Analytical theory of ideal polydisperse polymers at interfaces

We use a recently developed continuum theory to present an exact treatment of the interfacial properties of ideal polymers displaying Schulz-Flory polydispersity. Our results are remarkably compact and can be derived from the properties of equilibrium, ideal polymers at interfaces. We apply our theory to a number of cases, including, non-adsorbing and adsorbing surfaces, as well as telechelic chains.     

Biodegradable Multiblock Poly[N-(2-hydroxypropyl)methacrylamide] via Reversible Addition-Fragmentation Chain Transfer Polymerization and Click Chemistry

A new bifunctional chain transfer agent (CTA) containing alkyne end groups was designed, synthesized and used for direct synthesis of clickable telechelic polymers. Good control of reversible addition-fragmentation chain transfer (RAFT) polymerization of N-(2-hydroxypropyl)methacrylamide (HPMA) was achieved by using the new CTA, as indicated by a linear increase of number average molecular weight (Mn) with conversion and low polydispersity (PDI) (<1.1). In particular, enzymatically degradable multiblock HPMA polymers were readily prepared by subsequent reaction with αω, -diazido oligopeptide (GFLG) sequence via Cu(I) catalyzed alkyne-azide cycloaddition. Upon exposure of high molecular weight fractions of multiblock polyHPMA to papain or cathepsin B, the polymer was degraded into segments of molecular weight and narrow polydispersity similar to those of the initial telechelic polyHPMA.     

Polydispersity effects and the interpretation of polymer adsorption isotherms

In many cases, polymer adsorption is studied by measuring adsorption isotherms. Quite often it is found that the results are at variance with theoretical predictions. However, usually these adsorption isotherms are interpreted in terms of a single polymeric solute. Most polymers used in experimental studies are polydisperse and should be treated as mixtures. It is well established that the larger molecules in such mixtures adsorb preferentially over the smaller ones. In this paper we show that many discrepancies between polymer adsorption theory and experiment (e.g., the rounded shape of isotherms, the dependence of the adsorbance on adsorbent concentration, and the lack of desorption upon dilution) can be attributed to polydispersity. A quantitative analysis enables us to calculate isotherms for a polymer of arbitrary molecular weight distribution, provided the dependency of the plateau adsorbance on molecular weight is known. Experiments supporting the theory are reported. The fact that polymers do not desorb upon dilution with solvent is often regarded as a proof that polymer adsorption is irreversible. We show that, if a polydisperse sample is in equilibrium with an adsorbing surface, no detectable desorption may take place upon dilution. Therefore, the adsorption of polymers might well be reversible, even if desorption experiments would indicate apparent irreversibility.     

Many-body interactions between particles in a polydisperse polymer fluid

We use a continuum chain model and develop an analytical theory for the interaction between many spheres immersed in a fluid of ideal polydisperse polymers. Assuming local spherical symmetry of the polymer field about each particle, combined with a local approximation, compact expressions are derived for the many-body interaction between the spheres. We use a mean-field approximation to investigate the fluid-fluid phase diagram for the mixture.     

Molecular weight distribution effects on the structure of strongly adsorbed polymers by Monte Carlo simulation

Monte Carlo simulations are reported to study the structure of polymers adsorbed from solution onto strongly attractive, perfectly smooth substrates. Six systems spanning a range of molecular weight distributions are investigated with a coarse-grained united atom model for freely rotating chains. By employing a global replica exchange algorithm and topology altering Monte Carlo moves, a range of monomer-surface attraction from weak (0.27kT) to strong (4kT) is simultaneously explored. Thus for the first time ever, equilibrium polymer adsorption on highly attractive surfaces is studied, with all adsorbed molecules displaying similar properties and statistics. The architecture of the adsorbed layers, including density profiles, bond orientation order parameters, radii of gyration, and distribution of the adsorbed chain fractions, is shown to be highly dependent on the polydispersity of the polymer phase. The homology of polymer chains, and the ergodicity of states explored by the molecules is in contrast to the metastable, kinetically constrained paradigm of irreversible adsorption. The structure of more monodisperse systems is qualitatively similar to experimental results and theoretical predictions, but result from very different chain conformations and statistics. The polydispersity-dependent behavior is explained in the context of the competition between polymers to make contact with the surface.     

