The influence of variant PE‐b‐PEO segments on physical properties of LLDPE graft copolymers

A method was adopted to fix a series of polymers of PE‐b‐PEO with different PEO/PE segments on the chains of LLDPE. Maleic anhydride (MA) reacting with hydroxyl group of PE‐b‐PEO (mPE‐b‐PEO) was used as the intermediate. The structures of intermediates and graft copolymers were approved by ¹H NMR and FTIR. XPS analysis revealed a great amount of oxygen on the surface of grafted copolymers although the end group of PEO was fixed on the LLDPE chains through MA. Thermal properties of the graft copolymers as determined by differential scanning calorimetry (DSC) showed that PE segments in the grafted monomers could promote the heterogeneous nucleation of the polymer, increase T_c, and crystal growth rate. While the amorphous PEO segments which attached to the crystalline PE segments in LLDPE, impaired their ability to fit the crystal lattice, and depressed the crystallization of LLDPE backbones. In this study, it was also verified through the dynamic rheological data that increasing M_n of grafted monomers significantly increased the complex viscosity and enhanced the shear‐thinning behavior. Long‐branched chains formed by grafted monomers enhanced the complex moduli (G′ and G″) value and retarded relaxation rate. However, there were little influence on the rheological properties when increasing the amounts of PEO segments (or decreasing PE segments) of grafted monomers with similar molecular weight. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 506–515, 2008     

Self‐diffusion coefficient of ring polymers in semidilute solution

In a topologically constraining environment the size of a flexible nonconcatenated ring polymer (macrocycles) and its dynamics are known to differ from that of linear polymers. Hence, the diffusion coefficient of ring polymers can be expected to be different from linear chains. We present here scaling arguments for the concentration and molecular weight dependence of self‐diffusion coefficient of ring polymers in semidilute solutions, and show that contrary to expectations these scaling relations are identical to what is known for linear polymers. At higher concentrations excluded volume interactions arising from possibilities of segmental overlap can become effective for large ring polymers. In this regime the diffusion coefficient of large ring polymers shows a relatively weaker dependence on concentration and molecular weight. ©2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 2370–2379, 2008     

Polyisobutylene: A most unusual polymer

The influence of molecular weight, M, on the fragility and fast dynamics in polyisobutylene (PIB) was studied using dielectric and mechanical relaxation spectroscopies, calorimetry, and Raman spectroscopy. The measurements indicate a decrease in fragility with increasing M for shorter chains, in the range of M where T_g is M‐dependent. Such behavior is not observed for other polymers and is at odds with traditional theoretical models that predict an increase in fragility with chain length. These results confirm the unusual character of PIB, as evident in various properties including extremely low gas permeability, a low fragility, and a segmental relaxation spectrum much broader than expected for a low‐fragility material. The reason for this anomalous behavior remains unclear, but might be related to the symmetric structure of the PIB repeat unit, together with comparable flexibility of both structural components, the backbone and side groups. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 1390–1399, 2008     

Coil‐stretch transition in deformation flows

We present a novel Monte‐Carlo lattice model for the study of the coil‐stretch transition for polymer chains in deformation flows. Our results indicate that elongational flows are much more effective than shear flows in stretching polymer chains, in full agreement with experimental observation. Our model data also show that the ε˙_c∼M^−1.5 powerlaw observed experimentally for the dependence of critical flow rate on polymer molecular weight can be fully explained through a nonuniform stretching of the chain by the flow. A higher powerlaw exponent is predicted in more affine deformation cases. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 2422–2428, 2000     

