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Stress relaxation measurements under step strain γ are frequently utilized to characterize the nonlinear stress responses of polymeric materials. The reduction degree of the stress amplitude with increasing step strain is quantified by the so-called damping function, h(γ). In this review, we summarize a recent progress in molecular understanding of the damping behavior of associative polymers from both the experimental and theoretical perspectives. The damping is related to the rupture and reconstruction of associative network after applying step strain and before the terminal stress relaxation. Incorporation of this mechanism into the classic sticky Rouse model through the conformation pre-averaging protocol enables quantitative prediction of the damping behavior of randomly associating linear polymers as well as end-associative star polymers, both in the unentangled state. [ABSTRACT FROM AUTHOR]

Ionomers are associative polymers with diverse applications ranging from selective membranes and high-performance adhesives to abrasion- and chemical-resistant coatings, insulation layers, vacuum packaging, and foamed sheets. Within equilibrium melt, the ionic or associating groups are known to form thermally reversible, associative clusters whose presence can significantly affect the system's mechanical, viscoelastic, and transport properties. It is, thus, of great interest to understand how to control such clusters' size distribution, shape, and stability through the designed choice of polymer architecture and the ionic groups' fraction, arrangement, and interaction strength. In this work, we represent linear associating polymers using a Kremer–Grest type bead–spring model and perform large-scale MD simulations to explore the effect of polymer chain-length ( l ) and fraction ( f s ) of randomly placed associating groups on the size distribution and stability of formed clusters. We consider different chain-lengths (below and above entanglement), varying fractions of associating groups (represented by 'sticky' beads) between 5 and 20%, and a fixed sticky–sticky nonbond interaction strength of four times that between regular non-associating beads. For all melts containing associating groups the equilibrium structure factor S (q) displays a signature ionomer peak at low wave vector q whose intensity increases with increasing f s and l . The average cluster size N c increases with f s . However, the effect of chain-length on N c appears to be pronounced only at higher values of f s . Under extensional flows, the computed stress (and viscosity) is higher at higher f s and l regardless of strain rate. Beyond a critical strain rate, we observe fragmentation of the associative clusters, which has interesting effects on the stress/viscous response. [ABSTRACT FROM AUTHOR]

The trade-off between hardness and stretchability is a cornerstone of materials science. Balancing this trade-off is important in the molecular design of both chemical and physical networks. In this study, we report the quantitative trade-off at the molecular level for physical networks. Namely, we analyze, based on the reversible gelation model, a scaling relationship between the characteristic terminal relaxation modulus Gc in linear viscoelasticity and the stretch ratio λmax at the stress overshoot during the nonlinear elongation flow for unentangled randomly associative polymers, i.e., λmax ∼ Gc−0.17 and λmax ∼ Gc−0.33 in the mean-field and critical-percolation regimes, respectively. We use sulfonated polystyrene having different alkali counterions as a model system to test the relationship. The exponent of λmax ∼ Gc−0.25 seen in the experiment is in between the two theoretical values. We also discuss the quantitative deviation with respect to the size distribution of the network strands. [ABSTRACT FROM AUTHOR]

A linear stability analysis is carried out for viscoelastic filaments (formed by an unentangled polymer solution) during capillary thinning in the regime of unfolded polymer coils taking into account the relative motion of the solvent and the polymer. The conditions for the onset of filament instability with respect to axisymmetric modulation of its surface are found. The analysis is valid for relatively fast processes occurring at times shorter than the characteristic thinning time. It is shown that the growth rate of such pearling instability is determined by the osmotic modulus of the solution and the degree of orientation of macromolecules. In the case of nonassociative polymers, the instability develops (with the growth rate exceeding the rate of filament thinning) when the longitudinal length of stretched polymer chains exceeds the diameter of the filament. The theory is also applicable to soft gels and associative polymer solutions with very long relaxation times. The predictions of the theory are in agreement with experimental data. [ABSTRACT FROM AUTHOR]

The concentration and hydrophobicity-dependent hydrophobic associations are responsible for distinct rheological behavior for associative polymers (AP) to prove its application in various industrial operations. In this study, commercially available water-soluble, AP C319, P329, and D118 with similar weight-average molar masses with varying hydrophobicity were characterized by the field-flow fractionation method to determine molecular weight distribution and size distribution, steady shear flow, and the uniaxial elongation in capillary breakup experiments. The domination of intramolecular and intermolecular hydrophobic associations was found to be responsible for the polymer shrinkage (with hydrophobicity) and aggregation (with concentration), respectively. The tumbling of polymer macromolecules under the shear field resulted in a similar shear behavior for all polymers. However, higher shear viscosities due to the formation of polymer aggregates in the semi-dilute regime justify the domination of intermolecular hydrophobic associations. These associations also contributed to broader MWD for polymer solutions having higher relaxation time and extensional viscosity compared to the corresponding solutions in the dilute regime. For C319, the formation of flexible aggregates at 2000 ppm resulted in higher strain hardening compared to 1000 ppm, whereas, at 1000 ppm, the higher entanglements between polymer chains due to the lowest hydrophobicity for C319 resulted in the higher strain hardening. At high hydrophobicity, the coiled structure became rigid due to reduced solvent holding inside the compacted structure formed due to the domination of intramolecular hydrophobic associations. Therefore, the relaxation time and extensional viscosity decrease with an increase in the hydrophobicity in both regimes. [ABSTRACT FROM AUTHOR]

Associative polymers based on acrylic acid and n -butyl methacrylate were synthesized via precipitation polymerization in pressurized carbon dioxide. Physicochemical characterization confirmed BMA incorporation and good reaction yields (>67.1 mol%). Size exclusion chromatography showed bimodal polymer molar mass distribution with distinct average molar masses. Rheological properties of aqueous polymer solutions were assessed under varying pH, ionic strength, and salt concentrations and demonstrated increased viscosity with higher n -butyl methacrylate content, attributed to hydrophobic associations. The apparent viscosity of the synthesized polymers was strongly influenced by the ionic strength of the aqueous solutions. [Display omitted] • Polymers of acrylic acid and butyl methacrylate were obtained in supercritical CO 2. • Phase equilibria for scCO 2 + butyl methacrylate + acrylic acid were measured. • M w of the polymers yield values up to 2 ×106 g mol−1. • SEC-MALS-dri revealed distinct polymer populations with increased BMA in the feed. • The viscosity of aqueous solutions of the polymers increased with increasing BMA. [ABSTRACT FROM AUTHOR]

