A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of Electrical Engineering Doctor of Philosophy 202 1 ................................ ................................ ................................ .................. ................................ ................................ ................................ ................. ................................ ................................ ................................ ...................... ................................ ................................ ................................ .......................... ................................ ................................ ................................ .......................... ................................ ................................ ................................ ................................ ................................ ................................ ..................... ................................ ................................ ................................ ....................... ................................ ................................ .................... ................................ ................................ ................................ . ................................ ................................ ................................ ......... ................................ .......................... ................................ ..... ................................ ................................ .. ................................ ................................ ..................... ................................ ................................ .............. 2.4.1 Existing PM Monitoring Systems ................................ ................................ .............. PM monitoring Methods Developed by Research Groups ................................ ........ ................................ ................................ ............................ ................................ ................................ ... ............... ................................ ............. ................................ ................................ ................................ ................................ ..................... ................................ .................... ................................ ................................ ................................ .... ............ ................................ ..................... ................................ ................................ ................................ ........................ .............................. ................................ ................................ . ................................ ...................... 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..... ................................ ................................ ................................ ................................ .................. ................................ ................................ ................................ .. ................................ ................................ ................................ ................................ .................. ................................ ................................ ................................ ............................. ................................ ................................ ........................ ................................ ................................ ....................... ................................ ................................ .................. ................................ ................................ ................................ ......... ........... ................................ ................................ ................................ ........... ................................ ................................ ....................... ................................ ................................ ................................ ................... ......... ................................ ................................ ................................ ..................... ................................ ................................ ......... ................................ ................................ ................................ ................................ ................ .... ......... ................................ .............................. ............................... ................................ ................................ ................................ ......... 1 Introduction 1.1 1.2 Challenges 1.3 Approach and T hesis G oals 1.4 Thesis O utline 2 Background 2.1 Introduction to Air borne P ollutant s 2.1.1 Gas eous A ir P olluta nts 2.1.2 Particulate Matter 2.2 Air Pollutants Health E ffect s and E conomic I mpact 2.2.1 Gaseous Air Pollutants Health Effects and Economic Impact 2.2.2 PM Health Effects and Economic Impact 2.3 Gas Sensor Technologies R eview 2.4 PM Monitoring Technologies Review 2.4.1 Exist ing PM M onitoring S ystem s 2.4.1.1 2.4.1.2 2.4.1.3 2.4.1.4 2.4.2 PM monitoring Methods D eveloped by R esearch G roup s 2.4.2.1 2.4.2.2 2.4.2.3 2.4.2.4 2.4.2.5 3 Room Temperature Ionic Liquid ( RTIL ) Gas Sensor for Personal Gaseous Air Pollutant Exposure Monitoring 3.1 Our Pr eliminary Work on RTIL Gas Sensors 3.2 Verificatio n of S electivity in RTIL Electrochemical Gas Sens ing Technology 3.3 Microfabricated Planar RTIL Electrochemical Gas Sensor 3.3.1 MPRE Sensor Design 3.3.2 MPRE Sensor Fabrication and Array Assembling 3.4 Electrochemical T est for Gaseous Airborne Pollutants 3.4.1 Experimental Setup 3.4.2 Rapid T est A pproach to Overcome the Long Response and Drift Challenge 3.4.3 Electrochemical T est for M ultiple G as P ollutants 3.4.3.1 3.4.3.2 3.4.3.3 3.5 Conclusion 4 Microfluidic P latform for C ontinuous Personal PM M onitoring 4.1 Requirements Analysis and Design Approach 4.2 Technology O ptions for Continuous PM M onitoring 4.2.1 Methods for P article Capture 4.2.2 Methods for Continuous S ize F ractionation 4.2.2.1 4.2.2.2 4.2.3 M ethods for Continuous Q uantification 4.2.3.1 4.2.3.2 4.2.3.3 4.2.4 Method for Continuous C lassification 4.3 A Platform for R eal - time C ontinuous PM M onitoring 4.4 Discussion 5 Advanc ing Key Technologies for PM Monitoring 5.1 Electrochemical Quantification 5.1.1 Sample Preparation and Test Setup Commercial polystyrene bead solutions (Sigma - Aldrich, 10 wt% concentration) were obtained with 1 µ m and 10 µm particles. Each particle - containing solution was diluted by a factor of 10 and treated under ultrasonic for over 1 hour before each test to ensure the beads were not clustered. Several 80 mL samples with variable particle concentrations were pr epared for electrochemical measurement. Each 80 mL sample contained 24 mL of electrolyte solution (8 mL KCl, 16 mL K 3 [Fe(CN) 6 ]), P mL of particle - containing solution and (56 - P ) mL of DI water, where P is a variable volume of 10:1 - diluted particle - containin g solution. P was varied from 0 to 5 mL and represents the relative particle concentration that increases with P . For electrochemical measurements , a CHI 760 (CH Instrument, USA) electrochemical instrument was utilized for AC impedance, CV and DPV methods. Additional measurements using a custom thumb - sized electrochemical system are presented in section 5.1.6. Studies were conducted with commercial carbon, commercial gold, and custom microfabricated gold electrodes. All electrodes were immersed into beakers containing the 80 mL solutions of variable particle concentrations. Electrodes were cleaned between tests to avoid cross contamination between sa mples. The results below demonstrate some of the options available to designers who can analyze tradeoffs in cost, size, and performance to meet application needs . 5.1.2 Electrochemical Detection with Commercial Carbon Electrode 5.1.3 Electrochemical Detection with Commercial Gold Electrode 5.1.4 Ionic Electret Theory Analysi s ˘¥ ˘¥ 5.1.5 Electrochemical Detection with Microfabricated Gold Electrode 5.1.6 CV measurement results with aMEASURE 5.2 Microfluidi c Size Fractionation 5.2.1 I - shaped DLD Separation for PM Size Fractionation To design the PM microfluidic separation device, COMSOL Multiphysics fluid flow simulations were performed for a DLD structure with I - shaped pillar array . This study provided insight into the fluidic velocity profile and the effect of the pillar array on laminar flow in liquid samples with 2.5 µm as the critical separation diameter. Fig. 5. 9 (a) shows the COMSOL 3D model of a 4 - pillar segment. Following the reported DLD design approach that will separate micro particles of various sizes [9], we chose the I - shaped pillars to be 15 µm × 15 µm × 15 µm (height) with a 10 µm gap between pillars. Fig. 5. 9 (b) shows that the 3D simulated velocity magnitude exhibits peaks at the corners of the pillars as predicted by DLD theory. Fig 5. 