Two tube models of rubber elasticity

Polymer entanglements lead to complicated topological constraints and interactions between neighboring chains in a dense solution or melt. Entanglements can be treated in a mean field approach, within the famous reptation model, since they effectively confine each individual chain in a tube-like geometry. In polymer networks, due to crosslinks preventing the global reptation and constraint release, entanglements acquire a different topological meaning and have a much stronger effect on the resulting mechanical response. In this article we discuss two different models of rubber elasticity, both utilizing the reptation ideas. First, we apply the classical ideas of reptation statistics to calculate the effective rubber-elastic free energy of an entangled rubbery network. In the second approach, we examine the classical Rouse dynamics of chains with quenched constraints at their ends by crosslinks, and along the primitive path by entanglements. We then proceed to average a microscopic stress tensor for the network system and present it in a manageable form in the equilibrium t → ∞ limit. Particular attention is paid to the treatment of compressibility and hydrostatic pressure in a sample with open boundaries. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 2679–2697, 2006     

Poly(acrylonitrile) ultrafiltration membranes. I. Polymer‐salt‐solvent interactions

Fourier transform infrared spectroscopy was used to study the interactions among LiCl, ZnCl₂, and AlCl₃ with N,N‐dimethylformamide (DMF) and poly(acrylonitrile) (PAN). It was observed that all three salts complex with DMF as well as PAN. The strength of the cation interaction with the >C?O oxygen of DMF was found to be higher than that with the ? CN group of PAN. The >C?O stretching frequency of DMF with ZnCl₂ was red shifted, indicating stronger complex formation compared with other two cations. With the addition of salt, the salt–DMF pseudo solvent was found to become a θ solvent for PAN compared with neat DMF. This change in PAN solvation power was primarily the result of DMF–salt complexation. As a result of the complexation, Mark‐Houwink constant a, was found to reduce from 0.75 (for pure DMF) to ～0.6 for DMF–salt solvents, indicating decreased PAN chain expansion. Comparison of intrinsic viscosity [η] values indicated that addition of salts to PAN–DMF solutions resulted in: (i) decrease in the DMF solvation power, which causes less expanded polymer coils, and (ii) increased interpolymer chain entanglements via salt‐promoted chain association. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 2061–2073, 2005     

On microphase segregation of interpenetrating polymer networks

The topological entanglements between subchains of two interpenetrating polymer networks are described in the simplest approximation supposing that the primitive path of each subchain is influenced due to the shift of one network relatively to the other. The entanglement contribution to the free energy of the networks is shown to behave as 1/q² for the state with deviation from uniform densities with the wave vector of order q. This contribution is shown to cause the microphase type of segregation.     

Relating fracture energy to entanglements at partially miscible polymer interfaces

A new model has been developed to calculate the areal chain density of entanglements (Σ_eff) at partially miscible polymer–polymer interfaces. The model for Σ_eff is based on a stochastic approach that considers the miscibility of the system. The values agree between Σ_eff calculated from the model and literature values for the reinforced interfaces. Using Σ_eff calculated from the model, the interfacial width, and the average distance between entanglements, an equation for the fracture energy of nonreinforced polymer interfaces is proposed. This equation is used to model the transition from chain pullout to crazing. As a function of system miscibility, the model for Σ_eff also accurately predicts a maximum in mode I fracture energy (G_c) as a result of the transition from gradient‐driven to miscibility‐limited interdiffusion, which is observed experimentally. As Σ_eff increases, the fracture energy increases accordingly. Compared with a recent model developed by Brown, the new model correctly predicts a reduced G_c (attributed to chain pullout) when the interfacial width is less than the average distance between entanglements. Theoretical predictions of the change in fracture energy with respect to interfacial width agree with the experimental measurements. Finally, it is postulated that the use of a miscibility criterion for G_c may reveal the universal nature of the pullout to crazing transition. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 2292–2302, 2002     

Synthesis of a thermoresponsive shell‐crosslinked 3‐layer onion‐like polymer particle with a hyperbranched polyglycerol core

