Effect of the copolymer composition on the K and a constants of the Mark–Houwink equation: Styrene–methyl methacrylate random copolymers

This article reports a study of the effect of composition in styrene–methyl methacrylate random copolymers on K and a constants in the Mark–Houwink equation. Copolymers with a variety of compositions and chain lengths were prepared through a controlled free‐radical copolymerization, with benzyl diethyldithiocarbamate and tetraethyl thiuram disulfide as iniferters. The synthesized products were analyzed with several techniques, including Fourier transform infrared, ¹H NMR, gel permeation chromatography, and viscometry. By relating the determined constants K and a of various copolymers to their composition, we found that the constant varied nonlinearly with the composition. The constant a decreased with increasing poly(methyl methacrylate) (PMMA) content in the copolymer molecule up to 60 wt %. After that, the constant increased with the PMMA content, reaching the value of the PMMA homopolymer. However, the constant K initially increased with the PMMA content up to a critical composition (60 wt %) and subsequently decreased with further increasing PMMA content. These results suggest that the molecular weight of a polystyrene–PMMA random copolymer of known composition cannot be approximated with a simple linear equation comprising the K and a values of each relevant homopolymers. The aforementioned trends are qualitatively discussed in relation to some possible sequential distribution in the copolymer molecules and the resulting conformation. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 562–571, 2002; DOI 10.1002/polb.10119     

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     

聚对二炔苯Mark-Houwink方程参数的确定及分子量与分子量分布的研究

通过多个宽分布聚对二炔苯试样的凝胶渗透色谱（ＧＰＣ）和特性粘数（［η］）的测定，应用普适校正原理和Ｗｅｉｓ方法，确定了该聚合物在四氢呋喃溶液中２５℃下的Ｍａｒｋ Ｈｏｕｗｉｎｋ方程参数：Ｋ＝７６２×１０－３，α＝０２６．将这一结果运用到ＧＰＣ谱图的计算，所得［η］与用粘度法实测值比较，所得Ｍｎ与用ＶＰＯ法实测值比较，相对误差６％左右．还研究了聚合反应条件对聚对二炔苯分子量与分子量分布的影响，发现随着聚合时间的延长和聚合温度的升高，聚合物分子链间发生部分交联反应，支化程度加重．聚合过程中还可能存在向单体的链转移反应．     

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     

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     

Characterization of poly(D,L-lactic acid) by gel permeation chromatography

A number of samples of poly(D ,L -lactic acid) (PLA) with weight-average molecular weights M?_w in the range 15,000–350,000 were prepared by a ring-opening polymerization. The molecular weight distributions (MWDs) of these samples were determined by gel permeation chromatography (GPC). The method involves a universal calibration of the columns on the basis of polystyrene standards and a rapid iteration algorithm leading to the establishment of the Mark–Houwink relationship. In addition, osmometry and viscometry data are presented. The effect of hydrolytic degradation on the MWD of two PLA samples was studied by GPC.     

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．     

pH‐Responsive ampholytic terpolymers of acrylamide,sodium 3‐acrylamido‐3‐methylbutanoate,and (3‐acrylamidopropyl)trimethylammonium chloride. I. Synthesis and characterization

Low-charge-density ampholytic terpolymers composed of acrylamide, sodium 3-acrylamido-3-methylbutanoate (NaAMB), and (3-acrylamidopropyl)trimethylammonium chloride were prepared via free-radical polymerization in 0.5 M NaCl to yield terpolymers with random charge distributions. NaOOCH was used as a chain-transfer agent during the polymerization to eliminate the effects of the monomer feed composition on the degree of polymerization (DP) and to suppress gel effects and broadening of the molecular weight distribution. The terpolymer compositions were obtained via ¹³C NMR spectroscopy, and the residual counterion content was determined via elemental analysis for Na⁺ and Cl⁻. The molecular weights (MWs) and polydispersity indices (PDIs) were determined via size exclusion chromatography/multi-angle laser light scattering (SEC–MALLS); the terpolymer MWs ranged from 1.3–1.6 × 10⁶ g/mol, corresponding to DPs of 1.6–1.9 × 10⁴ repeat units, with all terpolymers exhibiting PDIs of less than 2.0. Intrinsic viscosities determined from SEC–MALLS data and the Flory–Fox relationship were compared to intrinsic viscosities determined via low-shear dilute-solution viscometry and were found to agree rather well. Data from the SEC–MALLS analysis were used to analyze the radius of gyration/molecular weight (R_g–M) relationships and the Mark–Houwink–Sakurada intrinsic viscosity/molecular weight ([η]–M) relationships for the terpolymers. The R_g–M and [η]–M relationships revealed that most of the terpolymers exhibited little or no excluded volume effects under size exclusion chromatography conditions. Potentiometric titration of terpolymer solutions in deionized water showed that the apparent pK_a value of the poly[acrylamide-co-sodium 3-acrylamido-3-methylbutanoate-co-(3-acrylamidopropyl)trimethylammonium chloride] terpolymers increased with increasing NaAMB content in the terpolymers and increasing ratios of anionic monomer to cationic monomer at a constant terpolymer charge density. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 3236–3251, 2004     