Monte Carlo study of the coil-to-globule transition of a model polymeric system

Monte Carlo computer simulations of single, flexible, self-avoiding chains on a cubic lattice have been performed upon conditions of increasing segment–segment cohesive energy (deteriorating solvent quality). The simulations spanned a wide range of chain lengths (20–10,000, i.e., up to molecular weights of a few millions) and cohesive energies (0.0–0.45k_BT, i.e., from athermal to very poor solvents). The chain length dependence of the chain size in poor solvents was characterized by a wide plateau of almost null growth for intermediate chain lengths. This plateau was linked to the development of the incipient constant density core, while genuine power law dependence (1/3) was not reached even for the longest chains and poorest solvents simulated here. The mere appearance of a core required substantial chain lengths (higher than 1000; molecular weights of a few hundred thousands), while short chains underwent a gradual densification devoid of any qualitative changes in the density distribution. Sufficiently long chains became more but not quite spherical and underwent a reasonably sharp second order phase transition. The findings were generally in agreement with predictions of mean-field theory and with the use of the standard scaling variables, despite slight inconsistencies. Nevertheless, the results stress the fact that short chains never form a constant density core and that core-dominance on the globule's properties (“volume approximation”) is only valid for extraordinarily long chains [molecular weight of O(10⁹)], an effect linked to the relatively diffuse nature of the surface layer and originating from chain connectivity in conjunction with spherical geometry. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 3651–3666, 2006     

Chain dynamics in entangled polymers: Diffusion versus rheology and their comparison

This review article scrutinizes and reanalyzes the extensively available literature data on the tracer and self chain diffusion coefficients D_tr and D_s along with the corresponding zero‐shear viscosity η₀ to show that D_s ∝ M^?ν starts with ν > 2.0 and converges to the asymptotic scaling exhibited by D_tr ∝ M^?2.0 as the molecular weight M increases beyond M/M_e = 10–20, in contrast to the onset of the asymptotic scaling M³ for η₀ taking place typically for M/M_e ? 10–20. A coherent analysis of these observations leads to the suggestion that the observed crossover in D_s is due to the constraint release effect, which diminishes around M/M_e = 10–20 and is negligible in measurements of D_tr when the matrix molecular weight P is much greater than M. The contour length fluctuation (CLF) effect, which is believed to cause the molecular weight scaling of η₀ to deviate significantly from its limiting behavior of M³, has little direct influence on the chain diffusion. The absence of the CLF effect on D_s leads to a much stronger than linear dependence of the product η₀D_s on M, which has been observed previously. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 1589–1604, 2003     

Grafting by in situ coupling of epoxy groups of a living copolymer with an anionic living polymer

A tetrahydrofuran (THF) solution of the living random copolymer of methyl methacrylate (MMA) and glycidyl methacrylate (GMA) was prepared by the living anionic copolymerization of the two monomers, using 1,1‐diphenylhexyllithium (DPHLi) as initiator, in the presence of LiCl ([LiCl]/[DPHLi]₀ = 3), at −50°C. The copolymer thus obtained has a controlled composition and molecular weight and a narrow molecular weight distribution. By introduction of an anionic living polystyrene (poly(St)) or anionic living polyisoprene (poly(Is)) solution into the above system at −30°C, a coupling reaction took place and a graft copolymer with a polar backbone and nonpolar side chains was produced. The solvent used in the preparation of the living poly(St) or poly(Is) affects the coupling reaction. When benzene was the solvent, a graft copolymer of high purity, controlled graft number and molecular weight, and narrow molecular weight distribution (M_w/M_n = 1.11–1.21) was obtained. In the coupling reaction, the living poly(St) reacted only with the epoxy groups and not with the carbonyls of the backbone polymer. © 1999 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 37: 105–112, 1999     

A successive route to amphiphilic graft copolymers with a hydrophilic poly(3‐hydroxypropyl methacrylate) backbone and hydrophobic polystyrene side chains

A successive method for preparing novel amphiphilic graft copolymers with a hydrophilic backbone and hydrophobic side chains was developed. An anionic copolymerization of two bifunctional monomers, namely, allyl methacrylate (AMA) and a small amount of glycidyl methacrylate (GMA), was carried out in tetrahydrofuran (THF) with 1,1‐diphenylhexyllithium (DPHL) as the initiator in the presence of LiCl ([LiCl]/[DPHL]₀ = 2), at −50 °C. The copolymer poly(AMA‐co‐GMA) thus obtained possessed a controlled molecular weight and a narrow molecular weight distribution (M_w /M_n = 1.08–1.17). Without termination and polymer separation, a coupling reaction between the epoxy groups of this copolymer and anionic living polystyrene [poly(St)] at −40 °C generated a graft copolymer with a poly(AMA‐co‐GMA) backbone and poly(St) side chains. This graft copolymer was free of its precursors, and its molecular weight as well as its composition could be well controlled. To the completed coupling reaction solution, a THF solution of 9‐borabicyclo[3.3.1]nonane was added, and this was followed by the addition of sodium hydroxide and hydrogen peroxide. This hydroboration changed the AMA units of the backbone to 3‐hydroxypropyl methacrylate, and an amphiphilic graft copolymer with a hydrophilic poly(3‐hydroxypropyl methacrylate) backbone and hydrophobic poly(St) side chains was obtained. © 2000 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 38: 1195–1202, 2000     

