Conformational end effects in unperturbed chains and star-branched polymers

End effects in unperturbed chains with a specified number of bonds, n, have previously been characterized using the conformations at individual bonds and the mean square unperturbed dimensions of subchains situated at various positions along the chain. Both criteria have found that the end effects are extremely weak in typical flexible chains, such as unperturbed polyethylene. Of course, these criteria detect no end effect at all in a freely jointed chain. This conclusion requires modification if the end effects are defined differently, using the mean square radius of gyration of the n+1 chain atoms about chain atom i, denoted . The values of depend on i in all chains, including the freely jointed chain. The range for the volume specified by suggests that the average density of chain segments about a terminal atom is roughly 1/3 of the average density of chain segments about the atom midway along the contour of any long unperturbed chain. The severity of these end effects in finite chains depends on the detailed local structure, becoming more severe for more extended chains. The end effect detected by in regular freely jointed star-branched polymers becomes more severe as the number of branches increases.     

Simulation of chain folding in polyethylene: A comparison of united atom and explicit hydrogen atom models

We performed a systematic study to show that the nicely folded lamellar structure of polyethylene chains derived from previous molecular simulations is a consequence of the use of the united atom model, which treats the CH₂ groups as a hard sphere. Simulations presented here with explicit hydrogen atoms show that the fold is not uniform, and that regularly aligned stems do not result. While it is known that polyethylene crystallizes with chain folded morphology, the irregular folding seen here is due to the neglect of the interactions between the hydrogen atoms attached to a carbon atom C_i and the atom C_i+2 in the united atom model. We present this paper to point out how the choice of force fields is important for polymers with a high degree of crystallinity. We hope that this paper stimulates further work on developing united atom models that take into account terms that we show to dictate the polymer conformations, such as the interactions between atoms attached to carbon atom C_i and the atom C_i+2 in polyethylene.     

Synthesis, Characterization and Surface Activity of Alkyl m-Xylene Sulfonate Isomers

This paper deals with the synthesis of a series of alkyl m-xylene sulfonate isomers (with the m-xylene located at the eighth carbon atom along the long alkyl chain) by the Friedel?CCrafts reaction, and the Grignard reaction followed by hydrogenation. The structures were confirmed by ¹H NMR. All analytical methods indicated high levels of purity of the isomers with the eighth carbon atom at the long alkyl chain. The critical micelle concentration (CMC), surface tension and maximum surface excess concentration at the CMC and area per molecule at the interface were determined. As the long alkyl chains increased the surfactant molecule tends to pack closely at the gas?Cliquid interface. Accordingly, the CMC decreased, the adsorption density increased, and the surface tension reduction was strengthened.     

Substituted poly(silylenemethylene)s with short range interactions that induce a preference for the same local conformation in unperturbed atactic, isotactic, and syndiotactic chains

A rotational isomeric state model has been developed for the poly(silylenemethylenes) with repeating sequence [Si(CH₃)R-CH₂]_x, R=-O(CH₂)_NOC₆H₄C₆H₅. The model incorporates all first- and second-order interactions, as well as higher order interactions that are mandatory in some of the conformations. Chains with all possible stereochemical sequences prefer a local conformation that is a run of trans states at the C-Si bonds in the backbone. This preference arises from an attractive second-order interaction of the first methylene group in the side-chain bonded to chain atom i with the silicon atoms indexed i±2. Unperturbed chains have larger dimensions than the simpler chain in which R is merely a methyl group. The temperature coefficients of the unperturbed dimensions are large and negative. The preference of unperturbed atactic, isotactic, and syndiotactic chains for the same local conformation may contribute to the facile formation of smectic phases by the presumably atactic chain, as reported by Park et al. [Macromolecules 35 (2002) 2776].     

表面接枝二分散聚合物的自洽场理论

建立了表面接枝多分散聚合物的自洽场理论.通过对二分散聚合物进行自洽场模拟,研究了排除体积参数对分子链密度分布的影响,考察了分子链的摩尔分数与自由端分布的关系并将模拟结果与强伸展理论进行了比较.通过计算分子链的链段密度分布和伸展轨迹,讨论了二分散聚合物分子链的伸展行为.     

