Evans R, Henderson J R
H H Wills Physics Laboratory, University of Bristol, Bristol BS8 1TL, UK.
J Phys Condens Matter. 2009 Nov 25;21(47):474220. doi: 10.1088/0953-8984/21/47/474220. Epub 2009 Nov 5.
We investigate the intermediate-and longest-range decay of the total pair correlation function h(r) in model fluids where the inter-particle potential decays as -r(-6), as is appropriate to real fluids in which dispersion forces govern the attraction between particles. It is well-known that such interactions give rise to a term in q(3) in the expansion of [Formula: see text], the Fourier transform of the direct correlation function. Here we show that the presence of the r(-6) tail changes significantly the analytic structure of [Formula: see text] from that found in models where the inter-particle potential is short ranged. In particular the pure imaginary pole at q = iα(0), which generates monotonic-exponential decay of rh(r) in the short-ranged case, is replaced by a complex (pseudo-exponential) pole at q = iα(0)+α(1) whose real part α(1) is negative and generally very small in magnitude. Near the critical point α(1)∼-α(0)(2) and we show how classical Ornstein-Zernike behaviour of the pair correlation function is recovered on approaching the mean-field critical point. Explicit calculations, based on the random phase approximation, enable us to demonstrate the accuracy of asymptotic formulae for h(r) in all regions of the phase diagram and to determine a pseudo-Fisher-Widom (pFW) line. On the high density side of this line, intermediate-range decay of rh(r) is exponentially damped-oscillatory and the ultimate long-range decay is power-law, proportional to r(-6), whereas on the low density side this damped-oscillatory decay is sub-dominant to both monotonic-exponential and power-law decay. Earlier analyses did not identify the pseudo-exponential pole and therefore the existence of the pFW line. Our results enable us to write down the generic wetting potential for a 'real' fluid exhibiting both short-ranged and dispersion interactions. The monotonic-exponential decay of correlations associated with the pseudo-exponential pole introduces additional terms into the wetting potential that are important in determining the existence and order of wetting transitions.
我们研究了模型流体中总对关联函数(h(r))的中程和长程衰减，其中粒子间势以(-r^{-6})衰减，这适用于色散力主导粒子间吸引力的实际流体。众所周知，这种相互作用在直接关联函数的傅里叶变换([公式：见正文])的展开式中产生了一个(q^{3})项。在此我们表明，(r^{-6})尾的存在显著改变了([公式：见正文])的解析结构，与粒子间势为短程的模型中的情况不同。特别是，在短程情况下产生(rh(r))单调指数衰减的(q = i\alpha(0))处的纯虚极点，被(q = i\alpha(0)+\alpha(1))处的复（伪指数）极点所取代，其实部(\alpha(1))为负且大小通常非常小。在临界点附近(\alpha(1)\sim -\alpha(0)^{2})，我们展示了在接近平均场临界点时如何恢复对关联函数的经典奥恩斯坦 - 泽尼克行为。基于随机相位近似的显式计算，使我们能够证明相图所有区域中(h(r))渐近公式的准确性，并确定一条伪费希尔 - 威多姆（pFW）线。在这条线的高密度侧，(rh(r))的中程衰减是指数阻尼振荡的，最终的长程衰减是幂律的，与(r^{-6})成比例，而在低密度侧，这种阻尼振荡衰减相对于单调指数衰减和幂律衰减都是次要的。早期分析未识别出伪指数极点，因此也未发现pFW线的存在。我们的结果使我们能够写出具有短程和色散相互作用的“实际”流体的一般湿润势。与伪指数极点相关的关联的单调指数衰减在湿润势中引入了额外项，这些项对于确定湿润转变的存在和顺序很重要。
