Galerne Yves, Najjar Rachid
Institut de Physique et Chimie des Matériaux de Strasbourg, 23 rue du Loess, BP 43, 67034 Strasbourg, France.
Phys Rev E Stat Nonlin Soft Matter Phys. 2004 Mar;69(3 Pt 1):031706. doi: 10.1103/PhysRevE.69.031706. Epub 2004 Mar 24.
The prefrozen films that may be observed at the surface of isotropic liquid crystal droplets, close to the isotropic-smectic phase transition, or surface-induced films, are essentially asymmetric. If moreover, the molecules are tilted inside the smectic layers, as in the smectic-C (SmC) or smectic-C(A) (SmC(A)) phases, the c director that we may define as the order parameter of the film, is a real vector. Thus, the surface-induced films of MHTAC exhibit vectorial or polar properties, though the molecules are not chiral. The film free energy therefore contains a surface-elasticity term, K(1)c(2) c, that is a linear function of the splay distortion, and that may be negative enough to promote a mechanical instability. A spontaneous c distortion, or c modulation, then invades the whole film and produces an array of parallel stripes, with a typical four-fringe periodicity when observed between crossed polarisers. Here, we present optical measurements of the distortion for different film thicknesses, and we propose a linear analysis of the data to test our model. Due to the limitations inherent to the Fourier expansion that we use, the calculations are valid only between two limits: a large q limit where splay domains collapse into disclination lines, and a small q borderline below which the distortion evolves towards a system of independent solitons. We find that the sign of the spontaneous splay elastic constant K1 alternates as a function of the number of layers, N, a property that is reminiscent of the alternate structure of the SmC(A) phase. We argue that the two-dimension elastic constant, K1, originates from the interactions between the molecules in contact to the isotropic phase, and we deduce K1 approximately -(-1)(N)x10(-11) N and the elastic anisotropy, with a ratio of the splay over bend elastic constants K(s)/K(b) approximately 4.5. Similar properties could be observed also in other types of ultrathin films, e.g., in free-standing, ferroelectric (SmC*) or antiferroelectric (SmC(*)(A)), films, in Langmuir films, and even in particular biological films. In some cases, a second, electric instability may occur and superimpose onto the elastic one.
在各向同性液晶微滴表面、接近各向同性-近晶相转变处可观察到的预冻薄膜，或表面诱导薄膜，本质上是不对称的。此外，如果分子在近晶层内倾斜，如在近晶-C（SmC）或近晶-C（A）（SmC（A））相中，我们可定义为薄膜序参量的c指向矢是一个实矢量。因此，尽管分子不是手性的，但MHTAC的表面诱导薄膜具有矢量或极性特性。薄膜自由能因此包含一个表面弹性项K(1)c(2) c，它是展曲畸变的线性函数，并且可能负到足以引发机械不稳定性。然后，自发的c畸变或c调制侵入整个薄膜，并产生一系列平行条纹，在正交偏振器之间观察时具有典型的四条纹周期性。在此，我们给出了不同薄膜厚度下畸变的光学测量结果，并提出对数据进行线性分析以检验我们的模型。由于我们使用的傅里叶展开固有的局限性，计算仅在两个极限之间有效：一个大q极限，此时展曲畴坍缩成位错线；一个小q边界，低于此边界畸变演化为独立孤子系统。我们发现，自发展曲弹性常数K1的符号随层数N交替变化，这一特性让人联想到SmC（A）相的交替结构。我们认为二维弹性常数K1源自与各向同性相接触的分子之间的相互作用，并推导出K1约为-(-1)(N)x10(-11) N以及弹性各向异性，展曲与弯曲弹性常数之比K(s)/K(b)约为4.5。在其他类型的超薄膜中也可观察到类似特性，例如在自支撑铁电（SmC*）或反铁电（SmC(*)(A)）薄膜、朗缪尔薄膜，甚至特定的生物薄膜中。在某些情况下，可能会出现第二种电不稳定性，并叠加在弹性不稳定性之上。
