Nonlinear stress relaxation of an entangled linear polystyrene in single step‐strain flow: A quantitative theoretical investigation

The nonlinear stress relaxation of a nearly monodisperse, moderately entangled polystyrene solution (i.e., roughly seven entanglements per chain at equilibrium) in single step‐strain flow is investigated quantitatively by a detailed comparison of an existing set of experimental data with a simulation based on the tube model. The proposed simulation enables the effects of primary nonlinear relaxation mechanisms other than chain retraction to be identified more clearly and investigated individually. Two peculiar nonlinear relaxation behaviors are observed in this experiment. One is concerned with an apparent enhancement in the stress relaxation at short times, and the other is responsible for a seeming slowdown of the stress relaxation at long times. These findings are discussed within the tube model, in view of the effects of convective constraint release, partial strand extension, and nonaffine deformation. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 1281–1293, 2003     

Communication: effects of stress on the tube confinement potential and dynamics of topologically entangled rod fluids

A microscopic theory for the effect of applied stress on the transverse topological confinement potential and slow dynamics of heavily entangled rigid rods is presented. The confining entanglement force localizing a polymer in a tube is predicted to have a finite strength. As a consequence, three regimes of terminal relaxation behavior are predicted with increasing stress: accelerated reptation due to tube widening (dilation), relaxation via deformation-assisted activated transverse barrier hopping, and complete destruction of the lateral tube constraints corresponding to microscopic yielding or a disentanglement transition.     

Relaxation by reptation and tube enlargement: A model for polydisperse polymers

Modern theories of the dynamics of concentrated polymeric liquids have not yet accounted for the effects of polydispersity to a sufficient extent. In order to approach quantitatively the problem of polydispersity, a model is proposed here which is based on the concept that the “tube” of constraints around a chain enlarges as the relaxation proceeds. Predictions of linear viscoelasticity obtained with this model compare favorably with experimental results on homopolymeric blends reported in the literature. However, the theory is limited to the case of very long chains and it embodies an arbitrary, if plausible, closure assumption in the self-consistency scheme. Thus, quantitative agreement remains incomplete.     

用耗散粒子动力学方法研究高分子链取向对形变液滴回缩法测定界面张力值的影响

在利用形变液滴回缩法(DDRM)测量了分子共混体系界面张力的过程中, 要求椭球液滴内高分子链应力松弛速度远快于椭球的回缩速度. 我们建立高分子链取向模型, 用耗散粒子动力学研究高分子链的取向及应力松弛对界面张力测量值的影响. 结果表明, 当高分子链沿着流场方向取向时, 应力是否完全松弛对界面张力测量值的影响较大, 当高分子链取向方向垂直于流场方向时, 应力是否松弛对测量值影响较小.     

Dielectric relaxation in segmented polyurethane elastomers: Influence of 1:3 and 1:4 butanediol cure on the dynamic properties

Dielectric relaxation measurements are reported on a series of segmented polyurethane elastomers produced with mixtures of varying 1:3 and 1:4 butanediol as chain extender. The changes observed in the glass transition temperature, activation energies for dipolar relaxation and the nature of the dispersion for varying composition of the chain extender are discussed in terms of the extent of phase separation and the influence of the “hard” phase structure on the relaxation of the “soft” phase.     

Interactions between Hydrophobically Modified Associating Polyacrylamide and Cationic Surfactant at the Water‐Octane Interface: Interfacial Dilational Viscoelasticity and Relaxation Processes