Mesoscale simulation of polymer reaction equilibrium: combining dissipative particle dynamics with reaction ensemble Monte Carlo. I. Polydispersed polymer systems

We present a mesoscale simulation technique, called the reaction ensemble dissipative particle dynamics (RxDPD) method, for studying reaction equilibrium of polymer systems. The RxDPD method combines elements of dissipative particle dynamics (DPD) and reaction ensemble Monte Carlo (RxMC), allowing for the determination of both static and dynamical properties of a polymer system. The RxDPD method is demonstrated by considering several simple polydispersed homopolymer systems. RxDPD can be used to predict the polydispersity due to various effects, including solvents, additives, temperature, pressure, shear, and confinement. Extensions of the method to other polymer systems are straightforward, including grafted, cross-linked polymers, and block copolymers. To simulate polydispersity, the system contains full polymer chains and a single fractional polymer chain, i.e., a polymer chain with a single fractional DPD particle. The fractional particle is coupled to the system via a coupling parameter that varies between zero (no interaction between the fractional particle and the other particles in the system) and one (full interaction between the fractional particle and the other particles in the system). The time evolution of the system is governed by the DPD equations of motion, accompanied by changes in the coupling parameter. The coupling-parameter changes are either accepted with a probability derived from the grand canonical partition function or governed by an equation of motion derived from the extended Lagrangian. The coupling-parameter changes mimic forward and reverse reaction steps, as in RxMC simulations.     

平行壁面间平衡聚合物吸附行为的自洽场分析

采用自洽场理论研究了平衡聚合物在平行壁面间的吸附规律.结果表明,平衡聚合物的吸附行为可根据壁面吸附强度划分为弱吸附和强吸附两个区间.在强吸附区间,平衡聚合物可以形成明确的吸附层,增大吸附强度能够引起平均分子链长的陡增,但不会改变链长分布的指数形式.平衡聚合物的长链分子在强吸附条件下较短链分子更靠近吸附壁面,在弱吸附条件下,则更接近体系中心.通过计算壁面压强发现:在弱吸附作用下,吸附壁面始终受到分子链的推斥作用;在强吸附作用下,分子链对壁面的作用随壁面间距的加大由推斥转变为吸引.平衡聚合物的溶解性和排空效应以及壁面吸附作用之间存在竞争关系,加大排除体积作用参数会引起分子链密度分布的均一化和壁面承受压强的降低.     

Theoretical study of cooperativity in multivalent polymers for colloidal stabilization

Multivalent polymers, i.e., copolymers with multiple binding sites, have been proposed recently for stabilization of fusogentic liposomes and other liposomal colloids useful for drug delivery. The performance of such polymers critically depends on their molecular architecture, in particular the strength and frequency of surface anchoring sites along the backbone of a highly soluble polymer. In this work, we investigate the adsorption and surface forces due to multivalent polymers based on coarse-grained polymer models. We find that for W-type polymers that form dangling tails when all anchoring segments are attached to a surface, increasing the chain length at fixed polymer composition leads to a stronger repulsive barrier in the polymer-mediated surface forces thereby increasing the ability of the polymer to stabilize colloidal particles. This prediction conforms to an earlier experiment indicating that increasing the number of hydrophobic anchors along poly(ethylene glycol) polymers results in the cooperative behavior for both surface adsorption and steric stabilization. For M-type multivalent polymers that have weakly anchoring sites placed at the ends, however, addition of binding sites at fixed polymer composition could lead to negative cooperativity, i.e., the more binding sites, the less the amount of adsorption or the weaker the ability of surface protection. The theory also predicts that polymers with two anchoring sites (e.g., telechelic copolymers) are most efficient for colloidal stabilization.     

