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.     

Relaxation of entangled polymers in melts

The stress relaxation function of a monodisperse or polydisperse melt, and the corresponding viscosity, have been calculated in the entanglement domain by applying the Doi-Edwards theory which relies on the reptation concept introduced by P. G. de Gennes. Though the theory has been considered as successful, the agreement with precise experiments is only qualitative, and strong anomalies remained to be explained. A new theory is presented here: it is obtained by introducing simple approximations derived from elementary but novel considerations. This theory is shown to be in good agreement with experiments on monodisperse and polydisperse melts. In particular, it explains the well-known fact that the viscosity of a monodisperse polymer melt of molecular mass M seems to increase proportionally to M^3,4 when M is large.     

Full‐chain dynamics of entangled linear and star polymers

The full‐chain dynamics and the linear viscoelastic properties of monodisperse, entangled linear and star polymers are simulated consistently via an equilibrium stochastic algorithm, based on a recently proposed full‐chain reptation theory 1 that is able to treat self‐consistently mechanisms of chain reptation, chain‐length fluctuations, and constraint release. In particular, it is the first time that the full‐chain simulation for star polymers is performed without subjecting to the great simplifications usually made. To facilitate the study on linear viscoelasticity, we employ a constraint release mechanism that resembles the idea of tube dilation, in contrast to the one used earlier in simulating flows, where constraint release was performed in a fashion similar to double reptation. Predictions of the simulation are compared qualitatively and quantitatively with experiments, and excellent agreement is found for all investigated properties, which include the scaling laws for the zero‐shear‐rate viscosity and the steady‐state compliance as well as the stress relaxation and dynamic moduli, for both polymer systems. The simulation for linear polymers indicates that the full‐chain reptation theory considered is able to predict very well the rheology of monodisperse linear polymers under both linear viscoelastic and flow conditions. The simulation for star polymers, on the other hand, strongly implies that double reptation alone is insufficient, and other unexplored mechanisms that may further enhance stress relaxation of the tube segments near the star center seem crucial, in explaining the linear viscoelasticity of star polymers. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 248–261, 2000     

Linear and Nonlinear Viscoelasticity of a Model Unentangled Polymer Melt: Molecular Dynamics and Rouse Modes Analysis

Summary: Using molecular dynamics simulations, we determine the linear and nonlinear viscoelastic properties of a model polymer melt in the unentangled regime. Several approaches are compared for the computation of linear moduli and viscosity, including Green‐Kubo and nonequilibrium molecular dynamics (NEMD). An alternative approach, based on the use of the Rouse modes, is also discussed. This approach could be used to assess local viscoelastic properties in inhomogeneous systems. We also focus on the contributions of different interactions to the viscoelastic moduli and explain the microscopic mechanisms involved in the mechanical response of the melt to external solicitation.

     

Shear and extensional rheology of entangled polymer melts: Similarities and differences

This work extends our previous understanding concerning the nonlinear responses of entangled polymer solutions and melts to large external deformation in both simple shear and uniaxial extension. Many similarities have recently been identified for both step strain and startup continuous deformation, including elastic yielding, i.e., chain disentanglement after cessation of shear or extension, and emergence of a yield point during startup deformation that involves a deformation rate in excess of the dominant molecular relaxation rate. At a sufficiently high constant Hencky rate, uniaxial extension of an entangled melt is known to produce window-glass-like rupture. The present study provides evidence against the speculation that chain entanglements tie up into dead knots in constant-rate extension because of the exponentially growing chain stretching with time. In particular, it is shown that even Instron-style tensile stretching, i.e., extending a specimen by applying a constant velocity on both ends, results in rupture. Yet, in the same rate range, the same entangled melt only yields in simple shear, and the resulting shear banding is clearly not a characteristic of rupture. Thus, we conclude that chain entanglements respond to simple shear in the manner of yielding whereas uniaxial extension is rather effective in causing some entanglements to lock up, making it impossible for the entanglement network to yield at high rates.     

