Freely jointed chain with variable segment number and length

The configurational properties of a molecular chain are investigated. The chain consists of rigid rod segments, which are consecutively correlated. This correlation is described by a two-state model. In the first state, neighboring segments are freely hinged togethers whereas in the second state they are parallel. The partition function and the force-extension relation are calculated. They show significant differences as compared to the usual results for a freely jointed chain. Thus the experimentally observed force-extension relation of polymeric networks buil up of such chains might be affected.     

FTIR separation of nylon-6 chain conformations: Clarification of the mesomorphous and γ-crystalline phases

Specific infrared absorptions for each form of Nylon-6 have been indentified. Quenched films were prepared by melt casting and converted in turn to the α-crystalline and γ-crystalline structures. The films were examined using Fourier transform infrared spectroscopy (FTIR) with the attenuated total reflection configuration and by X-ray diffractometry. The FTIR spectrum of the pure mesomorphous component of the quenched film was calculated by subtracting away the contribution of α-crystalline peaks present due to incomplete quenching. A curve-fitting procedure was applied to the pure mesomorphous and gamma crystalline spectra. Several peaks in the mesomorphous spectrum are observed to develop a shoulder upon conversion to the γ-crystalline form. This is due to the extra gauche character imparted to the C? N bond between the methylene unit and the amide group. These and other band assignments were confirmed by analysis of model compounds.     

Investigating the chain conformations of spin‐coated polymer thin films by ToF‐SIMS depth profiling

Thin films of bromine‐terminated poly(bisphenol A octane ether) (BA‐C10) were prepared using 1,2‐dichlorobenzene (ODCB) as the solvent. The organization of the chains in these amorphous polymer films was evaluated using time‐of‐flight secondary ion mass spectrometry (ToF‐SIMS) depth profiling. For the thin films, the bifunctional polymer chains were folded and anchored to the substrate via their two Br end groups and a polymer brush of chain loops was formed on the substrate. As the film thickness increased, polymer chains in a random coil conformation were found to reside on the top of the polymer brush. Depth profiling revealed that the polymer chains were densely packed at the interface. Moreover, the polymer films showed thermal stability, implying strong interactions between the end groups and the substrate. Copyright © 2015 John Wiley & Sons, Ltd.     

聚羧酸系高性能减水剂分子在稀溶液中尺寸及其在体积排除色谱表征中表观分子量的模型研究

针对被称为"第一代聚羧酸高性能减水剂"(以下简称为MPEG-type PCE)的甲基丙烯酸(MAA)/烯酸甲酯(MAA-MPEG)梳状共聚物分子,从高分子物理基础理论出发,构建等效自由连接链模型,结合前人的理论结果和实验数据,得到了MPEG-type PCE分子的回转半径、流体力学半径及其相应的支化参数的数学表达式.在此基础上,报道了以下三方面的工作:首先,将计算结果与文献中的实验结果进行比较,检验模型的合理性;其次,利用所建立的数学模型考察主链分子量、侧链分子量和侧链接枝密度对PCE分子的回转半径和流体力学半径的影响;最后,结合近年来发展的体积排除色谱分离理论,对PCE分子的真实分子量与其常规体积排除色谱"表观分子量"(又被称为GPC分子量)两者之间的差异进行了分析.本文所提出的计算模型和数学表达式没有不确定的指前因子,可用来估算MPEG-type PCE分子在稀水溶液中的尺寸以及根据其GPC分子量估算真实分子量.     

