Modeling the reversible addition–fragmentation transfer polymerization process

A kinetic model has been developed for reversible addition–fragmentation transfer (RAFT) polymerization with the method of moments. The model predicts the monomer conversion, number‐average molecular weight, and polydispersity of the molecular weight distribution. It also provides detailed information about the development of various types of chain species during polymerization, including propagating radical chains, adduct radical chains, dormant chains, and three types of dead chains. The effects of the RAFT agent concentration and the rate constants of the initiator decomposition, radical addition, fragmentation, disproportionation, and recombination termination of propagating radicals and cross‐termination between propagating and adduct radicals on the kinetics and polymer chain properties are examined with the model. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 1553–1566, 2003     

Counterion adsorption theory of dilute polyelectrolyte solutions: apparent molecular weight, second virial coefficient, and intermolecular structure factor

Polyelectrolyte chains are well known to be strongly correlated even in extremely dilute solutions in the absence of additional strong electrolytes. Such correlations result in severe difficulties in interpreting light scattering measurements in the determination of the molecular weight, radius of gyration, and the second virial coefficient of charged macromolecules at lower ionic strengths from added strong electrolytes. By accounting for charge-regularization of the polyelectrolyte by the counterions, we present a theory of the apparent molecular weight, second virial coefficient, and the intermolecular structure factor in dilute polyelectrolyte solutions in terms of concentrations of the polymer and the added strong electrolyte. The counterion adsorption of the polyelectrolyte chains to differing levels at different concentrations of the strong electrolyte can lead to even an order of magnitude discrepancy in the molecular weight inferred from light scattering measurements. Based on counterion-mediated charge regularization, the second virial coefficient of the polyelectrolyte and the interchain structure factor are derived self-consistently. The effect of the interchain correlations, dominating at lower salt concentrations, on the inference of the radius of gyration and on molecular weight is derived. Conditions for the onset of nonmonotonic scattering wave vector dependence of scattered intensity upon lowering the electrolyte concentration and interpretation of the apparent radius of gyration are derived in terms of the counterion adsorption mechanism.     

A novel one‐concentration method for improved multi‐angle laser light scattering

A novel data interpretation method is presented which is derived from weighted least squares analysis. Given the steep dependence of the Rayleigh factor on concentration, a Zimm‐plot based regression of weight average molar mass and the RMS radius of gyration is strongly influenced by data over an optimum concentration range, which can be quite narrow for some polymer‐solvent combinations. The “one‐concentration method” exploits this sensibility to improve the precision in molar mass and radius of gyration measurements to ±4%. The theoretical prediction of the optimum concentration is included. The one‐concentration method is applied to polymers in organic solvents as well as to water‐soluble polyelectrolytes.     

One‐step synthesis of poly(lactic‐co‐glycolic acid)‐g‐poly‐1‐vinylpyrrolidin‐2‐one copolymers

The radical polymerization of 1‐vinylpyrrolidin‐2‐one (NVP) in poly(lactic‐co‐glycolic acid) (PLGA) 50:50 at 100 °C leads to amphiphilic PLGA‐g‐PVP copolymers. Their composition is determined by FT‐IR spectroscopy. Thermogravimetric analyses agree with FT‐IR determinations. Saponification of the PLGA‐g‐PVP polyester portion allows isolating the PVP side chains and measuring their molecular weight, from which the average chain transfer constant (C_T) of the PLGA units is estimated. The MALDI‐TOF spectra of PVP reveal the presence at one chain end of residues of either glycolic acid‐ or lactic acid‐ or lactic/glycolic acid dimers, trimers and one tetramer, the other terminal being hydrogen. This unequivocally demonstrates that grafting occurred. Accordingly, the orthogonal solvent pair ethyl acetate—methanol, while separating the components of PLGA/PVP intimate mixtures, fails to separate pure PVP or PLGA from the reaction products. All PLGA‐g‐PVP and PLGA/PLGA‐g‐PVP blends, but not PLGA/PVP blends, give long‐time stable dispersions in water. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2016 , 54, 1919–1928     

