Living Polymer Systems Research Articles

Living Polymer Systems at a Solid Substrate: Computer Simulation of a Soft, Coarse-Grained Model and Self-Consistent Field Theory

Using particle-based simulation of a soft, coarse-grained model and self-consistent field theory (SCFT), we investigate the properties of dense living polymer systems with ring formation both in the bulk and in thin films. In the bulk, our results confirm that the molecular weight distribution of ring polymers exhibits a combination of an exponential decay and a power law. The exponential molecular weight distribution of linear chains is hardly affected by ring formation, only the corresponding mean molecular weight is slightly reduced. At lower segment density, the fraction of monomers of ring polymers is increased. In thin films, ring formation does not influence the width of the narrow interface, where the segment density rises to the bulk value. Since the molecular extension of ring polymers is smaller than that of linear chains, the spatial extent of the wide interphase is, however, reduced. In the narrow interface, we find that the local ring formation is affected by five aspects: (1) the mirroring of chain conformations and back-folding by the solid substrate (Silberberg argument) and other four aspects at the solid substrate, i.e., (2) the reduced segment density, (3) the enrichment of chain ends, (4) the pronounced segregation of nonbonded monomers, and (5) the reduced dimensionality of ring polymers. In the wide interphase, the local ring formation is enhanced mainly by the first aspect. By comparing the results from the particle-based simulation and SCFT, we observe good agreement in the wide interphase, but the difference in the local structure leads to differences in the narrow interface. Additionally, the SCFT results show that a decrease of the film thickness increases the global ring formation within the thin film.

Interfaces and Interphases in Dense, Polydisperse Living Polymer Systems: A Comparison Between Computer Simulation and Self-Consistent Field Theory

Using particle-based simulations of a soft, coarse-grained model and self-consistent field theory (SCFT) we investigate the properties of dense living polymer systems in bulk and thin films. Reversible bond formation and breaking is controlled by a bonding free energy, Eb, and results in a polydisperse melt of linear flexible polymers and rings. For bulk systems we observed an exponential decay of the molecular weight distribution for all but the smallest molecular weight. The latter affect stems from the indistinguishability of the two bonding sites of a living monomeric unit. Under confinement into a film, the presence of the solid substrates gives rise to a redistribution of living monomers and chains in the wide interphase and, therefore, alters the local molecular weight distribution and local mean molecular weight. Additionally, we find that the presence of a solid substrate enhances the formation of rings with high molecular weight by reducing the dimensionality of ring living polymers in the vicinity of solid substrate and increasing the probability of two chain ends belonging to the same linear living polymer chain to meet with each other. The result of particle-based simulations and numerical self-consistent field theory are compared and, although there are differences of the two descriptions in the narrow interface, qualitative agreement is found in the wide interphase.

Experimental study on the capillary thinning of entangled polymer solutions

The transient elongation behavior of entangled polymer and wormlike micelles (WLM) solutions has been investigated using capillary breakup extensional rheometry (CaBER). The transient force ratio X = 0.713 reveals the existence of an intermediate Newtonian thinning region for polystyrene and WLM solutions prior to the viscoelastic thinning. The exponential decay of X(t) in the first period of thinning defines an elongational relaxation time λ x which is equal to elongational relaxation time λ e obtained from exponential diameter decay D(t) indicating that the initial stress decay is controlled by the same molecular relaxation process as the strain hardening observed in the terminal regime of filament thinning. Deviations in true and apparent elongational viscosity are discussed in terms of X(t). A minimum Trouton ratio is observed which decreases exponentially with increasing polymer concentration leveling off at Trmin = 3 for the solutions exhibiting intermediate Newtonian thinning and Trmin ≈ 10 otherwise. The relaxation time ratio λ e/ λ s, where λ s is the terminal shear relaxation time, decreases exponentially with increasing polymer concentration and the data for all investigated solutions collapse onto a master curve irrespective of polymer molecular weight or solvent viscosity when plotted versus the reduced concentration c[ η], with [ η] being the intrinsic viscosity. This confirms the strong effect of the nonlinear deformation in CaBER experiments on entangled polymer solutions as suggested earlier. On the other hand, λ e ≈λ s is found for all WLM solutions clearly indicating that these nonlinear deformations do not affect the capillary thinning process of these living polymer systems.