A novel thermoresponsive shell crosslinked three‐layer onion‐like polymer particles were prepared using hyperbranched polyglycerol (PG) as parents compound, the periphery hydroxyl groups of PG were transformed into trithiocarbonates (? SC(S)S? ) first; then, it was used as chain transfer agent to prepare star‐like block copolymer of N‐isopropyl acrylamide (NIPA) and N,N‐dimethylaminoethyl acrylate (DMA) in sequence via reversible addition fragmentation chain transfer (RAFT) process. Thus, a three‐layer polymer, PG? [SC(S)S? (DMA)? b? (NIPA)]_n, was obtained. The middle layer of poly(DMA) was then crosslinked with 1,8‐diiodoctane, and the resulting onion‐like three‐layer polymer showed a lower critical solution temperature (LCST) in water because of the outer layer of poly(NIPA). The LCST value only slightly depended on the crosslinking degree. Finally, the ? SC(S)S? were transformed into thiols by sequential treating with sodium borohydride and formic acid; thus, the core molecule was chemically detached from the crosslinked shell and a novel shell crosslinked polymer particle was obtained. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 5652–5660, 2005     

Critical properties of thin films of polymer solutions

The critical properties of polymer solutions confined in thin‐film environments is studied with simple scaling arguments and a molecular theory. For purely repulsive surfaces, the critical volume fraction is a universal function of x = N^1/2/L, where N is the chain length and L is the film thickness. The critical volume fraction is nonmonotonic in x and shows a deep minimum at a film thickness several times larger than the chain's radius of gyration. This nonmonotonic behavior results from the interplay between the surface–polymer entropic repulsion and the tendency of the film to avoid large density gradients. The critical temperature is a monotonically increasing function of L, as L goes from the two‐dimensional limit to the three‐dimensional limit. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 1849–1853, 2005     

Viscoelasticity and self-diffusion in melts of entangled asymmetric star polymers

The crossover from linear to branched polymer dynamics in highly entangled melts was investigated with a series of asymmetric three-arm stars of poly(ethylene-alt-propylene). Two arms of equal length formed a linear backbone, kept constant through the series, while branches of various length were appended as the third arm. The materials were made by carbanionic polymerization of isoprene and the judicious application of chlorosilane linking chemistry. Subsequent saturation of the polymeric double bonds with deuterium and hydrogen, followed by fractionation, led to a set of structurally matched, nearly monodisperse pairs of deuterium-labeled and fully hydrogenous samples. Dynamic moduli were measured over wide ranges of frequency and temperature. With increasing branch length, the resulting master curves evolve smoothly, but with surprising rapidity, from the relatively narrow terminal spectrum of linear polymers to the much broader spectrum of symmetric stars. The viscosity η_o increases rapidly with branch length, and the diffusion coefficient D, obtained by forward recoil spectrometry, decreases even more rapidly. The product η_oD, however, distinguishes the transition from linear to branched polymer dynamics most clearly: for a backbone with about 38 entanglements, the crossover is already approaching completion for a single mid-backbone branch with only about three entanglements. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 1943–1954, 1997     

Flexibility transitions and looped adsorption of wormlike chains

When deposited from a solution onto a surface, superpolymeric chains display revealing transitions in their apparent stiffness. With simulated chains in adsorption, we varied the backbone rigidity and measured the chain persistence length (l_Pads). As the three‐dimensional persistence length (l_P3) increases toward the contour length, a transition can be seen from l_Pads = l_P2 (i.e., the two‐dimensional persistence length) to l_Pads = l_P3. Looped conformations decrease in frequency with a distinct nonlinear dependence. Finally, comparisons with experiments on polymeric worm micelles and purified neurofilaments demonstrate a simple new method for assessing the flexibility of these novel superpolymers. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 280–286, 2005     