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     

A new soluble conducting polymer and its electrochromic devices

A new polythiophene derivative was synthesized by both chemical and electrochemical oxidative polymerization of 1‐(1‐phenylethyl)‐2,5‐di(2‐thienyl)‐1H‐pyrrole (PETPy). Of which the chemical method produces a polymer that is completely soluble in organic solvents. The structures of both the monomer and the soluble polymer were elucidated by nuclear magnetic resonance (¹H and ¹³C NMR) and Fourier transform infrared (FTIR) spectroscopy. The average molecular weight has been determined by gel permeation chromatography to be M_n = 3.29 × 10³ for the chemically synthesized polymer. Polymer of PETPy was synthesized via potentiostatic electrochemical polymerization in acetonitrile (AN)/NaClO₄/LiClO₄ (0.1 M) solvent–electrolyte couple. Characterizations of the resulting polymer were performed by cyclic voltammetry, FTIR, scanning electron microscopy, and UV–vis spectroscopy. Four‐probe technique was used to measure the conductivities of the samples. Moreover, the spectroelectrochemical and electrochromic properties of the polymer films were investigated. In addition, dual‐type polymer electrochromic devices based on P(PETPy) with poly(3,4‐ethylenedioxythiophene) were constructed. Spectroelectrochemistry, electrochromic switching, and open circuit stability of the devices were studied. They were found to have good switching times, reasonable contrasts, and optical memories. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 2215–2225, 2006     

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.     

RAFT polymerization kinetics and polymer characterization of P3HT rod–coil block copolymers

Here an in‐depth analysis of reversible addition–fragmentation chain transfer (RAFT) polymerization kinetics is reported in order to provide better definition of poly(3‐hexylthiophene) (P3HT) rod–coil block copolymers thru a more thorough understanding of the RAFT polymerization of the coil block. To this end, a new P3HT macroRAFT agent is synthesized and utilized to prepare rod–coil block copolymers with P3HT and poly(styrene), poly(tert‐butylacrylate), and poly(4‐vinylpyridine), and the RAFT polymerization kinetics of each system are fully detailed. This is achieved by a comprehensive analysis of characterization data from ¹H nuclear magnetic resonance spectroscopy, gel permeation chromatography, and matrix‐assisted laser desorption ionization time of flight spectroscopy, which are used as complementary techniques in order to address difficulties in accurately characterizing the synthesized polymer systems. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2014 , 52, 3575–3585     

Preparation,fractionation, and dilute-solution behavior of ABA poly(methyl methacrylate-b-α-methylstyrene) block copolymers

The preparation by anionic polymerization of six ABA poly(methyl methacrylate-b-α-methylstyrene) block copolymers and of sixteen poly(α-methylstyrene)s is described. The block copolymers, of similar molecular weight but with different chemical compositions, were fractionated by preparative gel permeation chromatography and their behavior in dilute solution was investigated using viscometry. The results obtained indicate that the intramolecular phase separation does not occur under the conditions utilized, the block copolymers assuming randomcoil configurations in all of the copolymer/solvent systems studied. Consequently the block copolymer molecules are more expanded than homopolymers of the same molecular weight. The series of poly(α-methylstyrene)s covered the molecular weight range 2.7 × 10³–1.3 × 10⁶ and enabled the determination of Mark–Houwink–Sakurada constants for poly(α-methylstyrene) in the solvents chosen for the block copolymer studies.     