End-growth/evaporation living polymerization kinetics revisited

End-growth/evaporation kinetics in living polymer systems with "association-ready" free unimers (no initiator) is considered theoretically. The study is focused on the systems with long chains (typical aggregation number N ≫ 1) at long times. A closed system of continuous equations is derived and is applied to study the kinetics of the chain length distribution (CLD) following a jump of a parameter (T-jump) inducing a change of the equilibrium mean chain length from N(0) to N. The continuous approach is asymptotically exact for t ≫ t(1), where t(1) is the dimer dissociation time. It yields a number of essentially new analytical results concerning the CLD kinetics in some representative regimes. In particular, we obtained the asymptotically exact CLD response (for N ≫ 1) to a weak T-jump (ε = N(0)∕N - 1 ≪ 1). For arbitrary T-jumps we found that the longest relaxation time t(max ) = 1∕γ is always quadratic in N (γ is the relaxation rate of the slowest normal mode). More precisely t(max )∝4N(2) for N(0) < 2N and t(max )∝NN(0)∕(1 - N∕N(0)) for N(0) > 2N. The mean chain length N(n) is shown to change significantly during the intermediate slow relaxation stage t(1) ≪ t ≪ t(max ). We predict that N(n)(t)-N(n)(0)∝√t in the intermediate regime for weak (or moderate) T-jumps. For a deep T-quench inducing strong increase of the equilibrium N(n) (N ≫ N(0) ≫ 1), the mean chain length follows a similar law, N(n)(t)∝√t, while an opposite T-jump (inducing chain shortening, N(0) ≫ N ≫ 1) leads to a power-law decrease of N(n): N(n)(t)∝t(-1∕3). It is also shown that a living polymer system gets strongly polydisperse in the latter regime, the maximum polydispersity index r = N(w)∕N(n) being r∗ ≈ 0.77N(0)∕N ≫ 1. The concentration of free unimers relaxes mainly during the fast process with the characteristic time t(f) ∼ t(1)N(0)∕N(2). A nonexponential CLD dominated by short chains develops as a result of the fast stage in the case of N(0) = 1 and N ≫ 1. The obtained analytical results are supported, in part, by comparison with numerical results found both previously and in the present paper.

Ordering fluctuations in a shear-banding wormlike micellar system

We present a first investigation about the non-linear flow properties and transient orientational-order fluctuations observed in the shear-thinning lecithin-water-cyclohexane wormlike micellar system at a concentration near to the zero-shear isotropic-nematic phase transition. From rheological measurements the stress plateau was found shifted to very low values of the applied shear rate gamma, compared to most of the concentrated living polymer systems reported in the literature. Rheo-small angle neutron scattering (Rheo-SANS) experiments performed in the flow-vorticity plane revealed periodical fluctuations of both the order parameter P(2) and the angular deviation phi from the vorticity axis as determined from the scattering peaks. The periods of the oscillations were not found to depend on imposed gamma. A theoretical model was also developed to explain the oscillatory dynamics of the shear-induced nematic order parameter in terms of the presence of standing waves of the director orientation profile along the circumference of the Couette cell. The experimental results of the periodic order parameter fluctuations together with their theoretical modelling shed significant new insights on the shear banding phenomenon, particularly its microscopic mechanism.

The effect of stiffness in wormlike micelles

The effect of stiffness in a 2D living polymer system is investigated by Monte-Carlo simulation in a canonical ensemble. As the flexibility decreases, the mean chain contour length \(\) decreases and goes through a local maximum. The mean end to end square distance shows a non-monotonic behaviour due to the coil-to-rod transition and the decrease in chain contour length. Near the maximum of chain ordering in the bulk, the chain length distribution adapts itself to increase the configurational entropy. With the parameters used in this simulation, it seems that the effect of the stiffness for high stiffness is to decrease \(\) as in the isotropic case, since the ordering decreases again.

