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Self-assembly for high NLO susceptibilities
William Thomas*, Benjamin Olbricht†
*Department of Physics and †Department of Chemistry, University of Washington, Seattle, Washington
(7 March 2006)
The concept of self-assembly (SA) is explored for maximizing the second order macroscopic nonlinearity of both inorganic and organic non-linear optic (NLO) chromophores in terms of the relevant intermolecular forces driving the SA mechanism. The importance of noncentrosymmetic order as dipole alignment in 2nd order NLO is reviewed, and a variety of methods for manipulating this model via SA from the literature are highlighted and potentially viable SA routes are proposed. Highlighted are bulk formation mechanisms from poled and spin coated films and layer-by-layer technique to afford practical properties in devices.
Introduction
The first observation of non-linear optical process was published by J. Kerr in 1875 as the dependence of incident light and induced electric field in a sample of carbon disulfide. [J. Kerr, Phil. Mag. 50(4), 337 (1875).] Franken et al. reopened the field in 1961 with the advent of the laser. This phenomenon was the frequency doubling and spatial shift of an incident ruby laser beam on a photographic plate that coincided with generation of the second harmonic of the laser’s fundamental output frequency and the spatial division of the beam via interaction with a birefringent medium into incident and extraordinary beams, also known as the electro-optic (EO) effect, or Kerr effect for its original namesake. [P.A. Franken, A.E. Hill, C.W. Peters and G. Weinreich, Phys. Rev. Lett.7, 118 (1961).] Since that time the field of non-linear optics has been of interest to physicists and chemists alike and more recently has achieved unprecedented advances under the umbrella of photonics—that is, as a method of processing and storage of information in the form of light.
Nonlinear materials are fundamentally characterized by their non-steady-state interaction with incident electromagnetic (EM) radiation. When the electric field component of an EM wave interacts with the electric structure of a nonlinear media a nascent light wave is produced that has a perturbed phase or wavelength. The oscillatory behavior of EM waves is described by the asymmetry of the polarization oscillation about the nodal axis, where all interactions of polarization and electric fields satisfy Maxwell’s equations. In order to understand how this effect applies to NLO films we can consider a media acted on by an EM wave. There is a polarization induced into the media by the EM field, E (Ulman, 339). The polarization induced, P, is:
P = (1) E + (2) EE+ (3) EE E+ …….. (Eq. 1)
Source: Ubachs, W. Nonlinear Optics, Lecture Notes. Laser centre Vrije Universiteit Amsterdam,2001, 4.
Where, (1) is the linear susceptibility tensor and (2) and(3) are the higher order nonlinear susceptibilities tensors in the power series expansion of the electric field. If the nonlinear susceptibility tensors are nonzero the material is considered nonlinear (Shah, 70). Moreover, an important condition to note is the relation of induced polarization to inherent properties of the material being manipulated, foremost of which is the symmetry of the material’s lattice. In centrosymmetric lattices, i.e. lattices that contain inversion symmetry, an important distinction from the above summation is required. Use of the inversion symmetry operator, Î, on the induced polarization makes this distinction obvious:
Î E = -E(Eq. 2)
Î P = -P = -χ(1) . E + χ(2) . E . E - χ(3) . E . E . E ± Ö (Eq. 3)
Pcentrosymmetric(n)= χ(1) . E + χ(3) . E . E . E + Ö(2n-1) (Eq. 4)
Thus second and successive even-ordered nonlinear optical properties are only observed in noncentrosymmetric lattices. Furthermore, the more noncentrosymmetric the medium is, the more powerful the contribution of the even-ordered NLO terms. The second important material-dependant features neglected in the first macroscopic summation are the microscopic tensors associated with the electronic structure of the molecule, given by:
P = . E + . E . E+ . E . E . E + Ö(Eq. 5)
Where P and E remain analogous to the macroscopic relation above, and is the so-called linear polarizability for obvious reasons,is the second-order molecular polarizability (first-order molecular hyperpolarizability), andis the third-order molecular polarizability (second-order molecular hyperpolarizability). The physical interpretation of these terms arises from their relation to P and E, which is they signify the ability of the electrons to interact with incident electromagnetic radiation according to the Lorentz ‘push-pull’ model where electrons are delocalized by polarized light and relaxed via a restoring force with the removal of the incident perturbation. The chemical structure of push-pull chromophores elucidates this concept.