9 (c) is the 2D projection of the velocity magnitude distribution at the middle of the pillar height showing simulated streamlines. COMSOL simulation shows that large particles passing be tween pillars will experience different velocities along different portions of the particle, which can induce rotation that helps the particle follow the pillar gradient and thus enhance separation efficiency. Fig. 5. 9 (b) results were obtained using a liqu id sample with physical parameters listed in the figure caption that were taken from [195] . To separate particles greater than 2.5 µm for PM 2.5 monitoring, D C = 2.5 µm. For g = 10 µm, calculation from equation ( 5. 3) shows that N 41.8. The angle of the pillar gradient, , shown in Fig. 5. 8 , can be determined from For N = 41.8, 1.4 was used to set the pillar gradient. 5.2.2 I - shaped DLD Microchannel Fabrication 5.2.3 Particle Separation Results To verify microfluidic particulate separation, polystyrene beads were chosen because they are commercial available in various sizes appropriate for PM studies and have the same density as PM [28 , 29] . Prior to separation experiments, 1% w/v Pluronic F127 (Sigma Aldrich, USA) and DI - water were pumped into the microfluidic device to avoid clustering of particles as well as adhesion of particles to microfluidic channel walls. 1 mL of 1 µm and 10 µm polystyrene bead solutions (10 wt% concentration, contain 1 µm and 10 µm beads ~1 ) were both diluted 10 times before mixing to prepare the test sample. The experiment setup is shown in Fig. 5.1 1 (a), where the test sample solution containing the diluted mix of 1 µm and 10 µm particles was pumped into the sample inlet at the rate of 0.5 µL/min using a syringe pump. Two other syringe pumps were then used to introduce phosphate - buffered saline (PBS) buffer solution into side inlets at the rate of 0.2 µL/min . As seen in Fig. 5.1 1 (a), the solutions exiting from the three device outlets were collected in separate reservoirs. The entire separation experiment was recorded using a camera attached to the microscope on top of a probe station. Because the sample so lutions were pumped in the middle of the microfluidic channel, the smaller particles were expected to appear in the Middle - out and larger particles at the Bottom - out outlets. Following repeated experiments with the same results, the recorded videos clearly show the 10 µm polystyrene beads being shifted to flow along the pillar gradient to the Bottom - out outlet. As desired, the 1 µm polystyrene beads were observed to follow their initial flow paths to collect at the Middle - out outlet without being affected b y the pillars. These results exactly match design expectations. To further confirm the separation efficacy, samples from each of the collection reservoirs were extracted by pipettes and examined under a microscope. As shown in Fig. 5.1 1 (b), the Bottom - out outlet contained only 10 µm particles with no observable 1 µm particles, while the Middle - out outlet contained only 1 µm particles with no observable 10 µm particles. Additional experiments were run to observe the impact of flow rate on separation performa nce. As expected, at low flow rates, below 0.1 µL/min, 1 µm particles were occasionally observed at the Bottom - out outlet due to particle diffusion. 5.3 Discussion 6 Externally Balanced Cascade DLD for High Dynamic Range Multi - Size Particle Separation 6.1 Motivation . 6.2 Externally B alanced Cascade DLD Approach 6.2.1 Externally Balanced Cascade DLD Approach 6.2.2 Fluidic M echanisms and D esign R ules for M ulti - section DLD Variables Definition D ck Critical diameter of particle D p D p_max Biggest particle that will be separated D p_min Smallest particle that will be separated w Diameter of the pillar g Gap between pillar (in lateral direction) D x Center to center distance in flow direction D y Center to center distance in lateral direction Total length of the device NoS Number of sections SSF Section scaling factor N Number of rows required for one column shift Pillar diameter to gap ratio ( = w/g ) 1.1 design tolerance The gradient angle (tan( )=1/N) m 1 (number of columns to be displaced) 6.3 Multi - section Mathematic M odel 6.4 Modeling Results and Analysis: Theoretical Limits 6.4.1 L vs NoS R elationship for Different SSF 6.4.2 L vs SSF Relationship for Different NoS 6.4.3 L vs SSF Relationship for Different NoS 6.5 Modeling Results and Analysis : Practical Limits 6.5.1 Fabrication Limits 6.5.2 Gamma Variation ( ) 6.5.3 Pillar Shape 6.6 Discussion