Self‐entanglement of a single polymer chain confined in a cubic box

We study the self‐entanglement of a single linear polymer chain with N monomers confined to a cubic box (L × L × L) using the bond‐fluctuation lattice model and primitive path analysis. We probe chains with N between 30 and 750 and vary the degree of confinement L/R_g0 between 0.4 and 12, where R_g0 is the radius of gyration of an unconfined polymer. We find that the conformational properties R_g/R_g0 and L_p/R_g0, where L_p is the average primitive path length, collapse onto a single master curve as a function of the degree of confinement. In the strongly confined regime, L/R_g0 < 1, we find that R_g/R_g0 ～ (L/R_g0)^0.8 and (L_p/R_g0) ～ (L/R_g0)^?2. We verify that the simulation methodology used is quantitatively consistent with experimental data, and the Colby‐Rubinstein entanglement model for unconfined concentrated polymer solutions. The most significant difference between unconfined and confined systems is the variation of L_p with monomer density ?; L_p ～ ?^5/9, in the former, and L_p ～ ?^2/3, in the latter. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2014 , 52, 1283–1290     

N‐chloro amides,lactams, carbamates,and imides. New classes of initiators for the metal‐catalyzed living radical polymerization of methacrylates

Metal‐catalyzed living radical polymerization of methyl methacrylate initiated with N‐chloro amides (N‐chloro N‐ethyl propionamide, N‐chloro benzanilide, N‐chloro methylbenzamide, and N‐chloro acetanilide), lactams (N‐chloro caprolactam and N‐chloro 2‐pyrrolidinone), carbamates or urethanes (N‐chloro ethylcarbamate or N‐chlorourethane), imides (N‐chloro phtalimide, N‐chloro succinimide, trichloroisocyanuric acid, and N‐chloro saccharin) and catalyzed with the self‐regulated catalytic system Cu₂S/2,2′‐bipyridine is reported. The initiation efficiency of these initiators is determined by their structure. Regardless of the initiator efficiency, in all cases, poly (methyl methacrylate) with narrow molecular weight distribution and functionalized chain‐ends was obtained. These new classes of initiators open new strategies for the functionalization of polymer chain‐ends and for the synthesis of complex architectures by graft copolymerization initiated from N‐chloro proteins, aliphatic, aromatic and semiaromatic polyamides, and polyurethanes. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 5283–5299, 2005     

Stress relaxation under large step equibiaxial elongation for low‐density polyethylene

The stress relaxation under large step equibiaxial elongation for low‐density polyethylene with long‐chain branches revealed that the time‐strain separability holds in relaxation modulus G_B(t, ε_B), and damping function h_B(ε_B) exhibits weaker equibiaxial elongational strain ε_B dependence than that predicted by the Doi–Edwards theory without the independent alignment approximation. Dependencies of damping function h(γ) for step shear deformation and h_B(ε_B) on stretch ratio α of polymer contour length and orientation of a polymer chain in direction of the maximum orientation were evaluated, and it was found that the α dependencies of h(γ) and h_B(ε_B) are different, whereas dependencies of h(γ) and h_B(ε_B) on the orientation coincide fairly well. These results indicate that the damping is dominated by the chain orientation rather than α. This implies that withdrawal of long‐chain branches into tube of a backbone chain occurs when the orientation of the long‐chain branches is large and friction force against the branch point withdrawal is small. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 1275–1284, 2009     

Static and dynamic scaling behavior of a polymer melt model with triple-well bending potential

We perform molecular-dynamics simulations for polymer melts of the coarse-grained poly(vinyl alcohol) model that crystallizes upon slow cooling. To establish the properties of its high temperature, liquid state as a reference point, we characterize in detail the structural features of equilibrated polymer melts with chain lengths 5 ≤ N ≤ 1000 at a temperature slightly above their crystallization temperature. We find that the conformations of sufficiently long polymers with N > 50 obey essentially the Flory's ideality hypothesis. The chain length dependence of the end-to-end distance and the gyration radius follow the scaling predictions of ideal chains and the probability distributions of the end-to-end distance, and form factors are in good agreement with those of ideal chains. The intrachain correlations reveal evidences for incomplete screening of self-interactions. However, the observed deviations are small. Our results rule out any preordering or mesophase structure formation that are proposed as precursors of polymer crystallization in the melt. Moreover, we characterize in detail primitive paths of long entangled polymer melts and we examine scaling predictions of Rouse and the reptation theory for the mean squared displacement of monomers and polymers center of mass. © 2018 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2018 , 56, 1376–1392     