Before the introduction of organic push-pull chromophores, it is necessary to discuss the motivation for organic materials as NLO chromophores over the current inorganic crystalline technology. To avoid repetition, a chart below highlights the strengths and weaknesses of these materials. It is important, however, to note a few details. Firstly, very large scale integration (VSLI) has not been realized for devices based on organic materials, thus a production cost per unit has not been established and estimates vary drastically: in nearly every case below 6000USD, however. The phase relaxation time of π-electrons in organic materials is on the order of femtoseconds, producing ultrafast modulation in devices. It is also important to highlight the superiority of organics in EO coefficients and their inferiority for thermal stability. Lastly, it is important to note that consensus in the field indicates that inorganic NLO materials are reaching a limit, with doping being explored for miniscule gains. Organic chromophores, on the other hand, have nearly unlimited design and engineering possibilities.
Criteria / LiNbO3 / Organic / Note:Cost/unit (USD) / 6000 / <6000 / no VSLI/organics
Bandwidth (GHz) / 30 / 200
Refractive index (n) / 2.15-2.22 / 1.5-1.7 / @ 1.3 microns
EO Coefficient (pm/V) / 31 / ~400
Operating Voltage (V) / 6 / 1
Optical Loss (dB/cm) / ~0.2 / 0.7
Thermal Stability (deg C) / ~1500 / 200+
Dielectric Constant / 29-85 / 2.5-4 / @ 100 kHz
Highlights of Organic Chromophores vs. LiNbO3 crystals
Another crucial topic in NLO is the devices and how they operate. Many platforms for utilizing NLO materials have been developed, including micro-ring resonators (especially for wave division multiplexing applications), frequency-doubling crystals for OPO laser systems, phase array radar, and Mach-Zehnder (MZ) type devices. For the purpose of clarifying the purpose of materials in devices, the latter will be emphasized. The MZ modulator is simply SiO2 coated Si chip with arms etched via electron beam lithography. A fiber optic cable couples into the modulator and the light is divided equally into two arms, both containing a film of NLO material typically deposited by spin coating. One arm is poled and switched with a digital electrical signal, which switches the permittivity of that arm to EM radiation. The light then recouples with the unbiased arm and produces either coherent or destructive interference, effectively interconnecting optical and electronic digital signals.
Another feature of 2nd order NLO materials is second harmonic generation (SHG). SHG and phase matching are characteristic features demonstrated by NLO materials. Second harmonic generation is when two light waves of frequency and combine to form a nascent light wave of frequency in a nonlinear media as shown in Figure 1.
Figure 1. Second Harmonic Generation.
Source: Ulman, Abraham. An Introduction to Ultrathin Organic Films From Langmuir-Blodgett to Self-Assembly. San Diego: Academic Press, 1991, 341.
Phase matching is the characteristic of the nonlinear media to match the phases of the initial and second harmonic wave. These characteristics and others make the nonlinear materials very useful for different electronic and photonic devices such as repeaters (Ulman, 342). The usefulness of these characteristics demands inexpensive and reliable techniques for the generation of the materials that exhibit them.
Returning to the concept of push-pull chromophores, such an EO material is simply a molecule with an electron-rich donor, typically an amine or other nitrogen-based functional group, an electron-deficient electron acceptor, typically a heavily heteroatomically substituted cyclic hydrocarbon. These moieties are separated by a π-conjugated bridge, the motive for which is to facilitate efficient internal charge transfer (ICT) between the donor and acceptor.
Structure of a typical standard organic 2nd order NLO chromophore: FTC.
