Excluded volume effect for solutions of cellulose derivatives evaluated by wormlike chain model

Third-power law type equations of the linear expansion factor α_s and of the excluded volume effect $\text{z}$h($\text{z}$), expressed by a conventional notation, are derived for a wormlike chain as an extension of the Yamakawa and Stockmayer theory [J. chem. Phys.57, 2843(1972)], in which the corresponding fifth-power law type equations were obtained. The literature data on 11 systems of solutions of cellulose and its derivatives are analysed, by using a penetration function method based on the derived equations, to evaluate an excluded volume effect for a wormlike chain model. The results are compared with those deduced for a pearl necklace model.     

A new approach to the determination of the statistical segment length of wormlike polymers

The Stockmayer-Fixman-Burchard (SFB) and the Dondos-Benoit (DB) equations have been applied to determine the unperturbed dimensions parameterK of wormlike polymers. An empirical relation between the Flory's constant and the Mark-Houwink-Sakurada (MHS) exponenta has been proposed. The values found by this equation are lower than the value 2.5×10²³ used in the case of flexible polymers and this deviation is attributed to the influence of the draining effect. From theK value and the so calculated value of , we calculate the Kuhn statistical segment length of wormlike polymers. The obtained — for a great number of wormlike polymers — statistical segment lengths are almost the same as these calculated by the Yamakawa-Fujii and the Bohdanecky methods. The molecular mass regions in which the SFB, the DB, and the MHS equations are valid are explored. A criterion for the distinction between flexible and wormlike polymers is proposed based on the way of approach to the power law.     

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     

Distribution functions and dynamical properties of stiff macromolecules

An analytically tractable model for chain molecules with bending stiffness is presented and the dynamical properties of such chains are investigated. The partition function is derived via the maximum entropy principle taking into account the chain connectivity as well as the bending restrictions in form of constraints. We demonstrate that second moments agree exactly with those known from the Kratky-Porod wormlike chain. Moreover, various distribution functions are calculated. In particular, the static structure factor is shown to be proportional to 1/q at large scattering vectors q. The equations of motion for a chain in a melt as well as in dilute solution are presented. In the latter case the hydrodynamic interaction is taken into account via the Rotne-Prager tensor. The dynamical equations are solved by a normal mode analysis. In the limit of a flexible chain the model reproduces the well-known Rouse and Zimm dynamics, respectively, on large length scales, whereas in the rod limit the eigenfunctions correspond to bending motion only. In addition, the coherent and incoherent dynamic structure factor is discussed. For melts we show that at large scattering vectors the incoherent dynamic structure factor is a universal function of only the combination q^8/3tp^1/3, where 1/(2p) is the persistence length of the macromolecules. The comparison of the theoretical results with quasielastic neutron and light scattering experiments of various polymers in solution and melt exhibits good agreement. Our investigations show that local stiffness strongly influences the dynamics of macromolecules on small length scales even for long and flexible chains.     

Theoretical study on the polymerization mechanism of substituted maleimides by using a chiral catalyst with Zn

It is possible to synthesize poly(N-substituted maleimide) by using a chiral complex consisting of a zinc and N-diphenylmethyl-1-benzyl-2-pyrrolidinoethanamine (DPhBP). The optical specific rotations [α]₄₃₅²⁵ in obtained polymers depend on the chirality of ligands in the catalysts. In the present study, density functional theory (DFT) calculations were adopted to investigate the polymerization mechanism in detail. The bulky diphenylmethyl group in the chiral ligand is effective to enhance the formation of the product in the initiation reaction. The geometry related to the pyrrolidine ring of the chiral ligand in the Zn catalyst is responsible for determining the configuration of polymers. It was also confirmed that the bulky substituent on the N atom of the N-substituted maleimide is another factor for obtaining polymers with high [α]₄₃₅²⁵.     

