Low refractive index composite materials based on polyvinyl pyrrolidone embedded metal nanoparticles

Vietnam National University Acknowledgments Vietnam Japan University I would like to express my special thanks of gratitude to my Master of Nanotechnology Program supervisors Professor Kajikawa Kotaro and Pham Tien Thanh, Ph.D who helped me in doing a lot of Research and i came to know about so many new things I am really thankful to them I would also like to thank the administrators of Vietnam Japan University and Japan INTERNSHIP REPORT International Cooperation Agency because of the golden Low to refractive based on I also thank opportunity have a index great composite internshipmaterials period in Japan Polyvinyl Pyrrolidone embedded metal nanoparticles to my friends who are students of Kajikawa Lab because of their enthusiasm supports Internship university: Finally, I wouldDepartment like to of thank myand parents always care and try to Electrical Electronic who Engineering bring meSchool of Engineering Tokyo Institute of Technology the best Supervisor: Prof Kajikawa Kotaro Pham Tien Thanh, Ph.D Student name: Pham Dinh Dat Student code: 17110063 Tokyo, November, 2018 Pham Dinh Dat Comments of Supervisors Contents Chapter 1: Overview of internship site Chapter 2: Theoretical basis 2.1 Transfer Matrix Method (TMM) 2.2 Effective Medium Approximation 2.3 Finite Difference Time Domain (FDTD) Chapter 3: Research contents Chapter 4: Considerations 4.1 Complex refractive index 4.2 Comparison between FDTD and TMM 4.3 Experimental results Conclusions and Future plans References Graph and picture list Fig 1: The relation of index of refraction and index of extinction to wavelength in visible range of Polyvinyl Pyrrolidone (PVP) embedded metal nanoparticles materials with different volume fill fraction and different metal Fig 2: Comparison transmittance of 500nm thin films PVP embedded 15nm diameter gold particles with 0.001 fill fraction of gold and with 0.01 fill fraction of gold Fig 3a: Image of PVP embedded 15nm diameter gold particles thin films Fig 3b: Optical density of PVP embedded 15nm diameter gold particles thin films Chapter 1: Overview of internship site Student ID number: 17110063 Name: Pham Dinh Dat Supervisor of internship in Japan: Prof Kajikawa Kotaro, Department of Electrical and Electronic Engineering, School of Engineering, Tokyo Institute of Technology Supervisor candidate in VJU: Pham Tien Thanh PhD, Program Master of Nanotechnology Exact schedule of internship: Time 01/10/2018 – Location Osaka Work Get the tutorial for the internship time 03/10/2018 04/10/2018 – Tokyo Study the research topic at Tokyo 27/11/2018 27/11/2018 – Osaka Institute of Technology Prepare and present the report 29/11/2018 about internship period Chapter 2: Theoretical basis 2.1 Transfer Matrix Method (TMM) The problem about the propagation of Light through an interface between two medium could be considered [1] The reflection coefficients of Transverse Electric polarized (TE) and Transverse Magnetic polarized (TM) light are obtained follow below: rs = (TE) rp = (TM) where is incident angle, is refraction angle, n is relative index of refraction of the two mediums The above can be used to solve multilayer structure problems but this problem is quite complicated For treating optical propagation in layered structures, the matrix methods are used widely [2] Following these methods, we can consider the reflection and the transmission of light through considering the forward and backward-propagating of electric fields (E fields) which are denoted as E+ and E-, respectively When light propagate through multilayer, it has types of process which should be considered There are the propagation through interface and the propagation through mediums Considering the propagation at interfaces, it possible to derive the relationship between the amplitudes of E fields adjacent to the i-j interface (i and j are notation of medium i and medium j which are light propagate through): Ei = MijEj, Where Ei, for example, is the two-component vector Ei =, And Mij is the transfer matrix for i-j interface It can be defined by: Mij = , Where rij and tij are the reflection and transmission amplitudes for light incident upon i-j interface from medium i They can be determined through reduced wave-vector component according to light propagation N, following that: (TE) (TM) Where ni, for example, is refractive index of medium i and i for example, is complex dielectric constant of medium i Considering the propagation through a medium, the other ingredient in transfer matrix recipe is the propagation matrix i, which accounts for the phase and amplitude changes of light through medium i following that: Ei(zi + di) = i Ei(zi), Where i , With = exp(iNik0di) and where Ni is reduced wave-vector component according to light propagation through on medium i, k is vacuum wavevector magnitude and di is thickness of medium i Considering light propagate through on medium to medium f, the overall transfer matrix can be determined following that: T = Mf(f-1)f-1M(f-1)(f-2)f-2…M21 = Then, the overall reflection amplitude, r, and the overall transmission amplitude, t, can be calculated following that: r = -T21/T22, t = T11 + T12.r 2.2 Effective Medium Approximation J.E Sipe and R.W Boyd [3] considered about a composite structure where any length scales are reasonably well-defined and all much less than wavelength of light This condition guarantees that scattering due to the inhomogeneity resulting from the composite nature of the material will be negligible, and it is led to move to an effective medium picture In this case, the material with host dielectric constant h and inclusion dielectric constant i, can be replaced by a uniform effective medium with a dielectric constant eff for considering the propagation of light It has simple models of this type of material which are considered depend on the topology of structure The first is called the Maxwell Garnett composite geometry which includes well-defined spherical inclusion in a host background The second topology still disordered but where the constituent material are more or less interspersed, is referred to as the Bruggeman geometry And the third topology is an ordered, layered composite geometry Considering the Maxwell Garnett geometry, we can begin with the consideration of a polarizability  which characterize an ordered lattice of atoms in a vacuum Each atom is under impact of two factors those are the external electric field (E) and the interaction between each other atoms which can be considered as a local field So, it possible to derived the relation between atomic polarizability  and the dipole moment  following that: local field correction If the lattice consists of N atoms in a volume V, the dipole moment per unit volume, P is given by: P= = Then writing the dielectric displacement D = E + 4P = E, we can find that the dielectric constant  can be obtain by solving the so-called Claudius Mossotti equation, , Also referred to as Lorentz Lorentz relation when the relation between the refraction index n and the dielectric constant,  = n2, is used To apply arguments like this to Maxwell Garnett topology, it necessary to identify the effective polarizability of an inclusion sphere i Considering inclusions under the impact of the field E0 far from inclusion and the depolarization field in the sphere, the dipole moment of inclusion sphere within the host medium  i is  i =, Where a is the radius of the sphere, and we can identify an effective polarizability as = Then, for inclusion spheres are not in vacuum but in a host material with dielectric constant h, we can derive the Maxwell Garnett relation: f Where f = is the volume fill fraction of the inclusion Applying same arguments to consider two (or more) inclusions with fill fraction f and f2 and dielectric constant 1 and 2, respectively, in a host medium, the result is = f1 + f2 For consideration for Bruggeman topology, the two constituents are to be thought of on an equal footing, each interspersed with the other It might expect that the host medium should here be thought of as the effective medium itself So we can derive, with h = eff, that: = f1 + f2 In the layered case, the continuity of tangential component of the effective medium dielectric constant parallel appropriate for electric field in the plane defined by the layers parallel = faa + fbb, where the dielectric constants of layers are denoted a and b and their fill fraction by fa and fb, respectively Similarly, the effective medium dielectric constant perpendicular appropriate for an electric field perpendicular to that plane, 2.3 Finite Difference Time Domain The finite-difference time-domain (FDTD) method is arguably the simplest, both conceptually and in terms of implementation, of the fullwave techniques used to solve problems in electromagnetics The FDTD method loosely fits into the category of “resonance region” techniques, i.e., ones in which the characteristic dimensions of the domain of interest are somewhere on the order of a wavelength in size The FDTD method employs finite differences as approximations to both the spatial and temporal derivatives that appear in Maxwell’s equations (specifically Ampere’s and Faraday’s laws) [4] The FDTD algorithm as first proposed by Kane Yee in 1966 employs second-order central differences The algorithm can be summarized as follows: Replace all the derivatives in Ampere’s and Faraday’s laws with finite differences Discretize space and time so that the electric and magnetic fields are staggered in both space and time 2 Solve the resulting difference equations to obtain “update equations” that express the (unknown) future fields in terms of (known) past fields Evaluate the magnetic fields one time-step into the future so they are now known (effectively they become past fields) Evaluate the electric fields one time-step into the future so they are now known (effectively they become past fields) Repeat the previous two steps until the fields have been obtained over the desired duration Chapter 3: Research contents The assignment: Calculate to predict optical properties of material Fabricate real material and determine their properties to compare with prediction Implementation methods: Calculation: Transfer Matrix Method Simulation: Finite Difference Time Domain Experiment: Spin-coating Results: Calculation results: transmittance (wavelength dependence), refractive