Using apparent molecular weight from SEC in controlled/living polymerization and kinetics of polymerization

Apparent molecular weights from size exclusion chromatography, that is molecular weights relative to standards of a nature different to that of the polymer sample being studied, are frequently used. We use calculations corresponding to realistic cases to provide guidelines for situations when, and to what extent, apparent molecular weights (MWs) can be meaningful. In controlled polymerization, we show how, without due care, use of apparent MW, could lead to the incorrect conclusion that the reaction was not controlled, whereas the true MWs would be close to theoretical values. We show here that the quality of the eluent as a solvent for the standard and the polymer sample is a good indication of the accuracy and the significance of the apparent polydispersity index. Accurate Mark–Houwink–Sakurada parameters are of limited availability, but the data about solvent quality available in handbooks or available from static light scattering measurements. Apparent M_n is of no use in controlled polymerization if simple simulations as performed in this work do not validate their use. The determination of transfer constants by the Mayo plot can be performed using apparent M_n without introducing any significant error, contrary to apparent weight‐average molecular weight M_w or apparent ln number distribution. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 897–911, 2008     

Time evolution of the size distribution of nano-sphere droplets in the hexadecane-in-water miniemulsion stabilized by nonionic surfactants

Time evolutions of the droplet size distribution in miniemulsions, which is constituted of water/n-hexadecane/nonionic surfactants, were investigated by using light scattering techniques. A hard-sphere model is applied to characterize the polydispersity of miniemulsion droplets. Measuring the relative scattering intensity as a function of the volume fraction of dispersed phase, the variance of the droplets size distribution, σ², was evaluated. Miniemulsions developed gradually from monodisperse systems (σ²≅0.02) to polydisperse ones (σ²≥0.13) over 12 days after preparation. σ² increased rapidly in the early stage, and ceased to develop at about 6 days after preparation. The z-average hydrodynamic radius of miniemulsion droplets grew with time over the whole time range. The change with time of the total droplet number of miniemulsion is in agreement with that predicted by Smoluchowski's theory for diffusion-controlled coagulation. Although the characteristic coagulation time obtained here was much larger than that estimated by Smoluchowski's theory, the qualitative agreement between the theory and the experimental results obtained here is good. At the earlier stage of the destabilization process of miniemulsions, the growth mechanism of droplets may be explained in terms of a diffusion-controlled coagulation. Received: 1 April 2000 Accepted: 10 August 2000     

Brownian dynamics of polydisperse colloidal hard spheres: Equilibrium structures and random close packings

Recently we presented a new technique for numerical simulations of colloidal hard-sphere systems and showed its high efficiency. Here, we extend our calculations to the treatment of both 2- and 3-dimensional monodisperse and 3-dimensional polydisperse systems (with sampled finite Gaussian size distribution of particle radii), focusing on equilibrium pair distribution functions and structure factors as well as volume fractions of random close packing (RCP). The latter were determined using in principle the same technique as Woodcock or Stillinger had used. Results for the monodisperse 3-dimensional system show very good agreement compared to both pair distribution and structure factor predicted by the Percus-Yevick approximation for the fluid state (volume fractions up to 0.50). We were not able to find crystalline 3d systems at volume fractions 0.50–0.58 as shown by former simulations of Reeet al. or experiments of Pusey and van Megen, due to the fact that we used random start configurations and no constraints of particle positions as in the cell model of Hoover and Ree, and effects of the overall entropy of the system, responsible for the melting and freezing phase transitions, are neglected in our calculations. Nevertheless, we obtained reasonable results concerning concentration-dependent long-time selfdiffusion coefficients (as shown before) and equilibrium structure of samples in the fluid state, and the determination of the volume fraction of random close packing (RCP, glassy state). As expected, polydispersity increases the respective volume fraction of RCP due to the decrease in free volume by the fraction of the smaller spheres which fill gaps between the larger particles.     

Coupled Orientation and Stretching of Chains in Mesoscale Models of Polydisperse Linear Polymers in Startup of Steady Shear Flow Simulations

Polydisperse linear polymers are studied in startup of steady shear flow simulations using dissipative particle dynamics. The results show that with an increase in polydispersity the stress overshoot declines while the steady‐state stress increases. Various physical characteristics of the systems are studied including frequency of nonbonded interactions, gyration radius data, flow alignment angles, and average bond lengths. The patterns in the data suggest higher forces are necessary to orient and stretch long chain fractions in the flow direction. Relaxation modulus data prove the broad range of relaxation mechanisms in polydisperse systems. Linear viscoelasticity theory is used to quantify the relaxation spectrum. The results indicate an increase in the longest relaxation time in systems with higher polydispersity. The steady‐state shear viscosity results show higher viscosities with an increase in polydispersity at all shear‐rates. The good agreement of the characteristic behaviors of modeled polydisperse polymers with experiments is encouraging for future work.