Scaling laws in simple and complex proteins: size scaling effects associated with domain number and folding class

The native states of the most compact globular proteins have been described as being in the so-called “collapsed-polymer regime,” characterized by the scaling law R _g ~ n ^ν, where R _g is radius of gyration, n is the number of residues, and ν ≈ 1/3. However, the diversity of folds and the plasticity of native states suggest that this law may not be universal. In this work, we study the scaling regimes of: (i) one to four-domain protein chains, and (ii) their constituent domains, in terms of the four major folding classes. In the case of complete chains, we show that size scaling is influenced by the number of domains. For the set of domains belonging to the all-α, all-β, α/β, and α?+?β folding classes, we find that size-scaling exponents vary between 0.3?≤?ν?≤?0.4. Interestingly, even domains in the same folding class show scaling regimes that are sensitive to domain provenance, i.e., the number of domains present in the original intact chain. We demonstrate that the level of compactness, as measured by monomer density, decreases when domains originate from increasingly complex proteins.     

Application of thermal blob theory to intrinsic viscosity measurements of poly(4-chlorostyrene) above the theta point

Macromolecular chains obey purely Gaussian statistics close to the theta temperature. An asymptotic regime is also reached far above the theta point. Thermal blob theory permits an approximate calculation of thermal expansion factor. In this theory, an adjustable parameter is used as a prefactor (A*N₁) in order to calculate the reduced blob parameter (N/N_c). In this work, we proposed a different approach to evaluate (A*N₁) by plotting τM_ω^1/2/α_η⁵ against τM_ω^1/2. Chain expansion data of poly(4-chlorostyrene) in various solvents is used to evaluate viscosity expansion factors at various temperatures. It seems that predictions of thermal blob theory provide a better fit to experimental points rather than those evaluations based on Flory-type approaches. © 1996 John Wiley & Sons, Inc.     

Transport properties of polyimides containing phenylquinoxaline moieties

The gas permeabilities of a number of new structurally related polyimides containing phenylquinoxaline moieties were studied for the first time. The test polymers had different dianhydride units, whereas their diamine components differed in the presence of flexible ether bonds-O-in the main chain, a structure that is reflected in the effective packing of chains and, as a result, in transport parameters. The permeability, diffusion, and solubility coefficients for the gases H₂, He, O₂, N₂, CO, CO₂, and CH₄, as well as the ideal separation factors for gas pairs, were determined. The transport characteristics of polymers were compared within the given polymer series and with published data for other polymer series.     

Regularly alternating poly(amideimide)s containing pendent pentadecyl chains: Synthesis and characterization

Two new aromatic diamines containing preformed amide linkages, viz., N,N′-(4-pentadecyl-1,3-phenylene)bis(4-aminobenzamide) I and N,N′-(4-pentadecyl-1,3-phenylene)bis(3-aminobenzamide) II, were synthesized by reaction of 4-pentadecylbenzene-1,3-diamine with 4-nitrobenzoylchloride and 3-nitrobenzoylchloride, followed by reduction of the respective dinitro derivatives. A series of new poly(amideimide)s was synthesized by polycondensation of I and II with four commercially available aromatic dianhydrides, viz., pyromellitic dianhydride (PMDA), 4,4′-biphenyltetracarboxylic dianhydride (BPDA), 4,4′-oxydiphthalic anhydride (ODPA), and 4,4′-(hexafluoroisopropylidene)diphthalic anhydride (6-FDA) in N,N-dimethylacetamide (DMAc) employing conventional two step method via poly(amic acid) intermediate followed by thermal imidization. Reference poly(amideimide)s were synthesized by polycondensation of N,N′-(1,3-phenylene)bis(4-aminobenzamide) and N,N′-(1,3-phenylene)bis(3-aminobenzamide) with the same aromatic dianhydrides. Inherent viscosities of poly(amideimide)s containing pendent pentadecyl chains were in the range 0.37-1.23 dL/g in N,N-dimethylacetamide at 30 ± 0.1 °C indicating the formation of medium to high molecular weight polymers. The poly(amideimide)s containing pendent pentadecyl chains were found to be soluble in N,N-dimethylacetamide, N,N-dimethylformamide, 1-methyl-2-pyrrolidinone and pyridine and could be cast into transparent, flexible and tough films from their N,N-dimethylacetamide solution. Wide angle X-ray diffraction patterns exhibited broad halo indicating that the polymers were essentially amorphous in nature. X-ray diffractograms also displayed sharp reflection in the small angle region (2θ ≈ 3°) for poly(amideimide)s containing pentadecyl chains indicating the formation of layered structure arising from packing of flexible pentadecyl chains. The glass transition temperatures observed for reference poly(amideimide)s were in the range 331-275 °C and those for poly(amideimide)s containing pendent pentadecyl chains were in the range 185-286 °C indicating a large drop in T_g owing to the “internal plasticization” effect of pentadecyl chains. The temperature at 10% weight loss (T₁₀), determined by TGA in nitrogen atmosphere, were in the range 460-480 °C indicating their good thermal stability.     

