Intrinsic viscosity of polystyrene in mixed solvents

The intrinsic viscosity of a single sample of polystyrene was measured as a function of the composition of solvent in three mixed solvent pairs. The parameter Y introduced by Shultz and Flory was useful for prediction of trends, but severely overestimated the effect of solvent (1)–solvent (2) interaction on the expansion of polymer coils. The system polystyrene–cyclohexane–ethyl acetate was studied in detail for five samples of polystyrene. The analysis of the data provided strong experimental proof of a strict validity of the Mark–Houwink–Sakurada relation. The dependence of the Mark–Houwink–Sakurada exponent α on the composition of the solvent mixture was unexpectedly unsymmetrical. The unperturbed dimentions of the polystyrene chain are reduced by specific interaction of polystyrene with carbonyl groups in the solvent mixture.     

Scaling analysis of the temperature dependence of intrinsic viscosity

The scaling predictions for the temperature dependence of the intrinsic viscosity of flexible polymers are briefly reviewed. When the predictions are fit to a power law over a fixed range of chain length, a relation between the exponent and prefactor of the Mark–Houwink–Sakurada equation emerges. In comparing with the experimental data compilation of Rai and Rosen, we conclude that real polymer systems are nowhere near the true good solvent limit, even when the exponent matches the good solvent prediction. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 1989–1991, 1997     

Cellulose acetate butyrate in solution. I. Hydrodynamic behavior

Cellulose acetate butyrate has been studied in regard to its hydrodynamic properties in several solvents. The polymer was fractionated by precipitation, and the molecular weight distribution of the polymer fractions was determined by gel permeation chromatography. The number-average molecular weight was estimated by osmometry. The Mark–Houwink–Kuhn–Sakurada relations between viscosity and molecular weights were established, and the unperturbed dimensions of the polymer chains were evaluated. In light of these data, current theories of polymer solutions are discussed. A new method of estimating unperturbed dimensions is proposed for semiflexible linear polymers.     

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.     

Molecular Weight Distributions in Coupled Polymers Using Z‐Transform

A study of end‐to‐end coupling reactions of bifunctional linear prepolymers of the Schulz–Flory type is presented by use of Z‐transform. The application of Z‐transform allows one to derive exact expressions for the change of molecular weight distributions in dependence of the progress of the coupling reaction. After coupling the distribution is also of Schulz–Flory type, however, it depends in a relatively complicated manner on the extent of reaction of the prepolymer and on the extent of the coupling reaction. Further expressions are derived for various dependencies including the influence of the extent of coupling on the average molecular weights, chain lengths, and polymolecularity. By implementation of the Mark–Houwink–Sakurada equation, a correlation between intrinsic viscosity and the progress of coupling reaction is shown.     

A rapid method for the determination of Mark–Houwink constants from GPC and viscosity data on a single sample

A straightforward and rapid method for the determination of Mark–Houwink constants from GPC and viscometry is described. A single original polymer is sufficient since other samples were prepared by sonication. The use of a number of samples in this way is shown to improve the accuracy over determinations where only two polymer samples are used.     

Determination of molecular weights and Mark–Houwink constants for soluble electronically conducting polymers

Intrinsic viscosities and gel permeation chromatography data were used to evaluate the Mark–Houwink constants of the soluble electronically conducting polymer, poly(3-hexylthiophene) (P3HT):K and a are 2.28 × 10^-3 cm³/g and 0.96, respectively, in tetrahydrofuran (THF) at 25°C. Mark–Houwink constants were used to calibrate gel permeation chromatography (GPC) columns for P3HT. Number-average molecular weights of P3HT determined with modified calibration curves agreed well with those determined by an absolute method, embulliometry. Molecular weights estimated using unmodified polystyrene calibration procedures were significantly larger than true values.     

Determination of propagation rate coefficients for an α‐substituted acrylic ester: Pulsed laser polymerization of dimethyl itaconate

Pulsed laser polymerization experiments have been performed on the bulk polymerization of dimethyl itaconate over the temperature range 20–50 °C. The activation energy and frequency factor were calculated as 24.9 kJ/mol⁻¹ and 2.15 × 10⁵ L/mol⁻¹s⁻¹, respectively. The activation energy is comparable with the methacrylate series of monomers. The frequency factor is relatively small and reflects steric hindrance in the transition state caused by the bulky 1,1, disubstitution in the monomer (and consequently the radical). The Mark–Houwink–Kuhn–Sakurada constants were also determined for poly(dimethyl itaconate) in tetrahydrofuran, these are reported as 46 × 10⁻⁵ dL/g (K) and 0.51 (α). The influence of penultimate units (γ‐substituents) on homopropagation reactions is discussed particularly for polymerizations leading to significant 1,3 interactions in the resultant polymer. © 2000 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 38: 2192–2200, 2000     