In this paper, a bifunctional associative polymer with twin tail and long chain was synthesized. Its structure was confirmed by FT-IR and NMR. The goal is to find the solution of front-end drag reduction and tail-end sand carrying. Fluorescence spectrum, laser particle size, and scanning electron microscope (SEM) were used to analyze the microstructure of the polymer. Fracturing fluid friction meter was used to evaluate the drag reduction rate (DR) as a function of concentration, temperature, and flow. It shows a connection between the number, morphology, and concentration of hydrophobic microregions generated by the association polymer. A hydrophobic microregion of the tail supplies the tail end with increased viscosity and sand carrying at low concentrations. The intermolecular interactions get stronger with increasing concentrations at high concentrations. A space grid structure is constructed after a specified association concentration reaching. High shear will break some molecular chains at this time due to the weak bonding effect, limiting the drag reduction effect. The results show that drag reduction rate (DR) can reach 72% with the flow rate increasing from 15 to 40 L·min−1 when the concentration reaches 2000 mg/L and the temperature is 30 ℃. [ABSTRACT FROM AUTHOR]

We provide a canonical introduction to dual-junction-functionality associative polymer networks, which combine high and low functionality (f) dynamic cross-link junctions to impart load-bearing, dissipation, and self-repairing ability to the network. This unique type of network configuration offers an alternative to traditional dual-junction networks consisting of covalent and reversible cross-links. The high-f junctions can provide load-bearing abilities similar to a covalent cross-link while retaining the ability to self-repair and concurrently confer stimuli-responsive properties arising from the high-f junction species. We demonstrate the mechanical properties of this design motif using metal-coordinating polymer hydrogel networks, which are dynamically cross-linked by different ratios of metal nanoparticle (high-f) and metal ion (low-f) cross-link junctions. We also demonstrate the spontaneous self-assembly of nanoparticle-cross-linked polymers into anisotropic sheets, which may be generalizable for designing dual-junction-functionality associative networks with low volume fraction percolated high-f networks. [ABSTRACT FROM AUTHOR]

In this work, equilibrium molecular dynamics is used to predict the change in the Helmholtz free energy ( Δ A) for solutions of associative polymers of the telechelic type. Δ A is calculated using the thermodynamic integration method, wherein molecular chains are simulated in a coarse-grain scale within an NVT ensemble. Simulations take place in the concentration interval 0.03 ≤ c ≤ 0.25 , such that aggregate formation is possible. The initial configuration is that of dispersed free chains; the increase of interactions among stickers signals the onset of the micelle formation process. The solution with high concentration experiences substantial micelle aggregation despite little conformation changes. Therein, transient networks among micellar flowers are formed. The decrease in free energy is related to the formation of aggregates to achieve stability. When solutions are thermodynamically stable, the free energy and configurational entropy decrease and increase non-linearly with concentration, respectively. Below critical micellar concentration, this behaviour is associated with a step-by-step process along which the sticker groups gather to form the first thermodynamically stable aggregate. Above critical micellar concentration, the most probable distribution increases with concentration, therefore, free energy decreases with increasing aggregates that form the network. [ABSTRACT FROM AUTHOR]

Macromolecular phase separation is thought to be one of the processes that drives the formation of membraneless biomolecular condensates in cells. The dynamics of phase separation are thought to follow the tenets of classical nucleation theory, and, therefore, subsaturated solutions should be devoid of clusters with more than a few molecules. We tested this prediction using in vitro biophysical studies to characterize subsaturated solutions of phase-separating RNA-binding proteins with intrinsically disordered prion like domains and RNA-binding domains. Surprisingly, and in direct contradiction to expectations from classical nucleation theory, we find that subsaturated solutions are characterized by the presence of heterogeneous distributions of clusters. The distributions of cluster sizes, which are dominated by small species, shift continuously toward larger sizes as protein concentrations increase and approach the saturation concentration. As a result, many of the clusters encompass tens to hundreds of molecules, while less than 1% of the solutions are mesoscale species that are several hundred nanometers in diameter. We find that cluster formation in subsaturated solutions and phase separation in supersaturated solutions are strongly coupled via sequence-encoded interactions. We also find that cluster formation and phase separation can be decoupled using solutes as well as specific sets of mutations. Our findings, which are concordant with predictions for associative polymers, implicate an interplay between networks of sequence-specific and solubility-determining interactions that, respectively, govern cluster formation in subsaturated solutions and the saturation concentrations above which phase separation occurs. [ABSTRACT FROM AUTHOR]

Macromolecular phase separation is being recognized for its potential importance and relevance as a driver of spatial organization within cells. Here, we describe a framework based on synergies between networking (percolation or gelation) and density (phase separation) transitions. Accordingly, the phase transitions in question are referred to as phase separation coupled to percolation (PSCP). The condensates that result from PSCP are viscoelastic network fluids. Such systems have sequence-, composition-, and topology-specific internal network structures that give rise to time-dependent interplays between viscous and elastic properties. Unlike pure phase separation, the process of PSCP gives rise to sequence-, chemistry-, and structure-specific distributions of clusters that can form at concentrations that lie well below the threshold concentration for phase separation. PSCP, influenced by specific versus solubility-determining interactions, also provides a bridge between different observations and helps answer questions and address challenges that have arisen regarding the role of macromolecular phase separation in biology. Mittag and Pappu summarize a framework for biomolecular condensate formation that is based on phase separation coupled with percolation. This framework helps address recent challenges and helps highlight the fact that condensates are viscoelastic materials possessing distinctive internal structures and material properties that are sequence-, architecture-, and composition-specific. [ABSTRACT FROM AUTHOR]

