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Molecular dynamics study of structure formation at spreading of nanodroplets composed of rod-like molecules
Colloids and Surfaces A: Physicochem. Eng. Aspects 239 (2004) 119–124
Molecular dynamics study of structure formation at spreading of nanodroplets composed of rod-like molecules V.M. Samsonov∗ , V.V. Dronnikov Tver State University, Brigadnaya 37, Tver 170027, Russia Received 10 September 2003; accepted 6 January 2004 Available online 27 April 2004
Abstract Spreading of nanosized droplets has been simulated on the basis of isothermal molecular dynamics. Observed effects include orientational ordering and cluster parquet structure formation in nanodroplets composed of rod-like molecules. These peculiarities are observed for both continuous (structureless) substrates and structured (heterogeneous) surfaces represented by high- and low-energy segments, such as striped substrates and surfaces with quadratic high- and low-energy inclusions. © 2004 Elsevier B.V. All rights reserved. Keywords: Theoretical methods; Models and techniques; Computer simulation; Molecular dynamics; Wetting; Nanodrops; Rod-like molecules
1. Introduction Spreading phenomena are related to many fundamental and applied problems which are important for numerous natural and technological processes including surface covering, adhesion, spray painting, welding and soldering [1,2]. Some macroscopic technological processes, e.g. soldering and producing composite materials, may be extended to nanoscale systems. At the same time, a number of structure formation processes are specific only in the nanosize region. The design of nanostructures on solid interfaces may be based on different approaches: (i) with the aid of a precise instrument, such as the tip of an atomic force microscope; (ii) by directed chemical synthesis; (iii) providing conditions for the self-organization of nanostructures located in the field of the solid surface. Such self-organization may be found in the nanodroplet spreading over solid substrates. One of the most important designable factors of the self-organization in nanodroplet spreading is the nature of constituent molecules. On one hand, the structure formation will be more probable when the droplet molecules contain
∗
Corresponding author. Tel.: +7-822-421487. E-mail address: [email protected] (V.M. Samsonov).
0927-7757/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.colsurfa.2004.01.037
polar groups providing some specific interactions with the substrate. On the other hand, the results of our computer simulation [3–5] demonstrate that one of the self-organization processes, namely the dynamical layering, may be observed not only for polymer droplets [6,7] but also for simple Lennard–Jones ones. Moreover, the self-organization patterns in simple enough systems are of special fundamental and applied interest. The structure of the solid substrate is another factor affecting self-organization during nanodroplet spreading [8]. The wetting behavior is directly influenced by the patterns of heterogeneous structured surfaces, namely striped surfaces and those with quadratic high- and low-energy inclusions [9]. According to our computer simulation results, the effects of the self-organization, namely the crystal or liquid crystal ordering and the cluster (domain) structuring are most pronounced in the case of rigid rod-like molecules. The linear rod-like conformation is of interest in view of many natural and technological systems. For example, the tobacco mosaic virus molecule and polymer molecules used for the production of heat-resistant fibres are of the rod-like type [10]. Also rod-like are some molecules promising for application as nanowires [11]. The main goal of this paper is to elucidate the conditions of the structure formation at the spreading of nanodroplets composed of rod-like molecules. Apparently, the structures
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V.M. Samsonov, V.V. Dronnikov / Colloids and Surfaces A: Physicochem. Eng. Aspects 239 (2004) 119–124
formed on a substrate should replicate, to a greater or lesser extent, its morphology. However, there are no reasons to expect this replication to be perfect. So, one of the specific goals of this article is to clarify the correlations between the nanoscale mesostructure of the solid surface and the final morphology of the spread droplet. We have used the term ‘mesoscopic’ as it was introduced into consideration in synergetics [12]. According to [12], the linear scale of the macroscopic level corresponds to the size of the whole system under consideration; the microscopic level refers to separate atoms or molecules; whereas the intermediate, i.e. mesoscopic, level is attributed to the structures with characteristic linear parameters greater than the atomic size but smaller than the system dimension.