π-conjugation creates a state of intrinsically low bandgap due to the narrowing density of states in the π molecular orbitals. The “conduction” band forming creates an efficient ICT mechanism. These structural features are combined producing a molecule with a highest occupied molecular orbital (HOMO) consisting of electron density localized in the donor and a lowest unoccupied molecular orbital (LUMO) whose electron density is localized at the acceptor; this is the fundamental concept of the push-pull chromophore model.
Density functional theory computation results of a typical push-pull chromophore showing the electron density of the HOMO (left) and LUMO (right).
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Moreover, these molecules produce a strong dipole that is highly polarizable to favorable satisfy the microscopic relation of induced polarization and electric field—better stated, chromophores designed by this concept have a large dipole moment and I high first-order molecular hyperpolarizability. To satisfy the analogous macroscopic formulation, these dipoles must be arranged noncentrosymmetrically, that is, “pointing” in the same direction—otherwise known as acentric ordering. All these terms combined, the canonical equation resulting is:
(Eq. 6)
whereis the second-order molecular polarizability from above, n is the index of refraction of the material, cos3(> is a product of the average dipole order and the N is number density of the material. The vague relation of chi and r is simple best noted as tensorial, that the effective r of a material is the dominant component the susceptibility term per the definition of the axis of alignment related to the axis of incident EM radiation.
As is obvious by now, alignment and order, terms used interchangeably in the field, are essential to producing highly nonlinear materials, that is, N must be maximized and minimized in equation (6) above, signifying a high degree of long-range order. Macroscopic alignment is conventionally obtained by electrical field poling of the materials, either via electrode contact poling or corona poling. In both techniques, the idea is to heat the molecules to allow enhanced mobilities, specifically rotational mobility, that the molecules may align to the applied electric field. The lattice is then cooled down while still under the electric field, thereby reducing the mobility and phenomenologically producing ordered arrays of chromophores even when the electric field is removed. This process, however, requires fields typically on the order of MV/cm and temperatures that can decompose sensitive parts of the chromophore. An ideal process would involve assembly of aligned lattices without electric fields or elevated temperatures, such as SA.
Self-assembly by layer
Self-assembly offers many potentially viable options for the inexpensive and efficient means of creating ultrathin films for use in nonlinear optics. In order to understand the many self-assembly techniques it is necessary we understand the components of the self-assembly system. These components include the molecules and atoms in the system as well as the interactions and forces that are acting between them. The self-assembly process is driven by the intermolecular interactions between the atoms and molecules. These interactions have been ordered into three groups: Coulomb interactions, van der Waals interactions, and short-range repulsions. (Zhang, et al., 7)
The intermolecular interactions due to charged particles are called Coulomb interactions. These interactions include the ion-permanent dipole interaction (Eq. 2), ion-ion interaction (Eq. 3), and the permanent dipole-permanent dipole interaction (Eq. 4). They can be attractive or repulsive depending on the charge of the particle. (Zhang, et al., 8)
Source: Zhang, Jin., et al., Self-Assembled Nanostructures. New York: Kluwer Academic/ Plenum Publishers, 2003, 8.
Induced polarization by local molecules into other molecules causes the interactions known as van der Waals forces. The Debye, Keesom, and the London interaction are all examples of van der Waals forces. The Debye interaction is a permanent dipole-induced dipole interaction that stems from free and rotation dipoles (Eq. 5). The London interaction is an induced dipole-induced dipole interaction and are a result of shifts in the electron cloud (Eq. 6). The Keesom interaction is a permanent dipole-permanent dipole interaction and is caused byfixed or average angled dipoles (Eq. 7). (Zhang, et al., 8)
Source: Zhang, Jin., et al., Self-Assembled Nanostructures. New York: Kluwer Academic/ Plenum Publishers, 2003, 8.