• Associative polymers exhibit complex flow behavior in porous media. • Conventional shear rheology cannot decode the associative polymer's behavior in porous media. • Extensional rheology cannot decode the associative polymer's porous media behavior. • Retention complicates the transport behavior of associative polymers. • Conformational properties can decode the transport properties of associative polymer. This paper delves into the conformational and transport properties of three different associative polymers (C-319, P-329 and D-118) in porous media, focusing on the role of hydrophobicity at varying concentrations. In our latest paper it was reported that at 1000 parts per million (ppm), higher hydrophobic polymers (D-118) display a distinct increase in shear thickening but a decreased extensional viscosity compared to their less hydrophobic counterparts C-319 and P-329. This relationship inverts at 2000 ppm, where an increase in hydrophobicity is associated with a decrease in shear thickening, and extensional viscosity, suggesting extensional rheology of associative polymers could correlate with porous media behavior at higher concentrations but not at lower concentrations. Higher retention was found to be the reason for the higher resistance factor of higher hydrophobic polymers at 1000 ppm whereas at 2000 ppm they have less retention. Is there another phenomenon related to polymer physics that causes this contradiction, and plays a major role during the transport of associative polymeric flow in porous media? This paper aims to answer this question using the combination of extensional rheology and asymmetrical flow field-flow fractionation (AF4). The extensional viscosity of these systems at 1000 ppm are 90 Pa.s, 222 Pa.s and 201 Pa.s. At 2000 ppm, these values are 448 Pa.s, 344 Pa.s, and 196 Pa.s. The shape factor for D-118 was found to be between 0.41 (at 1000 ppm) and 0.20 (at 2000), an indication that the polymer chains are taking the conformation of random coils and spheres at 1000 and 2000 ppm respectively. For C-319 and P-329, respectively, these values are (0.51–0.57) and (0.40–0.49), an indication that they are even more random. It appears that the higher resistance factor shown by D-118 at 1000 ppm is due to the preserved randomness of the polymer chain and amplified Mw despite having the lower extensional viscosity. Contrarily at 2000 ppm, the shape factor was found to be 0.20, an indication that they are compacted. As the compacted polymer chain doesn't stretch, D-118 doesn't appears to get retained significantly at 2000 ppm. C-319 has more flexible chain than P-329 at both concentrations which is the reason why they have higher extensional viscosity and resistance factor. A novel contribution of this work is the elucidation of porous media transport properties of associative polymers, which are intricately tied to the randomness of polymer chains as well as their molecular weight and hydrophobic characteristics. The key novelty of this work is transport properties of the associative polymer in porous media are better delineated by a combination of AF4 and extensional rheology, and retention appears to be related to the randomness of the polymer chain. [ABSTRACT FROM AUTHOR]

Non-equilibrium molecular dynamics are used in a coarse-grained scale to simulate the simple shear flow of telechelic and non-telechelic associative polymer solutions. The work includes the study of inception of flow and stress relaxation in transient flows and the constitutive curve at steady state. The instabilities (plateau stress, stress maxima) and the formation of bands with different velocity gradient and concentration depend on the location of the hydrophobic sites (sticker sites, SS) in the chain. Results allow to shed light on the origin of banded flow within the transient state, related to depletion of bridges between aggregates. This situation induces instabilities in the velocity profiles and concentration inhomogeneities along the velocity gradient during the stress overshoot. As the steady state is reached, instabilities disappear for systems where the SS are in the middle of the chain. The conformation relaxation occurs during a time scale larger than that of the stress, but this is not sufficient condition for the presence of banded flow in telechelic polymer solutions, as it holds in polymer melts. The difference in concentration among the bands suggests the existence of a shear-gradient concentration coupling mechanism under banded flow conditions, such as spatial non-homogeneities in the network density, induces chain diffusivity in the gradient direction and increasing normal stresses, especially in telechelic chains. The role of normal stresses on the flow-concentration coupling instability is analyzed in detail. [ABSTRACT FROM AUTHOR]

Cells possess a multiplicity of non-membrane-bound compartments, which form via liquid-liquid phase separation. These condensates assemble and dissolve as needed to enable central cellular functions. One important class of condensates is those composed of two associating polymer species that form one-to-one specific bonds. What are the physical principles that underlie phase separation in such systems? To address this question, we employed coarse-grained molecular dynamics simulations to examine how the phase boundaries depend on polymer valence, stoichiometry, and binding strength. We discovered a striking phenomenon – for sufficiently strong binding, phase separation is suppressed at rational polymer stoichiometries, which we termed the magic-ratio effect. We further developed an analytical dimer-gel theory that confirmed the magic-ratio effect and disentangled the individual roles of polymer properties in shaping the phase diagram. Our work provides new insights into the factors controlling the phase diagrams of biomolecular condensates, with implications for natural and synthetic systems.

Nature uses bottom-up self-assembly to build structures with remarkable complexity and functionality. Understanding how molecular-scale interactions translate to macroscopic properties remains a major challenge and requires systems that effectively bridge these two scales. Here, we generate DNA and RNA liquids with exquisite programmability in their material properties. Nucleic acids are negatively charged, and in the presence of polycations, they may condense to a liquid-like state. Within these liquids, DNA and RNA retain sequence-specific hybridization abilities. We show that intermolecular hybridization in the condensed phase cross-links molecules and slows down chain dynamics. This reduced chain mobility is mirrored in the macroscopic properties of the condensates. Molecular diffusivity and material viscosity scale with the intermolecular hybridization energy, enabling precise sequence-based modulation of condensate properties over orders of magnitude. Our work offers a robust platform to create self-assembling programmable fluids and may help advance our understanding of liquid-like compartments in cells.

We show how two-species models, already proposed for the rheology of networks of associative polymer solutions, can be derived from nonequilibrium thermodynamics using the generalized bracket formalism. The two species refer to bridges and (temporary) dangling chains, both of which are represented as dumbbells. Creation and destruction of bridges in our model are accommodated self-consistently by assuming a two-way reaction characterized by a forward and a reverse rate constant. Although the final set of evolution equations for the microstructure of the two species and the expression for the stress tensor are similar to those of earlier models based on network kinetic theory, nonequilibrium thermodynamics sets specific constraints on the form of the attachment/detachment rates appearing in these equations, which, in some cases, deviate significantly from previously reported ones. We also carry out a detailed analysis demonstrating the capability of the new model to describe various sets of rheological data for solutions of associative polymers. [ABSTRACT FROM AUTHOR]

