Dilute solution behavior of polyelectrolytes. Intrinsic viscosity and light scattering studies

The conformational character of a random copolymer of ethyl acrylate and acrylic acid (mole ratio 3:1) has been examined by intrinsic viscosity and light scattering in organic and in aqueous media. The unperturbed dimensions of this copolymer in its un-ionized state in an organic theta solvent are 1.3 to 1.4 times those obtained for the fully ionized polymer in an aqueous theta solvent. The data also suggest that a change in conformation from a swollen random coil to a compact random coil occurs in aqueous media as a function of ionic strength. These results are interpreted in terms of the hydrophobic interaction of the ester groups on the chain. An application of the wormlike chain model shows that viscosity data can be used to predict the light scattering results well with in experimental error.     

What is the unperturbed state in polymer solutions?

We report theoretical results about amphiphilic random copolymers in a quasi‐ideal conformation with an overall size very close to that of the analogue homopolymers. We found that a few states may coexist with about the same free energy and a similar radius of gyration, but with different intramolecular conformations. We also argue that, in most cases, amphiphilic copolymers may never achieve the unperturbed Θ state, defined thermodynamically by a vanishing second virial coefficient. Thus, we suggest that such copolymers usually show neither an unperturbed conformation nor an unperturbed state from the thermodynamic viewpoint. We also briefly discuss star homopolymers, which show a depression of the Θ temperature with respect to linear chains and a significant, though finite, Θ swelling, as well as linear chains in the Θ state and in the melt. The main general conclusion is that interactions between chain segments do not cancel each other and are non‐negligible. Accordingly, we suggest that the word "unperturbed" be used only with reference to solution thermodynamics and not for the chain size or conformation.     

Excluded‐volume effects on the chain dimensions and transport coefficients of sodium poly(styrene sulfonate) in aqueous sodium chloride

Fifteen samples of sodium poly(styrene sulfonate) with weight‐average molecular weights of 3 × 10⁴ to 8 × 10⁵ have been studied by static and dynamic light scattering and viscometry in 0.05 and 0.5 M aqueous NaCl at 25 °C. The measured radii of gyration, translational diffusion coefficients, and intrinsic viscosities at the lower salt concentration exhibit molecular weight dependencies stronger than those predictable for uncharged flexible chains in the good solvent limit. These data and those at the higher NaCl concentration are analyzed, along with previous intrinsic viscosity data covering a broad molecular weight range, in the framework of the quasi‐two‐parameter (QTP) theory with the wormlike chain as the model. It is shown that the relevant theories for the expansion factors in the QTP scheme combined with these theories for the unperturbed wormlike chain are capable of describing the experimental data with a degree of accuracy similar to that known for nonionic flexible polymers. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 2728–2735, 2002     

Effects of chain flexibility on polymer conformation in dilute solution studied by lattice monte carlo simulation

Effects of chain flexibility on the conformation of homopolymers in good solvents have been investigated by Monte Carlo simulation. Bond angle constraint coupled with persistence length of polymer chains has been introduced in the modified eight-site bond fluctuation simulation model. The study about the effects of chain flexibility on polymer sizes reveals that the orientation of polymer chains under confinement is driven by the loss of conformation entropy.The conformation of polymer chains undergoing a gradual change from spherical iso-diametric ellipsoid to rodlike iso-diametric ellipsoid with the decrease of polymer chain flexibility in a wide region has been clearly illustrated from several aspects. Furthermore, a comparison of the freely jointed chain (FJC) model and the wormlike chain (WLC) model has also been made to describe the polymer sizes in terms of chain flexibility and quasi-quantitative boundary toward the suitability of the models.     

Treatment of high molecular weight wormlike polymers as random coiled polymers

The possibility of treating a wormlike polymer as a random coiled polymer is examined. Taking from the literature intrinsic viscosity data concerning several wormlike polymers, we use two graphical methods which have been proposed for flexible polymers. These methods are only applicable in the region of molecular weights where the wormlike polymer presents a relatively great number of statistical segments. From the values of unperturbed dimensions obtained by the graphical methods, we obtain the statistical segment of wormlike polymers at Θ conditions.     

Analysis of the conformation of wormlike chains by combination of small-angle x-ray and small-angle neutron scattering

An analysis of the conformation of a wormlike polymer by small-angle scattering is presented. By a combined investigation of small-angle X-ray and of small-angle neutron scattering the effect of the finite size of the repeating units can be eliminated. The procedure suggested herein therefore allows to obtain the scattering function for a respective infinitely thin chain. The latter quantity is compared to current models of the scattering function of wormlike chains.     

