Dynamic study of free volume properties in polyethylene/styrene butadiene rubber blends by positron annihilation lifetime method

Abstract

Positronium (Ps) formation in low and high-density polyethylene (LDPE and HDPE) and styrene butadiene rubber (SBR), as well as in their blends (LDPE/ SBR: 50/50 and HDPE/SBR: 50/50) has been investigated by positron annihilation lifetime (PAL) measurements as a function of low temperature (100-300 K). The glass transition temperature (T g ) for the initial polymers and their blends are determined by ortho-positronium (o-Ps) lifetime, s 3 versus temperature as well as by differential scanning calorimetry (DSC) measurements. The temperature dependence of nanoscale free volume size shows similar trend for all the investigated samples indicating an abrupt change at T g , which is found to be higher for SBR sample characterized by its high chain mobility. In addition, The T g values deduced from PAL measurements are compared with the corresponding data deduced from DSC. The variation of o-Ps formation probability I 3 versus temperature for polyethylene and their blends were interpreted in the frame work of spur reaction model of Ps formation. On the other hand, the lifetime coefficient below and above T g is found to be one order of magnitude larger than the linear expansion coefficient. This constitutes evidence that Ps is only probing free volumes. The results obtained from change in free volume-hole distribution with temperature reflect both thermal expansion and increase in free volume-hole size with the rise in temperature.

Detailed investigation on the insulation and permeability characteristics of rigid polyurethane foam loaded with micron-sized Turkey feather powder depending on the free volume change

“…In the light of that, it must be stated here that τ 3 is a measure of the free volume hole size and, I 3 is directly correlated with the number of the free cavities in the polymeric materials. 57 Moreover, it was assumed that a positronium ( Ps ) has an infinite spherical potential well of radius R . The semi-empirical equation showing the relation between the radius R and τ 3 was given as the following, which depends on a spherical approximation proposed by Tao-Eldrup model; 58–60 where R0=R+δR with δR=0.1656 nm as an empirical parameter implying the thickness of the electron layer inside the spherical potential well.…”

Investigation of the relation between free volume and physico-mechanical performance in rigid polyurethane foam containing turkey feather fibers: Part 2

“…o-Ps lifetime ( τ 3 ) can serve as a measure of the free volume cavity size and, in relation with that, I 3 depends on the number of free cavities presenting in the polymeric materials. 50 Moreover, a positronium ( Ps ) is considered to have an infinite spherical potential well of radius R . The relation 47,51,52 between the radius R and τ 3 was given in the following equation to find the average free volume in a spherical approximation known as Tao-Eldrup model;where R0=R+δR with δR=0.1656 nm as an empirical parameter for a measure of electron layer inside the spherical potential well.…”

Role of free volume in mechanical behaviors of side chain lcp grafted products of high density polyethylene

“…In the free volume model, the intensity I 3 is proportional to the number of free holes. The I 3 value increases with increasing number of the holes [49]. The variations in the I 3 intensity with poly(BPOCPMA) percentage in the products were plotted in Fig.…”

“…In the free volume model, the longest-live component τ 3 is correlated to the free volume hole radius, R whilst I 3 is correlated to the number of holes. That is, an increase in τ 3 value shows an enlargement in the volume of hole, while a rise in I 3 displays an increase in the number of the holes [49].…”