The interfacial dilational viscoelastic properties of hydrophobically associating block copolymer composed of acrylamide (AM) and a low amount of 2‐ethylhexyl acrylate (EHA) (<1.0 mol%) with a hydrolyzed degree of about 1.5–2.0% at the octane‐water interfaces were investigated by means of two methods: the interfacial tension response to sinusoidal area variations (oscillating barriers method) and the relaxation of an applied stress (interfacial tension relaxation method) respectively. The influence of cationic surfactant cetyl trimethylammonium bromide (CTAB) on the dilational viscoelastic properties was studied. The results obtained by oscillating barriers method showed that dilational modulus decreased moderately with the increase of CTAB concentration. The results obtained by interfacial tension relaxation measurements showed that two main relaxation processes exist in the interface at 7,000 ppm polymer concentration: one is the fast process involving the exchange of hydrophobic blocks between the proximal region and distal region in the interface; the other is the slow relaxation process involving conformational changes of polymer chain in the interface. By adding CTAB, the slow process changed obviously due to the strong electrostatic interaction between oppositely charged surfactant and hydrolyzed part of polymer chain. Only when the CTAB concentration was close to the “equal charge point,” the associations formed mainly by the hydrophobic interaction like that in SDS/polymer system appeared and the characteristic time of fast process decreased obviously. The information of relaxation processes obtained from interfacial tension relaxation measurements can explain the results from dilational viscoelasticity measurements very well.     

Polysoaps in Backbone‐Selective Solvents: Effects of Side‐Chain Length on Collapse Dynamics

Abstract

Molecular dynamics (MD) simulations of model comb‐graft heteropolymers were performed to understand general mechanistic features of coil‐to‐micelle relaxation after instantaneous quench from a nonselective solvent to solvent conditions selective for the backbone monomers and poor for the side‐chain monomers. The systems considered were single bead‐spring molecules with backbones of 30 monomers and 10 equally spaced side chains of 1, 5, 10, or 20 monomers each, immersed in dense liquids of 20,000 simple solvent particles. We find that the coil‐to‐micelle relaxation time, τ _r , averaged over 50 independent trajectories for each set of topological parameters considered, decreases with increasing side‐chain length. A two‐stage relaxation mechanism is observed: (1) a fast collapse and aggregation of neighboring side chains to form a chain of “protomicelles,” followed by (2) a slow intramolecular aggregation of protomicelles. Fast collapse dominates for molecules with relatively longer side chains due to relatively higher probabilities of initial contacts between side‐chain monomers in different side chains, while slow intramolecular aggregation dominates for molecules with relatively shorter side chains.     

The Estimation of Statistical Parameters Determining the Relaxation Times of Nematic Elastomers: A Three‐Chain Network Model

A simplified “three‐chain” network model formed from freely jointed polymer chains consisting of Gaussian elements with fixed mean‐square lengths is proposed for describing local dynamic properties of nematic elastomers. The boundaries of a polymer network are supposed to be fixed when sample volume and shape do not change with ordering. Relaxation times characterising intrachain motions in both isotropic and ordered states are determined by two factors. The first (“dynamic”) factor is related to the friction of chain elements and the second one (“statistical” factor) is determined by statistical mean–square fluctuations of segment projections on the three axes of rectangular frame of reference. The “statistical” factor of relaxation times is calculated here as a function of the order parameter and the parameter characterising the degree of network crosslinking. Statistical factor obtained in the framework of a network model consisting of Gaussian subchains is compared with that calculated here by using freely‐jointed‐rods chain model. Good agreement is shown between statistical factors obtained in the framework of the two chain models considered. This result confirms the validity of describing the dynamics of real rod‐like mesogenic groups in nematic elastomers in terms of a simplified chain model consisting of Gaussian segments with fixed average lengths which do not change with ordering. The influence of “dynamic” factor on the relaxation spectrum of a nematic elastomer is discussed qualitatively.     