Further we assume that ns as3 ∼ = 1 where ns is the density of the number of molecules in the solid phase (the strict equality takes place for the simple cubic lattice). Varying the ratio εs /εl = ε∗s , we can reproduce cases of low-energy (ε∗s = 0.5–2) and high-energy (ε∗s = 5–50) substrates [3]. It is noteworthy that the u(z) versus −1/z3 dependence also follows from the macroscopic theory of the van der Waals forces without recourse to the assumption of the Lennard–Jones origin of the substrate [3]. The nanodroplet evolution depends on the reduced temperature T ∗ = kT/εl (k is the Boltzmann constant). The value Tm∗ = 0.65 is of the order of the macroscopic melting temperature of such non-polar liquid as benzene. For systems presented by chain-like molecules Tm∗ ≥ 1.7.
2. Method of simulation The shape of the starting drop corresponds to a sphere of initial radius R0 with its centre located at the distance R0 + al from the smooth solid surface, where al is the effective molecular diameter or, in the case of chain-like molecules, the effective size of the interacting center. We performed the isothermal molecular dynamics simulation of the nanodroplet spreading kinetics by invoking the method of Berendsen thermostat [13]. One of the central problems of the nanoparticle evolution simulation in the field of the solid surface is an adequate description of van der Waals forces acting from the substrate. Assuming that the interaction between two molecules in the liquid–vapor subsystem and in the solid, correspondingly, is characterized by the Lennard–Jones pair potential asl 12 asl 6 Φ(r) = 4εsl (1) − r r and integrating over the solid half-space, we can readily obtain the next expression for the reduced potential of the solid substrate u(z) D C u∗ (z∗ ) = (2) = ∗9 − ∗3 4εl z z In (1) r is the intermolecular distance, εsl and asl are the energetic and the linear parameters of the pair potential, respectively. It is convenient to express εsl and asl in terms of the corresponding parameters of the interaction in the liquid–vapor (εl , al ) and solid (εs , as ) subsystems [14]. √ εsl = εs εl , asl = 21 (as + al ) The parameters as and al may be interpreted as the effective diameters of molecules in the solid and in the liquid–vapor subsystem, respectively. In (2) z∗ = z/al is the reduced coordinate (the z-axis is normal to the solid–vacuum interface), C and D are the attraction and repulsion constants, respectively. Particularly, C = πns as3 (εs /εl )1/2 /6 [3]. √ We have also taken into account that (as + a1 )/2 ≈ as a1 .
Fig. 1. The final configuration formed after the spreading of a nanodroplet consisting of rigid linear tetramers over the high-energy continuous substrate with ε∗s = 5: (a) the sight on the droplet from the above; (b) the first (lower) monolayer.
V.M. Samsonov, V.V. Dronnikov / Colloids and Surfaces A: Physicochem. Eng. Aspects 239 (2004) 119–124
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Fig. 2. The final configuration of a nanodroplet in the field of the chess-board (5al × 5al ) substrate (T ∗ = 1.7, ε∗s = 5 for high-energy (light) cells, ε∗s = 0.5 for low-energy ones).
The chain-like molecules with the degree of polymerization p are presented by the system of interacting centers. Non-valence interactions between the centers are described by the Lennard–Jones potential (1) while parabolic potential Kr (r − r0 )2 was used for valence interactions. In the latter case r is the distance between two neighboring interacting centers, r0 is its equilibrium value and Kr is the coefficient which is a measure of the intermolecular bond-strength. Our program gives also possibility to vary the equilibrium value αe of the valence angle α as well as of the chain rigidity coefficient Kα in the angular parabolic potential u(α) = Kα (α − αe )2 . The valence angle dependent forces are expressed in terms of the derivatives −(∂u(α)/∂α)(∂α/∂xi±1 ) where xi±1 are coordinates of two interacting centers (the angle α is formed by the (i − 1, i) and (i, i + 1) bonds). The value Kα = 0 corresponds to the ideally flexible chain, whereas Kα = 10 characterizes a very rigid chain. The rod-like molecules comply with αe = 180◦ .
3. Results The evolution of nanodroplets presented by rigid linear tetramers in the field of the high-energy substrate (ε∗s = 5) results in a planar parquet structure of the first (lower) monolayer consisting of 2D-clusters with the parallel ori-
entation of rod-like molecules (Fig. 1). Such a cluster may be interpreted as a domain with nematic ordering or as a 2D-crystallite. The interacting centers of the linear molecules under discussion locate in the points of the 2D hcp lattice. The 2D hcp structure yields a parallel shift of neighboring molecules (along rod axes) by about αe /2. This finding is in agreement with X-ray diffraction patterns [15], demonstrating that the same 2D hcp structure is formed by rod-like tobacco mosaic virus molecules. When the substrate has the chessboard structure with the cell size a little greater than the length of rod-like molecules, crystallites with parallel orientation are formed on high-energy cells at the droplet periphery (Fig. 2). Then two-layered cages are formed on some cells. The cluster structure may be also observed on high-energy segments of the striped substrate (Fig. 3).
