solar cells (DSSCs). The TiO₂ films with 10 wt% (vs. TiO₂ weight) light scattering particles showed enhanced performance (28%), compared with nanocrystalline TiO₂ films, which were used as the controls. In particular, the photocurrent density (J_sc) reached approximately 12.6 mA/cm² under a one-sun condition. This was attributed to the light scattering effect and decrease in internal resistance through the macroporous structure with a minor loss of electron transport. However, in the case of a larger concentration of light scattering particles (>10 wt%), there was a decrease in the efficiency of DSSCs, which resulted from the decreased surface area and degraded electron transport and charge recombination properties, as confirmed by the measurement of stepped light-induced photocurrent and photovoltage transients. Furthermore, the diffusion properties and kinetics of the composite polymer electrolyte with the nanoporous and macroporous TiO₂ films were compared and evaluated from the electrochemical impedance spectra.     

Thermal field-flow fractionation and multiangle light scattering of polyvinyl acetate with broad polydispersity and ultrahigh molecular weight microgel components

The challenging task of characterizing polydisperse polymer mixtures possessing ultrahigh molecular weight (MW) polymers and microgels in organic solvents is addressed with thermal field-flow fractionation (ThFFF) and multiangle light scattering-differential refractive index (MALS-dRI) detection. In initial experiments, a 350,000 g/mol poly(methyl methacrylate) (PMMA) standard is used to evaluate the effects of temperature gradient and temperature gradient programming on the measurements. dRI baseline fluctuations caused by temperature programming were minimized by using a mobile phase heater to thermostat connecting tubing. ThFFF–MALS-dRI is then used to separate and characterize a complex polyvinyl acetate (PVAc) sample containing ultrahigh MW polymers and microgels. The open channel design employed by ThFFF allowed the PVAc sample to be analyzed with minimal sample preparation. Unfiltered PVAc sample showed components with MWs close to 10⁹ g/mol and root mean square radius r_rms values approaching 400 nm. The same sample, filtered through a 0.5 μm pore-size membrane, yielded a MW that was at least one order of magnitude lower. These results demonstrated that the common practice of prefiltering polymer samples prior to analysis can lead to erroneously low average MWs and polydispersities. The accuracy of MW and r_rms calculated using standard light scattering equations developed for small scattering molecules and relatively high wavelengths is also examined.     

A new instrument for the measurement of very small electrophoretic mobilities using phase analysis light scattering (PALS)

A new instrument based on the principles of phase analysis light scattering (PALS) applied to the measurement of electrophoretic mobilities has been produced. Such measurements are particularly useful in the study of dispersions in non-polar media since for a given zeta potential, the mobility is proportional to the dielectric constant. It is also potentially useful where mobilities are low and the use of high electric fields (a traditional remedy) is inappropriate. This is the case when the ionic concentration and hence conductivity of the medium is high. The PALS configuration has been shown to be able to measure mobilities at least two orders of magnitudes lower than conventional LDE. The device is based on developments reported elsewhere (J. Miller et al., J. Colloid Interface Sci. 143 (2) (1991) [1]), but has a number of new features. In particular, all the signal processing is digital and the optical system a reference beam configuration.     

Interaction between light and crystallizing polymer: a simulation study

A study of light transmission through a crystallizing polymer has been carried out by graphic simulations, consisting of sporadic and pre-determinate nucleation and growth of disks (spherulites) in a rectangular area. Interaction between a light beam crossing a sample of polymer has been described by a series of simple graphical rules, accounting for both absorption and scattering. Results of the code well reproduce the experimental behavior observed in the literature of main beam light intensity emerging from a crystallizing polymer sample and allows a better understanding of the interaction between light and nucleating/growing units. Emerging light behavior calculated by the simulation has been adopted as the basis to suggest the dependence of the light scattering coefficient upon crystallization kinetic parameters.     

Light scattering in binary and ternary (polymer) solutions with specific interactions

Concentration dependence of basic light-scattering quantities in three binary low-molecular and two ternary polymer solutions was studied. Depolarization ratio alone may serve as a sensitive measure of presence of specific interactions. Experimental data of anisotropic scattering in low-molecular mixtures were in harmony with the idea that the parameters determining molecular orientation should be considered as continuous probability variables; in the case of polymer solutions specific interactions do not influence the anisotropic scattering.The presence of specific interactions with the formation of a minimum on the course of isotropic scattering is characterized. Transition from one solution structure to another with a local maximum on the course of composition light scattering is indicated.     

