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Abstract
It is proposed that the onset of entangled behavior with increasing N (degree of polymerization) in polymer solutions of concentration c > c* (overlap concentration) corresponds to the point where molecular diffusion becomes restricted to reptation alone. An internally self-consistent model for reptation in such solutions, based on a reptation and "tube"-reorganization concept, is developed. By treating the relaxation of molecules as a cooperative phenomenon the onset of reptation is identified as a second-order, ferromagnetic-like transition occurring at a critical N and entanglement density. It is possible to compare some predictions of our treatment with experiments on the variation of Nc (critical N for onset of entangled behavior) with c, by incorporating results of previous studies on static-correlation properties in semidilute polymer solutions. The agreement is surprisingly good.
... The tube relaxation time for constraint release, or tube reorganization, is determined by obstacle lifetime [8]. Various models account for the impermanence of entanglements [16][17][18]. The theory of constraint release involves tube dilation and tube-Rouse motion [13]. ...
... The diffusion spectrum at low frequencies starts from a constant for both processes and changes to the ω 1/2 at inverse values of the longest relaxation time of each process. In the case of a mono-dispersed polymer melt, the tube reorganization is slower than reptation and must have a small effect on the diffusion properties [16,17]; nevertheless, tube reorganization significantly affects the viscoelastic properties of the polymer melt, presumably because of the difference between the spectrum of the tube-Rouse modes and the spectrum of reptation [11]. ...
... The constraint release was originally termed tube reorganization by Pierre-Gilles de Gennes, where the obstacle lifetime determines the tube relaxation times [8]. Various models account for the impermanence of entanglements [16][17][18], among which is also the theory of constraint release involving the tube dilation and tube-Rouse motion [13]. In this theory, the constraint release is considered as the tube-Rouse motion, and the relaxation time is proportional to the lifetime of the obstacles [13]. ...
The translational motion of polymers is a complex process and has a big impact on polymer structure and chemical reactivity. The process can be described by the segment velocity autocorrelation function or its diffusion spectrum, which exhibit several characteristic features depending on the observational time scale—from the Brownian delta function on a large time scale, to complex details in a very short range. Several stepwise, more-complex models of translational dynamics thus exist—from the Rouse regime over reptation motion to a combination of reptation and tube-Rouse motion. Accordingly, different methods of measurement are applicable, from neutron scattering for very short times to optical methods for very long times. In the intermediate regime, nuclear magnetic resonance (NMR) is applicable—for microseconds, relaxometry, and for milliseconds, diffusometry. We used a variation of the established diffusometric method of pulsed gradient spin-echo NMR to measure the diffusion spectrum of a linear polyethylene melt by varying the gradient pulse width. We were able to determine the characteristic relaxation time of the first mode of the tube-Rouse motion. This result is a deviation from a Rouse model of polymer chain displacement at the crossover from a square-root to linear time dependence, indicating a new long-term diffusion regime in which the dynamics of the tube are also described by the Rouse model.
... 15,16 Similar corrections to the reptation prediction were observed for diffusion coefficient 17 D 3d ~ M −2.3 . Extensions of these models account for many-chain effects, such as constraint release 18,19 and tube dilation, 20 that are especially important in polydisperse systems 21 and for branched entangled polymers. 22 Tube dilation refers to the increase of the effective tube diameter during the relaxation of entangled polymer chains. ...
... The curvilinear displacement of the center of mass of this section along its primitive path during time τ e produced by the diffusion of l/a minimal loops along the same primitive path is (aN e /g) 2 (l/a). The resulting curvilinear diffusion coefficient of this section of g Kuhn monomers along its primitive path of length l ≈ a(g/N e ) 1/2 is where the Rouse diffusion coefficient D e of a minimal entanglement loop with N e Kuhn monomers (see eq 3) is (18) The time it takes the section of g Kuhn monomers to diffuse its size is on the order of its relaxation time (19) Thus, the DFLA model predicts that the relaxation time of a nonconcatenated ring with N Kuhn monomers is (20) Stress Relaxation: Kapnistos et al. 38 derived the stress relaxation modulus for a single nonconcatenated ring in the DFLA model. The stress is supported by the gate of entanglements through which loops have not yet been pulled out, and thus the stress relaxation modulus is on the order of kT per such gate of entanglements. ...
... The number density of gates associated with the loops containing g ≈ mN e monomers each is proportional to m −3/2 for 1 ≪ m ≪ N/N e . [35][36][37] The lifetime of a loop of g ≈ mN e monomers and hence the relaxation time of the corresponding gate is τ(m) ≈ τ e m β with β = 5/2 (see eq 19). As a result, the single-ring stress relaxation modulus in the DFLA model is (21) where ϕ(t) ≈ (t/τ e ) −1/(2β) is the fraction of unrelaxed gates at time t in the interval τ e < t < τ relax . ...
A scaling model of self-similar conformations and dynamics of nonconcatenated entangled ring polymers is developed. Topological constraints force these ring polymers into compact conformations with fractal dimension df = 3 that we call fractal loopy globules (FLGs). This result is based on the conjecture that the overlap parameter of subsections of rings on all length scales is the same and equal to the Kavassalis–Noolandi number OKN ≈ 10–20. The dynamics of entangled rings is self-similar and proceeds as loops of increasing sizes are rearranged progressively at their respective diffusion times. The topological constraints associated with smaller rearranged loops affect the dynamics of larger loops through increasing the effective friction coefficient but have no influence on the entanglement tubes confining larger loops. As a result, the tube diameter defined as the average spacing between relevant topological constraints increases with time t, leading to “tube dilation”. Analysis of the primitive paths in molecular dynamics simulations suggests a complete tube dilation with the tube diameter on the order of the time-dependent characteristic loop size. A characteristic loop at time t is defined as a ring section that has diffused a distance equal to its size during time t. We derive dynamic scaling exponents in terms of fractal dimensions of an entangled ring and the underlying primitive path and a parameter characterizing the extent of tube dilation. The results reproduce the predictions of different dynamic models of a single nonconcatenated entangled ring. We demonstrate that traditional generalization of single-ring models to multi-ring dynamics is not self-consistent and develop a FLG model with self-consistent multi-ring dynamics and complete tube dilation. This self-consistent FLG model predicts that the longest relaxation time of nonconcatenated entangled ring polymers scales with their degree of polymerization N as τrelax ∼ N7/3, while the diffusion coefficient of these rings scales as D3d ∼ N–5/3. For the entangled solutions and melts of rings, we predict power law stress relaxation function G(t) ∼ t–3/7 at t < τrelax without a rubbery plateau and the corresponding viscosity scaling with the degree of polymerization N as η ∼ N4/3. These theoretical predictions are in good agreement with recent computer simulations and are consistent with experiments of melts of nonconcatenated entangled rings.
