Intrinsic viscosity–number average molecular weight relationship for poly(1,4‐butylene adipate) diol

The relationship between number average molecular weight (M_n) and intrinsic viscosity ([η]) was studied for poly(1,4‐butylene adipate) diol (PBAD) in tetrahydrofuran, toluene, and ethyl acetate at 25°C. Thus, a series of PBAD samples were prepared by polymerization between 1,6‐adipic acid and 1,4‐butanediol. The values of M_n for the samples were determined by end‐group analysis as well as by ebulliometry, and the average difference of M_n between the two analysis ways was about 2.69%. The Mark–Houwink–Sakurada equations for PBAD were obtained to relate [η] with M_n in the range of 1900–10,000. © 2010 Wiley Periodicals, Inc. J Appl Polym Sci, 2010     

Viscometric determination of the molecular weight of polymers in the low molecular weight region

In order to overcome the difficulty of the determination of the molecular weight of a polymer in the low molecular weight region by viscometry using the Mark–Houwink–Sakurada (MHS) equation, we have proposed the Dondos–Benoit relationship [η]^?1 = A₂ + AM^?1/2, for a number of polymer–solvent systems, for which we give the numerical values of the parameters A₁ and A₂. Furthermore, we suggest a method for the determination of the above parameters using the MHS constants a and k.     

Cellulose molecular weights determined by viscometry

The equation suggested in the standard method SCAN C15:62 for the estimation of the degree of polymerization (DP) of a cellulose sample from its intrinsic viscosity ([η]) in cupriethylenediamine hydroxide (cuene) solution, P ^0.905 = 0.75 [η]/mL g^?1, where P is an indeterminate average DP, is incorrect. Although differences between the experimental results from several laboratories need to be resolved, a tentative replacement (P _V = 1.65 [η]) is suggested, based upon the pooled data and a conversion from the intrinsic viscosity of cellulose tricarbanilate (CTC) in tetrahydrofuran (THF) to that of cellulose in cuene. The treatment of statistical errors in Mark–Houwink–Sakurada parameters, and the nonlinearity of the log[η]?log P _v correlation are discussed.     

Viscosity‐molecular weight relationship for cellulose solutions in either NMMO monohydrate or cuen

The intrinsic viscosities, [η], of nine cellulose samples, with molar masses from 50 × 10³ to 1 390 × 10³ were determined in the solvents NMMO*H₂O (N‐methyl morpholin N‐oxide hydrate) at 80°C and in cuen (copper II‐ethlenediamine) at 25°C. The evaluation of these results with respect to the Kuhn–Mark–Houwink relations shows that the data for NMMO*H₂O fall on the usual straight line in the double logarithmic plots only for M ≤ 158 10³; the corresponding [η]/M relation reads log ([η]/mL g⁻¹) = –1.465 + 0.735 log M. Beyond that molar mass [η] remains almost constant up to M ≈ 10⁶ and increases again thereafter. In contrast to NMMO*H₂O the cellulose solutions in cuen behave normal and the Kuhn–Mark–Houwink relation reads log ([η]/mL g⁻¹) = −1.185 + 0.735 log M. Possible reasons for the dissimilarities of the behavior of cellulose in these two solvents are being discussed. The comparison of three different methods for the determination of [η] from viscosity measurements at different polymer concentrations, c, demonstrates the advantages of plotting the natural logarithm of the relative viscosities as a function of c. © 2010 Wiley Periodicals, Inc. J Appl Polym Sci, 2011     

Estimation of molecular weight averages from intrinsic viscosity

The weight-average molecular weight is estimated by an extrapolation technique based on a linear relation between the viscosity-average molecular weight M_v and a Mark–Houwink–Sakurada constant. This method may also be used to assess the unperturbed dimensions of polymers. If the M_v data are known with high accuracy, then the straight line may be stretched to reach the number-average molecular weight confidently. The slope of the linear plot is associated with the molecular weight distribution and as such can be utilized to compute the polydispersity index.     

