D. Göritz

The collapse transition of a single polymer chain in two and three dimensions: A Monte Carlo study

The collapse transition of a single polymer chain in two and three dimensions was studied using the bond‐fluctuation model. The obtained exponents ν of the scaling law 〈S2N〉∼N2ν agree with values proposed in the literature as well as above, at and below the Θ‐temperature TΘ. Transition curves and scaling analysis plots are presented. The scaling function α3SτN1/2 vs τN1/2 has a pronounced maximum before leveling off in the fully collapsed regime in accordance with the theory [α2S=〈S2N〉/〈S2N〉Θ, τ=‖(T−TΘ)/TΘ‖]. An analyzing of the subchain distances leads to disagreements with the blob model. The subchains are locally swollen for T≳TΘ and shrunken for T<TΘ. The probability distribution function of internal distances for T≥TΘ can be described by scaling functions of the form fs(x)∼xκs exp(−Dsxδs) for large x, x being the scaled distance. In contrast for T<TΘ none of these functions describe the data. The dynamic properties above TΘ are in agreement with the Rouse model, but below TΘ differences occur; the ce...

The double network, a model describing filled elastomers

Abstract The model presented here to describe the deformation behaviour of filled elastomers is based on the observation that deformation occurs inhomogeneously. As a result of extending a filled rubber, the filler particles become aligned in rows parallel to the stretching direction. The rows are connected to each other by strands emanating from the filler particles, forming a second network that is superimposed on the molecular network. The stress-strain behaviour can be described by writing the stress as a superposition of stresses of the individual networks, σ = (1 − Φ)σ1 + Φσ2. The parameter Ф gives the volume fraction of strands between the filler particles. Macroscopic properties such as stress-strain behaviour or stress-induced crystallization of filled elastomers are described well by this model.

Structure and swelling of end-linked model networks

In the framework of the three-dimensional bond-fluctuation model, the formation and swelling of end-linked monodisperse polymer networks is simulated. The kinetics of cross-linking show a cross-over from reaction controlled to diffusion-limited behaviour, depending on the reaction rate.On small scales the internal dimension of the resulting networks is ca. 1.3 while on large scales it adopts the dimension of 3. The cross-over between both regions can be interpreted as a back-folding mechanism leading to internal dimensions larger than 3 at intermediate scales. The same behaviour was previously obtained by simulating randomly cross-linked networks.In marked contrast to some theoretical models, the networks deform in a highly non-affine manner upon swelling. Small substructures swell much less than the whole sample as determined from the occupation density at the centre of the simulation lattice. More precisely, the swelling degree is a monotonically increasing function of the scale under consideration. This can be related to the unfolding of the network structure at scales much larger than a single precursor chain.

Surface structure of carbon black and reinforcement

From scanning tunneling microscopy (STM) and atomic force microscopy (AFM) measurements, it was found that the lateral dimensions of the nanocrystallites systematically decrease with decreasing diameter of the primary particles. Furthermore these experiments suggest that these nanocrystallites, unregularly tilted, form the rough surface of carbon blacks. Hence, the activity of carbon black is the result of the size of the nanocrystallites and the degree of disorder on the surface. Temperature treatments of carbon black lead to a continuous increase of the lateral dimensions of the crystallites and a steady decrease in roughness. In order to quantify the surface roughness small-angle X-ray scattering (SAXS) measurements, that spanned a large scattering vector range, were evaluated by a fractal analysis. The surface fractal dimensions systematically increased with rising activity of the carbon black. Reinforcement is discussed within the scope of interaction of network chains with the carbon black surface. For this purpose, the dependency of the Payne effect on temperature, prestrain and swelling is interpreted using an adsorption mechanism of network chains on the surface of the filler particles. This mechanism requires the existence of stable and unstable bonded chains. Only the weakly bonded chains seem to be responsible for the Payne effect.

Morphologie und mechanisches Verhalten von elastischen Hartfasern

ZusammenfassungMit der Methbde der Verstreckungskalorimetrie wird eine Erhöhung der Inneren Energie bei der Deformation von elastischen Hartfasern nachgewiesen. Die Zuordnung der Inneren Energieänderung zur Bildung von Oberflächen in der Probe ergibt einen Wert für die freie Oberflächenenergie von 145 erg/cm2. Diese Bildung von Oberflächen und deren Abbau beim Entlasten wird verantwortlich gemacht für den Rückstellmechanismus der elastischen Hartfasern, in Verbindung mit entropieelastischer Deformation der interlamellaren Bereiche.SummaryAn increase of internal energy during stretching of “elastic hard” polypropylene fibres can be measured by means of a deformation calorimeter. Comparing the change in internal energy with formation of the specific surface area yields a value of free surface energy σe = 145 erg/cm2. That formation of specific surface area and the decrease during unloading is responsible for the recovery mechanism of the “hard elastic” fibres. Additional there is a part originating in entropic change of interlamellar layers.