Chain radius dependence on concentration in a 2D living polymer system

A living polymer system is used to study the effect of concentration on a broad, polydisperse two-dimensional polymer system. It is found that the mean squared end-to-end radius of a chain of L monomers does not decrease by following a simple power law of the concentration but by a function of the form . An origin for such a behaviour is proposed.

Dynamics of living and dead polymers studied by electrooptical birefringence

We report on transient electrooptic birefringence experiments on dead (poly(styrene) in 1,4 dioxane) and living (lecithin/water/iso-octane microemulsions) polymer solutions. We find it impossible to obtain reliable information on the electrooptical behavior of dead polymers in the semi-dilute regime. Comparison with the behavior of worm-like micellar solutions forming living polymer systems is therefore also ruled out. The interesting data obtained on the latter system, however, easily compensate for this negative result. The data seem to support the idea that branching rather than entanglement plays a key role in this worm-like micellar systems.

Monomer-mediated relaxation in living polymers

We study the relaxation kinetics in living polymer systems, such as poly$(\ensuremath{\alpha}$-methylstyrene), where association-dissociation processes are monomer mediated, so that the molecular weight distribution adapts reversibly to the new thermodynamic parameters by monomer exchange at active sites at chain ends. Using both a system of rate equations for the concentration of $l$-mers, which is solved numerically, and Monte Carlo simulations in terms of a bond fluctuation model, we find a good description of the dynamic response of the system to large deviations from equilibrium in terms of a single relaxation time ${\ensuremath{\tau}}_{L}\ensuremath{\propto}{L}^{5}$, where $L$ is the average chain length in equilibrium. The response itself is found to decay with time $t$ as ${t}^{\ensuremath{-}1}$ in the late stages of relaxation. In contrast to wormlike micelles with scission-recombination kinetics, the average lifetime ${\ensuremath{\tau}}_{l}$ of chains of length $l$ is found to be practically independent of $l$ for $l\ensuremath{\gg}1$ for a given rate of dissociation which may essentially determine the dynamics of such systems.

Living polymers

A body of experimental evidence is now accumulating on the macroscopic and microscopic properties of living polymer solutions: solutions of active polymer molecules in dynamic chemical equilibrium with their constituent monomers. Computer simulations could provide a valuable complement to the experimental and theoretical work on these systems. We present the features of living polymer systems which are crucial to a relevant simulation. We give a set of questions which might be addressed by such simulations.

A Monte Carlo Study of Thermodynamic Relaxation in Living Polymers

We report the first numeric experiments on the thermodynamic relaxation in living polymers (polymers that can break and recombine reversibly) whose molecular weight distribution (MWD) is perturbed from equilibrium by a T-jump and then allowed to relax. In the simulation we use a modification of the Bond Fluctuation Method which is known to reproduce the correct Rouse dynamics of polymer chains. Our results indicate an excellent agreement with the predictions of a recently suggested theory [1, 2] of relaxation in living polymer systems

End-evaporation kinetics in living-polymer systems

We study theoretically the process of ‘‘end-evaporation’’ in living polymer systems, such as wormlike surfactant micelles. End-evaporation occurs when single monomers either break away from, or join onto, a chain end, the rates being described by the (mean-field) rate constants k and k′, respectively. Thus the chains can exchange material with one-another via a bath of free monomers. The relaxation of a system of living polymers after a small temperature jump (T-jump) is studied theoretically. The effect of a T-jump is to prepare the system with the wrong mean chain length, which relaxes to its equilibrium value L̄ by end-evaporation. It is found that the number of free monomers in the system relaxes almost completely in a time of order 1/kL̄, while the weight-average chain length, which is the quantity measured in light scattering experiments, relaxes on a time scale τD=4L̄2/k, which is three powers of L̄ longer. We also predict that the stress relaxation after a step strain is dominated by end-evaporation whenever τD≲τrep, where τrep is the reptation (disengagement) time for a chain of length L̄. In this case the stress relaxation is found to be ‘‘stretched exponential’’ for times smaller than τD and single exponential for longer times.

