The forces acting on macromolecules and small particles embedded in liquid crystalline (LC) media is of scientific and technological importance. The specific interaction between particles embedded in liquid crystals was discovered in 1978 by S.Lopatnikov and V.Namiot, who calculated the forces acting between particles of arbitrary shape embedded in a nematic and smectic liquid crystals [1] in both the absence and presence of the magnetic fields. S.Lopatnikov and V.Namiot also proposed also to use liquid crystals as a "smart solvents" for manipulation and separation of macromolecules and small particles [2]. They pointed out that the advantage of using LC as "smart solvents" for colloids with complex shape is that a "key-lock interaction" takes place during the interaction of particles and the fact that particles of the complex shape occupy in liquid crystal the most energetically effective orientation. Consequently, liquid-crystal colloids can be used for self-assembling and assembling of small objects. For example, the manipulation of the particles embedded in liquid crystal is now considered as the possible way for the assembling arrays of nano-tubes, separation of particles, etc. However, the challenge is how to provide increase forces to levels high enough for rapid and economical assembly and self-assembly of the embedded pariticles. The problem is that small-size particles are too light for fast sedimentation. Let us estimate, for example, the velocity of sedimentation of a single-wall carbon nano-tube having the length 10~(-3) cm and diameter 5*10~(-6)cm. The gravity force, acting on the particle and the velocity of sedimentation can be estimated as:f_G≈ 2pgLRh = 6.26 ? 3 ? 10~3 ?10~(-3) ? 5.10~(-7)0 * 10~(-8) = 10~(-13)Dy; V=F/4πηα=10~(-13)/ 4*3.14*l0~(-2)*5*l0~(-7)=lO~(-4)/62.8≈1.5*10~(-6)cm·s~(-1); This simple calculation shows that sedimentation of such tubes into a layer of 0.01 cm thick will need 7.10~4 seconds or 19 hours. Moreover, due to Brownian motion, this time will be practically infinite, because gravitational energy of these particles for this layer thickness is of the order of 10~(-15) erg, which is small in comparison with the room temperature (4.2*10~(-14)erg) A more practical approach to achieve oriented sedimentation of CNT [3] used a filtration through a penetrable LC substrate. The diameter of the pores was 10~(-5) to 2.10~(-5)cm and the area fraction occupied with pores (as estimated from the photographs in [3]) is in the range of 1%. Permeability of the material can be estimated as;
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