Recent advances in the modeling and simulation of metallocene catalysis,sequence distribution,chain conformations,and crystallization of polymers

This article is a review describing the latest advances in modeling and simulation of polymers. Sequence distributions in stereoblock polymers and copolymers greatly affect their chain conformations and thermal transitions. While no theory was able to fully predict the influence of chain conformations on polymer crystallization, modeling techniques have shown good reliance in simulating the conformational behavior of polymeric chains and the related physical properties. This is done by generating representative sequences, and studying the chain conformation and packing of such sequences into crystalline regions in multichain systems. Metallocene catalysts, a class of single site catalysts, also showed unprecedented performance in the polymerization of olefins, most notably their activity, copolymerization capabilities, and potential for precise control of stereostructures. These attributes are among the most important issues in the manufacture of polyolefins and olefin copolymers, and are too good to be ignored. These polymers consist of alternating atactic sequences, which are amorphous and act as elastomeric chains, and ordered isotactic or syndiotactic sequences which, if long enough, will crystallize and act as physical reinforcing crosslinks. Mesoscopic investigation utilizing computer modeling and simulation into the effects of the sequence length and sequence length distribution on the reinforcement of stereoblock and stereoregular polyolefins has also been reviewed. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 2524–2541, 2006     

高分子链形状与尺寸关联的Monte Carlo模拟

运用MonteCarlo方法对线型高分子链格点模型的构型进行了模拟,研究了构型的尺寸(采用平方末端距R²,平方回转半径S²来表征)和形状(由非球形因子A表征)之间的关联.对任何长度的高分子链,其关联系数CA,R²和CA,S²均为正值,表明高分子链的形状与尺寸之间存在正关联,即尺寸小的构型其非球形因子A一般也小,反之尺寸大的构型其非球形因子A一般也大.关联系数CA,R²和CA,S²均随链长的增大而减小,近似地与链长的倒数(n^-1)成正比.研究还表明,关联系数的极限值(链长n很大时)与格点的类型无关,与链样本产生的方式也无关,但与链是否考虑排斥体积有关,考虑了排斥体积后,关联系数增大.     

Effect of beta-O-glucosylation on L-Ser and L-Thr diamides: a bias toward alpha-helical conformations

Beta-D-O-glucosylation produces a remarkable effect on the peptide backbone of the model peptides derived from serine and threonine. Consequently, this type of glycosylation is responsible for the experimentally observed shift from extended conformations (model peptides) towards the folded conformations (model glycopeptides). The conclusion has been solidly assessed by a combined NMR/MD protocol. Interestingly, the MD (molecular dynamics) results for the glycopeptides point towards the existence of water-bridging molecules between the sugar and peptide moieties, which could explain the stabilization of the folded conformers in aqueous solution.     

Polymer chain diffusion in polymer blends: A theoretical interpretation based on a memory function formalism

The diffusion of polymer chains in miscible polymer blends with large dynamic asymmetry—those where the two blend components display very different segmental mobility—is not well understood yet. In the extreme case of the blend system of poly(ethylene oxide) (PEO) and poly(methyl methacrylate)(PMMA), the diffusion coefficient of PEO chains in the blend can change by more than five orders of magnitude while the segmental time scale hardly changes with respect to that of pure PEO. This behavior is not observed in blend systems with small or moderate dynamic asymmetry as, for instance, polyisoprene/poly(vinyl ethylene) blends. These two very different behaviors can be understood and quantitatively explained in a unified way in the framework of a memory function formalism, which takes into account the effect of the collective dynamics on the chain dynamics of a tagged chain. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019 , 57, 1239–1245     

Conformation of a chain polyelectrolyte in solution with low molecular weight salt: small angle neutron scattering measurements

Small angle neutron scattering measurements have been carried out on the tetramethylammonium salt of the polystyrenesulfonic acid withDP _w =310 and 1060 in water solution with tetramethylammonium chloride with ionic strength between 0.02 M and 1.0 M. The scattering curves in the scattering vector range 0.05 nm^–1Q1.8nm^–1 have been fitted using the form factor of a worm-like chain of finite thickness. The conformational parameters mean square radius of gyration, statistic chain element, mass per unit length and mean square radius of the cross-section have been determined experimentally and used for describing the conformation of the coils. By these molecular weights and ionic strengths, excluded volume is not necessary to explain the conformation changes depending on the salt content of the solutions; relatively short coil molecules can be described in their unperturbed dimensions even in a thermodynamically good solvent: a change in the stiffness of the chain according to Odijk's theory succeeds in describing the conformation of the polyions. Together with a slow decrease of the coil dimension by increasing salt content, a transition at ionic strength 0.1–0.5 M between two different conformations has been observed. The conformation at lower ionic strength is characterized by higher stiffness of the chain and lower mass per unit length than the form at higher salt concentration.     