... In the absence of topoisomerases, xobsl is equal to xrep/6 (Klein, 1978). Therefore, a>l, provided than N2>187i2, which [according to (1)] corresponds roughly to c/c*> 10. ...
... En absence d'enzyme, la réorganisation du tube est due exclusivement à la reptation des chaînes environnantes. La chaîne test suit alors un comportement analogue à celui de la reptation d'une chaîne autour d'obstacles fixes, à condition que les chaînes soient suffisamment longues et que la concentration soit suffisamment élevée(Klein, 1978). La concentration minimale est évaluée à 10 c*.Note présentée par Pierre-Gilles de GENNES. ...
This work describes the dynamic behaviour of entangled linear DNA molecules in the presence of type II DNA topoisomerase. In the absence of enzyme, entangled DNA molecules diffuse by a reptation process; they behave as an elastic solid up to a time proportional to the cube of the degree polymerization.
The addition of type II DNA topoisomerases is predicted to decrease this time to a Rouse time (proportional to the square of the degree polymerization).
... 45,46 In order to be suitable for polydisperse polymers, which are more relevant to the case of acrylic PSAs, Léonardi et al. 47 have proposed a generalized model that takes into account reptation in a polydisperse environment using the 'double reptation' concept 48 and tube renewal effects. 49,50 Using this model, Jullian et al. have shown that for linear poly(butyl acrylate) in the range 2000-4 600 000 g mol −1 the rheological behavior can be explained across a wide frequency range on the basis of the molecular weight distribution (see Fig. 4). 47 Although rheological models that link the molecular weight distribution to rheological behavior exist, precise prediction of rheological behavior in typical latexes used for PSAs is complex as emulsion polymerization of acrylic monomers tends to lead to nonlinear polymers with extremely broad molecular weight distributions. ...
Pressure‐sensitive adhesives (PSAs) are essential components of a large number of commercial products. The immense range of substrates that are required to be bonded, coupled with the challenging adhesive properties that are required in many applications, requires the development of PSAs with controllable structure. In this review, the development of acrylic latexes for use in PSA applications is discussed, with a particular emphasis on how to adjust the synthetic process to control adhesive properties. Following a general introduction to PSAs, a brief overview of the fundamental rheological properties that control adhesive behavior is given. Subsequently, routes to improve PSA performance through controlling the polymerization process are described. Finally, more complex systems that involve structured latexes and multiphase hybrids are detailed. The review concludes with a summary of future challenges for the field. © 2023 Society of Industrial Chemistry.
... Then, the probe chain relaxes by reptation. However, in real systems other mechanisms compete with reptation, mainly contour length fluctuations (CLF), i.e., fluctuations of the length of the tube, and constraint release (CR), which refers to the probe chain motions induced by the motions of the surrounding chains [3,4]. ...
The polymer dynamics in blends of long and short chains spans several decades in time and the understanding of the effect of the short chains on the relaxation mechanism of the long chains due to constraint release requires the combination of microscopic and macroscopic techniques. While the longtime dynamics can be accessed by mechanical or dielectric spectroscopy (DS), its relation to the microstructural details requires the application of theoretical models. In contrast, neutron spin echo (NSE) measures directly the dynamic structure factor reflecting the process of constraint removal at the molecular scale. Here the comparison of NSE and DS results in a model blend of short and long polyisoprene enables the exploration of the entire time regime showing that constraint release leads to a dilation of the confining tube. We show the description of the dynamic tube dilation using a simple model in which the time controlling the tube dilation for the long chain is the terminal time of the short chain.
... This limits the polymer motion and consequently affects the flow properties by increasing the viscosity and resulting in shear-thinning behavior. 56,57 The flow curve at higher temperatures displayed the same behavior and 58 A transient test was performed as well to study the steadystate behavior of the solutions. In fact, for low concentration, the viscosity is only stable above 10 s −1 , and for high concentration, only up to 300 s −1 on average. ...
The viscosity of polymer solutions is important for both polymer synthesis and recycling. Polymerization reactions can become hampered by diffusional limitations once a viscosity threshold is reached, and viscous solutions complicate the cleaning steps during the dissolution–precipitation technique. Available experimental data is limited, which is more severe for green solvents, justifying dedicated viscosity data recording and interpretation. In this work, a systematic study is therefore performed on the viscosity of polystyrene solutions, considering different concentrations, temperatures, and conventional and green solvents. The results show that for the shear rate range of 1–1000 s–1, the solutions with concentrations between 5 and 39 wt % display mainly Newtonian behavior, which is further confirmed by the applicability of the segment-based Eyring-NRTL and Eyring-mNRF models. Moreover, multivariate data analysis successfully predicts the viscosity of polystyrene solutions under different conditions. This approach will facilitate future data recording for other polymer–solvent combinations while minimizing experimental effort.
... Par exemple, selon ce modèle, la pelote polymère se meut à l'intérieur d'une matrice rigide et statique. Une approche plus sophistiquée pourrait prendre en compte la contribution de la dynamique du milieu pour décrire le processus de relaxation des chaînes [37,38]. Plusieurs travaux expérimentaux sur des polymères en solution semi-diluée ont montré que le coefficient de diffusion et le temps de reptation ne varient pas en fonction de la masse molaire selon M −2 et M 3 respectivement comme postulé dans la théorie de la reptation mais plutôt selon M −2.4 et M 3.4 . ...
Les stratifiés composites hautes performances semi-cristallins sont des candidats pour l’industrie aéronautique. Le soudage de ces structures apparaît comme une nouvelle méthode d’assemblage sans ajout de matériaux externes et consiste à fondre localement l’interface et à mettre en contact les deux substrats. Le développement de l’adhésion est historiquement décrit par deux étapes activées thermiquement : l’établissement du contact intime à l’interface et la cicatrisation permettant à l’assemblage de retrouver idéalement les propriétés mécaniques du matériau initial. Les procédés de mise en forme des composites actuels sont très rapides, voire continus, et le temps disponible pour le développement de l’adhésion est limité. Ce travail de thèse s’intéresse aux phénomènes multiphysiques qui ont lieu aux interfaces soudées à des temps courts à l’aide d’études expérimentales et théoriques. Pour cela, un nouveau dispositif expérimental de soudage a été développé, permettant l’identification de la cinétique de cicatrisation d’un composite hautes performances PEKKCarbone. Une corrélation entre les temps de soudage et de relaxation rhéologiques montre l’influence de la dégradation liée à l’histoire thermique du composite sur sa cinétique de cicatrisation. L’établissement du contact intime apparaît également comme le facteur limitant aux basses pressions. Il est montré que le modèle généralement utilisé n’est pas adapté pour la prédiction de cette cinétique. D’autre part, la cristallisation, favorisée par la présence de fibres, est couplée avec la cicatrisation et peut donc dégrader la qualité de l’adhésion car elle influence la propagation de fissure. Une évolution du banc permettant un chauffage radiatif plus rapide est présentée et ouvre des perspectives pour une étude plus proche des conditions industrielles.