Concepts of Trapping Topologically by Shell Molecules

Concepts of the synthesis of shell topological compounds, which consist of a guest molecule (or molecules) trapped by a host molecule with a spacial, egg shell-like structure are discussed. Generally, both constructing the shell molecule in the presence of a guest molecule and constructing the guest molecule in the presence of the shell (host) are ways to “shell” topological compounds. The preparation of shell molecules may consist of the completion of “preshell” molecules or of obtaining cascade branched oligomers and polymers. Cyclodextrins and substances like triquinance are considered to play a role in preshell molecules. Shell molecules may also be obtained by polyreaction of a monomer of the XRY_n type, which results in a cascade branched molecule of shell structure (spherical form). When the polyreaction is continued, the cascade branched molecule becomes a “cast” one. It is theoretically possible to enclose a guest molecule inside the shell during the cascade branching process if there is a good solvent (of high expansion coefficient value) in respect to the growing branches. A spacially developed molecule of both “empty” and “cast” structure may be obtained also by the known “step by step” cascade branching process which involves, for instance, a repeated cyanoethylation-reduction reaction.     

Correlation of Cooperatively Localized Rearrangement on the “Fluidized Domain” of Polymers to Their Nonexponentially Viscoelastic Behaviors at Double Aging Processes (I): A Set of Reduced Universal Equations on the Stress Relaxation Modulus and Creep Comp

Based on the structure of glass (or liquid) polymers consisting of α-domain, β-co-domain, and entanglement constituent chain networks, and the nonexponentially viscoelastic behavior, a “heterophase fluctuation” model was proposed. It was found that the dynamics of cooperative rearrangement on the “fluidized domain” has a great shear rate, domain size, and temperature dependences. When the shear rate, domain size, and temperature dependences were taken account into the cooperatively localized rearrangement on the fluidized domain by the degradation of primary α-domain and the reformation of secondary β-co-domain constituent chains. A new dynamic theory of cooperatively localized rearrangement on the fluidized domain constituent chains with different size and different network chain length during physical and mechanical aging was established. The total viscoelastic free en-ergy of deformation resulting from the change in conformations of α-domain, β-co-domain, crytallite, crosslinked, and trapped entanglement constituent chains during aging processes was calculated by the combining method of kinetics and statistical mechanics. The constitu-tive equations and reduced stress relaxation modulus and creep compliances for three types of polymers were also derived. Finally, two reduced universal equations on creep compliance and stress relaxation modulus with a non-linear and two nonexponential parameters α and β were theoretically derived from the dynamic theory and a statistically extended mode coupling theory for double aging effects of polymers was developed. Results show that the two reduced universal equations have the same form as Kohlraush-Williams-Watts (K-W-W) stretched exponential function. The nonlinearity and the nonexponentiality are, respectively, originated from the memory effects of nonthermal and thermal history. The correlation of nonlinearity, α and β to the aging time, aging temperature, and the mesomorphic structure of fluidized domains was also established.     

Intra- and inter-chain fluctuations in entangled polymer melts in bulk and confined to pore channels

It is known that topological restraints by “chain entanglements” severely affect chain dynamics in polymer melts. In this field-cycling NMR relaxometry and fringe-field NMR diffusometry study, melts of linear polymers in bulk and confined to pores in a solid matrix are compared. The diameter of the pore channels was 10 nm. It is shown that the dynamics of chains in bulk dramatically deviate from those observed under pore constraints. In the latter case, one of the most indicative signatures of the reptation model is verified 28 years after its prediction by de Gennes: The frequency and molecular mass dependencies of the spin-lattice relaxation time obey the power law T_! ∝ M⁰ v^3/4 on a time scale shorter than the longest Rouse relaxation time τ_R. The mean squared segment displacement in the pores was also found to be compatible to the reptation law < r²>∝ M^−1/2t^1/2 predicted for τ_R < t < τ_d, where τ_d is the so-called disengagement time. Contrary to these findings, bulk melts of entangled polymers show frequency and molecular mass dependencies significantly different from what one expects on the basis of the reptation model. The data can however be described with the aid of the renormalized Rouse theory.     

