[
    {
        "id": 1,
        "chunk": "North Dakota State University Coatings and Polymeric Materials  \n\n<html><body><table><tr><td>Paint Ingredients (reminder)</td></tr><tr><td>Most paints have four broad types of ingredients: Binder Pigment Additives</td></tr><tr><td>Solvent - controls viscosity, wetting (thus adhesion) and carries everything in the application stages.</td></tr><tr><td>Notable Exceptions (dealt with elsewhere in course):</td></tr><tr><td>1. 100% solids UV curable (the monomer is the medium) 2. Powder coatings (air is the delivery medium)</td></tr></table></body></html>  \n\nBackground. How much solvent is used in paints? 2005 data U.S. Census Bureau statistics - 2005 Manufacturing Profiles (Paint Varnish and Lacquer): Architectural coatings Exterior solvent type 80,161,000 gallons Interior solvent type 58,827, 000 gallons Architectural Lacquers  6,936,000 gallons Product Finishes for original equipment manufactures, excluding marine coatings 398,673,000 gallons containing solvent Special - purpose coatings 155,629,000 gallons - mainly solvent borne   \nTotal $\\sim$ 700,000,000 gallons of paint $\\textcircled{6}$ 3 lb/gal solvent $\\mathbf{\\sigma}=\\mathbf{\\sigma}$ 210,000,000 lb solvent or \\~ 20,000,000 gallons of solvent   \nIn addition, even waterborne coatings (no totals given here) contain cosolvents and plasticisers that contribute significantly to solvent emissions.  \n\n<html><body><table><tr><td>Choice of Solvent 1. greatly determined by the choice of the other ingredients</td></tr><tr><td>“Binders\" - Hold everything together and provide adhesion to the substrate · Binders are usually organic polymers ：Very convenient and versatile technology ： End use requires high molecular weight or X-linking</td></tr></table></body></html>  \n\nChoice of solvents  \n\n2. other issues. • Compatibility with dissolved ingredients (from previous) - Maintaining high solids content • Toxicity and other environmental issues Viscosity • Evaporation Rate • Surface Tension • Others, e.g. resistivity (for electrostatic application) • Cost",
        "category": " Introduction"
    },
    {
        "id": 2,
        "chunk": "# Roles for Solvents/Summary of Module  \n\n• Reaction medium  \n\nKinetics, Concentration, Reactant, e.g. reactive diluent, or end group   \n– See polymer synthesis modules  \n\n• Carrier – this module – Viscosity – Necessary for wetting a surface – compatibility with polymers is very important may need to replace a hazardous solvent with less hazardous substitute.  \n\n• Leave when required to do so – this module - Evaporation behavior is very important",
        "category": " Introduction"
    },
    {
        "id": 3,
        "chunk": "# Viscosity of Polymer Solutions  \n\n• Viscosity  \n\nresistance to flow,   \n– friction between molecules   \n– Larger molecules produce more friction   \n– Depending on the concentration, larger molecules get entangled » Viscosity increases greatly   \n– The larger molecules within a distribution determine the viscosity   \n– The greater the compatibility between polymer and solvent the more the polymer coil expands  \n\n» And so the viscosity increases  \n\nWe need to provide a usefully high molecular weight at a practical viscosity - one of the reasons for latex polymers – low viscosity means good leveling, flow out and gloss  \n\nViscosity increases greatly with concentration in polymer solutions.  \n\n![](images/732e67d1840df0dc915147218c87794e68daaebb436fe759197d235303ef5df2.jpg)  \n\nNote logarithmic axes.  \n\nThe exact nature of the curve varies with chemical structure, but depends hugely on molecular weight (see next)  \n\nThe requirement for high solids means that there is a restriction on the molecular weight that can be used.  \n\nStuart Croll  \n\nViscosity increases greatly with molecular size (weight)  \n\nEntanglement depends on concentration, molecular size and compatibility with the solvent (how much the molecule spreads out).  \n\n![](images/76dc2a49e0a1152f0c2d82549b52c186692313f2cc2b7c5173634dd20bcda5d8.jpg)  \n\n![](images/7f00482ca0505ad6827b043432ddd10c2dfe09082e73e45d571a95265819f98f.jpg)  \n\nLog. (Molecular Weight)  \n\nStuart Croll",