Translocation of compact polymer chains through a nanopore

We perform dynamical Monte Carlo simulation to study the forced translocation of compact polymer chains in three-dimensional lattices. The chains are driven through a nanopore connecting two infinite channels by an external field. The scaling properties of average translocation time τ and translocation time distribution (TTD) are studied. The effects of contact energy (?_C), electric field strength (E), and nanopore width (L) on the scaling exponent (α) of average translocation time τ ∼ N^α and the TTD are investigated. For the scaling behavior of τ ∼ N^α, we have found that there is no crossover behavior with weak field strength when the nanopore width is one lattice spacing, which is less than average bond length, while crossover behaviors are observed for larger nanopore widths. The scaling exponent α also depends on contact energy ?_C and electric field strength E. For the TTD, it shifts from the Gaussian to a right-skew distribution with the electric field E increasing for short chains; while for long chains, multi-peak distributions are observed. As a primary and simple model, compact polymer chains are extensively used to capture the structure and thermodynamic properties of proteins, therefore we can investigate the protein translocation by simulating compact chain translocation, and this study will be useful for exploring the complex translocation behaviors of proteins.     

Effect of chain length distribution on thermal characteristics of model polytetrahydrofuran (PTHF) networks

A series of model polytetrahydrofuran (PTHF) networks were synthesized via end-linking reactions of α, ω-allyl PTHF oligomers with a stoichiometric tetrafunctional crosslinker. The telechelic PTHF oligomers were synthesized by living cationic ring-opening polymerization of tetrahydrofuran followed by a termination reaction with allyl alcohol. Networks thus prepared have well-controlled architecture in terms of the inter-crosslink chain length (M_c) and chain length distribution: resulting in unimodal, bimodal and clustered structures. Unimodal network was prepared by using polymer chains of same molecular weight, bimodal networks were synthesized by using two groups of polymer chains with different average molecular weights, and the clusters are prepared by incorporating clusters of networks with small molecular weight chains in a network matrix made of longer chains. Thermal characteristics of these model networks were investigated as a function of crosslink density, as well as inhomogeneities of crosslink distribution using DSC. We demonstrate that glass transition temperature (T_g) and crystallization behavior (melting temperature and crystallinity) of the networks are both strongly influenced by crosslink density (M_c). By comparing the unimodal, bimodal and clustered networks with similar average M_c, the effects of inhomogeneities in the crosslink distribution on the thermal properties were also investigated. Results show that inhomogeneities have trivial influence on T_g, but strongly affects the crystallization behavior. Moreover, the effects of the content ratio and length ratio between long and short chains, and the effects of cluster size and size distribution on the thermal characteristics were also studied.     

Reversible coordinative chain transfer polymerization of isoprene and copolymerization with ε-caprolactone by neodymium-based catalyst

Coordinative chain transfer polymerization (CCTP) of isoprene was investigated by using the typical Ziegler–Natta catalytic system [Nd(Oi-Pr)₃/Al(i-Bu)₂H/Me₂SiCl₂] with Al(i-Bu)₂H as cocatalyst and chain transfer agent (CTA). The catalyst system exhibited high catalytic efficiency for the reversible CCTP of isoprene and yielded 6–8 polymer chains per Nd atom due to the high chain transfer ability of Al(i-Bu)₂H. The narrow molecular weight distribution (M_w/M_n = 1.22–1.45) of the polymers, the good linear relationship between the M_n and yield of the polymer, and the feasible seeding polymerization of isoprene indicated the living natures of the catalyst species. Moreover, the living Nd-polyisoprene active species could further initiate the ring-opening polymerization of polar monomer (ε-caprolactone) to afford an amphiphilic block copolymer consisting of cis-1,4-polyisoprene and poly(ε-caprolactone) with controllable molecular weight and narrow molecular weight distribution.     

Kinetic phase diagram for crystallization of bimodal mixtures of oligomers as predicted by computer simulations

We analyze the crystallization process of mixtures of long and short oligomers such as n-alkanes using a Sadler-Gilmer-type growth algorithm. The short chains are assumed to crystallize only in a fully stretched conformation, while the long chains take a pathway over a folded state. Increasing the concentration of long chains from zero to unity, the zero-growth temperature, which separates the stable growing phase from the non-growing phase, first decreases for low concentrations of long chains, reaching a minimum value at intermediate concentrations, and increases again for higher concentrations, as a result a growth-gap appears. Here, mixing long chains into the short chain liquid stops the growth process completely until it resumes at higher concentrations of long chains. This effect is explained by the particular kinetic pathway, the long chains take into the crystalline state. Since the folded state has to be passed at first, long chains are more likely to be desorbed again. At low concentrations, the long chains thus effectively dilute the short chain liquid leading to a decrease of the zero-growth temperature. At higher concentrations, the transition into the stretched state of the long chains leads more frequently to bonded pairs, which stabilizes the growth again due to the higher binding energy among fully stretched long chains.     