The short range repulsion (Eq. 8) arises as a result of the Pauli exclusion principle which states that two fermions can not occupy the same state. For fermions, if the two individual particle wave functions were equal then by the two particle wave function for fermions (Eq. 9) , the resultant two particle wave function would be zero (Griffiths, 204). The short range repulsion increases dramatically with a decrease in separation is usually summed together with the attractive van der Waals forces in the Lennard-Jones potential (Eq. 10). Other intermolecular forces are at work in the self-assembly system but these interactions contribute the most at close distances. The left hand of the Lennard-Jones potential represents the contribution of the short range repulsive force and the right hand is from the van der Waals contribution to the interaction. Figure 2 shows graphically the strength of the interaction energies with respect to the distance of separation between the particles. (Zhang, et al., 9)
Source: Zhang, Jin., et al., Self-Assembled Nanostructures. New York: Kluwer Academic/ Plenum Publishers, 2003, 9.
Figure 2: Graphical representation of the strength of the interaction energies as a function of distance
Source: Zhang, Jin., et al., Self-Assembled Nanostructures. New York: Kluwer Academic/ Plenum Publishers, 2003, 9.
The hydrogen bond is a type of polar covalent bond and is another interaction that must be considered in the self-assembly process. The hydrogen bond is a directional bond due the hydrogen atom being a positive charge. When the hydrogen atom is near a negatively charged atom there is a dipole-dipole interaction which is attractive (Zhang 11). Another characteristic of the hydrogen bond is its relative weakness compared to metallic and covalent bonds but its unusual strength compared to the van der Waals interactions. This adds an element of flexibility to the self-assembly process and can be helpful in terms of creating the dipolar order we want. There is an issue with the thermal stability of the hydrogen bond in that the orientation held by the hydrogen bond is often broken or relaxed when excessive heat is applied into films.
Amphiphiles are a type of molecule that consists of both hydrophobic and hydrophilic groups. Typical amphiphiles include detergents, dispersive agents for paints, and emulsifiers. The hydrophobic interaction is a result of non-hydrogen bonding molecules, such as fluorocarbons and alkanes, coming into contact with water. The hydrophobic part of the molecule, in order to attain a lower energy state, will reorient itself so that the hydrophobic element of the molecule will point away from the water interface. Hydrophilic molecules repel one another in water due to the fact they prefer contact with water. When hydrophilic molecules are in water they are apt to scatter which has an effect of disordering the water system (Zhang, 13). These properties make amphiphiles desirable molecules for the self-assembly process because of their organizational nature.
Surfactants are molecules that can be described as being cationic, anionic, zwitterionic, or nonionic. Surfactants have a single hydrophobic tail unit and a least one hydrophilic head unit. Positively charged head units are considered cationic surfactants which are usually made from long chains of ammonium salts or amines. Negatively charged head units are considered anionic surfactants which are usually made from sulfonic or carboxylic acid salts. Nonionic surfactants have a neutral head unit while zwitterionic surfactants have both positively and negatively charged head units (Zhang, 13). These different types of surfactants allow for a multitude of different interactions that can be used to bond molecules to substrates and each other. These interactions can be used to arrange the molecules into the preferred noncentrosymmetric polar ordered needed for NLO phenomena such as in ISAMs.
One thin film deposition technique that enables the generation of NLO materials is the dip coating process. The dip coating process involves dipping an activated substrate in to a solution or water subphase with a layer of amphiphilic molecules on the surface. The solute or amphiphiles thereby bond to the substrate either ionically or covalently typically with energies of 40-45 kcal/mol (Ulman, 237). Multiple immersions into the subphase or solution build up successive layers to the film.
There are three regions of film thickness in the dip coating process; the start up region, the entrainment region and the meniscus region. In the meniscus region there are several forces acting on the film. Gravitational forces which have the effect of draining the solution off the substrate. Viscous drag forces which are proportional to solution viscosity and the withdrawal velocity of the substrate. We can neglect inertial forces if the withdrawal velocity is slow enough but if the withdrawal is fast then the force is proportional to the square root of the substrate length, velocity, and solution density and viscosity. There is a force in the downward direction due to capillary forces that put pressure on the convex side of the meniscus. Disjoining pressure also becomes an issue with sufficiently thin films which is proportional to the inverse cube of the thickness of the film. (Kim, 8)