Network parameters for crosslinking of chains with length and site distribution

Polymer chains are crosslinked to form a network. The chains are polydispersed, with an arbitrary distribution of weight and functionality. Crosslinks may form in three different ways: direct coupling (homopolymerization), direct coupling with propagation, and coupling through copolymerization with small monomers. Various network parameters are calculated. We give computational formulae for gel point, weight fraction soluble, weight fraction pendant, weight fraction effective, concentration of effective junctions, concentration of effective network strands, and the entanglement trapping factor. These formulae give exact values for systems that previously have only been solved using simplifying approximations. Examples show that such simplification may lead to sizable errors in the computation of network parameters.     

Separation/enrichment of the low-content high molecular weight natural protein using protein-imprinted polymers with ARPCs

We introduce a new method for separation/enrichment of the low-content cellular protein in high mo-lecular weight on the basis of molecular imprinting. The template protein, bacterial cloned immu-noglobulin binding protein (BiP), was selectively assembled with assistant recognition polymer chains (ARPCs) from their library, which consists of numerous limited length polymer chains with randomly distributed recognition and immobilizing sites. The assemblies of proteins and ARPCs were adsorbed by porous polyme...     

Structural studies of ultrahigh-modulus polyethylene using nitric acid etching and gel permeation chromatography. II. Influence of polymer molecular weight,draw temperature,and annealing

The technique of nitric acid etching followed by gel permeation chromatography has been used to determine the crystal length distribution in ultrahigh-modulus polyethylenes. The crystal length distribution has been studied as a function of draw ratio, polymer molecular weight, processing conditions, and annealing. The results confirm that although there is a considerable broadening of the crystal length distribution on drawing, the majority of crystals have lengths less that 500 Å. There are detailed changes in the length distribution due to changes in draw temperature, molecular weight, and annealing which are not always reflected in corresponding changes in the long period determined from small-angle x-ray scattering. Possible reasons for these discrepancies are discussed.     

Calculation of molecular weight distribution in a batch thermal polymerization of styrene

Molecular weight averages have long been used as a measure of polymer molecular weight properties in industrial polymer manufacturing processes. With a kinetic model, it is possible to directly calculate the polymer chain length distribution by integrating an infinite number of the polymer population balance equations. However, when the polymer chain length is very large, such a direct integration of polymer population balance equations can be computationally demanding. In this paper, the method of finite molecular weight moments is applied to the calculation of polymer chain length distribution in a batch free radical thermal polymerization of styrene. The weight fraction of a finite chain length interval is directly calculated in conjunction with a kinetic model. The method of calculation is illustrated through model simulations.     

Molecular weight dependence of emission intensity and emitting sites distribution within single conjugated polymer molecules

We investigated exciton migration, trapping and emission processes occurring within a single conjugated polymer molecule by means of superresolution fluorescence localization microscopy. This methodology allowed us to locate the spatial distribution of emitting sites within single chains with nanometre precision. The study was done on individual poly[2-methoxy-5-(2'-ethyl-hexyloxy)-1,4-phenylene vinylene] (MEH-PPV) molecules with average molecular weights ranging from 215,000 to 1,440,000 and with narrow weight distributions. We found that the mean emission intensity increases proportionally to the polymer molecular weight. The localization experiments suggest that the emitting sites are distributed nearly uniformly within a single chain and that the sites are on average 10 nm apart, irrespective of the molecular weight of the polymer. Furthermore, spatial contours formed by all the combined emitting sites within one chain show elongated shapes, in agreement with a rod-like structure of MEH-PPV in a collapsed state.     

Preparation of molecular imprinted polymer with quaternary ammonium groups as recognition sites for separation of pig cyclophilin 18 and bovine serum albumin

We introduce a new type of molecular imprinted polymer (MIP) with immobilized assistant recognition polymer chains (ARPCs) to create effective recognition sites. In this work, cloned pig cyclophilin 18 (pCyP18) and BSA were used as templates, respectively. The template protein was selectively assembled with ARPCs from the library which consists of numerous limited length polymer chains with randomly distributed recognition sites of the quaternary ammonium cationic groups and immobilizing sites. The assemblies of protein and ARPCs were adsorbed by macroporous microspheres and immobilized by cross‐linking polymerization. After removing the templates, the two kinds of synthesized MIPs were used to adsorb cloned pCyP18 and BSA from protein mixtures respectively and both showed high selectivity. It confirms that this new method is suitable to separate proteins of both low and high molecular weight. The extended experiment on adsorption of natural pCyP18 from cytosol shows that the obtained MIP using cloned protein as template can be used to enrich natural protein of low content.     