Anomalies in evaporative light scattering detection

A two-dimensional (2-D) “heart-cutting” HPLC system was used to fractionate oligostyrenes into the respective diastereoisomers. For samples of known composition, the response of an ultraviolet (UV) absorbance detector followed the anticipated pattern. The response of an evaporative light-scattering (ELSD) detector on the other hand indicated quite different concentrations for the two diastereoisomers, relative to what was anticipated and what was indicated by the UV detector. Whereas approximately the same concentration was indicated by UV, ELSD in some cases indicated no detection of the later eluting isomer. The magnitude of the errors depended on both the molecular weight and the tacticity of the diastereomers. These anomalies appear to be an artifact of power transform functions imbedded within the firmware processor of the ELSD, invisible to the user.     

Molecular Weight and Aggregation of Erwinia Gum in Aqueous Solutions

Erwinia(E) gum is composed of glucose, fucose, galactose and glucuronic acid. The weight-average molecular weights Mw, number-average molecular weights Mn and intrinsic viscosities[η] of the four fractions and the unfractionated E gum in aqueous solutions at desired temperatures were studied by light scattering, membrane osmometry, size exclusion chromatography(SEC) and viscometry. The experimental results prove that E gum formed aggregates in the aqueous solution at 25 ℃ and the aggregates were broken gradually with increasing temperature. The dissociation of the aggregates of E gum in the aqueous solution started at 36 ℃, and was completed at around 90 ℃. The [η] values of E gum and its fractions are much higher than those of the conventional polymers with the similar molecular weights, and decrease with increasing NaCl concentration.     

Homogeneous immunoassay for soy protein determination in food samples using gold nanoparticles as labels and light scattering detection

A homogeneous aggregation immunoassay involving the use of gold nanoparticles (AuNPs) and light scattering detection is described for soy protein determination in food samples. AuNPs act as enhancers of the precipitate that appears when the antigen-antibody complex is formed. The AuNPs-antibody conjugate has been synthesized by physical adsorption of polyclonal anti-soy protein antibodies onto the surface of commercial AuNPs with a nominal diameter of 20 nm. The direct assay is based on the reaction of the conjugate with soy protein, which reaches the equilibrium in about 10 min, and the measurement of the light scattering intensity at 530 nm, which is proportional to the analyte concentration. The dynamic range of the calibration graph is 0.2-20 μg mL⁻¹ and the detection limit value is 65 ng mL⁻¹. The precision, expressed as relative standard deviation, has been assayed at two different concentrations, 0.2 and 1 μg mL⁻¹, giving values ranging from 4.7 to 5.9%. The interference of other proteins has been assayed. The usefulness of this method has been shown by its application to the analysis of fruit juice and “nonmilk yoghourt” samples. The results obtained with the proposed method are similar to those obtained by using a commercial ELISA kit, but the assay time is significantly shorter and the detection limit was about 10 times lower. A recovery study has been also performed, giving values in the range of 84.0-119.3%.     

Usefulness of gold nanoparticles as labels for the determination of gliadins by immunoaffinity chromatography with light scattering detection

A simple and fast immunoaffinity method is proposed for the determination of gliadins for the first time using gold nanoparticles (AuNPs) as labels. The tracer used consists in a gliadin-AuNP conjugate prepared by the adsorption of gliadins onto the nanoparticle surface. Two AuNP sizes with diameters of 10 nm and 20 nm were assayed to compare the behaviour of the corresponding tracer in the assay. The method relies on the injection in a commercial Protein G column of a preincubated mixture containing gliadins, polyclonal anti-gliadin antibodies, and the gliadin-AuNP tracer. This approach allows the separation of free and bound tracer fractions without any additional elution step, and the direct measurement of the resonance light scattering intensity of the free tracer through the peak height of the immunochromatogram, which is proportional to the analyte concentration. The immunocolumn can be used up to 25 times without eluting and it can be regenerated for at least 20 times. The dynamic ranges of the calibration graphs and the detection limits are 0.5-15.0 and 1.5-15.0 μg mL⁻¹ gliadins, and 0.2 μg mL⁻¹ and 0.8 μg mL⁻¹ gliadins, using 20-nm and 10-nm Au-NPs as labels, respectively. The precision, expressed as relative standard deviation, ranges between 2.7% and 2.9% using 20-nm AuNPs and 4% and 6.1% for 10-nm AuNPs. The method has been applied to the determination of the prolamin fraction in beer samples, obtaining recovery values in the range 71.2% and 101.7%.     

