Number‐average molecular weight of branched polymers from SEC with viscosity detection and universal calibration

BACKGROUND: Number‐average molecular weight, M?_n, is an important characteristic of synthetic polymers. One of the very few promising methods for its determination is size‐exclusion chromatography (SEC) using on‐line viscometric detection and assuming the validity of the universal calibration concept. RESULTS: We have examined the applicability of this approach to the characterization of statistically branched polymers using 22 copolymers of styrene and divinylbenzene as well as 3 homopolymers of divinylbenzene with various degrees of branching. SEC with three on‐line detectors, i.e. concentration, light scattering and viscosity, enables us to evaluate experimental data by various computational procedures yielding M?_n and weight‐average molecular weight, M?_w. Analysis of the results has shown that the universal calibration theorem has limited validity, apparently due to the dependence of the Flory viscosity function on the molecular shape, the molecular weight distribution and the expansion of molecules. CONCLUSION: For complex polymers, the universal calibration, i.e. the dependence of the product of intrinsic viscosity and molecular weight, [η]M, on elution volume, can differ in values of [η]M from those obtained for narrow molecular weight standards by 10–15%. The method studied is helpful for the determination of M?_n of polymers, in particular of those with very broad molecular weight distribution, such as statistically highly branched polymers. Copyright © 2008 Society of Chemical Industry     

Polymer rheology: Influence of molecular weight and polydispersity

Literature data on the non-Newtonian flow of bulk polymer and of polymer solutions are correlated on the basis of a four-parameter equation, η = η_∞ + (η₀ ? η_∞)/[1 + (τD)^m], η being the viscosity at shear rate D, and η₀ and η_∞ limiting values at D = 0 and D = ∞, respectively. The parameters η₀, η_∞, and τ all show dependence on molecular weight, and in general there is good correlation between τ and η₀. There is evidence that τ is related to a molecular weight higher than the weight-average. The exponent m shows dependence on molecular weight distribution and approaches an upper limit of unity for a monodisperse linear polymer. For linear unblended polymers it may be expressed empirically by m = (M?_n/M?_w)^1/5.     

Synthesis and characterization of BDSDA/APB polyimide

A novel linear aromatic polyphenylene ethersulfideimide (BDSDA/APB) has been synthesized. Its physical, mechanical, thermal, and flow properties and its resistance to some of the more commonly used solvents were determined. The results of these property evaluations indicate this polymer system can be processed via conventional thermoplastic techniques. It has been molded, used as a resin, and cast into thin films and, accordingly, may have a wide variety of applications. Its molecular weight was varied by endcapping with phthalic anhydride. Over the M?_n range 14,000–45,000 the apparent viscosities and G_Ic values varied only slightly. However, a change in M?_n from 14,000 to 8700 resulted in a dramatic decrease in the apparent viscosity at both 250°C and 280°C. The G_Ic values for these same molecular weight materials decreased in a like manner as the M?_n decreased, indicating tradeoffs can be made between process optimization and final mechanical properties when polymer systems are developed.     

SEC–viscometer detector systems. I. Calibration and determination of mark–houwink constants

Five different types of calibration curve currently used in size exclusion chromatography-differential viscometer (SEC–DV) systems were identified and their use summarized. A simple method of deriving weighting factors for fitting local intrinsic viscosity calibration curves was shown to greatly improve the precision of calculated molecular weight distributions. The problem of reliably extrapolating the fitted curves to allow for differences in sensitivity among detectors has yet to be examined. With regard to Mark—Houwink constants, a method of fitting data from the SEC–DV system to obtain more statistically sound values was derived. For the data used here, the new method involves fitting a plot of logarithm of the local intrinsic viscosity of the sample vs. logarithm of the universal calibration curve parameter, J_i. Results for the data obtained appeared only slightly more precise than those for the traditional method. However, the new method promises improved reliability. © 1993 John Wiley & Sons, Inc.     

Solution properties of poly(fluorostyrene-co-chlorostyrene) copolymers. I. Light scattering,differential refractometry and viscometry

The weight-average molecular weights (M?_w) of nominally random, unfractionated copolymers of ortho- and para-fluorostyrene and ortho- and para-chlorostyrene were determined by light scattering measurements in tetrahydro-furan, toluene, carbon tetrachloride and chloroform. It was shown that there is no significant variation in measured M?_w in the various solvents, a finding indicating that the copolymers are not compositionally heterogeneous. Intrinsic viscosity measurements in the same solvents established a consistent relationship between [n] and M?_w despite the differences in copolymer compositions. It was not possible to establish a similar relationship between the second virial coefficient A₂ and M?_w. It was concluded that measurements of the specific refractive index increment could be used for determining copolymer composition if the measurements were performed in thermodynamically poorer solvents. The results established for the Mark-Houwink constant α, intrinsic viscosity, and A₂ values indicated that these solvated copolymer molecules are in a less expanded conformation than are polystyrene molecules of similar molecular weights in a given solvent.     