Molecular geometry and chain entanglement: parameters for the tube model

The tube diameter in the reptation model is the distance between a given chain segment and its nearest segment in adjacent chains. This dimention is thus related to the cross-sectional area of polymer chains and the nearest approach among chains, without effects of thermal fluctuation and steric repulsion. Prior calculated tube diameters are much larger, about 5 times, than the actual chain cross-sectional areas. This is ascribed to the local freedom required for mutual rearrangement among neighboring chain segments. This tube diameter concept seems to us to infer a relationship to the corresponding entanglement spacing. Indeed, we report here that the critical molecular weight, M_c, for the onset of entanglements is found to be M_c = 28 A/(〈R²〉₀/M), where A is the chain cross-sectional area and 〈R²〉₀ the mean-square end-to-end distance of a freely jointed chain of molecular weight M. The new, computed relationship between the critical number of backbone atoms for entanglement and the chain cross-sectional area of polymers, N_c = A^0,44, is concordant with the cross-sectional area of polymer chains being the parameter controlling the critical entanglement number of backbone atoms of flexible polymers.     

Chain Conformation and Local Rigidity of Isomerized Polyimides in Dimethyl Formamide by Size Exclusion Chromatography Coupled with Multi-Detectors

Chain conformation and local rigidity of two isomerized polyimides (PIs), poly(6FDA/3,3′-DMB) and poly(6FDA/2,2′-DMB) in dimethyl formamide (DMF) with either 0.1 M LiBr or 3.1 mM tetrabutylammonium bromide at 35 °C, are investigated. Size exclusion chromatography (SEC) coupled with multi-angle laser light scattering detector, viscometer, and differential refractive index detector was used. The scaling exponents α and ν related to conformation are estimated from the above results. The values of α and ν for poly(6FDA/3,3′-DMB) are 0.68 ± 0.01 and 0.54–0.55 ± 0.01, respectively. The values of α and ν for poly(6FDA/2,2′-DMB) are 0.65 ± 0.02 and 0.55 ± 0.01, respectively, which indicate that both PIs in DMF have a random coil conformation. In particular, poly(6FDA/3,3′-DMB) exhibits more extended conformation than that of poly(6FDA/2,2′-DMB). Parameters related to chain flexibility of polymers, including persistence length l _p, shift factor M _L (relative molecular weight per unit contour length), and backbone diameter d are evaluated from the relationship between intrinsic viscosity and molecular weight based on the wormlike continuous cylinder model. The three parameters (l _p, M _L, and d) indicate that the two samples are flexible chains with local rigidity, and poly(6FDA/3,3′-DMB) is slightly stiffer than poly(6FDA/2,2′-DMB). In addition, influence of salt types on the parameters is also discussed.

     

Synthesis, crystal structures and thermal properties of new copper(I)halide 2-ethylpyrazine coordination polymers: the influence of solid-state kinetics on product formation