        "category": " Results and discussion"
    },
    {
        "id": 4,
        "chunk": "# Wetting  \n\n• Processes that depend on wetting – Spreading – Adhesion  \n\n• Necessary for optimizing contact between  \n\n– Soluble coating ingredients $\\&$ particulate materials   \n– Coating &  substrate » (Usually amounts to displacing air)   \n– Wetting is important  \n\nYoung’s Equation for surface wetting Cos $\\breve{\\theta}=(\\gamma_{s\\nu}-\\gamma_{s\\mathcal{V}})/\\gamma_{l\\nu}$ $\\theta=$ contact angle $\\gamma_{l\\nu}=$ liquid-vapor surface tension, (the only one easily controlled)  \n\nFor wetting, $\\theta$ should be small , i.e. the drop spreads, which means that $\\gamma_{l\\nu}$ should be low.  \n\n![](images/554d4adb2ed294e8eace56bdde5ee76bb6708b34384a8f13b9fce638edc647fb.jpg)  \n\nGood wetting $\\mathbf{\\tau}=\\mathbf{\\tau}$ even spreading; penetration of rough surface areas; $\\mathbf{\\Sigma}=\\mathbf{\\Sigma}$ intimate contact between coating and substrate $\\mathbf{\\Sigma}=$ adhesion; film properties; good corrosion resistance  \n\nStuart Croll  \n\n<html><body><table><tr><td>Surface Tension of Liquids - some examples</td></tr><tr><td>Water 72 mN/m [=dyn/cm] Acetone 23.5 1-propanol 23.3 Ethyl acetate 23.4 1-Butanol 25 MEK 24</td></tr></table></body></html>  \n\n![](images/eb585dac14c702707fd2432be01b80878b5d1e43d9c08cf6144d43a3004aee63.jpg)  \n\n![](images/6e435b180fe04c90d9dce73c958b1a6e8e60a8d07b18e54a98bc7fcb37a1cc9e.jpg)  \n\n![](images/6beb658ee2511409ebcfea0ac9b41b59fbc7f2cd5fdfc234b4d93a575e38edaf.jpg)  \n\nIn practice, dissolving a polymer is a slow process (thus many are created in solution)  \n\nStep 1: solvent diffuses into a polymer body and produces a swollen gel  \n\nStep 2: if the polymer-polymer   \nforces can be overcome by the   \npolymer-solvent interactions   \npolymer is released from the gel –rate limiting step –polymer chains are released into the bulk solution where they may be separate or entangled.  \n\nStuart Croll",
        "category": " Results and discussion"
    },
    {
        "id": 5,
        "chunk": "# Solubility Parameters: Based on Thermodynamics  \n\nWhat we are aiming for is:  \n\na useful scheme so that we can find out which solvents will dissolve a given polymer, or - How we can substitute one solvent for another  \n\nFirst two laws of thermodynamics are equivalent to considering Gibbs Free Energy, $G,$ if temperature and pressure are constant.  \n\nCriterion for dissolution is that upon mixing, G should  be reduced.  \n\n- thus solution must have a lower Gibbs Free Energy than the separate components.  \n\n$$\n\\varDelta G_{m i x i n g}=\\varDelta H_{m i x i n g}-T.\\ A S_{m i x i n g}\n$$  \n\n$\\varDelta H=$ change in enthalpy, $\\varDelta S=$ change in entropy $\\begin{array}{r l}{T}&{{}=}\\end{array}$ temperature, K  \n\nStuart Croll  \n\n<html><body><table><tr><td>I. Entropy of mixing</td></tr><tr><td>In a regular solution △S =-RN[ flog f,+flog f]</td></tr><tr><td>Where: f= molar fraction (i.e.<1) so log(f) is negative Change of entropy is positive, i.e. increasing entropy N = number of molecules</td></tr><tr><td>R = Gas Constant Entropy increase always helps mixing since it reduces</td></tr><tr><td>- Increasing temperature helps miscibility (see equation on previous slide) AGmixing</td></tr><tr><td>This theory ignores the entropy change since it always helps dissolution rather than controlling it</td></tr><tr><td></td></tr><tr><td></td></tr></table></body></html>  \n\n<html><body><table><tr><td>I. Enthalpy of mixing (Hildebrand and Scott - Regular Solutions)</td></tr><tr><td>Enthalpy = interaction (or cohesive) energy density, Cii Interactions between like molecules within materials 1-1 & 2-2 must become mixed interactions,i.e. 1-2,in the solution.