Carbonate reservoirs are heterogeneous from pore scale to field scale. Waterflood in carbonate reservoirs often leaves behind a substantial amount of oil due to pore-scale and large-scale bypassing. Polymer flooding can improve sweep efficiency and oil production. Most EOR polymers cannot be transported through low-permeability (< 30 mD) rocks. Hydrophobically modified associative polymers (APs) associate with each other during passage through pore throats and give a larger flow resistance than conventional polymers (Flopaam) of the same molecular weight. The goal of this work is to investigate the transport of associative polymers in low-permeability carbonate reservoirs (less than 50 md). An associative polymer similar in molecular weight to Flopaam 3330 was investigated in this study. Polymer rheology and the effect of salinity were studied at 60 °C. Mechanical shearing and aggressive filtration were used to modify the particle size distribution in polymeric solutions and improve transport through tight cores. Single-phase polymer transport experiments were performed in outcrop Edwards Yellow and Indiana limestone cores. Mechanical shear degradation reduced the particle size and improved the transport of the associative polymer in low-permeability carbonate cores. The permeability reduction factor and the residual resistance factor were higher for the sheared AP polymers than those for the sheared Flopaam polymer. The resistance factors for the associative polymer were higher than those for Flopaam for a given shear viscosity. Coreflood experiments with AP showed the evidence of two propagation fronts: polymer concentration front and pressure gradient stabilization front due to polymer network formation and polymer adsorption. As AP polymer concentration increased, permeability reduction factor, resistance factor, residual resistance factor and polymer adsorption increased. All the coreflood experiments suggest successful polymer transport in low-permeability carbonate cores even at significantly high polymer concentrations with pre-shearing. [ABSTRACT FROM AUTHOR]

Research advancement in polymer flooding for Enhanced Oil Recovery (EOR) has been growing over the last decade. This growth can be tied to increased funding towards the development of superior polymers such as hydrophobically associating polymers when oil prices were high and increasing concern that "easy oil" has been exploited with the focus now on "difficult to extract" oil. The use of hydrophobically associating polymers for EOR was discussed along with its limitations. In this context, the improved rheological properties of associating polymers cannot only be linked to the molecular structures arising from different synthesis methods. Equally, external parameters similar to conditions of oil reservoirs affect the rheological properties of these polymers. As such, this review placed critical emphasis on the molecular architecture of the polymer and the synthesis route and this was linked to the observed rheological properties. In addition, the influence of some key oilfield parameters such as temperature, salinity, pH, and reservoir heterogeneity on the rheological behavior of hydrophobically associating polymers were reviewed. In this respect, the various findings garnered in understanding the correlation between polymer rheological properties and oilfield parameters were critically reviewed. For associating polymers, an understanding of the molecular architecture (and hence the synthesis method) is crucial for its successful design. However, this must be theoretically linked to the preferred EOR application requirements (based on oilfield parameters). [ABSTRACT FROM AUTHOR]

Abstract Selective reduction of hydrogen bonds of a phenoxy resin gave samples particularly suitable to investigate specific interactions in associative polymers. The glass transition temperature decreased when reducing hydrogen bonds, but dielectric results indicated that α and β relaxations are rather affected by steric hindrances (bulky groups). A model accounting for the combined effect of entanglements and secondary interactions on viscosity, which can be generalised for other associative polymers, is proposed and hydrogen bonds/entanglements rate is determined. Dynamic viscoelastic results at T = 170 °C and T - T g = 80 °C, showed that hydrogen bonds did not constitute a network and were weakened by temperature. The non-linear viscoelastic parameter Q 0 decreased as the amount of hydrogen bonds was reduced. LAOS (Large Amplitude Oscillatory Shear) experiments constitute a new rheological tool to investigate associative polymers. Strain hardening in extensional flow was probed to be a consequence of the long relaxation times associated to hydrogen bonds and obtained from viscoelastic data. Graphical abstract Image 1 Highlights • Specific interactions in associative polymers are studied by modifying phenoxy resin. • Newtonian viscosity allows establishing the rate of hydrogen bonds to entanglements. • LAOS measurements are a promising tool to analyse the effect of hydrogen bonds. • Strain hardening of phenoxy results from long relaxation times due to hydrogen bonds. [ABSTRACT FROM AUTHOR]

Hydrophobically modified telechelic associative polymers (TAPs) composed of hydrophilic backbone and two hydrophobic end groups can form dynamic transient networks in water and have been widely used as thickeners for improving solution rheological properties in many industrial fields. In this work, we designed and prepared a novel telechelic associative model polymer (FcC11AzoTAP) end-functionalized by photo-responsive azobenzene (Azo) unit along with the redox-responsive ferrocene extremity, which was used to investigate the effects of stimuli responsive behaviors such as redox reaction or/and photo isomerization of end groups on its solution aggregation and rheological properties. It has been demonstrated that the network structures and rheological properties of FcC11AzoTAP aqueous solutions can be readily tuned by the magnitude of stimuli-responsive hydrophobicity change of end groups to a certain degree. Moreover, a rearrangement of network through bridge to inactive loop and/or pending arm transitions is proposed to describe the dense to sparse network conversion. This work will not only provide new insights into the effects of end groups on the network structure and rheological properties of solution but it also opens a new perspective for some special applications of TAPs in industrial fields. [ABSTRACT FROM AUTHOR]

Linear coreflood experiments are performed at 60 °C to test the effectiveness of a low molecular weight associative polymer as a displacing agent, and its ability to enhance oil recovery on chemically treated oil-wet Berea cores. Polymer injection tests revealed high mobility reductions (resistance factor (RF)) and reduced remaining oil saturations. Results obtained suggest that the incremental oil production is due to the high mobility reduction, as reported previously for water-wet porous media. The reduced remaining oil saturation is a function of the injected associative polymer treatment volume. Polymer mobility reduction is highly affected by the injected polymer velocity; this reduction is observed to be more significant at the lower velocity spectrum. Therefore, the established incremental oil production, even at reduced polymer injection rates (lower capillary numbers), could be explained by the increased mobility reduction. A correlation for the velocity-dependent mobility reduction is developed. Results are in agreement with previously reported ones in water-wet media and related to the enhanced oil recovery (EOR) nature of the injected associative polymer as opposed to the traditional mobility control of other polymer types. During injection, a column of oil-polymer emulsion is formed gradually in the separator causing operational difficulties and introducing produced fluid measurement (and core fluid saturations) uncertainties. Produced oil/water emulsion polymer volume content is used to correct overestimated oil production attributed to measurement uncertainties. Real-time resistivity measurements could also be a valuable tool for both fluids saturation monitoring and improved core fluids saturation evaluation in flooded porous media. [ABSTRACT FROM AUTHOR]