4. Discussion According to the results obtained in this work, 2D cluster structures with high enough orientation and translation ordering are formed at the nanodroplet spreading on both isotropic (continuous) and structured substrates. Each of these clusters may be interpreted (in dependence on the value of the order parameter) as a crystallite or as a domain with the nematic ordering.
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V.M. Samsonov, V.V. Dronnikov / Colloids and Surfaces A: Physicochem. Eng. Aspects 239 (2004) 119–124
Fig. 3. The resulting droplet configuration after the spreading on the striped surface.
Usually the liquid crystal (orientation) ordering occurs in systems with specific interactions between polar groups promoting translation and orientation ordering. In fact, the most known liquid crystals, for example, n-azoxy-anisole, have polar groups [16,17]. The tobacco mosaic virus is presented by cylinder particles of 15 nm in diameter and 300 nm in length. According to [18], for these molecules, all orientation effects may be explained by the geometrical anisotropy of rod-like molecules. However, as noted in [18], this explanation neglects the fact that the rods under consideration have some ionic charges. However, for mesogenic compounds the presence of polar groups is not necessary. For example, there are no polar groups in the molecule of the n-penta-phenglene. Aromatic rings in the para position are also typical for rod-like polymers, e.g. for the poly-(p-phenylene-ethylene). These rings may be adequately enough reproduced by localized force centers. In this connection, the working hypothesis was put forward that the localized nature of interacting centers is one of the structure formation factors affecting the clustering in the first monolayer of the spreading droplet. In contrast to the case of smooth molecules, the localized force centers produce local potential barriers, which may be interpreted as a kind of the internal friction preventing the relative sliding of rods.
To prove the above hypothesis, a special computer program was worked out to plot the potential curves describing different cases of the interaction between two rod-like molecules: (i) the distance between two parallel rods is varied; (ii) two rod-like molecules are perpendicular, the distance between one of the rods and the head of the other is varied; (iii) one of the molecules slides along the other. Corresponding potential curves are presented in Figs. 4–6. When there is no relative displacement along the axes of the parallel molecules (Fig. 4), the potential curves 1 and 2 (for parallel and normal orientations) practically coincide. A small displacement by the distance αe /2 results in a noticeable increase of the potential well depth (Fig. 5). From this point of view, there is an energetic gain in the cluster formation with some relative displacement of rod-like molecules along the director. At the same time, the free relative sliding of parallel rods is prevented by noticeable local potential barriers (Fig. 6). Obviously, just these barriers determine the stability of the cluster structure under consideration. The characteristic cluster size seems to correspond to the size of the potential well presented in Fig. 6a. The tendency to the orientated cluster formation in the bulk phase of rod-like molecules was observed earlier in molecular dynamics experiments [19]. In [19] the rod-like
Fig. 4. Potential curves corresponding to shifting of two parallel (curve 1) and perpendicular (curve 2) rods.
V.M. Samsonov, V.V. Dronnikov / Colloids and Surfaces A: Physicochem. Eng. Aspects 239 (2004) 119–124
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Fig. 5. Potential curves analogous to those presented in Fig. 4 with the exception of a relative shift of two parallel rods at the distance al /2.
Fig. 6. Potential curves for the case of the sliding of a rod head along the other rod-like molecule: (a) the both rods are parallel; (b) the rods are perpendicular.
molecules were also simulated by chains consisting of localized interacting centers. On one hand, the clustering in [19] could be an artifact induced by the periodic boundary conditions. On the other hand, in the simulation cell with ‘smooth’ ellipsoidal molecules [20], the above tendency was not observed. This fact confirms our conclusion on the principal role of the localized nature of the interacting centers forming the rod-like molecule.
odroplet consisting of rod-like molecules is induced by the following three factors: (i) the geometrical anisotropy of rod-like molecules; (ii) the planar geometry of the substrate, which determines the planar layered structure of the droplet; (iii) the localized nature of the interacting force centers in rod-like molecules.