新型缠绕结构配位聚合物的合成及结构的研究

以2,6-H2ndc（2,6-H2ndc=naphthalene-2,6-dicarboxylic acid）,bipe[bipe=bis（4-imidazolphenoxy）ethane]为配体,在水热反应条件下,生成了1个新型缠绕配位聚合物[Co（2,6-ndc）（bipe）],并对其进行了元素分析、红外光谱（IR）、热重（TG）、粉末X射线衍射和X射线单晶衍射等表征.结构表征结果表明,该配位聚合物（4,4）-连接的sql网络,通过2D→2D平行→3D平行互穿的方式形成了三维的结构.     

Evaluation of free-volume theories for solvent self-diffusion in polymer–solvent systems

An evaluation of free-volume theories for solvent self-diffusion is carried out using recent comprehensive data sets for penetrant self-diffusion in polymer solutions. Different theories are compared, and free-volume theories in the prediction of penetrant self-diffusion coefficients in glassy polymer systems is also evaluated. © 1993 John Wiley & Sons, Inc.     

穿插和缠绕结构配位聚合物的合成与性能研究

配位聚合物由于具有独特的结构和优异的性能,近年来受到国内外的持续广泛关注,已成为当前化学、物理、材料、医学以及生命科学等领域的热点研究之一,并日益呈现出迅猛发展的良好势头.有关此类化合物的显著特征是:在合成时,其结构中经常发生不同程度的穿插和缠绕现象,使得合成目标化合物的性能产生根本上的改变.因此,本文主要结合本课题组近期的研究工作,评述了穿插和缠绕结构配位聚合物及其相关化合物的合成、结构与气体吸附分离性能应用等方面的研究进展.     

Concentration relationships of coefficients of self-diffusion and viscosity of the adsorbate in narrow slit-like pores

Concentration relationships of dynamic characteristics of the adsorbate (coefficients of self-diffusion and shear viscosity) in narrow slit-like pores with different widths were considered. These coefficients were calculated using the simplest molecular model (lattice-gas model), which takes into account the intrinsic volume of molecules and their interactions in the quasi-chemical approximation. The values of coefficients of self-diffusion and shear viscosity of the adsorbate depend strongly on the distance to the pore wall.     

Effects of slip on the viscosity of polymer melts

We use existing scaling theories by de Gennes, Brochard, and Ajdari to calculate the apparent viscosity of multilayer blends with weakly entangled interfaces. The lowering of the apparent viscosity with respect to the bulk is a manifestation of interfacial slip. The theoretical predictions are compared with the recent experimental data of Zhao and Macosko. The theory is able to describe a continuous transition from a low-slip regime to a high-slip regime when the bulk rheology is still Newtonian, in agreement with experiments. However, the dependence of the apparent viscosity on the shear rate and layer thicknesses is much stronger than what is observed experimentally. The apparent viscosity is also calculated for dilute polymer emulsions. We modify a theory of Palierne, which is valid in the linear viscoelastic regime for the bulk, to include the effects of interfacial slip. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 1888–1904, 2004     

Multiarm star polymers with POSS at the periphery

Azide end‐functionalized polyhedral oligomeric silsesquioxane (POSS‐N₃) was incorporated into the periphery of well‐defined alkyne‐polystyrene₅₀‐poly(divinyl benzene) (alkyne‐PS₅₀‐polyDVB) and alkyne‐poly(tert‐butyl acrylate)₄₃‐poly(divinyl benzene) (alkyne‐PtBA₄₃‐polyDVB) multiarm star polymers via highly efficient azide‐alkyne click reaction, resulting in POSS‐PS₅₀‐polyDVB and POSS‐PtBA₄₃‐polyDVB multiarm star block copolymers respectively, in the solution of tetrahydrofuran/N,N‐dimethyl formamide, CuBr/N,N,N′,N″,N″‐pentamethyldiethylenetriamine (PMDETA) at room temperature for 24 h. Linear precursors and star polymers obtained in this study were characterized ¹H NMR, gel permeation chromatography (GPC), and triple detection GPC (TD‐GPC). Absolute molecular weight, hydrodynamic radius, and intrinsic viscosity ([η]) values for all star polymers were determined by TD‐GPC. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2010     

Molecular dimensions and melt rheology of an all‐aromatic liquid crystalline polymer

