Solvent Blend Formulation

ABSTRACT As ozone-depleting solvents are being phased out, the demand for solvent replacements in industrial cleaning applications grows. Asahiklin AK-225, a widelyused industrial cleaning solvent, was a replacement for a previously banned solvent but now has a phase-out date of January 2015. One way to replace a solvent or solvent blend is to locate a solvent or blend with similar solvation abilities as characterized by solubility parameters. The Hansen solubility parameters (HSPs) have proven themselves able to predict blend solvation character but not blend miscibility. The Godfrey miscibility index (M-number) is a miscibility ranking of over 400 solvents. To date, there has not been a thorough exploration of the relationship between the HSPs and Godfrey’s M-numbers. A statistical modeling approach to predicting the miscibility of blend components will be studied, and the connection of Godfrey’s M-numbers to the HSPs will be presented in a quantitative structure property relationship (QSPR) between HSPs and Godfrey’s M-numbers. The QSPR model will enable solvent blend miscibility to be estimated using an HSP database of over 10,000 solvents and help predict solvent blend miscibility without the requirement of costly trial and error benchwork. CHAPTER I INTRODUCTION For many years industry used solvents like CFC-113 and 1,1,1-trichloroethane for precision cleaning. These solvents are great for removing a soil from a surface. In industry, cleaning is concerned with safety, surface, soil, solvent, and savings. The safety concerns range from flammability to ozone depletion. The surface must not be damaged, deformed, or rusted by the cleaning process. The solvent should target the soil, which means the solvent and soil must mix spontaneously. The solvent must be affordable and must satisfy all of the above criteria. An ideal solvent should have a low surface tension and low viscosity to be able to penetrate between the soil and the surface. This is shown by the wetting index (w), which is calculated by w= 1000 ρ γη (1) where ρ is the density, γ is the surface tension, and η is the viscosity. 1 A high wetting index will allow solvent to go into crevices. The solvent should also have minimal nonvolatile residue (NVR) so rinsing is not required. Many of the substances that fit into the category are chlorofluorocarbons (CFCs). These CFCs are great for cleaning due to their low surface tension, heat of vaporization, and viscosity. They are highly volatile and inert, so they do not react with the surface being cleaned. Some of the bad qualities of these solvents are that they persist in the upper atmosphere and deplete the ozone layer. Sometimes the CFCs are so persistent they can exist in the upper atmosphere for over a hundred years. 2 So their use has been restricted or banned in industrial cleaning. Ozone-depleting Substances Ozone is naturally produced and destroyed in the upper atmosphere. The CFCs that enter the atmosphere undergo photodecomposition, which releases a chlorine atom. The chlorine atom acts as a catalyst in its reactions with ozone. 2 This process is very detrimental to the ozone layer so other cleaning solvents began to replace CFCs. These solvents are ranked on their ozone depletion potential (ODP) which is calculated from ODP = Global ∆O3 caused by substance Global ∆O3 caused by CFC − 11 (2) where each substance is compared to CFC-11, which is trichlorofluoromethane. 3 This ODP compares the amount of ozone the substance will destroy over its lifetime relative to the amount of ozone that would have been destroyed by an equal mass of CFC-11. While hydrochlorofluorocarbons (HCFCs) were used to replace some of the chlorofluorocarbons, they too are now on the list to be banned. The Montreal Protocol on Substances that Deplete the Ozone Layer is an agreement of nations to reduce the amount of ozone-depleting substances (ODS) in production and consumption and went into effect in 1989. 4 The goal of the Montreal Protocol is to assist in replenishing the ozone-layer though reduction of ODS worldwide. To date there are 197 parties involved in the Montreal Protocol. 4 To assist companies in the transition of selecting new solvents, the United States has the Significant New Alternatives Policy (SNAP) and is required by the Environmental Protection Agency to produce a list of acceptable and unacceptable replacements for ODS that are being phased out under the Federal Clean Air Act. 5 3 As regulations and restrictions tighten on industry for their solvent of choice for cleaning, their need for replacement solvents is ever increasing. One widely used industrial cleaning solvent is Asahiklin® AK-225 and has a phase out date of January 2015. 5 To be prepared for the phase out industry needs methods to find a suitable replacement for their solvent of choice, as AK-225 was a replacement for the previously banned CFC-113, and HCFC-141b. 5 AK-225 is a mixture of two isomers, HCFC-225ca (3,3-dichloro-1,1,1,2,2-pentafluoropropane) and HCFC-225cb (1,2-dichloro-1,1,2,2,3pentafluoropropane). Solubility Parameters One way to find a solvent replacement is to locate a solvent or solvent blend with similar properties and one set of properties used in industry for solvent selection are solubility parameters. Solubility parameters are derived from the Gibbs energy of mixing equation. ∆Gmix = ∆H mix − T∆S mix (3) Spontaneous mixing requires a negative Gibbs energy of mixing which is favored by the positive entropy of mixing (ΔSmix). It is the enthalpy of mixing (ΔHmix) that will typically prevent spontaneous mixing from occurring. The enthalpy of mixing can be related to the cohesive energy density of the individual components. 