The second and the third virial coefficients of athermal polymer solutions

The second and the third virial coefficients in the lattice model of athermal mixtures of molecules of different sizes are calculated. All computations have been done for two- and three-dimensional simple square and simple cubic lattices.     

Osmotic compressibility in dilute polystyrene‐cyclohexane and polystyrene‐methylcyclohexane solutions: Correlation of polystyrene virial coefficients with solvent quality

Osmotic compressibilities were determined as a function of temperature for solutions of polystyrene in cyclohexane and methylcyclohexane by static light scattering, the measurements extending well below the theta temperature, T = θ. Virial coefficients extracted from the data are compared with literature values obtained by light scattering, membrane osmometry, and phase equilibrium measurements, and successfully correlated over wide ranges of molecular weight, temperature, and solvent quality. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 39: 184–196, 2001     

Osmotic pressure,atomic pressure and the virial equation of state of polymer solutions: Monte Carlo simulations of a bead-spring model

A recently introduced coarse-grained model of polymer chains is studied analyzing various contributions to the pressure as obtained from the virial theorem as a function of chain length N, temperature T and density ϕ. The off-lattice model of the polymer chains has anharmonic springs between the beads, but of finite extensibility, and the Morse-type interaction between beads is repulsive at very short distances and attractive at intermediate distances. Solvent molecules are not explicitly included. It is found that the covalent forces along the chain (modelled by the spring potentials) contribute a negative term to the pressure, irrespective of temperature, which vanishes linearly in ϕ as ϕ → 0. In contrast, both contributions to the pressure due to intrachain nonbonded forces and due to forces between different chains change sign from high temperatures (T ≫ θ, θ the theta-temperature) where they are positive, to low temperature where both parts of the pressure become negative. It is shown that the total pressure has the expected behavior with temperature near the θ-temperature, i.e., Δp ≡ p_tot − k_B · T_p ∼ (T − θ). We study also the concentration and chainlength dependence of the various contributions to the pressure in the good solvent regime and interpret them with scaling predictions.     

Supermolecular structures in polymer solutions interpretation of static light scattering data

The characterization of supermolecular structures in polymer solutions by static light scattering requires an improved analysis of the scattering curves. A comparison of the experimental curves with model calculations for various basic structure types in a scaled plot offers the possibility to extend the range of a reliable determination of the structural parameters to particle sizes up to 500 nm. The influence of the polydispersity and problems of an unambiguous interpretation are discussed. Especially, a closed analytical expression for the scattering function of polydisperse systems of spheres with a Schulz-Zimm distribution of radii was derived.     

Size distribution of colloidal silica in sodium silicate solutions investigated by dynamic light scattering and viscosity measurements

Three types of aqueous sodium silicate solutions characterized by molar SiO(2):Na(2)O ratios of 2.2, 3.3, and 3.9 were investigated by dynamic light scattering and viscosity measurements. The solutions were prepared by diluting concentrated commercial products to SiO(2) content between 0.5 and 15 wt%. Dynamic light scattering (DLS) was used for the investigation of size distributions of colloids immediately after dilution. At least three size classes of colloidal particles were detected, which exist in parallel in the solutions. The respective radii are 0.4 to 0.6 nm, 2.5 to 13 nm, and 75 to 85 nm. The larger colloids dominate the mass distribution, whereas the smaller colloids control the surface area of the colloidal fraction. Material properties such as pH, viscosity, refractive index, and density were measured as a function of dilution. The evaluation of the viscosity data indicated that the colloids have a lower density than dense amorphous silica. Aging effects could be suppressed by measuring within 1 h after dilution.     

Flow injection analysis: Rayleigh light scattering technique for total protein determination

A novel flow injection analysis (FIA) method with Rayleigh light scattering (RLS) detection was developed for the determination of total protein concentrations. This method is based on the weak intensity of RLS of bromothymol blue (BB) (3',3"-dibromothymolsulfonephthalein) which can be enhanced by the addition of protein in weakly acidic solution. A common spectrofluorimeter was used as a detector. It was proved that the application of this method to quantify the total proteins in real samples by using bovine serum albumin was possible. The RLS signal was detected at lambda(ex)= lambda(em)=572 nm. The linear range was 7.0-70.0 microg mL(-1), the detection limit was 3.75 microg mL(-1), the reproducibility was 5.5% (n=7), and the sample throughput was 26 h(-1).     

Second virial coefficients of a polymer of 2-butene-2,3-dibromo-1,4-diol with adipic acid from light scattering measurements in benzene

Light scattering measurements of a polymer of 2-butene-2,3-dibromo-1,4-diol with adipic acid in benzene have been made in the temperature range 283.15–333.15 K. The second virial coefficients and excess thermodynamic functions have been calculated.     

