Effect of Polydispersity and Charge Heterogeneity on the Depletion Interaction in Colloidal Systems

The effect of polydispersity in the macromolecule size and surface potential on the depletion attraction and structural repulsion between two charged spherical particles in a solution of nonadsorbing charged spherical macromolecules was investigated using a modified form of the force-balance model of J. Y. Walz and A. Sharma [J. Colloid Interface Sci. 168, 495 (1994)]. The distribution of sizes and potentials was described by a log-normal distribution with values of the coefficient of variation (CV) as large as 60%. Comparisons with the case of purely monodisperse macromolecules were made under the condition of either constant macromolecule number density, rho(infinity), or constant volume fraction, φ. For purely hard spheres, polydispersity increases the depletion attraction at constant rho(infinity) but decreases the interaction at constant φ. A simple scaling analysis is used to show that these trends are true for any arbitrary distribution of macromolecule size. Surface charge is found to amplify the effect of polydispersity at constant φ but actually negates the effect at constant rho(infinity). The repulsive structural contribution, arising from the interaction between the macromolecules themselves, is significantly decreased by polydispersity except for the case of charged macromolecules at constant rho(infinity), where the effect is relatively small. Finally, polydispersity in the macromolecule surface potential (no polydispersity in size) has only a minor effect on both the depletion attraction and structural repulsion, even for CV values as large as 60%. Copyright 2000 Academic Press.     

Direct measurement of depletion and structural forces in polydisperse, charged systems

The effect of polydispersity in macromolecule size or surface potential on the depletion interaction between a spherical silica particle and a silica flat in solutions containing two different types of nonadsorbing charged spherical macromolecules was studied with an atomic force microscope (AFM). The macromolecules used here were negatively charged nanospheres of either polystyrene or silica. To investigate the effect of size polydispersity, experiments were performed under the condition of either constant macromolecule number density or constant volume fraction as the relative proportions of smaller and larger polystyrene nanospheres in the suspension were varied. Similarly, for the experiments with surface potential polydispersity, the suspensions contained varying fractions of more highly charged (polystyrene) and less highly charged (Ludox silica) nanospheres at constant number density. The experimental results were compared to the predictions of the modified force-balance model of Piech and Walz and semiquantitative agreement was found. In particular, the maximum attraction and repulsion observed in the measured force profiles were found to agree with the predicted trends as the makeup of the macromolecules was varied. The trend in the maximum attraction was also consistent with predictions made using a simple "scaling" analysis derived using the equation for hard-sphere interactions.     

Influence of polydispersity and long chain branching on the melt viscosity of polycarbonate

The Newtonian and non-Newtonian melt viscosities of bisphenol A polycarbonate (PC) at 280°C were treated according to the generalized multivariable power function, where the average molecular weights, polydispersity degree and branching degree are considered as variables. The shear rate was also considered as a variable for non-Newtonian conditions. In the same way, the melt fluidity was treated as a multivariable power function. It has been found that the same melt flow properties of polymer can be obtained by an appropriate combination of Newtonian melt viscosity (being a function of molecular weight) and long chain branching. The experimental data on PC agree with the theoretical approach of Bucche and Graessley.     

Dichlorocyclopropane derivatives of syndiotactic 1,2-polybutadiene

Polymeric products containing hem-dichlorocyclopropane units with a degree of functionalization of up to 97% are synthesized via the reaction of syndiotactic 1,2-polybutadiene with dichlorocarbene obtained by the interaction of chloroform with an aqueous solution of sodium hydroxide in the presence of a phase-transfer catalyst. The incorporation of dichlorocyclopropane groups into units of polydiene substantially changes its molecular mass and polydispersity, the solution viscosity, the polymer melt flowability, and the glass-transition temperature and flow temperature of the polymer.     