Dilute solution studies on a polycarbonate in good and poor solvents

Light-scattering, viscometric and osmometric studies have been carried out on dilute solutions of polycarbonate fractions both in a good solvent and in theta solvents. The data span the molecular weight interval 5 < 10^?3M < 760. It has been concluded that: (1) the overall behavior in dilute solution is consistent with a flexible chain conformation; (2) the ratio of the unperturbed mean-square radius to the molecular weight, or to the number of chain elements, is larger than commonly observed for vinyl polymers; (3) the ratio of the unperturbed radius to the radius calculated for a chain with free rotation about valence bonds has the unusually small value 1.3; and (4) the hydrodynamic behavior of the chain may reflect partical draining affects.     

Physical properties of xanthan,galactomannan and their mixtures in aqueous solutions

Some new information on the conformation of xanthan in aqueous solutions is given. A single helical chain conformation characterizes xanthan in the native state. When heated over the critical temperature for conformational change ( helixŕ coil), the xanthan is denatured and renatured when it is cooled down in a localy double helical structure. A galactomannan was also characterized and its persistence length was obtained (Lp ≈︁ 90A°). Then mixtures of the galactomannan and xanthan were investigated to propose a mechanism for the specific gelation. From the results of microcalorimetry and circular dichroism, it is concluded that a complex is formed between one disordered xanthan chain and one galactomannan chain and that an ordered conformation is stabilized at temperatures lower than 25°C when the galactomannan has a M/G ratio of ≈︁ 3. This temperature corresponds to the sol-gel transition. This is the first time that a structure of the crosslink points is demonstrated.     

Numerical Simulation of the Distribution Function and Free Energy of a Single Wormlike Polymer Confined between Hard Walls

We focus on the distribution and free energy of a wormlike polymer confined between two parallel hard walls.The variation in the distribution and free energy of the wormlike chain as the spacing between the walls decreases(or as the total contour length of the wormlike chain increases or as the persistence length of the chain increases)is simulated.The main reason for these changes is a degradation of the long wormlike chain into a Gaussian long chain under weak confinement.     

Numerical estimation of unperturbed dimensions of regioirregular poly(3-ethylthiophene)s

The unperturbed chain dimensions of poly(3-ethylthiophene)s have been calculated using the full-relaxation optimization of conformational energies and the chain statistical mechanics with a rotational isomeric state model of two states. The computation indicates that the conjugated polymer with side groups is more flexible than without, and that the orientation of the ethyl group and the regioirregular sequences perturb the chain conformation to a certain extent. Specially, the calculated chain conformations under θ-conditions are more rigid than those observed in good solvent. This supports experiments showing that the chain dimensions of conjugated polymers are very sensitive to variations of intermolecular interactions.     

alpha and piDL helical states of alternating poly(gamma-benzyl D-L-glutamate) in solution.

As in solid state, strictly alternating poly(gamma-benzyl D-L-glutamate) in solution can adopt two different helical conformations. Besides the alpha helix, a second helical conformation is found at higher temperatures in dioxane and chloroform, the properties of which correspond to that of the piDL4 helix. As the molecules have a finite length a screw sense is favored for both helical forms thus giving rise to optical activity allowing the study of the transconformation by optical rotatory dispersion and circular dichroism besides infrared and dielectric measurements. Thus, as the temperature is raised the equilibria right-left handed alpha helices and alpha-piDL helical forms can be followed. The favored screw senses are determined by the number of interacting side chains for the alpha helix and by the number of hydrogen bonds which are formed in the piDL helical conformation. The side chain-side chain interactions in the alpha helix are experimentally shown to be attractive.     

m-Phenylene ethynylene sequences joined by imine linkages: dynamic covalent oligomers

Imine metathesis between m-phenylene ethynylene oligomers of various lengths was performed in acetonitrile, a solvent in which oligomers containing eight or more repeat units adopt a compact helical conformation. The equilibrium constants and corresponding free energy change for the imine metathesis reactions were estimated. The results showed that the magnitude of equilibrium shifting measured by the free energy change for the formation of imine-containing oligomers increases linearly below a critical product chain length and grows asymptotically above it. The linear region is ascribed to the constant increase in contact area between monomer units of adjacent helical turns as the product chain grows to the 12-mer. Once the ligation product is 12 units in length, full contact is made between adjacent helical turns. On the other hand, for imine metathesis between oligomers leading to products having more than 12 units, the driving force is the difference between the folding energy of products and that of reactants. The additional stabilizing energy is roughly constant, regardless of the chain length, since the contact area between adjacent helical turns is unchanged. Consistent with the notion that the imine bond only minimally destabilizes the helical conformation, the position of the imine bond in the ligation product has been observed to have no significant effect on the folding stability. The magnitudes of equilibrium shifting are similar for ligation products of the same length but having the imine at various positions along the sequence. This suggests that the imine bond is compatible with the m-phenylene ethynylene backbone, regardless of the position in the sequence. Imine metathesis of m-phenylene ethynylene oligomers could allow a quick access to an unbiased, dynamic library of oligomer sequences joined by imine linkages.     