and Case Studies 6.6.1 Case 1 6.6.2 Case 2 6.6.3 Case 3 Cases DLD device length Case 1 : I - shape pillar (one section design) ; g k_fablim = 2 µm; w k_fablim 6 µm; D p_min = 0.01 µm ; D p_max = 10 µm L = 60 m Dynamic range =1000 Case 2: Circle - shape pillar (cascade design) ; g k_fablim = w k_fablim = 0.1 µm; D p_min = 1 µm ; D p_max = 10 µm ; L ~ 0.3 mm Dynamic range =10 D p_min = 0.01 µm ; D p_max = 10 µm ; L ~ 41 mm Dynamic range =1000 Case 3: Circle - shape pillar (cascade design) ; g k_fablim = w k_fablim = 10 µm; D p_min = 1 µm ; D p_max = 100 µm ; L ~ 8 mm Dynamic range =100 6.6.4 Conclusion 7 Internally B alanced Cascade DLD for a PM Monitoring Microsystem 7.1 Motivation 7.2 Internally Balanced Cascade DLD Approach Sections Dc (µm) g/w (µm /µm ) (degree) N (rows per column shift) 1 2.5 10 /10 1.582° ~40 2 1 4/4 or 4/8 1.582° ~40 3 0.5 2/3 or 2/6 1.582° ~40 4 0.2 1/2 or 1/4 0.994° ~60 5 0.1 1/1 or 1/2 0.235° ~250 7.3 Boundary Design Strategy to Minimize Wall Effect 7.4 H ydraulic R esistance B alance 7.4.1 Fluid Mechani cs 7.4.2 Hydraulic Resistance Analysis Using Circuit Analogy 7.4.3 Approach for Hydraulic Resistance Balance 7.4.4 CFD Simulati on of Hydraulic Resistance Balance fluid properties from material material (water) dynamic viscosity 8.9*10 - 4 (Pa·s) density 1000 (Kg/m3) temperature 293.15 (K) wall condition non - slip input (normal inflow velocity) 0.001 (m/s) output suppress backflow mesh finer big gap region (g1/w1) 10/10 (µm) small gap region (g2/w2) 4/8 (µm) 7.5 Section Interface D esign 7.5.1 Design Along the Flow Direction to Minimize the Anisotropic Zone 7.5.2 Design Approach Along the Lateral Direction to Minimize t he Anisotropic Zone Interface design Largest lateral pressure difference Anisotropic zone width (x direction) Anisotropic zone width (y direction) Long wall transition ~45 Pa ~ 420 µm ~ 260 µm No - pillar transition ~ 19 Pa ~270 µm ~380 µm Wave transition ~31 Pa ~ 460 µm ~ 200 µm Transition section ~ 9 Pa ~ 19 0 µm ~ 80 µm 7.6 A Five Section Internally Balanced Cascade DLD Design for Coarse to Ultrafine PM Monitoring Sections Dc (µm) g/w (µm/µm) (degree) N (rows per column shift) Anisotropic zone (Z, µm) Min imum section length (mm) 1 2.5 10/10 1.582° ~40 / 2.4 72 1 - 2 - 1 / 8/10 1.582° / 3.2 56 1 - 2 - 2 / 6/8 1.582° / 3.2 72 2 1 4/8 1.582° ~40 1.6 60 2 - 1 - 3 / 3/7 1.582° / 1.6 64 3 0.5 2/6 1.582° ~40 1.6 96 4 0.2 1/5 0.994° ~60 5 / 5 0.1 1/2 0.235° ~250 Interface design Minimum device length Minimum device width Fluid inlets/outlets Required Pumps Internally balanced cascade DLD ~ 15.4 mm ~0.6 mm 3/6 3 Externally balanced cascade DLD ~ 41 mm ~0.08 mm 10/10 6 7.7 Discussion 8 Summary, Contribution s , and Future work 8.1 Summary 8.2 Contributi ons The ionic liqui d (IL) gas sensing technology shows many promising features for wearable sensors in gaseous air pollutants exposure monitoring. In this work, the microfabricated planar room temperature ionic liquid based (MPRE) gas sensor array was developed through a new ly invented microfabrication procedure. Rapid test through a new transient double potential amperometry method was explored to resolve the drift issue with reported 63.2% relative stand variation (RSD) compare to traditional constant potential amperometry. Multiple air pollutants, including methane, sulfur dioxide and ozone, were measured with the MPRE gas sensor with a sensitivity of Microfluidic microsystem Electrochemical detection can offer accurate PM quantif ication as well as the potential for classification of chemical composition. In this work, the ionic electret effect - based electrochemical measurement of PM concentration was explored using different electrochemical methods and electrode materials, and dif ferential pulse voltammetry (DPV) with gold electrodes was found to give the best sensitivity and repeatability. A compact electrochemical instrumentation system was implemented to demonstrate this detection scheme as a wearable PM monitoring platform. DPV results with polystyrene particles This work paves a path which leads the electrochemical measurement to wearable PM quantification. DLD microfluidic s eparator provides the capability to continuously separate particles with high separation efficiency and resolution, as well as being predictable and easy to operate. In this work, an I - shape DLD device was microfabricated to achieve ~100% separation for fi ne PM. In order to fulfil the requirements of real - time continuous PM size fractionation, including both high dynamic range and