Percec-type substituted benzyl alcohol mini-dendrons as new hydrophobic end-cappers can effectively improve the thickening performance of hydrophobically modified ethoxylated urethanes (HEURs) in aqueous solution. To demonstrate the effects of substituted structure of Percec-type mini-dendritic end groups on aggregation and rheological properties of HEURs in aqueous solution and latex, three model HEURs end-functionalized by mono-, di- and tri-substituted benzyl alcohol mini-dendrons were synthesized, respectively. For a reasonable comparison, the total carbon number of substituted alkyl tails is set to be 24 for the three mini-dendritic end groups: HOCH 2 - Ph -C 24 H 49 ( C24 ), HOCH 2 - Ph -(C 12 H 25 ) 2 ( 2C12 ) and HOCH 2 - Ph -(C 8 H 17 ) 3 ( 3C8 ), which respectively correspond to single-, two- and three-tail according to their substituted degrees. Interestingly, rheological properties of these HEURs in aqueous solution and latex significantly depend on the substituted degree of mini-dendritic hydrophobes. The high-substituted mini-dendritic hydrophobes help HEURs to form a strong physical network with high thickening performance and fast relaxation in both aqueous solution and latex, because shorter alkyl tails in high-substituted dendritic hydrophobes will lead to a smaller aggregation number and a lower rheological activation energy. This work not only provides new insights into the connection of networks in solutions of mini-dendron functionalized HEURs but also offers a new approach to preparation of high performance thickeners used in water-borne systems. [ABSTRACT FROM AUTHOR]

Hydrogel films used as membranes or coatings are essential components of devices interfaced with biological systems. Their design is greatly challenged by the need to find mild synthesis and processing conditions that preserve their biocompatibility and the integrity of encapsulated compounds. Here, we report an approach to produce hydrogel films spontaneously in aqueous polymer solutions. This method uses the solvent depletion created at the surface of swelling polymer substrates to induce the gelation of a thin layer of polymer solution. Using a biocompatible polymer that self-assembles at high concentration [poly(vinyl alcohol)], hydrogel films were produced within minutes to hours with thicknesses ranging from tens to hundreds of micrometers. A simple model and numerical simulations of mass transport during swelling capture the experiments and predict how film growth depends on the solution composition, substrate geometry, and swelling properties. The versatility of the approach was verified with a variety of swelling substrates and hydrogel-forming solutions. We also demonstrate the potential of this technique by incorporating other solutes such as inorganic particles to fabricate ceramic-hydrogel coatings for bone anchoring and cells to fabricate cell-laden membranes for cell culture or tissue engineering. [ABSTRACT FROM AUTHOR]

Hydrophobically modified ethoxylated urethanes (HEURs) are an important class of telechelic associative polymers with various industrial applications, in which careful control of the rheology of the solution is required. We report the synthesis of three novel HEUR polymers end-functionalized by dendritic di-substituted benzene alcohol ( HEUR-2Cn , where n is the length of hydrophobic tails) and their rheological properties in aqueous solutions and latex. The concentrated solutions of these HEURs show interesting aggregation and viscoelastic properties dependent of their hydrophobe length: a viscoelastic liquid for HEUR-2C8 , and elastic gels for both HEUR-2C12 and HEUR-2C16 due to their different relaxation behavior. Interestingly, the concentrated solutions of HEUR-2C16 form the strongest transient network with the largest number density of active micellar junctions and slowest relaxation because of its longest hydrophobe. Furthermore, these HEUR polymers have highly efficient thickening performance in latex compared with a conventional HEUR-C16 with −C 16 H 33 end group, because the dendritic two-tail hydrophobes can form more stable absorption on the surface of the latex through bridging between the latex particles than a single hydrophobe. This work opens a new perspective for highly efficient thickeners and also provides new insights into the potential of these HEUR polymers in waterborne coating, cosmetics, dyestuff, medicines and so on. [ABSTRACT FROM AUTHOR]

Aqueous solutions of amphiphilic polymers usually comprise of inter- and intramolecular associations of hydrophobic groups often leading to a formation of a rheologically significant reversible network at low concentrations that can be identified using techniques such as static light scattering and rheometry. However, in most studies published till date comparing water soluble polymers with their respective amphiphilic derivatives, it has been very difficult to distinguish between the effects of molecular mass versus hydrophobic associations on hydrodynamic (intrinsic viscosity [η]) and thermodynamic parameters (second virial coefficient A), owing to the differences between their degrees of polymerization. This study focuses on the dilute and semi-dilute solutions of hydroxyethyl cellulose (HEC) and its amphiphilic derivatives (hmHEC) of the same molecular mass, along with other samples having a different molecular mass using capillary viscometry, rheometry and static light scattering. The weight average molecular masses ( M) and their distributions for the non-associative HEC were determined using size exclusion chromatography. Various empirical approaches developed by past authors to determine [η] from dilute solution viscometry data have been discussed. hmHEC with a sufficiently high degree of hydrophobic modification was found to be forming a rheologically significant network in dilute solutions at very low concentrations as opposed to the hmHEC with a much lower degree of hydrophobic modification which also enveloped the hydrophobic groups inside the supramolecular cluster as shown by their [η] and A. The ratio A M/[η], which takes into account hydrodynamic as well as thermodynamic parameters, was observed to be less for associative polymers compared to that of the non-associative polymers. [ABSTRACT FROM AUTHOR]

In this work, non-equilibrium molecular dynamics (NEMD) is used to simulate simple shear flow of associative polymer solutions of the telechelic and multi-sticker types. The objective of the work is the analysis of the effect of the hydrophobic groups of these polymers on the rheological behavior of the system. To generate the flow, the equations of motion are coupled to boundary conditions of Lees and Edward [A.W. Lees, S.F. Edward, J. Phys. C 5 (1972) 1921], where simulations are performed at constant temperature under a coarse-grain simulation scale. Three concentration regimes are identified: dilute, semi-dilute unentangled and semi-dilute entangled. In the dilute regime, the multi-sticker polymers exhibit a Newtonian constant-viscosity region, while in telechelic polymers a shear-thickening region is observed. In this regime, the molecules are isolated, so that the majority of hydrophobic interactions occur between sites of the same chain. Coordination number reveals the presence of a transient first-layer of hydrophobic neighbors, associated with the viscosity of the polymer. In the semi-dilute unentangled regime, both types exhibit a Newtonian region at low shear-rates followed by shear thinning. For telechelic polymers, the Newtonian viscosity increases with concentration with a slope of 4.4, attributed to the formation of non-isotropic aggregates with viscoelasticity levels of two orders of magnitude larger than those of the non-modified polymers. Static structure-factor suggests an increasing alignment of the multi-sticker polymer along the x -direction, revealing larger molecular mobility and lower viscosity than in the telechelic polymers. Finally, these results reveal that when the hydrophobic groups are located at the extremes of the polymer chain (telechelic type), the rheological behavior is strongly affected in the dilute regime by the formation of inter-connected aggregates. On the other hand, when the hydrophobic groups are located in the interior of the chain (multi-sticker type) hydrophobic associations are inhibited by topological restrictions, and in this case the viscoelastic response is only observed in the semi-dilute regime. [ABSTRACT FROM AUTHOR]