AFM imaging of adsorbed Nafion polymer on mica and graphite at molecular level

Perfluorosulfonic acid ionomer (PFSA, specifically Nafion at EW = 975 g/mol) was visualized at the single molecule level using atomic force microscopy (AFM) in liquid. The diluted commercial Nafion dispersion shows an apparent M(w) = 1430 kg/mol and M(w)/M(n) = 3.81, which is assigned to chain aggregation. PFSA aggregates, imaged on mica and HOPG during adsorption from EtOH-H(2)O solvent at pH(e) 3.0 (below isoelectric point), showed a stable, segmented rod-like conformation. This structure is consistent with earlier NMR, SAXS/SANS, and TEM results that support a stiff helical Nafion conformation with long persistence length, a sharp solvent-polymer interface, and an extension of the sulfonated side chain into solution. Adsorption of Nafion structures on HOPG was observed at even higher pH(e) from EtOH due to screening of the repulsive electrostatic interaction in lower dielectric constant solvent, while the chain adopted an expanded coil conformation. These measurements provided direct evidence of the chain aggregation in EtOH-H(2)O solution and revealed their equilibrium conformations for adsorption on two model surfaces, highly ordered pyrolitic graphite (HOPG) and mica. The commercial Nafion dispersion was autoclaved at 0.10% w/w in nPrOH/H(2)O = 4:1 v/v solvent at 230 °C for 6 h to give a single-chain dispersion with M(w) = 310 kg/mol and M(w)/M(n) = 1.60. The autoclaved chains adopt an electrostatically stabilized compact globule conformation as observed by AFM imaging of the single PFSA molecules after rapid deposition on mica and HOPG at a low surface coverage.     

A coarse-grained model for the formation of alpha helix with a noninteger period on simple cubic lattices

Periodicity is an important parameter in the characterization of a helix in proteins. In this work, a coarse-grained model for a homopolypeptide in simple cubic lattices has been extended to build an alpha helix with a noninteger period. The lattice model is based on the bond fluctuation algorithm in which bond lengths and orientations are altered in a quasicontinuous way, and the simulation is performed via dynamic Monte Carlo simulation. Hydrogen bonds are assumed to be formed between a virtual-carbonyl group in a residue and a downstream virtual-imino group in another residue. Consequently, the period of the formed alpha helix is a noninteger. An improved spatial correlation function has been suggested to quantitatively describe the periodicity of the helical conformation, by which helical period and helical persistent length can be calculated by statistics. The resultant periods are very close to 3.6 residues; the persistent length based upon the improved definition can be larger or smaller than the chain length and reflect the inherent regularity of a chain including one or multiple helical blocks. The simulation outputs agree with the calculation of the Zimm-Bragg theory based upon the associated nucleation parameter and propagation parameter as well.     

DIMENSIONS OF ATACTIC POLY（α-METHYLSTYRENE） CHAINS WITH SIDE GROUPS

An improved configurational-confomational statistical method is developed and the mean-square radius of gyration for atactic poly(α-methylstyrene)(PαMS)chains is studied,in which the effect of large side groups is considered. The deduced formulas,based on the rotational isomer state theory,are used to investigate the configuration-dependent properties of the atactic polymer chain,and the statistical correlation of the unperturbed polymer chain dimension and structure parameters are calculated.For the fraction of meso dyads w_m=0.4,the dependence of the radius of gyration R_g and the intrinsic viscosity[η]on the molecule mass M are R_g=2.63×10~(-2) M~(0.50) nm and[η]=7.36×10~(-2) M~(0.497),respectively, which are in agreement with the previous experimental data for the PαMS samples.A small hump is detected in the curve of the characteristic ratio of the unperturbed mean-square radius of gyration versus the chain length for short PαMS chains.The R_g increases linearly with the temperature T,and the effects of the chain length and the tacticity on the temperature coefficient are remarkable.These are quite different from the results for PαMS chains not considering side groups or for the monosubstituted polystyrene chain.     

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.     