Taylor expansion of polymer chain dispersion relations and spectral densities to calculate thermodynamic functions

It is shown how to calculate exactly the derivatives of the dispersion relation and the spectral density for arbitrary regular polymer chains in harmonic approximation. The theory is based on a generalization of the characteristic polynomial. In the vibrational part of the free energy and other thermodynamic functions, the integral over normal modes is done approximately by Taylor expanding the density of states.Dedicated to Professor Dr. F. H. Müller.     

A new correlation on predicting self- and mutual-diffusion coefficient of Lennard–Jones chain fluid

Based on the Chapman–Enskog theory of diffusion and molecular dynamics simulation data for Lennard–Jones chain (LJC) fluid, a new semi-empirical correlation for calculating the self-diffusion coefficient of LJC fluid is proposed. The new correlation introduces in two correction functions with six fitting parameter to modify the impact of intermolecular repulsive and attractive potential energy on molecular friction coefficient. The new correlation represents the experimental self-diffusion coefficients with an average absolute deviation (AAD) of 3.46% for 23 polyatomic compounds (1102 experimental data points) over wide ranges of temperature and pressure. On this basis, the van der Waals mixing rule is adopted to calculate the mutual-diffusion coefficient of binary LJC fluid. By comparison of calculated results with the experimental data of 12 binary LJC systems over wide range of temperature and composition, the average absolute deviation is 6.98% which verifies the accuracy and the effectiveness of the new correlation.     

A combined spectroscopic and theoretical study of a series of conformationally restricted hexapeptides carrying a rigid binaphthyl-nitroxide donor-acceptor pair

The structural features of a series of linear hexapeptides of general formula Boc‐B‐A_r‐T‐A_m‐OtBu, where A is L ‐Ala or Aib (α‐aminoisobutyric acid), B is (R)‐Bin, a binaphthyl‐based C^α,α‐disubstituted Gly residue, T is Toac, a nitroxide spin‐labeled C^α,α‐disubstituted Gly, and r+m=4, were investigated in methanol solution by fluorescence, transient absorption, IR and CD spectroscopic studies, and by molecular mechanics calculations. These peptides are denoted as B‐T/r‐m, to emphasize the different position of Toac with respect to that of the Bin fluorophore in the amino acid sequence. The rigidity of the B‐T donor–acceptor pair and of the Aib‐rich backbone allowed us to investigate the influence of the interchromophoric distance and orientation on the photophysics of the peptides examined. The excited state relaxation processes of binaphthyl were investigated by time‐resolved fluorescence and transient absorption experiments. Dynamic quenching of the excited singlet state of binaphthyl by Toac was successfully interpreted by the Förster energy transfer model, provided that the mutual orientation of the chromophores is taken into account. This implies that interconversion among conformational substates, which involves puckering of the Toac piperidine ring, is slow on the time scale of the transfer process, that is slower than 5 ns. By comparison of the experimental and theoretical data, the type of secondary structure (right‐handed 3₁₀ helix) from the B‐T/r‐m peptides in solution was determined; this would not have been achievable by using the CD and NMR data only, as the data are not diagnostic in this case. Static quenching was observed in all peptides examined but B‐T/1‐3, where the effect can be ascribed to a non‐fluorescent complex. Among the computed low‐energy conformers of these peptides, there is one structure exhibiting a NO ^. –naphthalene center‐to‐center distance <6 Å, which might be assigned to this complex. The overall results emphasize the versatility of fluorescence experiments in 3D‐structural studies in solution.     

