A simple method of evaluating the complex moduli of polystyrene blends

Schausberger, A.

doi:10.1007/bf01358168

Cited by 35 publications

(14 citation statements)

References 17 publications

(21 reference statements)

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“…These results are similar to earlier studies of the linear viscoelasticity of bidisperse polymer melts [14][15][16][17][18][19][20][21]31]. In particular, the ratio of molecular weights used in this study is close to that of sample 41L/435L in the study by Struglinski and Graessley [21].…”

Section: Shear Stress Measurementssupporting

confidence: 91%

Stress optical measurement of the third normal stress difference in polymer melts under oscillatory shear

1990

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Results are reported for the dynamic moduli, G' and G", measured mechanically, and the dynamic third normal stress difference, measured optically, of a series bidisperse linear polymer melts under oscillatory shear. Nearly monodisperse hydrogenated polyisoprenes of molecular weights 53000 and 370000 were used to prepare blends with a volume fraction of long polymer, q~L, of 0.10, 0.20, 0.30, 0.50, and 0.75. The results demonstrate the applicability of birefringence measurements to solve the longstanding problem of measuring the third normal stress difference in oscillatory flow. The relationship between the third normal stress difference and the shear stress observed for these entangled polymer melts is in agreement with a widely predicted constitutive relationship: the relationship between the first normal stress difference and the shear stress is that of a simple fluid, and the second normal stress difference is proportional to the first. These results demonstrate the potential use of 1,3-birefringence to measure the third normal stress difference in oscillatory flow. Further, the general constitutive equation supported by the present results may be used to determine the dynamic moduli from the measured third normal stress difference in small amplitude oscillatory shear. Directions for future research, including the use of birefringence measurements to determine N 2 / N 1 in oscillatory shear, are described.

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Section: Shear Stress Measurementssupporting

confidence: 91%

Stress optical measurement of the third normal stress difference in polymer melts under oscillatory shear

1990

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“…(20) Starting from measured data G', G " the discrete relaxation spectrum will be calculated first and from that, the discrete retardation spectrum is obtained. Our method can be demonstrated on a blend o f two (21) monodisperse polystyrenes of different molecular weight using the published dynamic mechanical data of Schausberger et al [16,17] as shown in Fig. 1.…”

Section: Calculated Discrete Relaxation and Retardation Spectramentioning

confidence: 97%

Determination of discrete relaxation and retardation time spectra from dynamic mechanical data

1989

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A powerful but still easy to use technique is proposed for the processing and analysis of dynamic mechanical data. The experimentally determined dynamic moduli, G'(co) and G"(co), are converted into a discrete relaxation modulus G (t) and a discrete creep compliance J(t). The discrete spectra are valid in a time window which corresponds to the frequency window of the input data.A nonlinear regression simultaneously adjust the parameters gi, 2i, i= 1,2,•.. N, of the discrete spectrum to obtain a best fit of G', G", and it was found to be essential that both gi and 2i are freely adjustable. The number of relaxa-

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“…(6a) does not hold for the relaxation times, because the molecules of different lengths show mutual influences on their relaxation times [10]. However, this fact and the possibility that the exponent in eq.…”

Section: Relaxation Timesmentioning

confidence: 92%

“…co --* 0 where the symbol 2;r indicates the summation of the relaxation times weighted according to a special rule [10]. In the course ofthe present considerations no specification of this rule is required, as one may simply assume that all relaxation times of the standard, which consists of molecules of similar lengths only, are changed by virtually the same factor, and the rule of summation is not altered, when the standard is diluted.…”

Section: (5 A)mentioning

confidence: 98%

The role of short chain molecules for the rheology of polystyrene melts.

1987

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Abstract." The influence of short chain molecules (with M < M c ) on the rheology of the melts of binary blends of long and short chain polymers was studied. For this purpose, the complex moduli as functions of circular frequency were examined for these melts and also for melts of unblended long chain samples. For pertinent blending a set of standard polystyrenes with narrow molar mass distribution was used.The short chain component causes a typical diluent effect. This is clearly revealed from the lowering of the plateau modulus of the long chain component. This lowering is found to be proportional to the square of the weight fraction w2 of the long chain component, as theoretically predicted. The reduction of the relaxation times of the long chain molecules turns out to be proportional to w~ '8, when the influence of an increased contribution of chain ends to the free volume is separately taken into account according to the results of the first paper of this series. As the power of w2 in the latter relation is not critical, one can formulate equations for the first normal-stress coefficient and for the zero-shear viscosity as functions of w2M~.~, which merge into the respective M 6'8-and M34-1aws well-established for undiluted high polymers (w2 = 1).

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A simple method of evaluating the complex moduli of polystyrene blends

Cited by 35 publications

References 17 publications

Stress optical measurement of the third normal stress difference in polymer melts under oscillatory shear

Stress optical measurement of the third normal stress difference in polymer melts under oscillatory shear

Determination of discrete relaxation and retardation time spectra from dynamic mechanical data

The role of short chain molecules for the rheology of polystyrene melts.

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