Evaluation of light-scattering detectors for size exclusion chromatography. I. Instrument precision and accuracy

A systematic evaluation of two types of light-scattering detectors for size exclusion chromatography (SEC) was completed. The two detectors were the low-angle laser light scattering photometer (LALLS) and the multiangle laser light-scattering photometer (MALLS). Instrument evaluations were performed at both room (30–40°C) and high (135–145°C) temperatures using the polystyrene standard, NBS 706, at room temperature and the polyethylene standard, SRM 1476, at high temperature. Results of the evaluation showed that when experimental uncertainties were taken into account LALLS and MALLS demonstrated equivalent precision and accuracy for molecular weight determination. The main source of inaccuracy found (particularly for SRM 1476) was the sensitivity difference between the light-scattering and the concentration (DRI) detectors; i.e., the DRI detector was unable to measure very low concentrations of very high molecular weight material present in SRM 1476, whereas the light-scattering detectors respond strongly. It was shown that for LALLS the overall weight-average molecular weight (M?_w) for the whole polymer calculated using an equation that did not require the DRI detector output circumvented this sensitivity problem while assuming that the low angle used was sufficiently close to zero. Use of this equation for MALLS is possible by extrapolating data from all angles used to obtain a light-scattering chromatogram at zero angle. However, this possibility was not examined here. A particular advantage of MALLS over LALLS is that MALLS can provide the z-average root mean square radius (commonly referred to here and in other light-scattering literature as the “radius of gyration”) values from the same data as those used to obtain molecular weight values. Although the radius of gyration values at each retention volume were not as precise as the corresponding weight-average molecular weights, at room temperature, precision was better than 2% for a significant portion of the chromatogram. © 1993 John Wiley & Sons, Inc.     

Network characteristics of homopolymer and some copolymers of poly(2-hydroxyethyl methacrylate)

Soluble poly(2-hydroxyethyl methacrylate) and copolymers of 2-hydroxyethyl methacrylate with n-butyl acrylate and 2-hydroxypropyl acrylate of varying compositions were synthesised by solution polymerisation. The polymers were characterised by dilute solution viscometry and shear viscosity. Crosslinked membranes were prepared from these polymers by introducing crosslinks in solution state through the reaction with 1,6-hexamethylene diisocyanate at a number of different crosslinker concentrations. The membranes swollen in dimethylformamide and water were characterised by performing equilibirium swelling measurements and calculating polymer volume fraction, the molecular mass between crosslinks (M?^c) and equilibrium water content (EWC) at 25°C. The calculation of M?^c used an expression developed by Peppas & Lucht for equilibrium swelling. This is a modified equation of the original Flory–Rehner expression, that allows non-Gaussian distribution of chain lengths. The variation of M?^c with crosslinker concentration and copolymer composition is discussed in terms of structural and molecular characteristics of these highly crosslinked networks.     

Basic dyeability and acid content of high-conversion polyacrylonitrile

Previous data have shown that the basic dyeability of acrylic polymers increases at a given specific viscosity as the peroxydisulfate-to-bisulfite ratio, that is, the catalyst-toactivator (C/A) ratio, is increased. This study represents an effort to understand better the role of the initiator system on the basic dyeability, the acid group composition, and the chain composition of acrylic polymers by preparing model polymers with radioactive initiators. As the C/A ratio is increased, the molecular weight distribution broadens as measured by the M?_v/M?_n ratio, the latter obtained by osmometry. There is also a significant effect of both C/A ratio and molecular weight on the sulfate group content per molecule, but there is no effect of C/A ratio on the number of basic dye sites per molecule, the number of sulfonate groups per molecule, or the weak acid groups per molecule. These effects can be explained by invoking a chain transfer to activator reaction in addition to the usual method of chain termination by recombination. The basic dyeability is found to correlate with the number-average molecular weight and with the number of strong acid groups plus the nonchromophoric weak acid groups.     

