Kuhn-Mark-Houwink-Sakurada Research Articles

Poly(butylene terephthalate) Copolyesters with Dilinoleic Derivatives: Solution Properties and Influence of Short‐Chain Branching

AbstractThe solution behavior of poly(butylene terephthalate) (PBT) copolyesters with dilinoleic monomer units (dilinoleic diol (LD) / dilinoleic diacid (LA)) is studied to understand the processing behavior from melt. NMR investigations show that the short‐chain branches are characterized by a distribution of different alkyl chain lengths, where n‐butyl (C4) and longer chains have the largest content (>55 mol%). High‐temperature size exclusion chromatography with threefold detection (multi‐angle light‐scattering, refractive index, and viscosity detector) in 1,2,4‐trichlorobenzene is performed to determine molar masses, hydrodynamic radii, viscosity radii, and Kuhn–Mark–Houwink–Sakurada (KMHS) exponents α in dependence of the molar amount of short‐chain branched comonomers. Low concentrations of dilinoleic comonomers in PBT copolyesters improve the solubility of the copolyesters significantly. Higher amounts cause contraction of the polymer coils as illustrated by smaller hydrodynamic radii as well as lower KMHS exponents. The α values decrease with increasing amount of short‐chain branched comonomer except for very low concentrations. The solution behavior of LA and LD copolyesters with a higher aliphatic content shows different trends of the influence of short‐chain branches on the melt behavior, which reflects the influence of intramolecular versus intermolecular entanglements in solution and in melt.

Homology Violation in a Series of Amphiphilic Comb-Like Statistical Copolymers of N-Methyl-N-vinylacetamide and N-Methyl-N-vinylamine with Moderate Density of Grafting of Side Dodecyl Groups

A series of water-soluble comb-like copolymers of N-methyl-N-vinylacetamide and N-methyl-N-vinylamine (MVAA‒со‒MVA) bearing hydrophobic dodecyl side groups С12Н25 has been investigated by means of molecular hydrodynamics (viscometry, translational diffusion, and analytical ultracentrifugation) in dilute solutions in 0.1 M NaCl, under conditions of suppression of the polyelectrolyte effects. The issues of homology of these amphiphilic copolymers have been considered. The viscometry data plotted as lnηr as function of c[η] have allowed to distinguish between macromolecules of the copolymers according to their hydrophobicity. Positive values of the second derivative B2 determined from the initial parts of these curves have served as a measure of hydrophobicity of the amphiphilic copolymers. The noticeable differences in the B2 values for different copolymers have shown that they do not form true homologous series. For the quasi-homologous series of the MVAA–со–MVAC12H25·HI copolymers with close values of B2, the Kuhn–Mark–Houwink–Sakurada relationships have been obtained and the equilibrium rigidity of the chains has been assessed using the modified Gray–Bloomfield–Hearst equation.

Incentives of Using the Hydrodynamic Invariant and Sedimentation Parameter for the Study of Naturally- and Synthetically-Based Macromolecules in Solution.

The interrelation of experimental rotational and translational hydrodynamic friction data as a basis for the study of macromolecules in solution represents a useful attempt for the verification of hydrodynamic information. Such interrelation originates from the basic development of colloid and macromolecular science and has proven to be a powerful tool for the study of naturally- and synthetically-based, i.e., artificial, macromolecules. In this tutorial review, we introduce this very basic concept with a brief historical background, the governing physical principles, and guidelines for anyone making use of it. This is because very often data to determine such an interrelation are available and it only takes a set of simple equations for it to be established. We exemplify this with data collected over recent years, focused primarily on water-based macromolecular systems and with relevance for pharmaceutical applications. We conclude with future incentives and opportunities for verifying an advanced design and tailored properties of natural/synthetic macromolecular materials in a dispersed or dissolved manner, i.e., in solution. Particular importance for the here outlined concept emanates from the situation that the classical scaling relationships of Kuhn–Mark–Houwink–Sakurada, most frequently applied in macromolecular science, are fulfilled, once the hydrodynamic invariant and/or sedimentation parameter are established. However, the hydrodynamic invariant and sedimentation parameter concept do not require a series of molar masses for their establishment and can help in the verification of a sound estimation of molar mass values of macromolecules.

