Polydisperse Polymer Research Articles

Surface segregation and surface tension of polydisperse polymer melts

The effect of polydispersity on surface segregation of a lower molecular weight polymer component in a higher molecular weight linear polymer melt host is investigated theoretically. We show that the integrated surface excess zM of a polymer component of molecular weight M satisfies a simple relation zM=2Ue(M/Mw-1)phiM, where Mw is the weight averaged molecular weight, phiM is the polymer volume fraction, and Ue is the attraction of polymer chain ends to the surface. Ue is principally of entropic origin, but also reflects any energetic preference of chain ends to the surface. We further show that the surface tension gammaM of a polydisperse melt of high molar mass components depends on the number average degree of polymerization Mn as, gammaM=gammainfinity+2UerhobRT/Mn. The parameter gammainfinity is the asymptotic surface tension of an infinitely long polymer of the same chemistry, rhob is the bulk density of the polymer, R is the universal gas constant, and T is the temperature. The predicted gammaM compare favorably with surface tension values obtained from self-consistent field theory simulations that include equation of state effects, which account for changes in polymer density with molecular weight. We also compare the predicted surface tension with available experimental data.

A correlation between velocity profile and molecular weight distribution in sheared entangled polymer solutions

In this work we attempt to answer several questions concerning the flow characteristics of entangled polymer solutions in a sliding plate shearing cell. We explore (a) how the molecular weight distribution affects the velocity profile in simple shear, (b) whether the observed shear banding is consistent with a nonmonotonic constitutive model, (c) whether the flow response and velocity profiles are different in simple shear depending on the different modes of shear. Our results provide a comparison with recent reports on a polydisperse polymer sample [Tapadia and Wang, Phys. Rev. Lett. 96, 016001 (2006); Tapadia, et al., Phys. Rev. Lett. 96, 196001 (2006)] that revealed the first evidence for inhomogeneous shear during startup in cone-plate flow geometry of a rotational rheometer. Using a highly monodisperse sample, we observed the sample to partition into two fractions with different local shear rates instead of possessing a smooth spatial variation of the local shear rate as seen for the polydisperse sam...

A rheology theory and method on polydispersity and polymer long-chain branching

Model calculations were performed to investigate the sensitivity of zero-shear melt viscosity (η0 or Eta0) on the molecular weight (MW) polydispersity of linear polymers. Simulated MW distributions (MWD) were generated with the generalized exponential (GEX) distribution function for various levels of polydispersity Mw/Mn and Mz/Mw. For linear entangled polymeric chains in the melt, the linear viscoelastic properties were predicted by using the double reptation blending rule and the so-called BSW relaxation time spectrum, named after the authors: Baumgaertel, Schausberger and Winter [Baumgaertel M, Schausberger A, Winter HH. Rheol Acta 1990;29:400–8]. Published rheological parameters appropriate for polyethylene were used in the calculations. It was found that Eta0 depended mostly on Mw, but it also significantly depended on the extent of high-MW polydispersity Mz/Mw. A revision to the fundamental MW dependency of Eta0 was proposed to compensate for this polydispersity effect. To offset the polymer polydispersity differences, we propose a new MW average (MHV or Mx with x=1.5) to replace Mw in the historical rheological power-law equation of Eta0∝Mwa, where the literature value of exponent “a” ranges from 3.2 to 3.6. The use of MHV instead of Mw in the power-law equation made the calculated Eta0 independent of the sample high-MW polydispersity. With the removal of the complication from polydispersity effect, the new Eta0 power law can now provide a more robust base for studying polymer long-chain branching (LCB). A new LCB index is thus proposed based on this new melt-viscosity power law. The values of MHV in the new power law can be calculated for polymer samples from the conventional gel permeation chromatographic (GPC) slice data.

Multiphase coexistence in polydisperse colloidal mixtures

The authors study the phase behavior of mixtures of monodisperse colloidal spheres with a depletion agent which can have arbitrary shape and can possess a polydisperse size or shape distribution. In the low concentration limit considered here, the authors can employ the free-volume theory and take the geometry of particles of the depletion agent into account within the framework of fundamental measure theory. The authors apply their approach to study the phase diagram of a mixture of (monodisperse) colloidal spheres and two polydisperse polymer components. By fine tuning the distribution of the polymer, it is possible to construct a complex phase diagram which exhibits two stable critical points.