the desire to separate particles into multi size bins, an externally balanced cascade multi - section DLD and an internally balanc ed cascade multi - section DLD were proposed. A mathematic model was built to aid the design for the externally balanced approach. To better extend the dynamic range of multi - size cascade DLD while make the device highly integrated for real - world PM monitoring, a monolithic design that are capable to solve these practical implementation challen ges would be the highly preferred choice. Computational fluid dynamic (CFD) simulation was performed to study the interface design for the internally balanced approach. This work provides a suitable approach for microfluidic size fractionation toward a wea rable PM pollutants exposure monitoring system covering PM from PM10 to ultra - fine particle (UFP). 8.3 Future work Th e selectivity of the MPRE gas sensor array rely on the fact that sensors which consist of the array have specific combination of design parameters, including electrochemical method, electrode and electrolyte material, when target for specific pollutants. In order to make the sensor array functiona l that each element can collect data simultaneously, design a multi - mode resource - sharing CMOS circuit tailored to the MPRE gas sensor array is critical. Lab - on - CMOS process which enable a monolithic design, can enhance the system miniaturization. PM element or component information can be extremely complex, which could make the component classification a heavily data intense work. In addition to the quantification functio n, a capacitively particle counter with the single particle counting capability could serve as a forerunner for the component classification . The externally balanced and internally balanced cascade multi - section DLD approach as well as the design developed in this work build up the foundation of the PM size fractionation system that can separate particles into multiple size bins with high dyn amic range. In future, the detailed device design with consideration of input and output, device fabrication, experimental setup, as well as the data analysis are required to implement the cascade multi - section DLD in real world application. The computational fluidic analysis of the internally balanced cascade multi - section DLD approach presented in this work build up the foundation of how to implement the int ernally balanced cascade DLD in a monolithic PM size fractionation system. In future, regarding the real implementation, alternative designs, such as tilting the channel and add serpentine path in big gap area, that can simplify the device fabrication proc edure and enhance the separation performance will be studied . Technologies for capture, size fractionation, quantitation, and classification were studied in this work. In order to develop the aPM system that can be widely distributed for real - time continuous air pollutants monitoring in real world, the integration pr ocedure need to consider many elements, including but not only, device size, power consumption, cost, pump system that drive the fluid, as well as the liquid replacement and waster dispose need to be carefully studied. A PPENDIX A : Fabrication flow recipes 1) Microchannel etching: 2) Soft lithography for PDMS lid: 3) Bonding: A PPENDIX B : MATLAB Code for the Mathematic Model of the Externally Balanced Cascade Multi - size DLD function [L,Dcmin,pos_001, pA_001, pos_01, pA_01, pos_1, pA_1] = DLD_theory(SSF_array,NoS_array,DR_array) %Declaration of variables %Section (Critical Dimension) Scale Factor, SSF [alpha], Dc(k)=SSF*Dc(k+1) %Number of Section, NoS [k], i form 1 to NoS %Separation Device Length, L %Dc, DLD critical dimension %Separation Device Resolution, DR (Dcmin) = f(SN,SSF) %**************************Theory********************************** %*****Fixed variables gkg = 2; lkg = 6; gamma = lkg/gkg; Beta = 1.1; % 10% more space based on the size of the particule %initial condition for k=1 %Dc1=5; g1=10*Beta; %Values to be evaluated alfa = SSF_array; %SSF k = NoS_array; %NoS %Total length of the device based on the previous declarated variables for j=1:length(alfa) Dck = 10/alfa(j); gk = g1; for i=1:length(k) if i==1 Nk(j,i) = (Dck(i)/(1.4*gk(i)))^( - 1/0.48); Dcmin(j,i) = Dck(i); else Dck(i) = Dck(i - 1)/alfa(j); gk(i) = Dck(i - 1)*Beta; Nk(j,i) = (Dck(i)/(1.4*gk(i)))^( - 1/0.48); Dcmin(j,i) = Dck(i); end %calculating length of each section yk(i) = ceil(Nk(j,i))*(gk(i)+(g k(i)*gamma)); L(j,i) = sum(yk(1:i)); end clear