A technique to infer structural information for low level long chain branched polyethylenes

A technique is proposed to relate the weight average molecular weight of linear chains, M_wBL, in low level long chain branched polyethylenes to their linear viscoelastic data. The new method is based on a previously reported empirical technique [Macromolecules 33 (2000) 7481] and was developed through the use of basic molecular theories. The new technique was applied to model systems whose linear viscoelastic properties were simulated using the molecular model of Milner et al. [Macromolecules 31 (1998) 9345] and to long chain branched metallocene polyethylenes. It is applicable to branched polyethylenes with low levels of long chain branching. In the case of a branched metallocene polyethylene, the structural parameter, M_wBL, inferred from the rheological data together with the GPC data such as M_w or M_n of the sample describes all aspects of the structure of the polymer. In the case of highly branched polymers, a possible modification of the technique is also proposed.     

Randomly branched styrene/divinylbenzene copolymers. II. Solution properties and structure

The [η] of randomly branched PSty/DVB continually decreases from linear polystyrene with increasing conversion. On the other hand, the relation of the 〈S²〉 to M of both low and high conversion series is equivalent, although the actual size is smaller than that of linear polystyrene of the same M. This fact, in conjunction with the previously published reactivity ratios, allows the following interpretation of the mechanism of copolymerization: namely, that branched molecules are formed in which the center core is higher in DVB content than is the periphery. Only about 1/7 of the available DVB units act as effective tetrafunctional branch points. An analysis of GPC data correlated with light scattering and viscosity dimensions allows the g value to be determined in the lightly and highly branched fractions. The viscosity ration is related to g^x, where x is 0.65 for low conversion fractions (A series) and becomes 1.41 for high conversion fractions (B series). This change in exponent is postulated to arise from an increase in branching density as conversion increases. The ratio of the hydrodynamic radius to the radius of gyration is higher for branched than for linear polymers. The theta temperature (θ) in cyclohexane for randomly branched polystyrene compared to linear polystyrene is always higher and can be as much as 2° higher.     

Mark–Houwink equation and GPC calibration for linear short-chain branched polyolefines,including polypropylene and ethylene–propylene copolymers

The reduction in molecular dimensions due to the presence of short side chains in otherwise linear polyolefins can very simply by calculated by assuming that the configuration of the main chain is not influenced by the side chains. This enables us to express the intrinsic viscosity–molar mass relationship as a function of the mass fraction of side chains (S): [η] = (1 ? S)^α+1K_PEM_ν^α and, with use of the universal calibration principle, to convert the GPC calibration for purely linear polymers samples into the calibration for short-chain branched polymers: M^* = (1 ? S)M. Experimental data from literature on short-chain branched poly-ethylenes, and our own data on ethylene–propylene copolymers are used to verify the above assumption. It appears that the experimentally found relations between [η], M_w and M^*_w (GPC) within the usual accuracy justify this approach.     

Forced translocation of polymer chains through a nanotube: A case of ultrafiltration

Translocation of polymer chains under the application of an external force has been studied through coarse-grained Monte Carlo simulations. The chains are pulled through a nanotube of finite length and diameter and their translocation times measured. The average translocation time, τ follows a scaling relation involving the chain length, N and applied force, F as, τ ∼ N^ν′F^−μ, where ν′ and μ are two different exponents (ν′ = 0.674, and μ = 0.95 ± 0.05). The scaling law is closely similar to the nanopore translocation scaling law reported by Milchev et al. [Ann N Y Acad Sci 2009;1161:95]. Characteristic signatures of the chain escape time have been exhibited by the square of end-to-end distance R², axial radius of gyration R_g−x and other constituent properties. The behavior of the linear polymers under the application of a pulling force has been exploited to gain insights into the ultrafiltration process of unentangled polymers in dilute solution. The generic pulling force-translocation time (F, τ) data obtained through simulation can be matched reasonably well with the hydrodynamic force-critical macroscopic flow time (f_h, Q_c⁻¹) data and also with the hydrodynamic force-reduced critical microscopic flow time (f_h, q_c⁻¹) data obtained in the ultrafiltration experiment on long linear polystyrene chains in cyclohexane, as recently reported by Ge et al. [Macromolecules 2009;42:4400] The simulation technique reported here may be extended to study biomolecular transports occurring in long protein channels, as studied experimentally through current-time or voltage-time traces.     