Evaluation of GPC methods for estimation of Mark–Houwink–Sakurada constants

Constants for the Mark–Houwink–Sakurada relation can be established in principle from GPC measurements on broad distribution polymers. The method requires use of two samples with different intrinsic viscosities or a single polymer for which [η] and M ⁿ M ^w are known. The [η]–M ^w combination is not reliable because M ^v and M ^w are often very similar in magnitude. The [η]M _n method is likewise not recommended because of the influence of skewing and axial dispersion effects on the GPC measurement of M _n. The simplest and safest way to use GPC data to estimate the MHS constants involves the measurement of GPC chromatograms of two polymer samples with different intrinsic viscosities. The method is not confined to the solvent used as the GPC eluant. The MHS constants derived from GPC appear to reflect the molecular weight range of the calibration samples and may not be as widely applicable as those from the more tedious classical methods which employ a series of fractionated samples.     

Synthesis of star‐shaped poly(ϵ‐caprolactone) by samarium‐based tetrafunctional initiator and its dilute‐solution properties

An in situ–generated tetrafunctional samarium enolate from the reduction of 1,1,1,1‐tetra(2‐bromoisobutyryloxymethyl)methane with divalent samarium complexes [Sm(PPh₂)₂ and SmI₂] in tetrahydrofuran has proven to initiate the ring‐opening polymerization of ?‐caprolactone (CL) giving star‐shaped aliphatic polyesters. The polymerization proceeded with quantitative conversions at room temperature in 2 h and exhibited good controllability of the molecular weight of polymer. The resulting four‐armed poly(?‐caprolactone) (PCL) was fractionated, and the dilute‐solution properties of the fractions were studied in tetrahydrofuran and toluene at 30°C. The Mark–Houwink relations for these solvents were [η] = 2.73 × 10^?2M_w^0.74 and [η] = 1.97 × 10^?2M_w^0.75, respectively. In addition, the unperturbed dimensions of the star‐shaped PCL systems were also evaluated, and a significant solvent effect was observed. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 102: 175–182, 2006     

Huggins' constant and unperturbed parameter of dilute polymer solutions

A novel method developed to evaluate the unperturbed parameter K_θ from the viscometric data of dilute polymer solutions can be considerably simplified by making the reasonable assumption that the Huggins' constant under theta conditions, k_Hθ, is equal to ½ for a number-average degree of polymerization of over about 2000. Two linear equations are derived pertaining to the present analysis, one to deal with the experimental data, and the other specially to estimate the intrinsic viscosity [η]θ which corresponds to κ_Hθ. All calculations were done by the linear least-squares method. The K_θ was computed by the Mark–Houwink–Sakurada equation. It is shown that reliable results on K_θ can be obtained for polystyrene and poly(vinyl acetate).     

Urea‐induced conformational changes of chitosan molecules and the shift of break point of Mark–Houwink equation by increasing urea concentration

Chitosan solutions of the same 83% degree of deacetylation (DD) but different weight average molecular weights (M_ws) (78–914 kDa) in 0.01M HCl containing different concentrations of urea (0–6M) were prepared. Intrinsic viscosity ([η]) and weight average molecular weight (M_w) of chitosan were measured with a capillary viscometer and light scattering, respectively. Mark–Houwink exponent a was used as the parameter of conformational index. The Mark–Houwink exponent a increased with increasing concentrations of urea. When solutions contained 0, 2, 3, 4, and 6M urea, the value of a increased from 0.715 to 0.839, 0.894, 1.000, and 1.060, respectively. This indicates the occurrence of urea‐induced conformational transitions of chitosans. The break point shifted from 223 kDa in solutions containing no urea to 280 kDa in 2M urea solutions, to 362 kDa in 4M urea solutions and further to 481 kDa in 6M urea solutions. © 2000 John Wiley & Sons, Inc. J Appl Polym Sci 75: 452–457, 2000     