Polydispersity-based homotopy/continuation for phase equilibria of polydisperse polymer systems

This paper proposes a homotopy/continuation algorithm for the solution of phase equilibrium problems for mixtures involving one or more polydisperse polymers. The algorithm constructs a continuous trajectory in polydispersity space, starting from the solution of a phase equilibrium problem involving monodisperse polymers. The trajectory is such that the weight-average molecular weight is constant throughout, but the number of phases may vary.

Competitive Adsorption of a Polydisperse Polymer during Emulsification: Experiments and Modeling

In this paper we study the selective adsorption of a high molar mass polymer, OSA-starch, at the cyclohexane/water interface during emulsification. This was made possible through the use of AsFlFFF-MALS-RI which enables us to characterize the size and molar mass of polydisperse ultrahigh molar mass polymers. The results show that the high molar mass components in the molar mass distribution of the polymer were selectively adsorbed. The selective adsorption is most likely due to convective mass transport in the turbulent flow fields, during formation of the emulsion, which favors transport to the interface of the high molar mass polymers in the sample. The rapid adsorption that occurs during emulsification is likely to give rise to nonequilibrium effects and jamming at the interface. Furthermore, we describe the adsorption process and illustrate its selective nature through a turbulent flow collision model.

Atom Transfer Radical Polymerization of Menthyl Acrylate

Atom transfer radical polymerization (ATRP) of menthyl acrylate (MnA) was performed with different catalytic systems. ATRP of MnA proceeds in a controlled/living manner as evidenced by narrow polymer polydispersity (<1.20), but with a very slow polymerization rate using 1-phenylethyl bromide (1-PEBr) or ethyl 2-bromopropionate (2-EBP) as initiators (monomer/initiator = 100/1) and N,N,N‘,N‘,N‘ ‘-pentamethyldiethylenetriamine (PMDETA) as ligand. Only 5.7% and 14.8% monomer conversion were obtained within 4 h using 1-PEBr and 2-EBP, respectively. In contrast, replacing the PMDETA ligand with 1,4,8,11-tetramethyl-1,4,8,11-tetraazacyclotetradecane (Me4cyclam) promotes a very fast but uncontrolled polymerization (97.1% conversion in 1 h with a polydispersity as broad as 1.70). However, a controlled/living polymerization system of MnA (with a relatively fast polymerization rate, 78.4% conversion in 1/2 h; Mn = 14 000 g/mol; Mw/Mn = 1.11) was achieved by using tris[2-(dimethylamino)ethyl]amine (Me6TREN) as ligand...

Nanostructured Epoxies Based on the Self-Assembly of Block Copolymers: A New Miscible Block That Can Be Tailored to Different Epoxy Formulations

Nanostructured thermosets may be obtained by self-assembly of amphiphilic block copolymers in a reactive solvent and fixation of the morphologies by the cross-linking reaction. Nanostructuration requires the presence of a bock that remains miscible in the polymer during polymerization. The selection of the miscible block depends on the particular system and in some cases (e.g., for epoxy-amine network based on diglycidyl ether of bisphenol A, and 4,4'- diaminodiphenylsulfone) it is very difficult to find such a block. In this manuscript it is shown that random copolymers of methyl methacrylate (MMA) and N,N-dimethylacrylamide (DMA) containing different molar fractions of DMA, can be used as a miscible block for the nanostructuration of epoxies. The miscibility of the random copolymer during formation of the epoxy network was first analyzed determining cloud-point conversions as a function of the molar fraction of DMA in the copolymer. A thermodynamic model of the phase separation was performed using the Flory-Huggins model and taking the polydispersities of both polymers into account. A single expression of the interaction parameter based on the theory of random copolymers provided a reasonable fitting of the experimental cloud-point curves. The significant increase in the miscibility produced by using small DMA molar fractions in the copolymer was explained by the high negative value of the binary interaction energy between DMA and the epoxy-amine solvent, associated to the positive value of the interaction energy between DMA and MMA units. Block copolymers with poly(n-butyl acrylate) as the immiscible block and the random copolymer P(MMA-co-DMA) as the miscible block were used for the nanostructuration of epoxy networks. The necessary molar fraction of DMA in the miscible block to stabilize a dispersion of nanosize domains depended on the fraction of the immiscible block.