Three new copper(I) coordination polymers were prepared by the reaction of copper(I) chloride with 2-ethylpyrazine in water at room temperature or under solvothermal conditions. In poly[CuCl(μ₂-2-ethylpyrazine-N,N′)] (I), “zig-zag”-like CuCl chains are present, which are connected by the 2-ethylpyrazine ligand to a three-dimensional network. In comparison in catena[Cu₃Cl₃(μ₂-2-ethylpyrazine-N,N′)₂] (II) six-membered Cu₃Cl₃ rings occur, which are connected to chains by the organic ligands. In poly[Cu₂Cl₂(μ₂-2-ethylpyrazine-N,N′)] (III), CuCl double chains are found, which are linked by the ligands to form sheets. The thermal behaviour of the different compounds was investigated using simultaneous thermogravimetry, differential thermoanalysis and mass spectroscopy as well as temperature-dependent X-ray powder diffraction. Two mass steps are found upon heating compound I in a thermobalance with 1°C/min, where the first corresponds to the transformation into compound III, and the second to the loss of the remaining ligands under formation of CuCl. If the heating rate is increased to 16°C/min, compound II is formed as an intermediate in a consecutive reaction. Therefore, the product formation depends on the actual heating rate, which shows that the solid-state kinetics plays an important role in such thermal reactions.     

Hydrodynamic properties and conformation of molecules of para- and meta-isomers of polyoxyphenylbenzoxazoleterephthalamide

Translational diffusion and intrinsic viscosity in 96% H₂SO₄ have been investigated for 20 samples of the para-isomer of polyoxyphenylbenzoxazoleterephthalamide (PpOPhBT) and 17 samples of its meta-isomer (PmOPhBT). The Mark-Kuhn equations have been obtained. The equilibrium rigidity of macromolecules in solution, calculated by using the wormlike chain theory, was characterized for PpOPhBT by the length of the Kuhn segment $\text{A = 320}\text{A}\text{?}$, the number of monomer units in a segment s = 17 and the coefficient of hindrance to intramolecular rotation in the chain σ = 1.5. For PmOPhBT the corresponding values are: $\text{A = 96}\text{A}\text{?}$, s = 5.9 and σ = 1.6. Analysis of flexibility mechanisms was carried out for PpOPhBT and PmOPhBT chains in solution.     

Thermal degradation kinetics of thermoresponsive poly(N-isopropylacrylamide-co-N,N-dimethylacrylamide) copolymers prepared via RAFT polymerization

Reversible addition-fragmentation chain transfer polymerization at 70 °C in N,N-dimethylformamide was used to prepare poly(N-isopropylacrylamide-co-N,N-dimethylacrylamide) copolymers in various compositions to afford well-defined polymers with pre-determined molecular weight, narrow molecular weight distribution, and precise chain end structure. The copolymer compositions were determined by ¹H NMR spectroscopy. The reactivity ratios of N-isopropylacrylamide (NIPAM) and N,N-dimethylacrylamide (DMA) were calculated as r _NIPAM = 0.838 and r _DMA = 1.105, respectively, by the extended Kelen–Tüdös method at high conversions. The lower critical solution temperature of PNIPAM can be altered by changing the DMA content in the copolymer chain. Differential scanning calorimetry and thermogravimetric analysis at different heating rates were carried out on these copolymers to understand the nature of thermal degradation and to determine its kinetics. Different kinetic models were applied to estimate various parameters like the activation energy, the order, and the frequency factor. These studies are important to understand the solid state polymer degradation of N-alkyl substituted polymers, which show great potential in the preparation of miscible polymer blends due to their ability to interact through hydrogen bonding.     

Esterification reactions on syndiotactic poly(2-methallyl alcohol). V. Homopolymers of 2-methallyl-(L)-dipeptidates and dipeptides cleaved from them

Syndiotactic poly(2-methallyl alcohol) (sPMA) is esterified with N^α-protected (L)-α-amino acids by the DCC/HOBT method. The resulting polymer is deprotected by HBr/glacial acetic acid. A second N^α-protected (L)-α-amino acid is condensed to the free α-NH₂ of the amino acid already bound to the sPMA by a water-soluble carbodiimide in mixed aqueous/organic solution. The formed N^α-protected dipeptide polymers were hydrazinolized to yield the N^α-protected dipeptide hydrazides. Alternatively, the dipeptidate polymers were N^α-deprotected and then hydrolyzed by aqueous KOH at pH = 11.0 to yield the deprotected dipeptides. All polymers and the dipeptides were characterized by ¹H- and ¹³C-NMR and the water-soluble N^α-deprotected polymers in addition by potentiometry. The synthetic procedures open a path to defined tactic polymers with chiral oligopeptide side chains and, after their cleavage, also to oligopeptides. During synthesis, the oligopeptide is bound to a dissolved polymer chain of relatively extended macroconformation which facilitates both the accessibility and reactivity of the reaction centers as well as the precipitation and filtration after each synthesis step. © 1995 John Wiley & Sons, Inc.     