Dck gk yk % for i=1:length(k) % L(j,i) = sum(yk(1:i)); % end end %Selection of DCmin values (name in the paper: DR) DC_values = DR_array; Z = size(Dcmin); for i=1:length(DC_v alues) for j=1:Z(2) %for n=1:Z(2) temp = find(Dcmin(:,j)<(DC_values(i)+DC_values(i)*0.15) & Dcmin(:,j)>(DC_values(i) - DC_values(i)*0.15)); if isempty(temp)==1 N_Dcmin(i,j) = 0; else N_Dcmin(i,j) = temp(1); end %end end end pos_001 = find(N_Dcmin(1,:) ~= 0); pA_001 = N_Dcmin(1,pos_001); pos_01 = find(N_Dcmin(2,:) ~= 0); pA_01 = N_Dcmin(2,pos_01); pos_1 = find(N_Dcmin(3,:) ~= 0); pA_1 = N_Dcmin( 3,pos_1); %pos_001, pA_001, pos_01, pA_01, pos_1, pA_1 end %Declaration of variables %Section (Critical Dimension) Scale Factor, SSF [alpha], Dc(k)=SSF*Dc(k+1) %Number of Section, NoS [k], i form 1 to NoS %Separation Device Length, L %Dc, DLD critical dimension %Separation Device Resolution, DR (Dcmin) = f(SN,SSF) %**************************Theory********************************** clear all %% Plot 1 of ISCAS paper; L vs K (1:30) for different alphas(1.5 - 3.4, 0.2 step) without Dcmin clear all SSF_array = 1.5:0.1:3.4; %alpha NoS_array = 1:15; %k DR_array = [0.01, 0.1, 1]; [L,Dcmin,pos_001, pA_001, pos_01, pA_01, pos_1, pA_1] = DLD_theory(SSF_array,NoS_array,DR_array); L = L./1000; %to convert units from micrometers to milimeters %Individual plot for L vs K for different alphas figure; CO(:,:,1) = ones(length(SSF_array)).*linspace(0,0.8,length(SSF_array)); % red CO(:,:,2) = ones(length(SSF_array)).*linspace(0.5,1,length(SSF_array)); % green CO(:,:,3) = o nes(length(SSF_array)).*linspace(0,0.1,length(SSF_array)); % blue plot(NoS_array,L(1,:), 'LineWidth' ,3, 'color' ,[CO(1,1,1) CO(1,1,2) CO(1,1,3)]); %legend(strcat('alpha = ',num2str(alfa(1)))) for n=2:length(SSF_array) hold on ; plot(NoS_array,L(n,:), 'L ineWidth' ,3, 'color' ,[CO(1,n,1) CO(1,n,2) CO(1,n,3)]); %plot(NoS_array,L(n,:))%,'DisplayName',strcat('alpha = ',num2str(alfa(n)))); end title( 'L vs NoS: Theoretical Analysis' ) xlabel( 'Number of Sections, NoS' ) ylabel( 'Separation Device Length, L (mm)' ) % \ mum grid on ylim([0.2 2.2]); figure;imagesc(SSF_array,SSF_array,CO) %% Plot 2 of ISCAS paper; L vs alpha (1.1 - 3.4) for different NoS (1 - 10) clear all SSF_array = 1.1:0.1:3.4; %alpha NoS_array = 1:15; %k DR_array = [0.01, 0.1, 1]; [L,Dcmin,pos_001, pA_001, pos_01, pA_01, pos_1, pA_1] = DLD_theory(SSF_array,NoS_array,DR_array); L = L./1000; %to convert units from micrometers to milimeters Lt = L'; %Individual plot for L vs K for different alphas figure; CO(:,:,1) = ones(length(NoS_ar ray)).*linspace(0,0,length(NoS_array)); % red CO(:,:,2) = ones(length(NoS_array)).*linspace(0,0.3,length(NoS_array)); % green CO(:,:,3) = ones(length(NoS_array)).*linspace(0,1,length(NoS_array)); % blue plot(SSF_array,Lt(1,:), 'LineWidth' ,3, 'color' ,[CO(1,1, 1) CO(1,1,2) CO(1,1,3)]); %legend(strcat('alpha = ',num2str(alfa(1)))) for n=2:length(NoS_array) hold on ; plot(SSF_array,Lt(n,:), 'LineWidth' ,3, 'color' ,[CO(1,n,1) CO(1,n,2) CO(1,n,3)]); %plot(NoS_array,L(n,:))%,'DisplayName',strcat('alpha = ',num2str(alfa(n)))); end title( 'L vs SSF: Theoretical Analysis' ) xlabel( 'Section Scale Factor, SSF' ) ylabel( 'Separation Device Length, L (mm)' ) % \ mum grid on ylim([0 2.2]); figure;imagesc(NoS_array,No S_array,CO) %% Plot 3 of ISCAS paper; 3D plot - L vs NoS vs SSF (1.1 - 3.4) for different NoS (1 - 10) clear all SSF_array = 1.1:0.1:3.4; %alpha NoS_array = 1:15; %k DR_array = [0.01, 0.1, 1]; [L,Dcmin,pos_001, pA_001, pos_01, pA_01, pos_1, pA_1] = D LD_theory(SSF_array,NoS_array,DR_array); L = L./1000; %to convert units from micrometers to milimeters %pos_X is the position on k %pA_X is the position of the alpha value figure surf(NoS_array,SSF_array,L) xlabel( 'Number of Sections, NoS' ) ylabel( 'Section Scale Factor, SSF' ) zlabel( 'Separation Device Length, L (mm)' ) % \ mum hold on for i=1:length(pos_001) hold on ; plot3(pos_001(i),SSF_array(pA_001(i)),L(pA_001(i),pos_001(i)), 'mo' , 'LineWidth' ,2, 'MarkerSize' ,5); end for i=1:length(pos_01) hold on ; plot3(pos_01(i),SSF_array(pA_01(i)),L(pA_01(i),pos_01(i)), 'ko' , 'LineWidth' ,2, 'MarkerSize' ,5); end for i=1:length(pos_1) hold on ; plot3(pos_1(i),SSF_array(pA_1(i)),L(pA_1(i),pos_1(i)), 'co' , 'LineWidth' ,2, 'MarkerSize' ,5); end hold off %% Plot 4 clear all SSF_array = 1.1:0.1:3.4; %alpha NoS_array = 1:15; %k DR_array = [0.01, 0.1, 1]; [L,Dcmin,pos_001, pA_001, pos_01, pA_01, pos_1, pA_1] = DLD_theory(SSF_array,NoS_array,DR_array); % %***********No log scale % figure; % CO(:,:,1) = ones(length(SSF_array)).