Osmotic deswelling of microgels by linear polyelectrolytes

Polyacrylate microgels used as absorbers or viscosifiers in water are known to have these useful qualities reduced in the presence of linear poly-electrolytes. An osmotic deswelling mechanism is postulated whereby the counterions from linear chains sterically excluded from the gel act to draw solvent from the gel phase. This postulate is tested using intrinsic viscosity measurements of Carbopol microgels, made with the linear polyelectrolyte considered as parr of the solvent. The intrinsic viscosity is used to calculate the swollen-to-dry volume ratio for the microgel in the presence or absence of 0.1% linear sodium polyacrylate over a range in ionic strength. Simultaneously, a standard treatment for the free energy of a network of non-Gaussian chains containing fixed charges is modified to include the osmotic effect of the excluded counterions. In the absence of linear polymer, the theory is fit to the data, the fitting parameter being the 3100 monomer units between crosslink sites in the network. In the presence of high (350 000) molecular weight linear polymer, good agreement is found between the observed deswelling and that predicted if the linear chains are totally excluded. Lower molecular weight linear chains are found to give a reduced deswelling which is shown to be self-consistent with their partitioning into the network.Presented in part at the 64th Colloid and Surface Science Symposium, Lehigh University, June 1990     

Reptation-breathing theory of pulsed electrophoresis: dynamic regimes, antiresonance and symmetry breakdown effects

We apply the concepts of tube and reptation to the pulsed electrophoresis of DNA, considering both biased reptation and "breathing" modes (internal modes of the chain). Using suitable preaveraging approximations, analytical expressions are derived which relate displacement in crossed field electrophoresis to molecular weight, field strength, field period, pore size of the gel, and the angle between the field. These expressions provide scaling laws for the change of mobility when one (or more) of the parameters is varied as well as "universal" velocity versus molecular weight versus pulse time curves. These results are quantitatively compared with experiments. At some point which depends on field angle, field strength and chain length, however, we predict a failure of this model due to symmetry breakdown and loss of ergodicity. Qualitatively, this should lead to considerable band spreading and/or splitting of the highest DNA bands into two bands migrating sideways from the diagonal. The case of field inversion is also investigated. It is shown that only breathing modes can explain the strong differences in mobility experienced by chains of different length when opposite fields of equal amplitude are applied: the "trapping" of chains in conformations of low mobility is associated with an antiresonance-like coupling between the external field and the internal modes.     

A New Model for the Evolution of the Molecular Weight Distribution of Polymers During Ultrasonic Chain Scission

A new model for ultrasonic scission of polymer chains has been developed. The model takes the coiled nature of the polymer chains into consideration. The time evolution of the molecular weight distribution for several values of the solvent quality parameter is obtained using the new model. It is seen that the model leads to higher scission rates and lower final molecular weights for better solvents in accord with the experiments. Simulated gel permeation chromatography results are also in line with the experiments.     

Crystallization of short aliphatic polymer chains. I. General chain-folding behavior

Short aliphatic polymer chains of different lengths were prepared by degrading polyethylene samples of appropriately chosen initial fold lengths to the chain lengths which correspond to a single chain traverse through the lamella. The resulting dicarboxylic acids were either used as such for further crystallization experiments or were first converted into diiodides to remove polar endgroups. The resulting short polymers all crystallized by chain folding even if the chains (peak of distribution) were only 1.5–4 times the length of a traverse through the lamella. In the diiodides the fold length varied continuously with crystallization temperature, as is usual in high molecular weight material, but with the dicarboxylic acids such variation, while observable, was only small. The effect of the molecular weight on the fold length due to its influence on supercooling at a given crystallization temperature has become apparent. Renewed degradation with nitric acid and subsequent GPC analysis of the degradation products confirmed the folded nature of the chains in the above crystals. This analysis combined with experiments on the reactivity of chain ends has led to the picture that each chain folds completely, once, twice etc. so that both folds and ends are in the surface zone but are located at varying heights, as appropriate to the overall layer thickness for the molecular weight distribution in question. This picture is consistent with other concurrent work.     

Cellulose acetate butyrate in solution. I. Hydrodynamic behavior

Cellulose acetate butyrate has been studied in regard to its hydrodynamic properties in several solvents. The polymer was fractionated by precipitation, and the molecular weight distribution of the polymer fractions was determined by gel permeation chromatography. The number-average molecular weight was estimated by osmometry. The Mark–Houwink–Kuhn–Sakurada relations between viscosity and molecular weights were established, and the unperturbed dimensions of the polymer chains were evaluated. In light of these data, current theories of polymer solutions are discussed. A new method of estimating unperturbed dimensions is proposed for semiflexible linear polymers.     

