Polydisperse Solutions Research Articles

On the determination of the average molecular weight, radius of gyration, and mass/length ratio of polydisperse solutions of polymerizing rod-like macromolecular monomers by multi-angle static light scattering

The angular dependence of the light scattered from polydisperse solutions of rod-like or worm-like linear polymers formed by the polymerization of rod-like macromolecular monomers was studied with the aid of computer simulations. Except at very low conversion degrees, these ensembles are characterized by curved Zimm-like plots. An appraisal of the use of polynomial fittings for the derivation of the weight-average molecular weight (Mw) and of the z-average square radius of gyration ( z) from such plots is presented and discussed. Depending on the average size and shape distribution, the use of polynomial fittings allows the applicability of the Zimm method well beyond the standard condition q2 z<<1, q being the scattering wavevector. In addition, the derivation of the w/z-average mass/length ratio ML of the polymers from only partially linear Casassa plots, from which large errors in the derived ML values can be made, is analyzed. By combining the Casassa method with the complementary Holtzer plots, it is usually possible to assess the reliability of the results and give an estimate of their accuracy. However, it was also found that apparently linear Casassa plots, allowing a good estimate of the ML value, may arise in particular situations even when the Holtzer plot would indicate otherwise.

Hindered diffusion of flexible polymers through polyimide ultrafiltration membranes

The hindered diffusion of polystyrene in dilute solutions of ethyl acetate through polyimide ultrafiltration membranes has been investigated. The present system did not show specific membrane-solute interactions; furthermore, polystyrene can be considered as a flexible polymer coil. It is shown that the hindered diffusive permeability for monodisperse dilute solutions for a series of molecular weights can be compared well with the diffusive permeability curve of one polydisperse dilute polystyrene solution. In the case of very dilute solutions, the polymer coils have no interaction with each other, and the whole range of molecular-weight-dependent permeabilities can be determined from only one measurement. The diffusion behavior of polydisperse solutions through various polyimide membranes has been investigated as well. It was found that the diffusive permeability curve is strongly dependent on the type of membrane, that is, on the pore size distribution. It was not possible to calculate a pore size distribution from diffusion experiments due to mathematical limitations. Nevertheless, it was shown that hindered diffusion measurements are useful to estimate a maximum pore size for each membrane.

Orientation of semiflexible biopolymers in a magnetic field

A theory is presented to explain the stretching and orientation of a semiflexible chain such as the biopolymeric filamentous actin and deoxyribonucleic acid in a magnetic field. Both dilute and concentrated solutions are considered. The theory predicts the requirement of a high magnetic field to achieve a high degree of orientation in a dilute solution. The experimental value of the order parameter for a dilute, polydisperse F-actin solution has been compared with the theoretical value. On the other hand, a molecular field (nematic liquid crystal) which exists in a concentrated solution can achieve the same effects of stretching and orientation and can be assisted by a magnetic field. Sources of diamagnetic anisotropy in biopolymers have been cited. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 3256–3270, 2000

Inverse size-exclusion chromatography for distributed pore and solute sizes

The pore-size distribution (PSD) of a liquid-saturated porous medium can be determined by inverse size-exclusion chromatography (ISEC) under suitable conditions. To quantify the limitations of longitudinal dispersion, intraparticle diffusion, and adsorption, we present a mathematical model for chromatographic procedures with polydisperse solutes. Results are applicable to either inverse or ordinary SEC. The conventional ISEC procedure with monodisperse polymer standards is a special case of the general development. Chromatographic responses for polydisperse solutes permit determination of the pore-size distribution by a deconvolution procedure if adsorption is negligible.

