Monte Carlo Simulation of Randomly Branched Step‐Growth Polymers: Generation and Analysis of Representative Molecular Ensembles

A Monte Carlo simulation procedure has been set up and applied to generate representative ensembles of randomly branched step‐growth polymers based on their reaction recipe. The molecular distributions thus obtained are consistent with those from statistical/analytical approaches. However, because the current method gives access to the complete ensemble of simulated molecules, a very detailed structural analysis is possible. Our procedures are applicable to any ‘A_fB_g’ system with f + g ≥ 1. We apply this approach to randomly branched polyamides in order to gain insight into their molecular structure and understand the effect of the reaction recipe on the final product.

     

Highly Asymmetric Phase Diagram of a Poly(1,2‐octylene oxide)–Poly(ethylene oxide) Diblock Copolymer System Comprising a Brush‐Like Poly(1,2‐octylene oxide) Block

The phase diagram of a series of poly(1,2‐octylene oxide)–poly(ethylene oxide) (POO–PEO) diblock copolymers is determined by small‐angle X‐ray scattering. The Flory–Huggins interaction parameter was measured by small‐angle neutron scattering. The phase diagram is highly asymmetric due to large conformational asymmetry that results from the hexyl side chains in the POO block. Non‐lamellar phases (hexagonal and gyroid) are observed near f_PEO = 0.5, and the lamellar phase is observed for f_PEO ≥ 0.5.

     

The Role of Oxidation in the Migration Mechanism of Layered Silicate in Poly(propylene) Nanocomposites

Summary: Evidence of clay migration from the core to the surface of poly(propylene)/montmorillonite nanocomposites is provided. A three‐ to fivefold increase in the clay concentration of the surface is obtained during isothermal heating in oxidative atmosphere. The mechanism of migration is investigated by means of attenuated total reflectance Fourier transform infrared spectrometry. It is shown that oxygen plays a fundamental role in the migration mechanism.

ρ_Si versus c for the annealed samples.     

Photochemically Cross‐linked Poly(aryl ether ketone) Rings

Summary: Macrocyclic phenyl ether ketones were prepared via pseudo high dilution condensation. Irradiation of these rings with UV light in a solution containing isopropyl alcohol as hydrogen donor resulted in a photo‐induced reduction of benzophenone to benzopinacol and the formation linked macrocycles. These rings can be heated to undergo ring‐opening polymerization and produce a polymer network or they can be added to a polycondensation reaction to prepare poly(ether ether ketones) with variable degrees of cross‐linking.

Photochemical cross‐linking of PEK rings and ring opening polymerization (n: 2–6). (a) hν, iPrOH, DCM; (b) CsF, 260 °C (polymer 3 ); (c) 4,4′–difluorobenzophenone, hydroquinone, diphenylsulphone, K₂CO₃, 260 °C (2% polymer 4 ; 6% polymer 5 ).     

Ethylene Polymerization Catalyzed by Titanium(IV) Complexes of a Triaryloxoamine Ligand [TiX{(OArCH2)3N}]

Summary: Titanium complexes containing a triaryloxoamine ligand, [TiX{(O‐2,4‐R₂C₆H₂‐6‐CH₂)₃N}] (R = Me, tBu; X = OiPr, O‐2,6‐iPr₂C₆H₃), exhibited notable catalytic activity for ethylene polymerization in the presence of MAO, especially at temperatures between 100 and 120 °C. Their activity increased upon the addition of a small amount of AlMe₃.

     

Morphology of ABCD Tetrablock Copolymers Predicted by Self‐Consistent Field Theory

Summary: We studied the two‐dimensional (2D) microphase‐separated morphology of linear ABCD tetrablock copolymers by self‐consistent field theory. By varying the interaction parameters and the compositions, we found at least twelve structures, two of which – “four‐color” lamellae and “three‐color” core‐shell hexagonal phase – prove the existing experimental observations. These morphologies were discussed in correlation with the volume fraction of the components and the interaction parameters. A specific behavior of symmetrical tetrablock copolymers, i.e., f_A = f_D and f_B = f_C, is that the stable phases are lamellae, which is different from symmetrical ABC triblock copolymer having order‐to‐order transition. These results are helpful for the design of new block copolymer‐based nanomaterials.

     

Titanium‐Catalyzed Norbornene Oligomerization. Isolation of a Crystalline Heptamer with a 2,3‐exo‐Disyndiotactic Structure

Summary: Norbornene (NB) was oligomerized at 0 °C using AlEt₂Cl‐TiCl₄ at a monomer/titanium molar ratio of about 11. The oligomerization product consists of a fraction soluble in diethyl ether, amorphous by X‐ray examination, and of a crystalline fraction, insoluble in diethyl ether. The crystalline fraction was shown by powder X‐ray diffraction to consist of a NB heptamer. Single‐crystal X‐ray analysis indicated that the heptamer had a stereoregular 2,3‐exo‐disyndiotactic structure. The heptamer adopts a strained, highly irregular, folded conformation in the crystalline state. Structural differences with respect to NB oligomers obtained with zirconocene catalysts are discussed.