Electrostatic Long-Range Interactions in Macromolecules of Flexible-Chain Linear Polyelectrolytes with Low Charge Density in Aqueous Solutions of Different Ionic Strength

Molecular hydrodynamics methods (translational diffusion, velocity sedimentation, viscometry) have been used to study copolymers of N-methyl-N-vinylacetamide and N-methyl-N-vinylamine hydrochloride with an average content of charged groups (4.4 ± 0.2) mol % in aqueous 0.2 M NaCl solution. Kuhn–Mark–Houwink–Sakurada scaling relationships have been obtained. Viscous flow has been studied in the widest possible range of ionic strengths of aqueous solutions, from salt-free to 6 M NaCl. The data have been compared with those previously obtained for neutral poly-N-methyl-N-vinylacetamide. It has been shown experimentally for the first time that the character of the dependence of the intrinsic viscosity on the molecular mass of a copolymer of such a composition in solutions of minimal ionic strength is typical of the chains exhibiting intrachain volume effects, i.e. electrostatic long-range interactions.

Influence of Electrostatic Long-Range and Short-Range Effects on the Conformations of Flexible-Chain Linear Polyelectrolyte Macromolecules with Different Charge Density in Salt-Free Aqueous Solutions

A series of copolymers of N-methyl-N-vinylacetamide and N-methyl-N-vinylamine hydrochloride with an average content of charged groups of (4.4 ± 0.2) mol % and molecular mass in the range of 22 < M × 10–3, g/mol < 630 are synthesized and characterized. Fractions are studied by sedimentation-diffusion methods in 0.2 mol/L NaCl under almost suppressed polyelectrolyte effects. In salt-free aqueous solutions, their viscous flow is investigated and intrinsic viscosity is determined as [η] ≡ lim(∂lnηr/∂c) at c → 0. The results are compared with the previous data obtained for the copolymer containing (15.7 ± 0.5) mol % of charged groups and the homopolymer. It is shown that the type of intrinsic viscosity dependence on the molecular mass of the copolymer containing 4.4 mol % of charged groups is typical of chains manifesting intrachain volume interactions, while at a 15.7 mol % content of charged groups the type of the dependence is characteristic of chains demonstrating intrachain short-range effects; hence, the chains behave as rigid-chain, permeable. The statistical segment lengths of copolymer macromolecules in salt-free solutions and in 0.2 mol/L NaCl are determined. The data are analyzed in terms of the normalized Kuhn–Mark–Houwink–Sakurada relation.

Diels–Alder Hyperbranched Pyridylphenylene Polymer Fractions as Alternatives to Dendrimers

The results of the hydrodynamic study of hyperbranched pyridylphenylene polymers synthesized via Diels–Alder cycloaddition reaction of multifunctional monomers are reported. The synthesized polymers were fractionated into a much narrowly dispersed fractions. The in-depth analysis of molecular characteristics and conformation of the initial polymers and corresponding fractions was performed using the unique combination of hydrodynamic approaches. The intercorrelation and self-consistency of obtained data were ensured using the hydrodynamic invariant concept and classical Kuhn–Mark–Houwink–Sakurada scaling relations. The evaluated data suggest that hyperbranched pyridylphenylene demonstrates the hydrodynamic behavior typical for asymmetrical compact macromolecular species. Furthermore, hydrodynamic characteristics of herein studied hyperbranched pyridylphenylene polymer fractions were compared with known hydrodynamic data for pyridylphenylene dendrimers. Nearly identical hydrodynamic behavior was found for the compared macromolecules, especially for low molecular mass fractions, which may suggest that the fractionation of hyperbranched polymers results in dendrimer-like structures. The oblate ellipsoid model provides reasonable correlation between hydrodynamic properties of hyperbranched pyridylphenylene polymer fractions and pyridylphenylene dendrimers.