Controlled radical polymerization of a trialkylsilyl methacrylate by reversible addition–fragmentation chain transfer polymerization

The reversible addition–fragmentation chain transfer (RAFT) polymerization of a hydrolyzable monomer (tert‐butyldimethylsilyl methacrylate) with cumyl dithiobenzoate and 2‐cyanoprop‐2‐yl dithiobenzoate as chain‐transfer agents was studied in toluene solutions at 70 °C. The resulting homopolymers had low polydispersity (polydispersity index < 1.3) up to 96% monomer conversion with molecular weights at high conversions close to the theoretical prediction. The profiles of the number‐average molecular weight versus the conversion revealed controlled polymerization features with chain‐transfer constants expected between 1.0 and 10. A series of poly(tert‐butyldimethylsilyl methacrylate)s were synthesized over the molecular weight range of 1.0 × 10⁴ to 3.0 × 10⁴, as determined by size exclusion chromatography. As strong differences of hydrodynamic volumes in tetrahydrofuran between poly(methyl methacrylate), polystyrene standards, and poly(tert‐butyldimethylsilyl methacrylate) were observed, true molecular weights were obtained from a light scattering detector equipped in a triple‐detector size exclusion chromatograph. The Mark–Houwink–Sakurada parameters for poly(tert‐butyldimethylsilyl methacrylate) were assessed to obtain directly true molecular weight values from size exclusion chromatography with universal calibration. In addition, a RAFT agent efficiency above 94% was confirmed at high conversions by both light scattering detection and ¹H NMR spectroscopy. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 5680–5689, 2005     

Solution characterization of the novel organometallic polymer poly(ferrocenyldimethylsilane)

A series of four well‐defined poly(ferrocenyldimethylsilane) (PFS) samples spanning a molecular weight range of approximately 10,000–100,000 g mol⁻¹ was synthesized by the living anionic polymerization of dimethyl[1]silaferrocenophane initiated with n‐BuLi. The polymers possessed narrow polydispersities and were used to characterize the solution behavior of PFS in tetrahydrofuran (THF). The weight‐average molecular weights (M_w ) of the polymers were determined by low‐angle laser light scattering (LALLS), conventional gel permeation chromatography (GPC), and GPC equipped with a triple detector (refractive index, light scattering, and viscosity). The molecular weight calculated by conventional GPC, with polystyrene standards, underestimated the true value in comparison with LALLS and GPC with the triple detection system. The Mark–Houwink parameter a for PFS in THF was 0.62 (k = 2.5 × 10⁻⁴), which is indicative of fairly marginal polymer–solvent interactions. The scaling exponent between the radius of gyration and M_w was 0.54, also consistent with marginal polymer–solvent interactions for PFS in THF. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 3032–3041, 2000     

Vinyl‐type polymerization of norbornene by nickel(II) bisbenzimidazole catalysts

Novel nickel(II) bisbenzimidazole complexes were prepared via a three‐step synthetic procedure consisting of aniline/diacid condensation, ligand N‐alkylation, and metal complexation. The complexes were characterized by X‐ray crystallography and found to possess a pseudotetrahedral geometry. Upon activation with methylaluminoxane, these nickel bisbenzimidazoles did not polymerize simple olefins (e.g., ethylene, propylene, and 1‐butene) but were found to carry out the rapid and efficient polymerization of norbornene. The polynorbornene products were characterized by gel permeation chromatography/light scattering, ¹³C NMR, and IR, and their Mark–Houwink and dn/dc parameters were determined. The molecular weights of the polynorbornenes were very high (weight‐average molecular weight = 587,000–797,000 g/mol). ¹³C NMR suggested that the polymerization occurred via vinyl addition (i.e., a 2,3‐linked polymer); no ring‐opened product was observed. Thermogravimetric analysis indicated that the polynorbornenes were stable up to 400 °C under nitrogen. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 2095–2106, 2003     

Solution properties of poly(dimethyl siloxane)