The influence of the adsorbent amount on the changes in molecular mass distribution of polymers under adsorption from mixtures

Changes in the molecular mass distribution (MMD) for polymer as a result of adsorption from binary and ternary solutions have been studied by the exclusion chromatography method. It was found that the affinity of polymer components to a surface has a crucial influence on the changes in MMD of polymers. The diminution of polydispersity in solutions after adsorption was observed for two polymers. In the case of the polar polymer poly(butyl methacrylate) (PBMA) the diminution of polydispersity is caused mainly by the preferential adsorption of low-molecular-mass fractions, whereas in the case of the nonpolar polymer polystyrene (PS) it is caused by the transition of the high-molecular-mass fractions onto the adsorbent surface. The analysis of experimental results indicates that the quantity of the adsorbent affects the composition of the adsorption layer formed by polymers of different chemical nature.     

Theory of liquid chromatography of mono- and difunctional macromolecules. I. Studies in the critical interaction mode

The theory of liquid chromatography of mono- and difunctional polymers based on the model of ideal polymer chain in wide slit-like pores is presented. Analytical equations describing chromatographic behavior of functional macromolecules in both adsorption, exclusion and critical modes are derived and compared with experiments. The focus of this experimental study was on the verification of the theory in chromatography at critical conditions. Chromatographic behavior of low molar mass end-functionalized polyethylene glycols was found to be in a very good qualitative and in a reasonable quantitative agreement with the theory.     

The structure and phase transitions in polymer blends,diblock copolymers and liquid crystalline polymers: The Landau-Ginzburg approach

The polymer systems are discussed in the framework of the Landau-Ginzburg model. The model is derived from the mesoscopic Edwards Hamiltonian via the conditional partition function. We discuss flexible, semiflexible and rigid polymers. The following systems are studied: polymer blends, flexible diblock and multi-block copolymer melts, random copolymer melts, ring polymers, rigid-flexible diblock copolymer melts, mixtures of copolymers and homopolymers and mixtures of liquid crystalline polymers. Three methods are used to study the systems: mean-field model, self consistent one-loop approximation and self consistent field theory. The following problems are studied and discussed: the phase diagrams, scattering intensities and correlation functions, single chain statistics and behavior of single chains close to critical points, fluctuations induced shift of phase boundaries. In particular we shall discuss shrinking of the polymer chains close to the critical point in polymer blends, size of the Ginzburg region in polymer blends and shift of the critical temperature. In the rigid-flexible diblock copolymers we shall discuss the density nematic order parameter correlation function. The correlation functions in this system are found to oscillate with the characteristic period equal to the length of the rigid part of the diblock copolymer. The density and nematic order parameter measured along the given direction are anticorrelated. In the flexible diblock copolymer system we shall discuss various phases including the double diamond and gyroid structures. The single chain statistics in the disordered phase of a flexible diblock copolymer system is shown to deviate from the Gaussian statistics due to fluctuations. In the one loop approximation one shows that the diblock copolymer chain is stretched in the point where two incompatible blocks meet but also that each block shrinks close to the microphase separation transition. The stretching outweights shrinking and the net result is the increase of the radius of gyration above the Gaussian value. Certain properties of homopolymer/copolymer systems are discussed. Diblock copolymers solubilize two incompatible homopolymers by forming a monolayer interface between them. The interface has a positive saddle splay modulus which means that the interfaces in the disordered phase should be characterized by a negative Gaussian curvature. We also show that in such a mixture the Lifshitz tricritical point is encountered. The properties of this unusual point are presented. The Lifshitz, equimaxima and disorder lines are shown to provide a useful tool for studying local ordering in polymer mixtures. In the liquid crystalline mixtures the isotropic nematic phase transition is discussed. We concentrate on static, equilibrium properties of the polymer systems.     