Molecular weight and polydispersity estimation of adsorbing polymer brushes by atomic force microscopy

We have estimated the molecular weight, Mn, and polydispersity, PDI, of densely grafted poly(N-isopropylacrylamide) (PNIPAM) brushes using a novel atomic force microscopy (AFM) approach. When compression of a polymer brush induced adsorption of multiple chains to an AFM tip, the resulting decompression force profile exhibited a maximum attractive force at a separation, Lm, that decayed to zero with increasing tip-sample separation. We have found that the separation Lm approximates the average contour length, Lc, determined by gel permeation chromatography (GPC). The detection of a decaying attractive force at separations larger than Lc suggests that chains of above average length sequentially break free from the tip as they are stretched away from the grafting surface. The shape of the decompression profile in this region approximately paralleled the cumulative weight fraction of the grafted chains determined by GPC. The fraction of chains of a given molecular weight determined from a single force curve fit a log-normal distribution, having a standard deviation that provided an estimate of the PDI. We have characterized two PNIPAM brushes by this AFM technique as well as by GPC coupled to a multiangle laser light-scattering detector (MALLS). The values obtained by AFM-(1) Mn,AFM = (3.8+/-0.5) x 10(4), PDI,(AFM) = 1.3+/-0.1 and (2) Mn,AFM = (9.4+/-1.4) x 10(4), PDI,(AFM) = 1.3+/-0.1-agreed quite well with the corresponding GPC/MALLS values of (1) Mn,GPC = 4.77 x 10(4), PDI,GPC = 1.33 and (2) Mn,GPC = 9.49 x 10(4), PDI = 1.35. This technique requires only a single force curve to obtain a statistical distribution of contour lengths and provides a novel method for estimating the Mn and PDI of appropriate uniformly grafted dense polymer layers.     

Unraveling the Bimodality of Polypropylene Film Grades Using Rheological Shear and Elongational Measurements: Inconsistent Results of Gel Permeation Chromatography

As the main parameter to describe the molecular structure of a linear polymer, molecular weight distribution of five different polypropylene grades was evaluated through measurements of gel permeation chromatography and rheology experiments. From their dynamic shear data, the relaxation spectra, h(τ), were calculated from which molecular weight distribution was estimated using molecular viscoelastic theories and then compared with the gel permeation chromatography results. Generally good agreement, yet with narrower molecular weight distribution rheology curves was found. Exception was observed for one grade for which rheological data predicted bimodal distribution curve comprising a small shoulder of high molecular weight, not seen in the corresponding gel permeation chromatography curve. Additionally, a higher value of the generalized mixing parameter (i.e. β) was found for this bimodal grade which was attributed to an increase in the number of entanglements per chain and better network connectivity. Furthermore, measurements of the transient extensional viscosity also revealed enhanced strain hardening and melt strength for this particular grade. The results showed that small amount of high molecular weight fraction of linear chains could drastically alter the processing behavior of polypropylene film grades.     

SYNTHESIS AND CHARACTERIZATION OF POLYMERS BEARINGAZOBENZENE AND CARBAZOLE GROUPS VIA POST-AZO-COUPLING REACTION

A series of polymers bearing azobenzene and carbazole groups for photorefractive purpose were prepared viapost-azo-coupling reaction.The successful reaction was identified by spectroscopic analysis and gel permeationchromatography.This approach is more facile compared with the direct polymerization of corresponding functionalmonomer.The polymers prepared have weight average molecular weight of higher than 1.5×10~4 and are easily soluble incommon organic solvents like chloroform and tetrahydrofuran,polymer films with high optical quality could be easilyfabricated through solution casting.Glass transition temperature (T_(?)) of the polymers ranges from 60℃to 182℃,dependingon the alkylene spacer length between the functional side group and the polymer backbone,and the polymers are relativelystable under 300℃.     

Synthesis of well‐defined comb‐like graft (co)polymers by nucleophilic substitution reaction between living polymers and polyhalohydrocarbon

A series of graft (co)polymers were synthesized by nucleophilic substitution reaction between iodinated 1,2‐polybutadiene (PB‐I, backbone) and living polymer lithium (side chains). The coupling reaction between PB‐I and living polymers can finish within minutes at room temperature, and high conversion (up to 92%) could be obtained by effectively avoiding side reaction of dimerization when living polymers were capped with 1,1‐diphenylethylene. By virtue of living anionic polymerization, backbone length, side chain length, and side chain composition, as well as graft density, were well controlled. Tunable molecular weight of graft (co)polymers with narrow molecular weight distribution can be obtained by changing either the lengths of side chain and backbone, or the graft density. Graft copolymers could also be synthesized with side chains of multicomponent polymers, such as block polymer (polystyrene‐b‐polybutadiene) and even mixed polymers (polystyrene and polybutadiene) as hetero chains. Thus, based on living anionic polymerization, this work provides a facile way for modular synthesis of graft (co)polymers via nucleophilic substitution reaction between living polymers and polyhalohydrocarbon (PB‐I). © 2013 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2013     