... Two polymer chains act as separate entities, provided that the concentration is below the overlap concentration (C*). However, once the overlap concentration occurs, the polymer's cooperative motion starts, and the behaviour of the solution changes 38,39 . ...
The formation of complex structures in thin films is of interest in many fields. Segregation of polymer chains of different molecular weights is a well-known process. However, here, polystyrene with bimodal molecular weight distribution, but no additional chemical modification was used. It was proven that at certain conditions, the phase separation occurred between two fractions of bimodal polystyrene/methyl ethyl ketone solution. The films were prepared by spin-coating, and the segregation between polystyrene phases was investigated by force spectroscopy. Next, water vapour induced secondary phase separation was investigated. The introduction of moist airflow induced the self-assembly of the lower molecular weight into islands and the heavier fraction into a honeycomb. As a result, an easy, fast, and effective method of obtaining island/honeycomb morphologies was demonstrated. The possible mechanisms of the formation of such structures were discussed.
... However, once the overlap concentration occurs, the cooperative motion of the polymer starts and the behavior of the solution changes. (37,38) up to 75% was performed. By combining entropic interactions between longer and shorter polymer chains and interfacial tension between the polymer solution and condensing water from moist air, it was shown that this conditions leads to a complex morphology consisting of a honeycomb filled with micropillars. ...
The formation of complex structures in thin films is of interest in many fields. Segregation of polymer chains of different molecular weights is a well-known process. However, here, polystyrene with bimodal molecular weight distribution, but no additional chemical modification was used. It was proven that at certain conditions, the phase separation occurred between two fractions of bimodal polystyrene/methyl ethyl ketone solution. The films were prepared by spin-coating, and the segregation between polystyrene phases was investigated by force spectroscopy. Next, water vapour induced secondary phase separation was investigated. The introduction of moist airflow induced the self-assembly of the lower molecular weight into islands and the heavier fraction into a honeycomb. As a result, an easy, fast, and effective method of obtaining island/honeycomb morphologies was demonstrated. The possible mechanisms of the formation of such structures were discussed
... Given that the network cannot be crossed, the lateral movement of the individual chain is limited and the molecule is confined in a tube-like space by the mesh of constraints. Therefore, the polymer can only move in a wormlike fashion (back and forth movement) called "reptation" (Klein 1978). If the concentration is increased above C*, the molecules in solution are contracted. ...
The behaviour has been examined of two samples of Berea and Vosges sandstones submitted
to the circulation of solutions of different natures, at different temperatures. Solutions of CaCI2 and NaC1
at ionic strengths I = 0.01, I = 0.1 and I = 1, taken in the increasing and then decreasing directions, were
heated to temperatures of 20, 30, 40, 50, 60, 70, 80 and 90°C. These temperatures were taken in the
increasing and then decreasing directions.
For the two sandstones, each temperature variation in the percolating solution was accompanied by a
sharp variation in permeability, in the opposite direction to the temperature variation. The permeability
versus temperature variation describes hysteresis loops whose area is greater when hot than when cold.
These curves are typical of two types of behaviour. The first is obtained with diluted solutions (I = 0.01 and
I = 0.1), and is characterized by a greater permeability during the rising temperature cycle than during the
decreasing temperature cycle. The second, obtained with concentrated solutions, is characterized by an
inverse variation: the permeability is greater during the decreasing temperature cycle than during the
rising cycle.
These different behaviours are interpreted in terms of flocculation-deflocculation of the clays
contained in the porous media.
Key words: sandstones, permeability, Berea and Vosges.
... Given that the network cannot be crossed, the lateral movement of the individual chain is limited and the molecule is confined in a tube-like space by the mesh of constraints. Therefore, the polymer can only move in a wormlike fashion (back and forth movement) called "reptation" (Klein 1978). If the concentration is increased above C*, the molecules in solution are contracted. ...
Porous media are inherent in many industrial applications such as oil recovery, soil
remediation, CO2 underground storage, liquid separation and geothermal energy. Highly
irregular cavities and tortuous interconnected pathways surrounded by a solid skeleton extend
throughout the hollow at the interior of the medium, so macroscopic properties such as
porosity or permeability are not sufficient to characterize the local shape and dimension of the
pore space. Although the void space is continuous, it is usually discretized as being a
succession of individual pores, which is a useful idealization to quantify local characteristics.
Indeed, the size of the pores and their relative distribution determine numerous transport
properties of porous media so they are of vital importance. A practical and commonly used
approach lies in modelling the pore space as a combination of capillaries whose radii are
distributed following a specific distribution, known as Pore Size Distribution (PSD). PSD
influences the distribution of fluids and capillary pressures inside the material, its
permeability, particles retention, solute dispersion, etc.
Some properties that are intimately linked to the PSD, e.g. capillary pressure curves, are used
as inputs to reservoir simulation software and provide valuable information for management
and decision making. Likewise, several methods used in Enhanced Oil Recovery (EOR) are
based on flooding with chemicals such as polymer solutions, foams or emulsions with the
purpose of reducing the mobility ratio of displacing fluid to the displaced fluid. This results in
reduction of viscous fingering and therefore in improved sweep efficiency in the reservoir
(Sheng 2011). The PSD of the reservoir rock influences the propagation of the fluid front and
is often determinant to choose the most appropriate technique.
As a consequence of the interest in PSD of porous media, engineers and researchers have
developed a multitude of techniques for its characterization, each of them having particular
advantages and drawbacks. Recent advances provide improved spatial and temporal
resolution for microtomography. At present, multiphase flow and displacement can be
quantified with this non-destructive technique, regardless of whether the images contain
diverse phases. Even dynamic processes can be imaged. However, several obstacles have not
yet been overcome. Resolution (~1 μm) and reliable segmentation of the images are some of
the limiting factors. Besides, acquisition time is long and not all materials can be
characterized. Other methods are convenient to obtain PSD of macroporous materials (> 50
nm) but they are often time-consuming and require meticulous preparation. This is the case of
water-desorption calorimetry, which allows determination of PSDs typically ranging from 50
nm to a 10 μm from interpretation of water desorption isotherm.
Nowadays, mercury porosimetry is the most widespread technique to determine pore size
distributions of porous media. Some of its strengths are the broad range of analyzable pore
sizes (~1 nm – 500 μm), the relatively short duration of the tests (~ 3h) and the benefits and
popularity of a well-established method which is the reference when characterizing PSDs.