Acknowledgements 5. Conclusion According to the above discussion, the self-assembly effect of the oriented cluster formation in the spreading nan-
Support of the Russian Foundation for Basic Research (grant no. 01-03-32014) is acknowledged. The authors are grateful to L.B. Boinovich and A.M. Emelyanenko for discussion.
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V.M. Samsonov, V.V. Dronnikov / Colloids and Surfaces A: Physicochem. Eng. Aspects 239 (2004) 119–124
References [1] P.G. de Gennes, Rev. Mod. Phys. 57 (1985) 827. [2] B.D. Summ, V.M. Samsonov, Colloids Surf. 160 (1999) 63. [3] V.M. Samsonov, S.D. Muravyev, P.G. Khalatur, Colloid J. 60 (1998) 401. [4] V.M. Samsonov, S.D. Muravyev, M.A. Kirillova, Russian J. Phys. Chem. 72 (1998) 599. [5] V.M. Samsonov, S.D. Muravyev, V.V. Dronnikov, Vacuum 61 (2002) 339. [6] F. Heslot, N. Fraysse, A.M. Cazabat, Nature 338 (1989) 640. [7] F. Heslot, A.M. Cazabat, P. Levinson, N. Fraysse, Phys. Rev. Lett. 65 (1990) 599. [8] P. Lenz, Adv. Mater. 11 (1999) 1531. [9] V.M. Samsonov, V.V. Dronnikov, A.A. Volnuhkin, S.D. Muravyev, Surf. Sci. 532–535 (2003) 560. [10] A. Blumstein (Ed.), Liquid Crystalline Order in Polymers, Academic Press, New York/San Francisco/London, 1978.
[11] J.M. Lehn, Supramolecular Chemistry, VCH Varlagsgesellschaft mbH., Weinheim/New York/Basel/Cambridge/Tokyo, 1995. [12] H. Haken, Advanced Synergetics, Springer, Berlin/Heidelberg/New York/Tokyo, 1983. [13] H.J.C. Berendsen, J.P.M. Postma, W.F. van Gusteren, A. Di Nola, J.R. Haak, J. Chem. Phys. 81 (1984) 3684. [14] R.B. Bird, J.O. Hirshfelder, C.F. Curtis, Molecular Theory of Gases and Liquids, NY, 1954. [15] J.D. Bernal, I. Fankuchen, J. Wen. Pkysiol 25 (1941) 111. [16] P.G. de Gennes, The Physics of Liquid Crystals, Clarendon Press, Oxford, 1974. [17] S. Chandrasekhar, Liquid Crystals, Cambridge University Press, Cambridge/London/New York/Melbourn, 1977. [18] H. Marawetz, Macromolecules in Solutions, Interscience, Wiley, New York/London/Sydney, 1965. [19] V.K. Pershin, S.A. Skopinov, Fizika Tverdogo Tela 21 (1979) 946 (in Russian). [20] A.L. Tsykalo, A.D. Bagmet, Kristallografiya 21 (1976) 1101 (in Russian).
Molecular dynamics study of structure formation at spreading of nanodroplets composed of rod-like molecules V.M. Samsonov∗ , V.V. Dronnikov Tver State University, Brigadnaya 37, Tver 170027, Russia Received 10 September 2003; accepted 6 January 2004 Available online 27 April 2004
Abstract Spreading of nanosized droplets has been simulated on the basis of isothermal molecular dynamics. Observed effects include orientational ordering and cluster parquet structure formation in nanodroplets composed of rod-like molecules. These peculiarities are observed for both continuous (structureless) substrates and structured (heterogeneous) surfaces represented by high- and low-energy segments, such as striped substrates and surfaces with quadratic high- and low-energy inclusions. © 2004 Elsevier B.V. All rights reserved. Keywords: Theoretical methods; Models and techniques; Computer simulation; Molecular dynamics; Wetting; Nanodrops; Rod-like molecules
1. Introduction Spreading phenomena are related to many fundamental and applied problems which are important for numerous natural and technological processes including surface covering, adhesion, spray painting, welding and soldering [1,2]. Some macroscopic technological processes, e.g. soldering and producing composite materials, may be extended to nanoscale systems. At the same time, a number of structure formation processes are specific only in the nanosize region. The design of nanostructures on solid interfaces may be based on different approaches: (i) with the aid of a precise instrument, such as the tip of an atomic force microscope; (ii) by directed chemical synthesis; (iii) providing conditions for the self-organization of nanostructures located in the field of the solid surface. Such self-organization may be found in the nanodroplet spreading over solid substrates. One of the most important designable factors of the self-organization in nanodroplet spreading is the nature of constituent molecules. On one hand, the structure formation will be more probable when the droplet molecules contain
∗
Corresponding author. Tel.: +7-822-421487. E-mail address: [email protected] (V.M. Samsonov).
