Multiple Particle Tracking Microrheology And The Dynamic Heterogeneity During The Sol-gel Transition

In 1905,Albert Einstein gave the mathematical explaination of Brownian motion,which verified the thermal motion of molecule through the microscopic particles.For one century,the researches based on the Brown motion keep being fundamental and hot whatever in mathematics,physics,chemistry or biology.Multiple particle tracking microrheology is a characterization technology that relates the the motion of the probe paticles with the stress of the system.Compared with the other rheological methods,this technology has the advantage of testing the heterogeneity of the system which attracts more and more rheologists.In this region,most researches used the dynamic heterogeneity of the probe particles to describe the dynamic heterogeinty of the system.In other words,they introduced the van Hove function into the probe particles system,which originally described the distribution of the spatial particles.Based on the above background,we added the probe particles into the gelation system and characterized the gelation process.In this thesis,we researched and distinguished the dynamic heterogeneity between the probe particles and the system.We stressed that the Scale Coupling between the probe particles and the system played an important role in the dynamic heterogeneity of the probe particles.The present work was divided as following parts.1.The detailed relationship between the stress and the particle displacement was given.The Gerneiralized Stokes-Einstein Relation?GSER?was fully explained which help to link and distinguish the marocrheology and the microrheology.The dynamic heterogeneity including the van Hove function and 4-point correlation function were discussed.Besides the distribution of the particle displacement was also provided.2.The video-based particle tracking was established with detailed procedure containing the image restoration,the particles localization and the trajectory links.The static error and the dynamic error were analyzed theoretically.Besides,the experiments were also performed which showed the pratical effect of the photobleaching and the exposure time.Then the optimum parameters of shooting were chosen which succeffully obtained the viscosity of the water within 0.2%relative error.Finally,the detailed issues and the methods in statistic and calculation were given.3.The gelation process of 4 wt%gelatin at indicated waiting time t_w was characterized.The MSD-?t curves at indicate temperature?22°C,23°C,24°C,25°C,26°C,30°C?were observed which showed the universal behaviors of gelatin during the gelation.Comparing the non-Gaussian parameter?₂ of the probe particles in the initial gelation and the final gelation,the dynamic heterogeneity was found during the gelation and had the tendency to decrease with the higher lag time?t.These phenomenons were attributed to the contribution of the gelation.Then the 4-point dynamic susceptibility was used in the gelatin system which finally showed the similar relaxation mode compared with the traditional chemical gels.The probe particles with different size 2a were chosen to discuss the same and the different results of a?MSD-?t curves during the gelation process.4.The gelation process of 6 wt%gelatin was characterized.The GSER and the scaling law were used to estimate the gel point and both of them gave the same results.The difference between the marcorheology and the microrheology were also discussed.With the exisiting theories of polymer physics,we successfully calculated the time scale?_max?t_w?and the length scale??t_w?during the gelation process.Meanwhile,the probe scale was also estimated using the lag time?t and the particle displacement MSD^1/2.The dynamic heterogeneity of the probe particles was found at the time when the length scale between the gelatin and the probe particles met.This important finding showed the scale coupling made the contribudtion to the heterogeneity of the probe particles.Finally,the distribution of the diffusion constant P?D?was given which showed the double peak during the gelation.This was attrbutied to the gel part and the sol part.5.The gelation of 2 wt%Laponite with 5 mM NaCl was characterized.The time scale?_max?t_w?and the length scale??t_w?of the system were also calculated with the exsiting universal law of the Laponite.The results were almost the same compared with the gelatin system.The dynamic heterogeneity of the probe particles occurs when the two length scale??t_w?and MSD^1/2 intersected,which again confirmed conclusions from the gelatin system.6.The carbopol systems with concentration from 0.1 wt%to 2.0 wt%were characterized.The carbopol microgel had the lenth scale around 0.1-1?m which was rather close to the probe particles.The results showed the abundant ergodic and non-ergodic behaviors between the carbopol microgel and the probe particles.The scale coupling theory was used and successfully explained the dynamic heterogeneity of the probe particles in the carbopol system.The MSD-?t of individual particles showed the heterogeneity and the non-ergodicity of the carbopol system.The non-Guassian parameter of individual particle?₂^sp-?t showed the abundant scale coupling phenomenon between the probes and the carbopol system.7.The scale coupling of the gelatin-probe particles-E.coli was studied.The adding of E.coli did not affect the universal behavior of MSD-?t curves obviously.However the motion of E.coli was limited by the network formation with mean velocity decreased from 25?m/s to6?m/s.The dynamic heterogeneity of the probe particles was completely different with the gelatin-probe particles system.The scale coupling was also used to explain the dynamic heterogeneity of the probe particles in this system.The results showed the dynamic heterogeneity occured at the length of about 0.5?m which was close to the scale of the probe particle and E.coli.While the time scale of the dynamic heterogeneity occurred at about 1-2s which was different with about 0.1 s in gelation-probe particles system.This time scale was considered to relate the swing motion of E.coli.