Synthesis and Characterization of Trimethylsilylcellulose in Solution

Abstract

Five samples of cellulose, with different polymerization degrees, were used to obtain corresponding trimethylsilylcellulose derivatives by reaction with trimethylchlorsilan. The trimethylsilylcellu -lose (TMSC) samples were characterized in solution by osmometry, viscometry and gel permeation chromatography. The Mark-Houwink-Sakurada (M-H-S) equation coefficients were determined in chloroform, 1, 1, 1-trichloroethane and o-xylene, in all cases the exponent “a” being higher than 10, indicating great stiffness of the macromolecules in solution. Also, the temperature dependence of both the limiting viscosity number and M-H-S coefficients for TMSC in o-xylene were studied. The exponent from M-H-S equation is also higher than 1. 0 and increases linearly with the tern -perature. The GPC studies indicate a relatively high polydispersity of the studied samples; the polydispersity index being situated between two and three.     

Controlling the growth of polymer trees: concepts and perspectives for hyperbranched polymers

This article summarizes basic principles and recent progress in the field of cascade-branched polymers. Methods for the preparation of macromolecules with hyperbranched structures are presented and compared concerning the extent of control over molecular weights and polydispersity. Step-growth and recently developed chain-growth strategies as well as enzyme and transition metal catalyzed polymerizations are discussed with respect to mechanism and future potential.     

Polydisperse polymer liquid crystals near the anisotropic-isotropic transition

Polydisperse systems of polymer liquid crystal (PLC) macromolecules consisting of LC and flexible sequences are considered, particularly at the phase transition LC-i from an anisotropic to the isotropic phase. The Flory and Matheson lattice model is used for formulation of the partition function; the orientation distribution function for LC orienting potential interactions introduced by Flory and Ronca is included. Using a Landau approach to calculating the Helmholtz function of the system as a function of the orientation parameter s, we obtain the formulae for parameters of the model in the vicinity of the LC-i transition. The critical values at the transition of s, of the strength of orienting interactions, the system temperature, and the anisotropy of LC sequences are calculated and discussed as functions of the polydispersity parameter d. Regions of d are found where polydispersity has a weak influence on the LC-i equilibrium parameters. There is also a region of d values in which the influence of polydispersity is quite pronounced.     

Experimental Study of the Polydispersity of Aqueous Colloid of Palygorskite and Suspensions of Escherichia Coli and Pseudomonas Fluorescens by an Electrooptical Method

The results of experimental study on the polydispersity of an aqueous colloid of palygorskite and aqueous suspensions of Escherichia coli (E. coli) and Pseudomonas fluorescens(Ps. fluorescens) are reported. The study is based on the use of a new method; i.e., on the investigation of an electrooptical effect appearing when a weak sinusoidal electric field with sinusoidal amplitude modulation is applied on the system. This method was developed for studying systems in which only slight particle orientation is possible under action of an external electric field. Disperse systems with a high conductivity, including cell suspensions and other biocolloids, colloids containing small particles, as well as solutions of macromolecules and polyelectrolytes, are among such systems. The experimental setup developed in this work is described. The results obtained are compared with data of microscopic measurements and the results of the study of polydispersity in strong fields based on the investigation of the relaxation of electrooptical effect.     

Influence of molecular stiffness on the dynamic structure factor

Characteristic features of the influence of molecular stiffness on the dynamic structure factor of macromolecules are briefly outlined. The relaxation times characterizing the internal dynamics of the macro‐molecules exhibit a crossover from Rouse‐Zimm to bending modes with increasing mode number. As a consequence the dynamic structure factor is strongly influenced by the molecular stiffness. In particular, a stretched exponential relaxation of the dynamic structure factor at scattering vectors larger than the inverse persistence length is predicted and confirmed by a comparison with experimental data. Moreover, the influence of polydispersity is discussed.     

A control of primary structure in the products of macromolecular reactions

Basing on the theory of macromolecular reactions, an influence of various factors on a units' distribution (UD) of the forming macromolecules is considered. In diluted solutions UD is determined by a competition between external reagent and intrachain interaction of reacted and unreacted units, first by neighbor effect. Should accelerating action of remote units is commensurable with that of nearest neighbors, such a conformational effect enlarges the formation of alternating sequences. In a melt, interchain effect shifts UD to a random one. In a polymer blend consisting of reacting and non-reacting but influencing the reactivity components, UD of transforming macromolecules is formed under concerted action of the reaction and interdiffusion. Thus modern achievements of the theory permit to analyze peculiarities of a wide set of reaction systems and facilitate a choice of optimal conditions for the preparation of tailor-made macromolecules.     