Synthesis and characterization of multifunctional polymers via atom transfer radical polymerization of N‐(ω′‐alkylcarbazolyl) methacrylates initiated by Ru(II) polypyridyl chromophores

A series of poly(N‐(ω′‐alkylcarbazoly) methacrylates) tris(bipyridine) Ru‐centered bifunctional polymers with good filming, thermal, and solubility properties were synthesized and characterized. Atom transfer radical polymerization (ATRP) of N‐(ω′‐alkylcarbazoly) methacrylates in solution was used, where Ru complexes with one and three initiating sites acted as metalloinitiators with NiBr₂(PPh₃)₂ as a catalyst. ATRP reaction conditions with respect to polymer molecular weights and polydispersity indices (PDI) of the target bifunctional polymers were examined. Electronic absorption and emission spectra of the resultant functional polymers provided evidence of chromophore presence within a single polymeric chain. The thermal properties of all polymers were also investigated by differential scanning calorimetry (DSC) and thermogravimetric analysis (TGA), and these analyses have indicated that these polymers possess higher thermal stabilities than poly(methyl methacrylate) (PMMA) obtained via free radical polymerization. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 6057–6072, 2005     

Dynamics of supramolecular associative polymer networks at the interplay of chain entanglement,transient chain association,and chain‐sticker clustering

The dynamic mechanical properties of supramolecular associative polymer networks depend on the average number of entanglements along the network‐forming chains, N_e, and on their content of associative groups, f . In addition, there may be further influence by aggregation of the associative groups into clusters, which, in turn, is influenced by the chemical structure of these groups, and again by N_e and f of the polymer. Therefore, the effects of these parameters are interdependent. To conceptually understand this interdependency, we study model networks in which (a) N_e, (b) f , and (c) the chemical structure of the associative groups are varied systematically. Each network is probed by rheology. The clustering of the associative groups is assessed by analyzing the rheological data at the end range of frequency covered and by comparison of the number of supramolecular network junctions with the maximum possible number of binary transient bonds. We find that if the total number of the network junctions, which can be formed either by interchain entanglement or by interchain transient associations, is greater than a threshold of 13, then the likelihood of cluster formation is high and the dynamics of supramolecular associative polymer networks is mainly controlled by this phenomenon. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019 , 57, 1209–1223     

Synthesis of novel crosslinkable polymers by atom transfer radical polymerization of cardanyl acrylate

In this work, the successful application of atom transfer radical polymerization (ATRP) to cardanyl acrylate, a polymerizable monomer derived from a renewable resource cardanol, is reported. Polycardanyl acrylate and poly(methylmethacrylate)‐cardanyl acrylate copolymers were prepared in bulk ATRP, using Copper(I) bromide/N, N, N′, N′, N″‐pentamethyl diethylene triamine (PMDETA) catalyst system at 95 °C in combination with ethyl‐2‐bromo isobutyrate initiator. The copolymers had mol. wt. (M_n) in the range 8300–2400 g/mol and polydispersity index (PDI) 1.27–2.00, depending upon the [M]₀/[I]₀ ratio. ¹H NMR analysis of the copolymer showed that unsaturation in the side chain of cardanyl acrylate is unaffected under the conditions of ATRP. This was further confirmed by studying the curing reaction of polycardanyl acrylate by supported dynamic mechanical thermal analysis (DMTA) in dual cantilever mode. The thermogravimetric analysis shows that the copolymers have improved thermal stability, by about 35 °C, in comparison with pure PMMA. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 5953–5961, 2005     

Circular dichroism induced by the helical conformations of acylated chitosan derivatives bearing cinnamate chromophores

Through regioselective modifications, some acylated chitosan derivatives, O‐cinnamoyl chitosans with degree of substitution (DS) varying from 0.8 to 2.0 and N‐fatty acyl‐O‐dicinnamoyl chitosans with different fatty acyl chain lengths (C₂–C₁₂), were prepared, and their chiroptical properties in dilute solutions were investigated by circular dichroism (CD). Exciton coupling between two vicinal cinnamoyl chromophores appended to the helical mainchains gave rise to bisignate Cotton effects (CEs), which were used to deduce the absolute sense of the twisting structures in solution phase. It was found that the absolute helicities vary with DS, length of the fatty chain, and solvent property, but are nearly independent of thermal stimulus. The molecular interactions (hydrogen bonding and hydrophobic interaction) involved possibly in the self‐assembled ordered structures were discussed. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 1354–1364, 2005     

