Critical Degree Of Polymerization Research Articles

On the electrophoretic mobilities of partiallycharged oligosaccharides as a function of charge patterning and degree of polymerization.

Fully or partially charged oligosaccharide molecules play a key role in many areas of biology, where their fine structures are crucial in determining their functionality. However, the separation of specific charged oligosaccharides from similar moieties that typically coexist in extracted samples, even for those that are unbranched, and in cases where each saccharide moiety can only carry a single charge or not, is far from trivial. Typically such molecules are characterized by a degree of polymerization n and a number m (and distribution) of charged residues, and must be separated from a plethora of similar species possessing different combinations of n and m. Furthermore, the separation of the possible n!/m!(n-m)! isomers of each species of fixed n and m is a formidable challenge to analytical chemists. Herein, we report the results of molecular dynamics simulations that have been performed in order to calculate the free solution electrophoretic mobilities of galacturonides and charged oligosaccharides derived from digests of the important plant cell-wall polysaccharide pectin. The simulations are compared with an experiment and are found to correctly predict the loss of resolution of fully charged species above a critical degree of polymerization n and the ionic strength dependence of the electrophoretic mobilities of different partially charged oligosaccharides. It is expected that having a predictive tool for the calculation of the electrophoretic mobilities of differently charged oligosaccharide species in hand will allow experimental conditions that optimize the resolution of particular species to be ascertained and understood.

Conformations of Low-Molecular-Weight Lignin Polymers in Water.

Low-molecular-weight lignin binds to cellulose during the thermochemical pretreatment of biomass for biofuel production, which prevents the efficient hydrolysis of the cellulose to sugars. The binding properties of lignin are influenced strongly by the conformations it adopts. Here, we use molecular dynamics simulations in aqueous solution to investigate the dependence of the shape of lignin polymers on chain length and temperature. Lignin is found to adopt collapsed conformations in water at 300 and 500 K. However, at 300 K, a discontinuous transition is found in the shape of the polymer as a function of the chain length. Below a critical degree of polymerization, Nc =15, the polymer adopts less spherical conformations than above Nc. The transition disappears at high temperatures (500 K) at which only spherical shapes are adopted. An implication relevant to cellulosic biofuel production is that lignin will self-aggregate even at high pretreatment temperatures.

Hierarchical Self-Organization and Uniaxial Alignment of Well Synthesized Side-Chain Discotic Liquid Crystalline Polymers

Liquid crystalline polymers (LCPs) combine the attributes of liquid crystals and polymers, while discotic LCPs have been less developed in sharp contrast to their calamitic counterparts mainly due to lack of suitable discotic LCP materials. Here we successfully prepared a series of well-defined triphenylene (TP) based discotic LC polyacrylates via reversible addition–fragmentation chain-transfer (RAFT) polymerization for the first time, and through a combination of multiple analysis techniques and phase transition kinetics study, a remarkable molecular weight effect or polymer effect at a critical degree of polymerization (DP) around 20 has been disclosed. Moreover, the first proposed discrete columnar stacks (DCS) based hierarchical self-organization model accounts well for the formation and transformation of ordered hexagonal columnar lattice Colho dominated by side-chain TP stacking and oblique columnar superlattice Colob-s induced by compaction and ordering of polymer backbones. The in-depth understanding of their superstructures and readily achieved uniaxial alignment pave the way for the rational design and preparation of such kind of solution processable cutting-edge polymeric semiconducting materials and may boost various fascinating optoelectronic applications.

Effect of polymerization on hierarchical self-assembly into nanosheets.