     

Effects of Shape of Crowders on Dynamics of a Polymer Chain Closure

Using 3D Langevin dynamics simulations,we investigate the effects of the shape of crowders on the dynamics of a polymer chain closure.The chain closure in spherical crowders is dominated by the increased medium viscosity so that it gets slower with the increasing volume fraction of crowders.By contrast,the dynamics of chain closure becomes very complicated with increasing volume fraction of crowders in spherocylindrical crowders.Notably,the mean closure time is found to have a dramatic decrease at a range of volume fraction of crowders 0.36-0.44.We then elucidate that an isotropic to nematic transition of spherocylindrical crowders at this range of volume fraction of crowders is responsible for the unexpected dramatic decrease in the mean closure time.     

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.     

A Probability Model of Star‐Branched Polymers Formed by Connecting Polydispersed Primary Chains Onto a Multifunctional Coupling Agent

Summary: A probability model, based on the “in‐out” recursive analysis, is developed for obtaining the average molecular weights of star polymers formed by connecting polydispersed primary chains onto a multifunctional coupling agent. The average properties and the polydispersity index of the formed star polymers can be described as a function of the reaction conversion and the average properties of the polydispersed primary chains without the knowledge of the whole distribution. The results indicate that, although PI of the resulting star polymers might increase at the intermediate conversion for the higher functionalities of the core molecules, the resulting star polymers generally have narrower molecular weight distributions at the complete conversion compared to the initial polydispersed polymer chains.

A schematic illustration of the star polymer formation.     

Unimodal molecular weight distribution of commercial polymers from viscoelastic data

This article presents a method that provides the molecular weight distribution (MWD) of polymeric material from rheological data. The technique has been developed to deal with linear polymers with a log‐normal molecular weight distribution. The rheological data must include the shear storage modulus, G′(ω), and the shear loss modulus, G″ (ω), ranging from the terminal zone to the rubberlike zone. It was not necessary to achieve the relaxation spectrums via the extremely unstable problem of inverting integral equations. The method has been tested with different polymers (polydimethylsiloxane, polyisoprene, random copolymer of ethylene and propylene, and polystyrene) and the calculated MWDs were in good agreement with experimental data. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 1539–1546, 2000     

Block Copolymers From Living Emulsion Polymerization: Reactor Operating Strategies and Blocking Efficiency

Diblock copolymers are generated using xanthate‐based RAFT agents in conjunction with emulsion polymerization via stage‐wise operations. First, emulsion polymerization is conducted for styrene, methyl acrylate, and butyl acrylate monomers to obtain polymers of specified molar mass. At the second stage, polymers undergo chain extension to produce block copolymers. Linear growth of molecular weight with respect to conversion establishes the living characteristics of the process. Under batch conditions, partly homopolymers are produced. Semi‐batch operation produces copolymers of higher purity with low polydispersity. The choice of blocking sequence is crucial for reducing the influence of the terminated chains on the distribution sequence of copolymers produced.

     

Atom Transfer Radical Polymerization (ATRP) of Ethyl Acrylate: Its Mechanistic Studies

Atom transfer radical polymerization (ATRP) of ethyl acrylate was carried out in bulk using ethyl 2-bromoisobutyrate as initiator, CuBr as well as CuCl as catalyst in combination with different ligands e.g., 2,2′ bipyridine (bpy)andN,N, N′,N″,N″-pentamethyldiethylenetriamine (PMDETA). In most of the cases very high conversion (72–98%) was achieved. The polymerization was well controlled with a linear increase of molecular weight (M_n^SEC) with conversion and relatively narrow molecular weight distributions (polydispersity index 1.2–1.3). Use of PMDETA as the ligand resulted in faster polymerization rate (98% conversion in 1 h) than those using bipyridine (72% conversion in 5 h). The MALDI-TOF-MS analysis of poly (ethyl acrylate) (PEA) prepared by using bpy as ligand showed the presence of halogen as the end group. On the contrary, when PMDETA was used as the ligand, the mass analysis showed no trace of this end group.