Statistical thermodynamics in the framework of the lattice fluid model, 1. Polydisperse polymers of special distribution

The Gibbs free energies and equations of state of polymers with special molar mass distributions, e.g., Flory distribution, uniform distribution and Schulz distribution, are derived based on a lattice fluid model. The influence of the polydispersity (or the chain length) on the close-packed mass density, the close-packed volume of a mer and the mer-mer interaction energy or the scaling temperature is discussed. The diagrams of the Gibbs free energies as a function of temperature and chain length are simulated with a computer. The results suggest that a polydisperse polymer is thermodynamically more stable than the corresponding monodisperse polymer and that the thermodynamical properties of a polydisperse polymer are identical with those of the corresponding monodisperse polymer when the average degree of polymerization is sufficiently high.     

Crosslinking index,molecular weight distribution and rubber equilibrium shear modulus during polyfunctional crosslinking of existing polymer: Part 4, recapitulation and presentation of general results of calculations for a hypothetical crosslinking process

In previous papers a statistical theory was presented concerning network formation by polyfunctional crosslinking of existing polydisperse (non-uniform) primary polymers. Relationships were derived between network parameters and the equilibrium shear modulus during crosslinking processes of polymers of various molecular weight distributions. In the present paper the various relationships obtained are compared. Moreover, results of calculations for a hypothetical crosslinking process are presented, such as the weight fractions of sol, ideal network and free or dangling ends and the molecular weights between crosslinks as functions of the equilibrium shear modulus for various molecular weight distributions. Furthermore, the results of fractionation of the primary polymer, as a consequence of the crosslinking process, are shown and also the crosslinking indexes as functions of the sol fraction.     

Molecular dynamics simulations of supramolecular polymer rheology

Using equilibrium and nonequilibrium molecular dynamics simulations, we studied the equilibrium and rheological properties of dilute and semidilute solutions of head-to-tail associating polymers. In our simulation model, a spontaneous complementary reversible association between the donor and the acceptor groups at the ends of oligomers was achieved by introducing a combination of truncated pseudo-Coulombic attractive potential and Lennard Jones repulsive potential between donor, acceptor, and neighboring groups. We have calculated the equilibrium properties of supramolecular polymers, such as the ring/chain equilibrium, average molecular weight, and molecular weight distribution of self-assembled chains and rings, which all agree well with previous analytical and computer modeling results. We have investigated shear thinning of solutions of 8- and 20-bead associating oligomers with different association energies at different temperatures and oligomer volume fractions. All reduced viscosity data for a given oligomer length can be collapsed into one master curve, exhibiting two power-law regions of shear-thinning behavior with an exponent of -0.55 at intermediate ranges of the reduced shear rate β and -0.8 (or -0.9) at larger shear rates. The equilibrium viscosity of supramolecular solutions with different oligomer lengths and associating energies is found to obey a power-law scaling dependence on oligomer volume fraction with an exponent of 1.5, in agreement with the experimental observations for several dilute or semidilute solutions of supramolecular polymers. This implies that dilute and semidilute supramolecular polymer solutions exhibit high polydispersity but may not be sufficiently entangled to follow the reptation mechanism of relaxation.     

Modeling of molecular weight development in atom transfer radical polymerization

A kinetic model has been developed for atom transfer radical polymerization processes using the method of moments. This model predicts monomer conversion, number‐average molecular weight and polydispersity of molecular weight distribution. It takes into account the effects of side reactions including bimolecular radical termination and chain transfers. The determining parameters include the ratios of the initiator, catalyst and monomer concentrations, as well as the ratios of the rate constants of propagation, termination, transfer and the equilibrium constant between radicals and their dormant species. The effects of these parameters on polymer chain properties are systematically simulated. The results show that an ideal living radical polymerization exhibiting a linear relationship between number‐average molecular weight versus conversion and polydispersity approaching unity is only achievable under the limiting condition of slow monomer propagation and free of radical termination and transfers. Improving polymerization rate usually accompanies a loss of this linearity and small polydispersity. For polymerization systems having a slow initiation, the dormant species exercise a retention effect on chain growing and tend to narrow the molecular weight distribution. Increasing catalyst concentration accelerates the initiation rate and thus decreases the polydispersities. It is also shown that for a slow initiation system, delaying monomer addition helps to reduce the polydispersities. Radical termination and transfers not only slow down the monomer conversion rates but also broaden polymer molecular weight distributions. Under the limiting conditions of fast propagation and termination and slow initiation, the model predicts the conventional free radical polymerization behaviors.     