However, this technique presents several drawbacks including toxicity of the employed fluid
2 1. General Introduction
and low performance with unconsolidated porous media. Despite the existence of other less
toxic porosimetry methods, none of them is efficient enough to replace mercury porosimetry.
Furthermore, the new international legislation that will be put in place following the
ratification of the Minamata Convention on Mercury in October 2013 is intended to ban or
severely restrict mercury porosimetry, forasmuch as it is one of the main sources of mercury
use. Moreover, it is always advisable to replace a toxic technique as this one with a new
environmentally-friendly technique which in addition does not threaten the user’s health. It is
for that reason that the IUPAC (International Union of Pure and Applied Chemistry) recently
appealed to the international scientific community (Rouquerol et al. 2012) emphasizing the
interest and the need to develop new effective and non-toxic porosimetry methods.
The most likely outcome of the decline of mercury porosimetry is that 3D microtomography
takes its place as the dominant technique to obtain PSD. However, there is an absence of
alternatives during the years ahead until microtomography reaches full development… and
even then, because this method may remain unaffordable for most research centers and is not
applicable to all types of porous samples. In this context, the objective of the present thesis is
to answer the following question: is it possible to develop a simple, efficient and nontoxic
method to characterize porous media in terms of their Pore Size Distribution?
To answer this question, the starting point is the work of Ambari et al. (1990), who proposed
the theoretical basis of a new method to obtain the PSD by injecting yield stress fluids
through porous media while measuring the flow rate Q at several pressure gradients ∇P. On
the grounds of these theoretical considerations, an intuitive approach to calculate PSD from
Q(∇P) is presented in this work. It relies on considering the extra increment of Q when ∇P is
increased, as a consequence of the pores of smaller radius newly incorporated to the flow. The
underlying principle of such behavior is the rheology of yield stress fluids in porous media.
The procedure is first tested and validated on numerically generated experiments. Then, it is
applied to exploit data coming from laboratory experiments and the resulting PSDs are
compared with those provided by mercury porosimetry and in some cases also with results
from 3D micro tomographies.
The performances that are pursued with this new technique are diverse. Obviously, the first
requisite will be nontoxicity in contrast to mercury porosimetry. In addition, we seek a simple
and inexpensive method which allows rapid characterization of a large spectrum of porous
media without needing any exclusive equipment. Furthermore, it is also preferred that the
analyzed cores can be subsequently analyzed by other means, so the tests should be
nondestructive. Moreover, the characterized pore dimensions must be associated with
macroscopic properties of interest. This method is expected to be especially useful in EOR
due to the nature of the experiments, which involve injection of commonly used flooding
materials.
Other important goals of the present work are to identify and assess the most critical questions
regarding the experimental feasibility of the method, determine its strengths, its weaknesses,
and propose ways to improve its performance without scarifying any of the main criteria. In
... The original tube model predicts the scaling of 3 for entangled linear polymers [32], while it is found that the exponent has a value of about 3.4 within a certain limit of molecular weights. A number of theoretical additions to the tube model have provided closer predictions, such as including contour length fluctuation [33] and constraint release [34]. The scaling of the zero-shear viscosity has also been shown to reveal topological differences. ...
Rheological measurements in which the applied stress or strain is oscillated are widely used to interrogate viscoelastic properties due to the independent control over the time scale and length scale afforded by changes in amplitude and frequency. Taking a nontraditional approach, we treat stress-controlled oscillatory tests as creep tests with transiently varying stress and apply an analysis typically used for steady creep and recovery experiments. Defining zero strain as the state prior to external shearing, it is shown that strain responses to small-amplitude oscillatory stressing are naturally shifted from the starting point by an amount proportional to the phase of the applied stress. The phenomenology is experimentally observed with entangled polymerlike micelles and polyethylene oxide solutions. A theory of strain shifting in the steady alternating state is provided based on recovery rheology, where differences between total strain and recoverable strains are acknowledged. User-controlled variables, such as the amplitude of the stress, the angular frequency, and the phase of the stress, as well a lone material parameter, the zero-shear viscosity, are shown to dictate the amount of shifting. A rapid and efficient approach of determining the zero-shear viscosity is, therefore, presented. We investigate the microstructural evolution via in situ small-angle neutron scattering when strain shifting appears. The microscopic orientation is shown to correlate to the recoverable strain independent of the shifting. Additional measurements are carried out on collagen, pluronic-hyaluronic acid, alginate gels, and polystyrene melts to show the generic nature of the strain shift phenomenon. In addition, we demonstrate that the strain-shift knowledge can be applied to determine the horizontal shift factor in time-temperature superposition, free of any numerical fitting procedures.
... 4,19,35 Beyond the analysis of constraints themselves there are many discussions in the literature 8 dealing with the motion of polymers due to entanglement constraints and the time such constraints last. For entangled chains, processes of contour length fluctuation (CLF) [36][37][38] of the PPs, and constraint release (CR) 37,[39][40][41] also contribute in addition to pure reptation, i.e. the motion of the polymer along the hypothetical reptation tube, and have to be considered. However, it is not yet clear in which way all the above mentioned concepts can be employed for describing the behavior of polymer melts in the non-linear viscoelastic regime. ...
Polymer melts undergoing large deformation by uniaxial elongation are studied by molecular dynamics simulations of bead-spring chains in melts. Applying a primitive path analysis to strongly deformed polymer melts, the role of topological constrains in highly entangled polymer melts is investigated and quantified. We show that the over-all, large scale conformations of the primitive paths (PPs) of stretched chains follow affine deformation while the number and the distribution of entanglement points along the PPs do not. Right after deformation, PPs of chains retract in both directions parallel and perpendicular to the elongation. Upon further relaxation we observe a long-lived clustering of entanglement points. Together with the delayed relaxation time this leads to a metastable inhomogeneous distribution of topological constraints in the melts.
... According to the intensity of the interaction between molecular chains in HMPAM, the HMPAM solution with different concentrations is divided into "dilute", "semi-dilute" and "concentrated regime". When the solution concentration is at the range of "dilute", it is less likely for polymer molecules to intertwine with each other, and the viscosity has a linear relation with polymer concentration [78]. When the concentration of the solution rises to the range of "semi-dilute", molecular chains begin to intertwine with each other, the existence of salt increases intermolecular association and causes increased viscosity [79]. ...
