Study on Foaming Properties and Dynamic Surface Tension of Sodium Branched-alkyl Benzene Sulfonates

Foaming properties and the dynamic surface tension (DST) were carried out with aqueous solutions of sodium branched-alkyl benzene sulfonates to elucidate the relationship between foaming properties and surfactant structures. The parameters of the DST (t*, n, R _1/2 ) are correlated with the foaming ability for alkyl benzene sulfonates with benzene ring substituting at positions 2, 4, and 8 of hexadecane. The parameters of the DST (t*, n, R _1/2 ) are correlated with the foaming ability of the same surfactant solutions. The results indicated that the molecular diffusion in the solution, adsorption, and arrangement at the air/water interface were changed with different molecular structures: changing the substituted position of benzene ring from 2 to 8 of hexadecane, the value of t* and n decrease, and the value of R _1/2 increases, which lead to the high dynamic surface activity and high foam volume. The foam stability is correlated with the high surface dilational elasticity and the strength of surface monolayer: changing the substituted position of benzene ring from 2 to 8 of hexadecane, the branched-alkyl chain becomes more flexible, which is characterized by densely packed adsorbed molecules and high film elasticity of the adsorption film. Therefore, the foam stability increases.     

Kinetic Behaviors of a Competitive Population and Fitness System in Exchange-Driven Growth

We proposed an aggregation model of two species aggregates of fitness and population to study the interaction between the two species in their exchange-driven processes of the same species by introducing the monomer birth of fitness catalyzed by the population, where the fitness aggregates perform self-death process and the population aggregates perform self-birth process. The kinetic behaviors of the aggregate size distributions of the fitness and population were analyzed by the rate equation approach with their exchange rate kernel K1（k,j） = K1kj and K2（k,j） = K2kj, the fitness aggregate＇s self-death rate kernel J1 （ k ） = J1 k, population aggregate＇s self-birth rate kernel J2（ k ） = J2k and population-catalyzed fitness birth rate kernel I（k,j） = Ikj＇. The kinetic behavior of the fitness was found depending crucially on the parameter v, which reflects the dependence of the population-catalyzed fitness birth rate on the size of the catalyst （population） aggregate. （i） In the v ≤ 0 case, the effect of catalyzed-birth of fitness is rather weak and the exchange-driven aggregation and self-death of the fitness dominate the process, and the fitness aggregate size distribution αk（t） does not have scale form. （ii） When v ≥0, the effect of the population-catalyzed birth of fitness gets strong enough, and the catalyzed-birth and self-death of the fitness aggregates, together with the self-birth of the population aggregates dominate the evolution process of the fitness aggregates. The aggregate size distribution αk （t） approaches a generalized scaling form.     

Kinetics of Infection-Driven Growth Model with Birth and Death

We propose a two-species infection model, in which an infected aggregate can gain one monomer from a healthy one due to infection when they meet together. Moreover, both the healthy and infected aggregates may lose one monomer because of self-death, but a healthy aggregate can spontaneously yield a new monomer. Consider a simple system in which the birth/death rates are directly proportional to the aggregate size, namely, the birth and death rates of the healthy aggregate of size k are J1 k and J2k while the self-death rate of the infected aggregate of size k is J3k. We then investigate the kinetics of such a system by means of rate equation approach. For the J1 〉 J2 case, the aggregate size distribution of either species approaches the generalized scaling form and the typical size of either species increases wavily at large times. For the J1 = J2 case, the size distribution of healthy aggregates approaches the generalized scaling form while that of infected aggregates satisfies the modified scaling form. For the J1 〈 J2 case, the size distribution of healthy aggregates satisfies the modified scaling form, but that of infected aggregates does not scale.     

Exchange-Driven Growth with Birth Rate Less Than Death

We further study the kinetic behavior of the exchange-driven growth with birth and death for the case of birth rate kernel being less than that of death based on the mean-field theory. The symmetric exchange rate kernel is K(k,j)=K'(k,j)=Ikj^υ, and the birth and death rates are proportional to the aggregate's size. The long time asymptotic behavior of the aggregate size distribution a_k(t) is found to obey a much unusual scaling law with an exponentially growing scaling function Φ(x)=exp(x).