Ole Kramer

Towards a phenomenological definition of the term ‘gel’

Abstract The term ‘gel’ is used so indiscriminately that it has become ambiguous. Existing definitions are reviewed, examples of unfortunate uses of the term are discussed, and important phenomenological characteristics of gels are identified. We propose that the term ‘gel’ should be limited to systems which fulfil the following phenomenological characteristics: (a) they consist of two or more components one of which is a liquid, present in substantial quantity and (b) they are soft, solid, or solid-like materials. We further propose a definition of the solid-like characteristics of gels in terms of the dynamic mechanical properties, viz. a storage modulus, G′(ω), which exhibits a pronounced plateau extending to times at least of the order of seconds and a loss modulus, G″(ω), which is considerably smaller thatn the storage modulus in the plateau region.

Determination of polymer melt viscosity by squeezing flow with constant plate velocity

Abstract A universal rheometer which measures squeezing flow properties of liquids at constant plate velocity has been built. The smallest plate velocity is 0.5 μm s −1 and plate distance is determined with a precision of approximately 0.2 μm, allowing accurate squeezing flow measurements to be performed at plate distances down to approximately 20 μm. The squeezing flow properties of three different polymer melts with viscosities ranging from 127 to 28 000 Pa s were measured at 25°C. Normal stress effects are found to contribute significantly to the squeezing force for polymer melts with typical melt viscosities of about 10 4 Pa s except at very small plate distances. A simple correction for normal stress effects gives promising results but the corrected Newtonian melt viscosities are slightly lower than the steady shear viscosities measured with cone-and-plate on a rotational instrument. The corrected melt viscosity of silicone elastomer SE-30 determined by squeezing flow in the non-Newtonian region is also somewhat lower than the dynamic viscosity η* obtained from oscillatory measurements, in disagreement with the Cox-Merz Rule. The effects of plate velocity, excess material and non-parallel plates were studied experimentally.

Nonlinear Stress Relaxation of Polyisobutylene in Simple Extension

Relaxation of stress in simple extension of polyisobutylene (viscosity‐average molecular weight 2.3×106) has been measured at stretch ratios (λ) up to about 2. Data at 3, 25, and 50°C were reduced to 25°C. At any instant of reduced time, the dependence of stress on λ could be described by the Mooney‐Rivlin equation; the coefficients C1 and C2 were obtained from two linear plotting procedures. At short times, C1 decreased rapidly while C2 remained essentially constant. Two to three logarithmic decades of time later, C2 decreased. Thus, the terminal zone of viscoelastic behavior corresponds solely to the C2 contribution. This result confirms measurements by Arai and Niinomi (Kogyo Kagaku Zasshi, 74, 2525 (1971)) on polyisoprene and styrene‐butadiene rubber and measurements by Noordermeer and Ferry (J. Polym. Sci., (1976), in press) on 1,2‐polybutadiene. Tentative interpretations in terms of motions of entanglements are discussed. Similar measurements on a sample of polyisobutylene which had been heated with...

Dynamic Mechanical Properties

Publisher Summary This chapter focuses on various dynamic mechanical properties and viscoelastic functions. Rubber is frequently used for applications in which it undergoes rapid cyclic deformations at a certain frequency or over a range of frequencies. The dynamic mechanical properties are strongly dependent on temperature, frequency, the presence of fillers, and the extent of deformation if it is large. For very small deformations, the properties are found to be independent of the magnitude of the deformation (linear viscoelasticity), and temperature–frequency superposition can be applied in many cases, a feature that greatly facilitates obtaining or predicting the dynamic response over a wide frequency range. It is important to note that the dynamic mechanical properties of different unfilled amorphous elastomers are quite similar when the proper reference state is used. Dynamic mechanical properties refer generally to responses to periodically varying strains or stresses. They are most simply defined for a small sinusoidally varying strain or stress for which the response is a small sinusoidally varying stress or strain, respectively, with the same frequency but generally out of phase.