Theoretical Study of Equilibrium Bipolar Charge Distribution on Nonuniform Primary Straight Chain Aggregate Aerosols

A general theory describing the equilibrium bipolar charge distribution for straight chain aggregate aerosols consisting of primary spheres of different diameters was derived from a theory previously developed for linear chain aggregate of uniform spheres. The present theory is based on the assumptions that (1) the individual primary particles of a straight chain aggregate are charged independently, (2) the probability that a particular primary particle has acquired q elementary charges is governed by the Gaussian distribution predicted by Boltzmann's law, based on particle size; and (3) the resultant charge of a straight chain aggregate is the algebraic sum of the charges carried by the constituent primary spheres. The present theory can be stated as follows: The equilibrium bipolar charge distribution of straight chain aggregate aerosols with nonuniform primary spheres can be expressed by Boltzmann's law with an equivalent diameter such that d_eL = Σ ⁿ _i=1 d_i . The limitations imposed by the assumptions are also discussed.     

Does PNIPAM block really retard the micelle-to-vesicle transition of its copolymer?

The well-known coil-to-globule transition of poly(N-isopropyl acrylamide) (PNIPAM) at its LCST lasts as short as hundred of seconds with fully reversibility. However, for the PNIPAM-containing block copolymers, thermal transformation from micelles to vesicles caused by the conformation transition of PNIPAM took as long as several weeks, even at the temperatures much higher than the LCST, and without satisfactory reversibility. In the literature, this slow process has been attributed to the strong interchain hydrogen bonding in PNIPAM, which retards the transition. In this work, asymmetrically modified PNIPAM (Mw 10K), i.e. C₁₂-PNIPAM-CA with a hydrophobic hydrocarbon chain -C₁₂H₂₅ (C₁₂) at one end and a hydrophilic carboxyl group -COOH (CA) at the other, was prepared and found to form micelles with a core of the lightly associated hydrocarbon chains. When temperature is increased to the LCST of PNIPAM, the transformation from micelles to vesicles can be realized within 30 min, while the reverse process only takes a few minutes. Based on full monitoring of the transition process, it is proposed that the micelles serve as building blocks in constructing the vesicles via processes of combination, fusion, and etc., in which only local conformation adjustment of PNIPAM is involved. Therefore, reducing the restriction to the conformation change of PNIPAM chains, which is imposed by the micellar core, is one of the key factors in realizing the fast transition.     

Packing mode and conformational transition of alkyl side chains in N-alkylated poly(p-benzamide) comb-like polymer

A series of rigid-rod poly(p-benzamide) polymers (PBA) with different length of flexible alkyl side chains, denoted as PBA(n)Cs, have been prepared by N-alkylation method. The alkyl side chain lengths varied from decyl (n=10) to octadecyl (n=18), with an interval of two carbon atoms. The packing mode and conformational transition of the alkyl side chains of the prepared PBA derivatives were characterized by wide-angle X-ray diffraction (WAXD), differential scanning calorimertry (DSC), and Fourier transform infrared spectroscopy (FTIR). WAXD results revealed that the derivatives form layered structure in which the distance between the backbones depends on the length of alkyl side chains. DSC studies indicated that melting transition temperature of PBA(n)Cs increases accordingly with increasing the alkyl chain length of the substituents. Meanwhile, DSC results proved that as the carbon atom number of the side group exceeds 14, alkyl side chains in PBA(n)Cs tend to crystallize FTIR spectroscopic investigation showed that the all-trans zigzag conformation is the most stable state for the alkyl side chain in PBA18C comb-like polymer. Temperature variation caused the reversible transition between trans and gauche conformational states of the side octadecyl group, and in turn made the molecular chain packing mode of PBA18C comb-like polymer undergo an reversible transformation from ordered packing to disordered packing.     

Effects of high molecular weight species on shear-induced orientation and crystallization of isotactic polypropylene