Molecular structure regulation of functional polylactic acid based on chain expansion reaction and its improved hydrolysis resistance

In this work, the functional polylactic acid (PLA) was synthesized using epoxy chain extender (ADR) as a chain extender agent through melt blending method. The effects of ADR content on the molecular structure, thermal properties, and tensile properties of the functional PLA were investigated. Meanwhile, the hydrolytic behavior of the PLA/ADR materials at different hydrolysis temperatures was explored. It was found that ADR effectively regulated the molecular structure of PLA in the molten state and significantly increased the relative molecular weight, storage modulus, and complex viscosity of PLA. In addition, the Cole-Cole diagram results suggested the branched structure of PLA chain expansion systems. Based on mechanical property tests, it was noted that the addition of ADR made the molecular chain form a micro-crosslinked structure. Additionally, the mass loss rate of PLA/1.6ADR (the dosage of ADR was 1.6 wt%) was 14.75% after 14 weeks of hydrolysis under hydrolysis conditions at 58°C, while that of pure PLA was 25.89%. Moreover, the functional PLA/ADR materials exhibited significantly slower decrease rates in molecular weight, melting temperature, and tensile strength, and still maintained intact morphology after 14 weeks of hydrolysis compared to pure PLA. Therefore, the molecular structure of PLA is effectively regulated by ADR, which greatly enhances the hydrolysis resistance and further promotes the range of application of PLA.     

Analysis of the substituent distribution in the glucosyl units and along the polymer chain of hydroxypropylmethyl celluloses and statistical evaluation

Three hydroxypropylmethyl celluloses (HPMC 1, 2, 3; DS_Me=2.06, 1.99, 2.04; MS_HP=0.21, 0.19, 0.21) have been analyzed with respect to their methyl and hydroxypropyl pattern in the glucosyl units and along the polymer chain. The determination of the methyl pattern in the glycosyl unit was performed by GLC/MS after hydrolysis, reduction, and acetylation, while the distribution of hydroxypropyl residues in the monomers could be analyzed with higher sensitivity including a permethylation step prior to hydrolysis. To determine the distribution of the substituents along the polymer chain, a method developed for hydroxyethylmethyl cellulose (HEMC) was applied. This method comprises random partial acid hydrolysis after perdeuteromethylation and reductive amination with propylamine, followed by N- and O-alkylation, yielding completely alkylated and permanently charged oligosaccharide derivatives. These compounds could be quantitatively analyzed by means of matrix-assisted laser desorption ionization time-of-flight mass spectrometry (MALDI-TOF-MS), since all discrimination effects related to the hydroxyalkyl groups are leveled off by the sample preparation procedure in combination with the choice of a MALDI-TOF instrument. Methyl data deviate to some extent from the random distribution calculated from the monomer composition, but in contrast to methyl cellulose (MC) or HEMC, it is not heterogeneous, but more regular. The distribution of HP groups is random within experimental error as has been found for HEMC as well.     

A quantum-mechanical study of the chain-length dependent stability of the extended and 310-helix conformations in dehydroalanine oligopeptides

Summary A quantum-chemical study of the chain-length dependent stability of the extended, 2₇-ribbon and 3₁₀-helix conformations in dehydroalanine (Ala) oligopeptides has been performed by using both semiempirical AM1 and ab initio 4–31G methodologies. The validity of both methods in the study of the conformational properties of Ala oligopeptides was tested first on the dipeptide. The results of this test showed that 4–31G and AM1 calculations are in good agreement with 6–31G^* calculations and experimental data. In order to monitor the conformational conversions, Ala oligopeptides comprising two to six residues were constructed. Molecular geometries were fully optimized using AM1, and the final conformations were verified to be minima by analysis of the corresponding second-derivative matrices. Conformational studies revealed that the 3₁₀-helix is stabilized with respect to the 2₇-ribbon when the number of residues is three or four, at the AM1 and ab initio 4–31G level respectively, while the extended form is the most stable in all the calculations performed. On the other hand, if a linear behaviour is assumed for longer chains, our calculations show a trend that would predict a conversion from extended form to 3₁₀-helix in oligopeptides with around six (ab initio 4–31G) or eight (AM1) Ala residues. In order to explain these conformational changes, the cooperative effects for the different conformers were investigated. Large cooperative energy effects were found for the 3₁₀-helix conformation.     