Kuhn–Mark–Houwink–Sakurada Coefficients for Determination of Molecular Parameters of cis-Polybutadiene Rubbers by Gel Permeation Chromatography

Industrial samples of polybutadiene rubbers with a high (95% or more) content of cis-1,4-units obtained on the neodymium-containing catalysts are studied by GPC and NMR spectroscopy (600 MHz). The GPC data obtained under different experimental conditions are analyzed taking into account the molecular weight calculated from NMR data. As a result, the coefficients of the Kuhn–Mark–Houwink–Sakurada equation for the solutions of cis-polybutadiene rubbers in toluene and tetrahydrofuran are refined.

Strong Linear Polyelectrolytes in Solutions of Extreme Concentrations of One–One Valent Salt. Hydrodynamic Study

Two series of highly charged linear aliphatic polymers—sodium polystyrene-4-sulfonate and random copolymer of N-methyl-N-vinylacetamide and N-methyl-N-vinylamine hydrochloride—were studied in water solution without added salts and in solutions containing up to 5 M NaCl. Intrinsic viscosity in salt-free solutions was estimated by a method proposed earlier [Pavlov et al. Russ. J. Appl. Chem. 2006, 79, 1407–1412]. Molecular characteristics were obtained in 0.2 M NaCl. The polyelectrolytes were studied in more than 10-fold range of molar mass. Qualitatively, the conformational status of the polyelectrolyte chains in different ionic strength was defined with the Kuhn–Mark–Houwink–Sakurada plots normalized by the value of linear chain density. In salt-free solution both polyelectrolytes could be attributed to extra rigid chains with the statistical segment length of 650 nm for sodium polystyrene-4-sulfonate and 100 nm for copolymer chains. Such statistical segment lengths are provided by short-range electrostatic intrachain interactions and are comparable with the Debye screening length. At extremely high NaCl concentration polyelectrolyte chains became discriminated by their degree of hydrophobicity. Chains of hydrophobic nature are compacted up to preglobular state, whereas the chains of the hydrophilic nature stay in the conformation of swelling coils at the highest concentration of NaCl.

Random cross-linked poly(styrene- co-maleic anhydride): Characterization of cross-linking intermediates by size exclusion chromatography

The cross-linking reaction of poly(styrene- co-maleic anhydride) (SMA) with ethylene glycol (EG) was monitored using size exclusion chromatography. On-line viscosity and static light scattering detection provided [ η] and R g for structural analysis of the cross-linking intermediates. With increasing reaction time a decrease of the expansion exponent α of the Kuhn–Mark–Houwink–Sakurada relationship was observed. A change from coiled structures to spherical molecules during the cross-linking reaction was confirmed by analyzing the fractal dimensions of the molecules after different reaction times. The calculation of the branching parameters g and g′ revealed the formation of contracted branched molecules. The connection of SMA chains by EG leads to a contraction of the polymers with increasing molecular weight.

Poly(tetrahydropyranyl-2-methyl methacrylate): Comparative study in solution and at the air/water interface

In this work a comparative study of different molecular-weight fractions of the amphiphilic polymer poly(tetrahydropyranyl-2-methyl methacrylate) (PTHPMM) in solution and at the air/water interface is reported. The synthesis of the polymer was carried out in solution by radical polymerization. The polymer was fractionated and five fractions were studied in solution and at the air/water interface. The weight-average molecular weight M ¯ w , the second virial coefficient A 2 , and the radius of gyration R g were determined in toluene by static light scattering. Intrinsic viscosities [ η] of the polymer fractions in three solvents were obtained. The Kuhn–Mark–Houwink–Sakurada relationships were established. The Langmuir isotherms for different polymer fractions were obtained at the air/water interface by monolayer compression at constant temperature. The overlap surface concentrations were determined, and from these results the radius of gyration in two dimensions was calculated. The thermodynamic power of the toluene and the air/water interface for PTHPMM were estimated from the empirical relationship between the radius of gyration in two and three dimensions and the weight-average molecular weight.