Rouse's dynamics of networks with pendant chains

A model to describe the dynamics of networks with linear pendant chains has been formulated based on the properties of ensembles of micronetworks, using the Rouse model. This development indicates that the terminal relaxation time of pendant chains with relatively large molecular weight scales with the square of the molecular weight of those chains. On the other hand, when the molecular weight of pendant and elastically active chains are comparable, a nearly exponential growth of the terminal relaxation time with the molecular weight is predicted. The main predictions of the model are compared with experimental results of model poly(dimethyl siloxane) (PDMS) networks, with controlled amounts of linear pendant chains of known molecular weight. The terminal relaxation time of these networks was estimated from the values of the loss modulus G″(ω) measured experimentally. An exponential dependence on the molecular weight of pendant chains was derived for the terminal relaxation time. This behavior is in good agreement with the predictions of our model for micronetworks, provided that the friction coefficient scales linearly with the number of entanglements. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 1121–1130, 1999     

An experimental investigation on the evolution of the molecular weight distribution in styrene emulsion polymerization

Styrene ab initio emulsion polymerizations were conducted at 70°C in an automated reaction calorimeter. Two polymerizations were performed, one above and the other below the critical micelle concentration (CMC) of the surfactant, thus ensuring differing polymerization kinetics between the two: the system below the CMC gave large particles that were expected to follow pseudobulk kinetics, while that above the CMC gave small particles that were expected to follow zero-one kinetics. The evolutions of the molecular weight distributions (MWDs) were characterized by removing samples periodically during the course of the reactions and analyzing with gel permeation chromatography. Interpretation of the data used average molecular weights, the GPC MWDs, and the number MWDs, as functions of conversion. It was found that all of the number MWDs (plotted as ln (number of polymer chains) vs. molecular weight of polymer chains) were concave-up at low molecular weights and become nearly linear at molecular weights (≥3−4 × 10⁶); this linearity is expected from theory. The slope of the high molecular weight region was consistent with theory for the dominant mode for chain stoppage: termination and transfer for the pseudobulk system and (predominantly) chain transfer to monomer for the zero-one system. The most likely explanation for the concavity of the number MWDs is a heterogeneity of radicals: some surface anchored with sulfate end groups and others (with hydrogen end groups arising from transfer to monomer and/or reentry) being more mobile. Thus, two types of termination are proposed: slow reaction-diffusion for the less mobile surface anchored chains, and rapid short-long (center of mass) termination for the more mobile hydrogen-terminated chains. © 1997 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 35: 989–1006, 1997     

Intercalation of solvent and polymer in galleries of mobile clay platelets by a Monte Carlo simulation

The intercalation of solvent particles and polymer chains of concentration C_w = 0.2 and C_p = 0.2, respectively, in a layer of (4) clay platelets is studied by a Monte Carlo simulation on a cubic lattice. Polymer chains and platelets are modeled by bond fluctuations. Besides the excluded volume, a set of polymer-clay (cs) and solvent-clay (ws) interactions with (i) cs = 1, ws = −2, (ii) cs = −2, ws = 1 and (iii) cs = ws = −2 are considered. The global dynamics of platelets is constrained due to the presence of three components, i.e., solvent, polymer, and platelets, which retain their interstitial spacing with well-defined galleries. Intercalation of solvent particles and polymer chains (low molecular weight) occurs with their attractive interaction with the platelets, which further reinforces the layered clay morphology. The density profiles of the solvent particles are similar to previous studies with platelets in a mobile solvent. The density profile of polymer chains differs considerably from the platelets in a polymer matrix alone, particularly with its attractive interaction (ii). For the same attractive interaction of solvent and polymer chains with the clay platelets (iii), the solvent particles (the smallest constituents) intercalate the fastest in the clay galleries, whereas the intercalation of polymer chains decreases with their molecular weight. The polymer density profiles, both longitudinal (x) and transverse (y), show maxima peaks around outer platelets (surface) of the layer and decay sharply both in the adjacent galleries and in the bulk. The amplitude of oscillation in the transverse density profiles, a measure of the degree of intercalation, decreases with increasing molecular weight of the polymer. The intercalation of the polymer is driven by its attractive interaction at the low molecular weight, but reduces considerably at high molecular weight because of both entanglement and larger radius of gyration. Variations of the gyration radius of the diffusing polymer chains with molecular weight and interaction with the clay are consistent with the results of their corresponding density profiles. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 2487–2500, 2009     

