Modeling of the Phase Separation Behavior of Polydisperse Semi‐Flexible Diblock Copolymers

Summary: A modified random phase approximation method with a cumulant expansion for the semi‐flexible structure factor of diblock copolymers was exercised to describe the phase separation behavior of semi‐flexible and polydisperse diblock copolymers. Scattering curves and spinodal diagrams were calculated applying monomer specific input parameters. The influence of polydispersity was included applying basic concepts of mathematical statistics utilizing several probability density distributions in the case of the two single blocks. In contrast to semi‐flexibility, the main effect of polydispersity was found to shift the spinodal up, thus to enlarge the range of existence of the homogeneous phase.

Twofold Schultz‐Zimm distribution of diblock copolymers.     

Diffusion Coefficients for Binary, Ternary, and Polydisperse Solutions from Peak-Width Analysis of Taylor Dispersion Profiles

Binary mutual diffusion coefficients D can be estimated from the width at half height W _1/2 of Taylor dispersion profiles using D=(ln 2)r ² t _R/(3W ² h) and values of the retention time t _R and dispersion tube radius r. The generalized expression D _h=−(ln h)r ² t _R/(3W ² _h ) is derived to evaluate diffusion coefficients from peak widths W _h measured at other fractional heights (e.g., (h = 0.1, 0.2,…,0.9). Tests show that averaging the D _h values from binary profiles gives mutual diffusion coefficients that are as accurate and precise as those obtained by more elaborate nonlinear least-squares analysis. Dispersion profiles for ternary solutions usually consist of two superimposed pseudo-binary profiles. Consequently, D _h values for ternary profiles generally vary with the fractional peak height h. Ternary profiles with constant D _h values can however be constructed by taking appropriate linear combinations of profiles generated using different initial concentration differences. The invariant D _h values and corresponding initial concentration differences give the eigenvalues and eigenvectors for the evaluation of the ternary diffusion coefficient matrix. Dispersion profiles for polymer samples of N i-mers consist of N superimposed pseudo-binary profiles. The edges of these profiles are enriched in the heavier polymers owing to the decrease in polymer diffusion coefficients with increasing polymer molecular weight. The resulting drop in D _h with decreasing fractional peak height provides a signature of the polymer molecular weight distribution. These features are illustrated by measuring the dispersion of mixed polyethylene glycols.     

Synthesis of Multiblock Polymer Containing Narrow Polydispersity Blocks

Summary: We have developed a new strategy to prepare multiblock polymers and copolymers via one‐ or two‐step polymerization using a polymerizable cyclic trithiocarbonate (CTTC), 4,7‐diphenyl‐[1,3]dithiepane‐2‐thione. CTTC undergoes ring‐opening process to incorporate a trithiocarbonate moiety. The trithiocarbonate moiety in turn, functions as a reversible addition fragmentation chain transfer (RAFT) agent. Through this mechanism, multiblock polystyrenes and polystyrene‐block‐ poly(butyl acrylate) copolymers containing various narrow polydispersity blocks can be prepared.

Integrated process of ring‐opening and RAFT polymerizations involving cyclic trithiocarbonates.     

Random Computer Generation of 3D Molecular Structures: Theoretical and Statistical Analysis

Summary: A computer program has been developed to generate three‐dimensional molecular structures randomly from a given collection of elementary chemical functional groups: the so‐called fragment database. The gradual assembly of the various fragments present in the database is performed according to a “self‐generation algorithm” (SGA). The latter is based on the covalent binding, step by step, between the unoccupied electronic valencies associated with the fragments of the database, and those of the growing molecular structure. When the number of electronic valencies of the molecular structure is zero, the growth process for this particular molecule is completed. It is shown that SGA is able to reproduce the asymmetric mass distributions of some natural colloids, like humic substances. In this article, particular attention is given to the analysis of the relationship existing between the fragment composition of the database and that of the collection of molecules generated. Mathematical expressions are derived and discussed, to understand the relationship between the proportions of the different types of fragments and the final composition of the generated molecular ensembles. For that purpose, a “pathway” formalism is proposed to describe exhaustively the whole set of generated molecules by specifying the distribution function of all of the fragments therein integrated. A statistical analysis that satisfactorily reproduces the predictions of the pathway model is extensively discussed.

Example of a three‐dimensional structure obtained with the “self‐generation algorithm” (SGA).     

Compositionally symmetric diblock copolymer blends of moderate polydispersity

Recent experimental evidence and theoretical predictions indicate that binary blends of relatively monodisperse diblock copolymers remain miscible if the molecular weight disparity of the constituent copolymers is not too great. In this work, we examine the effect of moderate copolymer polydispersity on both the microstructural characteristics and phase behavior of blends prepared from four compositionally symmetric poly(styrene-b-isoprene) (SI) diblock copolymers ranging in polydispersity (M̄_w/M̄_n) from 1.02 to 1.30. Blend periodicities, measured by small-angle X-ray scattering, compare favorably with predictions from a strong segregation theory proposed for lamellar diblock copolymer blends composed of monomolecular copolymers. Transmission electron microscopy, employed to ascertain the real-space morphological characteristics of these blends, reveals that a lamellar → cylindrical transition occurs in macrophase-separated blends. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 2653–2658, 1997     

Thermal behavior of polystyrene synthesized in the presence of carboxymethyl cellulose

Summary Study of the decomposition kinetics is an important tool for the development of polymer recycling in industrial scale. In this work, parameters such as activation energy, frequency factor and reaction order, were measured under dynamic conditions. Flynn-Wall-Ozawa, Van Krevelen, Horowitz-Metzger, Coats-Redfern, Madhusudanan and Vyazovkin methods were used to determine the kinetic parameters. The analysis of the results obtained by the Coats-Redfern method shows that the thermal degradation process of LDPE and HDPE corresponds to a phase boundary controlled reaction (mechanism R2). This method shows that the reaction order values of LDPE and HDPE are about 0.7 and 0.6, respectively.     