Lower critical solution temperature (LCST) and theta temperature of aqueous solutions of nonionic surface active agents of various polyoxyethylene chain lengths

Cloud points of aqueous solutions of homogeneous poly(oxyethylene)dodecyl ether derivatives (C₁₂(OE)_n: n=2–8) and the apparent theta temperatureT ^ap were determined from the abrupt changes in optical transmittance and the temperature dependence of the second virial coefficient obtained by light scattering measurements. It was found that the lower critical solution temperature (LCST) shifts to a lower temperature and lower concentration as the number of oxyethylene units in a molecule decreases. Because of this behavior of LCST, the modified Flory-Schultz plot of phase separation was applied to the present nonionic surfactant-water system, and its theta temperature obtained. The dependence ofT ^ap on the number of oxyethylene units suggests that the polyoxyethylene chain has different effects on the solubility of C₁₂(OE)_n in water forn less than or equal to 3 from those forn greater than or equal to 4.     

Inclusion of the effects of polydispersity and volatility on the random chain scission statistical analysis for polymer degradation

The statistical product distribution for a linear polydisperse polymer of finite molecular weight was included into the statistical analysis for a system undergoing random chain scission showing the effect of volatilization of species other than monomer. Two sets of equations were derived. One set is for the nonvolatile fraction; the other is for the volatile fraction. Within each set there are three equations, one for the number of polymer molecules, the second for the molar (or number) fraction, and the third for the weight fraction of polymer molecules containing a specific number of repeat units. As degradation proceeds the polydispersity index should converge to a value of 1 rather than 2, which has been reported previously. The expected effects of polydispersity, number‐average degree of polymerization, and volatility were treated individually, and we determined that the molecular weight of a polymer has no theoretical influence on the product distribution. As for the effect of volatility, we determined that only the volatile product distribution would change. © 2000 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 38: 3690–3696, 2000     

Single crystal morphology and structural data of a series of polyesters derived from 1,8-octanediol

The morphology of solution grown single crystals of a series of polyesters derived from 1,8-octanediol and either an even or an odd dicarboxylic acid has been investigated. Different crystallization conditions (solvent and temperature) were tested for these polyesters whose dicarboxylate unit varied from pimelate to sebacate. Crystals showed a lozenge morphology with a degree of truncation which for a given solvent changed with the crystallization temperature. Curvature of growth faces, striations on the lamellar surface and a bilayered morphology were features that were observed in some cases. Polyethylene decoration highlighted a crystal sectorization and suggested a molecular folding parallel to the crystal growth faces.The studied polyesters always showed a single crystalline structure, according to electron and X-ray diffraction data. A practically all trans molecular conformation could always be deduced. Unit cell geometry changed from orthorhombic to monoclinic and the molecular content was variable in the studied series (two or four molecular segments).Lamellae gave rise to well-defined electron diffraction patterns that allowed the setting angle of molecular segments to be determined. A good agreement between simulated and experimental hk0 diffraction patterns was always found. Packing along the chain axis direction was completely defined for the sebacate derivative.     

A Correlation of the Drag Force Coefficient on a Sphere with Interface Slip at Low and Intermediate Reynolds Numbers

The hydrodynamics of a sphere with interface slip has been numerically investigated for flows of Reynolds number ranging 0 < Re ≤ 75. A simple correlation of the drag force coefficient in the present of interface slip has been derived based on our numerical simulations. The correlation takes the slip coefficient and Reynolds number as two input parameters. By comparing results found in the literature, we believe that the present correlation is more accurate; it provides a source for future experiment study and for numerical simulations of large multi-particle system where the interface slip is important.