Intrinsic viscosity–molecular weight relationship for chitosan

The intrinsic viscosity–molecular weight relationship for chitosan was determined in 0.25 M acetic acid/0.25M sodium acetate. Chitosan samples with a degree of acetylation (DA) between 20 and 26% were prepared from shrimp‐shell chitosan by acid hydrolysis (HCl) and oxidative fragmentation (NaNO₂). Absolute molecular weights were measured by light scattering and membrane osmometry. Size exclusion chromatography (SEC) was used to determine average molecular weights (M_n, M_v, and M_w) and polydispersity. The following Mark–Houwink–Sakurada equation (MHS) is proposed for chitosan of M_w in the range of 35–2220 kDa: The value of the MHS exponent a suggests that chitosan behaves as a flexible chain in this solvent. Examination of MHS constants obtained in this work and those available in the literature with other solvents indicates that a and K are inversely related and that they are influenced by DA, and pH and ionic strength of the solvent. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 2591–2598, 2000     

Molecular characterization and glassy-state properties of poly(spiro[2,4]hepta-4,6-diene)

Poly(spiro[2,4]hepta-4,6-diene) (PSHD) is a random copolymer composed of 1,2 and 1,4 units. Although PSHD has been reported to have a very large Sakurada–Mark–Houwink exponent (a = 1.71) characteristic of rigid rods, a new determination of the intrinsic viscosity–molecular-weight relation for fractionated samples with known copolymer composition gives a smaller value (0.81). The rigidity of the PSHD molecule was also investigated by calculations of the conformational energy associated with the main chain and the dynamic viscoelasticity associated with the molecular motion in a solid state. A sharp potential energy minimum occurs at a dihedral angle χ₁ = 260° in polymer composed of all trans 1,4 units. The dynamic loss tangent for the primary absorption decreases with increasing fraction of the 1,4 unit. These properties result from the characteristics of the stiff 1,4 unit sequences in the molecular chain. The density of PSHD decreases with increasing content of 1,4 units and was found to be considerably smaller than values for typical polymers, in relation to the occupied volume of the repeat unit. This fact can be explained by the peculiar aggregation state of molecular chains composed of rigid and flexible units.     

Synthesis and properties of a deuterated phenolic resin

A highly deuterated novolac‐type phenolic resin was prepared by polycondensation of deuterated phenol and formaldehyde using oxalic acid as an acid catalyst. The polycondensation of deuterated monomers and the formation of the highly deuterated phenolic resin were confirmed by the gel permeation chromatography, IR, and ¹H NMR analyses. With the exception of hydroxyl groups, the degree of deuteration was estimated to be more than 98%. The polymer conformation in THF solution was evaluated by the scaling exponent of the Mark–Houwink–Sakurada equation. The exponent of the deuterated phenolic resin is 0.26 in THF at 40 °C and is close to that of a nondeuterated phenolic resin, which suggests that phenolic resins behave like a compact sphere irrespective of deuteration. The curing behavior of the deuterated phenolic resin with hexamethylenetetramine was confirmed by differential scanning calorimetry analysis. The cured highly deuterated phenolic resin exhibits a lower incoherent neutron scattering background than that of the nondeuterated phenolic resin, which suggests that the former is suitable for matrix resins with low incoherent backgrounds for small‐angle neutron scattering studies of thermosetting resins. © 2011 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2011.     

Molecular weight control of polyacrylamide with sodium formate as a chain‐transfer agent: Characterization via size exclusion chromatography/multi‐angle laser light scattering and determination of chain‐transfer constant

We discuss the synthesis and characterization of polyacrylamide (PAM) homopolymers with carefully controlled molecular weights (MWs). PAM was synthesized via free‐radical solution polymerization under conditions that yield highly linear polymer with minimal levels of hydrolysis. The MW of the PAM homopolymers was controlled by the addition of sodium formate (NaOOCH) to the polymerization medium as a conventional chain‐transfer agent. MWs and polydispersity indices (PDIs) were determined via size exclusion chromatography/multi‐angle laser light scattering analysis; for polymerizations carried out to high conversion, PAM MWs ranged from 0.23 to 6.19 × 10⁶ g/mol, with most samples having PDI ≈2.0. Zero‐shear intrinsic viscosities of the polymers were determined via low‐shear viscometry in 0.514 M NaCl at 25 °C. Data derived from the polymer characterization were used to determine the chain‐transfer constant to NaOOCH under the given polymerization conditions and to calculate Mark–Houwink–Sakurada K and a values for PAM in 0.514 M NaCl at 25 °C. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 560–568, 2003     