Relationships of graft polymerization of vinyl monomers onto cellulose. Reaction kinetics and polymer structure

Graft polymerization of acrylamide and sulfuric salt of 2-methyl-5 vinylpyridine onto cellulose using CO(III) salts was studied. It was shown that graft polymerisation of water-soluble polymers can be described by general relationships of radical reaction. The relation between elementary reaction constants of the formation and termination of active centers in cellulose, as well as relation between constants of the propagation, transfer and termination of chains were determined for different cellulose materials and monomers. The translational diffusion, sedimentation, viscosity, and flow birefringence of copolymers have been investigated in different solvents. Experimental data showed that the copolymers obtained are graft copolymers with two to five grafted chains onto macromolecules. The minimum distance between the branch points is 100 ± 20 glucoside units. The peculiarity of these copolymers is relatively low polydispersity. The conformation of macromolecules of such copolymers in solution depends on the compatibility of the copolymer components and the thermodynamic properties of the solvent.     

Effects of Polydispersity on the Phase Behavior of Additive Hard Spheres in Solution

The ability to separate enzymes, nucleic acids, cells, and viruses is an important asset in life sciences. This can be realised by using their spontaneous asymmetric partitioning over two macromolecular aqueous phases in equilibrium with one another. Such phases can already form while mixing two different types of macromolecules in water. We investigate the effect of polydispersity of the macromolecules on the two-phase formation. We study theoretically the phase behavior of a model polydisperse system: an asymmetric binary mixture of hard spheres, of which the smaller component is monodisperse and the larger component is polydisperse. The interactions are modelled in terms of the second virial coefficient and are assumed to be additive hard sphere interactions. The polydisperse component is subdivided into sub-components and has an average size ten times the size of the monodisperse component. We calculate the theoretical liquid–liquid phase separation boundary (the binodal), the critical point, and the spinodal. We vary the distribution of the polydisperse component in terms of skewness, modality, polydispersity, and number of sub-components. We compare the phase behavior of the polydisperse mixtures with their concomittant monodisperse mixtures. We find that the largest species in the larger (polydisperse) component causes the largest shift in the position of the phase boundary, critical point, and spinodal compared to the binary monodisperse binary mixtures. The polydisperse component also shows fractionation. The smaller species of the polydisperse component favor the phase enriched in the smaller component. This phase also has a higher-volume fraction compared to the monodisperse mixture.     

Size-exclusion liquid chromatography of poly(<Emphasis Type="Italic">N</Emphasis>-vinylformamide)s in aqueous solutions

The exclusion mechanism of the separation of poly(N-vinylformamide) and its derivatives with a cysteamine terminal group in gel permeation chromatography implemented by the suppression of polyelectrolyte swelling and the electroexclusion of macromolecules was established by the transport analytical methods of molecular hydrodynamics (HPLC, velocity sedimentation, and intrinsic viscosity). Based on an analysis of the hydrodynamic characteristics and molecular weights of polymer fractions determined by velocity sedimentation, it was found that the molecular characteristics and polydispersity of the water-soluble poly(N-vinylamide) s of aliphatic carboxylic acids and their derivatives can be calculated with the use of the Benoit universal calibration dependence.     

Effect of polydispersity on the cloud-point curves of polymer mixtures

A method is presented for the calculation of cloud-point curves of polymer–polymer mixtures when the polymers involved are polydisperse. The method is based on the Flory–Huggins free energy of mixing with a concentration-independent χ parameter. Numerical results are given for cases in which the molecular weight distributions are represented by the Schulz–Flory type. When the two polymers have similar average molecular weights and polydispersities, the cloud-point curves become flatter as the polydispersity increases. When the two polymers have similar average molecular weights but differ in polydispersity, the cloud-point curves become more skewed as the difference in the polydispersity increases. The results point out that, if the polydispersity effect is not properly accounted for, the value of χ deduced from experimental cloud points is liable to be in error, especially with regard to its temperature coefficient and its concentration dependence.     

Grafting of Glycidyl Methacrylate to Polypropylene in an Extruder,Initiated with Organic Peroxides

The efficiency of grafting of glycidyl methacrylate to polypropylene and the degree of degradation of macromolecules, evaluated from the melt flow index, were studied in relation to the structure of the peroxide initiator.     