The interactions between hydrophobically modified polyacrylamides (HMPAM) and the anionic surfactant SDS (sodium dodecyl sulfate) and/or the cationic surfactant DTAB (dodecyltrimethylammonium bromide) were studied in aqueous solution using steady flows and oscillatory rheological experiments. The structure of the HMPAM used consisted of a telechelic polymer (with hydrophobic groups at the chain ends) and a multisticker polymer (with hydrophobic groups along the polymer chain). The multisticker polymer was prepared with acrylamide and N-hexadecylacrylamide (HDAM), whereas the telechelic polymer was prepared with acrylamide and a hydrophobic initiator that was derived from 4,4′-azobis(4-cyanopentanoic acid) (ACVA) and contained a long linear chain of 16 carbon atoms (ACVA). In both polymers, the rheological behavior depended strongly on the amount of surfactant added. For the telechelic and multisticker polymers, the terminal relaxation time T exhibited a maximum when the surfactant concentration was augmented (SDS or DTAB). An increase or decrease in the plateau modulus G was observed, depending on the structure of the polymer (telechelic or multisticker). [ABSTRACT FROM AUTHOR]

Nanoassemblies are spontaneously formed in dilute aqueous solutions by mixing of two dextrans modified with lauroyl and β-cyclodextrin moieties, respectively. This association process is mainly driven by host/guest interactions between the two polymers. The nanoassemblies' size depends on the substitution degrees of the polymers, and on the total concentration and composition of the mixtures. The results are compared to those previously obtained with adamantyl grafted dextrans. The number and the strength of the individual guest-host complexes between the two grafted dextrans is the key parameter to obtain small and stable nanoassemblies. [ABSTRACT FROM AUTHOR]

Drag correction factors are calculated for the creeping motion of spheres descending in various associative polymers of different concentration with various sphere-container ratios and Weissenberg numbers. The simple-shear rheology and linear viscoelasticity of these polymeric fluids have been previously presented and modeled with the BMP (Bautista–Manero–Puig) equation of state (Mendoza-Fuentes et al., Phys Fluids 21:033104, ). The drag on the sphere is initially kept nearly constant for small Weissenberg numbers, We < 0.1. As the Weissenberg number increases, We < 0.1, a reduction in drag is found. Experimental results show the presence of a critical Weissenberg number at which a drag reduction occurs. The reduction in the drag correction factor is associated to the onset of extension-thinning, which coincides with the formation of a negative wake. No increase in the drag correction factor was observed, due to the simultaneous opposing effects of extension-thickening and shear-thinning viscosity. The shape of the drag correction factor curve may be predicted considering the extensional properties of the solutions, as suggested elsewhere (Chen and Rothstein, J Non-Newton Fluid Mech 116:205–215, ). [ABSTRACT FROM AUTHOR]

Abstract: The aim of this paper was to study the associations between a neutral β-cyclodextrin polymer and amphiphilic dextrans substituted with two kinds of groups able to make inclusion complexes with β-cyclodextrin. The first kind of substituent is purely hydrophobic (dodecyl C12 or adamantyl Ada groups) and the second one, cyclohexancarboxylic acid group CHX, brings pH-dependent charge density on the dextran chains. Synthesis and characterization of the di-substituted dextrans have been detailed in a first part where it has been shown that the incorporation of CHX groups (up to 7mol.%) did not modify the self assembling properties of the amphiphilic dextrans. Affinity of the amphiphilic dextrans for β-cyclodextrin polymer has been studied by different methods including isothermal titration calorimetry, dynamic light scattering and zeta potential. An original pH sensitive behaviour has been obtained for polymer–polymer associations at low concentrations. Nanoassemblies are formed at pH around 4 which are destabilized at lower pH and swollen into soluble aggregates at higher pH. The nanoassemblies formed at pH 4 have also been evidenced by transmission electron microscopy and have revealed a spherical shape of few hundred nanometers. [Copyright &y& Elsevier]

Abstract: A linear water soluble β-cyclodextrin terpolymer (P(MVE-AM)-g-βCD) was synthesized by grafting different amounts of βCD on the copolymer P(MVE-AM). The resulting terpolymer showed a pH sensitive behaviour in aqueous solution, due to the presence of carboxylic acid groups. Whatever the substitution degree in βCD, the terpolymer behaved like a polyacid at pH 7, and had neutral properties at pH 2. The mixture of P(MVE-AM)-g-βCD with an amphiphilic poly(ethylene oxide) (PEO-Ad3) showed an associative phase separation influenced by the pH and concentration of the medium. In the dilute range and intermediate range, associative phase separations were induced reversibly by decreasing the pH from 7 to 2. The results in the semi-dilute range showed that networks were elaborated with much stronger dynamic modulus at low pH (pH 2) than at higher pH (pH 7). Coupled inclusion complex interactions (between the adamantyl groups of PEO-Ad3 and the cyclodextrin cavities of P(MVE-AM)-g-βCD) with hydrogen bonding (between carboxylic acid groups and PEO backbone) could be a way to modulate the strength of the interactions in supramolecular assemblies. These results suggest that the mixture of P(MVE-AM)-g-βCD with PEO-Ad3 could be a potential pH sensitive system. [Copyright &y& Elsevier]

Abstract: New water soluble and amphiphilic PCL-grafted-alginates with two different molar masses of PCL (530 and 1250gmol−1) and molar hydrophobe contents from 3.5 to 15% have been prepared by new aqueous micellar grafting technique. Physico-chemical behaviour in aqueous solution (pure water and NaCl 0.1M) has been studied by means of viscosity measurements and on-line Flow field flow fractionation/Multi-angle laser light scattering/Quasi-elastic light scattering/Differential refractive index analyses. Expected associative behaviour has been evidenced in pure water whatever the length of the PCL chains. In salt media, the associative behaviour strongly depends on the length of PCL chains. For PCL chains of 530gmol−1, intramolecular hydrophobic interactions are predominant, even in semi-dilute regime. This non-classical behaviour for an associative polyelectrolyte opens the way to the conception of amphiphilic matrices with hydrophobic clusters for controlled release applications. [Copyright &y& Elsevier]