Star‐shaped polymers by Ru(II)‐catalyzed living radical polymerization. II. Effective reaction conditions and characterization by multi‐angle laser light scattering/size exclusion chromatography and small‐angle X‐ray scattering

Star poly(methyl methacrylate)s (P*) of various arm lengths and core sizes were synthesized in high yields by the polymer linking reaction in Ru(II)‐catalyzed living radical polymerization. The yields of the star polymers were strongly dependent on the reaction conditions and increased under the following conditions: (1) at a higher overall concentration of arm chains ([P*]), (2) with a larger degree of polymerization (DP) of the arm chains (arm length), and (3) with a larger ratio (r) of linking agents to P* (core size). In particular, the yields sharply increased in a short time at a higher temperature, in a polar solution, and at a higher complex concentration after the addition of linking agents. These star polymers were then analyzed by multi‐angle laser light scattering to determine the weight‐average molecular weight (3.8 × 10³ to 1.5 × 10⁶), the number of arm chains per molecule (f = 4–63), and the radius of gyration (R_z = 2–22 nm), which also depended on the reaction conditions (e.g., f and R_z increased as [P*], DP, and r increased). Small‐angle X‐ray scattering analyses of the star polymers showed that they consisted of spheres for which the radius of the microgel core was 2.7 nm. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 40: 2245–2255, 2002     

Simulation of GPC‐Distribution Coefficients of Linear and Star‐Shaped Molecules in Spherical Pores

Simulations of the distribution coefficients of linear and star‐shaped polymers in spherical pores were performed in order to predict the GPC‐elution behavior of star‐shaped polymers relative to that of linear polymers. Self avoiding walks were generated on a tetrahedral lattice to simulate good solvent conditions. It was found that neither the molecular weight nor the mean squared radius of gyration of the polymer serves as a universal factor to determine the distribution coefficient. However, the calculated distribution coefficients correlate well with the calculated hydrodynamic radii even for different topologies. For molecules at same elution volume the ratios of molecular weights of star and linear polymer agree well with exact calculations for Gaussian chains. These ratios are nearly independent of pore geometry (spherical or cylindrical).     

Free‐radical polymerization of methyl methacrylate with a tetrafunctional peroxide initiator

This study examined the use of a new tetrafunctional peroxide initiator in the bulk free‐radical polymerization of methyl methacrylate. The objective was to investigate the effect of using a multifunctional initiator through an examination of the rates of polymerization and the polymer properties. The molecular weights and radii of gyration were obtained with a size exclusion chromatograph equipped with an online multi‐angle laser light scattering detector. The performance of the tetrafunctional initiator was compared to that of a monofunctional counterpart [tert‐butylperoxy 2‐ethylhexyl carbonate (TBEC)]. The results showed that the new tetrafunctional peroxide initiator produced a faster rate of polymerization than TBEC at an equivalent concentration but also generated a polymer of a lower molecular weight. This trend was the opposite of what was observed in a previous study with styrene. When TBEC was used at a concentration four times that of the new tetrafunctional peroxide initiator, both produced equal rates of polymerization and similar molecular weights. The degree of branching was also investigated with radius‐of‐gyration plots. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 5647–5661, 2004     

Molecular characterization of a hyperbranched polyester. II. Small‐angle neutron scattering

A series of fractions of a hyperbranched polyester in deutero tetrahydrofuran solution were investigated by small‐angle neutron scattering. Concentrations of polymer from 2 to 5% w/v were used, and the molecular parameters were obtained from Zimm plots of the data. Second virial coefficients were positive, and these values were confirmed by dilute‐solution light scattering on a small number of fractions with deutero tetrahydrofuran as a solvent. The small‐angle neutron scattering data exhibited the general features predicted for the particle scattering functions of nonrandomly branched polymers, but an exact fit of the theoretical equation to the data could not be obtained for all fractions of the hyperbranched polymer, particularly those of high molecular weight. Excluded volume effects were cited as a possible cause for this disagreement. A fractal dimension of ～2.5 was obtained from the scattering vector dependence of the differential scattering cross section of the polymer in deutero tetrahydrofuran solution, which agreed with the scaling exponent for the dependence of the radius of gyration on weight‐average molecular weight. Hydrogenous tetrahydrofuran solutions of the hyperbranched polymer exhibited negative second virial coefficients that were attributed to isotopic influences on the thermodynamic properties of the polymer–solvent combination. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 1352–1361, 2003     