Synthesis, Dilute Solution Properties, and Chain Flexibility of Poly(Difluorobenzyl Methacrylates)

The synthesis and dilute solution behavior of poly(2,5-difluorobenzyl methacrylate) (P2,5-DFBM) and poly(2,6-difluorobenzyl methacrylate) (P2,6-DFBM) are described. The polymers were characterized by viscosity and classical light-scattering and size exclusion chromatography (SEC) measurements. The Kuhn-Mark-Houwink-Sakurada (KMHS) relationships were established. Unperturbed dimensions <r 0 2>1/2, the rigidity factor σ, the characteristic ratio C ∞, and the thermodynamic parameters were determined using the Stockmayer-Fixman treatment. The double substitution in the 2,5 and 2,6 positions by fluorine atoms increases the conformational parameters. The presence of substituents such as ─CH3─ or fluorine atoms close to the main chain (2,6 position) affects the internal rotation potential in the same way.

Solution properties of poly(di-1′-methylalkyl itaconates)

Di-1′-methylalkyl itaconates and the corresponding poly(di-1′-methylalkyl itaconates) (PD1′Al) containing 2-propyl (PDiPI), 2-butyl (PDiBI), 1′-methylbutyl (PDiAI), 1′-methylpentyl (PDiHI) and 1′-methyiheptyl (PDiOI) groups as side chains were synthesized and characterized. The polymers were fractionated by fractional precipitation. The fractions were characterized by viscometry in THF and acetone, and by light scattering and size exclusion chromatography in THF. The K a and a parameters of the Kuhn—Mark—Houwink—Sakurada equations were determined in THF and acetone. The stiffness of the polymer chain was estimated through the rigidity indices, a, and the characteristic ratio, C α, using the conformational parameter K Θ obtained from the Stockmayer—Fixman plots. The effect of the side-chain structure on the stiffness, conformational behaviour and glass transition temperatures, T g, of these polymers is discussed and the results compared with those corresponding to other related polymer analogues.

Viscosity of fractions from end‐linked polystyrene star macromolecules

AbstractA number of OH‐terminated three‐arm star molecules were prepared by anionic polymerization with a specially functionalized initiator. The stars were crosslinked over the OH groups with varying amounts of toluene‐2,4‐diisocyanate. The samples were fractionated by size exclusion chromatography (SEC) on‐line with a low angle laser light scattering (LALLS) and a viscosity (VISC) detector. The Kuhn—Mark—Houwink—Sakurada (KMHS) relationships from the various samples resulted in a common relationship. Shrinking parameters g′j≡[η]j,b/[η]j,lin were determined for each slice and could satisfactorily be interpreted on the basis of the Zimm—Stockmayer theory in connection with a suggestion by Kurata et al. The Kurata suggestion was checked with data from star molecules. The examination revealed that randomly branched and star‐branched macromolecules exhibit significantly different hydrodynamic behavior. The ratio of the Fox—Flory coefficients Φb/Φlin in the relationship [η] = Φ(R/M) increases in both cases with branching. This is a consequence of the enhanced segment density and the resulting increase in the hydrodynamic interaction.

Polymethacrylates containing indanyl groups—I. Poly(5-indanyl methacrylate). Synthesis, conformational and viscometric behaviour in dilute solution

The synthesis and dilute solution behaviour of poly(5-indanyl methacrylate) (PS-IM) is studied in THF, toluene and butanone at 298 K, by intrinsic viscosity, light scattering measurements and size exclusion chromatography (SEC). The Kuhn-Mark-Houwink-Sakurada (KMHS) relationships were established in all the solvents studied. The flexibility factors σ and C ∞ and the thermodynamic parameters A 2 and B were calculated using Zimm plots and the Stockmayer-Fixman equation, respectively. The A 2 and the B values are indicative of the presence of the excluded volume effect. The results obtained about the rigidity factors are compared with those previously found for other aromatic poly(methacrylates) and discussed in terms of the influence of the volume and interactions of the lateral chains.

