Avoiding waviness of relaxation spectra

Spectra are material functions, whose different integral transforms yield the measurable rheological quantities in the linear viscoelastic regime. Therefore, their knowledge is of high fundamental interest. However, the calculation of spectra from experimental data is an ill-posed problem. Thus, it is hampered by the problem that a too low density of relaxation modes does not lead to a good description of the input data, while a higher one usually causes a wavy spectrum which cannot be interpreted. To overcome this problem, an additional criterion assuming only gradual changes in the spectrum is introduced allowing for an increase in mode density without an enhanced waviness of the spectrum. This is novel in comparison to previously published spectra algorithms and commercial software packages

On the Determination of the Enthalpy of Fusion of α‐Crystalline Isotactic Polypropylene Using Differential Scanning Calorimetry, X‐Ray Diffraction, and Fourier‐Transform Infrared Spectroscopy: An Old Story Revisited

The crystallinity determination of polymers using differential scanning calorimetry (DSC) is a standard procedure in industrial and university research. Its value strongly depends on the enthalpy of fusion, which cannot be determined directly using DSC, but must be calibrated using external methods such as X‐ray diffraction (XRD) or density measurements. In addition, the determination of the enthalpy or heat of fusion is not trivial and thus error‐prone; hence, values from 60 to 260 J g−1 are quoted for polypropylene in the literature. It is therefore of great relevance to devise a consistent method to determine the heat of fusion. To determine the heat of fusion for polypropylene, a sample set with a broad range of crystallinities is produced using cooling rates between 1 and ≈3500 K min−1. The melting enthalpy of the samples is determined using DSC measurements. The determination of the melting enthalpy based on XRD measurements is discussed in detail, validated using Fourier‐transform infrared spectroscopy (FTIR), and compared with values quoted in the open literature. Although two different approaches are used to determine the enthalpy of fusion, a value of 170 ± 3 J g−1 is determined

Molar mass and molecular weight determination of UHMWPE synthesized using a living homogenous catalyst

Understanding of the physical characteristics of a polymer requires molar mass determination. For the commercially available polymers, having average molar mass below 1 000 000 g/mol, chromatography is the method that is often applied to determine the molar mass and molar mass distribution. However, the application of conventional chromatography techniques for polymers having molar mass >1000 000 g/mol becomes very challenging, and often the results are disputed. In this article, melt rheometry based on the modulus model is utilized to measure the molar mass and polydispersity of ultra high-molecular-weight polyethylenes (UHMWPEs) having molar mass >1000 000 g/mol. Results are compared with the chromatography data of the same polymer samples and the boundary conditions where the chromatography technique fails, whereas the rheometry provides the desired information is discussed. The rheological method is based on converting the relaxation spectrum from the time domain to the molecular weight domain and then using a regularized integral inversion to recover the molecular weight distribution curve. The method is of relevance in determining very high molar masses (exceeding 3 000 000 g/mol) that cannot be ascertained conclusively with the existing chromatography techniques. For this study,UHMWPEs with various weight-average molar masses, where the number-average molar mass exceeds>1000 000 g/mol, are synthesized. Catalyst used for the synthesis is a living homogeneous catalyst system: MAO-activated bis(phenoxy imine) titanium dichloride. The rheological behavior of the thus synthesized nascent reactor powders confirms the disentangled state of the polymer that tends to entangle with time in mel

Characterization of branched ultrahigh molar mass polymers by asymmetrical flow field-flow fractionation and size exclusion chromatography

The molar mass distribution (MMD) of synthetic polymers is frequently analyzed by size exclusion chromatography (SEC) coupled to multi angle light scattering (MALS) detection. For ultrahigh molar mass (UHM) or branched polymers this method is not sufficient, because shear degradation and abnormal elution effects falsify the calculated molar mass distribution and information on branching. High temperatures above 130°C have to be applied for dissolution and separation of semi-crystalline materials like polyolefins which requires special hardware setups. Asymmetrical flow field-flow fractionation (AF4) offers the possibility to overcome some of the main problems of SEC due to the absence of an obstructing porous stationary phase. The SEC-separation mainly depends on the pore size distribution of the used column set. The analyte molecules can enter the pores of the stationary phase in dependence on their hydrodynamic volume. The archived separation is a result of the retention time of the analyte species inside SEC-column which depends on the accessibility of the pores, the residence time inside the pores and the diffusion ability of the analyte molecules. The elution order in SEC is typically from low to high hydrodynamic volume. On the contrary AF4 separates according to the diffusion coefficient of the analyte molecules as long as the chosen conditions support the normal FFF-separation mechanism. The separation takes place in an empty channel and is caused by a cross-flow field perpendicular to the solvent flow. The analyte molecules will arrange in different channel heights depending on the diffusion coefficients. The parabolic-shaped flow profile inside the channel leads to different elution velocities. The species with low hydrodynamic volume will elute first while the species with high hydrodynamic volume elute later. The AF4 can be performed at ambient or high temperature (AT-/HT-AF4). We have analyzed one low molar mass polyethylene sample and a number of narrow distributed polystyrene standards as reference materials with known structure by AT/HT-SEC and AT/HT-AF4. Low density polyethylenes as well as polypropylene and polybutadiene, containing high degrees of branching and high molar masses, have been analyzed with both methods. As in SEC the relationship between the radius of gyration (Rg) or the molar mass and the elution volume is curved up towards high elution volumes, a correct calculation of the MMD and the molar mass average or branching ratio is not possible using the data from the SEC measurements. In contrast to SEC, AF4 allows the precise determination of the MMD, the molar mass averages as well as the degree of branching because the molar mass vs. elution volume curve and the conformation plot is not falsified in this technique. In addition, higher molar masses can be detected using HT-AF4 due to the absence of significant shear degradation in the channel. As a result the average molar masses obtained from AF4 are higher compared to SEC. The analysis time in AF4 is comparable to that of SEC but the adjustable cross-flow program allows the user to influence the separation efficiency which is not possible in SEC without a costly change of the whole column combination. © 2011 Elsevier B.V.Articl

Thermorheological Behavior of Various Short- and Long-Chain Branched Polyethylenes and Their Correlations with the Molecular Structure

This paper deals with the characterization of a broad range of linear polyethylenes (PE) by means of thermorheology. It is demonstrated, in which way the thermorheological behavior can be related to the comonomer type and content of copolymers. In the first part of this paper, well-established analytical and theological methods are applied to distinguish linear and branched samples. The resolution limit of these methods is demonstrated by the investigation of a blend from a linear-low density PE (LLDPE) and a branched low density PE (LDPE). Special attention is paid to nuclear-magnetic resonance (NMR) spectroscopy in order to reliably determine the comonomer type and content of the samples chosen. The main focus of this paper lies on thermorheological investigations and correlations with the molecular structure. The comparatively high sensitivity of such investigations is highlighted: even small amounts of long-chain branches (LCB) are revealed. The activation energy (E-u) of linear samples increases with growing comonomer length and content, respectively. As such, thermorheology is demonstrated to be an interesting theological "tool" to get an insight into branching structures. Moreover, the experimental effort is relatively small as solely usual dynamic-mechanical experiments at different temperatures are required