Effect of dispersity on the Tll (>Tg) transition in polystyrene

The presence of a high temperature (>T_g) relaxation in amorphous polystyrene has been investigated further. In the previous work,¹ the techniques of differential thermal analysis (DTA) and torsional braid analysis (TBA) were employed to study polystyrene as a function of “monodisperse” molecular weight. The occurrence of the T_ll transition appeared to be associated with the attainment of a critical viscosity level with also corresponded with a free volume level. An entanglement network developed at a critical value of molecular weight, M_c, giving a break in the T_ll-versus-M plots. The present work deals with the influence of dispersity on the T_ll transition, below and above M_c. A series of binary blends of “monodisperse” anionically polymerized polystyrenes with systematic changes in M?_n and heterogeneity index (M?_w/M?_n) was tested by TBA. The results show that when both components have molecular weights below M_c, single and average values of T_g and T_ll are observed which are linearly related to M?_n^?1, as predicted by free volume arguments. Although a single T_g is observed when one component has a molecular weight above and the other has a molecular weight below M_c, the components appear to undergo the T_ll relaxation independently. The results indicate that both the glass transition and the T_ll transition are basically governed by the same type of molecular motion but at different length ranges.     

Thermoplastic urethane elastomers. II. Effects of variations in hard-segment concentration

The dynamic mechanical properties of thermoplastic urethane elastomers have been charac-terized for polymers composed of varying hard-segment concentrations and for two different molecular weight polyester diols as soft segments. The urethane polymers based on an 830 M?_n polycaprolactone diol exhibited a progressive increase in glass transition temperature at increased levels of hard segments. In contrast, a similar series of polymers prepared with a 2100 M?_n polycaprolactone diol as the soft segment maintained a relatively constant glass transition temperature. These differences are attributed to the relative degree of phase separation between the constitutive blocks of the copolymer. The polymers of both series possessed two lower-temperature, secondary relaxations, which are ascribed to methylene sequence mobility within the polycaprolactone units and to possible disruption of interfacial associations between the hard- and soft-segment structures.     

Characterization of copolymers fractionated using supercritical fluids

In this study supercritical fluids were used to process several different types of oligomers. Supercritical fluid processing was found to be quite effective at removing low vapor pressure monomers from polymers and for fractionation of polymers according to molecular weight. This resulted in high purity materials with low M?_w/M?_n ratios. The polymer fractions obtained were analyzed by size exclusion chromatography, differential scanning calorimetry, and melt rheometry. Their physical and chemical properties are described.     

Estimation of long-chain branching in ethylene–propylene terpolymers from infinite-dilution viscoelastic properties

A method is outlined for estimation of small degrees of long-chain branching in polymers with moderately narrow molecular weight distribution (M?_w/M?_n <1.4). The storage and loss shear moduli, G′ and G″, are measured in dilute solution by the Birnboim-Schrag multiple-lumped resonator and extrapolated to infinite dilution, choosing a suitable solvent viscosity and frequency range such that the data lie in the terminal zone where G′ and G″ are proportional to the second and first powers of frequency, respectively. The intrinsic reduced steady-state shear compliance is determined from these data and corrected for moderate molecular weight heterogeneity (assuming a Gaussian distribution) from knowledge of M?_w/M?_n and the Mark-Houwink exponent a. The resulting value of S₂/S (where S₁ = Στ_p/τ₁, S₂ = Σ(τ_p/τ₁)², the τ_p's being the relaxation times and τ₁ the longest one) is compared with values calculated by the Zimm-Kilb theory as evaluated by Osaki for comb polymers of regular geometry and different numbers of branch points. The method has been illustrated by measurements on four ethylene–propylene copolymers. One containing no termonomer and one containing a saturated termonomer appeared to be linear; two containing unsaturated termonomers showed small degrees of branching. The method appears to be promising for detecting from one to four branch points per molecule.     

Silylation of water glass. IV. Synthesis and characterization of silylated silicic acids

Trimethylsilylated (TMSS) and dimethylphenylsilylated silicic acids (DMPS) were prepared via extraction with tetrahydrofuran, started from aqueous sodium silicate. Characterization of these silylates based on the ¹³C and ²⁹Si NMR spectra, X-ray diffraction, gel permeation chromatography, and solution viscosity were conducted to study their molecular structures. It was found that the GPC elution volume was significantly deviated from the calibration curve and also the exponents in solution viscosity vs. molecular weight (M?_n) relationship were very low, almost 0.3. These solution properties suggest that such silylates have compact spherical structures with a high degree of branching, also supported from the other data.     