Evaluation of different branching functions used in the determination of random branching by GPC

Three branching functions are evaluated for use in the measurement of random branching by GPC. Initial evaluations of the functions g^1/2, g^3/2, and h³ were made by computer simulations of GPC experiments using published data of lightly and highly randomly branched polymers. Actual GPC experiments were then performed on characterized samples of lightly and highly branched styrene–divinylbenzene copolymers. The results indicate that h³ adequately predicts branching and molecular weight at all branching densities, whileg^1/2 is accurate only for lightly branched polymers and g^3/2 is accurate only for highly branched polymers. A means for predicting the M–[η] curve for branched polymers from the M–[η] calibration curve for linear polymer is proposed.     

Novel biocidal polymers based on branched and linear poly(hydroxystyrene)

New biocidal polymers based on branched as well as linear poly(p-hydroxystyrene) were synthesized. Biocidal polymers were synthesized in two steps by creation of active centers via chloroacetylation of linear and branched poly(p-hydroxystyrene) using chloroacetyl chloride. The second step involves the immobilization of onium salts onto the chloroacetylated polymers. All the prepared polymers were characterized using elemental microanalysis, FT-IR, ¹H NMR spectra, and TGA. Antimicrobial activity of the prepared polymers was tested against various pathogenic microorganisms. The antimicrobial activity was found to be affected by the active group and the tested microorganism. The phosphonium salts showed higher activity than ammonium salts.     

Thermodynamic properties of polyolefin solutions at high temperature: 1. Lower critical solubility temperatures of polyethylene,polypropylene and ethylene-propylene copolymers in hydrocarbon solvents

Lower critical solubility temperatures (LCST) of linear polyethylene (PE), isotactic polypropylene (PP) and of five random ethylene-propylene (EP) copolymers of different composition have been measured in (i) five linear alkanes (n-C₅ to n-C₉); (ii) sixteen branched alkanes and (iii) four cycloalkanes. The effect of correlations of molecular orientations (CMO) on the LCST was investigated. The main results of this work are the following: (1) the LCST for PE are much lower than those for PP although the expansion coefficients of the two polymers are similar. Calculations using the van der Waals model for a liquid would predict them 10° to 20° apart while the experimental difference can reach 90°. (2) In PE solutions, the linear alkanes are much better solvents than those which are branched. This constitutes a rare example in non-polar solutions in which the magnitude of the equation of state term is not sufficient to predict or even to compare the LCST. The importance on x of polymer-segment and solvent shapes even above the boiling point of the solvent is to be noted. (3) The LCST of the five copolymer samples are almost a linear function of their composition over all the composition range. (4) These results can be understood if the existence of CMO between the (CH₂Ch₂) sequences is assumed in the pure PE melt and in the copolymers but not between the CH(CH₃)CH₂ sequences. CMO in solution between the polymeric chains and the linear alkanes make the linear alkanes better solvents than the branched ones. From LCST data in n-C₇ and its isomers, the temperature to which CMO in PE disappear can be estimated to be above 170°C, a value which is consistent with those found for long linear alkanes. (5) Branched volatile alkanes such as 2,2-dimethylpentane appear to be a good choice for dosage of the ethylene content of an EP copolymer because of the large interval of LCST between PP and PE in such solvents. LCST measurements could become a sensitive and routine analytical tool for polymer and copolymer characterization for some polymers in well-chosen solvents.     