A new methodology for the estimation of drop size distributions of dilute polymer blends based on LAOS flows

A new methodology for the estimation of drop size distributions in dilute polydisperse polymer blends is proposed. The procedure exploits the capabilities of large amplitude oscillatory shear (LAOS) flows to discriminate the behavior of drops of different size. The methodology is tested on synthetic data obtained by mimicking rheological responses of polydisperse immiscible polymer blends. The procedure allows a quantitative description of the original distribution, and is also robust to experimental noise.

Advances in modeling of polymer melt rheology

T he development of theories to predict the rheological (i.e., flow) properties of densely packed polymers in the melt or solution state is important because such theories might enable rational design of polymer processing methods for shaping polymers into products, and because they can be used in rheological characterization of polymer molecular weight and long-chain branching. These are important topics, given the enormous volume of polymers produced each year (100’s of billions of pounds).The seminal work of de Gennes and Doi and Edwards in the late 1970s established their ‘‘tube model’’ as the standard theory for predicting polymer rheological properties. The ‘‘tube’’ idea arises from the notion that entanglements of a long polymer with its neighbors in a dense melt restrict motion of the polymer to a ‘‘tubelike’’ region — see Figure 1a. Until very recently, the ‘‘entanglements’’ between densely packed long chains that produce a phenomenological ‘‘tube’’ constraining the motion of each chain could not be experimentally imaged or simulated, nor could their existence be rigorously derived from microscopic physics, and so acceptance of the tube model has not come without controversy. In addition, most predictions of the tube model in the early years were hardly better than qualitative. Still, it was generally recognized early on that, despite its limitations, the Doi-Edwards ‘‘tube’’ provides a plausible ansatz for understanding qualitatively how linear polymers in the entangled state relax, namely, they relax by ‘‘reptation’’ or sliding of the chain along its tube axis, and by retraction within the tube. Moreover, the tube model offered the greatest hope for eventually attaining a quantitative understanding of polymer melt rheology. In the years since 1978, many efforts have been made to improve upon the Doi-Edwards model. Broadly speaking, the 1980s witnessed a sustained attack on the problems of ‘‘primitive-path fluctuations’’ — that is, changes in the length of the tube due to accordion-like motions of the chain in the tube, and of ‘‘constraint release’’ — that is, loss of entanglements due to motions of the surrounding chains that define the tube. It was found that as long as the chain ‘‘feels’’ the existence of the tube before the entanglements are lost, one can describe the chain’s relaxation as reptation in a tube, where the tube itself is moving through space due to loss, and recreation of entanglements with surrounding mobile chains. This tube movement (now called ‘‘constraint release Rouse motion’’) is especially significant for polydisperse polymers, where the entanglements imposed on long chains by surrounding short chains can relax quite rapidly, and, hence, enhance the mobility of the tube containing the long chain. Finally, in some cases, one can regard the tube diameter to be continuously expanding or ‘‘dilating,’’ if the surrounding chains are so much more mobile than the chain in the tube that they act as ‘‘solvent’’ that ‘‘dynamically dilutes’’ the entanglement density. These ways of incorporating constraint release into tube models have Perspective

Theoretical study of polymer brushes by a new numerical mean field theory

We present a new numerical self-consistent mean field approach in order to investigate poly-disperse polymer brushes dissolved in solvent. In this new method, the polymer segments are contained in a tube filled with solvent, which allow the realization of several configuration of the chain. The tube conformation is developed on a lattice using Kuhn segment, such that the volume of the polymer chain is the same with the one measured experimentally. In order to deal with the depletion layer observed in the volume fraction profile in previous theoretical investigations and obtain more brush-like conformations at high enough concentrations, we introduce a new parameter (disturbed walk parameter), which characterizes the degree of the deviation from the random walk growth. The results show a better description of the brush at high concentrations. Close to the surface, disappearance of the depletion layer was observed. Also we have accomplished the correct description of the brush extension.