Synthesis,characterization, and application of helical polymers

This review mainly describes the asymmetric synthesis of optically active polymers with helical conformation. Bulky methacrylates such as triphenylmethyl methacrylate and 1-phenyldibenzosuberyl methacrylate give one-handed helical and optically active polymers with almost perfectly isotactic main chain conformation by polymerization with chiral anionic initiators. The radical polymerization and copolymerization of these monomers under chiral conditions also afford optically active polymers with prevailing one-handed helicity. N, N-Disubstituted acrylamides also give optically active, helical polymers in the asymmetric anionic polymerization. Optically active polyisocyanates with a prevailing one-handed helical structure have been prepared in the copolymerization of an achiral isocyanate with a small amount of an optically active isocyanate and also in the polymerization of alkyl and aromatic isocyanates with optically active lithium alkoxide or amide compounds. The existence of a stable helical structure for polychloral has been successfully proved with the helical oligomers of chloral. One-handed helical polyisocyanides have been prepared by helix-sense-selective polymerization of bulky isocyanides and also by the cyclopolymerization of a 1, 2-diisocyanobenzene derivative with the Pd complex of a one-handed helical oligomer.     

基于2,5-二(4′-甲酰基苯基)苯乙烯的螺旋链光学活性聚合物的合成与表征

通过2,5-二溴苯乙烯与对甲酰基苯硼酸的Suzuki偶联反应得到2,5-二(4′-甲酰基苯基)苯乙烯.在催化剂量的冰乙酸存在下,与光学纯的(S)-(-)-α-甲基苄胺或(R)-(+)-α-甲基苄胺发生缩和反应,得到了一对手性非外消旋单体,(+)-2,5-二{4-′[(N-(S)-α-甲基苄亚胺基)次甲基]苯基}苯乙烯和(-)-2,5-二{4′-[(N-(R)-α-甲基苄亚胺基)次甲基]苯基}苯乙烯.以偶氮二异丁腈(AIBN)或过氧化苯甲酰(BPO)为引发剂,经自由基溶液聚合得到光学活性聚合物.比旋光度、紫外-可见吸收光谱以及圆二色光谱研究表明,聚合物主链可能形成了某一方向占优的稳定螺旋构象,且该螺旋构象的旋光方向与单体的旋光方向相反.聚合条件对聚合物的光学活性有很大影响,在极性较大的芳香族溶剂和较高温度下得到的聚合物具有和单体相差更大的比旋光度.侧基的手性基团脱除后,聚合物仍具有一定的旋光性,说明聚合过程中形成的螺旋手性具有一定的记忆效应.     

Effects of hydrophobic chain length on the characteristics of the micelles of octaoxyethylene tetradecyl C(14)E(8), hexadecyl C(16)E(8), and octadecyl C(18)E(8) ethers

Size, shape, and flexibility of micelles of octaoxyethylene tetradecyl C(14)E(8), hexadecyl C(16)E(8), and octadecyl C(18)E(8) ethers in dilute aqueous solutions were determined at finite surfactant concentrations c by static light scattering (SLS) and dynamic light scattering experiments at several temperatures T below the critical points. The SLS results were successfully analyzed with the aid of the thermodynamic theory formulated with wormlike spherocylinder model for SLS of micelle solutions. The analysis yielded the molar mass M(w) of the micelles as a function of c and the cross-sectional diameter d. The hydrodynamic radius R(H) and the radius of gyration S(2)(1/2) of the micelles as functions of M(w) were found to be also well-described by the corresponding theories for the wormlike spherocylinder or wormlike chain models. The results of the stiffness parameter lambda(-1) have revealed that the micelles are far from rigid rods but rather stiff compared with typical flexible polymers and they grow in size with increasing T to greater length for longer hydrophobic chains, i.e., alkyl groups of the surfactants. As the alkyl group becomes longer, the d value increased, while the spacings s between adjacent hexaoxyethylene chains on the micellar surface were found to remain substantially constant.     

Molecular recognition directed self-assembly of tubular supramolecular architectures from building blocks containing monodendrons as exo-receptors and crown- or pseudo-crown-ethers as endo-receptors

The principles of self-assembly of tapered exo-receptors constructed from monodendrons containing crown-ether, oligooxyethylenic groups and polymer backbones as endo-receptors into tubular supramolecular architectures are described with selected examples. In the case of polymers with flexible backbones it is suggested that a helical chain conformation is induced during the assembly of its own tapered side groups. This mechanism is supported by the enhanced self-assembling ability of tapered side groups attached to a backbone with rigid helical conformation.