Dynamical problems in the theory of polymer solutions

Qualitative discrepancies are found between what is predicted by available theory and what is actually observed, for several concentration regimes of the dynamical properties of polymer solutions. The difficulties are most severe, from the standpoint of experiment or simulation as well as theory, for the entanglement concentration regime. However, the classical problems of chain polymers in dilute solution are not fully understood. For example, the constants of proportionality that relate hydrodynamic radii to the radius of gyration, in the nondraining limit and in theta solvents, may not be universal constants. That is, the proportionality constants may vary with polymer and solvent species. Discrepancies between theory and experiment are discussed for the two different systems, dilute chains and semidilute rods. Speculation is offered on the resolution of these difficulties.     

Copolymerization of Ethylene with 1,9‐Decadiene: Part II—Prediction of Molecular Weight Distributions

In the present work, adaptive orthogonal collocation and a Monte Carlo method are used to compute the molecular weight distributions (MWD) of ethylene/1,9‐decadiene copolymers produced with a constrained geometry catalyst. Predictions from each model are compared to each other and to the experimental MWDs, allowing for the evaluation of relative strengths and weaknesses of each mathematical modeling method. Comparisons with experimental results indicate that the rate of macromonomer incorporation in the growing polymer chains decays with the macromonomer radius of gyration. In all cases, the proposed models are able to fit appropriately the available experimental MWDs.     

Mean-square radius of gyration of polymer chains

The calculations of the mean-square radius of gyration for more than thirty sorts of polymer chains are reviewed on the basis of a unified approach. A general expression of the mean-square radius of gyration was developed for polymer chains with side groups and/or heteroatoms. It consists of two parts. The first part is the mean-square radius of gyration of a model chain, in which every side group, R, was considered to be located in the centroid of the substituent flanking the related skeletal atom, and the second one is the total contribution of the square radius of gyration of every substituent around its centroid. Numerical calculations showed that the logarithmic relationship between the mean-square radius of gyration and the degree of polymerization becomes linear when x is greater than 100, and the dependence of the mean-square radius of gyration on the molecular weight can be expressed by the general formula 〈S²〉 = aM^b, which was supported by a number of experimental measurements. A comparison of our expression for the mean-square radius of gyration with that reported by Flory was made. The difference is obvious in the range of lower molecular weight, and gradually declines with increasing degree of polymerization.     

How does solvent molecular size affect the microscopic structure in polymer solutions?

Monte Carlo simulation has been used to investigate the effects of linear solvent molecular size on polymer chain conformation in solutions. Increasing the solvent molecular size leads to shrinkage of the polymer chains and increase of the critical overlap concentrations. The root-mean-square radius of gyration of polymer chains (R(g)) is less sensitive to the variation of polymer concentration in solutions of larger solvent molecules. In addition, the dependency of R(g) on polymer concentration under normal solvent conditions and solvent molecular size is in good agreement with scaling laws. When the solvent molecular size approaches the ideal end-to-end distance of the polymer chain, an extra aggregation of polymer chains occurs, and the solvent becomes the so-called medium-sized solvent. When the size of solvent molecules is smaller than the medium size, the polymer chains are swollen or partially swollen. However, when the size of solvent molecules is larger than the medium size, the polymer coils shrink and segregate, enwrapped by the large solvent molecules.     