index (volume fill fraction dependence, wavelength dependence, type of metal sphere inclusion) of material Simulation results: transmittance of PVP-Au nanoparticles thin film Experimental results: transmittance and optical density of PVP – Au nanoparticles (15nm diameter) thin films Chapter 4: Considerations 4.1 Complex refractive index I used Maxwell Garnett topology and Bruggeman topology to predict complex refractive index of PVP embedded metal nanoparticles composite materials The results are shown below 1.6 1.1 1.4 0.9 1.2 0.7 Value Value 0.8 0.6 0.5 0.4 0.3 0.2 0.1 0.38 0.43 0.48 0.53 0.58 0.63 0.68 0.73 0.78 -0.10.38 0.43 0.48 0.53 0.58 0.63 0.68 0.73 0.78 4.5 3.5 2.5 1.5 0.5 0.38 0.43 0.48 0.53 0.58 0.63 0.68 0.73 0.78 Wavelength (mm) Wavelength (mm) 3.5 2.5 Value Value Wavelength (mm) 1.5 0.5 0.38 0.43 0.48 0.53 0.58 0.63 0.68 0.73 0.78 Wavelength (mm) Fig 1: The relation of index of refraction (a,c) and index of extinction (b,d) to wavelength in visible range of Polyvinyl Pyrrolidone (PVP) embedded metal nanoparticles materials with different volume fill fraction and different metal (a) and (b) were calculated following Bruggeman topology (c) and (d) were calculated following Maxwell Garnett topology Fig shows the significant different between calculation results following Bruggeman topology and it following Maxwell Garnett topology This thing is not very clear with low fill fraction of metal but it become cannot negligible A number of studies reported about this problem [3],[5], [6] J I Gittleman and B Abeles [5] conclude that the Bruggeman topology is not applicable to metal dispersions while the Maxwell Garnett topology provides a reasonably good description of the dielectric constant of such systems And, almost of report relating to metal particles in dielectric host I have read using Maxwell Garnett topology to predict properties of materials I think that the main reason of the favors for Maxwell Garnett topology is that it gives better results relating to absorption properties It can be seen in Fig 1, while the index of extinction calculated following Bruggeman topology not show any specific point, the index of extinction calculated following Maxwell Garnett topology show noticeable absorption peaks of metal particles However, I will calculate following both two types of topology because of two reasons Firstly, I want to study properties of composite material with volume fill fraction of metal nanoparticles on wide range Maxwell Garnett topology gives a good description for the matrix and the inclusions in an unsymmetrical fashion and is in principle limited to low values of fill fraction It is able to describe qualitatively the surface plasmon resonances for metal–dielectric composites, but cannot account for percolation among the inclusions, except for the trivial case of fill fraction equal In contrast to the Maxwell Garnett topology, Bruggeman topology includes the percolation among the inclusions for filling factors higher than 0.3, although it is not able to represent appropriately the surface plasmon resonances of isolated metal particles embedded in a dielectric matrix [6] The other reason is that the behavior of the index of refraction relating to wavelength of light is very different on two calculation topologies There is very interesting point which can be easily verify by comparison with experimental results 4.2 Comparison between FDTD and TMM The optical properties of material were predicted using both TMM and FDTD method I tried to use FDTD simulation to verify result of Maxwell Garnett topology and Bruggeman topology However, because of the limitation of time, I just had a comparison of transmission results between FDTD simulation and calculation using TMM The results are showed in below Transmittance 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 a 380 Maxwell Garnet topology Bruggeman topology FDTD 430 480 530 580 630 680 730 780 Transmittance Wavelength (nm) 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 b 300 Maxwell Garnet topology Bruggeman topology FDTD 350 400 450 500 550 600 650 700 750 800 Wavelength (nm) Fig 2: Comparison transmittance of 500nm thin films PVP embedded 15nm diameter gold particles with 0.001 fill fraction of gold (a) and with 0.01 fill fraction of gold (b) The results in Fig 2.a are quite similar There is fit with conclusion which is mentioned in [3] In case of low fill fraction, Maxwell Garnett topology and Bruggeman topology give almost same results There are differences in case of higher fill fraction In Fig 2, the transmittance result calculated following Maxwell Garnett topology shows significant signal of the absorption while it does not exist in spectra which is calculated following Bruggeman topology Besides that, it might have a strange result at wavelength is about 550nm given by FDTD method There are many reasons for this problem The simplest reason is that it just a error of calculation process But, it can be due to the mesh not enough “smooth” or number of result taken point is low… The other idea is that it is not a problem but it just right for a model which I made for simulation but not right for this type of materials Anyway, it’s necessary to optimize the model and gain