SynopsisIn this article it is shown that the relaxation time spectrum can be analytically related to the molecular weight distribution regarding a recently derived generalized mixing rule. This analytical relation greatly reduces the computational effort to determine the molecular weight distribution from the relaxation time spectrum. In this mixing rule a generalized mixing parameter ␤ has been introduced. This parameter has been controversially discussed in the literature. The value of ␤ has been determined theoretically by Doi and Edwards ͓The Theory of Polymer Dynamics ͑Clarendon, Oxford, 1986͔͒ as ␤ ϭ 1 and Des Cloizeaux ͓Europhys. Lett. 5, 437-442 ͑1988͒; 6, 475 ͑1988͔͒ and Tsenoglou ͓Polym. Prepr. ͑Am. Chem. Soc. Div. Polym. Chem.͒ 28, 185-186 ͑1987͔͒ (␤ ϭ 2) and experimentally by Maier et al. ͓J. Rheol. 42, 1153-1173 ͑1998͔͒ ( ␤ ϭ 3.84). In this article the influence of ␤ on shape and position of peaks in bimodal molecular weight distributions is emphasized. FIG. 4. Peak positions in dependence of ␤: MWD of a binary PS mixture with 20% of PS60 and 80% of PS177 obtained with SEC is shown. The dashed lines indicate the positions of the peaks M max , which correspond to the different values of the generalized mixing parameter ␤ ͓M max given in ϫ10 4 ͑g/mol͔͒.

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Based on a recently introduced generalized mixing rule, which contains the results of the reptation and double reptation model as special cases, it is possible to determine the molecular weight distribution (MWD) from rheological data. By evaluating data from bimodal PS-mixtures Maier et al. (1998) have shown how the MWD can be estimated from the relaxation shear modulus, G(t), using an inversion method. Thimm et al. (1999) derived an analytical relation between the relaxation time spectrum and the MWD, which is able to reproduce the result of Maier et al. (1998) with less computational effort. In this article we compare both methods by evaluating data from three different series of polymer mixtures: Polystyrene (PS), Polymethylmethacrylate (PMMA) and isotactic Polypropylene (iPP). We compare the MWD obtained from rheological data with results from size exclusion chromatography (SEC) and discuss differences.

SynopsisIn this paper, a model is proposed for the kernel in the generalized mixing rule recently formulated by Anderssen and Mead (1998). In order to derive such a model, it is necessary to take account of the rheological significance of the kernel in terms of the relaxation behaviour of the individual polymers involved. This leads naturally to consider a way how additional physical effects, which depend on the molecular weight distribution, can be included in the mixing rule. The advantage of this approach is that, without changing the generality derived by Anderssen and Mead (1998), the choice of the model proposed here for the kernel guarantees the enhanced physical and rheological significance of their mixing rule.

This paper proposes a new induction heating (IH) coil using Halbach-arranged coils for cooktop. In general, a control inverter is placed on the back side of the coil, but by using the Halbach array coils, magnetic flux leakage to the back of the coil can be prevented without using a ferrite cores for magnetic shielding. Further, the magnetic flux can be concentratedly linked to the pot. First, differences and advantages of the magnetic flux distribution between the conventional IH-coil and the proposed IH-coil will be described based on electromagnetic field analysis. Next, the results of verification of the effect of the Halbach array coil via the prototype for principle verification are demonstrated.