Polymer grafted nanoparticles: Effect of chemical and physical heterogeneity in polymer grafts on particle assembly and dispersion

Macroscopic properties of polymer nanocomposites depend on the microscopic composite morphology of the constituent nanoparticles and polymer matrix. One way to control the spatial arrangement of the nanoparticles in the polymer matrix is by grafting the nanoparticle surfaces with polymers that can tune the effective interparticle interactions in the polymer matrix. A fundamental understanding of how graft and matrix polymer chemistries and molecular weight, grafting density, and nanoparticle size, and chemistry affect interparticle interactions is needed to design the appropriate polymer ligands to achieve the target morphology. Theory and simulations have proven to be useful tools in this regard due to their ability to link molecular level interactions to the morphology. In this feature article, we present our recent theory and simulation studies of polymer grafted nanoparticles with chemical and physical heterogeneity in grafts to calculate the effective interactions and morphology as a function of chemistry, molecular weights, grafting densities, and so forth. © 2013 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2013     

The unperturbed conformation and interaction parameters of polyvinylalcohol in aqueous solutions. Polydispersity effects

Summary Unperturbed conformation and interaction parameters of polyvinyl alcohol in aqueous solutions have been determined. To this end intrinsic viscosity-molecular weight data have been analyzed in terms of the Burchard-Stockmayer-Fixman (BSF) equation. A special form of this equation for polydisperse polymers has been derived. Values of the Flory-Huggins interaction parameter x, the polymer constantK ₀ and other related quantities have been obtained using the original data of Matsumoto and Ohyanagi. For sake of comparison intrinsic viscosity-molecular weight data of several commercial PVA samples were measured and analyzed. The parameters obtained, are discussed in relation to other literature data of PVA. The viscosimetric value agrees very well with literature values of if the cubed viscosity radius expansion factor is given by the theoretical equation derived by Shimada and Yamakawa: ³ =1+1.14 z +....

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Zusammenfassung Ungestörte Konformations- und Wechselwirkungsparameter von Polyvinylalcohol (PVA) in wäßriger Lösung wurden bestimmt. Dazu wurde die Beziehung zwischen der Grenzviskosität [] und dem Molekulargewicht mit Hilfe derBurchard-Stockmayer-Fxman-Gleichung analysiert. Zuerst aber wurde eine besondere Form der BSF-Gleichung für polydisperse Polymere abgeleitet. Die gefundenen Werte für den Wechselwirkungsparameter und die PolymerkonstanteK ₀ wurden auf den originellen Daten von Matsumoto und Ohyanagi basiert. Zum Vergleich wurden verschiedene kommerzielle PVA-Muster analysiert. Die gemessenen -Werte stimmen mit den Literaturwerten für am besten überein, wenn für die Expansionskoeffizienten die theoretische Gleichung von Shimada und Yamakawa ³ = 1 + 1.14 z ... eingeführt wird. Die Ergebnisse wurden anhand weiterer Literaturdaten über PVA erörtert.

     

Effect of size polydispersity on the structural and vibrational characteristics of two-dimensional granular assemblies

Two-dimensional disordered granular assemblies composed of 2048 polydispersed frictionless disks are simulated using the discrete element method. The height of the first peak of the pair correlation function, g1, the local and global gbond orientational parameters lψ6and ψ6, and the fluctuations of these parameters decrease with increasing polydispersity s,implying the transition from a polycrystalline state to an amorphous state in the system. As s increases, the peak position of the boson peak ωBP shifts towards a lower frequency and the intensity of the boson peak D(ωBP)/ωBP increases, indicating that the position and the strength of the boson peak are controlled by the polydispersity of the system. Moreover, the inverse of the boson peak intensity ωBP/D(ωBP), the shear modulus G, and the basin curvature SIS all have a similar dependence on s, implying that the s dependence of the vibrational density of states at low frequencies likely originates from the s dependence of the basin curvature.     

Phase Diagram for a System of Polydisperse Components Consisting of the Precursor of an Epoxy/Diamine Thermoset and a Thermoplastic: Analysis Based on a Lattice Theory Model

Summary: The miscibility of a thermoplastic modifier with the precursors of an epoxy/diamine thermoset without chemical reaction was studied thermodynamically. The experimental cloud point curve showed a UCST behavior. A model based on the Flory‐Huggins lattice theory and on the Koningsveld approach was used for the thermodynamic analysis, in which the polydispersity of components was taken into account and the interaction parameter was considered depending on the temperature and composition. A phase diagram for the unreacted system was obtained. Calculations of species distributions in both separated phases were realized for different compositions of the modifier. Finally, the miscibility of our system was compared with that of the same system without diamine, obtaining a greater miscibility in the system with diamine.

Phase diagram for the system formed by the precursors of an epoxy thermoset without chemical reaction modified with different amounts of polystyrene.