more data from simulation in the future 4.3 Experimental results I fabricated samples to compare with calculation results Fig 3a shows image of those sample The homogeneous solution of PVP and gold nanoparticles were coated on glass substrates using spin-coater The amounts of solution used for samples to are 300l, 400l, 600l and 700l, respectively Samples to were dried on air for 24 hours After that, sample was added methanol while drying using hot plate with 90 o temperature set Using MCPD-3000 spectrometer, I also investigate results of optical density of those samples which are showed in Fig 3b The absorption signal at wavelength about 530nm and pink color verify existence of gold nanoparticles However, we can see that the gold particles were not had uniform distributed on thin films base on images 1 3 Optical Density 0.3 Sample 0.25 Sample 0.2 Sample 0.15 Sample 0.1 0.05 2 4 380 430 480 530 580 630 680 730 780 Wavelength (nm) a Fig 3: (a) Image of PVP embedded 15nm diameter gold particles thin films, (b) Optical density of those samples These results should be used for compare with calculation results Unfortunately, I could not complete this work in time because of a problem For comparison, real thickness of fabricated thin films is very important With tools those are available in laboratory; the thickness can be evaluated from linear relation of absorption and thickness This idea includes steps 1st step is evaluation thickness of think films (at least 3-4 films which have thickness about micron) 2nd step is fabrication thickness films (same thickness as 1st step) which are added defined dye and derive linear relation between thickness and absorption However, the fabrication method for st step has been not achieved PVP solution has very low viscosity Besides that, the used Au colloidal solution is very low concentration Therefore, spin-coating can’t be used to make requirement films until now Low rotation speed gives inhomogeneous films, non-uniform concentration and consumes long time It takes more than a day for about 400l of solution Using hot plate can shorten time but gives worse quality of films High rotation speed gives homogenous and almost uniform concentration but critically consume chemical Increase concentration of polymer to get more viscous solution is a promise able idea until last of internship periods although it still poses a problem about limitation of metal particles fill fraction on material Conclusions and Future plans Conclusions - Practiced using of MCPD-2000 optical measurement system for Bauhinia Purpurea and Pistia Stratiotes leaf samples and PVP embedded Au nanoparticles films, using of thermal evaporation system to evaporate Chromium and Gold for fabrication gold substrate, using spin-coater to fabricate PVP embedded Au nanoparticles films - Practiced using Mathematica Software to predict optical properties (transmittance, reflectance, optical density, extinction, scattering) of single layer of dielectric and metal, multilayer structure metal-dielectric included, nanoparticles, microparticles, multilayer hyperbolic metamaterial, metal nanoparticles embedded on dielectric matrix metamaterial - Practiced using FullWAVE Software (based on FDTD method) to simulate metal nanoparticles embedded on dielectric matrix metamaterial Future plans - Continue calculation and simulation for metal nanoparticles embedded on dielectric matrix metamaterial to optimize prediction - Fabrication Poly-Vinyl-Pyrrolidone embedded Silver nanoparticles and PolyVinyl-Pyrrolidone embedded Gold nanoparticles samples then determines those optical properties References [1] Fowles, Grant R Introduction to modern optics Courier Corporation, 1989 [2] Bethune, D S "Optical harmonic generation and mixing in multilayer media: analysis using optical transfer matrix techniques." JOSA B 6.5 (1989): 910-916 [3] Sipe, John E., and Robert W Boyd "Nanocomposite materials for nonlinear optics based on local field effects." Optical Properties of Nanostructured Random Media Springer, Berlin, Heidelberg, 2002 1-19 [4] Schneider, John B Understanding the Finite-Difference Time-Domain Method, April 5, 2017 [5] Gittleman, J I., and B Abeles "Comparison of the effective medium and the MaxwellGarnett predictions for the dielectric constants of granular metals." Physical Review B 15.6 (1977): 3273 [6] Jordi Sancho-Parramon, Amin Abdolvand, Alexander Podlipensky, Gerhard Seifert, Heinrich Graener, and Frank Syrowatka, "Modeling of optical properties of silver-doped nanocomposite glasses modified by electric-field-assisted dissolution of nanoparticles," Appl Opt 45, 8874-8881 (2006) ... International Cooperation Agency because of the golden Low to refractive based on I also thank opportunity have a index great composite internshipmaterials period in Japan Polyvinyl Pyrrolidone embedded. .. relation of index of refraction and index of extinction to wavelength in visible range of Polyvinyl Pyrrolidone (PVP) embedded metal nanoparticles materials with different volume fill fraction and... plans - Continue calculation and simulation for metal nanoparticles embedded on dielectric matrix metamaterial to optimize prediction - Fabrication Poly-Vinyl -Pyrrolidone embedded Silver nanoparticles