Effect of molecular weight on conformational characteristics of poly(3‐hexyl thiophene)

This research focused on the effect of molecular weight and investigated the conformational characteristics of poly(3‐hexyl thiophene) (P3HT). An integrated system consisting of a gel permeation chromatograph, a static light scattering unit, and a viscometer was used for the study. It also estimated the radius of gyration (R_g) values of unsubstituted poly(thiophene) (PT) chains computationally using rotational‐isomeric‐states modeling and compared them with the experimental data for P3HT. In the low molecular weight region (20,000 to 30,000), both chains had nearly the same R_g values, meaning that the effect of side‐chains is limited. At higher molecular weights, the P3HT chains expanded more than the PT chains. In the molecular weight region from 20,000 to 60,000, both characteristic ratio and persistence length showed considerable molecular weight dependence. Beyond a molecular weight of 60,000, the molecular weight dependence decreased, and these parameters approached constant values, 16 and 3 nm, respectively. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2017 , 55, 1273–1277     

Photoinduced controlled/living free‐radical polymerization of 4‐methacryloyl‐1,2,2,6,6‐pentamethyl‐piperidenyl

The photoinduced solution polymerization of 4‐methacryloyl‐1,2,2,6,6‐pentamethyl‐piperidinyl (MPMP), used as a reactive hindered amine piperidinol derivative, was performed. The obtained MPMP homopolymer had a very narrow molecular weight distribution (1.06–1.39) according to gel permeation chromatography. The number‐average and weight‐average molecular weights increased linearly with the monomer conversion, this being characteristic of controlled/living free‐radical polymerizations. Electron spin resonance signals were detected in the MPMP homopolymer and in a polymer mixture solution, and they were assigned to nitroxide radicals, which were bound to the polymer chains and persisted at a level of 10^?9 mol/L during the polymerization. Instead of the addition of mediated nitroxide radicals such as 2,2,6,6‐tetramethyl‐piperidinyl‐1‐oxy (TEMPO), those radicals (>N? O ·) were formed in situ during the photopolymerization of MPMP, and so the reaction mechanism was understood as being similar to that of TEMPO‐mediated controlled/living free‐radical polymerization. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 2659–2665, 2004     

Exfoliation of a stack of platelets and intercalation of polymer chains: Effects of molecular weight,entanglement, and interaction with the polymer matrix

Exfoliation of a stack of sheets (a model for clay platelets) in a dynamic matrix of polymer chains is investigated by a computer simulation model. How the interplay between the thermodynamics (interaction-driven) and conformational (structural constraints) entropy affects the exfoliation of sheets is the subject of this study. A stack of four sheets with a small initial interlayer distance constitutes the layer on a discrete lattice. The layered platelets are immersed in a matrix represented by the mobile polymer chains which occupy a fraction (concentration) of the lattice sites. Both sheets and chains are modeled by the bond-fluctuation mechanism and execute their stochastic motion via Metropolis algorithm. An attractive and a repulsive interaction between the polymer matrix and platelets are considered. Exfoliation of the sheets is examined by varying the molecular weight of the polymer chains forming a dynamic network matrix with various degrees of entanglements. At low-molecular weight of the polymer, exfoliation is achieved with repulsive interaction and the exfoliation is suppressed with attractive matrix as sheets stick together via polymer mediated interaction introduced by intercalated polymer chains. Increasing the molecular weight of the polymer matrix suppresses the exfoliation of sheets primarily due to enhanced entanglement—at high-molecular weight (with the radius of gyration of polymer chains larger than the characteristic linear dimension of the platelets), the stacked (layered) morphology is arrested via entropic trapping and exfoliation ceases to occur. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 2696–2710, 2008     

Monte Carlo simulation on rate enhancement of nitroxide‐mediated living free‐radical polymerization

Four rate enhancing cases of nitroxide‐mediated living free‐radical polymerizations are simulated by the Monte Carlo method to investigate the effects of parameters on kinetics and molecular weight distribution of the resulting polymers. In all cases the equilibrium between growing and dormant chains shifts in favor of the growing chains under corresponding reaction conditions. The polymerization rates are therefore increased substantially without much loss in control of molecular weight and distribution of the products. The optimization of rate‐enhancement in living free‐radical polymerization is also discussed.     