Synthesis and characterization of bulky side chain methacrylate polymers

AbstractThe synthesis, and dilute solution behavior of poly(2,4‐dimethylphenyl methacrylate) (2,4DMP), poly(2,5‐dimethylphenyl methacrylate) (2,5DMP), and poly(3,5‐dimethylphenyl methacrylate) (3,5DMP) is described. Comparison is made with results reported for other bulky side chain polymers. The Kuhn‐Mark‐Houwink‐Sakurada (KMHS) relationships were established. The unperturbed dimensions 〈r2〉, the rigidity factor σ, the characteristic ratio C∞, and the thermodynamic parameters were determined, using the Stockmayer‐Fixman equation, from viscometric data in good solvents. The high rigidity observed for these polymers is explained assuming that these polymers behave as kinked‐chains.

Intrinsic viscosity and the molecular weight of kraft lignin

This study developed Kuhn-Mark-Houwink-Sakurada (KMHS) equations for kraft lignin, based on the absolute molecular weight characterized with low-angle laser light scattering. The KMHS exponential factors of kraft lignin were found to be 0.11, 0.13 and 0.23 in dimethylformamide (DMF) at 318.2 K, in DMF at 350.7 K and in 0.5 N sodium hydroxide at 303.2 K, respectively. Lignin molecules in solution are approximately spherical particles and slightly solvated with solvent.

Synthesis, solution properties and chain flexibility of poly(2,6-dimethylphenyl methacrylate)

The dilute solution properties of poly(2,6-dimethylphenyl methacrylate) (PDMP) in various solvents were studied by viscosity, size exclusion chromatography (s.e.c.) and osmotic pressure measurements. The Kuhn-Mark-Houwink-Sakurada (KMHS) relationships were established. The unperturbed dimensions <r 2> 1 2 0 , the rigidity factor σ, the characteristic ratio C ∞, and the thermodynamic parameters were determined by using the Stockmayer-Fixman equation, from viscometric data in good and theta conditions in pure and mixed solvents. The results show that preferential adsorption of water in the mixture THF/water, should not play an important role in the determination of the conformational parameters in this system. In addition, the measured rigidity of PDMP can be explained assuming that this polymer behaves as a kinked-chain molecule. The conformational behaviour of this polymer is analysed in terms of the effect of the side chain structure in relation to poly(phenyl methacrylate) (PPh).

Solution properties and chain flexibility of poly(thiocarbonate) from 1,1-bis(4-hydroxyphenyl)phenyl ethane

The dilute solution properties of poly[oxythiocarbonyloxy-1,4-phenylene(methyl)phenyl methylene-1,4-phenylene] (PMPhT) in θ and in good solvents were studied by viscosity, osmotic pressure and size exclusion chromatography measurements. The unperturbed dimensions were determined and the Kuhn-Mark-Houwink-Sakurada (KMHS) relations were established. The characteristic ratio value for this polymer is compared with those previously found for other poly(thiocarbonates). The flexibility of the chain is discussed in terms of the influence of the phenyl group of the side chain.

The Effect of Uncertainties in the Kuhn-Mark-Houwink-Sakurada Constants on the Quantitative Analysis by Gel Permeation Chromatography

The effect of uncertainties in Kuhn-Mark-Houwink-Sakurada (KMHS) constants on weight average and number average molecular weights and molecular weight distributions of some poly(ethyl methacrylate) samples have been investigated. Parameters were computed by the Weiss and Cohn-Ginsberg method. Whereas errors introduced in Mw, Mn and HI values due to uncertainty in the K value are insignificant, uncertainties in the KMHS exponent present a serious problem. Deviations of ± 3% around a particular a value cause a ± 20% error in Mw and ± 15% error in Mn, values. The effect of deviations in the KMHS exponent on the HI values is dependent on the polydisperity of the sample investigated.

A non‐linear approach to the Kuhn‐Mark‐Houwink‐Sakurada equation

AbstractIntrinsic viscosities and molecular weights were evaluated to obtain Kuhn‐Mark‐Houwink‐Sakurada (KMHS) relationships for some selected polymers by means of a non‐linear regression analysis. The proposed method yields unbiased values of the KMHS parameters a and K, improves the fitting and shows that KMHS relationship must be considered as a simple correlation with two interdependent parameters, a and K.