Statistics And Statistical Thermodynamics Simulation Of Surface Tension For Emulsion System

Emulsion is used widely in the field of energy resource, chemicalengineering, foodstuff, etc. Surface tension of emulsion is one of themost important criterions to judge the emulsion and coatings because itcan affects straightly the physical chemistry property of emulsion film.Emulsion is composed of water, polymer, fluoropolymer, etc. Inthis paper, a mathematic model of surface tension for complicatedemulsion has been established using statistic method. Attention wasfocused on the basal factor just like volume fraction of mixed monomer,water, and fluoropolymer powder dosage.γ is the surface tension of emulsion, γ₀ is the surface tension ofpolymer, γ_H2O is the surface tension of water,γ_PTFE is the surfacetension of PTFE, c₁ is monomer volume fraction, c₂ is the rate ofPTFE and emulsion. Different methods were used to simulate thesurface tension of polymer.First, a "volume relationship method" that reflect the relationshipbetween polymer surface tension and monomer surface tension andvolume fraction was used to simulate polymer surface tensionmacroscopically. Comparing "volume relationship method" withparachor which is often used to simulate liquid surface tension, theresults are followingTable 1 different methods simulation γ 0MMA:BA:ST vmoeltuhmode r eγl 0a(timonNs/hmip) paracγh 0o(rm sNim/mul)a tion18:10:5 56.35 45.383122:11:0 41.31 45.382021:11:1 50.94 45.383520:10:3 54.41 45.3826Table 1 show that volume relationship method can reflect theinfluence of different dosage of monomer more rightly than parachor.The process of prediction was made easier by a program with VBlanguage.Second, statistical thermodynamics method was used to predictedthe polymer surface tension base on the micromechanism. A modifiedsquare well analytical radial distribution function was derived.()()4131512 23342315U S = Ï€ ??? λ?G+λ?G+λ?G???NVAσNAσεIn the equatio, there are three alterable parameters. ε is moleculepotential energy, σ is molecule diameter, λ is the distance betweenmolecules .COMPASS (Condensed-phase Optimized Molecular Potentialsfor Atomistic Simulation Studies) is used to calculate moleculepotential energy in the method. COMPASS is the first forcefield fromquantum mechanics. It can predict accurately properties of gas-phaseand condensed-phase. So it is applied widely in a broad range ofmolecules and polymers. It is also the first high quality forcefield toconsolidate parameters of organic and inorganic materials. The secondmethod can be easier by using MATLAB language. Good agreementwas obtained between calculated data and experimental data in broadtemperature range. Table 2 give the comparing results betweenvolume relationship method and statistical thermodynamics method.Table2 different methods simulateγMonomer volume MMA:BA:ST 22:11:0 10:20:3 11:21:1 11:22:0Experimental dataγ 45.56 47.57 47.67 48.41volume relationshipmethod γ 0 41.31 54.92 51.44 41.84volume relationship method γ 45.17 49.55 48.44 45.36Error(%) -2.01 4.16 1.60 -6.30statisticalthermodynamics γ 0 41.33 47.62 47.91 50.23statistical thermodynamicsγ 46.10 49.00 45.50 49.00Error(%) -1.17 -2.9 4.76 -1.2Table 2 show that good agreement can be got through both volumerelationship method and statistical thermodynamics method. Therelative error was less than 10%.As a practical method, the surface tension predicated by themathematics model presented in this paper can be used to predict otherimportant property of emulsion film.