The largest eigenvalue method for stereo-regular vinyl chains

We derived the analytical solution of the eigenvalue problem for stereo-regular vinyl chains, such as stereo-regular polypropylene chains. The solution is applicable to all stereo-regular polymers of the type (AB)_x which do not have symmetry between gauche⁺ and gauche⁻ states, and to polymers, such as polyoxymethylene or polydimethylsiloxane, for which symmetry between the gauche⁺ and gauche⁻ states does exist. For symmetric chains, the general solution of the eigenvalue problem is reduced to the known solution for polyoxymethylene chains. To illustrate the method the calculations have been performed for the three rotational states (trans, gauche⁺ and gauche⁻) model, but the general algebraic solution is applicable for any ν rotational states models of polymer chains. We used the analytical solution of the eigenvalue problem to calculate numerically elastic properties of stereo-regular polypropylene chains within the framework of Mark-Curro theory (J Chem Phys, 79, 5705, 1983).     

The further understanding of chain topology effect on the properties of single polymer in good solvent: Special behaviors of single tadpole chain

Chain topology strongly affects the static and dynamic properties of polymer melts and polymers in dilute solution. For different chain architectures, such as ring and linear polymers, the molecular size and the diffusion behavior are different. To further understand the chain topology effect on the static and dynamic properties of polymers, we focus on the tadpole polymer which consists of a cyclic chain attached with one or more linear tails. It is found that both the number and the length of linear tails play important roles on the properties of the tadpole polymers in dilute solution. For the tadpole polymers with fixed linear tail length and number, with increasing the degree of polymerization of tadpole polymers, a transition from linear-like to ring-like behavior is observed for both the static and dynamic properties. By studying the radii of gyration for different chains, we define a ratio of the number of monomers in linear tails (N_tail) to the total degree of polymerization (N), and found that when the ratio N_tail/N is more than about 0.73, tadpole chains behave as linear chains, while, when N_tail/N is less than about 0.29, they behave as ring chains. This result will be helpful in further understanding of the chain topology dependence on the static and dynamic properties of polymer in dilute solution. Furthermore, the tadpole polymers behave as what Zimm theory expected before they deviate from the linear-like regime, or after they reach the ring-like regime, however, in the intermediate regime, the behavior of tadpole polymer does not show what Zimm model expected.     

Gel permeation chromatography: the behaviour of polystyrenes with long-chain branching

The gel permeation chromatography (g.p.c.) behaviour of a wide range of branched polystyrenes, in which the branching frequency and the branch length are varied, is described. It is found that, qualitatively, the separation of these branched polymers by g.p.c. does depend on size but contrary to other results reported in the literature, the hydrodynamic volume[η]M of the polymer molecules is not the appropriate size parameter to use. That is, a single plot of log[η]M against elution volume embracing all the branched polystyrenes prepared and linear polystyrenes is not obtained. Because the mean square radii of gyration of these branched polystyrenes could not be measured directly no positive evidence as to the nature of the correct size-separation parameter was obtained. It is pointed out that, even if the correct size-separation parameter were known, g.p.c. could not be used to characterize branched polymers unambiguously.     

Branched polysilanes from tetrafunctional monomers

Tetrafunctional silicon monomers have been incorporated into soluble branched polysilanes. Tetrakis(chlorodimethylsilyl)silane has been homopolymerized to form an irregular branched polymer which may contain some spiro and some bicyclic units. This polymer shows weak absorption at 300 nm, the region of the linear polysilane chains. It emits broadly in the region from 400 to 500 nm. The copolymers of tetrakis(chlorodimethylsilyl)silane with dichlorodimethylsilane are also soluble and in the presence of l ge amount of the tetrakis monomer emit in the region from 400 to 500 nm. By contrast, copolymers with phenyltrichlorosilane emit strongly at 450 to 650 nm, due to the phenylsilane hyperbranched structure. Small amounts of tetrachlorosilane can be incorporated into soluble polysilanes. Incorporation of =Si=units into polymers withn-hexyl substituents is very inefficient but leads to minor changes in emission spectra. Incorporation into polymers with phenyl substituents affects luminescence and increases molecular weights and broadens polydispersities. Reaction with dimethyldichlorosilane provides soluble low molecular weight oligomers and polymers. Polymers prepared with a small proportion of tetrachlorosilane show absorption and emission typical for linear polymers. Polymers synthesized with higher proportion of tetrachlorosilanes emit broadly at 400 to 500 nm, indicating the presence of Si clusters. The silicon clusters entrapped into soluble polymers are very easily oxidized as seen by the siloxane peaks in²⁹Si NMR spectra and they should be treated under complete exclusion of oxygen.     