*linspace(0,0.8,length(SSF_array)); % red linspace(0.5,1,length(SSF_array)) % CO(:,:,2) = ones(length(SSF_array)).*linspace(0.5,1,length( SSF_array)); % green linspace(0,0.8,length(SSF_array)) % CO(:,:,3) = ones(length(SSF_array)).*linspace(0,0.1,length(SSF_array)); % blue linspace(0,0.1,length(SSF_array)) % plot(NoS_array,Dcmin(1,:),'LineWidth',2,'color',[CO(1,1,1) CO(1,1,2) CO(1,1,3)]); % for n=2:length(SSF_array) % hold on; % plot(NoS_array,Dcmin(n,:),'LineWidth',2,'color',[CO(1,n,1) CO(1,n,2) CO(1,n,3)]); % end % title('DR vs NoS: Theoretical Analy sis') % xlabel('Number of Sections, NoS') % ylabel('Separation Device Resolution, DR (in \ mum)') % grid on % figure;imagesc(SSF_array,SSF_array,CO) %************Log scale figure; CO(:,:,1) = ones(length(SSF_array)).*linspace(0,0.8,length(SSF_array)); % r ed CO(:,:,2) = ones(length(SSF_array)).*linspace(0.5,1,length(SSF_array)); % green CO(:,:,3) = ones(length(SSF_array)).*linspace(0,0.1,length(SSF_array)); % blue semilogy(NoS_array,Dcmin(1,:), 'LineWidth' ,2, 'color' ,[CO(1,1,1) CO(1,1,2) CO(1,1,3)]); for n=2:length(SSF_array) hold on ; semilogy(NoS_array,Dcmin(n,:), 'LineWidth' ,2, 'color' ,[CO(1,n,1) CO(1,n,2) CO(1,n,3)]); end title( 'DR vs NoS: Theoretical Analysis' ) xlabel( 'Number of Sections, NoS' ) ylabel( 'Separation Device Resolution, DR (in \ mum)' ) grid on figure;imagesc(SSF_array,SSF_array,CO) % %% Individual plot for L vs K for different alphas with Dcmin % figure; % plot(k,L(1,:),'k'); % for n=2:length(alfa) % hold on; plot(k,L(n,:),'k'); % for i=1:length(pos_001) % hold on; plot(pos_001(i),L(pA_001(i),pos_001(i)),'bo','LineWidth',2,'MarkerSize',5); % end % for i=1:length(pos_01) % hold on; plot(pos_01(i),L(pA_01(i),pos_01(i)),'go','LineWidth',2,'MarkerSize',5); % end % for i=1:length(pos_1) % h old on; plot(pos_1(i),L(pA_1(i),pos_1(i)),'ro','LineWidth',2,'MarkerSize',5); % end % end % grid on; % title('L vs K') % xlabel('Number of sections, K') % ylabel('Length of the device') function [yk,yk_normalized,gk,Dck,gamma] = CP_DLD_gamma(Dp_min,Dp_max,gamma_min,gamma_step_less1,gk_fablim,D0k_fablim,NoS,gamma_max, gamma_step_high1) %UNTITLED2 Summary of this function goes here % CIRCLE PILLARS %*****Defining gamma range based on gamma_lim and gamma_max (which is %defined based on the fab limits) %gamma_max = lkmin2/gkmin; gamma = [1./((1/gamma_min):( - 1*gamma_step_less1):1.1) 1:gamma_step_high1:gamma_max]; %change step variable for gamma less than 1 %*****Fixed vari ables syms x ; SSF = max(double(solve(x^NoS == Dp_max/Dp_min, x, 'Real' , true))); Beta = 1.1; % 10% more space based on the size of the particule %*******Restrinctions of practical implementation - circle pillars %gkmin = 1; %lkmin = gkmin*gamma; %lkmin2 = 1; %this will be a limitation when gamma is less than one... need to check! DcminR = 0.001; gamma_fablim = D0k_fablim/gk_fablim; %initial condition to k=1 g1=ceil(Dp_max*Beta); gk(1:length(gamma),1) = g1; Dck = Dp_max/SSF; %loop variable q=0; for i=1:No S for ga=1:length(gamma) lkmin = gk_fablim*gamma(ga); if (q==0) if i==1 Nk(i) = (Dck(i)/(1.4*gk(ga,i)))^( - 1/0.48); DRmin(i) = Dck(i); else Dck(i) = Dck(i - 1)/SSF; if Dck(i) <= DcminR Dck(i) = DcminR; end gk(ga,i) = ceil(Dck(i - 1)*Beta); % gi=g(i - 1) will be the case whenever the fab limits are reached if gamma(ga) >= gamma_fablim && (l <= lkmin || gk(ga,i) <= gk_fablim) gk(ga,i) = gk_fablim; glim = gk_fablim; l = lkmin; q=1; elseif gamma(ga) < gamma_fab lim && (l <= D0k_fablim || gk(ga,i) <= gk_fablim) %ASK ABOUT THIS l=D0k_fablim; %lkmin to use gk(ga,i) = l/gamma(ga); glim = l/gamma(ga); %glim to use q=1; end Nk(i) = (Dck(i)/(1.4*gk(ga,i)))^( - 1/0.48); DRmin(i) = Dck(i); end %calculating length of each section l=gk(ga,i)*gamma(ga); if gamma(ga) >= gamma_fablim && (l <= lkmin || gk(ga,i) <= gk_fablim) gk(ga,i) = gk_fablim; glim = gk_fablim; l = lkmin; q=1; elseif gamma(ga) < gamma_fablim && (l <= D0k_fablim || gk(ga,i) <= gk_fablim) l=D0k_fablim; %lkmin to use gk(ga,i) = l/gamma(ga); glim = l/gamma(ga); %glim to use q=1; end yk(ga,i) = ceil(Nk(i))*(gk(ga,i)+l); %L (j,i) = sum(yk(j,1:i)); %Second loop that will be used after reaching fabrication %limits else Dck(i) = Dck(i - 1)/SSF; if Dck(i) <= DcminR Dck(i) = DcminR; end gk(ga,i) = glim; % gi=g(i - 1) will be the case whenever the fab limits are reached Nk(i) = (Dck(i)/(1.4*gk(ga,i)))^( - 1/0.48); DRmin(i) = Dck(i); yk(ga,i) = ceil(Nk(i))*(gk(ga,i)+l); %L(j,i) = sum(yk(j,1:i)); end q=0; if i==1 yk_normalized = yk; yk_normalized(:,i) = yk(:,i)./yk(1,i); else