Density functional theory study on the structure and capillary phase transition of a polymer melt in a slitlike pore: effect of attraction

A density functional theory is proposed to investigate the effects of polymer monomer-monomer and monomer-wall attractions on the density profile, chain configuration, and equilibrium capillary phase transition of a freely jointed multi-Yukawa fluid confined in a slitlike pore. The excess Helmholtz energy functional is constructed by using the modified fundamental measure theory, Wertheim's first-order thermodynamic perturbation theory, and Rosenfeld's perturbative method, in which the bulk radial distribution function and direct correlation function of hard-core multi-Yukawa monomers are obtained from the first-order mean spherical approximation. Comparisons of density profiles and bond orientation correlation functions of inhomogeneous chain fluids predicted from the present theory with the simulation data show that the present theory is very accurate, superior to the previous theory. The present theory predicts that the polymer monomer-monomer attraction lowers the strength of oscillations for density profiles and bond orientation correlation functions and makes the excess adsorption more negative. It is interesting to find that the equilibrium capillary phase transition of the polymeric fluid in the hard slitlike pore occurs at a higher chemical potential than in bulk condition, but as the attraction of the pore wall is increased sufficiently, the chemical potential for equilibrium capillary phase transition becomes lower than that for bulk vapor-liquid equilibrium.     

Studies on fluids and their mixtures using the Born-Green-Yvon integral equation technique

We have developed the Born-Green-Yvon (BGY) integral equation theory for investigating the equilibrium properties of fluids and their mixtures both on the lattice and in the continuum. Using the continuum theory we have studied hard sphere fluids over a range in density having chain lengths between one and fifty sites. We have also investigated the collapse transition of a square well chain and a square well ring, each having up to four hundred sites, and have predicted the theta temperature for these systems. Turning to the case of a dilute (hard-sphere) solution we have been able to show the effect of solvation on a hard sphere chain, and captured the dependence of this effect on the ratio of hard sphere diameters of the solvent and chain segments. In all the continuum studies we have found good to excellent agreement with simulation results. We have also derived a lattice BGY theory which, while less sophisticated than the continuum version, has the advantage of producing simple closed-form expressions for thermodynamic properties of interest. This theory is capable of exhibiting the full range of miscibility behaviour observed experimentally, including upper and lower critical solution temperatures and closed-loop phase diagrams. We find that the theory does an excellent job of fitting to different kinds of experimental data and, making use of the parameters derived from fits to pure component data alone, we have been able to predict properties ranging from pure fluid vapour pressures and critical temperatures to changes in the volume and enthalpy on mixing as well as coexistence curves for solutions.     

Effect of excluded volume interactions on the interfacial properties of colloid-polymer mixtures

We report a numerical study of equilibrium phase diagrams and interfacial properties of bulk and confined colloid-polymer mixtures using grand canonical Monte Carlo simulations. Colloidal particles are treated as hard spheres, while the polymer chains are described as soft repulsive spheres. The polymer-polymer, colloid-polymer, and wall-polymer interactions are described by density-dependent potentials derived by Bolhuis and Louis [Macromolecules 35, 1860 (2002)]. We compared our results with those of the Asakura-Oosawa-Vrij model [J. Chem. Phys. 22, 1255 (1954); J. Polym Sci 33, 183 (1958); Pure Appl. Chem. 48, 471 (1976)] that treats the polymers as ideal particles. We find that the number of polymers needed to drive the demixing transition is larger for the interacting polymers, and that the gas-liquid interfacial tension is smaller. When the system is confined between two parallel hard plates, we find capillary condensation. Compared with the Asakura-Oosawa-Vrij model, we find that the excluded volume interactions between the polymers suppress the capillary condensation. In order to induce capillary condensation, smaller undersaturations and smaller plate separations are needed in comparison with ideal polymers.