Prediction of melt rheological properties from GPC molecular weights

The SCLAIR^® solution polymerization platform produces a wide variety of ethylene-α-olefin copolymers and polyethylene homopolymers. Commercial products exhibit density and melt index values ranging from about 0.920 to 0.962 g/cm³ and 0.3–75 g/10 min respectively. Polymer molecular weight distributions can be tailored to meet a broad selection of end-use requirements. In this study, we have used a chemometric analysis approach using The Unscrambler^® software to demonstrate statistical correlations between rheological properties and fundamental structural parameters for thirty-three commercial SCLAIR polyethylenes. We demonstrate that molten rheological properties such as melt index, stress exponent, zero-shear viscosity, characteristic relaxation time, cross-over modulus and frequency show good non-linear correlations with molecular weight characteristics of SCLAIR products as determined by gel permeation chromatography (GPC). We also show that, with the use of Partial Least Squares (PLS) regression techniques, most melt rheological properties can be accurately predicted on the basis of GPC data.     

Ratios of average molecular weights and molecular weight distributions in polymers

If M_min and M_max are lower and upper bounds, respectively, to the molecular weights of different molecular weight species contained in a polymer, the weight-average to number-average molecular weight ratio M _w/M _n cannot exceed (1 + M_max/M_min)²/(4M_max/M_min). The ratio attains this maximum possible value if the masses of the two species with molecular weights M_min and M_max are equal and the masses of all the other species are negligibly small, corresponding to maximum spread in the molecular weight distribution within the specified bounds. Also for a given value of M _w/M _n = α, the M_max cannot be smaller than [2α ? 1 + 2α^1/2(α ? 1)^1/2]M_min. The minimum possible value of M_max/M_min consistent with α given is obtained in the case of maximum spread described above. If only one species is predominant, then both M _w/M _n and M_max/M_min approach unity, as is well known. Similar relations hold for the ratios of higher-order average molecular weights for which the role of the mass fractions is replaced by higher-order distribution functions.     

Determination of molecular-weight distribution and average molecular weights of block copolymers by gel-permeation chromatography

The problem of preparation of a block copolymer of precise molecular-weight distribution (MWD) and with heterogeneous composition on the basis of gel-permeation chromatography (GPC) data has been investigated. It has been shown that in MWD calculations the distribution f(p) of the composition p in individual GPC fractions should be taken into account. The type of the f(p) functions can be simultaneously established by an independent method, such as use of adsorption-column or thin-layer chromatography sensitive to the composition of the copolymer. It has also been shown that the actual f(p) may be replaced by a corresponding piecewise distribution, of simple form, without decrease in the precision of calculation of the MWD and average molecular weights of most known block copolymers.     

Quantitative determination of the average molecular weights of dextrans by diffusion ordered NMR spectroscopy

Diffusion ordered NMR (DOSY) was applied to the determination of the average molecular weights of polymers based on the dependence of the measured self-diffusion coefficient D on the corresponding weights of a number of polymers of the same type. As a rule, a calibration function is plotted by varying DOSY experimental parameters for each particular test sample; however, this approach is inapplicable to the development of a standard procedure for the quantitative assessment of the molecular weights of dextrans. In this article, an optimization method is considered to ensure high resolution in terms of the values of D for dextrans without varying experimental conditions; this method makes it possible to evaluate the average molecular weights of dextrans with a high accuracy over a wide range of their values.     

A new derivation of average molecular weights of nonlinear polymers.

A new method for calculating average molecular weights is presented for nonlinear polymers. In contrast to the previous methods of Flory and Stockmayer which first calculate the distribution of all species and then use the distributions to calculate average properties, the new method calculates these properties directly. In contrast to the method of Gordon, probability generating functions are not required. Starting with elementary probability and utilizing the recursive nature of network polymers property relations can be developed more simply. We illustrate the method for calculations of Mw Mz, and the gel point for a wide variety of polyfunctional polymerizations.     