Pressure driven flow of polymer solutions in nanoscale slit pores

Polymer solutions subject to pressure driven flow and in nanoscale slit pores are systematically investigated using the dissipative particle dynamics approach. The authors investigated the effect of molecular weight, polymer concentration, and flow rate on the profiles across the channel of the fluid and polymer velocities, polymer density, and the three components of the polymers radius of gyration. They found that the mean streaming fluid velocity decreases as the polymer molecular weight and/or polymer concentration is increased, and that the deviation of the velocity profile from the parabolic profile is accentuated with increase in polymer molecular weight or concentration. They also found that the distribution of polymers conformation is highly anisotropic and nonuniform across the channel. The polymer density profile is also found to be nonuniform, exhibiting a local minimum in the center plane followed by two symmetric peaks. They found a migration of the polymer chains either from or toward the walls. For relatively long chains, as compared to the thickness of the slit, a migration toward the walls is observed. However, for relatively short chains, a migration away from the walls is observed.     

Kinetics of the reactions of OH radicals with 2‐methoxy‐6‐(trifluoromethyl)pyridine,diethylamine, and 1,1,3,3,3‐pentamethyldisiloxan‐1‐ol at 298 ± 2 K

Rate constants for the reactions of 2‐methoxy‐6‐(trifluoromethyl)pyridine, diethylamine, and 1,1,3,3,3‐pentamethyldisiloxan‐1‐ol with OH radicals have been measured at 298 ± 2 K using a relative rate method. The measured rate constants (cm³ molecule^?1 s^?1) are (1.54 ± 0.21) × 10^?12 for 2‐methoxy‐6‐(trifluoromethyl)pyridine, (1.19 ± 0.25) × 10^?10 for diethylamine, and (1.76 ± 0.38) × 10^?12 for 1,1,3,3,3‐pentamethyldisiloxan‐1‐ol, where the indicated errors are the estimated overall uncertainties including those in the rate constants for the reference compounds. No reaction of 2‐methoxy‐6‐(trifluoromethyl)pyridine with gaseous nitric acid was observed, and an upper limit to the rate constant for the reaction of 1,1,3,3,3‐pentamethyldisiloxan‐1‐ol with O₃ of <7 × 10^{? 20} cm³ molecule^?1 s^?1 was determined. Using a 12‐h average daytime OH radical concentration of 2 × 10⁶ molecule cm^?3, the lifetimes of the volatile organic compounds studied here with respect to reaction with OH radicals are 7.5 days for 2‐methoxy‐6‐(trifluoromethyl)pyridine, 1.2 h for diethylamine, and 6.6 days for 1,1,3,3,3‐pentamethyldisiloxan‐1‐ol. Likely reaction mechanisms are discussed. © 2011 Wiley Periodicals, Inc. Int J Chem Kinet 43: 631–638, 2011     

Free‐radical trapping in the precipitation polymerization of acrylamide

Electron spin resonance spectroscopy revealed that some free radicals were trapped in the precipitated polymer during the precipitation polymerization of acrylamide conducted in nonsolvents of the polymer [t‐butyl alcohol (TBA), acetone and methanol]. The trapped radical concentration decreased with an increase in the chain‐transfer activity of the aforementioned liquids. A 100% polymerized acrylamide in TBA prepared with a 10% monomer concentration and a 3 × 10^?3 mol/dm³ azobisisobutyronitrile concentration at 50 °C contained approximately 2 radicals per 100 polymer molecules. The trapped radicals on exposure to air decayed with time according to second‐order kinetics. The rate constant was evaluated and found to be in reasonably good agreement with the rate constant evaluated from data published long ago for the decay of trapped polyacrylonitrile radicals following their exposure to air. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 1192–1197, 2003