Unique description of chemical structures based on hierarchically ordered extended connectivities (HOC procedures). I. Algorithms for finding graph orbits and canonical numbering of atoms

An iterative algorithm is described for finding topological equivalence, ordering, and canonical numbering of vertexes (atoms) in molecular graphs. Like the Morgan algorithm, it is based on extended connectivities but: (i) the latter are used hierarchically, i. e., the discrimination in the next iteration is carried out only for the vertices having the same extended connectivities (ranks) at the previous iteration; (ii) at equal extended connectivities, additional discrimination is introduced by the ranks of adjacent vertices; (iii) there is no “best name” search; (iv) three levels of complexity of chemical structures are distinguished and handled by different procedures. Two schemes of application of HOC procedures are presented: one directed towards a fast canonical numbering for coding systems, and another one yielding levels of topological equivalence allowing a unique topological representation of the molecule with possible applications to similarity search, structure-activity correlations, etc.     

ORDERED STRUCTURAL EVOLUTION AND RELAXATION BEHAVIORS OF A SERIES MICROPHASE SEPARATED “HAIRY-ROD” POLYIMIDES WITH MULTIPLE ALKYL SIDE CHAINS

A series of “hairy-rod” polyimides, BBPA(n), with multiple alkyl side chains was prepared from 3,3′,4,4′-biphenyltetracarboxylic dianhydride (BPDA) and 4,4′-biphenyldiamine substituted in the 2,2′-positions with benzoate, which was substituted in the 3,4,5-positions with ether side chains of varying lengths. The number of the methylene units, n, in these alkyl side chains were in even numbers ranging from 8 to 18. Combining techniques of one-dimensional (1D) and 2D wide angle x-ray diffraction, 1D small angle X-ray scattering, differential scanning calorimetry experiments, it was found that this series of “hairy-rod” polyimides possess a micro-phase separation between the backbones and side chains. This led to the formation of ordered structures in two different length scales, of which both are hexagonal packing: one is attributed to the alkyl side chains on the sub-nanometer scale, and another is for the whole polymer chains on the nanometer scale. The development of the hexagonal structure on the sub-nanometer scale was critically dependent upon the lengths of the alkylside chains. Three relaxation processes were captured by dynamic mechanical analysis, i.e., segmental motion of the backbones, α the melting of the side chain crystals, β1, which exits only for the materials with longer side chains(n=18,16); and the subglass relaxation of side chains, β2- The peak relaxation temperature of the α process decreased with increasing the length of side chains, while the one of the β2 process increased. The activation energy of the α relaxation was relatively independent on the length of side chain, whereas, β2 process showed the increasing of activation energy with increasing the length of side chains.     

Dielectric and depolarization thermocurrent study of the γ relaxation in polyethylene isophthalamide

The depolarization thermocurrents (DTC) from polyethylene isophthalamide are studied below the glass-transition temperature. The “entire” DTC spectrum is analyzed in terms of a continuous distribution of relaxation times; the corresponding distribution function is very close to that which fits data deduced from bridge measurements. The complex DTC spectrum can be experimentally resolved into single relaxation time processes. The analysis of each “elementary” DTC peak yields dielectric dispersion and relaxation time which allow one to calculate the frequency variation of the complex dielectric constant. The corresponding Cole–Cole plot is in good agreement with that deduced from studies of the “unresolved” γ relaxation.     

Viscoelastic properties of polymers: From molecular models to non-linear behavior

The molecular models of polymer physics (reptation, tube renewal) give a reasonable picture of the diffusion and relaxation of long and flexible chains: the concept of “tube renewal” (constraint release) added to the reptation idea explains the polydispersity effects for multimodal blends as well as for commercial linear polymers. The real issue now is to introduce these concepts in the formalism of non-linear viscoelasticity in order to explain the experimental data, as a first step in the range of moderate rates of deformation, then at very high strains.     

Topological analysis of complex molecular surfaces

An algorithm for the calculation of local and global curvatures of molecular surfaces is presented. The analysis is based on a surface representation as a set of points in 3-D space (“dotted surface” representation). The surface data are used to subdivide the surfac into domains with different curvatures. All domains are characterized by a reference point with a corresponding curvature profile specifiying the topological properties in its neighborhood. The curvature profiles provide a method for a systematic comparison of the shapes of different molecules. Such a strategy is important for the treatment of molecular recognition problems. The enzyme-inhibitor complex trypsin/BPTI was chosen to demonstrate the scopes of the method.     

