Filled polymers fitting experimental data

A6.4.5 Fitting Experimental Data for Filled Polymer Systems... 

Fitting experimental data with the above model is not straightforward and requires both an extanded set of data and the appropriate fitting strategy, as demonstrated below with shear viscosity data on a series of Ti02 filled polystyrene at 180°C, as published by Minagawa and White [/. Appl. Polym. Sci, 20,501-523,1976]. 

Figure 2.14 The relative shear modulus, G> = G/GN, of an HEUR gel filled with polyethylmethacrylate particles. GN = 0.4 kPa. Experimental points are shown with the curves calculated for a non-interactive and an interactive filler. The amount of adsorbed polymer, T = 78g/kg offiller, gave a good fit to the experimental data...

PVT measurements The PVT apparatus from Gnomix Research was described in detail elsewhere. The sample cell was filled with approximately 1 g polymer and mercury. The cell was closed on one end by a flexible bellows and the expansion was measured with changing temperature in order to determine the volume. In the isothermal mode volume measurements were carried out at fixed pressure intervals (10 MPa) in the range from 0 to 200 MPa. The process was repeated for temperature intervals of approximately 10 C. In order to obtain the characteristic or hard core parameteis P, Vj and T, the experimental data were fitted to Flory s equation-of-state (EOS) by using a nonlinear least squares fit... 

Fig. 62. Normal force response in step to zero type of deformation history for a PMMA polymer glass, showing the comparison between the experimental data (filled squares), the K-BKZ model predictions (crosses), and the predictions (filled circles) from the Zapas strain-clock model (118). Note that the clock terms for the normal force response were determined by fitting the shear stress response in the same experiment. After McKenna and Zapas (112).

Fig. 6 Representation of nucleation density N versus polymer concentration cp as determined from off-equilibrium filled symbols) and equilibrium empty symbols) experiments carried out under ambient conditions at low humidity right pointing triangles) and at high humidity left pointing triangles). The dotted and solid arrows indicate the experimental Ccriticai (solubility in chloroform) of about 25 =b 3% and 16 2% determined for less and more humid environments, respectively. Note that below these Ccriticai no structures could be detected experimentally. The lines represent the theoretical fits obtained using (2). The isolated line at high cp represents a fit for data points presented in Fig. 4f...

Nonnally the adjustable parameter m" taken as a constant should suffice for theoretical fit of the storage modulus versus frequency curves using Eq. (2.62). However, in certain cases such as in filled polymer melt systems, it becomes necessary [114] to assume m" as an adjustable variable dependent exclusively on the frequency in order to get a good theoretical fit of the experimental data. Shenoy and Saini [114] have chosen the following form based on the shape of the plot of m versus l/(i> ... 

A review is presented of the electrical properties of polymers filled with different types of conducting particles. Following a theoretical description of a general effective media equation, experimental conductivity-volume fraction data for thermoplastic filled with vanadium oxide particles as well as thermosetting polymer composites, were fitted to the equation. The calculated property-related parameters in the equation are discussed. Data are given for PVC, HDPE, LLDPE, LDPE, and epoxy resin. 12 refs. 

It has been remarked that time (frequency) - temperature reduced data on carbon black filled rubbers exhibit increased scatter compared to similar data on unfilled polymers. Payne (102) ascribes this to the effects of secondary aggregation. Possibly related to this are the recent observations of Adicoff and Lepie (174) who show that the WLF shift factors of filled rubbers giving the best fit are slightly different for the storage and loss moduli and that they are dependent on strain. Use of different shift factors for the various viscoelastic functions is not justified theoretically and choice of a single, mean ar-funetion is preferred as an approximation. The result, of course, is increased scatter of the experimental points of the master curve. This effect is small for carbon black... 

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