As many oilfields shift from high permeability and medium-high permeability to low permeability and ultra-low permeability, the complexity and specificity of their formation channels increase, and the requirements on injectivity and liquidity of polymer flooding become increasingly stricter. This paper, from the perspective of the molecular configuration of poly(acrylamide) (PAM), gives an introduction to their respective characteristics, and analyzes the applicability of PAMs in tertiary oil recovery on the basis of the applications of polymer flooding in China. The study suggests that, on the one hand, the problem that urgently needs to be solved at present is achieving the viscosification of polymers with medium-low molecular weight or low molecular weight in high-temperature and high-salt conditions; on the other hand, researchers shall change their original research thoughts, shift from large-scale design of original PAM products to one-to-one “customized” research on and development for meeting specific oilfield demands from the perspective of polymer molecular structure.
... Independently, Mackay et al. 14,15 suggested the constraint release mechanism that is applicable to cases where the host polymer is entangled and the particles are smaller than the Edwards tube. For samples with these attributes, it was argued that the nanoparticles may cause the tube renewal time to shorten 46 and the viscosity to decrease. ...
The effects of thermal annealing, 12–50 K above the glass transition temperature, on the zero-shear viscosity, η, of polymer nanocomposites (PNCs) and the corresponding host polymers were studied. For all specimens, including neat and 4 wt% dioctyl phthalate (DOP)-plasticized polystyrene (PS), neat poly(methyl methacrylate) (PMMA), and PNCs containing bare and grafted silica nanoparticles in neat and DOP-plasticized PS, the η increased with time initially, and only asymptotically approached a steady-state value after thermal annealing for ∼100 to ∼200 h. We found that this phenomenon occurred regardless of the solvent used to prepare the sample although the fractional changes in η (δη/η) are visibly bigger for tetrahydrofuran (THF). Moreover, the PNCs not plasticized by DOP showed bigger δη/η than their host polymers while the plasticized ones behave essentially the same as the neat hosts. Interestingly, some unplasticized PNCs prepared from THF exhibited smaller viscosities than the host polymer, but this anomaly disappeared on thermal annealing. By correlating the viscosity measurements with the evolution of the solvent content, average NP aggregate size and the amount of adsorbed PS on silica for samples prepared from different solvents, we infer that the temporal viscosity evolution originates from out-of-equilibrium chain conformations produced during sample preparation. Because these relaxations are limited by the rearrangement of the polymer chains adsorbed on the NP or sample substrate surface, the timescales over which η changes can be much longer than the polymer reptation time, as observed.
... The behavior of polymer chain diffusion and randomization has been widely studied over the past decades. De Gennes [318] has discussed the molecular chain diffusion and randomization by a tube model [319,320], through which the molecular chain was allowed to reptate randomly through one-dimensional back-and-forth Brownian motion, along the randomly coiled conformational tube during a certain time. The diffusion mechanism was discussed by Bousmina et al., who described the diffusion process by Fick's law [321]. ...
Healing-on-demand materials exhibit the capability to close cracks and heal the closed/narrowed cracks when needed and to recover functionality using intrinsic or extrinsic resources. In this review, advances in healing-on-demand polymers and polymer composites in the past decade are reviewed, covering different schemes and technologies used to trigger crack closure and to heal molecularly. A balanced review on non-load-bearing polymers and polymer composites as well as load-carrying polymers and polymer composites is presented. The progress in self-healing polymers and polymer composites has been well discussed recently in the literatures. In this review, therefore, less attention has been paid on what has been widely reported; we primarily focus on healing-on-demand materials concerned with large volume damage healing by a close-then-heal (CTH) strategy. The healing-on-demand material by the CTH approach undergoes a process of crack closure, followed by crack healing with healing agents. Healing theories, including those within the continuum damage mechanics framework, and healing efficiency evaluations are also reviewed. Perspectives on future development in this emerging research area are discussed.
Extensive experiments have established that the constraint release (CR) relaxation takes place in binary blends of chemically identical long and short polymer chains wherein the long chains are dilute and entangled only with the short chains. Recently, Hannecart and coworkers focused on polymers of various chemical structures, polystyrene (PS), polyisoprene (PI), polybutadiene (PB), and poly(methyl methacrylate) (PMMA), and compared the CR relaxation time of the long chains in the binary blends of each polymer species (Hannecart, Clasen, and van Ruymbeke, Polymers 15, 1569 (2023)). From this comparison, they concluded that a normalized lifetime of the entanglement obstacle, with ZL = ML/Me (entanglement number of the long chain) and τe being the Rouse relaxation time of the entanglement segment, is determined only by the entanglements number of the short chain, ZS = MS/Me, irrespective of the chemical structure of the chains. This universality (independence from chemistry) would be an important feature if it were unequivocally concluded from experimental data. However, the values of the molecular weights utilized in their comparison, ML, MS, and Me, should have unavoidably included experimental uncertainties, which disturbs rigid conclusion of the universality. Aiming at a rigid experimental test avoiding those uncertainties, this study focuses just on data of the linear viscoelastic moduli G* of entangled monodisperse polymers of various chemical structures, PS, PI, PMMA, and poly(t-butyl styrene) (PtBS). We were able to find several pairs of chemically different but viscoelastically equivalent monodisperse polymers exhibiting indistinguishable G*GN data (with GN being the plateau modulus) from the local Rouse relaxation zone to the terminal relaxation zone. For binary blends of those equivalent polymers in each chemical species, i.e., long-X/short-X blends with X = PS, PI, PMMA, or PtBS, our experiments revealed that the CR relaxation of the dilute long chain does not complete at the same reduced frequency wte even when the chemically different component chains were viscoelastically equivalent in their monodisperse bulk state. It turned out that the CR relaxation is slower in the order of PS (slowest) < PMMA < PI < PtBS (fastest) and this difference was by a factor of 3-4 in total (well above the experimental resolution limit), rigidly showing the non-universal character of CR. An origin of this non-universality is briefly discussed within the framework of existing CR models, for example, Graessley’s CR model that already involved a chemistry-dependent parameter z representing a number of local CR hopping sites per entanglement segment.
In this chapter, various self-healing composites per the close-then-heal strategy were studied. Two types of stimuli-responsive fibers were used as the crack closing device or suture: one is tension programmed shape memory polymer fiber, and the other is pre-stretched polymeric artificial muscle that is fabricated by twisting and coiling of precursor fibers through twist insertion. The comprehensive experimental programs prove that the combination of a thermoset matrix, the stimuli-responsive fibers, and solid healing agent, is able to heal macroscopic or structural scale damage in the matrix repeatedly, efficiently, timely, and molecularly. Some future perspectives in this research direction are also discussed.
