Wilemski Gerald, Li Jin-Song
Department of Physics and Cloud and Aerosol Sciences Laboratory, University of Missouri-Rolla, Rolla, MO 65409-0640, USA.
J Chem Phys. 2004 Oct 22;121(16):7821-8. doi: 10.1063/1.1801273.
We investigate the diverging size of the critical nucleus near the spinodal using the gradient theory (GT) of van der Waals and Cahn and Hilliard and mean field density functional theory (MFDFT). As is well known, GT predicts that at the spinodal the free energy barrier to nucleation vanishes while the radius of the critical fluctuation diverges. We show numerically that the scaling behavior found by Cahn and Hilliard for these quantities holds quantitatively for both GT and MFDFT. We also show that the excess number of molecules Deltag satisfies Cahn-Hilliard scaling near the spinodal and is consistent with the nucleation theorem. From the latter result, it is clear that the divergence of Deltag is due to the divergence of the mean field isothermal compressibility of the fluid at the spinodal. Finally, we develop a Ginzburg criterion for the validity of the mean field scaling relations. For real fluids with short-range attractive interactions, the near-spinodal scaling behavior occurs in a fluctuation dominated regime for which the mean field theory is invalid. Based on the nucleation theorem and on Wang's treatment of fluctuations near the spinodal in polymer blends, we infer a finite size for the critical nucleus at the pseudospinodal identified by Wang.
我们使用范德瓦尔斯、卡恩和希利厄德的梯度理论（GT）以及平均场密度泛函理论（MFDFT）来研究旋节线附近临界核的发散尺寸。众所周知，GT预测在旋节线处成核的自由能垒消失，而临界涨落的半径发散。我们通过数值计算表明，卡恩和希利厄德发现的这些量的标度行为对于GT和MFDFT在定量上都成立。我们还表明，分子过剩数Δg在旋节线附近满足卡恩 - 希利厄德标度，并且与成核定理一致。从后一个结果可以清楚地看出，Δg的发散是由于流体在旋节线处平均场等温压缩率的发散。最后，我们为平均场标度关系的有效性建立了一个金兹堡判据。对于具有短程吸引相互作用的实际流体，近旋节线标度行为发生在涨落主导的区域，对于该区域平均场理论是无效的。基于成核定理以及王对聚合物共混物中旋节线附近涨落的处理，我们推断出王所确定的伪旋节线处临界核的有限尺寸。