Monte-Carlo calculations on statistical chains enclosed inside a sphere

Statistical chains have been generated inside a sphere of variable radius R. The mean square root end-to-end distance, the radius of gyration, and the entropy of the chains have been determined as a function of R for absorbing boundary (AB) and reflecting boundary (RB) statistics to be defined below in this paper. It is found that the entropy change ΔS from the unbounded (free)chain varies as R^?2 for AB statistics and as R^?1 for RB statistics.     

Prediction of mean square radius of gyration of tree-like polymers by a general kinetic approach

This paper describes a kinetic method to predict the z-average molecular mean square radius of gyration of tree-like polymers formed by irreversible reactions, assuming Gaussian chains. It is based on the population balance equations for the two-sided molecular distributions of pendant chains associated with every chemically distinguishable kind of bonds. An automated method for the solution of those equations is valid both before as well as after gelation for complex kinetic schemes. Examples of its use are presented with polycondensation systems leading to hyperbranched polymers, the anionic polymerization of mono- and divinyl monomers and a radical polymerization with terminal branching and transfer to polymer.     

Synthesis and gas permeability of ester substituted poly(p-phenylene)s

Polymerizations of various ester substituted 2,5-dichlorobenzoates [substituent: linear alkyl groups (1a-f), branched alkyl groups (1g-l), cyclohexyl groups (1m-o), phenyl groups (1p-r), and oxyethylene units (1s-v)] were investigated with Ni-catalyzed/Zn-mediated system in 1-methyl-2-pyrrolidone (NMP) at 80 °C. Most of monomers bearing linear and branched alkyl groups successfully polymerized to give relatively high-molecular-weight polymers (M_n = 10,000-20,800). However, the molecular weight of the polymer having eicocyl groups was low because of steric hindrance of long alkyl chain. The polymerizations of cyclohexyl 2,5-dichlorobenzoate and phenyl 2,5-dichlorobenzoate produced low-molecular-weight polymers, while the polymerizations of monomers with alkyl cyclohexyl and alkyl phenyl groups proceeded to afford polymers with relatively high-molecular-weights. The polymers possessing oxyethylene units were obtained, but the molecular weights were low when the oxyethylene chains were long. The gas permeability of membranes of poly(p-phenylene)s with alkyl chains increased as increasing the length of alkyl chain. The membranes of poly(p-phenylene)s with phenyl groups and oxyethylene units exhibited high densities and relatively low gas permeability. However, the CO₂/N₂ separation factor of membrane of poly(p-phenylene) having oxyethylene units was as large as 73.6.     

Calculation of the f.i.r. absorption frequencies of polyethylene using a proved semiempirical potential function

A potential function successful in describing the properties of isolated chains of several polymers as well as crystal properties of polyethylene is applied to calculate frequencies of lattice modes of this polymer. The B_1u and B_2u frequencies are determined as 86 and 105 cm^?1, respectively, for the crystal at T = OK. These values are compared with the extrapolated frequencies from temperature dependent f.i.r. absorption spectrum of linear PE (6011 L) measured by Frank et al. The values are 83 and 108 cm^?1, respectively. An influence of the setting angle to the transition moment is discussed.     