Small-angle neutron scattering from a living polymer solution: preliminary experiment

The first study by SANS of a living polymer system, poly(α-methylstyrene), evolving as a function of temperature and preseting a polymerization transition, is reported. The preliminary results are in reasonable qualitative agreement with the behavior expected from a mean field theory modeling the polymeriation as a phase transition

Simultaneity of initiation and propagation in living polymer systems

ADVERTISEMENT RETURN TO ISSUEPREVArticleNEXTSimultaneity of initiation and propagation in living polymer systemsMichael. Szwarc, M. Van Byelen, and D. Van HoyweghenCite this: Macromolecules 1987, 20, 2, 445–448Publication Date (Print):February 1, 1987Publication History Published online1 May 2002Published inissue 1 February 1987https://doi.org/10.1021/ma00168a042RIGHTS & PERMISSIONSArticle Views109Altmetric-Citations19LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InReddit PDF (515 KB) Get e-Alerts Get e-Alerts

Thermodynamic enhancement of oligomers in dynamic living polymer system involving end-group interaction. Distribution of living oligomers in equilibrated polydimethylsiloxanes

The concentrations of living oligomers of structure MtO[Si(Me) 2O] nMt ( n = 1 to 8, Mt = Na, K or Cs) are studied at equilibrium in the polymerization of permethylcyclopolysiloxanes initiated with alkali metal silanolates. The amounts of these oligomers are considerably higher than expected from the most probable distribution of molecular sizes, which is generally accepted as the distribution of linear chain size in equilibrated polydimethylsiloxane. This phenomenon is a consequence of interaction between living ends in connection with a dynamic character of a living polydimethylsiloxane system in which fast chain scrambling occurs. Other systems showing these features are expected to exhibit similar effects.

Electrolytic Polymerization of Tetrahydrofuran

The electrolytic polymerization of tetrahydrofuran (THF) was carried out in bulk by using tetrabutylammonium perchlorate as an electrolyte. Poly-THF was obtained from the anolyte. The yield of the polymer increased with the reaction time and leveled off at about 70%. The molecular weight of the polymer increased proportionally to the yield of the polymer as was observed in the living polymer system. About two moles of hydroxyl end group were determined per mole of the polymer. In the polarographic measurement, THF gives no oxidation wave. From the results obtained an initiation mechanism is proposed, involving the perchlorate radical and proton. The presence of radical species is indicated by the electrolytic copolymerization of methyl methacrylate and acrylonitrile.

Lactone polymers. III. Polymerization of ε‐caprolactone

AbstractPolymerization of ε‐caprolactone catalyzed by dibutylzine and triisobutylaluminum has been examined. Monomer conversion and polymer molecular weight increase simultaneously during the polymerization suggesting a living polymer system. Also, molecular weight is proportional to the reciprocal of catalyst concentration. However, the polymer molecular weights are three to five times that which would be calculated from the catalyst concentration assuming a living polymer system. In addition, fractionation of poly‐ε‐caprolactone prepared with dibutylzinc revealed that the distribution is considerably broader than expected for a Poisson distribution. While no mechanistic explanation for the broad molecular weight distribution observed has been defined, examination of the metal alkyl‐catalyzed polylactones shows that the molecular weight distributions can and do change with time. This change is due to an ester interchange process occurring subsequent to polymerization. This phenomenon can be used to change the molecular weight distribution from very broad to the most probable distribution.

Theoretical reaction kinetics of reversible living polymerization

AbstractAmplifying an early study by SZWARC and BROWN, we have investigated the mathematical problem of the reversible living polymer system without transfer or termination reactions, concentrating particularly on the molecular weight distribution. This problem is identical to that for the kinetics of BET adsorption. A complete analytical solution is obtained when the monomer concentration is kept constant. In the much harder case of polymerization in a closed system, numerical solutions of the equations are used as guides to analytical approximations, and a perturbation approach is also helpful. The time required for the initial narrow POISSON distribution to go over into the final „most probable”︁ equilibrium or SCHULZ distribution is proportional to the square of the average chain length. For polystyrene at room temperature, the POISSON polymer is produced in a few seconds, but the final equilibration requires of the order of 100 years, although the unreacted monomer concentration very early reaches its equilibrium value. Thus the equilibrium constant for polymerization can be accurately measured long before complete equilibrium is attained in the system.