0927-7757/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.colsurfa.2004.01.037
polar groups providing some specific interactions with the substrate. On the other hand, the results of our computer simulation [3–5] demonstrate that one of the self-organization processes, namely the dynamical layering, may be observed not only for polymer droplets [6,7] but also for simple Lennard–Jones ones. Moreover, the self-organization patterns in simple enough systems are of special fundamental and applied interest. The structure of the solid substrate is another factor affecting self-organization during nanodroplet spreading [8]. The wetting behavior is directly influenced by the patterns of heterogeneous structured surfaces, namely striped surfaces and those with quadratic high- and low-energy inclusions [9]. According to our computer simulation results, the effects of the self-organization, namely the crystal or liquid crystal ordering and the cluster (domain) structuring are most pronounced in the case of rigid rod-like molecules. The linear rod-like conformation is of interest in view of many natural and technological systems. For example, the tobacco mosaic virus molecule and polymer molecules used for the production of heat-resistant fibres are of the rod-like type [10]. Also rod-like are some molecules promising for application as nanowires [11]. The main goal of this paper is to elucidate the conditions of the structure formation at the spreading of nanodroplets composed of rod-like molecules. Apparently, the structures
120
V.M. Samsonov, V.V. Dronnikov / Colloids and Surfaces A: Physicochem. Eng. Aspects 239 (2004) 119–124
formed on a substrate should replicate, to a greater or lesser extent, its morphology. However, there are no reasons to expect this replication to be perfect. So, one of the specific goals of this article is to clarify the correlations between the nanoscale mesostructure of the solid surface and the final morphology of the spread droplet. We have used the term ‘mesoscopic’ as it was introduced into consideration in synergetics [12]. According to [12], the linear scale of the macroscopic level corresponds to the size of the whole system under consideration; the microscopic level refers to separate atoms or molecules; whereas the intermediate, i.e. mesoscopic, level is attributed to the structures with characteristic linear parameters greater than the atomic size but smaller than the system dimension.
Further we assume that ns as3 ∼ = 1 where ns is the density of the number of molecules in the solid phase (the strict equality takes place for the simple cubic lattice). Varying the ratio εs /εl = ε∗s , we can reproduce cases of low-energy (ε∗s = 0.5–2) and high-energy (ε∗s = 5–50) substrates [3]. It is noteworthy that the u(z) versus −1/z3 dependence also follows from the macroscopic theory of the van der Waals forces without recourse to the assumption of the Lennard–Jones origin of the substrate [3]. The nanodroplet evolution depends on the reduced temperature T ∗ = kT/εl (k is the Boltzmann constant). The value Tm∗ = 0.65 is of the order of the macroscopic melting temperature of such non-polar liquid as benzene. For systems presented by chain-like molecules Tm∗ ≥ 1.7.
2. Method of simulation The shape of the starting drop corresponds to a sphere of initial radius R0 with its centre located at the distance R0 + al from the smooth solid surface, where al is the effective molecular diameter or, in the case of chain-like molecules, the effective size of the interacting center. We performed the isothermal molecular dynamics simulation of the nanodroplet spreading kinetics by invoking the method of Berendsen thermostat [13]. One of the central problems of the nanoparticle evolution simulation in the field of the solid surface is an adequate description of van der Waals forces acting from the substrate. Assuming that the interaction between two molecules in the liquid–vapor subsystem and in the solid, correspondingly, is characterized by the Lennard–Jones pair potential asl 12 asl 6 Φ(r) = 4εsl (1) − r r and integrating over the solid half-space, we can readily obtain the next expression for the reduced potential of the solid substrate u(z) D C u∗ (z∗ ) = (2) = ∗9 − ∗3 4εl z z In (1) r is the intermolecular distance, εsl and asl are the energetic and the linear parameters of the pair potential, respectively. It is convenient to express εsl and asl in terms of the corresponding parameters of the interaction in the liquid–vapor (εl , al ) and solid (εs , as ) subsystems [14]. √ εsl = εs εl , asl = 21 (as + al ) The parameters as and al may be interpreted as the effective diameters of molecules in the solid and in the liquid–vapor subsystem, respectively. In (2) z∗ = z/al is the reduced coordinate (the z-axis is normal to the solid–vacuum interface), C and D are the attraction and repulsion constants, respectively. Particularly, C = πns as3 (εs /εl )1/2 /6 [3]. √ We have also taken into account that (as + a1 )/2 ≈ as a1 .