The oligomers consisting of phenyl-capped bithiophene and tetra(ethylene glycol)s linked by azide-alkyne Huisgen cycloaddition were synthesized. The relationship between the degree of polymerization and self-assembling ability was investigated in o-dichlorobenzene and dimethyl sulfoxide. From the absorption spectrum, it was confirmed that the critical degree of polymerization (CDP) for thiophene unit aggregation was 4. The morphology of the aggregated product was observed by atomic force microscopy. The oligomers 4mer and 5mer could not self-assemble into well-defined structures due to the weak driving force for the self-assembly. In the cases of 6mer and 7mer, aggregates with nonwell-defined and nanosheet structures coexisted. In the cases of 8mer and 9mer, the nanosheet was the main product. The critical point between 7mer and 8mer could be confirmed by different aggregation behaviors in the cooling process of the solution (nonsigmoidal and sigmoidal). In the cases of 8mer and 9mer, polymer folding prior to intermolecular self-assembly, which was supported by sigmoidal aggregation behavior, leads to the nanosheet formation. On the contrary, shorter oligomers than 8mer experience intermolecular aggregation prior to intramolecular polymer folding, which was supported by the nonsigmoidal aggregation behavior. This is the first report to prove the existence of CDP for folded polymer nanosheet formation which requires hierarchical self-assembly, i.e., polymer folding followed by intermolecular self-assembly.

Cure Depth of Photo‐Polymerized Gels

Cure depth of photo‐polymerized gels is theoretically analyzed. The critical point in a frontally photo‐polymerized sample is determined by the critical degree of polymerization, which is derived by the concentration ratio of monomer and initiator. While the total polymer depth or gel depth weighed by the monomer conversion depends on both radiation energy and light intensity, the averaged cure depth around the critical point depends on radiation energy only. The profile is consistent with experimental results. This is a practical formulation of the cure depth of photo‐polymerized gels without any empirical parameter.

A study of critical phenomena and dissipative nanostructures in self-organizing polymer systems

A research methodology based on scaling concepts is developed in detail for nonequilibrium polymer systems. Melt-crystallized linear high-density polyethylene is chosen as an example. In flexible-chain semicrystalline polymers, the transition from a solid isotropic or oriented state to a melt or from a solid isotropic state to an oriented state below the critical degree of polymerization occurs through necking at a nonzero external field on the combined line of first- and second-order phase transitions. A melt is a symmetric phase with a zero order parameter. Lamellar and fibrillar semicrystalline phases are phases with inherent order parameters that are periodic functions of one coordinate, and the neck draw ratio is another order parameter. At the critical degree of polymerization, all the phases are identical. In terms of the fluctuation theory of phase transitions and critical phenomena, the quantitative dependence of macroscopic properties on nanostructure parameters in this polymer material is revealed. The neck draw ratio and the draw ratio at break are macroscopic properties. The structure is characterized by the average thickness of amorphous layers. The square of the neck draw ratio is equal to the product of the square of the draw ratio at break and the probability of collision of chain ends. In turn, this probability is proportional to the average thickness of amorphous layers in an isotropic sample. The problems of dynamic scaling and entanglements are discussed.

Effect of Monomer Loading and Pressure on Particle Formation in Nitroxide-Mediated Precipitation Polymerization in Supercritical Carbon Dioxide

The critical degree of polymerization (Jcrit) at which polymer chains become insoluble in the continuous medium and particle formation commences has been estimated under a variety of experimental conditions for the nitroxide-mediated precipitation polymerizations of styrene (St) at 110 °C and tert-butyl acrylate (t-BA) at 118 °C in supercritical carbon dioxide (scCO2) mediated by N-tert-butyl-N-[1-diethylphosphono(2,2-dimethylpropyl)]oxy (SG1). The value of Jcrit increases with increasing target molecular weight, initial monomer loading, and pressure. Under the conditions investigated, Jcrit for t-BA is higher than that for St, which is consistent with greater solubility of poly(acrylates) in neat scCO2. A simple graphical approach has been developed and successfully employed, whereby Jcrit can be predicted as a function of both target molecular weight and initial monomer loading on the basis of a data set of Jcrit versus initial monomer loading.