Cyclopolymerization of tert-Butyl α-(Hydroxymethyl) Acrylate (TBHMA) Ether Dimer via Atom Transfer Radical Polymerization (ATRP)

Atom transfer radical polymerization (ATRP) was used in the cyclopolymerizaton of a symmetrical dimethacrylate, the ether dimer of tert-butyl α-(hydroxymethyl)acrylate (TBHMA). The cyclopolymerization was succesfully carried out with high cyclization efficiency in xylene using CuBr/PMDETA at 70 °C. Cyclopolymers with six membered tetrahydropyran repeat units were obtained in high conversions with controlled molecular weights and low polydispersities. It was found that at higher temperatures (100 °C), the polymerization became less controlled and polydispersities increased slightly whereas at lower temperatures (50 °C) the intermolecular reactions lead to pendent vinyl groups and cross-linking. The livingness of the propagating cyclopolymers was shown through successful block copolymerization with tert-butyl acrylate where the former was used as macroinitiator. The physical properties of the cyclopolymers were investigated and it was found that ring microstructures and polymer polydispersities affected the...

Minimal model of relaxation in an associating fluid: Viscoelastic and dielectric relaxations in equilibrium polymer solutions

Cluster formation and disintegration greatly complicate the description of relaxation processes in complex fluids. We systematically contrast the viscoelastic and dielectric properties for models of equilibrium polymers whose thermodynamic properties have previously been established. In particular, the monomer-mediated model allows chain growth to proceed only by monomer addition, while the scission-recombination model enables all particles to associate democratically, so that chain scission and fusion occur at the interior segments as well as at chain ends. The minimal models neglect hydrodynamic and entanglement interactions and are designed to explore systematically the competition between chemical reaction and internal chain relaxation and how this coupling modifies the dynamics from that of a polydisperse solution of Rouse chains with fixed lengths (i.e., "frozen" chains). As expected, the stress relaxation is nearly single exponential when the assembly-disassembly reaction is fast on the time scale of structural chain rearrangements, while multiexponential or nearly stretched exponential relaxation is obtained when this reaction rate is slow compared to the broad relaxation spectrum of almost unperturbed, nearly "dead" chains of intrinsically polydisperse equilibrium polymer solutions. More generally, a complicated intermediate behavior emerges from the interplay between the chemical kinetic events and internal chain motions.

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.

Synthesis, Characterization, and AFM Studies of Dendronized Polyferrocenylsilanes

Dendronized polyferrocenylsilanes were synthesized by a substitution reaction of reactive poly(ferrocenylchloromethylsilane) with monodendrons with a focal hydroxy group. The resulting dendronized polymers were studied by 1H NMR, differential scanning calorimetry (DSC), and polarized optical microscopy (POM). To facilitate the direct visualization of single polymer chains by atomic force microscopy (AFM), an interaction chromatography technique (IC) was used to fractionate the polydisperse polymers to separate the high molecular weight dendronized PFSs. AFM studies of the fractionated high molecular weight PFSs revealed a spherical cocoon for the single chains of the dendronized polymer as well as elongated single-chain structures. The cocoon of the dendronized PFS could be interesting as a unimolecular micelle with the transition-metal-rich core which is isolated by the dense outer layer of the dendrons.

Facile and Efficient One‐Pot Transformation of RAFT Polymer End Groups via a Mild Aminolysis/Michael Addition Sequence

AbstractSummary: The trithiocarbonate end groups of polymers prepared by RAFT polymerization are converted into colorless and stable thioethers in a one‐pot process that combines aminolysis of the trithiocarbonate functions and Michael addition of the resulting thiols to α, β‐unsaturated carbonyl derivatives. This post polymerization procedure, which is carried out under mild conditions to near quantitative conversion, is described in the case of a telechelic poly(N‐isopropylacrylamide) sample bearing isobutylsulfanylthiocarbonylsulfanyl end groups. The chemical composition, purity, and molar masses of the modified polymers are assessed by GPC, 1H NMR spectroscopy and UV‐vis spectroscopy, which together demonstrate the efficiency of the method and confirm that the molecular weight and polydispersity of the precursor RAFT polymer are not affected by the treatment.The facile, one pot synthesis combines the reactions of trithiocarbonate aminolysis and Michael addition of a thiol to an α, β‐unsaturated ester to transform the labile, colored thiocarbonylthio moiety into a stable, colorless thioether.imageThe facile, one pot synthesis combines the reactions of trithiocarbonate aminolysis and Michael addition of a thiol to an α, β‐unsaturated ester to transform the labile, colored thiocarbonylthio moiety into a stable, colorless thioether.

