Numerical Simulation Method Of Random Closest Packing Of Particle Granular Systems With Large Particle Size Ratios And Multiple Particle Sizes And Its Influencing Factors

The main purpose of the thermal interface material（TIM1）required for electronic packaging is to solve the heat dissipation problem of electronic components,and it needs to have good thermal conductivity.In general,the higher the packing density of the system filler,the higher the thermal conductivity.Therefore,we can provide some guidance for the optimization of the gradation scheme by simulating the closest packing density of the system.In this paper,a discrete element method is used to develop a numerical simulation method for simulating random closest packing of systems with larger particle size ratios and multiple particle sizes,and the accuracy and stability of our method are verified through experiments and other simulation methods.Finally,this study also explored the factors influencing packing density using our simulation method.The details are as follows:（1）Numerical simulation method of random closest packing of hard spherical particle systems with larger particle size ratios and multiple particle sizesIn fact,there are many methods that can simulate packing density,but the existing simulation methods have problems such as harsh conditions and difficult parameter adjustment,and cannot simulate particle systems with large particle size ratios,which do not match the actual application conditions.Therefore,this study developed a new simulation method using the discrete element method.Firstly,similar to other methods,we need to build a model and perform simulations that increase the packing density of the system.Through the LIGGGHTS software,the initial model was constructed according to the requirements of particle size and corresponding volume ratio.Then,using the LAMMPS software,the box was gradually compressed in equal proportions to increase the system packing density.Next,after each compression of the box and the system reaching equilibrium,we need to determine whether the system has reached the closest packed state.Generally,when the particles are in close contact,the particles will overlap,so the overlapping state of the particles can characterize the packing state of the system.However,the particle size will affect the amount of overlap,making this standard not universal,so this study further calculate the relative overlap of the system.However,at the same time,the function of relative overlap and packing density is a curve,and the mutation point is not clear and it is not easy to fit the formula for the next calculation.Therefore,this study calculated the relative overlap change rate V_S of the system again,as a criterion for judging whether the system reached the closest packed state.This value is approximately a straight line with the function graph of the packing density.When the calculated rate of change exceeds the threshold,it can be considered that the system has reached the closest packed state.At this time,stop compressing the box and calculate the closest packing density corresponding to the system through the fitted formula.Finally,comparing our simulation method with experimental values,PAL model,3PPM,TPDM and other results of the closest packing state judgment conditions,it is found that the prediction error of our method is only 0.12%,and the ternary packing density contour of our simulation result is the closest to the experimental result.It shows that our method is both accurate and stable,and can be applied to the numerical simulation of the packing density of fillers with larger particle size ratios and multiple particle sizes in composite materials.（2）Influencing factors of random closest packing of hard spherical particle systems with larger particle size ratios and multiple particle sizesAt present,the research on the influencing factors is mostly in the aspects of vibration and particle shape of single particle size or small particle size ratio systems.This paper is aimed at the large particle size ratio systems and supplements the related research.The first is the particle size ratio and volume ratio.This study simulated a single particle size system and found that its packing density was not affected by particle size and was always around 0.64.Then the two-particle size system was simulated,and it was found that when the volume ratio of the system was the same,the larger the particle size ratio,the higher the closest packing density.And when the particle size ratio is the same,the effect of the volume ratio is not monotonous.The closest packing density will increase first and then decrease with the increase of the proportion of small-sized particles,and reach the maximum value at the point where the proportion of small-sized particles is 0.3.Finally,the three-particle size system is simulated,and the conclusion is similar to the two-particle size system.When the volume ratio is the same,the larger the ratio of large particle size to small particle size,the higher the closest packing density.When the particle size ratio is the same,the closest packing density almost reaches the maximum value when the volume ratio of small-medium-large is 0.2-0.1-0.7.At the same time,this study simulated the system with increased particle size distribution,and found that the proportion of small-sized particles in the particle size distribution is larger and the particle size distribution is wider,which is conducive to improving the closest packing density.In addition,by analyzing the average number of Voronoi polyhedrons and the proportion of icosahedral coordination structure,we found that when the proportion of small-sized particles is 0.1 to 0.2,and the proportion of medium-sized particles is 0 to 0.1,the system structure is more conducive to a higher closest packing density,in agreement with the simulation results.Finally,by analyzing the average contact number of the system,it can be known that the effect of the closest packing density on the thermal conductivity is not linear and monotonic,but it is beneficial to the improvement of thermal conductivity as a whole.The above exploration of the influencing factors is conducive to the development and optimization of the gradation scheme of composite materials with large particle size ratio fillers in actual production,and can improve the thermal conductivity of the composite materials.