Polydisperse solution of randomly branched homopolymers, inversion symmetry and critical and theta states

We discuss the phase behavior of a model of a binary mixture of randomly branched homopolymers in a solution. The monomer–solvent interaction is determined by a Boltzmann weight w. The theory has been presented recently and is obtained by approximating the underlying lattice by a Bethe lattice of the same coordination number q. Of special interest is the class of randomly branched polymers with inversion symmetry (see the text). This class includes linear polymers. The phase diagram for the special class of polymers is very simple. There is a line C of critical points in the dilute limit on which branched polymers become a critical object in a good solvent. This is an extension of the result due to de Gennes for linear chains in an athermal solution to the above class of branched polymers in any good solvent. The line C meets with another critical line C′ for phase separation in a poor solvent. We identify the theta point as a tricritical point as first suggested by de Gennes for linear chains only. The theta point appears only in the limit of infinite polymers such that the second virial coefficient A2 vanishes. We calculate various exponents and identify the order parameter. We point out a subtle difference between the theta state and the random walk state. However, the radius of gyration exponent does have its mean-field value of 1/2 in the theta state but only in d⩾3. There does not exist a tricritical point for randomly branched polymers without inversion symmetry.

Biaxial phases in polydisperse mean-field model solution of uniaxial micelles

We consider a discretized Maier–Saupe model for a polydisperse solution of micelles of axial symmetry. An exact mean-field solution is presented. The phase diagram displays a biaxial phase at small average anisometries and finite dispersion in size, and two opposite uniaxial nematic phases for large average anisometries. Relations to the experimental phase diagram for ternary mixtures are discussed.

Growth mechanism of the (110) face of tetragonal lysozyme crystals.

The measured macroscopic growth rates of the (110) face of tetragonal lysozyme show an unexpectedly complex dependence on the supersaturation. In earlier studies it has been shown that an aggregate growth unit could account for experimental growth-rate trends. In particular molecular packing and interactions in the growth of the crystal were favored by completion of the helices along the 4(3) axes. In this study the molecular orientations of the possible growth units and the molecular growth mechanism were identified. This indicated that growth was a two-step process: aggregate growth units corresponding to the 4(3) helix are first formed in the bulk solution by stronger intermolecular bonds and then attached to the crystal face by weaker bonds. A more comprehensive analysis of the measured (110) growth rates was also undertaken. They were compared with the predicted growth rates from several dislocation and two-dimensional nucleation growth models, employing tetramer and octamer growth units in polydisperse solutions and monomer units in monodisperse solutions. The calculations consistently showed that the measured growth rates followed the expected model relations with octamer growth units, in agreement with the predictions from the molecular level analyses.

Particle Coarsening in Polypropylene/Polyethylene Blends

We report the results of particle growth in a polydisperse blend system as a function of (i) heat treatment temperature (190, 220, 250, and 280 °C) and (ii) time of heat treatment (0−290 min) for three blends of isotactic polypropylene and linear low-density polyethylene, prepared by melt extrusion. To a first approximation, the growth of the particles obeys the t1/3 law; however, the polydispersity of the solute polymer has an effect on this relationship. The dependence on molecular weight is analyzed, and it is shown that for polydisperse solute the gradient of growth should decrease with time.

Deconvolution of Gel Filtration Chromatographs of Human Plasma Lipoproteins

Gel filtration chromatographs of lipoproteins represent a superposition, or convolution, of the intrinsic polydispersity of the solute and the dispersion due to transport phenomena. We describe a deconvolution technique for improving the resolution of gel filtration chromatographs applicable to lipoproteins and other polydisperse solutes. A matrix of spreading functions, characterizing the dispersive properties of the column, was determined by fitting chromatographic data from a series of monodisperse standards with the solution to the transport equations and interpolating between the fit parameters. A successive approximation scheme was used in which a test distribution was incrementally corrected by an amount proportional to the error between the measured chromatograph and that derived from the test distribution. A nonlinear relaxing function was used to constrain the correction term such that the solution remained physically realizable (i.e., nonnegative absorbance) as it evolved. Deconvolved chromatographs of lipoproteins provided resolution of peaks that were obscured by spreading in the original data. The distribution of particle sizes within each fraction was calculated and verified experimentally by further separating the contents of fractions by gradient gel electrophoresis. Our technique, however, provided comparable resolution of the peaks without the additional experimental procedure.

