Conditions under which a natural iterative method for calculating the orientation distribution of rodlike particles decreases the free energy at each step,Physical Chemistry Chemical Physics

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Conditions under which a natural iterative method for calculating the orientation distribution of rodlike particles decreases the free energy at each step
Physical Chemistry Chemical Physics ( IF 2.9 ) Pub Date : 2024-08-27 , DOI: 10.1039/d4cp02217c
Alan E Berger ₁

Affiliation

It is shown that under certain conditions the iterative method suggested by the calculus of variations for calculating a cylindrically symmetric orientation distribution function (ODF) for rodlike particles strictly decreases the free energy at each full step. This monotonic behavior has strong implications for convergence of the sequence, or a subsequence, of the calculated ODFs. The result is valid not only for the reference system of hard core particles with indistinguishable ends, but also for free energy functions of similar type. The effect of an applied field is also permitted. Since the behavior of the iteration is intrinsic to the general form of the free energy function it applies to rod mixtures and may extend to a wider class of free energy functions. Outside the conditions that guarantee a monotonically decreasing free energy, we find that the iteration can fail to converge.

中文翻译：

用于计算棒状粒子取向分布的自然迭代方法在每一步减少自由能的条件

结果表明，在某些条件下，由变分法提出的用于计算棒状粒子的柱对称取向分布函数（ODF）的迭代方法会严格降低每个完整步骤的自由能。这种单调行为对于计算的 ODF 的序列或子序列的收敛具有很强的影响。该结果不仅对于具有不可区分末端的硬核颗粒参考系有效，而且对于类似类型的自由能函数也有效。应用场的影响也是允许的。由于迭代的行为是自由能函数的一般形式所固有的，因此它适用于杆混合物，并且可以扩展到更广泛的自由能函数类别。在保证自由能单调递减的条件之外，我们发现迭代可能无法收敛。

更新日期：2024-08-27

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