Artificial muscle is an emerging material in the field of smart materials with application in aerospace, robotic, and biomedical industries. Recently, innovative actuation devices based on artificial muscles with performances surpassing those of natural muscles in many aspects have been developed. However, most of the artificial muscles are facing big challenges including short life cycle and loss of stored energy due to dissipative mechanisms mainly rooted in hysteresis cycle and low work efficiency. Driven by a motivation in developing new category of artificial muscles with almost zero structural loss, artificial muscles from low cost fishing lines or sewing threads have been proposed to provide highest efficiency of a hysteresis-free actuation. Since then, our group has developed different models from phenomenological model to multi-scale models to simulate the actuation behaviors of the fishing-line-based artificial muscles. Due to the advantage in almost zero structural loss, artificial muscles have a great potential in the applications of self-healing composite systems. In this article, we demonstrate the applications of low-cost fishing-line-based artificial muscles in 1-D and 2-D configurations, with the aim at macro-scale damage healing for polymer composites.
Assisted with a direct current (DC) electric field membrane forming device, the Polyethersulfone (PES) ultrafiltration (UF) membrane was fabricated by non solvent induced phase inversion method. The membrane morphology and performance were simultaneously changed because the PES polymer chains were polarized by the DC electric field. As a result, the M-0-DC membrane showed a porous and thinner separation layer structure with a water permeability of 280.1 L m⁻² h⁻¹·bar⁻¹, which is ∼55% higher than that of M-0. Further, a novel antifouling PES membrane containing carbon quantum dots (CQDs) with a concentration of 0.5 was prepared combined with the electric field. The water permeability (∼164% higher than M − 0) of M-0.5-DC was substantially improved and the rejection rate for BSA was 98.4%. The M-0.5-DC also exhibited excellent antifouling property, that is, its BSA flux recovery rate reached as high as 95.3%. Apart from, the Congo red self-cleaning ability investigation of M-0.5-DC showed that the membrane became clean again after the irradiation of ultraviolet light for 2 h. The simultaneously enhanced water permeability and improved anti-fouling property by DC electric field and CQDs are promising advances that may promote the applications of UF membranes in water treatment.
This review article focuses on the transport phenomena of entangled polymeric liquids. The study of transport phenomena is one of the fundamental fields in chemical engineering, which addresses the transport of mass, momentum, and energy. For simple transport cases, such as the flow of a Newtonian fluid, the methodology of transport phenomena has been established. However, for an entangled polymeric liquid, which is an example of a viscoelastic liquid, various problems remain due to the various time and length scales involved. In this review article, we summarize studies of entangled polymeric liquids for problems on different time and length scales and multiscale problems that connect different scales.
Polymer melts undergoing large deformation by elongation are studied by molecular dynamics simulations of bead–spring chains in melts. By applying a primitive path analysis to strongly deformed polymer melts, the role of topological constraints in highly entangled polymer melts is investigated and quantified. We show that the overall, large scale conformations of the primitive paths (PPs) of stretched chains follow affine deformation while the number and the distribution of entanglement points along the PPs do not. Right after deformation, PPs of chains retract in both directions parallel and perpendicular to the elongation. Upon further relaxation we observe a long-lived clustering of entanglement points. Together with the delayed relaxation time this leads to a metastable inhomogeneous distribution of topological constraints in the melts.
We determine experimentally the "dilution exponent" α for entangled polymers from the scaling of terminal crossover frequency with entanglement density from the linear rheology of three 1,4-polybutadiene star polymers that are blended with low-molecular-weight, unentangled linear 1,4-polybutadiene at various star volume fractions, ϕ s. Assuming that the rheology of monodisperse stars depends solely on the plateau modulus G N (ϕ s) ∝ ϕ s 1+α , the number of entanglements per chain M e (ϕ s) ∝ ϕ s −α , and the tube-segment frictional Rouse time τ e (ϕ s) ∝ ϕ s −2α , we show that only an α = 1 scaling superposes the M e (ϕ s) dependence of the terminal crossover frequency ω x,t of the blends with those of pure stars, not α = 4/3. This is the first determination of α for star polymers that does not rely on any particular tube model implementation. We also show that a generalized tube model, the "Hierarchical model", using the "Das" parameter set with α = 1 reasonably predicts the rheological data of the melts and blends featured in this paper.
We use computer simulations to study the relaxation of strongly deformed highly entangled polymer melts in the nonlinear viscoelastic regime, focusing on anisotropic chain conformations after isochoric elongation. The Doi-Edwards tube model and its Graham-Likhtman-McLeish-Milner (GLaMM) extension, incorporating contour length fluctuation and convective constraint release, predict a retraction of the polymer chain extension in all directions, setting in immediately after deformation. This prediction has been challenged by experiment, simulation, and other theoretical studies, questioning the general validity of the tube concept. For very long chains we observe the initial contraction of the chain extension parallel and perpendicular to the stretching direction. However, the effect is significantly weaker than predicted by the GLaMM model. We also show that the first anisotropic term of an expansion of the 2D scattering function qualitatively agrees to predictions of the GLaMM model, providing an option for direct experimental tests.
We propose and verify methods based on the slip-spring (SSp) model [ Macromolecules2005, 38, 14] for predicting the effect of any monodisperse, binary, or ternary environment of topological constraints on the relaxation of the end-to-end vector of a linear probe chain. For this purpose we first validate the ability of the model to consistently predict both the viscoelastic and dielectric response of monodisperse and binary mixtures of type A polymers, based on published experimental data. We also report the synthesis of new binary and ternary polybutadiene systems, the measurement of their linear viscoelastic response, and the prediction of these data by the SSp model. We next clarify the relaxation mechanisms of probe chains in these constraint release (CR) environments by analyzing a set of “toy” SSp models with simplified constraint release rates, by examining fluctuations of the end-to-end vector. In our analysis, the longest relaxation time of the probe chain is determined by a competition between the longest relaxation times of the effective CR motions of the fat and thin tubes and the motion of the chain itself in the thin tube. This picture is tested by the analysis of four model systems designed to separate and estimate every single contribution involved in the relaxation of the probe’s end-to-end vector in polydisperse systems. We follow the CR picture of Viovy et al. [ Macromolecules1991, 24, 3587] and refine the effective chain friction in the thin and fat tubes based on Read et al. [ J. Rheol.2012, 56, 823]. The derived analytical equations form a basis for generalizing the proposed methodology to polydisperse mixtures of linear and branched polymers. The consistency between the SSp model and tube model predictions is a strong indicator of the compatibility between these two distinct mesoscopic frameworks.
Suitably modified versions of the Langevin equation introduced in Chap. 2 will be taken as a general basis for analytical explanations of macromolecular-chain motions. The reader will straightforwardly be led from the dynamics of freely draining polymer chains as the simplest case to entangled-chain phenomena and finally to mesoscopic confinement effects. The Langevin equation-based treatments will be supplemented step by step by additional force terms specific for the diverse model scenarios. The restriction to this equation-of-motion strategy is expected to favor the comprehensibility of this demanding field. The relaxation-mode solutions will be expressed in the form of predictions for diverse experimental techniques outlined in Chap. 3. This in particular refers to spin–lattice relaxation, coherent and incoherent neutron scattering, and mechanical relaxation.