Fig. 1. The final configuration formed after the spreading of a nanodroplet consisting of rigid linear tetramers over the high-energy continuous substrate with ε∗s = 5: (a) the sight on the droplet from the above; (b) the first (lower) monolayer.
V.M. Samsonov, V.V. Dronnikov / Colloids and Surfaces A: Physicochem. Eng. Aspects 239 (2004) 119–124
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Fig. 2. The final configuration of a nanodroplet in the field of the chess-board (5al × 5al ) substrate (T ∗ = 1.7, ε∗s = 5 for high-energy (light) cells, ε∗s = 0.5 for low-energy ones).
The chain-like molecules with the degree of polymerization p are presented by the system of interacting centers. Non-valence interactions between the centers are described by the Lennard–Jones potential (1) while parabolic potential Kr (r − r0 )2 was used for valence interactions. In the latter case r is the distance between two neighboring interacting centers, r0 is its equilibrium value and Kr is the coefficient which is a measure of the intermolecular bond-strength. Our program gives also possibility to vary the equilibrium value αe of the valence angle α as well as of the chain rigidity coefficient Kα in the angular parabolic potential u(α) = Kα (α − αe )2 . The valence angle dependent forces are expressed in terms of the derivatives −(∂u(α)/∂α)(∂α/∂xi±1 ) where xi±1 are coordinates of two interacting centers (the angle α is formed by the (i − 1, i) and (i, i + 1) bonds). The value Kα = 0 corresponds to the ideally flexible chain, whereas Kα = 10 characterizes a very rigid chain. The rod-like molecules comply with αe = 180◦ .
3. Results The evolution of nanodroplets presented by rigid linear tetramers in the field of the high-energy substrate (ε∗s = 5) results in a planar parquet structure of the first (lower) monolayer consisting of 2D-clusters with the parallel ori-
entation of rod-like molecules (Fig. 1). Such a cluster may be interpreted as a domain with nematic ordering or as a 2D-crystallite. The interacting centers of the linear molecules under discussion locate in the points of the 2D hcp lattice. The 2D hcp structure yields a parallel shift of neighboring molecules (along rod axes) by about αe /2. This finding is in agreement with X-ray diffraction patterns [15], demonstrating that the same 2D hcp structure is formed by rod-like tobacco mosaic virus molecules. When the substrate has the chessboard structure with the cell size a little greater than the length of rod-like molecules, crystallites with parallel orientation are formed on high-energy cells at the droplet periphery (Fig. 2). Then two-layered cages are formed on some cells. The cluster structure may be also observed on high-energy segments of the striped substrate (Fig. 3).
4. Discussion According to the results obtained in this work, 2D cluster structures with high enough orientation and translation ordering are formed at the nanodroplet spreading on both isotropic (continuous) and structured substrates. Each of these clusters may be interpreted (in dependence on the value of the order parameter) as a crystallite or as a domain with the nematic ordering.
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V.M. Samsonov, V.V. Dronnikov / Colloids and Surfaces A: Physicochem. Eng. Aspects 239 (2004) 119–124
Fig. 3. The resulting droplet configuration after the spreading on the striped surface.
Usually the liquid crystal (orientation) ordering occurs in systems with specific interactions between polar groups promoting translation and orientation ordering. In fact, the most known liquid crystals, for example, n-azoxy-anisole, have polar groups [16,17]. The tobacco mosaic virus is presented by cylinder particles of 15 nm in diameter and 300 nm in length. According to [18], for these molecules, all orientation effects may be explained by the geometrical anisotropy of rod-like molecules. However, as noted in [18], this explanation neglects the fact that the rods under consideration have some ionic charges. However, for mesogenic compounds the presence of polar groups is not necessary. For example, there are no polar groups in the molecule of the n-penta-phenglene. Aromatic rings in the para position are also typical for rod-like polymers, e.g. for the poly-(p-phenylene-ethylene). These rings may be adequately enough reproduced by localized force centers. In this connection, the working hypothesis was put forward that the localized nature of interacting centers is one of the structure formation factors affecting the clustering in the first monolayer of the spreading droplet. In contrast to the case of smooth molecules, the localized force centers produce local potential barriers, which may be interpreted as a kind of the internal friction preventing the relative sliding of rods.