Controlled/living heterogeneous radical polymerization in supercritical carbon dioxide

AbstractSupercritical carbon dioxide (scCO2) is an inexpensive and environmentally friendly medium for radical polymerizations. ScCO2 is suited for heterogeneous controlled/living radical polymerizations (CLRPs), since the monomer, initiator, and control reagents (nitroxide, etc.) are soluble, but the polymer formed is insoluble beyond a critical degree of polymerization (Jcrit). The precipitated polymer can continue growing in (only) the particle phase giving living polymer of controlled well‐defined microstructure. The addition of a colloidal stabilizer gives a dispersion polymerization with well‐defined colloidal particles being formed. In recent years, nitroxide‐mediated polymerization (NMP), atom transfer radical polymerization (ATRP), and reversible addition fragmentation chain transfer (RAFT) polymerization have all been conducted as heterogeneous polymerizations in scCO2. This Highlight reviews this recent body of work, and describes the unique characteristics of scCO2 that allows composite particle formation of unique morphology to be achieved. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 3711–3728, 2009

Harmonic oscillations in a polymerization

AbstractA simple radical polymerization is proposed in this paper, with step‐by‐step chain growth (Ri + M → Ri+1), and termination by transfer to a third body (Ri + S → polymer) such as the solvent. It is assumed that, for a certain critical degree of polymerization n, the propagator Rn reacts with substrate H to produce a deactivator (V) of the first propagator (H + Rn → Rn + V; V + R1 → P1) R1. Assuming that monomer, M, and precursor concentrations are constant, and assuming that the deactivator reaches fast a steady state, the resulting kinetic equations are formally linear, but they admit, perturbations rj(t) of the steady‐state concentrations of the propagators R1, R2, …, Rn, which are periodic functions of time. Even more, they can be purely sinusoidal functions (which have been called “harmonic,” in analogy to the solutions of the well‐known classical harmonic oscillator) with phase shift between perturbations rj(t) = Rj− (Rj)0 and rj+1(t) = Rj+1 − (Rj+1)0. Based on these periodic solutions and aiming to a model as simple as possible, a theoretical analysis is made, resulting in that the minimum value for n would be n = 3. Of course, these harmonic oscillations “driven by trimer” are equally found in the group of all the remaining propagators with polymerization degree higher than 3 (variable Y = ∑ Rj). © 2009 Wiley Periodicals, Inc. Int J Chem Kinet 41: 507–511, 2009

Polybrusselator‐type models

AbstractIn this paper, the possibility for autocatalysis in polymerization reactions is explored by introducing part of a polymerization mechanism in a model known as Brusselator. It is assumed that monomer concentration is practically constant. Four possibilities are examined: (1) a first radical propagator X, which has an isomer of position of the free electron, Y, dimerizes reversibly and this dimer catalyzes the isomerization of Y to X; (2) the radical propagator X is a polymer with a critical degree of polymerization and has an isomer of position of the free electron Y. This critical radical propagator catalyzes the conversion of Y to X; (3) any radical propagator has an isomer of position of the free electron, Y, and any polymer obtained by recombination of the radicals can catalyze the conversion of Y into its corresponding isomer X; and (4) any radical propagator with a critical degree of polymerization can catalyze the conversion of Y into its corresponding isomer. Isomorphism equations are obtained in all mechanisms, which implies the possibility of limit cycle oscillations (Brusselator model). © 2008 Wiley Periodicals, Inc. Int J Chem Kinet 40: 617–623, 2008

A molecular theory for particle nucleation: Primary particle formation in emulsion polymerization

Homogeneous nucleation is fundamentally important in emulsion polymerization. A molecular theory is proposed to quantify primary particle formation in the process. The proposed model divides a polymerization system into three portions: the domains formed by growing radicals, their surrounding aqueous solution, and dispersed monomer droplets. In general, the total free energy of the domains is contributed from the mixing among the molecules including monomer and water, the elasticity of oligomeric radical chains, and the transferable free energy of electrolytes; while that of the outer solution is from the mixing of monomer and water molecules and the transferable energy of electrolytes. Application of this theory to vinyl acetate emulsion polymerization has shown that the critical degree of polymerization ( j cri ) predicted is in a good agreement with the value derived from experimental data reported in literature. Furthermore, this model can also estimate the concentrations of VAc and water in the domain at the degrees of polymerization around j cri .