Dilute solution properties of poly(2-methoxycyanurate) of bisphenol F and bisphenol A

Poly(2-methoxycyanurate) of bisphenol F and bisphenol A (PMCBFA) was synthesized and fractionated by a fractional precipitation method. The fractions were characterized by viscometry, osmometry and gel permeation chromatography. The Mark–Houwink–Kuhn–Sakurada (MHKS) parameters were established in four solvents and at four different temperatures. The unperturbed dimensions and their coefficients in different solvents were computed using the Stockmayer–Fixman excluded volume theory. From the solution study it was found that PMCBFA is highly flexible. This may be due to the ether linkage present in the main chain.     

Solution properties of triphenylsilyl cellulose

Five samples of triphenylsilyl cellulose (TPSC) are characterized in solution by osmometry, viscometry, and size exclusion chromatography. The isolated and purified cellulose ethers are prepared in a N,N‐dimethylformamide and pyridine medium under heterogeneous starting conditions and a nitrogen atmosphere by silylation of activated celluloses with triphenylchlorosilane at 115–120°C. TPSCs are characterized by their polydispersities and degrees of substitution by osmometry and viscometry in various solvents. The Mark–Houwink–Sakurada equation coefficients are evaluated in 1,1,1‐trichloroethane, chloroform, and o‐xylene at 30°C and in o‐xylene over a temperature range of 30–70°C. Values of 2.12–2.18 are obtained for exponent a. This indicates, in combination with low values of the preexponential factor (on the order of 10^?12), strong stiffness of the macromolecular chains. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 103: 1257–1261, 2007     

Aggregate formation in poly(ethylene oxide) solutions

Static light scattering and viscosity measurements were performed on different molecular weight poly (ethylene oxide) to see the formation of aggregates in its dilute solutions. Viscosity measurements were carried out for PEO samples in water and methanol at 20–45°C and in chloroform at 20–30°C. Using Huggin's equation, the viscosity plots showed distinct upward curvature indicating the presence of aggregates in both PEO/H₂O and PEO/CH₃OH solutions The [η] values for PEO/H₂O and PEO/CH₃OH system were 2–4 times as large as observed for other linear flexible polymers in good solvents thus showing extensive coil swelling/aggregation. This is also apparent from the exponent a values of the Mark–Houwink–Sakurada equation. Light Scattering results using Zimm method showed that aggregation occurred in low molecular weight samples; however, in higher molecular weight samples there was a little evidence for aggregation both in water and methanol. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 102: 2578–2583, 2006     

Molecular weight determination of 83% degree of decetylation chitosan with non‐Gaussian and wide range distribution by high‐performance size exclusion chromatography and capillary viscometry

Molecular weight determination of 83% degree of deacetylation (DD) chitosan with non‐Gaussian and broad molecular weight distribution by high‐performance size exclusion chromatography (HPSEC) and by capillary viscometry were proposed. The relationships between weight average retention volumes (RVw) of HPSEC and intrinsic viscosities ([η]) measured by capillary viscometer and the weight average molecular weight (Mw) measured by static light scattering were established for routine molecular weight determination of chitosans either by HPSEC or by the capillary viscometry method, respectively. These results showed: relationships of RVw and Mw for different Mw of 83.0% DD chitosans can be expressed by the equation Log Mw = −0.433 RVw + 11.66. The RVw of other DD chitosans do not correlate well with this equation. It indicated that DD of chitosan affected the relationship of RVw and Mw of chitosans studied. The Mark–Houwink constant a decreased from 0.715 to 0.521, as the solution ionic strength increased from 0.01M to 0.30M, whereas constant k increased from 5.48 × 10⁻⁴ to 2.04 × 10⁻³ over the same range of ionic strength solutions. The established RVw and Mw equation and [η] and Mw equation (Mark–Houwink equation) can be routinely used to determine the molecular weight from RVw or [η] of chitosan by HPSEC or by capillary viscometer, respectively, without the need of expensive instrumentation. © 1999 John Wiley & Sons, Inc. J Appl Polym Sci 71: 1905–1913, 1999     