Plant protein-polysaccharide interactions in solutions: application of soft particle analysis and light scattering measurements

The soft particle analysis theory was applied to plant proteins and polysaccharides in solution, to determine the charge density of these polymers and the depth of the layer accessible by counterions according to pH conditions. In addition to the macromolecule shape characterized by light scattering measurements, these properties are also correlated with the optimum coacervation condition, so as to establish the prevalent plant protein-polysaccharide interactions governing the coacervate formation. Globulin was found to be highly charged and spherically shaped. The best coacervation condition was obtained at the pH value, which corresponds to the protein conformation with a dense and compact accessible layer. On the contrary, for the alpha gliadin, bearing a lower charge, a more extended conformation seems to be more favourable. For the plant proteins studied, the coacervation seems to be controlled by the structure of the counter polyanion used: from our model, it turns out that the rod-like structure of arabic gum observed at acidic pH allows the interaction with plant proteins to form coacervates, contrary to the highly charged and spherical structure of alginate.     

Modification to the cumulant analysis of polydispersity in quasielastic light scattering data

The electric field correlation function of light scattered from a polydispersed population of spherical particles having log-normal distribution with varying polydispersity is simulated. The correlation function with different polydispersity is compared with the method of cumulants over a wide range of correlation time. The large positive deviation of the method of cumulants at long correlation time is identified. This necessitates the truncation of the data at long correlation time or use of an appropriate weighting function to eliminate errors in the analysis. A modified cumulant analysis is used to overcome the limitation of truncating the correlation function. QELS data from polydisperse samples of micelles, liposomes and polyaniline nanoparticles are compared using the two methods. This method can be extended to the analysis of other multi-exponential decays such as stress relaxation, positron annihilation and NMR relaxation.     

A comparison of diffusion coefficients for ternary mixed micelle solutions measured by macroscopic gradient and dynamic light scattering techniques

Taylor dispersion is used to measure ternary mutual diffusion coefficients (D(ik)) for aqueous solutions of decylsulfobetaine (SB10) (1) + dodecylsulfobetaine (SB12) (2), SB10 (1) + SB14 (2), and SB12 (1) + SB14 (2) mixed zwitterionic micelles. Cross-coefficient D(21) for the coupled flow of surfactant 1 produced by a concentration gradient in surfactant 2 is relatively small for these solutions, but D(12) reaches values as large as the main D(ii) coefficients. The results are interpreted by using the equation D(ik) = partial differential(C(i)D(i))/ partial differentialC(k) to relate the ternary mutual diffusion coefficients to the concentration-weighted average diffusion coefficients D(i) of the micellar and free-monomer forms of the surfactants. The macroscopic-gradient Taylor measurements are compared with diffusion coefficients measured by dynamic light scattering (DLS), which monitors microscopic concentration fluctuations. At most compositions, the intensity autocorrelation function G(tau) is a single exponential decay in D((2)), the smaller eigenvalue of the mutual diffusion coefficient matrix. A contribution from D((1)) is identified at high solute fractions of surfactant 1. The DLS results are consistent with contributions to G(tau) from uncoupled fluctuations in the concentrations of eigencomponents defined as the linear combinations of surfactants 1 and 2 that diagonalize the D(ik) matrix. A procedure for the rapid and convenient DLS measurement of ternary mutual diffusion coefficients, including the cross-coefficients for coupled diffusion, is suggested, using the Onsager reciprocal relation together with the eigenvalues and pre-exponential factors from G(tau).     

Osmotic and activity coefficients in dilute solutions of ethanol in cyclohexane from freezing-point measurements

The calorimeter developed in this laboratory for isothermal enthalpy-of-dilution measurements is adapted for use as an adiabatic calorimeter for freezing-point studies. Results are obtained for ethanol solutions in cyclohexane at mole fractions of ethanol from 0.001 up to 0.08. Activities calculated from the results are used to test association models.     

Osmotic and activity coefficients of ammonium thiocyanate in aqueous solutions at 25°C

Osmotic and activity coefficients of ammonium thiocyanate determined by the isopiestic vapor pressure method are compared with the data recently reported by Covington and Matheson. Activity coefficients calculated using the Pitzer equation are now in much better agreement although a systematic difference is evident in the two sets of data.Comment to the paper by Covingtonet al. (see ref. 2).We thank Mr. P. Kordes for programming.     

Determination of fluid--solid transitions in model protein solutions using the histogram reweighting method and expanded ensemble simulations

Protein crystallization conditions are usually identified by empirical screening methods because of the complexity of the process, such as the existence of nonequilibrium phases and the different crystal forms that may result from changes in solution conditions. Here the crystallization of a model protein is studied using computer simulation. The model consists of spheres that have both an isotropic interaction of short range and anisotropic interactions between patch-antipatch pairs. The free energy of a protein crystal is calculated using expanded ensemble simulations of the Einstein crystal, and NpT-Monte Carlo simulations with histogram reweighting are used to determine the fluid-solid coexistence. The histogram reweighting method is also used to trace out the complete coexistence curve, including multiple crystal phases, with varying reduced temperature, which corresponds to changing solution conditions. At a patch-antipatch interaction strength five times that of the isotropic interaction, the protein molecules form a stable simple cubic structure near room temperature, whereas an orientationally disordered face-centered-cubic structure is favored at higher temperatures. The anisotropic attractions also lead to a weak first-order transition between orientationally disordered and ordered face-centered-cubic structures at low temperature, although this transition is metastable. A complete phase diagram, including a fluid phase, three solid phases, and two triple points, is found for the six-patch protein model. A 12-patch protein model, consistent with the face-centered-cubic structure, leads to greater thermodynamic stability of the ordered phase. Metastable liquid-liquid phase equilibria for isotropic models with varying attraction tails are also predicted from Gibbs ensemble simulations.     