One of the important problems in the field of orthopedic medicine is the ability to create a stable bone-materials interface with an implant, particularly when faced with the difficult condition of bone infection. Only recently have we come to understand the significance of addressing infection during the bone wound healing process; however, to apply this understanding toward an effective treatment requires the ability to deliver exacting amounts of therapeutics of different types over the appropriate timeframes in and around the implant. This task must be accomplished while maintaining the mechanical integrity of the implant materials and allowing for bone integration on their surfaces. Here we present a novel, particularly enabling next-generation implant solution for both eradication of an established biofilm within the bone cavity and accelerated bone repair via the controlled delivery of antibiotic and growth factor in sequence from stable nanometer scale coatings on the implant surface. Infection is by far the most common reason for complications, which often lead to complete removal of implants (74.3%). Infection significantly increases morbidity, and places huge financial burdens on the patient and the healthcare system-projected to exceed $1.62 billion/year by 2020. Because infection is much more common in implant replacement surgeries, these issues greatly impact long-term patient care for a continually growing part of the population. For revision arthroplasty of an infected prosthesis, a prolonged and expensive twostage procedure requiring two surgical steps and a 6-8 week period of joint immobilization exists as today's gold standard. A single-stage revision is preferred as an alternative; however, traditional bulk polymer systems such as bone cement cannot load sufficient amounts of therapeutic to eradicate existing infection, are insufficient or infeasible for the release of sensitive biologic drugs that considerably aid in bone regeneration, and lead to substandard mechanical properties and retarded bone repair. To address these issues, we created conformal, programmable, and degradable dual therapy coatings (~500 nm thick) in a layer-by-layer fashion using the enabling nanofabrication tool of electrostatic multilayer assembly. The nanolayered construct allows large loadings of each drug, thus enabling ultrathin film coatings to carry sufficient treatment and precise independent control of release kinetics and loading for each therapeutic agent in an infected implant environment. The coating architecture was adapted to allow early release of antibiotics contained in top layers sufficient to eliminate infection, followed by sustained release above the MIC over several weeks; whereas, the underlying BMP-2 growth factor layers enabled a long-term sustained release of BMP-2, which induced more significant and mechanically competent bone formation than a short-term burst release. In rats, the successful growth factor-mediated osteointegration of the multilayered implants with the host tissue improved bone-implant interfacial strength by impressive amounts (15-fold) when compared with the bare implant control, and yields a mechanical bond 17-fold higher than that created with the use of clinically available bioactive bone cement. Here we focused on dual delivery of an antibiotic and a growth factor owing to the urgent need for enhanced infection-reducing and tissue-integrating strategies in orthopedic applications, but the excellent modularity of multilayers for incorporation and release of diverse therapeutics suggests this approach should be also applicable to different implant applications such as vascular graft and artificial heart implants for which the risks of infection are often ignored. Our findings demonstrate the potential of this layered release strategy to introduce a durable implant solution, ultimately an important step forward in the design of biomedical implant release coatings for multiple medical applications. In addition to focusing on multi-therapeutic multilayer coatings for macroscale implants and scaffolds, I have also extended the work to understand release properties of the therapeutic agents, guided by predictive mathematical modeling of the release mechanisms involved in polyelectrolyte multilayer films and cell uptakes based on the principles of polymer physics and molecular and cellular biology. The potential impact of this work is substantial: introduce the next-generation biomaterials and implantable devices, save billions of dollars in the healthcare cost, and directly benefit the rapidly growing current and future generations of patients relying on medical device.
Linear aromatic poly(p-benzanilide nitroterephthalamide)s of increasing molecular weight, were synthesized and used as the macromolecular diffusant through gels of their crosslinked analogs. Intrinsic viscosity measurements in concentrated H2SO4 yielded the relationship \left[ \eta \right] = 9.0 \times {10^{ - 5}}{M_n}^{1.07}
The formation of cracks, i.e. fracture, and the healing of cracks in polymer solids are two complementary processes. Some of the molecular mechanisms described in the previous chapters on fracture also apply — by simply changing direction — to crack healing, such as relaxation of chains towards an equilibrium conformation, establishment of network isotropy, closure of voids and formation of entanglements. The role of these mechanisms in fracture has become clearer through the study of crack healing. It is for this reason that a chapter on this subject is included in a book on fracture.
Polymers are widely used in practice and have a number of unique rheological and physicomechanical properties [1– 5]. They differ from other substances in the size of their molecules, which are correctly called macromolecules. At temperatures above the glass transition temperature or melting point, a polymer system (concentrated solution or melt of a polymer) can be considered as a viscoelastic liquid whose behavior is determined by a system of weakly bound macromolecules. When a system is excited (mechanically or by heat), the macromolecules easily change their neighbors, but the intactness of each of them is not disturbed.
This article is the first from a series of three papers presenting the behaviour of polymer smelt during the formation of the film within the process of heat scaling.
Doi and Edwards have recently proposed a molecular theory for the dynamics of entangled polymer liquids based on a tube model to represent the mutual constraints on configurational rearrangement of the chains. Expressions for diffusion coefficient, plateau modulus, zero-shear viscosity, steady-state recoverable compliance, and terminal relaxation time can be devloped, and relations among these properties that depend only upon observable quantities can be obtained. Several such relations are derived and are compared with experimental observations.
Porcine Submaxillary Mucin (PSM) is a glycoprotein whose primary structure consists of a protein core with frequent, short oligosaccharide side chains. Previous static and dynamic light scattering data indicate, in dilute aqueous 0. 1M NaCl, PSM exists as quasi-spherical, internally branched, highly hydrated, polydisperse aggregates which slowly dissociate till a stable species of weight average molecular weight (M//w) 7. 4 multiplied by 10**6 is reached. A discrete change in the solution properties of PSM in 0. 1 M NaCl at a concentration of 2 mg/ml, manifested by a sudden decrease in the translational diffusion coefficient, increase in viscosity number and decrease in slope of the osmotic compressibility, was observed. The authors tentatively propose that a weak secondary association process occurs at this concentration although it cannot be ruled out that hydrodynamic interaction of the congested macromolecules are responsible for the observed effect.
In 1964, Pecora(1) showed theoretically the utility of quasielastic light scattering (QLS) for characterizing the translational, rotational, and internal dynamics of polymer chains. In 1967, the theory was brought to experimental realization in two quite different types of biological systems. Benedek and co-workers(2) used QLS to measure translational diffusion coefficients of proteins and nucleic acids, and Berge et al
(3) measured the motility of spermatozoa. These two types of biological applications—macromolecular characterization and physiological analysis—have both developed enormously since the late 1960s, but the major themes emerged early.