In situ rheo-SAXS (small-angle X-ray scattering) and—rheo-WAXD (wide-angle X-ray diffraction) techniques were used to investigate the role of high molecular weight species on the evolution of oriented microstructure in isotactic polypropylene (iPP) melt under shear flow. The two iPP samples, designated as PP-A and PP-B, respectively, had the same number-average (M_n) but different weight-average (M_w) and Z-average (M_z) molecular weights. Molecular weight distribution (MWD) of PP-A and PP-B was such that for MW<10⁵ the MWD curves overlapped; whereas in the high MW tail region, the amount of high molecular weight species was higher in PP-B than PP-A. Both samples were subjected to an identical shear condition (rate=60 s⁻¹, duration=5 s, T=155 °C). In situ 2D SAXS and WAXD images allowed the tracking of shear-induced oriented structures in the melt. It was found that the shish structures evolved much earlier, and the degree of crystal orientation and oriented crystal fractions were higher in PP-B than PP-A. Moreover, PP-B exhibited faster crystallization kinetics than PP-A. These results, along with the predictions of double reptation models of chain motion and experimental studies of chain conformation dynamics in dilute solutions under flow, suggest the following: When a polymer melt that consists of entangled chains of different lengths is deformed, the chain segments aligned with the flow eigenvector can undergo the abrupt coil-stretch-like transition, while other segments would remain in the coiled state. Since, flow-induced orientation decays much more slowly for long chains than for short chains, oriented high molecular weight species play a prominent role in formation of the stretched sections, where shish originates. Our experimental results are strong evidence of the hypothesis that even a small increase in the concentration of high molecular weight species causes a significant increase in the the formation, stability and concentration of the flow-induced oriented microstructure.     

Adsorption of Homopolymer Chains on a Strip-Patterned Surface: A Monte Carlo Study

In this study we investigated the process of chemisorption of polymers on solid surfaces. The formation of a strongly adsorbed polymer film was studied by Monte Carlo simulations. The adsorbing planar surface was patterned with strip-like repulsive sites. The polymer chains were represented by a sequence of schematically constructed objects (united atoms) and we considered star-branched macromolecules with f = 3 arms of equal length. The chains were studied at good solvent conditions and thus the excluded volume was the only potential of interaction between the polymers. A Metropolis-like sampling algorithm was employed in order to calculate the properties of the adsorbed chains. The influence of the chain length, the system density and the type of the pattern on the adsorbing surface on size of chains and the structure of the polymer film were determined and discussed. We found that the roughness of the polymer film surface depends non-monotonics on the number of polymer beads in the system. The shape of this surface reflects the pattern imposed on the substrate.     

Registration Probabilities and Pulse-Height Distributions of Coincidences in Optical Particle Counters

In conventional optical particle counters chains of particles' coincidences may occur as a result of continuous view volume illumination and sampling. Because of these coincidences, probability of the presence of several particles in a view volume given by the well-known Poisson distribution cannot be interpreted as a coincidence registration probability. Particle registration probability distribution accounting for chain coincidences is calculated for optical counters with the first maximum of the counter pulse chosen for counting. Registration probability of the doublets is obtained numerically also for counters with the choice of the global maximum of the counter pulse for counting. Pulse-height probability density functions (pdf) are calculated for square, triangular, and Gaussian pulses. It is shown that pdfs of apparent multiplets are resolved in counters with rectangular response pulses and sufficiently high resolution. However, in counters with any nonrectangular response pulses the coincidences have overlapping pulse height distributions. It is shown that counters with the Gaussian pulses allow measuring 30% higher aerosol concentrations compared with the square pulse counters. Aerosol size distribution distortions invoked by coincidences are estimated.

A method of counter view volume determination using coincidences is suggested.     

Linear viscoelastic relaxation modulus of polydisperse poly(dimethylsiloxane) melts containing unentangled chains

This work analyzes the relationship between the shear relaxation modulus of entangled, linear and flexible homopolymer blends and its molecular weight distribution (MWD) when a fraction of the sample contains chains with molecular weight M lower than the effective critical molecular weight between entanglements Mc_eff. This effective critical parameter is defined in terms of the critical molecular weight between entanglements M_c of the bulk polymer that forms the physical network and the effective mass fraction Wc_eff of the unentangled chains. In the terminal zone of the linear viscoelastic response, the double reptation mixing rule for blended entangled chains and a modified law for the relaxation time of chains in a polydisperse matrix are considered, where the effect of chains with M<Mc_eff is included. Although chain reptation with contour length fluctuations and tube constraint release are still the relevant mechanisms of chain relaxation in the terminal zone when the polydispersity is high, it is found that the presence of a fraction of molecules with M<Mc_eff modifies substantially the tube constrain release mode of chain relaxation. In this sense, a modified relaxation law for polymer chains in a polydisperse entangled melt that includes the effect of the MWD of unentangled chains is proposed. This law is validated with rheometric data of linear viscoelasticity for well-characterized polydimethylsiloxane (PDMS) blends and their MWD obtained from size exclusion chromatography. The short time response of PDMS, which involves the glassy modes of relaxation, is modeled by considering Rouse diffusion between entanglement points of chains with M>Mc_eff. This mechanism is independent from the MWD. The unentangled chains with M<Mc_eff occluded in the polymer network also follow Rouse modes of relaxation although they exhibit dependence on the MWD.     