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.     

Equations of state for fluids: empirical temperature dependence of the second virial coefficients

In this paper, an empirical dependence of the second virial coefficients is derived from equations of state. The second virial coefficient B2 is found to be a linear function of 1/T1+beta, where T is the temperature and beta is a constant and has different value for different substances. Excellent experimental supports to this relationship are reported for nonpolar fluids, polar fluids, heavy globular molecule fluids, and quantum fluid He-4.     

Characterization of globular protein solutions by dynamic light scattering, electrophoretic mobility, and viscosity measurements

In this work, physicochemical properties of two globular proteinsbovine serum albumin (BSA) having a molecular weight of 67 kDa and human serum albumin (HSA) having a molecular weight of 69 kDawere characterized. The bulk characteristics of these proteins involved the diffusion coefficient (hydrodynamic radius), electrophoretic mobility, and dynamic viscosity as a function of protein solution concentration for various pH values. The hydrodynamic radius data suggested an association of protein molecules, most probably forming compact dimers. Using the hydrodynamic diameter and the electropheretic mobility data allowed the determination of the number of uncompensated (electrokinetic) charges on protein surfaces. The electrophoretic mobility data were converted to zeta potential values, which allowed one to determine the isoelectric point (iep) of these proteins. It was found to be at pH 5.1 for both proteins, in accordance with previous experimental data and theoretical estimations derived from amino acid composition and p K values. To determine further the stability of protein solutions, dynamic viscosity measurements were carried out as a function of their bulk volume concentration for various pH values. The intrinsic viscosity derived from these measurements was interpreted in terms of the Brenner model, which is applicable to hard spheroidal particles. It was found that the experimental values of the intrinsic viscosity of these proteins were in good agreement with this model when assuming protein dimensions of 9.5 x 5 x 5 nm3 (prolate spheroid). The possibility of forming linear aggregates of association degree higher than 2 was excluded by these measurements. It was concluded that the combination of dynamic viscosity and dynamic light scattering can be exploited as a convenient tool for detecting not only the onset of protein aggregation in suspensions but also the form and composition of these aggregates.     

The segment-cloud model of the second virial coefficient of polymer solutions: effects of chain length and branching

The segment-cloud model for polymer molecules has been used, and the second virial coefficient A₂ obtained as a function of the interaction parameter z for linear and branched chains having different values of n. It is observed that the chain length effect, though much smaller than in the perturbation theory, increases as the degree of branching increases. Also, the branching parameter g is found to be a better correlating parameter than the segment density distribution for A₂. This is in contrast to earlier results for the perturbation theory of the excluded volume.     

Analysis of osmotic pressure data for aqueous protein solutions via a multicomponent model

Integral equation theories and Monte Carlo simulations were used to study the Donnan equilibrium, which is established by an equilibrium distribution of a simple electrolyte between an aqueous protein-electrolyte mixture and an aqueous solution of the same simple electrolyte, when these two phases are separated by a semipermeable membrane. In order to describe the unusually low osmotic pressure found in many experiments we assumed that protein molecules can form dimers. The model solution contains proteins in a monomeric form, represented as charged hard spheres, or in a dimerized form, modeled as fused charged hard spheres. The counterions and coions were also modeled as charged hard spheres but of a much smaller size. The associative mean spherical and hypernetted-chain approximations were applied to this model. In addition, Monte Carlo computer simulations were performed for the same model system mimicking a lysozyme solution in the presence of 0.1 M sodium chloride. Theory and simulations were found to be in reasonably good agreement for the thermodynamic properties such as chemical potential and osmotic pressure under these conditions. Using the theoretical approaches mentioned above, we analyzed the experimental data for the osmotic pressure of bovine serum albumin in 0.15 M sodium chloride, human serum albumin solution (HSA) in 0.1 M phosphate buffer, and lysozyme in sulphate and phosphate buffers. The theoretically determined osmotic coefficients were fitted to the existing experimental data in order to obtain the fraction of dimers in solution. Our analysis indicated that there was relatively small self-association of protein molecules for bovine serum albumin solutions at pH=5.4 and 7.3, with the fraction of dimers smaller than 10%, while at pH=4.5 the dimer fraction was equal to 50%. In the case of HSA solutions, strong negative deviations from the ideal value were found and at pH=8.0 a reasonably good agreement between the theory and experiment is obtained by assuming full dimerization. For HSA solution at pH=5.4, the best fit to the experimental results was obtained for a fraction of dimers equal to 80%.