Small Angle Neutron Scattering (SANS) is an experimental technique introduced since about ten years for the investigation of polymer conformation in all the concentration range from dilute solution to the melt (1–4).
Polymer liquids have fascinating dynamical properties: they flow like conventional viscous liquids when subjected to perturbations slowly varying with time, but behave like elastic solids at higher frequencies. These mechanical properties strongly depend on the molecular structure (linear, branched, flexible, rigid…) but unifying concepts have emerged in the past two or three decades, especially for the easiest case of linear flexible chains, pointing out the crucial role of chain entanglements. The reptation model has provided a fruitful and simple framework to analyze the wide range of available dynamical experiments. The reptation model qualitatively well describes how the dynamic properties depend on the molecular weight of the chains, and yields simple and good estimations of the different time scales involved. Small quantitative discrepancies remain, however, which are at the origin of a vigorous debate on the validity of the reptation hypothesis, and of a growing number of proposed refinements.
In this review, we shall present the reptation ideas in their simple version, see how they apply to self-diffusion, viscoelasticity and more local processes, critically analyze the underlying hypothesis, and sketch the additional effects which have to be included to get a realistic description of the dynamic properties of entangled polymers.
Viscoelastic behavior in polymer solutions is a reflection of dynamical processes at the molecular level. These processes are driven by Brownian motion, and they govern diffusion and the rate of rearrangement of chain orientation and conformation. Mechanical response and molecular relaxation go hand in hand. Properties which depend on large-scale chain motions are strong functions of the molecular architecture (chain length, long chain branching, etc.) at all levels of polymer concentration.
It has been proven (see for instance [1–11] that dielectric spectroscopy is a useful tool to study the molecular dynamics of polymers. This is due to the fact that a broad dynamical range from the milli- to the Giga-Hertz region can be covered by this method in its modern form (see Chap. 2). Therefore motional processes which take place for polymeric systems on extremely different time scales can be investigated in a broad frequency and temperature range. Moreover the motional processes depend on the morphology and micromorphology of the system under investigation. Therefore information on the structural state of the material can be indirectly extracted by taking the molecular mobility as a probe for the structure.
The mechanical properties at the interface of ABS/zeolite composites developed during hot plate welding were investigated using the lap-shear joint method. The self-bonding strength was proportional to one fourth the power of the welding time proposed by the diffusion models. The strength value of the ABS/zeolite system was lower than that of neat ABS due to the bad interfacial strength between the ABS and the zeolite, and the obstruction by the natural zeolite for the diffusion of the ABS molecular chains. As regards the fracture behavior, the welded specimens showed two types of failure; shear failure and tensile failure due to the stress concentration effect. When the lap shear joint samples were slipped by shear stress, plastically deformed ridges, which were the main feature of the welded specimens appeared on the fractured surface. Stress-whitening by crazing and local drawing was also observed at the edge of the bonded region on the deformed surface.
This paper reviews new perspectives on polymer adhesion mechanisms. Professor P.G. de Gennes’ theories about polymer melts and networks have enlightened us about polymer adhesion mechanisms. Both reptation theory and related experiments have demonstrated the existence of either self-diffusion or interdiffusion of polymer at the interfaces. Thus, adhesive strength, green strength and tack of elastomeric adhesives can be at least partially explained on the basis of the diffusion mechanism. Besides diffusion, Dr. de Gennes and his colleagues’ studies on the kinetics of spreading and wetting of polymers have provided us with new understandings about the adsorption mechanism. Without wetting, polymer molecules can not achieve adequate adsorption at the interfaces to result in van der Waals attraction and/or acid-base (or donor-acceptor) interaction. The latter has not been explored by the French school. In addition to the above mechanisms, we shall mention briefly the mechanisms of mechanical interlocking, chemical bonding and electronic adhesion.
The flow birefringence and polarized light scattering techniques were applied to study semidilute water-salt solutions of a high-molecular-mass (Mw = 6 × 106) flexible-chain polyelectrolyte, the copolymer of 2-acrylamido-2-methylpropanesulfonic acid with acrylamide, at different ionic strengths of the medium (I = 1 and 0.1 mol/l). It was shown that "domain" structures with the morphology predetermined by the solution ionic strength were formed in the solutions of this copolymer. In the case of suppressed electrostatic interactions, a fluctuation network of entanglements was formed.
ENTANGLEMENTS, their nature and their role in the dynamic properties of concentrated polymer solutions and melts are not well understood1,2. The classical molecular view of entanglements has been one of rope-like intermolecular couplings at a number of points along the length of a molecule; molecules in motion would drag past these couplings, the essential effect being one of enhanced friction1,3. There has been a growing realisation that this model is inadequate2,4,5. The essence of the problem, rather, seems to be that of the topological restrictions imposed on the motion of each polymer molecule by its neighbours: movement of a given polymer chain is constrained at the points of entanglement or intersection with adjacent chains2. Theoretical treatment of the topological problem is difficult6, and has met only with limited success5. An interesting proposal regarding the motion of molecules within entangled polymer systems has been put forward by De Gennes4,7: according to this, the motion of a given polymer molecule is confined within a virtual ‘tube’ defined by the locus of its intersections (or points of ‘entanglement’) with adjacent molecules (Fig. 1). The molecule is constrained to wriggle, snake-like, along its own length, by curvilinear propagation of length defects such as kinks or ‘twists’8 along the tube; this mode of motion has been termed reptation4 (from reptile). Reptative motion clearly satisfies the central requirement of entangled systems: that of the non-crossability by a given chain of the contours of its adjacent neighbours. In a real polymer melt the topological environment of any given molecule (that is, the virtual ‘tube’ surrounding it) will itself change with time. This is because the adjacent molecules defining it are themselves mobile. If this reorganisation is sufficiently slow then the translational motion of the enclosed molecule will be effectively curvilinear (reptative). Consideration of the problem9 suggests that this will be the case in an entangled system. One then expects translational diffusion to be dominated by reptation. There is no direct experimental evidence supporting the physical reality of curvilinear motion in entangled polymer systems. I report here the results of experiments on diffusion within a polyethylene melt critically designed to test the reptation concept.
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Viscoelastic Properties of Polymers reviews the entanglement concept in polymer rheology
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(a) W. W. Graessley, Ado. Polym. Sci., 16, 1, (19741, reviews
the entanglement concept in polymer rheology; (b) K. Freed
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reviews the entanglement concept in polymer rheology
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W. W. Graessley, Ado. Polym. Sci., 16, 1, (19741, reviews
the entanglement concept in polymer rheology; (b) K. Freed
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