A view of the molecular structure of the crystalline NB heptamer.     

Synthesis and Characterization of Long‐Chain‐Branched Polyolefins with Metallocene Catalysts: Copolymerization of Ethylene with Poly(ethylene‐co‐propylene) Macromonomer

Poly(ethylene‐co‐propylene) macromonomer (EPM) was synthesized in a high‐temperature continuous stirred tank reactor (CSTR) with [C₅Me₄(SiMe₂N^tBu)]TiMe₂ (CGC‐Ti) as the catalyst system. PE samples with EPM long chain branching (LCB) were produced by semi‐batch copolymerization of ethylene and EPM with CGC‐Ti. The LCB frequencies were up to 21.8 EPM side chains per PE backbone. The effects of temperature and ethylene pressure on the degree of EPM grafting and catalyst activity were examined.

Incorporation of EPM into a growing PE chain forming an LCB polymer.     

An Infrared Approach toward Measuring the Thickness of Polyelectrolyte Films

IR spectroscopy is applied to study polyelectrolyte films of 0.1–5 μm thickness. This approach permits to obtain not only the usual chemical information about polymer conformation, chemical bonds, interacting groups, and molecular/ionic state, but also important structural parameters of the film, such as total thickness, average thickness of each layer, and sparseness of polymer packing. All these information can be obtained from one single sample.

IR cell for thickness measurements of a polyelectrolyte film. The pathlength d of the cell is measured twice: before and after film deposition. The film thickness, Δd = d_e − d_f, can be calculated using the interference maxima that determine values d_e and d_f.     

Nanoporous Network Channels from Self‐Assembled Triblock Copolymer Supramolecules

Supramolecular complexes of a poly(tert‐butoxystyrene)‐block‐polystyrene‐block‐poly(4‐vinylpyridine) triblock copolymers and less than stoichiometric amounts of pentadecylphenol (PDP) are shown to self‐assemble into a core–shell gyroid morphology with the core channels formed by the hydrogen‐bonded P4VP(PDP)complexes. After structure formation, PDP was removed using a simple washing procedure, resulting in well‐ordered nanoporous films that were used as templates for nickel plating.

     

Free Energy of Deformation of the Radius of Gyration in Semiflexible Chains

The distribution function P(S) of the radius of gyration S, the corresponding elastic free energy A(S) and the mean force were computed from simulations based on the wormlike chain (WLC) model. The relation of the S‐conjugated elastic functions to the analogous functions based on the chain vector R and their connection to the statistical‐mechanics ensembles was elucidated. Simulation data revealed that available analytical functions for P(S) fail to predict the behavior of semiflexible chains. When the power‐law function P(S) was used instead, the exponents sizeably raised with stiffness at chain expansion. The exponents deduced from elastic compression of a chain agreed fairly with the scaling exponents for chain confinement into a sphere.

     

Hydration Changes during Thermosensitive Association of a Block Copolymer Consisting of LCST and UCST Blocks

Summary: Thermosensitive association of a diblock copolymer consisting of poly(3‐dimethyl(methacryloyloxyethyl) ammonium propane sulfonate) (PdMMAEAPS), as an upper critical solution temperature (UCST) block, and poly(N,N‐diethylacrylamide) (PdEA), as a lower critical solution temperature (LCST) block, has been investigated by using IR spectroscopy. The ν(CO) and ν(SO) bands of the PdMMAEAPS block and the amide I band of PdEA block critically changed at the UCST and LCST, respectively, indicating that the segmental interaction of each block is altered at each transition.

The double temperature responsiveness of a UCST block and LCST block containing diblock copolymer. Micelles form at temperatures both below the UCST and above the LCST of the blocks.     

pH Dependent Elasticity of Polystyrene‐block‐poly(acrylic acid) Vesicle Shell Membranes by Atomic Force Microscopy

We assess the elastic properties of PS‐b‐PAA vesicle membranes under different pH values by AFM force measurements. We find that based on the shell deformation theory, the values of the estimated apparent Young's modulus of the vesicle membranes decrease as the pH of the solution increases. The onset of the decrease of E coincides with the surface pK_a determined from ζ‐potential measurements. This decrease of E at higher pH is attributed to electrostatic repulsion between the deprotonated PAA chains resulting in the thinning of the vesicle membrane.

     

Molecular Weight Distribution of Linear Chains in Step‐Growth Polymerization Under the Influence of Cyclization Reactions

Two different equations are presented describing the frequency distribution (f_l) of linear chains in step‐growth (SG) polymerizations. Two related equations for the weight distribution (w_l) are formulated as well. All equations contain either an exponent α that represents the reaction rates (or probabilities) of chain growth versus cyclization reactions or they contain a cyclization factor β′. Plots of f_l and w_l versus conversion or degree of polymerization are presented and discussed. Distribution curves of individual oligomers versus conversion and versus β′ are described. Furthermore, the consequences for hyperbranched polymers resulting from polycondensations of ab_n monomers are discussed. Analogous to Flory's theory all equations concern kinetically controlled SG polymerizations.