Comparison of topological properties between end-linked and statistically cross-linked polymer networks

This paper compares topological properties of computer-generated unimodal end-lined and statistically cross-linked polymer networks. The bond-fluctuation algorithm was used to obtain the different networks. The networks were analyzed by using knot theory. The results show that the average number of trapped entanglements increases linearly with the length of the subchains. The slope is about 2 times higher in the case of end-linked networks. Although the overall number of entanglements is higher in the end-linked case, swelling experiments reveal that the distribution of subchain lengths of statistically cross-linked networks produces inhomogeneities in the structure which lead to a stronger contribution than for the end-linked networks. A homogeneous mean-field ansatz for the influence of entanglements to the deformation modulus used by most theories therefore appears to be not applicable to statistically cross-linked networks.

3-D morphological characterization of carbon black aggregates using atomic force microscopy

We use atomic force microscopy (AFM) to characterize the structure of carbon black aggregates. From the images we determine the lateral sizes and the height of the aggregates and from this data we calculate the flatness index. The flatness indices reveal that aggregates generally exhibit anisotropy, in the form of a reduction of aggregate breadth, or flatness, in one direction. The flat sides tend to align preferentially along the plane of the substrate. The flatness index depends on the grade and is related to the turbulence of the flow of gases inside the reactor. The data on the flatness index are compared with similar data obtained from transmission electron microscopy (TEM) and compressed CDBP analysis.

A Monte Carlo study of the glass transition in three-dimensional polymer melts

Abstract The glass transition of densely packed linear polymer chains has been investigated by means of the three-dimensional bond-fluctuation model including van der Waals interaction and bond-length potential. The computer simulations presented here are based on different chain-lengths, cooling rates, and a wide range of temperatures. All monitored static and dynamic properties of the polymer melt change distinctly at one characteristic temperature, identified as Tg. Variations of the chain-length from 50 up to 200 monomers per chain yield nearly identical behavior, while an increase of the cooling rate from ΓQ = 2.7 × 10−8 MCS−1 (Monte Carlo steps) to infinity causes pronounced differences below Tg both in static and dynamic properties.

THE DISTRIBUTION FUNCTION OF INTERNAL DISTANCES OF A SINGLE POLYMER CHAIN WITH EXCLUDED VOLUME IN TWO AND THREE DIMENSIONS : A MONTE CARLO STUDY

The probability distribution functions Ps(r) of the distance r between the end points of subchains of a single excluded volume chain in two and three dimensions were studied using the bond‐fluctuation model. The index s refers to three principle cases. Case s=0: the subchain is identical to the whole chain. Case s=1: the subchain constitutes one extremity of the whole chain. Case s=2: the subchain belongs to the central part of the whole chain. It is shown that the data can be described by the functions fs(x)∼xθs for small x and fs(x)∼xκs exp(−Dsxδs) for large x, x being the scaled distance. All exponents θs, κs, and δs were calculated and compared with existing values in the literature. In two dimensions a crossover between θs and κs was detected whereas in three dimensions θs≂κs within statistical errors.

Messung der Volumenänderung beim uniaxialen Dehnen

ZusammenfassungEs wird ein Dehnungsdilatometer vorgestellt, das gleichzeitig die Messung der Kraft und der Volumenänderung einer Probe bei uniaxialer Dehnung ermöglicht. Die Proben befinden sich in einer gasgefüllten Meßzelle; Volumenänderungen werden über die Druckänderungen im Meßraum relativ zu einem Vergleichsvolumen registriert. Für vernetzte Elastomere findet man einen linearen Zusammenhang zwischen Volumenänderung und Dehnung in einem weiten Dehnungsbereich. Darüber hinaus kann die dehnungsinduzierte Kristallisation sicher verfolgt werden.Bei der Kaltverstreckung spiegeln sich der Hookesche und der nichtlineare Bereich in der Volumenmessung wider. Die Yieldspannung wird durch einen Kohäsionsbruchmechanismus, der vorwiegend zwischen Ketten in den amorphen Bereichen erfolgt, erklärt.SummaryA dilatometer is presented allowing the simultaneous recording of force and volume change during extension. The sample is strained in a gasfilled cylinder. Volume changes are detected by means of change of pressure in the cylinder, relative to a second cylinder which is connected to the first one by a differential manometer. In the case of crosslinked rubbers a linear relationship is found between volume change and strain in a broad range of elongation. For higher degrees of elongation strain-induced crystallisation can be measured.For colddrawing there is a correspondence for both Hookean and non-linear behaviour of stress-strain curves with the volume-strain diagrams. Yield stress can be explained by the mechanism of cohesive failure fracture (Kohäsionsbruch) of chains belonging to the amorphous regions.