INTERCONNECTION BETWEEN FREQUENCY-DOMAIN HAVRILIAK-NEGAMI AND TIME-DOMAIN KOHLRAUSCH-WILLIAMS-WATTS RELAXATION FUNCTIONS
INTERCONNECTION BETWEEN FREQUENCY-DOMAIN HAVRILIAK-NEGAMI AND TIME-DOMAIN KOHLRAUSCH-WILLIAMS-WATTS RELAXATION FUNCTIONS
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DOI：
10.1103/physrevb.47.125
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发表时间：
1993-01-01
影响因子：
3.7
通讯作者：
COLMENERO, J
中科院分区：
文献类型：
--
作者：
ALVAREZ, F;ALEGRIA, A;COLMENERO, J
近年来，Kohlrausch-Williams-Watts（KWW）和Havriliak-Negami（HN）弛豫函数被广泛用于描述玻璃形成液体和复杂体系的弛豫行为。HN松弛函数是频域函数，而KWW函数适用于时域。在以前的论文中，我们讨论了这两个功能之间的互连提出了一种方法，我们发现，在频域中的最佳HN描述对应于一个给定的KWW功能在时域中。从这项工作中，我们提出了几个经验关系，使我们能够确定对应于一组给定的KWW的HN参数。还概述了如何以相反的方式进行，即，以获得对应于频域中给定HN松弛函数的最佳KWW时域描述。这就是我们在这项工作中通过改变HN参数来寻找最佳KWW拟合的值。同样，我们可以对HN和KWW函数兼容的区域进行限制，因为它们可以通过选择正确的参数变化来同等地使用。这个过程的一个可靠的证实是，当考虑文献中报道的用于玻璃形成液体的α弛豫的HN参数时，它们的值直接落在这个区域上，在这里我们发现HN和KWW函数偏离较小。对于其他动力学过程，如聚合物的二次弛豫或聚合物共混物的α弛豫，所报道的HN参数表明，函数不能描述时间衰减行为。
The Kohlrausch-Williams-Watts (KWW) and the Havriliak-Negami (HN) relaxation functions have been widely used to describe the relaxation behavior of glass-forming liquids and complex systems over the last several years. The HN relaxation function is a frequency-domain function while the KWW function applies for the time domain. In a previous paper we discussed the interconnections between these two functions by presenting a method where we found that the best HN description in the frequency domain corresponds to a given KWW function in the time domain. From that work we proposed several empirical relationships that allow us to determine the HN parameters corresponding to a given set of KWW ones. It was also outlined how to proceed in the opposite way, i.e., to obtain the best KWW time-domain description corresponding to a given HN relaxation function in the frequency domain. This is what we develop in this work by varying the HN parameters in search of the values of the best KWW fits. Likewise we can put a limit to the region where the HN and the KWW functions are compatible in the sense that they can be equally used by just choosing the right parameter change. A confident confirmation of this procedure is that when the HN parameters reported in the literature for the a relaxation of glass-forming liquids are considered, their values fall directly upon this region, where we find that the HN and KWW functions deviate less. However, for other dynamical processes like secondary relaxations of polymers or the a relaxation of polymer blends the HN parameters reported indicate that a single KWW relaxation function is not able to describe the time-decay behavior.