6 ∆H mix = φ1φ2Vtotal (δ T ,1 − δ T , 2 ) 2 where δ T ≡ ∆H vap Vm The Hildebrand solubility parameter (δT) is the square root of the energy of vaporization (ΔHvap) divided by the molar volume (Vm). The ϕ1 and ϕ2 in eq 4 are the volume ratios of the individual components. Equation 4 shows that the closer the (4) solubility parameter of one component is to the other component the enthalpy of mixing comes closer to zero, ensuring spontaneous mixing. 7 If the solubility parameters are too far apart, then spontaneous mixing will not occur. Hildebrand’s work involved only hydrocarbons, so problems developed when predicting the mixing behavior of polar molecules. The Hildebrand solubility parameter is a single number and does not take into account the polar or hydrogen bonding association between molecules. A quick example of where the Hildebrand solubility parameters fail is ethanol (26.5) and nitromethane (25.3), they have similar δT values, but only ethanol is water soluble. 8 Hansen separated Hildebrand’s solubility parameter into three individual parts to account for dispersion (δD), polarity (δP), and hydrogen bonding ability (δH). 8 δ T2 = δ D2 + δ P2 + δ H2 (5) These (δD, δP, and δH) are known as the Hansen solubility parameters (HSPs). In the 1960s, Hansen used polymer swelling experiments to compile a self-consistent table of HSP values, which has grown to over 10,000 substances. 8 Since then, Hansen and others have explored other ways to determine the various HSP values. 9, 10 Small, Hoy, van Krevelen, and others have developed group contribution methods to compute the solubility parameters. 11 The group contribution (GC) method is a QSPR that uses the number and type of chemical structure elements as input to compute the HSP values. The HSPiP software has the van Krevelen, Hoy, Stefanis-Panayiotou, and Yamamoto methods. 12 The software takes the Simplified Molecular-Input Line-Entry System (SMILES) structure as input. 13 The dispersion (δD), polarity (δP), and hydrogen bonding ability (δH) can also be calculated using various physical properties of the solvent. The polar and dispersion terms, in MPa1/2, can be calculated from knowing the dipole moment (µ) in Debye, molar volume (Vm) in cm3/mol, and index of refraction (RI) as shown in eq. 6 and 7. 12 δP = δD = 36.1 × µ Vm 0.5 (RI − 0.784) 0.0395 (6) (7) There is not an agreed-upon method to determine the hydrogen bonding term. The δH is frequently determined by the difference once the other terms are measured or computed from the Hildebrand parameter as shown in eq 8. δ H 2 = δT 2 − δ D2 − δ P 2 (8) Another major strength the Hansen solubility parameters have over the Hildebrand parameter is the ability to visualize the components of cohesion in 3D space (Figure 1). For a solvent to interact with another, it should be within the Hansen sphere (R0) of the other solvent. The Hansen sphere is a volume calculated area utilizing empirical data and represents the interaction radius in which solvents, and the trajectory of solvent blends, will interact with the soil of interest. 8 The method to empirically determine the Hansen sphere is explained in Hansen Solubility Parameters: A User’s Handbook. 8 R0 δH δP δD Figure 1. Example of HSP 3D space with Hansen sphere. If one solvent cannot match the HSPs of a soil targeted for removal, then a solvent blend can be utilized. The HSPs of a solvent blend can be calculated by the volumefraction-weighted sum of each term. The sum of the volume-weighted-fraction for the dispersion term is shown in eq 9 and the same format is used for the polarity and Hbonding terms. By preparing a solvent blend, one can obtain desired δD, δP, and δH values within the Hansen sphere of the soil to ensure spontaneous mixing. It is simple to search for blends using eq 9 and the Hansen distance (Ra) to the HSPs of the soil as shown in eq 10. However, this is a tedious task to go through every possible combination of solvent blends to match the HSPs of the soil. δ D = ∑ φ i δ D ,i (9) i Ra = (2δ − 2δ D , soil ) + (δ P ,blend − δ P , soil ) + (δ H ,blend − δ H , soil ) 2 D , blend 2 2 (10) In 2008, Dr. Brian Loft Associate Professor of Mathematics at Sam Houston State University was contracted to provide an algorithm using Mathematica (Wolfram Inc.) that can predict two-, three-, and four-solvent blends to target or match a soil’s δD, δP, and δH values. While the current algorithm can predict solvent blends to match the values, it cannot predict if the paired solvents will be sufficiently miscible to form a single homogeneous phase. Thus, the top ranked solvent blends must be tested for miscibility before they can be applied to the soil to test for solvency. This results in a waste of solvents and time. Godfrey’s Miscibility Numbers Hildebrand and Scott reported a miscibility limit of (δT,1 – δT,2) = 3.4 MPa1/2. 6 Godfrey found many exceptions to this rule of thumb. 