Universal calibration in GPC: A new approach for the calculation of molecular weights

A method has been developed for determining simultaneously the molecular weight of a broad-distribution polymer and the Mark-Houwink coefficients for that polymer type by using only GPC and intrinsic viscosity data. Standardized samples of poly(vinyl chloride), polystyrene, polybutadiene, and an experimental cycloolefin polymer were analyzed by this method. Shear-corrected intrinsic viscosities were used in all cases because of the high molecular weights involved. Molecular weight data for all samples were found to be in good agreement with molecular weight data obtained by membrane osmometry and from other GPC techniques. The proposed technique provides a means for calculating the molecular weight of a single polymer sample through universal calibration of GPC without knowledge of the Mark-Houwink coefficients for that polymer type.     

Determination of the molecular weight of polyacrylamide fractions by osmometry

The polymerization of acrylamide, initiated with permanganate/oxalic acid, has been studied at 35 ± 0.2 in an aqueous medium under nitrogen. Samples of polyacrylamide were fractionated by the triangular fractionation method using methanol as non-solvent. Molecular weights of the fractions have been determined by viscometry and osmometry. Integral and differential distribution curves were plotted using the fractionation data. The narrow molecular weight distribution for high conversion polymers has been discussed. For fractionated samples of polyacrylamide in water at 30°, the equation $\text{[η]}{}_{\mathrm{ml/g}}\text{= 6.5 × 10}{}^{\mathrm{?3}}\text{M}{}_{\mathrm{n}}{}^{0.82}$ is applicable for the molecular weight range 4 × 10⁴ to 127 × 10⁴. This equation is very similar to the equation $\text{[η]}{}_{\mathrm{ml/g}}\text{= 6.31 × 10}{}^{\mathrm{?3}}\text{M}{}_{\mathrm{/}}{}^{0.80}$ of Scholtan. Other parameters (osmotic second virial coefficient and unperturbed dimension) have also been evaluated.     

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.     

Proton transport properties of poly(aspartic acid) with different average molecular weights

We synthesized seven partially protonated poly(aspartic acids)/sodium polyaspartates (P-Asp) with different average molecular weights to study their proton transport properties. The number-average degree of polymerization (DP) for each P-Asp was 30 (P-Asp30), 115 (P-Asp115), 140 (P-Asp140), 160 (P-Asp160), 185 (P-Asp185), 205 (P-Asp205), and 250 (P-Asp250). The proton conductivity depended on the number-average DP. The maximum and minimum proton conductivities under a relative humidity of 70% and 298 K were 1.7 · 10^?3 S cm^?1 (P-Asp140) and 4.6 · 10^?4 S cm^?1 (P-Asp250), respectively. Differential thermogravimetric analysis (TG-DTA) was carried out for each P-Asp. The results were classified into two categories. One exhibited two endothermic peaks between t = (270 and 300) °C, the other exhibited only one peak. The P-Asp group with two endothermic peaks exhibited high proton conductivity. The high proton conductivity is related to the stability of the polymer. The number-average molecular weight also contributed to the stability of the polymer.     

A study of the molecular weights of tetrahydrofuran–propylene oxide copolymers by gel permeation chromatography and other methods

The cationic copolymerization of tetrahydrofuran and propylene oxide was studied in a batch system. Boron fluoride ethyl ether and 1,2-propanediol were used as catalyst—co—catalyst system. Number-average molecular weights M?_n of various copolymers were determined by vapor-pressure osmometry (VPO) and hydroxyl endgroup analysis (OH). The VPO and OH molecular weights differed considerably. To explain the differences, several copolymers were analyzed by gel permeation chromatography (GPC). The chromatograms obtained showed for each copolymer analyzed two peaks, one located in the high molecular weight region, the other in the low molecular weight region. An attempt is made to correlate the results and to show the usefulness of GPC in the characterization of THF—PO copolymers.     

Thermodynamical properties and structural data of radicals calculated by MNDO–UHF

The MNDO –UHF method has been applied to a large number of organic and inorganic radical species. The obtained results demonstrate that thermodynamical data as well as their equilibrium structures are in reasonable agreement with experimental findings.     