Synthesis of novel hyperbranched polymer through cationic ring‐opening multibranching polymerization of 2‐hydroxymethyloxetane

The cationic ring‐opening multibranching polymerization of 2‐hydroxymethyloxetane ( 1 ) as a novel latent AB₂‐type monomer was carried out using trifluoromethane sulfonic acid or trifluoroboron diethyl etherate by a slow‐monomer‐addition (SMA) method. The polymer yield of poly‐1 ranged from ca. 58–88%, which increase with the increasing monomer addition time on the SMA method. The absolute molecular weights (M_w,MALLS) and the polydispersities of poly‐1 were in the range of 8,000–43,500 and 1.45–4.53, respectively, which also increased with the increasing monomer addition time. The Mark‐Houwink‐Sakurada exponents α in 0.2 M NaNO₃ aq. were determined to be 0.02–0.25 for poly‐1 , indicating that poly‐1 has compact forms in the solution because of the highly branched structure. The degree of the branching value of poly‐1 , which was calculated by Frey's equation, ranged from ca. 0.50 to 0.58, which increased with the increasing monomer addition time. The steady shear flow of poly‐1 in aqueous solution exhibited a Newtonian behavior with steady shear viscosities independent of the shear rate. The results of the MALLS, NMR, and viscosity measurements indicated that poly‐1 is composed of a highly branched structure, i.e., the hyperbranched poly (2‐hydroxymethyloxetane). © 2011 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2011     

Pulsed‐laser radical polymerization and propagation kinetic parameters of some alkyl acrylates

Pulsed‐laser photoinitiated polymerization was used to determine, in toluene solution, the propagation kinetic parameters of a series of acrylates with increasing size of the alkyl side group. Transfer to monomer and to toluene did not occur significantly in our PLP conditions and our temperature range since no broadening of the MMD was observed, allowing generally to work with two inflection points. In contrast, depending on the nature of the acrylate and on the PLP conditions, transfer to polymer, and thus long chain branching, can critically interfere. Indeed, the Mark‐Houwink‐Sakurada parameters, which are used to calculate the absolute molar mass at the inflection point, strongly depend on the polymer structure and thus, should be carefully measured for each PLP sample. Although still preliminary, the results show that the k_ps measured in toluene solution present a tendency to continuously decrease when increasing the size of the side group. This observation is conflicting with the reported behaviour for PLP experiments in bulk, revealing a possible solvent effect.     

聚环硫氯丙烷Mark-Houwink方程参数的测定

提出了利用多个宽分布聚合物试样的［η］和ＧＰＣ谱图在计算机上运用五点搜索法寻找［η］的最小偏差的程序来解得聚合物的Ｍａｒｋ Ｈｏｕｗｉｎｋ方程参数的新方法．并应用此法确定了聚环硫氯丙烷在四氢呋喃溶液中３０℃下的Ｍａｒｋ Ｈｏｕｗｉｎｋ方程参数为：α＝０７７１，Ｋ＝０５９２×１０－４．经［η］的误差分析及ＶＰＯ证实，得到的Ｋ、α值是可靠的，用于计算［η］及分子量时，相对误差均在６％之内．     

Assessment of errors in the determination of Mark–Houwink–Sakurada and Stockmayer–Fixman constants using size‐exclusion chromatography with on‐line viscometric detection: Analyses of poly(p‐substituted styrenes) in tetrahydrofuran

In this work, we present values for the Mark–Houwink–Sakurada (MHS) and Stockmayer–Fixman (SF) constants for a series of homopolymers of para‐substituted styrenes (4‐X‐styrene; X = OCH₃, OCH₂CH₃, CH₃, F, Cl, and Br) in THF at room temperature. The respective values of K (in 10⁻⁵ dL/g) and α were: 0.685 and 13.2; 0.662 and 14.1; 0.740 and 8.41; 0.781 and 5.24; 0.726 and 8.95; 0.700 and 7.79. The respective values for K_θ (in 10⁻⁴ dL/g) and K' (in 10⁻⁷ dL/g) were: 6.01 and 16.1; 6.22 and 9.07; 7.64 and 17.4; 5.59 and 23.7; 6.29 and 17.3; 4.44 and 10.3. These constants were measured using size‐exclusion chromatography with on‐line viscometry. As part of this work, we investigate the applicability of common model fitting procedures to this method of measuring MHS/SF constants and the effect of uncertainties in their estimated values on the accuracy of molecular weight analysis. © 1999 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 37: 2557–2570, 1999     