Column fractionation of polymers. VII. Computer program for determination of molecular weight distributions from gel permeation chromatography

Gel permeation chromatography produces a type of differential molecular weight distribution directly and rapidly. Conversion of these data to conventional molecular weight distributions and plots of distributions is time-consuming. A computer program is described to perform these operations readily. Input data from the automated chromatograph, elution volume, and recorder deflection are converted to unit sensitivity and base line corrections applied. The curve is then numerically integrated and a calibration curve used to convert elution volumes into molecular weights. Various calibration curves can readily be introduced into the program. The output, in addition to tabulation of cumulative and differential molecular weight distributions, contains values of M?_n, M?_v, M?_w, M?_z, and M?_z+1. Importantly, a reduced absolute area, i. e., area computed for unit sensitivity on a unit concentration basis, is tabulated. An additional time-saving eature is the printing out of differential and cumulative molecular weight distribution curves and of a differential histogram.     

The effects of pressure and temperature upon the viscosities of liquids with special reference to polymeric liquids

From a consideration of the work required for expansion of a liquid, the following relationship between viscosity η, pressure P and temperature T is put forward. For unassociated liquids with molecules which are not too large, V* is taken as the parachor, log₁₀ (η* in Ns/m²) is ?3.88, P* is 8.58 × 10⁶ N/m², R is the gas constant, and T* is a constant characteristic of each liquid. The equation can be applied to polymeric liquids if V* and η* are taken as disposable constants. For example, for polystyrene V* is found to be 3 × 10^?3 m³ mol^?1 and log₁₀ (η* in Ns/m²) to be 3.4 log₁₀ M?_w ?10.2 where M?_w is the weight-average molecular weight (kg/mol) from 5 kg/mol upwards. In the equation, the same constants serve for the variation of viscosity with pressure and with temperature. The viscosity under a high pressure can therefore be estimated from viscosities all measured at normal pressures but at different temperatures. The viscosities of a number of polymers have been measured over a range of temperature and pressure and the results support the equation. Support is found for the view that segments are involved in the flow of polymeric liquids and V* gives a measure of the volume of the segment. The size of the segment seems to increase as the flexibility of the polymer chain decreases. The lowest values for V* are found for polysiloxanes in which the segment seems to be only four atoms long. Larger values of V* are found for polymers with units of the type –CH₂–CHR-. Larger values still of V* are given by polymers with units of the type –CH₂-CR₁R₂- and even larger V* values are found for those polymers with benzene rings constituting a major part of the main chain. As V* rises the viscosity of the polymeric liquid becomes much more dependent upon pressure and temperature. Thus whilst the polysiloxanes have viscosities which are relatively insensitive to pressure and temperature, the aromatic polysulphones and poly(2,6-dimethylphenylene oxide) have viscosities which are very sensitive to pressure and temperature.     

Influence of molecular weight and molecular weight distribution on the tensile properties of amorphous polymers

Tensile property data for polystyrene samples of varying polydispersity are correlated with various parametric measures of molecular weight. Traditional measures of molecular weight, such as M?_n, M?_w, and M?_z, are shown to be unable to account for the variation of tensile properties with molecular weight. However, a new molecular weight parameter, termed the failure property parameter, is able to provide a single relationship between tensile strength and the parameter for both the broad and narrow distribution polymers. The form of this parameter is consistent with its having origins in the view that it is the entanglement network in an amorphous polymer that provides the observed strength properties. Specifically for polystyrene, the failure property parameter results indicate that material below 60,000 molecular weight does not contribute to polymer strength. Although the results of this investigation are specifically for polystyrene, the arguments used to develop the failure property parameter are not dependent on polymer chemical structure. Consequently, we believe that both the concepts and definition of this new parameter are applicable to all amorphous polymers.     

Flow injection analysis estimation of diffusion coefficients of pauci- and polydisperse polymers such as polystyrene sulfonates

Flow injection analysis, often used for determination of diffusion coefficients of nonpolymeric substances, has now been applied to the characterization of pauci- and polydisperse polymers in solution. A relative method was found useful for obtaining moderate quality evaluations of diffusion coefficients and related parameters of polymers. The width at half-height W_1/2 of the trace peak is found to be proportional to the number average molecular weight M?_n of pauci- and polydisperse polymers, allowing estimation of M?_r and diffusion coefficients. For sodium polystyrene sulfonates at substantially infinite dilution in 1.0 g L^?1 Na₂SO₄, a linear relation has been observed between the logarithms of the molecular weight M?_n and the mean diffusion coefficient D in the M?_n range of 1000–90,000 g mol^?1 or the D range of 30 × 10^?7 to 2 × 10^?7 cm² s^?1.     