     

The Effect of Pressure on the Microphase Separation of Diblock Copolymer Melts Studied by Dynamic Density Functional Theory Based on Equation of State

The effect of pressure on the microphase separation of diblock copolymer melts was investigated by dynamic density functional theory based on equation of state. The results correspond well with experiment data. With the application of high pressure, all of the phase regions corresponding to the different ordered morphologies become narrower. However, the pressure dependence of the order‐disorder transition temperature (T_ODT) relies on the symmetry of the diblock copolymer. In the very non‐symmetrical case when f is small, T_ODT decreases with increasing pressure, while in the symmetrical case when f = 0.5, T_ODT increases with increasing pressure. For the latter case, the increase in the total bead number of the system at the ODT is found, which is in good accordance with the experimental phenomenon that there is an increase in volume accompanying with the transition from ordered to disordered state. In contrast to the temperature, the pressure does not influence the starting time and the duration of microphase separation.

     

Monte Carlo Simulation of ABA Triblock Copolymer Melts Confined in a Cylindrical Nanotube

Monte Carlo simulations were used to identify the microphase morphologies of ABA triblock copolymer melts confined in a cylindrical nanotube. The influences of the volume fraction of mid‐block B (f_B), the radius of nanotube (R) and the asymmetry of ABA triblock copolymer chain were discussed in detail. When f_B varies, a series of double‐continuous, three‐layer concentric cylinder barrel, porous net, double helixes and the new multiplex structures were observed under different conditions. In addition, the stacked disk, catenoid‐cylinder and multi‐layer concentric cylinder barrel structures occur in turns at changing R. The relation between circular lamellae period L and layer number N_layer of concentric cylinder barrel with the increase of R was investigated to further explain the put‐off phenomenon of microphase transition of the multi‐layer concentric cylinder barrel structures. As for the increase of the asymmetry of ABA triblock copolymer chain, it was concluded that the short A_I segments tend to site at the interface between rich A and B circular lamellae.

     

Reactivity of Diamine Monomers in Non‐Equilibrium Copolycondensation Toward Aromatic Copolyamides

Based on the Hammett equation, a general method is established to relate the polycondensation monomer reactivity with both the monomer structural parameters and the properties of the solvent used for the non‐equilibrium ternary copolycondensation to give copolyamides. Linear plots of the logarithm of the monomer reactivity ratio, log r, versus structure parameter ΔpK could be represented by the equation log r = ρΔpK.

Relationship between log r and ΔpK using THF as the solvent.     

Dewetting and Phase Behaviors for Ultrathin Films of Polymer Blend

Summary: Dynamics of dewetting and phase separation in ultrathin films (thickness is ca. one radius of gyration, ≈1 R_g) of poly(methyl methacrylate) (PMMA) and poly(styrene‐ran‐acrylonitrile) (SAN) blends on Si substrate has been studied by in situ atomic force microscopy (AFM). In the miscible region, a “spinodal‐like” dewetting driven by a composition fluctuation recently predicted by Wensink and Jérôme (Langmuir 2002 , 18, 413) occurs. In the two‐phase region, the dewetting of the whole film is followed by phase separation in the droplets, coupling with the wetting of the substrate by the PMMA extracted by the strong attractive interaction between them.

     

Predicting the Limit of Control in the ATRP Process: Results from Kinetic Simulations

Kinetic simulations are reported, where the ATRP equilibrium constant K_ATRP is varied and the rates and degree of control in different ATRP systems are evaluated. The apparent rate constant k_app increases with increasing K_ATRP, but a maximum is reached. The limit of control is passed before the maximum, i.e. when K_ATRP is increased further, apparent first‐order kinetics and well‐controlled molecular weights will no longer be obtained. The equilibrium constant at which the limit of control is reached varies linearly with the propagation rate constant. This enables the design of well controlled ATRP systems. The influence of the conversion and chain length dependence of the termination rate constant on the simulation results is discussed.

     

Chain Transfer and Efficiency of End‐Group Introduction in Free Radical Polymerization of Methyl Methacrylate in the Presence of Poly(methyl methacrylate) Macromonomer

Summary: Experimental and modeling studies of addition–fragmentation chain transfer (AFCT) during radical polymerization of methyl methacrylate in the presence of poly(methyl methacrylate) macromonomer with 2‐carbomethoxy‐2‐propenyl ω‐ends (PMMA‐CO₂Me) at 60 °C are reported. The results revealed that AFCT involving PMMA‐CO₂Me formed in situ during methyl methacrylate polymerization has a negligible effect on the molecular weight distribution.