Prediction and measurement of the interparticle depletion interaction next to a flat wall

A theoretical and experimental study was performed to investigate the depletion interaction between two colloidal particles next to a solid wall in a solution of nonadsorbing macromolecules. By calculating the change in free volume available to the macromolecules upon approach of the two particles, a relatively simple expression was developed for the interparticle depletion attraction in hard sphere systems as a function of the particle-particle and particle-plate spacing. Perhaps the most useful result obtained from this analysis was that the wall has no effect whenever the ratio of the particle radius to the macromolecule radius is greater than four. (In charged systems, this ratio would apply to the effective particle and macromolecule sizes.) A series of experiments was then performed in which the hydrodynamic force balance (HFB) apparatus was used to measure the shear force needed to separate a colloidal doublet consisting of two particles trapped in a secondary energy well formed by a repulsive electrostatic force and an attractive depletion force. The macromolecules used here were small, nanometer-sized spheres of either silica or polystyrene. Agreement between the measured separation forces and those predicted using the force balance model of J. Y. Walz and A. Sharma (J. Colloid Interface Sci. 168, 485 (1994)) was within a factor of 1.3 using no adjustable parameters and accounting for polydispersity and uncertainty in the macromolecule size. It is shown that this remaining discrepancy could be caused by the Brownian (stochastic) nature of the doublet breakup process.     

Simulation of heterogeneous end-coupling reactions in polydisperse polymer blends

The influence of polydispersity on the interfacial kinetics of end-coupling and microstructure formation in the melt of immiscible polymers was studied using dissipative particle dynamics simulations. The irreversible reaction started at a flat interface between two layers, each of which contained polymer chains of two different lengths with functionalized or unreactive end groups. As in the case of fully functionalized monodisperse reactants [A. V. Berezkin and Y. V. Kudryavtsev, Macromolecules 44, 112 (2011)], four kinetic regimes were observed: linear (mean field coupling at the initial interface), saturation (decreasing the reaction rate due to the copolymer brush formation or reactant depletion near the interface), autocatalytic (loss of the initial interface stability and formation of a lamellar microstructure), and terminal (microstructure ripening under diffusion control). The interfacial instability is caused by overcrowding the interface with the reaction product, and it can be kinetically suppressed by increasing chain length of the reactants. Main effects of polydispersity are as follows: (i) the overall end-coupling rate is dominated by the shortest reactive chains; (ii) the copolymer concentration at the interface causing its instability can be not the same as in the lamellas formed afterwards; (iii) mean length of the copolymer product considerably changes with conversion passing through a minimum when a microstructure is just formed.     

Gradient separation of polymers at critical point of adsorption

Theoretical and experimental analysis of interaction polymer chromatography revealed a new mode of polymer separation: gradient elution at the critical point of adsorption (the eluent composition where size-exclusion and adsorption interactions completely compensate each other). This mode allows for molecular-mass-independent separation by chemical composition and/or other structural differences between macromolecules. The isocratic and gradient elution of narrow polydispersity polystyrenes and poly(methylmethacrylates) on reversed- and normal-phase columns confirmed all basic theoretical assumptions and conclusions. The gradient separation of poly(alkylmethacrylate) and poly(alkylacrylate) blends, as well as styrene-butadiene copolymers provided further experimental verification of the theory.     

Adsorption of polyethyleneimine and polymethacrylic acid onto synthesized hematite

An influence of different functional groups of polymer, its molecular weight, polydispersity ratio (M(w)/M(n)) and presence of impurities on its adsorption in different pH values (3, 6 and 9) onto synthesized hematite (Fe(2)O(3)) was measured. A structure of adsorbed macromolecules of PMA and PEI was obtained according to S-F theory. Two polymers were used: polymethacrylic acid (PMA) of 6500 and 75,100 molecular weight as well as polyethyleneimine (PEI) 25,000 commercial and fractionated. Electrokinetic properties of the interface oxide-polymer solution (surface charge density and zeta potential) were also measured as well as adsorption layer thicknesses (with use of viscosimetric measurements). Obtained data show, that all above-mentioned factors do influence not only the adsorption process itself but also a surface charge, zeta potential and structure of adsorbed polymer layers on polymer/hematite interface.