Composition determination of binary polymer mixtures by size exclusion chromatography with light scattering detection

<正>Base on the principle of absolute quantification of size exclusion chromatography(SEC),a light scattering(LS) detector coupled with a concentration detector(refractive index detector) is utilized to determine the compositions of complicated binary mixtures.A theoretical analysis predicts that the response factors for both LS and RI detectors are linear functions with the composition of any specified polymer mixtures in the binary polymer mixtures.Two pairs of complicated binary mixtures were used to test the theory mentioned in the present paper,and the experimental results show an excellent accordance with the theory.     

Light scattering near and from interfaces using evanescent wave and ellipsometric light scattering

The broad range of interface light scattering investigations in recent years shows the power and the versatility of these techniques to address new and open questions in colloid and interface science and the soft condensed matter field. Structural information for polymers, liquid crystals, or colloids close to planar or spherical colloidal interfaces are either captured with long range light scattering resolution, or in a complementary approach by high resolution ellipsometric techniques. Of special interest is the dynamic behavior close to or in interfaces, since it determines material properties and responses to external fields. Due to the broad dynamical range and the high scattering contrast for visible light, interface light scattering is a key to elucidate soft matter interfacial dynamics. This contribution reviews experimental and related theoretical approaches for interface light scattering and further gives an overview of achievements based on such techniques.     

Proposed performance qualification and calibration method for evaporative light scattering detectors

Summary A method for the performance testing of Sedex 55 Evaporative Light Scattering Detectors (ELSD) has been developed as part of our regulatory compliance programme. The method uses a readily available chromatographic column, caffeine as the test probe and can be completed in less than one hour.     

Temperature-induced association and gelation of aqueous solutions of pectin. A dynamic light scattering study

Dynamic light scattering (DLS) measurements were carried out on aqueous solutions of low-methoxyl pectin at different temperatures and polymer concentration. Low temperature and increased polymer concentration promote the formation of multichain aggregates. The time correlation data obtained from the DLS experiments revealed, for all polymer solutions, the existence of two relaxation modes, one single exponential at short times followed by a stretched exponential at longer times. In the semidilute regime, a temperature reduction induced enhanced chain associations in the solutions with high values of the slow relaxation time and a strong wave vector dependence of the slow mode. These features could be rationalized in the framework of the coupling model of Ngai. At low temperatures (10 °C), gelation occurs in the semidilute regime and a transparent gel is formed. In this state, the profile of the correlation function changes and nonergodic signs are observed. The conjecture is that the association complexes and the gel network are stabilized through intermolecular hydrogen bonds, which are broken-up at higher temperatures. The hydrogen-bonded structures are formed in a process where the polymer chains have been “zipped” together in a cooperative manner.     

Dynamic light scattering from micelle complexes of cetyltrimethylammonium bromide-sodium salicylate in aqueous solutions

The diffusion coefficient of cetyltrimethylammonium bromide-sodium salicylate in aqueous solutions has been determined, using the dynamic light-scattering technique, as a function of sodium salicylate concentration, as well as of temperature. Using a gel model the results are discussed in terms of intermicellar pseudo-linkages, entanglements of threadlike micelles, and formation of pseudo-network.     

A new cubic equation of state for prediction of VLE of polymer solutions

A new cubic equation of state (CEOS) is proposed based on temperature–pressure superposition principle. A generic CEOS form, with the Peng–Robinson parameters, is used and a temperature-dependent attractive term a(T)$a(T)$ is developed, allowing an easy calculation of thermodynamic properties and vapor–liquid equilibrium. The new equation is applied to pure polymer and polymer solutions and its results are compared with those of two others equations of state. For polymer solutions, two mixing rules without binary interaction parameters were used. The vapor–liquid equilibrium (VLE) predictions showed good agreement with experimental data as well as pressure–volume–temperature (PVT) behavior of polymer liquids, attesting the appropriate form of the new equation proposed.