Molecular weights and molecular weight distribution of polymers by equilibrium ultracentrifugation. Part I. Average molecular weights

From the sedimentation-diffusion equilibria of some polymer solutions the average molecular weights M?_n, M?_w, M?_z, and M?_z+1 have been determined in different ways. In particular, the applicability of Fujita's method, which utilizes concentration gradient values at the midpoint of the solution column at a number of rotor speeds, was examined. It appears that if the gradients at some other places in the column are also used, a smaller range of rotor speeds suffices. This method is generally applicable for determining the average molecular weights specified above.     

Polarization effects on peptide conformations at water–membrane interface by molecular dynamics simulation

The electrostatic image method was applied to investigate the conformation of peptides characterized by different hydrophobicities in a water–membrane interface model. The interface was represented by a surface of discontinuity between two media with different dielectric constants, taking into account the difference between the polarizabilities of the aqueous medium and the hydrocarbon one. The method consists of a substitution of the real problem, which involves the charges and the induced polarization at the surface of discontinuity, by a simpler problem formed with charges and their images. The electric field due to the polarization induced at the surface by charge q was calculated using a hypothetical charge q′ (image of q), symmetrically located on the opposite side of the surface. The value of q′ was determined using the appropriate electrostatic boundary conditions at the surface. By means of this procedure, the effect of the interface can be introduced easily in the usual force field. We included this extension in the computational package that we are developing for molecular dynamics simulations (Thor ). The peptides studied included hydrophilic tetraaspartic acid (Asp–Asp–Asp–Asp), tetralysine (Lys–Lys–Lys–Lys), hydrophobic tetrapeptide (His–Phe–Arg–Trp), an amphiphilic fragment of β-endorphin, and the signal sequence of the E. coli λ-receptor. The simulation results are in agreement with known experimental data regarding the behavior of peptides at the water–membrane interface. An analysis of the conformational dynamics of the signal sequence peptide at the interface was performed over the course of a few nanoseconds. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 971–982, 1999     

Heterochain model for simultaneous long‐chain branching and crosslinking. I. Matrix formula for the weight‐average molecular weights

The hetrochain model was applied to develop a matrix formula describing the weight‐average molecular weights for a reaction system that involves simultaneous long‐chain branching and crosslinking. The heterochain model describes the molecular architecture formed through the primary chain connection that follows the Markovian statistics; therefore, this matrix formula is valid regardless of the chemical and reactor systems used, as long as the Markovian nature is preserved for the chain‐connection statistics. Application to free‐radical (co)polymerization systems is described in subsequent research. The gel point is simply described as a point at which the largest eigenvalue of the matrix M , which defines the chain‐connection statistics, reaches unity. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 2780–2790, 2004     

Comparison of RHF,NDDO, and MOM molecular one-electron expectation values calculated using weighted and unweighted STO–NG (ω) basis functions

The effect of basis functions on molecular one-electron property expectation values calculated by approximate methods is examined using weighted and unweighted least-squares Gaussian-type orbital function expansions of Slater-type orbital functions.     

Analysis of the accuracy of determining average molecular weights of narrow polydispersity polymers by matrix-assisted laser desorption ionization time-of-flight mass spectrometry

Matrix-assisted laser desorption ionization time-of-flight mass spectrometry (MALDI-TOFMS) can be used to determine number- and weight-average molecular weights of narrow polydispersity polymers. In this work, several possible sources of error in determining molecular weights of polymers with narrow polydispersity by MALDI-TOFMS are rigorously examined. These include the change in polymer distribution function, broadening or narrowing of the overall distribution, and the truncation of selected oligomer peaks within a distribution (i.e., the oligomer peaks at the high-and low-mass tails expected to be observed are not detected). These variations could be brought about by a limited detection sensitivity, background interference, and/or mass discrimination of oligomer analysis in MALDI-TOFMS. For narrow polydispersity polystyrenes, it is shown that by using an appropriate MALDI matrix and sample preparation protocol and a sensitive ion detection instrument, no systematic errors from these possible variations were detected within the experimental precision (0.5% relative standard deviation) of the MALDI method. It is concluded that MALDI mass spectrometry can provide accurate molecular weight and molecular weight distribution information for narrow polydispersity polymers, at least for polystyrenes examined in this work. The implications of this finding for polymer analysis are discussed.     