Structural relaxation behavior of strain hardened shape memory polymer fibers for self‐healing applications

In this study, shape‐memory polyurethane (SMPU) fibers were strain hardened by cold‐drawing programming (CDP) process. The programmed fibers are experimentally studied on the physical and thermomechanical properties. Structural relaxation, which determines shape memory capability of the SMP fibers, is quantified by conformational entropy change. Based on the entanglement tube theory and reptation theory, the entropic force is derived as a “bridge” to link the stress relaxation and structural relaxation, and thus structural relaxation can be evaluated by stress relaxation. It was found that the CDP SMPU fibers would still have good crackclosing capability after 13 years of hibernation in polymer matrix composite. © 2013 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2013 , 51, 966–977     

Toward a Consistent Interpretation of the QTAIM: Tortuous Link between Chemical Bonds,Interactions, and Bond/Line Paths

Currently, bonding analysis of molecules based on the Quantum Theory of Atoms in Molecules (QTAIM) is popular; however, “misinterpretations” of the QTAIM analysis are also very frequent. In this contribution the chemical relevance of the bond path as one of the key topological entities emerging from the QTAIM’s topological analysis of the one‐electron density is reconsidered. The role of nuclear vibrations on the topological analysis is investigated demonstrating that the bond paths are not indicators of chemical bonds. Also, it is argued that the detection of the bond paths is not necessary for the “interaction” to be present between two atoms in a molecule. The conceptual disentanglement of chemical bonds/interactions from the bonds paths, which are alternatively termed “line paths” in this contribution, dismisses many superficial inconsistencies. Such inconsistencies emerge from the presence/absence of the line paths in places of a molecule in which chemical intuition or alternative bonding analysis does not support the presence/absence of a chemical bond. Moreover, computational QTAIM studies have been performed on some “problematic” molecules, which were considered previously by other authors, and the role of nuclear vibrations on presence/absence of the line paths is studied demonstrating that a bonding pattern consistent with other theoretical schemes appears after a careful QTAIM analysis and a new “interpretation” of data is performed.     

Structure-property relations in linear and crosslinked liquid crystalline polymers

This paper reviews structure-property relations in liquid crystalline side group polymers, as investigated by X-ray scattering of fibres, by small angle X-ray scattering in solution, by dielectric relaxation measurements and by melt rheology, as well as synthetic ways to “combined liquid crystalline polymers”. The synthesis of liquid crystalline elastomers from side group, main chain and combined liquid crystalline polymers is described. First structure-property relations are discussed.     

Time evolution of the pulsed HF chemical laser system. II. Irreversible thermodynamic analysis

The time rates of change of level populations and radiation densities derived from a detailed kinetic model of the F + H₂ → HF + H laser are employed as input data for a time dependent thermodynamic analysis of this system. The laser is regarded as an irreversible heat engine generating thermodynamic work in the form of laser light. The development in time of the thermodynamic functions, efficiency and irreversible entropy production is determined by computing the contributions of pumping, radiation and relaxation to the entropy and energy of the lasing molecules. Effects of specific rate processes are evaluated by considering different kinetic schemes, i.e. different combinations of kinetic processes and initial conditions. It is shown, among others, that a laser without relaxation processes (“frictionless”) has poor efficiency despite the absence of energy losses and the low irreversible entropy production. On the other hand, the efficiency is high in lasers governed by fast rotational relaxation. This is because rotational relaxation, though leading to some energy losses and irreversible entropy production, compensates for the entropy decrease of the system (while lasing under partially inverted populations) by increasing the bath entropy. The major general conclusion of the analysis is that the thermodynamic constraints related to the kinetic scheme and not the extent of irreversibility of the lasing process is the crucial factor in determining the laser efficiency.