14 An exception is shown in Table 1. Godfrey meticulously tested pair-wise miscibility of 31 solvents at many concentrations and temperatures. These became Godfrey’s standards and were arranged in order of increasing lipophilicity (1 to 31). Godfrey then compared these standards to many other solvents and created a Miscibility Index (M) Number for over 400 solvents. Godfrey stated that a pair of solvents with ΔM < 15 are miscible in all concentrations at 25 ° C. 14 Table 1 Problem with Hildebrand and Scott Rule of Thumb Solvent δT/ MPa1/2 hexadecane 8.0 benzonitrile 8.4 isoprene 7.5 methanol 14.5 ΔδT Miscible 0.4 No 7.0 Yes Godfrey also assigned some solvents a dual M-number to compensate for some of the observations he witnessed where miscibility was not predicted by the ΔM < 15 rule. The dual M-number helped accommodate the miscibility outliers in some of the tested solvents. If Godfrey assigned a solvent with a dual M-number the lower number restricted the miscibility range on the higher end of the scale while the higher number restricted the miscibility range on the lower end of the scale. To help visualize the purpose of a dual M-number consider the values for nitromethane (10, 19) on a number line (Figure 2). The lower number, 10, restricts the upper miscibility limits to 25 and the upper number 19 restricts the lower miscibility limit to 4 giving a miscibility range of 4 to 25. If nitromethane had the single M-number value of 15, utilizing a ΔM ± 15, nitromethane would have a miscibility range of 0-30. The purpose of the dual M-number is to further restrict the outer miscibility limits of the solvent closer than the ΔM ± 15 range. If nitromethane was assigned the M-number 14.5, the ΔM would be ± 11 and it would follow the same constraints as the assigned dual Mnumber. lower limit upper limit 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 Figure 2. Example of upper and lower miscibility limits for dual M-numbers. Miscibility Modeling While Godfrey empirically tested different solvent concentrations, testing every possible combination would have been impractical. If Godfrey tested each pairing at one concentration he would have performed over 82,000 experiments. Godfrey states a wide enough range of concentrations were tested, so at four concentrations he would have performed over 330,000 tests. This amount of testing is impractical. Instead, Godfrey compared the solvents to the 31 standards in order to effectively perform the miscibility testing. By designing the experiment in such a way Godfrey saved a lot of time without sacrificing the integrity of the experiment. To expand Godfrey’s list of solvents, a miscibility model, based on the solubility parameters of Godfrey’s solvents as a training set, can be used to assign other solvents an M-number. The modeling can be performed in MiniTab with a Quantitative Structure Property Relationship (QSPR). An example of two different ways a QSPR can be performed is a stepwise and best subsets regression. The stepwise method will add and remove factors until a final model is selected. The best subsets method will try every combination of factors and will give many models from which the user must make a final selection. Figures of Merit To assist in determining the appropriate model to be used in predicting solvent miscibility, certain standards or figures of merit must be utilized. Dr. Ananda Manage, Associate Professor of Statistics at Sam Houston State University, was consulted to explain the many numerical figures of merit and to assist in the selection of the most reasonable QSPR. The coefficient of determination (R2) is used to show how well the model fits the data. 15 The value of R2 is the proportion of the variation that is accounted for by the model and is always between 0 and 1. The higher the value of R2 the more effective the model. The value of R2 increases as more factors are added to the model, so an adjusted R2 should also be utilized. 15 The adjusted R2 takes into account the number of factors in the model and reduces the R2 accordingly. Another consideration is the p-value which determines if coefficients of the factors given in the linear regression equation between the predictor and the response are significant. 15 The p-value is the probability that a given coefficient of a factor is caused by noise. In this work if the p-value is greater than 0.05, the coefficient is deemed insignificant statistically. The confidence is 1-p, or 95%. If factors are correlated with each other, problems can occur by influencing the model. The variance inflation factor (VIF) is used to determine if the factors are influencing each other in the model. 15 The values of the VIF are greater than 1 and the rule of thumb is to have a VIF below 10. 16, 17 Some have a stricter VIF requirement of 1 to 5 and 1 to 4 to ensure minimal multicollinearity. 18, 19 If the best subset method is used in Minitab, it is imperative to know which model to select. The Mallows’ Cp assists in not overfitting the data and is a good starting point on the path to selecting a good model. 15 The value of the Mallows’ Cp should be close to the number of factors in the model. 15 Since the best subsets method does not provide the p or VIF values, regressions of each equation must be performed until an equation that meets all the set requirements are met.