Characterization of Polydisperse Solutions of Branched Poly(methyl methacrylate) Using Size Exclusion Chromatography with Online Multiangle Light Scattering and Viscosity Detection

We have studied the mass distribution (N(M)) of branched poly(methyl methacrylate) (PMMA) formed by radical copolymerization of methyl methacrylate and ethylene glycol dimethacrylate by size exclusion chromatography (SEC). We show how the static structure factor of monodisperse branched PMMA can be obtained using a new type of on-line multiangle light scattering detector. We compare the monodisperse static structure factor with that of the polydisperse solutions and show that the polydisperse static structure factor can be derived from the monodisperse function using N(M) obtained from SEC. Both the static structure factor and the mass distribution are found to be consistent with predictions from percolation theory. Using an on-line viscometer we have determined the molar mass dependence of the intrinsic viscosity.

A Polydisperse polymer solution as a critical system

Polydisperse solutions of polymers, formed by a reversible polymerization process, are studied by computer simulation. The system is described by a stepwise elongation and contraction process which is based on adding (or deleting) one link to a chain end. In such a process, cyclic polymers cannot be formed. The growth of a polymer is controlled by two chemical potentials that determine the number of polymers and their length and, hence, the concentration of the system. Such a reversible polymerization process can be described by a magnetic analog of the n-vector model. Thus, this system can be used to emphasize the correspondence between polymer models and critical magnetic models. The entire phase space of concentrations of a polydisperse solution is studied

Brush adsorption from polydisperse solutions

A self-consistent field model is used to investigate the effect of solution polydispersity on the adsorbed, equilibrium polymer brush. It is found that the composition of the brush, i.e., distribution of chain molecular weights, is comparable to that of the solution only when the end adsorbing energy is very small. Increasing the end adsorengtion energy leads to preferential adsorption of the shorter chains

Effects of DNA Polymer Length on Its Adsorption to Soils

Three different DNA fragments ranging size from 2.69 kbp (1.75 MDa) to 23 kbp (14.95 MDa) were used as tracers to study the adsorption of polydisperse solutions of calf thymus DNA to eight model soils. The adsorption of the three tracers to all soils was described by the Freundlich adsorption model, with adsorption coefficients (K) ranging from 1.1 for acid-washed sand to over 300 for one soil. An inverse relationship between tracer size and K was observed with six of the eight soils, indicating that smaller fragments are sorbed preferentially versus larger fragments in these soils. No significant correlation between K and the organic carbon contents, clay contents, pHs, or cation exchange capacities of the model soils was observed.

The size, shape and stability of complement component C9

Electron microscopy of specimens of C9 tilted through 90° visualized this protein to be a globular ellipsoid with dimensions of 77 × 70 × 52 Å. To check the congruence of this observation with physical properties of the molecule, hydrodynamic parameters for C9 were determined. From this work a frictional ratio of 1.32 was calculated. C9 was compared with several other proteins of similar frictional ratios whose tertiary structures are known. All examples found of such proteins whose frictional ratios were between 1.26 and 1.37 are either heart-shaped or globular ellipsoids, but none are prolate ellipsoids. By comparison the size and shape of C9 determined by electron microscopy are congruent with its hydrodynamic parameters. Both electron microscopy and physical measurements suggest that the length (110–120 Å) of C9 determined by neutron and X-ray scattering experiments is an overestimate. The source of the discrepancy was identified by the demonstration that the high concns of C9 employed in neutron and X-ray scattering work lead to aggregation of the protein. Thus, investigations involving neutron and X-ray scattering were measuring polydisperse solutions of C9. The deduced value of the radius of gyration from that work (33–35 Å) is now recognized as being statistical and significantly higher than the correct value of monomeric C9 (26 Å), which was calculated from electron microscopy measurements. Also high-resolution electron microscopy clearly visualized poly(C9) to be a barrel-stave construct. These results suggest that monomeric C9 must undergo a major conformational alteration to extend by 55–70 Å in order to self-associate laterally in order to fashion the cylindrical poly(C9).

Confinement of dilute solutions of living polymers

We investigate the thermodynamic properties of a dilute solution of living polymers confined between two solid repulsive walls. We consider both the case of rigid and of flexible macromolecules. When the confined system is taken to be at equilibrium with an external reservoir the living polymers behave similarly to a polydisperse solution of unbreakable chains. However for closed gaps the behaviour is quite different from a classical polymer solution because the worm-like micelles can adapt their intrinsic polydispersity in order to release the confinement constraint. In particular, for rigid living polymers this leads to a divergence of the average chain-length in the limit of strong confinement, as well as to a non-monotonic behaviour of the pressure acting on the walls.