Elastic behavior of adsorbed single compact chains

Elastic behaviors of short single two-dimensional compact chains adsorbed on the attractive surface are investigated in this paper by using the enumeration calculation method. In our model a single compact chain is fixed with one of its end at a position above the impenetrable surface, and then it is pulled away from the attractive surface slowly through elastic force acting. We investigate the chain size and shape of adsorbed compact chains, such as mean-square end-to-end distance per bond 〈R²〉/N mean-square radii of gyration per bond 〈S²〉_x/N and 〈S²〉_y/N, shape factors 〈δ〉, and fraction of adsorbed monomers f_a in order to illuminate how the size and shape of adsorbed compact chains change during the process of tensile elongation. Especially for strong attraction interaction there are some special behaviors in the chain size and shape during this process. If there exits adsorption interaction, single compact chain is first almost pulled down to the adsorption surface and then moves in the direction of force until to leave the adsorption surface. These changes become more obvious with strong adsorption interaction. Our calculation can show this elastic process of adsorbed compact chains visually and simply. On the other hand, some thermodynamics properties are also studied here. We use average energy per bond, average Helmholtz free energy per bond, elastic force f and energy contribution to elastic force f_u to study the elastic behavior of adsorbed single compact chains in the process of tensile elongation. Elastic force f has a long plateau during the tensile elongation for strong adsorption interaction, which agrees well with experimental and theoretical ones. These investigations can provide some insights into the elastic behaviors of adsorbed protein chains.     

High-energy mechanical alloying of thermoplastic polymers in carbon dioxide

High-energy ball milling was performed on low density polyethylene (LDPE) and isotactic polypropylene (iPP) as well as on 20/80 binary mixture of both polymers. Mechanical alloying was carried out at high pressure with carbon dioxide for a short period. The presence of CO₂ avoids oxidative mechano-chemical degradation of polymers and enhances the effectiveness of the milling. The effects of the mechano-chemical treatment on the molecular and physical properties of both single polymers and blends of intrinsically incompatible polymers were explored by FTIR spectroscopy, thermal analysis, intrinsic viscosity determination and solvent fractionation. Structural changes on PP and PP/LDPE blend were observed and have a strong dependence on the milling time. Mechanical tests confirm an overall improvement in blend properties by mechanical alloying. Experimental evidences are presented to suggest that CO₂ high-energy ball milling causes a self-compatibilization of the blend LDPE-iPP by breaking iPP polymer chains and allowing them to recombine with the neighboring LDPE chains.     

Reactivity of polymeric carbon chains reduced from poly(tetrafluoroethylene)

Electrochemical reduction of poly(tetrafluoroethylene) (Teflon), which contains very long linear carbon atom chains, yields in the presence of Li⁺ a solid mixture of lithium fluoride and polymeric carbon. The latter is probably in the sp state and is very chemically reactive. Its chains begin to bind into a solid carbon skeleton only after separation from the salt sheaths, so that chemical bonds are formed between certain carbon atoms of neighbouring chains. The form of the skeleton is much influenced by physico-chemical conditions during the separation process. The porous carbon layer consisting from sporadically bound carbon chains was found to be plastic as long as the skeleton does not become more rigid by the formation of additional chemical bonds. Three different carbonaceous materials were prepared from the same mixture (C, LiF) by different technologies. Differences between them were studied by elementary chemical analysis, nitrogen adsorption, wide-angle and small-angle X-ray scattering, and electron microscopy. The obtained results enable to discuss the course of formation of the carbon skeleton.     

An application of Monte Carlo method to simulate disorders in polymer crystals

The Monte Carlo method is applied to polymer crystals of idealized linear chain molecules of 30 carbon atoms, and the unharmonic, large-amplitude, oscillations and the subsequent conformational disorders of the chains are investigated. A crystalline field that confines the chain is treated by the molecular field approximation, and assumed to be cylindrical in this work. A production type simulation is adopted taking into account rigorous statistical weights for each sample conformation. Both the rotational isomeric model and the continuous rotation model of chain conformation are considered. By averaging over 10⁴–8 × 10⁴ chains, mean-square end-to-end distance, fractions of gauche and trans states and a detailed distribution of internal rotation angle are obtained. The effects of temperature and pressure on the conformation of the chain in the crystals are also simulated.