Determination of solution viscosity characteristics of rubber seed oil based alkyds resins

Three medium oil alkyd samples of different oil length [(I) 45%, (II) 50%, and (III) 55%] were synthesized with rubber seed oil. Dilute solution viscosity measurements were carried out on the alkyd in acetone and in toluene. The parameters investigated include intrinsic viscosity [η], Huggins constant (k_H), and Mark‐Houwink Sakurada constants (κ and α). The [η] values for the alkyd samples were found to be larger in acetone than in toluene. The K_H values showed a regular order in acetone but not in toluene. The K_H values showed no regular order in their variation with the oil content of the alkyd samples and the solvent, but the values obtained are higher in acetone than in toluene. Correlation of molecular weight (M) with [η] was also examined. [η] was observed to increase with the increase in the molecular weight of the resins. The α values obtained are in reasonable agreement with the reported ranges of α values in good solvent. The characteristics examined suggest that acetone is a better solvent for rubber seed oil alkyd resin than toluene. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 101: 3073–3075, 2006     

Accurate description of intrinsic viscosity changes under polymer degradation: Narrow schulz distributions

For the Shulz distributions with weight—polydispersity from 1.4 to 2.0, the following equation is correct: ln [η] = ln [η]₀ ? a{ln P₀ + DD ? ln[P_F ? P₀) × exp(?1.2 × DD)]}. Here, P₀ and P_F are viscosity–polydispersities of the initial molecular weight distribution (MWD) and the Flory distribution, respectively; a is the Mark–Houwink exponent; and DD = ln(M_n0/M_n). For more narrow MWDs, the complicated equation is required: ln [η] = ln[η]₀ ? a{ln P₀ + DD ? ln[P_F ? (P_F ? P₀ × exp(?0.9 × DD ? 0.28 × DD²)]}. The inaccuracy of these equations is less than 1.5%. © 1995 John Wiley & Sons, Inc.     

Procedure for evaluation of the Mark–Houwink constants

An iterative procedure for evaluation of the Mark–Houwink constants, using the GPC universal calibration principle and the extended [η]–M relationship, is described. The procedure is recommended for newly prepared polymers of unknown average molecular weights. An example is given for bisphenol C-2 polycarbonate.     

Syntheses of poly[N-(2,2 dimethoxyethyl)-N-methyl acrylamide] for the immobilization of oligonucleotides

Radical-initiated polymerization of N-(2,2 dimethoxyethyl)-N-methylacrylamide has been carried out either in chloroform or methanol using 2,2′-azobisisobutyronitrile as an initiator, allowing us to prepare acetal containing water-soluble polymers. A kinetic study in both solvents showed that this monomer fairly homopolymerized (k_p · k_t^−1/2 = 1 mol^−1/2 L^1/2 s^−1/2). Static light scattering was used to characterize the molecular weight of these polymers. In addition, the Mark–Houwink–Sakurada relationship was established based on viscosity measurements performed at 25°C in water. Recovery of the aldehyde moieties on the polymer was achieved under mild conditions using a diluted inorganic solution. The analysis of the formation of aldehyde groups was performed by ¹H- and ¹³C-NMR. The covalent binding of oligodeoxyribonucleotides was carried out in water/acetonitrile mixtures with subsequent NaBH₄ reduction of the imine bonds so as to stabilize the polymer/oligodeoxynucleotide conjugates. © 1996 John Wiley & Sons, Inc.     