Light scattering and sedimentation equilibrium of a concentrated multicomponent hard rod dispersion

Starting from scaled particle theory, compact expressions for sedimentation equilibrium and light scattering at zero angle for concentrated polydisperse solutions of colloidal hard spherocylinders are derived. These expressions are used to assess the influence of length and diameter polydispersity on the light scattering of dispersions of rod-like particles as a function of the volume fraction.

Thermomechanical degradation of macromolecules

Extensional flow techniques are used to investigate thermomechanical scission of polymer solutions from ambient temperatures up to 150°C. We report precise central scission of chains beyond a critical fracture strain-rate. These results can be well accounted for by a Thermally Activated Barrier to Scission (TABS) model. We speculate upon the origin of degradation in simple shear flows and report novel results on degradation in porous media and ultrasonic sound fields, which contain dominant extensional components. Finally, we show how the nature and degree of degradation is affected by concentration and polydispersity. In semi-dilute entangled solutions, the degradation rates increase, are much higher for polydisperse solutions and the scission becomes progressively more random along the chain.

Pharmacologie des hydroxyéthylamidons de bas poids moléculaire

In the last ten years, the practice of plasma volume expansion has changed significantly. Most clinicians have put a stop to the use of fresh frozen plasma because of growing concerns about hepatitis and AIDS transmission. Today, natural and synthetic colloids and crystalloids are used to a great extent. Although clinical practice varies from one institution to another, the most widely observed change was a major increase in the administration of human serum albumin (HSA). As a result, the cost of plasma volume expansion became so high that it justified finding safe and cheaper alternatives to HSA. Low molecular weight, hydroxyethylstarches (HES) are the synthetic colloids which are closest to HSA. HES are modified natural polymers whose physico-chemical properties are defined by their molecular weight and molar substitution ratio. Average molecular weights of these polydispersed solutions are approximately 200 to 250 kd (in weight) and 60 kd (in number). Hydroxyethylation, which slows down hydrolysis by α-amylase, is best quantified by the molar substitution ratio between the proportions of hydroxyethylether and glucose. HES have pharmacokinetic properties which are independent of molecular weight and directly related to the molar substitution ratio. The two HES available in France are Elohes ® and Lomol ®, Elohes ®, at a concentration of 6 %, has a colloid-osmotic effect close to that of plasma. It induces an initial plasma volume expansion greater than that of the infused volume, and has a long lasting effect (24 h) related to its molar substitution ratio (0.62). Lomol ®, at a concentration of 10 %, is hyperoncotic. Its initial effect is greater than that of Elohes ®, but it is eliminated more rapidly because its lower molar susbtitution ratio (0.45). The good tolerance to these products is also an advantage in comparison with the other colloids.

Application of continuous thermodynamics to polymer fractionation

Abstract

Effect of polydispersity and second virial coefficient on light scattering by randomly cut random coils

The light scattering by an initially monodisperse population of Gaussian random coils in a theta solvent is described by the well known Debye function: P(θ)=D[u(θ)] =(2/u2)(e−u−1+u), where u=u0≡〈S2〉q2. S is the radius of gyration, and q=(4πñ/λ)sin(θ/2) is the magnitude of the scattering vector, λ being the vacuum wavelength of the incident light, ñ the index of refraction, and θ the scattering observation angle. If the molecules undergo random scission, P(θ)=D(u0+r), where r is the average number of scissions per original molecule. In a good solvent, one should include the effect of the second virial coefficient A2 on the light scattering. In the single contact approximation this can be done by using Kc/R=1/MP(θ)+2A2c for an originally monodisperse solution. K is a constant, R the absolute Rayleigh scattering ratio, and c the concentration. The above equation is generalized to originally polydisperse solutions and branched random coils without loops. We discuss its mathematical limits and range of validity, and how to apply it to experimental situations. It is speculated that it may work fairly well when the penetration function ψ is less than about 0.1. We also discuss possible methods of extending its range of validity.