Dilute solution properties of branched polymers

For calculating the ratio of the intrinsic viscosities of branched and linear polymers of the same molecular weight, [η]_B/[η]_L, a new theory taking into account the excluded volume effect is presented. By using the modified Flory equation, the excluded volume effect of branched polymers is predicted with the aid of the first-order perturbation theory. The linear expansion factor α_s is converted to the hydrodynamic expansion factor α_η by using the Kurata-Yamakawa theory. Our calculated results, i.e., [η]_B/[η]_L and 〈s²〉_B/〈s²〉_L, agree well with experiment for various type branched polymers, i.e., randomly branched and comb-shaped polymers of poly(vinyl acetate).     

Solubility and solution rheology of acrylamide-sulfobetaine copolymers

The copolymer of acrylamide and 3-[N-(2-methacryloxylethyl)-N,N-dimethylammonio]-propane sulfonate (PAM-MDMPS) was prepared via free radical copolymerization. Solubility of the copolymers was studied by turbidimetric titration method under different conditions. It was found for the first time that the critical salt concentration to dissolve the copolymer showed a plateau over one order of magnitude up to the critical overlap concentration. Rheological behavior and chain conformation of the copolymers in 1 M NaCl solution were also studied. The concentration regions according to scaling theory were found the same as neutral polymers in good solvent. The specific viscosities could be normalized by the overlap parameter. According to the Huggins relation, the copolymers adopted a more compact conformation in 1 M NaCl with increasing MDMPS content due to the hydrophobic association of the betaine unit in the macromolecular backbone, which was stabilized by the strongly hydrated dipolar pendant chains.     

Structure-property relationships for novel wholly aromatic polyamide-hydrazides containing various proportions of para-phenylene and meta-phenylene units: I. Synthesis and characterization

A series of novel wholly aromatic polyamide-hydrazides was synthesized by a low temperature solution polycondensation reaction of either 4-amino-3-hydroxybenzhydrazide or 3-amino-4-hydroxybenzhydrazide with an equimolar amount of either terephthaloyl chloride (TCl), isophthaloyl chloride (ICl), or mixtures of various molar ratios of TCl and ICl in anhydrous N,N-dimethylacetamide (DMAc) as a solvent. Polymer structures were identified by elemental analysis and infrared spectroscopy. All the polymers have the same structural formula except the way of linking phenylene units inside the polymer chain. The content of para- and meta-phenylene moieties was varied within this series so that the changes in the latter were 10 mol % from polymer to polymer, starting from an overall content of 0-100 mol %. The prepared polymers were characterized for their properties in order to acquire clear understanding of the influence exerted by controlled structural variations in these polymers upon some of important properties, such as solubility, intrinsic viscosity, moisture regain, mechanical properties and thermal as well as thermo-oxidative stability. The polymers were readily soluble in several organic polar solvents such as DMAc, N,N-dimethylformamide, dimethyl sulphoxide, N-methyl-2-pyrrolidone and hexamethyl phosphoramide and could be cast into flexible films. Their solubilities were found to increase remarkably with introduction of meta-phenylene moieties into the polymer chains. Their intrinsic viscosities ranged from 0.73 to 4.83 dl g⁻¹ in DMAc at 30 °C and increased with the increase of para-phenylene units content. Mechanical properties of the films produced from these polymers are improved markedly by substitution of para-phenylene units for meta-phenylene units. Thermogravimetric studies revealed that the completely para-oriented type of polymer has better thermal and thermo-oxidative stability relative to that of the other polymers. Moreover, the results reveal that the prepared polymers have a great affinity to water sorption. The hydrophilic character increases as a function of meta-oriented phenylene rings incorporated into the polymer chains.