Synthesis and characterization of functional copolymer of Linalool and vinyl acetate: A kinetic study

Linalool (LIN) and vinyl acetate (VA) were copolymerized by benzoyl peroxide (BPO) in p‐xylene at 60°C for 90 min. The system follows nonideal kinetics: R_pα[I]^0.6[LIN]^1.2[VA]^1.1. It results in the formation of alternating copolymer as evidenced from reactivity ratios as r₁ (VA) = 0.01, r₂ (LIN) = 0.0015, which have been calculated by Kelen–Tudos method. The overall activation energy is 82 kJ/mol. The FTIR spectrum of the copolymer shows the presence of the band at 3425 cm^?1 due to alcoholic group of LIN and at 1641 cm^?1 due to >C?O group of VA. The ¹H‐NMR spectrum shows peaks at 7.0–7.7 δ due to hydroxy proton of LIN and at 1.0–1.4 δ due to acetoxy protons of VA. ¹³C‐NMR spectrum of copolymer shows peaks at 167 ppm due to acetoxy group and at 75–77 ppm due to C? OH group. The Alfrey–Price Q–e parameters for LIN has been calculated as Q₂ = 1.24 and e₂ = 3.11. The copolymer is highly thermally stable and has a glass transition temperature (T_g) of 85°C, evaluated from DSC studies. The mechanism of copolymerization has been elucidated. This article also reports measurement of Mark–Houwink constants in THF at 25°C by means of GPC as α = 0.8 and K = 3.0 × 10^?4 dl/g. The thermal decompositions of copolymer are established with the help of TGA technique. © 2004 Wiley Periodicals, Inc. J Appl Polym Sci 92: 1134–1143, 2004     

Preparation and characterization of melamine–formaldehyde–polyvinylpyrrolidone polymer resin for better industrial uses over melamine resins

Melamine–formaldehyde–polyvinylpyrrolidone (MFP) polymer resin was prepared with 1 : 16 : 1 ratios of melamine, formaldehyde (CH₂O), and polyvinylpyrrolidone amounts, respectively, by condensation polymerization at 6.9 pH. Structures were determined with IR, ¹H‐NMR, and ¹³C‐NMR spectroscopies. Chemical shifts (δ, ppm) were analyzed with singlet at δ 4.5, duplet from 3.13 to 3.17 and a quartet at 1.5 to 2.2 ppm for methylene (? CH₂? ) bridging group, pyrrolidone, and polyvinyl constituents. The 3389.25, 1290.38, and 1655.28 cm^?1 stretching frequencies of ? N?, ? CH? and ? C? O? O? groups, respectively, were noted on FTIR spectrum. The ? C?N? melamine units reacted with CH₂O to adjoin with polyvinylpyrrolidone (PVP). An average viscosity molecular weight ( _v) 57,000 g mol^?1 was obtained with Mark–Houwink–Sakurada equation. The chemical shift of ? N(CH₂O)₂? C? pyrrolidone ring on ¹³C‐NMR spectra was shifted toward lower magnetic field at 175.18 ppm. The resin was partially miscible with water thereby densities and viscosities of aqueous solutions were measured at 298.15 K temperature. It showed higher densities and viscosities than those of water. The resin developed exceptionally higher adhesive strengthen when its 62.29‐μm uniform thin film was applied on surfaces of wooden strips. The resin showed micellar behavior at about 0.009 g/100 mL aqueous solution. © 2009 Wiley Periodicals, Inc. J Appl Polym Sci, 2009     

Viscometric Behavior of Solution of Polyisobutylene in Hexane and Cyclohexane Solvents: Viscosity-Molecular Weight Relationships

The behavior of three different high molecular weight polyisobutylenes (PIB) in solutions of hexane and cyclohexane at 30°C has been investigated by viscometry. Mark–Houwink relations have been examined, the polymer–solvent interaction is discussed in terms of the calculated Huggins constant, k; parameter a of the Mark–Houwink equation; and equivalent hydrodynamic volumes V _e. The molecular weights of the three sample of polyisobutylene are remarkably well fitted with the intrinsic viscosity data.