Polymer depletion-induced instability of silica suspensions in the presence of flexible and semiflexible polymers

Polymer depletion-induced instability of silica suspensions in dilute toluene solutions of flexible polystyrene (PS) or semiflexible poly(hexyl isocyanate) (PHIC) was investigated by direct observation and oscillatory moduli measurements as functions of silica volume fraction and polymer molecular weight. Addition of the respective polymers to the gelled silica suspensions induces a gel settling. Below the silica volume fraction phi=4 vol%, PS chains compress the volume of the sediment silica phase, whereas PHIC chains expand it and play a role in swelling agents. Thus, PHIC chains lead to the formation of aggregates in the silica suspensions that are larger and less compact than those formed by the PS chains. On the other hand, above phi=4 vol% where the silica suspension occurs gelation, the effect of nonadsorbing polymers on changes in the volume of the silica phase is opposite. Moreover, polymer depletion interaction results in a mechanically stronger gelled phase, leading to the storage modulus G' values larger than those without polymer, but the effects of polymer concentration and polymer molecular weight on the G' values are not clear.     

Simulation study of semi-crystalline polymer interphases

The study of structure and properties of semi-crystalline polymer inter-phases is important to explain and extend polymer applications. In this region, polymer chains exist in three distinct populations: tie chains that bridge the two crystals, chain folds and chain ends. The distribution of these populations influences the properties of the interphase. We have developed off-lattice Monte Carlo simulations of constrained interphases of semi-crystalline polymers which utilize robust off-lattice moves. A united atom model with polyethylene-like interactions and with freely rotating bonds is used to mimic the prototypical flexible chain structure. These simulations capture the limiting distributions of tight and loose chain folds and of tie chains within the metastable phase. The dissipation in order and density between the crystal and amorphous regions has been studied, and results for freely rotating chains indicate that the characteristic decay of anisotropy occurs in a length scale of ca. 10 Å. Simulation results for the effect of system size and molecular weight for freely rotating chains have also been investigated.     

Ion transport and molecular organization are coupled in polyelectrolyte-modified nanopores

Chemically modified nanopores show a strong and nontrivial coupling between ion current and the structure of the immobilized species. In this work we study theoretically the conductance and structure in polymer modified nanopores and explicitly address the problem of the coupling between ion transport and molecular organization. Our approach is based on a nonequilibrium molecular theory that couples ion conductivity with the conformational degrees of freedom of the polymer and the electrostatic and nonelectrostatic interactions among polyelectrolyte chains, ions, and solvent. We apply the theory to study a cylindrical nanopore between two reservoirs as a function of pore diameter and length, the length of the polyelectrolyte chains, their grafting density, and whether they are present or not on the outer reservoir walls. In the very low applied potential regime, where the distribution of polyelectrolyte and ions is similar to that in equilibrium, we present a simple analytical model based on the combination of the different resistances in the system that describes the conductance in excellent agreement with the calculations of the full nonequilibrium molecular theory. On the other hand, for a large applied potential bias, the theory predicts a dramatic reorganization of the polyelectrolyte chains and the ions. This reorganization results from the global optimization of the different interactions in the system under nonequilibrium conditions. For nanopores modified with long chains, this reorganization leads to two interesting physical phenomena: (i) control of polyelectrolyte morphology by the direction and magnitude of ion-fluxes and (ii) an unexpected decrease in system resistance with the applied potential bias for long chains due to the coupling between polyelectrolyte segment distribution and ion currents.     

双烯化合物类单体合成支化聚合物的支化结构的研究

分别以二乙烯基苯(DVB)、双甲基丙烯酸二缩三乙二醇酯(tri-EGDMA)和1,6-双马来酰亚胺基正己烷(BMIH)为支化单体,采用原子转移自由基聚合合成支化聚苯乙烯;以先核后臂法合成的星状支化聚苯乙烯为参照对合成的支化聚合物的支化形态进行研究.采用气相色谱(GC)、核磁共振氢谱(1H-NMR)和三检测凝胶渗透色谱(TD-SEC)测定了苯乙烯的转化率,聚合物分子量及其分布,特性黏数和均方回转半径.实验结果表明3个支化聚合反应体系内悬垂双键是逐步消耗的,不存在明显的成核过程.反应前期,以形成带有悬垂双键的初级链和轻度支化聚合物为主,聚合物分子量随单体转化率逐步上升;反应后期,悬垂双键聚合导致的分子之间的偶合更加明显,使得聚合物分子量快速上升,合成得到的都是无规支化聚合物.