Nitroxide-Mediated Radical Dispersion Polymerization of Styrene in Supercritical Carbon Dioxide Using a Poly(dimethylsiloxane-b-methyl methacrylate) Stabilizer

Nitroxide-mediated controlled/living dispersion polymerization of styrene in supercritical carbon dioxide (scCO2) has been performed successfully to high conversion using N-tert-N-butyl-N-[1-diethylphosphono-(2,2-dimethylpropyl)] nitroxide (SG1) and a poly(dimethylsiloxane-b-methyl methacrylate) stabilizer at 110 °C. The molecular weight distributions were narrow (Mw/Mn = 1.12−1.43), and the number-average molecular weight (Mn) values agreed well with theory. A large excess of free SG1 was required to obtain satisfactory control in the dispersion polymerization, possibly due to SG1 partitioning. The critical degree of polymerization at which the polymer precipitates (Jcrit) was determined as 28 by visual observation using a novel approach. Polymerizations conducted in solution (toluene) proceeded at a similar rate (∼20% faster) to those in scCO2. The number of chains increased with conversion in both dispersion and solution, with the greater increase being observed in the dispersion system.

Emulsion Polymerization of Vinyl neo-Decanoate, a “Water-Insoluble” Monomer

Rate and particle size data for the emulsion polymerization of vinyl neo-decanoate, where inhibitor/retarder effects are obviated through rigorous purification, can be quantitatively fitted by conventional mechanisms for particle formation and growth, even though the monomer has a very low water solubility. These mechanisms are (1) radical entry is by an oligomeric radical (z-mer) arising from aqueous-phase propagation at a critical degree of polymerization (z between I and 2 for this monomer) where the species becomes surface-active, (2) radical loss is by transfer to a species which desorbs into the aqueous phase and eventually terminates' (after reentry into another particle) rather than undergoing further propagation, and (3) particle formation is by a z-mer entering a micelle. These hypotheses are consistent with gamma relaxation data which give direct information on radical loss.

STAR POLYMERS IN GOOD SOLVENTS FROM DILUTE TO CONCENTRATED REGIMES: CROSSOVER APPROACH

An introduction is given to the crossover theory of the conformational and thermodynamic properties of star polymers in good solvents. The crossover theory is tested against Monte Carlo simulation data for the structure and thermodynamics of model star polymers. In good solvent conditions, star polymers approach a ``universal'' limit as $Nto; however, there are two types of approach towards this limit. In the dilute regime, a critical degree of polymerization $N^*$ is found to play a similar role as the Ginzburg number in the crossover theory for critical phenomena in simple fluids. A rescaled penetration function is found to control the free energy of star polymer solutions in the dilute and semidilute regions. This equation of state captures the scaling behaviour of polymer solutions in the dilute/semidilute regimes and also performs well in the concentrated regimes, where the details of the monomer-monomer interactions become important.

Photocrosslinkable Star Polymers: Precursors for Model Polyelectrolyte Networks

A new synthetic route for the preparation of well-defined model polyelectrolyte networks based on the photodimerization of monodisperse star polymers, bearing terminal anthryl groups, is presented. Poly(tert-butyl methacrylate) (PtBMA) star precursor polymers were prepared via living anionic polymerization. 1-(2-anthryl)-1-phenylhexyllithium (APH-Li) served as the novel initiator by which photo-dimerizable anthryl groups were introduced. In order to vary the functionality of the stars, two different terminating agents were used: 1,3,5-trisbromomethylbenzene (TBMB) and octa[(3-iodopropyl)]-silsesquioxane (T 8 -(prop-I) 8 ). The length of the respective star arms was varied accordingly: 14 ≤ P a ≤ 195. Subsequent cleavage of the tert-butyl ester moieties by acidic hydrolysis gave access to photocrosslinkable, monodisperse polyelectrolyte star polymers. Fluorescence experiments indicated on aggregation of low molecular weight poly/ methacrylic acid) (PMAA) stars in salt containing solutions. Upon irradiation with UV light (λ = 366 nm) photodimerization of the terminal anthryl groups was induced and thus formation of a well-defined polyelectrolyte network was accomplished. In model experiments we demonstrated by 1 H-NME. UV-VIS spectroscopy as well as GPC analysis, that linear ω-anthryl-functionalized precursor PtBMA polymers dimerize quantitatively, as long as a critical degree of polymerization (P n 100) is not exceeded.