Rigid rod-random coil transformation,Mark-Houwink constants,and Millich's intrinsic isoviscosity, [η]M,and isohydrodynamic volume, [η]MMM

On the basis of values of Mark–Houwink constants of rigid rod—polymer systems and their conformers a unique stage can be recognized which is common to all polymers of this type, independent of polymer conformation and solvent medium. The crude values derived for these polymer–solvent systems at 20–30°C. of Millich's intrinsic isoviscosity, [η]_M, is 0.28 ± 0.04 dl/g, occurring at the coordinate molecular weight, M_M, of 42,700, and produces a value of ca. 170 Å of Millich's isohydrodynamic polymer volume at this stage and temperature. Utility in the use of [η]_MM_M as a standard reference state, assuming reliable Mark–Houwink constants that obtain for strictly linear, monodisperse polymer samples, is indicated.     

Dimethyl‐methylphenyl copolysiloxanes by dimethylsilanolate‐initiated ring opening polymerization. Evidence for linearity of the resulting polymer structures

Recently, we reported that dimethylsilanolate‐initiated anionic ring opening polymerization of dimethylsiloxy‐ and diphenylsiloxy‐cyclic siloxanes results in polymer chain branching by dimethylsilanolate‐induced cleavage of only one Si‐C_Ar side bond in diphenylsiloxy repeat units, leading to formation of “Ph‐T‐branches”, and not extending to the cleavage of the second phenyl group. We attributed this behavior to electronic structures of the participating dimethylsiloxy‐, diphenylsiloxy and Ph‐T‐branch silicons and predicted that copolymers prepared by this synthetic route from dimethylsiloxy‐ and methylphenylsiloxy‐cyclics should not undergo branching at all but should have perfect linear chain configuration. Here, we describe results of a study of two such dimethylsilanolate‐initiated ring opening polymerizations of dimethylsiloxy‐ and methyphenylsiloxy‐cyclic tetramers and characterization of the resulting polymers by SEC‐MALS‐VIS, Mark‐Houwink‐Sakurada relationship and ²⁹Si NMR. The results obtained clearly confirmed our prediction of expected linearity of these polymer chains and also indicated that the resulting polymers were completely amorphous even at as low methylphenylsiloxy‐content as 3.9 mol %. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2019 , 57, 1122–1129     

Using apparent molecular weight from SEC in controlled/living polymerization and kinetics of polymerization

Apparent molecular weights from size exclusion chromatography, that is molecular weights relative to standards of a nature different to that of the polymer sample being studied, are frequently used. We use calculations corresponding to realistic cases to provide guidelines for situations when, and to what extent, apparent molecular weights (MWs) can be meaningful. In controlled polymerization, we show how, without due care, use of apparent MW, could lead to the incorrect conclusion that the reaction was not controlled, whereas the true MWs would be close to theoretical values. We show here that the quality of the eluent as a solvent for the standard and the polymer sample is a good indication of the accuracy and the significance of the apparent polydispersity index. Accurate Mark–Houwink–Sakurada parameters are of limited availability, but the data about solvent quality available in handbooks or available from static light scattering measurements. Apparent M_n is of no use in controlled polymerization if simple simulations as performed in this work do not validate their use. The determination of transfer constants by the Mayo plot can be performed using apparent M_n without introducing any significant error, contrary to apparent weight‐average molecular weight M_w or apparent ln number distribution. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 897–911, 2008     

Study of the Topological Structure of Bamboo <Emphasis Type="Italic">Bambusa</Emphasis> sp. Lignin Macromolecules

The topological structure of macromolecules of Pepper lignin isolated from bamboo stems is studied. The molecular properties of dilute lignin solutions in dimethylformamide are investigated by the methods of high-velocity sedimentation, translational diffusion, and viscometry. The molecular mass of fractions, the scaling coefficients of the Kuhn–Mark–Houwink equation, and the Tsvetkov–Klenin hydrodynamic invariant are determined. It is first shown that the lignin of bamboo stems belongs to the universal class of chaotically branched polymers, and the degree of branching of macromolecules is estimated.