Miscibility of styrene/unsaturated polyester quasibinary systems: Unsaturated polyester chemical composition and molecular weight influence

AbstractUnsaturated polyester prepolymers were synthesized with different chemical compositions and molecular weights. Cloud‐point curves (CPC) were measured in St‐UP quasibinary solutions, showing UCST behavior in all cases. The miscibility of the first UP samples series in St comonomer was enhanced when AA chemical comonomer concentration in UP prepolymer increased. In the second series, UP prepolymer miscibility increased with the molecular weight up to a maximum and, after that, the miscibility decreased. A thermodynamic analysis of experimental CPCs was performed using the Flory‐Huggins (F‐H) theory for polydisperse polymer solutions. A simple relationship between the interaction parameter and the temperature inverse could fit the measured CPCs in wide concentrations and molecular weight ranges. In the temperature interval where this fit took place, the positive enthalpic contribution to the interaction parameters determined the miscibility dependence with temperature in both UP sample series. The St‐UP miscibility behavior was also correlated with UPs structural chemical parameters as: (a) the final HO and HOOC high polar groups concentration, (b) the chain backbone polar adipate and phthalate groups concentration, and (c) the UP size dependent mixing entropy. All these parameters are molecular weight dependent. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 102: 6064–6073, 2006

Depletion Interaction Mediated by a Polydisperse Polymer Studied with Total Internal Reflection Microscopy

Total internal reflection microscopy (TIRM) was applied to measure depletion forces between a charged colloidal sphere and a charged solid wall induced by dextran, a nonionic nonadsorbing polydisperse polysaccharide. The polymer size polydispersity is shown to greatly influence the depletion potential. Using the theory for the depletion interaction due to ideal polydisperse polymer chains, we could accurately describe the experimental data with a single adjustable parameter.

Synthesis and antibacterial activities of water‐soluble methacrylate polymers containing quaternary ammonium compounds

AbstractNew water‐soluble methacrylate polymers with pendant quaternary ammonium (QA) groups were synthesized and used as antibacterial materials. The polymers with pendant QA groups were obtained by the reaction of the alkyl halide groups of a previously synthesized functional methacrylate homopolymer with various tertiary alkyl amines containing 12‐, 14‐, or 16‐carbon alkyl chains. The structures of the functional polymer and the polymers with QA groups were confirmed with Fourier transform infrared and 1H and 13C NMR. The degree of conversion of alkyl halides to QA sites in each polymer was determined by 1H NMR to be over 90% in all cases. The number‐average molecular weight and polydispersity of the functional polymer were determined by size exclusion chromatography to be 32,500 g/mol and 2.25, respectively. All polymers were thermally stable up to 180 °C according to thermogravimetric analysis. The antibacterial activities of the polymers with pendant QA groups against Staphylococcus aureus and Escherichia coli were determined with broth‐dilution and spread‐plate methods. All the polymers showed excellent antibacterial activities in the range of 32–256 μg/mL. The antibacterial activity against S. aureus increased with an increase in the alkyl chain length for the ammonium groups, whereas the antibacterial activity against E. coli decreased with increasing alkyl chain length. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 5965–5973, 2006

Nematic-isotropic phase behaviours of polydisperse polymer/liquid crystal systems: Applicability of continuous thermodynamics

Phase behaviours of polydisperse polystyrene (PS)/nematic liquid crystals (LCs) P-ethoxy-benzylidene- p- n-butylaniline (EBBA) are investigated by thermo-optical analysis (TOA) technique. In this study, to describe nematic-isotropic transition of the polydisperse PS/EBBA systems, a continuous distribution function to obtain the composition of polydisperse polymers is considered precisely. We apply these molar mass distributions to the extended Flory–Huggins model. The proposed semi-empirical model gives a remarkable agreement with experimental data for the model systems.