Flow enhanced diffusion-limited polymerization of rodlike molecules

Polymerization of rigid rodlike molecules with reactive end groups requires near parallel orientation of the molecules. The reaction is diffusion limited because of the low mobility of the molecules in the later stages of the reaction. Experimental studies have shown that flow-induced molecular orientation enhances the rate of polymerization [Agarwal and Khakhar, Nature 360, 53 (1992)]. Here a theoretical study of the polymerization under axisymmetric extensional flow is carried out to obtain the effective reaction rate constant (keff) for the reaction. Computations show that an increase in the intrinsic rate constant (kh) results in a decrease in the relative rate constant krel=keff/kh. Reduction in the rotational diffusivity (Dr) results in a significant reduction in krel; however, the variation of the translational diffusion coefficient perpendicular to the rod axis D⊥ has only a small effect for D⊥/D‖≪1, where D‖ is the diffusivity parallel to the rod axis. The imposition of flow increases the effective rate constant, however, the variation of krel with other parameters remains qualitatively similar at different Peclet numbers (Pe=ε/Dr, where ε is the extensional rate). To simulate the variation of the rate constant during polymerization, computations are carried out for different rod lengths using correlations to estimate rod diffusivities. Results indicate that krel initially decreases and then increases after a certain critical degree of polymerization, which reduces with increase in Peclet number. For sufficiently high extensional rates (ε∼200 s−1) the rate constant becomes higher than the intrinsic value (krel>1).

Crossover approach to scaling behavior in dilute polymer solutions: Theory and simulation

We develop a crossover theory for dilute polymer solutions, analogous to crossover theories for critical phenomena in simple fluids. In this theory, a critical degree of polymerization N* is found, which plays a similar role as the Ginzburg number in second-order phase transitions. To test the predictions of this theory, we perform Monte Carlo simulations of polymer chains composed of rigidly bonded hard spheres of various diameters and chain lengths. Various properties of these chains were analyzed, including the end-to-end distance distribution and mean-square radius of gyration. We find that the approach to the asymptotic scaling regime displays two types of crossover behavior, depending on the value of the model parameter ū, which is a measure of the strength of the monomer–monomer excluded volume interaction: (i) ū<1 and (ii) ū>1. In case (i), the system exhibits crossover from a Gaussian chain to the Kuhnian chain, as the degree of polymerization increases. In case (ii), the system exhibits crossover from the rigid rod to a Kuhnian chain. Our crossover theory is found to work well for polymers with ū>1 only near the asymptotic scaling regime. However, for ū<1, the theory works well in all regimes.

Kinetics of Living Polymerization with Propagation Rate Constants Depending on Degree of Polymerization

Abstract A study is presented on the kinetics of living polymerization in which the propagation rate constants decrease to zero at a certain degree of polymerization of the propagating chain. The general solution for the distribution function and the rate of polymerization is given and two special cases are discussed. When all the propagation rate constants are the same up to a critical degree of polymerization and null beyond it, the polymerization proceeds approximately as a normal living polymerization until the number-average degree of polymerization reach 85 to 90% of the critical value. When the propagation rate constants decrease linearly with the degree of polymerization, the distribution of living polymer is narrower than the usual Poisson distribution and the reaction order of the rate of polymerization with respect to monomer concentration is between first and second and is affected by the initial monomer and catalyst concentrations.