Tube dilation process in star‐branched cis‐polyisoprenes

In current tube models for entanglement, the tube representing the topological constraint is considered to move with time. This tube motion results in the constraint release (CR) as well as the dynamic tube dilation (DTD), and an importance of DTD has been argued for entangled star chains. Under these backgrounds, this article examines the validity of the DTD molecular picture for the star chains. For monodisperse star chains having noninverted type‐A (parallel) dipoles in respective arms, the normalized viscoelastic and dielectric relaxation functions μ(t) and Φ(t) were found to obey a relationship μ(t) ≅ [Φ(t)]² if the tube actually dilates in the time scale of the star relaxation. For 6‐arm star cis‐polyisoprene (PI) chains (having those type‐A dipoles), dielectric and viscoelastic measurements were conducted to test this DTD relationship. Both viscoelastic and dielectric properties exhibited characteristic behavior expected from DTD models (assuming the arm retraction in the dilating tube), the exponential increase of the relaxation time and broadening of the relaxation mode distribution with increasing arm molecular weight M_a. However, in the range of M_a examined, M_a ≤ 8M_e (M_e = entanglement spacing), the above DTD relationship was not valid for a dominant part of the slow relaxation (and the models failed in this sense). Thus, for star chains at least in this range of M_a, the simple DTD picture assuming very rapid CR motion (rapid equilibration in the dilated tube) did not explain the slow relaxation behavior of star chains. This result in turn suggested the importance of the CR motion in this behavior. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 1024–1036, 2000     

Living radical graft polymerization of methyl methacrylate to polyethylene film with typical and reverse atom transfer radical polymerization

Nickel‐mediated atom transfer radical polymerization (ATRP) and iron‐mediated reverse ATRP were applied to the living radical graft polymerization of methyl methacrylate onto solid high‐density polyethylene (HDPE) films modified with 2,2,2‐tribromoethanol and benzophenone, respectively. The number‐average molecular weight (M_n) of the free poly(methyl methacrylate) (PMMA) produced simultaneously during grafting grew with the monomer conversion. The weight‐average molecular weight/number‐average molecular weight ratio (M_w/M_n) was small (<1.4), indicating a controlled polymerization. The grafting ratio showed a linear relation with M_n of the free PMMA for both reaction systems. With the same characteristics assumed for both free and graft PMMA, the grafting was controlled, and the increase in grafting ratio was ascribed to the growing chain length of the graft PMMA. In fact, M_n and M_w/M_n of the grafted PMMA chains cleaved from the polyethylene substrate were only slightly larger than those of the free PMMA chains, and this was confirmed in the system of nickel‐mediated ATRP. An appropriate period of UV preirradiation controlled the amount of initiation groups introduced to the HDPE film modified with benzophenone. The grafting ratio increased linearly with the preirradiation time. The graft polymerizations for both reaction systems proceeded in a controlled fashion. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 40: 3350–3359, 2002     

Mean‐Field Calculation of MZ for Randomly Branched Condensation Polymers

The mean‐field theory of Flory–Stockmayer for randomly branched polymers in the regime of strong chain overlap is extended to a calculation of M_Z via the recursive method of Miller and Macosko. The formalism includes condensation polymers, copolymers, chain stoppers, bifunctional diluents to control the chain length between branch points, multiple branching agents, and arbitrary stoichiometries. M_Z closely approximates the largest branched polymer in the system and is therefore a key parameter describing static scaling behavior near the gel point. Nonuniversal static scaling of M_Z is illustrated with examples from the literature. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019 , 57, 1415–1422     