Abstract: The shear imposed oscillation technique was employed to probe the shear-induced structural changes of 3wt% hydrophobically modified polyelectrolyte solutions that possess shear-thinning and shear-thickening behavior. The shear-thickening behavior is related to the transformation of predominantly intra-molecular to inter-molecular associations. On the other hand, the shear-thinning behavior under moderate shear deformation is caused by the re-organization of the transient network structure. Under high shear deformation, the shear-thinning behavior is solely caused by the shear-induced effect that increases the chain-end exit rate, which reduces the mechanically active chains and lifetime of the hydrophobe in the micellar junctions. [Copyright &y& Elsevier]

Abstract: In this study, steady state, dynamic shear and normal stress differences of the polymer solutions containing telechelic hydrophobically modified ethoxylated urethane (HEUR) associative polymers have been investigated. The intermediate steady state and dynamic shear thickening were observed for both ascending and descending shear rate and frequency, respectively. The dynamic amplitude stress sweep measurements showed that maxima in G′ and G″ occurred at the frequencies of 1, 5 and 10rad/s. At lower shear rates and frequencies, the ratio of complex viscosity to steady shear viscosity was observed to be greater than unity. This phenomenon is believed to be associated with the formation of a micro-gel like structure. The modified Cox–Merz rule (Delaware–Rutgers rule) explained the dynamic and steady state viscosity behaviors well in the shear thinning zone but not at the plateau or shear thickening regions. [Copyright &y& Elsevier]

Abstract: Hydrophobically modified ethoxylated urethanes (HEUR) associative copolymers are prepared through the hydrophobic modification of polyethylene glycol based polyurethanes. These types of thickeners are categorized as anionic associative thickeners. To investigate the effect of structure of the hydrophobic groups on the thickening properties, three different hydrophobic groups were selected. These groups were comprised of cetyl alcohol (16 carbons), dodecyl alcohol (12 carbons) and a cyclic group such as cyclo hexanol. These functional groups were substituted on the identical prepolymers made from H12MDI and polyethylene glycol. Here, three different urethane associative polymers containing hydrophobic segments and different hydrophobic groups were synthesized. The viscoelastic characteristics of all the samples were determined using a cone and plate rheometer. The viscosities of the examined HEUR samples showed both Newtonian and non-Newtonian behaviours (shear thinning and thickening) for the explored shear rates window. The steady shear viscosity results were interpreted using the theories by Raspaud [Macromolecules 27 (1994) 2956] and Semenov [Macromolecules 28 (1995) 1066]. The Cox–Merz rule happened to be applicable to these systems for the various hydrophobic ends and concentrations at lower shear rates indicating typical associative polymer behaviour. The cyclic end groups did not show viscoelasticity for the frequencies window explored. The zero shear viscosity increased by almost two orders of magnitude from HEUR-cyc to HEUR-dod and by four orders of magnitude from HEUR-cyc to HEUR-cet. The intermediate shear thickening was only observed for the concentrated HEUR-cet samples. [Copyright &y& Elsevier]

Water-soluble polyacrylamides hydrophobically modified with small amounts of N,N-dialkylacrylamides [ N,N-dihexylacrylamide (DHAM) and N,N-dioctylacrylamide (DOAM)] have been prepared through free radical solution polymerizations using two hydrophobic initiators derived from 4,4′-azobis(4-cyanopentanoic acid) (ACVA) and long linear chains consisting of 12 and 16 carbon atoms (C12 and C16). This procedure resulted in polyacrylamides containing hydrophobic groups along the chain as well as at the chain ends.We compare the properties of this class of polymers, termed 'combined associative polymers', with those of the multisticker (with hydrophobic groups along the polymer chain) and telechelic (with hydrophobic groups at the chain ends) associative polymers. These materials were prepared using DHAM or DOAM and a hydrophobic initiator (ACVA) modified with alkyl chains of two different lengths. Polymers having molecular weights ( M ) of ca. 175,000 and hydrophobic contents [H] of ca. 0.8 mol% were prepared using 0.07 mol% of initiator relative to the total monomer feed. We investigated the effects that the type, localization, and concentration of the hydrophobic groups have on the viscosities of the associative polymer solutions. [ABSTRACT FROM AUTHOR]

A number of models are available to describe the rheological behaviour of associative polymers. Model evaluation has most often been limited to the linear properties and to a qualitative prediction of the characteristic shear thickening at intermediate shear rates. Several other nonlinear features of associative behaviour have, however, been identified. These include failure of the Cox–Merz analogy and an unusual response in nonlinear stress relaxation, large amplitude oscillatory flow and in superposition flows. Here, experimental results for such experiments are compared with the predictions of a transient network model, i.e. the Vaccaro–Marrucci model [J. Non-Newtonian Fluid Mech. 92 (2000) 261], which has only a single adjustable parameter to describe nonlinear behaviour. It is shown that the various nonlinearities are well predicted qualitatively. The only deviation is a substantial overprediction of the critical strain or strain rate for the onset of these nonlinearities. The effect of changing the value of the model parameters and of relaxing the model assumptions on the predictions is investigated. The results suggest that the presence of a small number of highly stretched chains could be responsible for the observed deviation from the experimental data. [Copyright &y& Elsevier]

A novel zwitterionic surfactant monomer containing a carboxybetaine moiety and a 10 carbon aliphatic tail was synthesized and copolymerized with acrylamide to yield a water‐soluble, hydrophobically modified zwitterionic polymer [Poly(acrylamide‐co‐(3‐(N,N‐dimethyl‐N‐3′‐(N′‐acryloyl)aza‐tridecyl) ammonio butanoate))]. The response of aqueous polymer solutions to the addition of various classes of surfactant was investigated and compared to that of an analogous novel polymer containing the sulfobetaine zwitterion [Poly(acrylamide‐co‐(N,N‐dimethyl‐N‐3′‐(N′‐acryloyl) aza‐tridecyl) ammonio propane sulfonate))]. It was found that the addition of sodium dodecyl sulfate (SDS) produced a pronounced maximum in viscosity, while dodecyltrimethylammoniumbromide (DTAB), N‐dodecyl‐N,N‐dimethylammonio‐1‐propanesulfonate (SB3‐12), and Triton X‐100 either had no effect, or produced a decrease in viscosity. The effect of pH on polymer–SDS interaction was also studied. Lowering pH increased the SDS–polymer interaction and significantly shifted viscosity enhancement to a higher SDS concentration. #Paper Number 108 in a series entitled Water Soluble Polymers. [ABSTRACT FROM AUTHOR]

