Lennard-Jones液體中原子對的短時間動力學

Abstract

微觀的簡單液體系統中的原子對動力學可以用時變原子對分布函數和 平均 相對位移函數來描述。在本文中，我們利用等加速近似法求得上述 的兩個函數。並且用分子動力模擬的方法求這兩個函數。其中在等加速近 似法中，我們假設 粒子所受到的力是起始時的□力。 在等加速近似法中，時變原子對分布函數是一個由中心隨著平均相對位移 函數移動的高斯函數和起始機率密度函數相乘的函數。為了避免原子對互 相穿 過，我們把在等加速近似法中所得到的時變原子對分布函數中的起 始機率分布 函數改成起始時和時間等於ｔ時的機率分布函數的乘積的平 方根。 我們把平均相對位移函數展開成一個時間的級數，並且忽略時間四次方以 後的項。在這裡，我們把作用在原子上的力展開到位移的二次方。 在得到時變原子對分布函數和平均相對位移函數之後，我們利用在等加速 近似法下的時變原子對分布函數計算能量變動相關函數。我們不但在理論 計算 上發現能量變動相關函數有一個起伏而且在分子動力模擬上也有這 樣的起伏。 不過這兩個起伏發生在不同的時間。最後我們比較我們和 Skinner的模型。 The microscopic dynamics of an atomic pair in a simple liquid is described in terms of the time-dependent pair distribution function and the mean relative displacement function. We calculate these two functions under constant acceleration approximation (CAA), in which particles are assumed to be affected by the initial constant forces, and also calculate with molecular dynamics simulation. We derive the time- dependent pair distribution function under CAA. Under CAA, the time-dependent pair distribution function is a product of a Gaussian function with a propagating center according to the mean relative displacement function and the initial probability density. In order to prevent the two atoms of the pair penetrating through each other, we modify the time- dependent pair distribution function under CAA by replacing the initial probability distribution with the square root of the product of the probability distributions at initial and at time t. In expanding the mean relative displacement function as a time series, we get the exact formula up to the 4th order of time. In deriving the mean relative displacement function, we go beyond CAA and expand the force up to the second order of displacement. After deriving these two functions, we calculate the energy fluctuation correlation function based on the time-dependent pair distribution function under modified CAA. We find a bump in the energy fluctuation correlation function both in theoretical calculation and from molecular dynamics simulation; however, at different times. We also compare our result with that based on Skinner's model.