The solution properties of poly(dimethyl siloxane) (PDMS) were studied with light scattering (LS), gel permeation chromatography/light scattering (GPC/LS), and viscometry methods. PDMS samples were fractionated, and the weight‐average molecular weights, second virial coefficient, and the z‐average radius of gyration of each fraction were found according to the Zimm method with the LS technique. In this work, the molecular weight range studied was 7.5 × 10⁴ to 8.0 × 10⁵. Molecular weights and molecular weight distributions were determined by GPC/LS. The intrinsic viscosities of these fractions were studied in toluene at 30 °C, in methyl ethyl ketone (MEK) at 20 °C, and in bromocyclohexane (BCH) at 26 °C and 28 °C. The Mark–Houwink–Sakurada relationship showed that toluene was a good solvent, and MEK at 20 °C and BCH at 28 °C were θ solvents for PDMS. The unperturbed dimensions were calculated with LS and intrinsic viscosity data. The unperturbed dimensions, expressed in terms of the characteristic ratio, were found to be 6.66 with different extrapolation methods in toluene at 30 °C. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 2678–2686, 2000     

Dilute solution properties of cellulose in LiOH/urea aqueous system

Cellulose was dissolved rapidly in 4.6 wt % LiOH/15 wt % urea aqueous solution and precooled to –10 °C to create a colorless transparent solution. ¹³C‐NMR spectrum proved that it is a direct solvent for cellulose rather than a derivative aqueous solution system. The result from transmission electron microscope showed a good dispersion of the cellulose molecules in the dilute solution at molecular level. Weight‐average molecular weight (M_w), root mean square radius of gyration (〈s²〉_z^1/2), and intrinsic viscosity ([η]) of cellulose in LiOH/urea aqueous solution were examined with laser light scattering and viscometry. The Mark–Houwink equation for cellulose in 4.6 wt % LiOH/15 wt % urea aqueous solution was established to be [η] = 3.72 × 10^?2 M in the M_w region from 2.7 × 10⁴ to 4.12 × 10⁵. The persistence length (q), molar mass per unit contour length (M_L), and characteristic ratio (C_∞) of cellulose in the dilute solution were given as 6.1 nm, 358 nm^?1, and 20.8, respectively. The experimental data of the molecular parameters of cellulose agreed with the Yamakawa–Fujii theory of the worm‐like chain, indicating that the LiOH/urea aqueous solution was a desirable solvent system of cellulose. The results revealed that the cellulose exists as semistiff‐chains in the LiOH/urea aqueous solution. The cellulose solution was stable during measurement and storage stage. This work provided a new colorless, easy‐to‐prepare, and nontoxic solvent system that can be used with facilities to investigate the chain conformation and molecular weight of cellulose. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 3093–3101, 2006     

Propagation Rate Coefficients for Homogeneous Phase VDF–HFP Copolymerization in Supercritical CO2

For the first time, propagation rate coefficients, k_p,COPO, for the copolymerizations of vinylidene fluoride and hexafluoropropene have been determined. The kinetic data was determined via pulsed‐laser polymerization in conjunction with polymer analysis via size‐exclusion chromatography, the PLP‐SEC technique. The experiments were carried out in homogeneous phase with supercritical CO₂ as solvent for temperatures ranging from 45 to 90 °C. Absolute polymer molecular weights were calculated on the basis of experimentally determined Mark–Houwink constants. The Arrhenius parameters of k_p,COPO vary significantly compared with ethene, which is explained by the high electronegativity of fluorine and less intra‐ and intermolecular interactions between the partially fluorinated macroradicals.     

Kinetic models for solution imidization of polyamic acid containing naphthalene‐pendant group

The kinetics and mechanisms of the solution imidization of polyamic acid resulting from a diamine, bis(4‐aminophenoxy‐3,5‐dimethylphenyl)naphthylmethane, and a dianhydride, 3,3′4,4′‐diphenylsulfonetetracarboxylic dianhydride, were studied at three various temperatures (145, 165, and 180 °C). The results were confirmed by means of ¹H NMR and gel permeation chromatography (GPC). Kinetic parameters were obtained by an isothermal study, and the results were quite close to second‐order kinetics for the homogeneous solution imidization. In addition, Carother's equation, Mark–Houwink theory, and GPC were used to explain the molecular weight of the imidization processes. The apparent activation energy (E_a) was 104 KJ/mol, and the pre‐exponential factor (k₀) was 3.48 × 10¹⁴. The proposed kinetic mechanism is in good agreement with the kinetic models. © 2001 John Wiley & Sons, Inc. J Polym Sci Part A: Polym Chem 39: 4139–4151, 2001