Viscometric properties of dilute polystyrene/dioctyl phthalate solutions

We report viscometric data collected in a Couette rheometry on dilute, single‐solvent polystyrene (PS)/dioctyl phthalate (DOP) solutions over a variety of polymer molecular weights (5.5 × 10⁵ ≤ M_w ≤ 3.0 × 10⁶ Da) and system temperatures (288 K ≤ T ≤ 318 K). In view of the essential viscometric features, the current data may be classified into three categories: The first concerns all the investigated solutions at low shear rates, where the solution properties are found to agree excellently with the Zimm model predictions. The second includes all sample solutions, except for high‐molecular‐weight PS samples (M_w ≥ 2.0 × 10⁶ Da), where excellent time–temperature superposition is observed for the steady‐state polymer viscosity at constant polymer molecular weights. No similar superposition applies at a constant temperature but varied polymer molecular weights, however. The third appears to be characteristic of dilute high‐molecular‐weight polymer solutions, for which the effects of temperature on the viscosity curve are further complicated at high shear rates. The implications concerning the relative importance of hydrodynamic interactions, segmental interactions, and chain extensibility with increasing polymer molecular weight, system temperature, and shear rate are discussed. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 787–794, 2006     

Dynamics of Adsorbed Star‐Branched Polymer Chains: A Computer Simulation Study

The simple cubic‐lattice model of polymer chains was used to study the dynamic properties of adsorbed, branched polymers. The model star‐branched chains consisted of f = 3 arms of equal lengths. The chain was modeled with excluded volume, that is, in good solvent conditions. The only interaction assumed was a contact potential between polymer segments and an impenetrable surface. This potential was varied to cover both weak and strong adsorption regimes. The classical Metropolis sampling algorithm was used for models of star‐branched polymers in order to calculate the dynamic properties of adsorbed chains. It was shown that long‐time dynamics (diffusion constant) and short‐time dynamics (the longest relaxation time) were different for weak and strong adsorption. The diffusion of weakly adsorbed chains was found to be qualitatively the same as for free nonadsorbed chains, whereas strongly adsorbed chains behaved like two‐dimensional polymers. The time‐dependent properties of structural elements such as tails, loops, and trains were also determined.

The mean lifetimes of tails, loops, and trains versus the bead number for the chain with N = 799 beads for the case of the weak adsorption ε_a = −0.3.     

Synthesis of well‐defined aromatic polyesters by chain‐growth polycondensation under suppression of transesterification

For the synthesis of aromatic polyesters with defined molecular weights and narrow molecular weight distributions (MWDs), we investigated the chain‐growth polycondensation of active amide derivatives of 4‐hydroxybenzoic acid, 1a and 1b , having an octyl or 4,7‐dioxaoctyl side chain, respectively. To suppress the transesterification of the polymer backbone with the monomer, the polymerization of 1 was carried out in tetrahydrofuran (THF) at −30 °C in the presence of initiator 2 and Et₃SiH/CsF/18‐crown‐6, which generated a hydride ion as a base in situ. The number‐average molecular weight (M_n) of poly 1a was controlled, and narrow MWDs were maintained, until the [ 1a ]₀/[ 2 ]₀ feed ratio was 14.3 (M_n ≤ 3500), whereas that of poly 1b was controlled until the feed ratio was 30 (M_n ≤ 7250). The difference stemmed from the higher solubility of poly 1b in THF. This chain‐growth polycondensation was applied to the synthesis of a diblock copolyester of 1a and 1b of a defined architecture. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 4109–4117, 2005     

Scaling law of poly(ethylene oxide) chain permeation through a nanoporous wall

This paper presents a study of the permeation of poly(ethylene oxide) (PEO) chains through the nanoporous wall of hollow polymeric capsules prepared by self-assembly of polyelectrolytes. We employ the method of pulsed field gradient (PFG) NMR diffusion to distinguish chains in different sites, i.e., in the capsule interior and free chains in the dispersion, by their respective diffusion coefficient. From a variation of the observation time, the time scale of the molecular exchange between both sites and thus the permeation rate constant is extracted from a two-site exchange model. Permeation rate constants show two different regimes with a different dependence on chain length. This suggests a transition between two different mechanisms of permeation as the molecular weight is increased. In either regime, the permeation time can be described by a scaling law tau approximately N (b) , with b = (4)/ 3 for short chains and b = (1)/ 3 for long chains. We discuss these exponents, which clearly differ from the theoretical predictions for chain translocation.