1、偶氮彈性體表面光柵的形成探究    1.Introduction When exposing amorphous or liquid crystalline azobenzene polymers to an interference pattern of light, surface relief gratings can be inscribed (Rochon et al. 1995; Kim et al., 1995; Pedersen et al., 1998). The process is not destructive, and can

2、be implemented even at room temperature, several tens of kelvin below the glass transition temperature of the polymers. The resulting surface features are stable when kept at room temperature, and easily erased by heating the samples above the glass transition temperatures (Jiang et al., 1998). Alth

3、ough the deriving force for spontaneous formation of surface relief gratings is still in debate (Barret et al. 1998; Kumar et al. 1998; Lefin et al. 1998; Bublitz et al. 2001), large-scale mass transport is well manifested in the polymers under irradiation (Karageorgiev et al., 2005). Recently, simi

4、lar inscription of surface relief grating on azobenzene-containing elastomers has also been reported (Devetak et al., 2009). In these materials, cross-link between chains resists large-scale mass transport, and the distortion is due to light-induced trans-cis transition of azo molecules that further

5、 disturbs the orientational order of the sample (de Gennes and Prost, 1993). Towards a semi-quantitative understanding of the phenomenon, the present work attempts to give a simple model so as to predict the period of the gratings. Our main attention will be paid to the illumination pattern of p-p g

6、eometry.    2.Model formulation The system under consideration is shown in Fig. 1. Two coherent beams of wavelength and equal intensity 0I are introduced to the polymer film of thickness . The spatial wavelength of the resulting interference pattern on the film surface can be def

7、ined by Braggs law hD2sinD=, but the exact nature of this periodic interference depends on the polarization states of the incident light. To be clear, suppose that the local electric field vector of the light at a typical point makes an angle between the 3x axis, and its projection onto the surface

8、spans an angle with the 1x direction. Then the photostrain components, *ij, induced by irradiation can be written as where123(,)xxx= depends on the light intensity and thus attenuates with penetration depth. In general, these photostrains are not uniform, and produce an inhomogeneous deformation in

9、the film. Denote the corresponding displacement components by . The total strains are expressed by iu(,)/2ijijjiuu=+, and the elastic strains read. Here and in the following, repeated subscripts mean summation from 1 to 3, and a comma is used to denote differentiation with respect to the suffix coor

10、dinate. Therefore, the linearly elastic constitutive law of the incompressible elastomer can be represented by where /3kkp=. In quasi-static case, neglecting the effect of body force, the stress obeys the equilibrium equations,The incompressibility condition for the elastomer demands,Eqs.are the gov

11、erning equations of the present model to describe the photo-induced deformation of amorphous azobenzene-containing elastomers. A key step is to determine the detailed form of the photostrains caused by inhomogeneous illumination. Associated with suitable boundary conditions, the deformation can be s

12、olved. In particular, when the exposed surface is free of external force, the boundary conditions are expressed by.    3.Pattern of the p-p geometry There are in general three main inscription geometries: the p-p geometry, the s-s geometry and the circ-circ geometry. Here the sym

13、bols “p” and “s” indicate horizontal and vertical linear polarization, respectively, while “circ” means circular counterpolarization. For brevity, only the p-p geometry is discussed here. Since the film used in the experiments has the thickness of only about 0.5m, the optical attenuation through the

14、 film is assumed negligible, i.e. the strain induced by light irradiation is uniform across the film thickness. The substrate is considered rigid, and the 1x axis is always chosen to be along the grating vector. In this situation, the electric field and light intensity on the surface of the film are

15、 assigned, respectively, as where 2/D=, 20IE= and is the base vector of the 1e1x axis. Due to 0=, Eq.and the other components vanish. Here is obtained as0(1cos)/2Ix =+ with 2/(159)BBNkTNkT=+. From symmetry consideration, the displacement components in the film take the forms of , 1113(,)uuxx=20u= an

16、d . Thus, from Eqs. (2)-(4) one gets illustrates schematically the periodic morphology of the resulting surface relief grating. It can be seen that the wavelength of the grating is the same as that of the interference pattern. Yet, the amplitude depends on many factors such as the intensity of light

17、, the thickness of the film, the angle frequency of illumination pattern, as well as other quantities involved in the parameter . The diversity of the dependence provides many ways that enable one to tune the profile of the grating.    4.Conclusions The formation of surface relief gratings on amorphous azo elastomers induced by linearly polarized light is analysed via a continuum model. Special attention is focused on the illumination of p-p geometry. It is shown that the wavelength of the grating is the same as that of t