• A new approach for mapping different retention mechanisms in porous media. • Based on the knowledge of the intermolecular interactions between polymer molecules. • Predict the threshold concentration for the onset of each type of retention mechanisms. • A novel experimental approach for the determination of polymer retention mechanisms. The retention of associative polymer molecules poses a significant challenge for its transport in porous media, and this arises due to the hydrophobic interactions that exists between the retained molecules. The known experimental approach in literature for quantifying polymer retention under static or dynamic conditions reports a generalized outcome without adequate estimates for each type of retention mechanisms. Thus, an accurate quantitative description of the various retention mechanisms (monolayer adsorption, multilayer adsorption and entrapment) attributable to associative polymers is crucial for proper optimization of its transport in porous media. In this work, a novel predictive approach was developed for quantitative mapping of the various retention mechanisms connected with associative polymers. The basis was a first-principles method adopted in mapping static to dynamic retention. This novel approach was achieved by relating the characteristic time scale for static and dynamic retention to the variation in polymer and reservoir properties, thus making it possible to correlate static retention results to large-scale dynamic retention with minimal fitting parameters. Furthermore, the mapping of the static to dynamic retention ensured an accurate quantification of the different retention mechanisms attributable to associative polymers. In this model, the in-situ entrapment was linked to the effective pore radius and the hydrodynamic size of the polymer molecules. Entrapment of polymer molecular aggregates was predicted based on the assumption that this occurs when the hydrodynamic size of the molecules becomes equal/greater than the effective pore size in the porous media. In addition, a threshold concentration value was estimated from which mechanical entrapment of polymer molecules would occur in a porous media alongside adsorption on pore surface. Similarly, a concentration value was estimated at which entrapment of polymer molecules becomes the dominant retention mechanism in the porous media. [ABSTRACT FROM AUTHOR]

Core-based laboratory experiments were performed on water- and chemically-treated-oil-wet Berea sandstone long-core samples to investigate the disproportionate permeability reduction (DPR) potential of a low-molecular weight associative polymer. The impact of single- and two-phase DPR treatments were considered at 60 °C. In the experiments conducted, real-time electrical resistivity measurements were obtained during the coreflood tests to serve as (a) a valuable tool for fluids saturation monitoring and (b) improved core fluids saturation evaluation in flooded porous media. Results from DPR treatments in water-wet cores showed high initial oil residual resistance factors, RRF o (≈20), followed by relatively long clean-up times; stabilized RRF o was achieved at relatively high PVs of oil injection (≈25). For the range of the post-treatment pressure gradients applied in the laboratory experiment, no DPR effects were observed for the water-wet core samples. However, the different shear-dependent behavior for the oil and water phases in the treated zone suggests that a positive DPR effect is possible at extrapolated low post-treatment applied pressure gradients; this could also be translated as higher clean-up times. For the two-phase DPR treatments in water-wet cores, RRF o can be significantly reduced to approximately 8, while RRF w stabilized at the relatively high value of 40. However, the required significantly long clean-up period during oil flow through the treated zone may question the efficiency of the achieved DPR effect. For the two-phase DPR treatment in oil-wet cores, stabilized RRF o were achieved at considerably lower injected oil PVs, i.e., shorter post-treatment clean-up periods were required. In addition, distinguishably smaller RRF o values were achieved for the oil-wet cores compared to the water-wet ones with a substantial separation from the achieved RRF w values (i.e., faster attainment of low values ranging between 6 and 4 for 15 to 40 injected PVs clean-up duration). These results indicate greater potential for effective positive DPR treatment for oil-wet medium treated through two-phase injection methods. Multi-rate tests conducted during polymer injection showed that the mobility reduction (resistance factor, RF) during DPR treatments, for both single- and two-phase methods, are shear dependent. In addition, post-treatment water and oil injection (production) showed different behavior regarding permeability reduction (RRF). In both core wettability cases, water flow experienced a noticeable power-law dependency to the applied differential pressure. On the other hand, the oil flow behavior in the two wettability cases was different; slightly shear-thinning for the water-wet cases and weakly shear-thickening for the oil-wet cores. In both cases the shear dependency of oil flow was much less pronounced than that of the water flow. Finally, the production water cut can be decreased to a noticeable amount using associative polymer DPR treatments. However, one must note that the water cut reduction (economic gain) is associated with a reduced total (oil) production rate (time loss); therefore, implementation of an associative polymer DPR treatment should be considered carefully. • Produced water cut can be decre ased using polymer DPR treatments. • Treatments in water-wet cores suggest potential positive DPR effects and long clean-up times. • Low volume treatment in oil-wet cores yield stabilized oil residual resistance factors. • Field-scale treatment implementation requires a proper design based on laboratory studies. [ABSTRACT FROM AUTHOR]

A new kind of water-soluble polymer was obtained by grafting side chains, characterized by a phase separation on heating (Lower Critical Solution Temperature LCST), on a hydrosoluble backbone. For semidilute solutions, the side chains associate as the temperature exceeds a critical temperature ( T), which is close to their LCST. Microdomains are formed which act like physical crosslinking units between the main chains, and an increase in the aqueous solution viscosity is observed. Systems based on 2-Acrylamido-2-methyl propane sulfonic acid (AMPS) backbone and polyethylene oxide (PEO) side chains were developed. Their rheological behavior in both dilute and semi-dilute states was studied by varying differents parameters such as polymer and salt concentrations, grafting ratio, etc. Fluorescence measurements indicate the formation of hydrophobic microdomains on heating, in agreement with the thickening properties of the solutions. [ABSTRACT FROM AUTHOR]

The concentration and molecular weight dependence of the self-diffusion coefficient ( D) of associative polymers of HEUR-type in aqueous solution have been investigated using FT-PGSE-NMR technique. The idea of three-dimensional network formation as a result of aggregation of the hydrophobic end-groups of the polymer in junctions is supported through the observed dramatic lowering of D with increased concentration. The network-formation efficiency depends on the polymer molecular weight as well as the hydrophobicity of the end-groups. A double logarithmic dependence of the self-diffusion coefficient versus concentration ( c) has been observed: D∝ c. The first exponent, a, is valid at low concentration, <1% polymer per weight solution, and ranges from 0.5 to 1, whereas the second exponent, a, describing systems of higher concentration, ranges from 2 to 2.7. [ABSTRACT FROM AUTHOR]