Interplay of critical Casimir and dispersion forces.
Interplay of critical Casimir and dispersion forces.
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临界卡西米尔力和色散力的相互作用。
DOI：
10.1103/physreve.76.011121
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发表时间：
2007
期刊：
影响因子：
--
通讯作者：
S. Dietrich
中科院分区：
文献类型：
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作者：
D. Dantchev;F. Schlesener;S. Dietrich
利用一般的标度守恒量结合平均场理论，我们研究了厚度为L的流体薄膜中Casimir力的临界(T约为T_c)和非临界(T不等于T_c)行为，该流体薄膜受色散力和长程衬底电势控制，且薄膜两侧的势相等。我们研究了作用在约束衬底上的有效作用力作为T和化学势的函数的结果。我们发现，总力在T_c以下和T_c以上都是有吸引力的。然而，如果减去底物-底物的直接贡献，力在任何地方都是排斥的，除了在出现临界密度波动的整体临界点(TC，Mu(C))附近，或者除了在低温和(L/a)(β(Delta)(Mu))=O(1)，其中Delta(Mu)=Mu-Mu(C)<；0和流体分子之间的特征距离，即在毛细冷凝区域。在临界点附近，吸力的最大幅值约为L(-d)的数量级，在毛细冷凝区，力要大得多，最大幅值衰减为L(-1)。在后一种情况下，我们观察到，与仅具有短程相互作用的系统相比，流体-流体和衬底-流体相互作用的长程尾巴进一步增加了该振幅。尽管在临界区，系统渐近地属于具有短程作用力的伊辛普适性类，但我们发现，即使对于xi，L；>；xi0(+/-)，xi[t=(T-TC)/TC-->；+/-0，Delta(U)=0]=xi0(+/-)/t/-nu，也偏离了xi(Ln)(xi/xi0(+/-))>；L的标准有限尺寸标度。在这种情况下，对自由能和力的主要有限尺寸贡献来自相互作用的长程代数衰减尾；对于膜厚小于或近似等于Lcrit的薄膜，Lcrit=X0(+/-)(16/S/)nu/beta，nu和β是标准的体相临界指数，而S=O(1)是表征流体-流体相互作用中长尾相对强度的无量纲参数。我们给出了适用于这种情况的修正的有限尺寸标度，并详细分析了该区域的有限尺寸行为。仅恢复了L的标准有限尺寸标度行为。
Using general scaling arguments combined with mean-field theory we investigate the critical (T approximately Tc) and off-critical (T not equal Tc) behavior of the Casimir forces in fluid films of thickness L governed by dispersion forces and exposed to long-ranged substrate potentials which are taken to be equal on both sides of the film. We study the resulting effective force acting on the confining substrates as a function of T and of the chemical potential mu. We find that the total force is attractive both below and above Tc. If, however, the direct substrate-substrate contribution is subtracted, the force is repulsive everywhere except near the bulk critical point (Tc, mu(c)), where critical density fluctuations arise, or except at low temperatures and (L/a)(beta(Delta)(mu))=O(1), with Delta(mu)=mu-mu(c)<0 and a the characteristic distance between the molecules of the fluid, i.e., in the capillary condensation regime. While near the critical point the maximal amplitude of the attractive force if of order of L(-d) in the capillary condensation regime the force is much stronger with maximal amplitude decaying as L(-1). In the latter regime we observe that the long-ranged tails of the fluid-fluid and the substrate-fluid interactions further increase that amplitude in comparison with systems with short-range interactions only. Although in the critical region the system under consideration asymptotically belongs to the Ising universality class with short-ranged forces, we find deviations from the standard finite-size scaling for xi(ln)(xi/xi0(+/-)) >>L even for xi, L>>xi0(+/-), where xi[t=(T-Tc)/Tc-->+/-0,Delta(mu)=0]=xi0(+/-)/t/-nu, is the bulk correlation length. In this regime the dominant finite-size contributions to the free energy and to the force stem from the long-ranged algebraically decaying tails of the interactions; they are not exponentially small in L, as it is the case there in systems governed by purely short-ranged interactions, but exhibit a power law decay in L. Essential deviations from the standard finite-size scaling behavior are observed also within the finite-size critical region L/xi=O(1) for films with thicknesses L less than or approximately equal Lcrit, where Lcrit=xi0(+/-)(16/s/)nu/beta, with nu and beta as the standard bulk critical exponents and with s=O(1) as the dimensionless parameter that characterizes the relative strength of the long-ranged tail of the substrate fluid over the fluid-fluid interaction. We present the modified finite-size scaling pertinent for such a case and analyze in detail the finite-size behavior in this region. The standard finite-size scaling behavior is recovered only for L>>Lcrit.