Influence of the degree of acetylation of o-cresol resin on its molecular conformation in solution

o-Cresol-formaldehyde resin (OC) and five kinds of acetylated OC (AC-X-OC; X is the degree of acetylation) were prepared. The Θ-temperature for each resin was determined by means of the Shultz-Flory method, and their molecular conformations in both tetrahydrofuran (THF) and Θ-solvent were estimated from the values of the exponents in the Mark–Houwink–Sakurada equations. The effect of the degree of acetylation on the exponent was negligible in THF, but was remarkable in Θ-solvent. In THF, the molecular chains of these resins are relatively extended, because the hydrogen bond between phenolic hydroxyl groups is loosely formed. In Θ-solvent, however, the molecular conformation is compact and the resins are considered to form a pseudo cross-linked network structure through inter- and/or intra-molecular hydrogen bonds. The Mark–Houwink–Sakurada equation for AC-100-OC in 2-ethoxyethanol at 92.0°C was found to be [η]_θ = 0.0773 M?^0.50_n, where [η]₀ is the limiting viscosity number under the Θ-condition, and M?_n is the number-average molecular weight. The unperturbed dimension, (〈r²₀〉/M?_n)^1/2, 〈r²₀〉 being the unperturbed mean square end-to-end distance, for AC-100-OC was found to be 0.659×10^?8 cm g^?1/2 mol^1/2.     

The Tll (>Tg) transition of atactic polystyrene

Torsional braid analysis (TBA) (～0.3 Hz) and differential thermal analysis (DTA) data are presented for the temperature for the region 0–200°C for two series of atactic polystyrenes with narrow molecular weight distributions: (a) anionic series, M?_n = 600–2×10⁶, M?_w/M?_n ? 1.1; (b) fractionated thermal series, M?_n = 2,000–1.1×10⁵, M?_w/M?_n < 1.25. Preliminary results on bimodal blends are also reported. Heating and cooling cycles were employed with TBA; only the heating mode was used with DTA. In addition to a dynamic mechanical loss peak at T_g, a higher temperature loss peak was also found. Designated the T_ll or liquid–liquid transition (relaxation), its temperature is 1.1 to 1.2 T_g (°K) for polymers with molecular weight below the critical molecular weight (M_c) for chain entanglements. Above M_c ? 35,000, it rises steeply, being ?200°C for M?_n = 110,000. The common dependence of T_g and T_ll on M?_n^?1 below M_c suggests a common molecular origin. The two facts, (a) that T_ll > T_g and (b) that T_ll reflects chain entanglements, further suggest that T_ll involves a longer chain segment length and possibly the entire molecule. Comparison of T_ll versus log M plots with T versus log M isoviscous state plots based on zero-shear melt viscosity data from the literature implies that T_ll measured by the TBA technique corresponds to an isoviscous state of 10⁴–10⁵ poises. The employment of narrow molecular weight polymers is presumably responsible for both the linear variation of the T_ll transition with M?_n^?1 (which suggests a free volume basis for the relaxation) and the form of the variation of the T_ll transition with log M (which suggests an isoviscous basis for the relaxation). The sharpness of the T_ll loss peak by TBA decreases with increasing molecular weight and dispersity. The DTA endothermic event corresponding to T_ll is clearly related to the occurrence of flow since the fused films which result from heating granules to 200°C and cooling to R.T. do not reveal a T_ll on reheating. If a fused film is crushed, a T_ll event is observed on heating. For bimodal blends with M?_n < M_c for both components, the T_ll transition was averaged; with one component less than and one greater than M_c, the T_ll transitions of the components appeared to occur independently at temperatures corresponding to those of the isolated components. In accordance with Ueberreiter and Orthmann, T_g appears to separate a glassy state from a fixed liquid state, whereas T_ll separates the fixed liquid from a true liquid state. Possible molecular interpretations for the T_ll process are discussed. Systematic bodies of data from the literature which indicate the presence of the T_ll process in other polymers are summarized.     

Cellulose degradation in xanthate process

Changes in degree of polymerization (DP) of cellulose during the viscose process were investigated by determining the number average molecular weight (M̄_n), weight average molecular weight (M̄_ω), and polydispersity (M̄_ω/M̄_n) giving molecular weight distribution (MWD). In general, a reduction in DP from the pulp stage to the final filament stage was noticed. Maximum degradation was observed to take place during xanthation and not during aging as sometimes claimed. Among the four methods used for gel permeation chromatography (GPC), Universal calibration HDV method, not involving viscosity measurement, gave the best and most reproducible values.