yk_normalized(:,i) = yk(:,i)./yk(1,i); end %clear Dck gk end % figure; % plot(gamma,(yk(:,i)')./1000,' - o') % title(strcat('Length vs Gamma for section',num2str(i))) % xlabel('Gamma') % ylabel('Section length (mm)') end %end of function end clear all %Outputs of function CP_DLD_g amma are [yk,gk,Dck], %where yk is matrix with length values for each section (columns) and each %gamma value (rows), gk is matrix with gap values for each section (columns) and each %gamma value (rows), and Dck an array of particle size being filter by each %section % CIRCLE PILLARS %% Select the desire DR, NoS, and gamma_min %(can modify other values as desired except for gamma_max) %Variables related to particule sizes Dp_min = 1; Dp_max = 100; %Number of sections (each section will be k) NoS_k = 5; %Parameters to evaluate pillar diameter to gap ratio gamma_min = 0.3; gamma_step_less1 = 0.3; gamma_step_high1 = 0.3; gamma_max = 3; %Fabrication limits gk_fablim = 10; D0k_fablim = 10; %Calling function "CP_DLD_gamma" [yk,yk_normalized,gk,Dck,gamma ] = ... CP_DLD_gamma(Dp_min,Dp_max,gamma_min,gamma_step_less1, ... gk_fablim,D0k_fablim,NoS_k,gamma_max,gamma_step_high1); %*****Plots***** figure;bar3(yk_normalized) xlabel( 'k, section number' ) ylabel( 'Gamma' ) set(gca, 'YTick' ,1:length(gamma)) set(gca, 'YTickLabel' ,gamma) %yticklabels(num2str(gamma)) zlabel( 'Length, L (normalized)' ) figure;bar3(yk./1000) xlabel( 'k, section number' ) ylabel( 'Gamma' ) set(gca, 'YTick' ,1:length(gamma)) set(gca, 'YTickLabel' ,gamma) %yticklabels(num2str(gamma)) zlabel( 'Section length (mm)' ) %% Fig. 7 of the paper Dp_array = [0.01 1]; NoS = [5 10]; for i=1:length(Dp_array) for NoS_k=1:length(NoS) %Number of sections (each section will be k) %Variables related to partic ule sizes Dp_min = Dp_array(i); Dp_max = 10; %Parameters to evaluate pillar diameter to gap ratio gamma_min = 0.3; gamma_step_less1 = 0.3; gamma_step_high1 = 0.3; gamma_max = 3; %Fabrication limits gk_fablim = 10; D0k_fablim = 10; %Calling function "CP_DLD_gamma" [yk,yk_normalized,gk,Dck,gamma] = ... CP_DLD_gamma(Dp_min,Dp_max,gamma_min,gamma_step_less1, ... gk_fablim,D0k_fablim,NoS(NoS_k),gamma_max,gamma_step_high1); %*****Plots***** figure;bar3(yk_normalized) xlabel( 'k, section number' ) ylabel( 'Gamma' ) set(gca, 'YTick' ,1:length(gamma)) set(gca, 'YTickLabel' ,gamma) zlabel( 'Length, L (normalized)' ) title(strcat( 'Dp_min =' ,num2str(Dp_min), ' and NoS = ' ,num2str(NoS(NoS_k)))) figure;bar3(yk./1000) xlabe l( 'k, section number' ) ylabel( 'Gamma' ) set(gca, 'YTick' ,1:length(gamma)) set(gca, 'YTickLabel' ,gamma) zlabel( 'Section length (mm)' ) title(strcat( 'Dp_min =' ,num2str(Dp_min), ' and NoS = ' ,num2str(NoS(NoS_k)))) end end %% Fig.8 and Fig. 9: Total length of a device vs NoS for different Dp values col_array = [ 'b' , 'g' , 'm' ]; Dp_array = [0.01 0.1 1]; NoS_init = 2; figure; for i=1:length(Dp_array) for NoS_k=1:10 %Variabl es related to particule sizes Dp_min = Dp_array(i); Dp_max = 10; %Parameters to evaluate pillar diameter to gap ratio gamma_min = 0.3; gamma_step_less1 = 0.3; gamma_step_high1 = 0.3; gamma_max = 3; %Fabrication limits gk_fablim = 10; D0k_fablim = 10; %Calling function "CP_DLD_gamma" [yk,yk_normalized,gk,Dck,gamma] = ... CP_DLD_gamma(Dp_min,Dp_max,gamma_min,gamma_step_less1, ... gk_fablim,D0k_fablim,NoS_k,gamma_max,gamma_step_high1); for j=1:NoS_k Min_length(j)=min(yk(:,j)); s(i).gamma(NoS_k,j)=gamma(find(yk(: ,j)==min(yk(:,j)))); end if NoS_k==1 TotalMinL_samegamma(i,NoS_k)=min(yk); TotalMinL_samegamma_value(i,NoS_k)=gamma(find(yk==min(yk))); else TotalMinL_samegamma(i,NoS_k)=min(sum(yk')); TotalMinL_samegamma_value(i,NoS_k)=gamma(find(sum(yk')==min(sum(yk')))); end LvsNoS(i,NoS_k)=sum(Min_length); clear Min_length end plot(NoS_init:NoS_k,LvsNoS(i,NoS_init:end)./1000, ' -- o' , 'Color' ,col_array(i), 'LineWidth' , 2, 'MarkerSize' ,5) %ylim([0 1000]) %[0 6] hold on plot(find(LvsNoS(i,NoS_init:end)==min(LvsNoS(i,NoS_init:end))),LvsNoS(i,find(LvsNoS(i,NoS_init:end)== min(LvsNoS(i,NoS_init:end))))/1000, ... '*' , 'Color' , 'k' , 'LineWidth' , 2, 'MarkerSize' ,9) end xlabel( 'NoS' ) ylabel( 'Overall shortest length when using different gammas per section' ) hold off figure for i=1:length(Dp_array) plot(NoS_init:NoS_k,LvsNoS(i,NoS_init:end)./TotalMinL_samegamma(i,NoS_init:end), ' -- o' , ' Color' ,col_array(i), 'LineWidth' , 2, 'MarkerSize' ,5) hold on end xlabel( 'NoS' ) ylabel( 'Ratio of overall shortest length using different gammas per section and shortest length using the same gamma for all' ) hold off