To prove the above hypothesis, a special computer program was worked out to plot the potential curves describing different cases of the interaction between two rod-like molecules: (i) the distance between two parallel rods is varied; (ii) two rod-like molecules are perpendicular, the distance between one of the rods and the head of the other is varied; (iii) one of the molecules slides along the other. Corresponding potential curves are presented in Figs. 4–6. When there is no relative displacement along the axes of the parallel molecules (Fig. 4), the potential curves 1 and 2 (for parallel and normal orientations) practically coincide. A small displacement by the distance αe /2 results in a noticeable increase of the potential well depth (Fig. 5). From this point of view, there is an energetic gain in the cluster formation with some relative displacement of rod-like molecules along the director. At the same time, the free relative sliding of parallel rods is prevented by noticeable local potential barriers (Fig. 6). Obviously, just these barriers determine the stability of the cluster structure under consideration. The characteristic cluster size seems to correspond to the size of the potential well presented in Fig. 6a. The tendency to the orientated cluster formation in the bulk phase of rod-like molecules was observed earlier in molecular dynamics experiments [19]. In [19] the rod-like
Fig. 4. Potential curves corresponding to shifting of two parallel (curve 1) and perpendicular (curve 2) rods.
V.M. Samsonov, V.V. Dronnikov / Colloids and Surfaces A: Physicochem. Eng. Aspects 239 (2004) 119–124
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Fig. 5. Potential curves analogous to those presented in Fig. 4 with the exception of a relative shift of two parallel rods at the distance al /2.
Fig. 6. Potential curves for the case of the sliding of a rod head along the other rod-like molecule: (a) the both rods are parallel; (b) the rods are perpendicular.
molecules were also simulated by chains consisting of localized interacting centers. On one hand, the clustering in [19] could be an artifact induced by the periodic boundary conditions. On the other hand, in the simulation cell with ‘smooth’ ellipsoidal molecules [20], the above tendency was not observed. This fact confirms our conclusion on the principal role of the localized nature of the interacting centers forming the rod-like molecule.
odroplet consisting of rod-like molecules is induced by the following three factors: (i) the geometrical anisotropy of rod-like molecules; (ii) the planar geometry of the substrate, which determines the planar layered structure of the droplet; (iii) the localized nature of the interacting force centers in rod-like molecules.
Acknowledgements 5. Conclusion According to the above discussion, the self-assembly effect of the oriented cluster formation in the spreading nan-
Support of the Russian Foundation for Basic Research (grant no. 01-03-32014) is acknowledged. The authors are grateful to L.B. Boinovich and A.M. Emelyanenko for discussion.
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V.M. Samsonov, V.V. Dronnikov / Colloids and Surfaces A: Physicochem. Eng. Aspects 239 (2004) 119–124
References [1] P.G. de Gennes, Rev. Mod. Phys. 57 (1985) 827. [2] B.D. Summ, V.M. Samsonov, Colloids Surf. 160 (1999) 63. [3] V.M. Samsonov, S.D. Muravyev, P.G. Khalatur, Colloid J. 60 (1998) 401. [4] V.M. Samsonov, S.D. Muravyev, M.A. Kirillova, Russian J. Phys. Chem. 72 (1998) 599. [5] V.M. Samsonov, S.D. Muravyev, V.V. Dronnikov, Vacuum 61 (2002) 339. [6] F. Heslot, N. Fraysse, A.M. Cazabat, Nature 338 (1989) 640. [7] F. Heslot, A.M. Cazabat, P. Levinson, N. Fraysse, Phys. Rev. Lett. 65 (1990) 599. [8] P. Lenz, Adv. Mater. 11 (1999) 1531. [9] V.M. Samsonov, V.V. Dronnikov, A.A. Volnuhkin, S.D. Muravyev, Surf. Sci. 532–535 (2003) 560. [10] A. Blumstein (Ed.), Liquid Crystalline Order in Polymers, Academic Press, New York/San Francisco/London, 1978.
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