Nonlocal Polymerization Driven Diffusion Model Research Articles

Holographic Grating Enhancement Induced by a Dual-Photo-Initiator System in PMMA Substrate Polymers.

Polymer systems induced by the reaction between monomers and photo-initiators play a crucial role in the formation of volume-phase gratings. In this paper, we fabricated a dual-photo-initiator photopolymer by doping EY (Eosin Yellow) molecules into a TI (Titanocene, Irgacure 784@BASF) dispersed PMMA (poly-[methyl methacrylate]) substrate system, with the aim of promoting the diffusion and polymerization processes in volume holographic storage. The two-wave interference system is adopted to record a permanent grating structure in our materials. The temporal diffraction variations of photopolymerization (during the interference exposure) and dark diffusion (after the interference exposure) processes have been investigated and analyzed. Aiming to analyze the influence of EY doping ratios on holographic performances, some key parameters were examined in the experiment. We first measured the temporal evolution of diffraction efficiency, then an exponential fitting was adopted to obtain the response time. Finally, the angular selectivity was evaluated by the Bragg condition after holographic recording. Also, the temporal evolution of each component is described by the nonlocal polymerization-driven diffusion model with a dual-photo-initiator composition, theoretically. Furthermore, we experimentally achieved the holographic grating enhancement in both the dark diffusion and photopolymerization processes by doping appropriate EY concentrations, respectively. This work provides a foundation for the acceptability of TI&EY/PMMA polymers in further holographic storage research.

Shrinkage Simulation of Holographic Grating Using Diffusion Model in PQ-PMMA Photopolymer

An extended model based on nonlocal polymerization-driven diffusion model is derived by introducing shrinkage process for describing photopolymerized dynamics in PQ-PMMA photopolymer. The kinetic parameters, polymerization rate and diffusion rate are experimentally determined to provide quantitative simulation. The numerical results show that the fringes at edge of grating are firstly shifted and consequently, it leads to a contrast reduction of holograms. Finally, theoretical results are experimentally checked by temporal evolution of diffraction efficiency, and the shrinkage coefficient 0.5% is approximately achieved under incident intensity 25.3mw/cm2. This work can enhance the applicability of diffusion model and contribute to the reasonable description of the grating formation in the photopolymer.

Monomer diffusion rates in photopolymer material Part I Low spatial frequency holographic gratings

For photopolymers, knowing the rate of diffusion of the active monomer is important when modeling the material evolution during recording in order to understand and optimize their performance. Unfortunately, a confusingly wide range of values have been reported in the literature. Re-examining these results, experiments are carried out for both coverplated (sealed) and uncoverplated material layers and the measurements are analyzed using appropriate models. In this way, a more detailed analysis of the diffraction processes taking place for large-period gratings is provided. These results, combined with those in Part II, provide unambiguous evidence that the monomer diffusion rate in a commonly used acrylamide polyvinyl alcohol-based material is of the order of 10−10 cm2/s. This value closely agrees with the predictions of the nonlocal polymerization-driven diffusion model.

Holographic photopolymer materials: nonlocal polymerization-driven diffusion under nonideal kinetic conditions

The kinetics of photosensitive polymer holographic recording materials are examined assuming a material that exhibits nonideal kinetic behavior. Previously, a linear relationship between monomer concentration and polymerization was assumed when deriving the nonlocal polymer-driven diffusion (NPDD) model. This is consistent with ideal kinetic conditions in which chain termination is governed by a bimolecular process. However, these models have been reported to disagree with experimental results. In a limiting case of nonideal kinetics it is assumed that primary termination is dominant. In this case the NPDD model must be modified to incorporate a quadratic relationship between the monomer concentration and the polymerization rate. By use of a multiharmonic expansion method of solution the predictions of ideal (bimolecular or linear) and nonideal (primary or quadratic) kinetic models are compared. By using these models we carried out numerical fits to experimental growth curves of gratings recorded in an acrylamide-based cross-linked photopolymer system. Superior fits are achieved by use of the primary termination model. Physical parameters such as the diffusion constant are extracted and compared with results previously reported in the literature.

Nonlocal polymerization-driven diffusion-model-based examination of the scaling law for holographic data storage

For the first time to our knowledge, a detailed theoretical basis is provided for the well-known inverse-square scaling law of holographic diffraction, which states that replay diffraction efficiency eta = gamma/M2, where M is the number of gratings stored and gamma is a constant system parameter. This law is shown to hold for photopolymer recording media governed by the predictions of the nonlocal polymerization-driven diffusion model. On the basis of the analysis, we (i) propose a media inverse scaling law, (ii) relate gamma to photopolymer material parameters and the hologram geometry and replay conditions, and (iii) comment on the form and validity of the diffraction efficiency inverse-square scaling law for higher-diffraction-efficiency gratings.

Temporal analysis of grating formation in photopolymer using the nonlocal polymerization-driven diffusion model

The nonlocal polymerization-driven diffusion model (NPDD) has been shown to predict high spatial frequency cut-off in photopolymers and to accurately predict higher order grating components. We propose an extension to the NPDD model to account for the temporal response associated with polymer chain growth. An exponential response function is proposed to describe transient effects during the polymerization process. The extended model is then solved using a finite element technique and the nature of grating evolution examined in the case when illumination is stopped prior to the saturation of the grating recording process. Based on independently determined refractive index measurements we determine the temporal evolution of the refractive index modulation and the resulting diffraction efficiency using rigorous coupled wave theory. Material parameters are then extracted based on fits to experimental data for nonlinear and both ideal and non-ideal kinetic models.

Generalized non-local responses and higher harmonic retention in non-local polymerization driven diffusion model based simulations

Non-local and non-linear models of photopolymer materials, which include diffusion effects, have recently received much attention in the literature. The material response is described as non-local as it is assumed that monomers are polymerized to form polymer chains and that these chains grow away from a point of initiation. The non-locality is defined in terms of a spatial non-local material response function. The material model is non-linear as a general non-linear material response to the incident light is included. Typically the numerical method of solution has involved retaining only up to four harmonics of the Fourier series of monomer concentration in the calculations. In this paper a general set of coupled first-order differential equations is derived which allow the inclusion of a higher number of harmonics. The resulting effect on the convergence of the algorithm, as the number of harmonics retained is increased, is investigated. Special care is taken to note the effect of physical parameters, i.e. the non-local material variance σ, the power-law degree k, and the rates of diffusion, D, and polymerization, F0.

Holographic data storage: optimized scheduling using the nonlocal polymerization-driven diffusion model

The choice of an exposure schedule that maximizes the uniformity and capacity of a holographic recording medium is of critical importance in ensuring the optimum performance of any potential holographic data storage scheme. We propose a methodology to identify an optimum exposure schedule for photopolymer materials governed by the nonlocal polymerization-driven diffusion model. Using this model, the relationship between the material properties (nonlocality and nonlinearity), the recording conditions and the schedule are clarified. In this way, we provide a first-order comparison of the behavior of particular classes of photopolymer materials for use as holographic storage media. We demonstrate, using the nonlocal polymerization-driven diffusion model, that the exposure schedule is independent of the number of gratings to be recorded and that the optimum schedule may necessitate leaving unpolymerized monomer at the end of the recording process.