Topologically entangled polymers

Summary The statistical mechanics of a ring polymer confined to a plane and entangled with many randomly placed thin rods perpendicular to the plane are considered. The entanglements are characterized by the Gauss linking number. If the statistics of the random distribution of the rods is given by only the second cumulant then it is shown that the resulting entanglement problem can be solved formally exactly. For this special case the exact solution becomes possible because the problem can be reduced to one involving the winding of the polymer around one infinitely thin rod. The exact solution can be obtained for both the annealed and the quenched random distribution of obstacles. The entanglement of the ring polymer around the obstacles leads to a repulsive topological potential which is an effective interaction between the polymer and the rods. The origin of this potential is solely due to the constraint that the winding number be conserved. It is shown that forR ²/Lll (R is the location of the polymer segment,L is the total length of the polymer, andl is the length of the monomer) the topological potential for the annealed random case goes asN ln ln(Ll/R ²) whereN is the number of obstacles whereas for the quenched random case the potential is given byC lnLl/R ², whereC is a numerical constant that depends onN.     

Development of Entanglements in a Fully Disentangled Polymer Melt

A long‐lived metastable “new melt” state of polymers has been recently reported, where monomers exhibit different mobilities due to an unusual distribution of entanglements. We study the relaxation of (fully disentangled) globules to the entangled state by means of computer simulations, and compare our data to the scenario of de Gennes' explosion upon melting. The entanglement length N_e is measured using the primitive path analysis method. The results show that in the case of relatively short chains (N ≈ 20N_e), the relaxation of the entanglement length is very fast compared to that of the chains' size which slows down as the chain length N exceeds the equilibrium value of N_e.

     

Preparation of thermoresponsive polymers bearing amino acid diamide derivatives via RAFT polymerization

We report here the synthesis of well‐defined homopolymer bearing amino acid diamide, poly(N‐acryloyl‐L ‐valine N′‐methylamide), via reversible addition fragmentation chain transfer (RAFT) polymerization using alkynyl‐functionalized 2‐dodecylsulfanylthiocarbonylsulfanyl‐2‐methyl‐propionic acid propargyl alcohol ester as chain transfer agent (CTA) and 2,2′‐azobis(isobutyronitrile) as initiator. The effects of a variety of parameters, such as temperature and solvent, on RAFT polymerization were examined to determine the optimal control of the polymerization. The controlled nature of RAFT polymerization was evidenced by the controllable molecular weight and low‐molecular‐weight polydispersity index (M_w/M_n) of resulting homopolymers and further demonstrated to have retained end‐group functionality by the fact of the successful formation of block copolymers from further RAFT polymerization by using the resultant polymer as macro‐CTA, as well as from “click” chemistry. Thermoresponsive property of the prepared polymer was evaluated in terms of the lower critical solution temperature in aqueous solution by measuring the transmittance variation at 500 nm from UV/vis spectroscopy. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 48: 3573–3586, 2010     

Dynamics response of polyethylene polymer nanocomposites to shock wave loading

The shock response of polyethylene polymer modified by nanoparticles (NP) is investigated using a coarse‐grained molecular dynamics simulation. The u_s‐u_p Hugoniot analysis yields a linear relationship under the range of particle velocity investigated, in agreement with previous simulation and experimental results. NP addition improves the mechanical properties of the composites, as reflected by the increased Young's modulus and yield strength especially in the case of shorter chain length of polymer. This is directly related to the increased shock impedance with NP volume fraction, as demonstrated by the enhanced pressure in the shocked state, slightly reduced microscopic deformation, and increased shock velocity. The layered structure with alternate soft and hard regions, with NP addition only in the hard regions, leads to significantly enhanced microscopic deformation in the soft regions. It is also important that the shock impedance difference between the soft and hard region to be large enough to facilitate the energy absorption through plastic deformation in the soft regions. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 1292–1302