The molecular dimensions and melt rheology of a thermotropic all‐aromatic liquid crystalline polyester (TLCP) composed of p‐hydroxy benzoic acid, hydroquinone, terephthalic acid, and 2,4‐naphthalenedicarboxylic acid is examined. The Mark–Houwink exponent (α) of 0.95 is estimated for the TLCP. The persistence length estimated from molecular weight (M) and intrinsic viscosity ([η]) data using the Bohdanecky–Bushin equation is about 95 Å, whereas that estimated from light scattering data is 117 Å. These persistence lengths and the observed α value, both higher than those for flexible polymers, suggest that the present TLCP is a semirigid polymer. The zero shear melt viscosity (η₀) varies with approximately M⁶ for molecular weight M > 3 × 10⁴ g/mol; below this molecular weight, η₀ varies almost linearly with M. Widely different entanglement molecular weights (M_e) are predicted, depending on the method used; the plateau modulus estimates M_e of about 8 × 10⁵ g/mol, whereas the ratio of mean square end‐to‐end distance and molecular weight (〈R²〉₀/M) predicts M_e's either too small (0.33 g/mol) or too large (2.5 × 10⁶ g/mol), depending on the theory used. Although the change in the molecular weight dependency of melt viscosity appears to be associated with the onset of entanglement coupling of the semirigid molecules, its origin needs further investigation. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2378–2389, 2001     

Influence of associations on self-diffusion of styrene–methylmethacrylate random copolymers in semidilute acetone solution

The self-diffusion of four styrene–methylmethacrylate random copolymers dissolved in acetone, a thermodynamically bad solvent for the styrene sequences in the copolymer, were investigated by pulsed-field gradient NMR. The echo attenuations S_inc(q,t) are dominated by diffusion of clusters. At higher concentrations, physical gelation sets in (formation of a transient network), which is manifested in an anomalous, restricted diffusion at short observation times. The measured fluctuations of the positions of the chain segments in the transient network have an amplitude of about 100 nm. The free long-range diffusion attained at long observation times shows a much stronger concentration dependence than in the nonassociating solvent benzene. The results are in accord with light-scattering investigations. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 2931–2939, 1998     

The interaction parameter of crosslinked networks and star polymers

Recent results on blends containing star polymers have revived the interest on the interaction parameters of structures that contain junctions between chains, a matter which can be connected with the earlier studies on the influence of crosslinks on the interaction parameters of polymer networks and gels. Here, we review results on crosslinked networks and star polymer solutions together with the more recent work on star polymer blends. The review covers swelling and elastic deformation of gels, differential vapour sorption between crosslinked and uncrosslinked polymers, osmotic equilibrium of gels and of star polymer solutions, and neutron scattering of polymer blends containing star polymers. In the systems reviewed, the interaction parameters of stars and networks differ from those of linear chains, and the difference is attributed mainly to entropic effects.     

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     

Enhancement of two-photon absorption cross section and singlet-oxygen generation in porphyrin-cored star polymers

We report a newly synthesized polymer of a star-shaped porphyrin compound(TPA-FxP) with four oligofluorene arms at its meso positions with the pronounced enhancement of the two-photon properties and the generation of singlet oxygen by utilizing the two-photon excited fluorescence resonance energy transfer.The steady-state spectra and transient triplet-triplet absorption spectra give evidence that the enhanced two-photon absorption cross section results from not only the through-space energy transfer(Frster...     

Chain diffusion in the melt of an asymmetric diblock copolymer in the disordered and ordered state

 The self-diffusion in a polystyrene-b-polyisoprene diblock copolymer with a strongly asymmetric composition was investigated with dependence on temperature by pulsed field gradient (PFG) NMR. The diblock shows with decreasing temperature a disorder-to-order-transition at T _ODT=393 K from a micellar liquid-like to a bcc ordered state which was recently measured by SAXS [M. Schwab and B. Stühn, Phys. Rev. Lett. (1996) 76: 924]. Two diffusivities were observed, one of the free diblock chains and one of the diblock chains fixed in micelles. The volume fraction of free chains decreases with decreasing temperature. The diffusivity of the free chains must be related to chain stretching. The experiments show that within the time of the NMR experiment (300 ms) there is no exchange between the diblock chains in the free state and those fixed in the core of the micelles. Received: 25 March 1997 Accepted: 25 April 1997