Styrene‐vinyl pyridine diblock copolymers: Achieving high molecular weights by the combination of anionic and reversible addition–fragmentation chain transfer polymerizations

Anionic and reversible addition–fragmentation chain transfer (RAFT) polymerizations were combined for the preparation of high molecular weight (MW) amphiphilic diblock copolymers based on the hydrophobic styrene (Sty) and the more polar 2‐vinyl pyridine (2VPy) or 4‐vinyl pyridine (4VPy). In particular, four amphiphilic Sty‐VPy diblock copolymers with MWs up to 271,000 g mol^–1 were prepared. For the polymer synthesis, first, living anionic polymerization of Sty using sec‐butyl‐lithium as initiator in tetrahydrofuran at ?70 °C, followed by termination with ethylene oxide were employed for the preparation of OH‐functionalized homopolyStys. Subsequently, a modification of the OH‐terminal group was performed by the attachment of a 4‐cyanopentanoic acid dithiobenzoate chain transfer agent (CTA) group, giving a polySty macroRAFT CTA, which was extended with 2VPy or 4VPy units using RAFT polymerization. Thus, the prepared diblock copolymers comprised a first block which was near‐monodisperse in size, and a second more heterogeneous block. All diblock copolymers were characterized in terms of their MWs and compositions by gel permeation chromatography and ¹H NMR spectroscopy, respectively, giving results close to the theoretically expected values. Films cast from chloroform solutions of the diblock copolymers were investigated in terms of their bulk morphologies using transmission electron microscopy, which indicated that the minority block consistently formed the discontinuous microphase, spherical or cylindrical. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2013     

Studies of methyl methacrylate–glycidyl methacrylate copolymers: Copolymerization to low molecular weights and modification by ring-opening reaction of epoxy side groups

The copolymerization of methyl methacrylate (MMA) with glycidyl methacrylate (GMA) at 60°C with 2,2′-azobisisobutyronitrile (AIBN) as radical initiator and in the presence of thiophenol (TP) as chain-transfer agent has been investigated. Monomer reactivity ratios for MMA and GMA are found to be r₁ (MMA) = 0.80 ± 0.015 and r₂ (GMA) = 0.70 ± 0.015, from which Q and e values are calculated to be 0.68 and ?0.36 for GMA. The initial rate of copolymerization R_p at 60°C with AIBN (0.02 mole/l.) and TP (0.1, 0.01 mole/l.) were found to increase nonlinearly with increasing GMA concentration in the monomer feed. Homopolymerizations of MMA and GMA monomers were studied in the presence and in the absence of thiophenol. The values of δ (= k_t^1/2/k_p) for MMA and GMA were determined to be 10.25 and 3.00 (mole-sec/l.)^1/2, respectively. Using the values r₁ (MMA), r₂ (GMA), δ₁ (MMA), δ₂ (GMA), and R_p, the cross-termination constants ? for MMA–GMA monomers were determined (average value ? = 0.42). The increase in R_p values with increasing GMA content has been attributed to the cross-termination of MMA–GMA radicals. The transfer constant of TP has also been determined for GMA and found to be 1.00. A MMA–GMA copolymer of low molecular weight, containing 2.01% of oxirane oxygen, was modified by opening of the oxirane ring of GMA by reaction with diethanolamine (DEA). The reaction was carried out at 70 ± 1°C, the copolymer content of epoxy groups and the amine being assumed to be in the molar ratio of 1:4. Addition of a hydrogen-bond acceptor like nitrobenzene decreases, while addition of a hydrogen-bond donor like phenol increases the rate of epoxy ring opening with DEA. This indicates that a hydrogen-bonded intermediate is involved in this reaction and that it weakens the epoxy ring and enhances the rate of its opening with DEA. From the studies of the conversion rates, existence of a “nonspecific” side reaction has been shown which involves the reaction of the terminal epoxy groups of the copolymer and the hydroxyl groups of DEA or formed in the reaction with DEA (involves a chain coupling). DEA can be trifunctional in this reaction. This has been further confirmed from the increase of number-average molecular weights M?_n of the copolymers resulting from this coupling and the nitrogen content in the copolymers after modification with DEA.