Determination of the conformation of polymers in the amorphous solid state and in concentrated solution by neutron diffraction

From the coherent neutron scattering on dilute solid solutions of the ordinary polymer within the deuterated polymer, conformation parameters of polymer chains in amorphous solid states can be determined. In this way vitreous poly(methyl methacrylate) (PMMA) has been investigated. The chains form unperturbed coils and the radius of gyration is very near to the corresponding value in dilute solutions of the same polymer in the low molecular θ-solvent butyl chloride. The same principle of measurement has been applied to concentrated solutions of PMMA in D-acetone. The solutions contained 50% polymer, the main part of which (98% and more) was deuterated so that the system was optically dilute for neutron scattering on H-PMMA. A monotonic dependence of the radius of gyration and of thermodynamic parameters on the concentration has been found. A first result is presented for a mixture of two polymers. A dilute solid dispersion of poly(α-methylstyrene) (PMS) within D-PMMA has been investigated at M_w = 250 000. The samples are limpid. The PMS forms micelles of 16 molecules (weight average). The radius of gyration of the micelles, r_z is 170 Å.     

支化结构对树枝状聚合物静态吸附特征的影响

采用浸泡法研究了不同支化程度的驱油用树枝状聚合物在石英砂上的静态吸附特征,并利用动静态激光光散射仪和环境扫描电子显微镜测定了聚合物溶液的分子尺寸和微观结构。结果表明,不同支化程度的树枝状聚合物溶液的等温吸附曲线均呈现三段式的吸附特点;在初始阶段,支化结构小的聚合物支链条数较少以及流体力学半径较小,其在固定表面积的石英砂上吸附位阻比支化结构大的聚合物小,导致吸附量较大;在吸附形式为多层吸附的Ⅱ、Ⅲ阶段,支化程度大的聚合物支化链间相互作用越强,易缠结形成网络结构,致使其在石英砂表面吸附层数多,吸附量比支化程度小的聚合物多。     

Synthesis and characterization of cationic polymeric salts: derivatives of 2‐(dimethylamino)ethyl‐2‐methacrylate,containing oligomeric ethylene oxide side‐chains

A novel set of cationic polyelectrolytes has been prepared. The polyelectrolytes have a high cationicity with each segment carrying one positively charged quaternary ammonium group. The polyelectrolytes also contain grafted oligo(ethylene oxide) (EO) chains. The grafted EO chains are, according to NMR measurements, six units long. The graft density of EO chains has been varied and polymers having approximately 100%, 20% and 10% of the segments with a grafted EO chain have been prepared. The obtained products were characterized using ¹H and ¹³C NMR spectroscopy. Aqueous solutions of the cationic polymers were characterized by dynamic light‐scattering (DLS) measurements. It was found to be important to include a radical inhibitor to prevent crosslinking reactions during isolation and purification. In general the DLS measurements showed a bimodal size distribution. The majority of the polymers (about 75 wt%) were found to have a hydrodynamic radius of 6–8 nm, with the remaining polymers being dominated by a fraction with a hydrodynamic radius in the range 120–140 nm. © 2003 Society of Chemical Industry     

The preparation and rheology characterization of long chain branching polypropylene

In order to study the rheological behavior of long chain branching (LCB) polypropylene (PP), linear polypropylene was modified by melt grafting reaction in the presence of 2,5-dimethyl-2,5(tert-butylperoxy) hexane peroxide and pentaerythritol triacrylate (PETA) in mixer. The transient torque curves and Fourier transformed infrared spectroscopy (FTIR) results indicated that macroradical recombination reactions took place and PETA had been grafted onto PP backbone. Various rheological plots including viscosity curve, storage modulus, loss angle, Han plot, Cole-Cole plot were used to distinguish LCB PP from linear PP. On the other hand, to quantify the LCB level in modified PPs, a new method was suggested on the basis of macromolecular dynamics models. The results showed that the level of LCB was in the range of 0.025-0.38/10⁴ C . Moreover, the length of the branched chains and the content of the branched component increase with PETA concentration. Furthermore, the LCB efficiency of monomer can also be calculated, less than 20% of grafting monomers was used to form branch structure.