Contribution of entanglements to rubber elasticity

Abstract Uncrosslinked polymers show rubber-like properties above the glass transition temperature and at times short enough to prevent flow. This effect is thought to be due to a temporary entanglement network. Several studies indicate large entanglement contributions to the equilibrium elastic modulus of crosslinked networks. Three methods are discussed in greater detail: stoichiometric crosslinking with a suitable peroxide, the Langley method, and the two-network method. The two latter methods give equilibrium entanglement modulus contributions which are equal to the pseudo-equilibrium modulus of the uncrosslinked polymer. They also indicate that the entanglement contribution to the stress is responsible for departures from neo-Hookean behaviour observed in simpler extension.

A direct experimental determination of the elastic contribution of chain entangling in a tightly cross‐linked elastomer

A polybutadiene with a 88% vinyl‐content was studied in order to confirm previous results of the Langley and two‐network methods.(AIP)

A non-rotational universal rheometer. Part II. Experimental procedures and results

Abstract Stress-strain, stress relaxation, creep, dynamic mechanical and squeezing flow measurements are performed on different solids and liquids to demonstrate the capabilities of the new instrument. The modulus of steel determined by stress-strain and dynamic mechanical measurements is 2·007 × 10 11 Pa with a precision of about 0·1%. The limiting factors in the determination of modulus are therefore sample preparation and determination of sample dimensions. Compression of a vertical cylinder is used for the determination of the modulus of rubber but simple compression is obtained only when the end surfaces of the cylinder are lubricated. Steady-state and dynamic viscosity on low to medium viscosity liquids are measured with the annular pumping geometry. The instrument is very good for stress relaxation measurements and less good for creep measurements. For dynamic mechanical measurements, the accuracy of the phase angle is approximately 0·2 degrees for frequencies below 0·1 rad/s, decreasing to about 1 degree at the highest possible frequency of 1 rad/s. Squeezing flow is used for the determination of polymer melt viscosity.

A non-rotational universal rheometer: Part I. description of instrument

Abstract A small-size universal rheometer which operates exclusively by axial motion of the sample holders has been built. The force transducer is a digital balance and the displacement transducer is a micropositioner which both produces and measures the displacement. The digital balance is extremely accurate (1 in 105) but it has a slow response. The micropositioner has a total travel of 25mm with a precision of about 0·2 μm. All the main types of rheological properties can be measured with the new rheometer, i.e. stress-strain, stress relaxation, creep and dynamic mechanical properties of solids; steady-state and dynamic viscosity of liquids of low and intermediate viscosity; and the viscosity of highly viscous polymer melts by squeezing flow. The computer programs used for controlling the instrument are written in the programming language TURBO PASCAL, making it easy to adapt the instrument to special applications. The simplicity and versatility of the instrument makes it particularly useful for applications in research and teaching.

A simple stress-strain and stress relaxation instrument for applications in teaching, research and quality control

Abstract A simple, small and accurate instrument for making stress-strain and stress relaxation measurements has been constructed. The instrument consists of an aluminum frame in which a micrometer screw is mounted as a displacement transducer and a standard digital balance is used as a very accurate force transducer. Stiff solids such as steel and hard plastics are measured in three-point bending while soft solids such as rubber and biological gels may be measured either in simple shear or in compression. The standard deviation for the determination of the modulus of steel is 0·5% for repeated measurements on the same sample. Stress relaxation with superimposed intermittent small strains may be used as a powerful research technique for studying structural changes in biological and synthetic networks.

An algorithm for fast determination of complex moduli

Traditionally, the complex modulus is determined by Fourier analysis of steady state oscillatory data. However, steady state is not obtained immediately and data from the first period of oscillation must therefore be discarded. In the present work a recursive analysis algorithm for the determination of complex moduli from oscillatory data of the first period, which includes a transient response alongside the steady state response, is derived. The algorithm is based on Boltzmann’s principle of superposition. At any given time, the analysis algorithm provides the best possible estimate of the complex modulus on the basis of the information available at that time, i.e., the stress and strain history. The analysis algorithm has been tested on simulated data from a mathematical model of an amorphous polymer. The tests show that the new analysis algorithm can determine the dynamic mechanical properties with very good accuracy from oscillatory data of the first period, where Fourier analysis fails. Thus, use of ...