</td></tr><tr><td>Enthalpy changes = C11 + C22 - 2C21 (both type 1 and type 2 change)</td></tr><tr><td>Bertelot's approximation: C21 = (C11.C22)1/2</td></tr><tr><td>How do we measure these interactions, i.e. energy holding the molecules together? identify as cohesive energy/volume</td></tr><tr><td>How do we measure cohesive energy/volume (Cii)?</td></tr><tr><td>= heat of vaporization Stuart Croll 18</td></tr></table></body></html>",
        "category": " Results and discussion"
    },
    {
        "id": 6,
        "chunk": "# Enthalpy of Mixing - consequences  \n\n<html><body><table><tr><td colspan=\"2\"></td></tr><tr><td colspan=\"2\">after some algebra: AHmixing = Vm1N.[C11/2 - C221/2]2</td></tr><tr><td colspan=\"2\">Vm= molar volume averaged over mixture Φ= volume fraction of each Φ+ Φ= 1,</td></tr><tr><td colspan=\"2\">AHmixing is usualy a positive quantity, so we need to minimize it to get 4G to be negative (given help from entropy changes).</td></tr><tr><td>1. is easier,</td><td> Solvents with small molar volumes, Vm, reduce AHmixing so dissolving</td></tr><tr><td>2.</td><td>e.g. acetone is a small molecule and a very useful solvent The product ΦΦ is smaller when one of the concentrations is small</td></tr><tr><td></td><td>i.e. dissolving a small amount of solute is always easier than trying to dissolve a lot</td></tr><tr><td>3.</td><td>If we can make C1 = C22, then the enthalpy change is minimized, i.e. zero i.e. the two materials are identical</td></tr></table></body></html>  \n\n<html><body><table><tr><td>Solubility Parameter</td></tr><tr><td>Hildebrand identified a solubility parameter for a given material as:</td></tr><tr><td>8 = C1/2 etc.= (cohesive energy density)1/2 = (AEevap/ Vsolwent)1/2</td></tr><tr><td>See equation on previous slide. Thus materials should stand a better chance of mixing when their solubility parameters more closely match, i.e. difference in Ci is</td></tr><tr><td>minimized. What do we have?</td></tr><tr><td>A mixing parameter that uses enthalpy (only), i.e. depends on energy, i.e. chemistry, i.e. like dissolves like!</td></tr><tr><td></td></tr></table></body></html>",
        "category": " Results and discussion"
    },
    {
        "id": 7,
        "chunk": "# Having a single value for the solubility parameter has proved to be too simple.  \n\nSolubility parameter, $\\delta,$ must include all the contributions from how materials interact in solution  \n\n– dispersion,   \n– polar and   \n– hydrogen bonding interactions  \n\nEach type of interaction is represented by a component of  – represented in a three dimensional cartesian space  \n\n» dispersion » polar » hydrogen  \n\n $\\mathbf{\\Sigma}=\\mathbf{\\Sigma}$ distance to the origin $=(\\delta_{\\mathrm{d}}^{~2}+\\delta_{\\mathrm{p}}^{~2}+\\delta_{\\mathrm{h}}^{~2})^{1/2}$ $\\mathbf{\\Sigma}=$ Hansen scheme (dominates these days)  \n\n![](images/afa908d4b6caf33c962f25853677e6f263b8a84f74942182d352c822fca219a5.jpg)  \n\nCrowley, Teague, and Lowe (Eastman Chemical, 1966) published [Journal of Paint Technology Vol $39\\#504$ , Jan 1967] a representation with the Hildebrand parameter, a hydrogen bonding number, and the dipole moment (lumps the dispersion into the overall value).  \n\nStuart Croll",
        "category": " Introduction"
    },
    {
        "id": 8,
        "chunk": "# Interactions $\\mathbf{\\tau}=\\mathbf{\\tau}$ reasons how materials can differ  \n\n• “London” Dispersion forces  \n\n– Van der Waals forces   \n– Interactions between instantaneous dipoles induced by a neighboring dipole.   \n– Occurs in all materials to roughly same extent   \n– Weak ${\\sim}1/\\mathrm{r}^{6}$  \n\nPolar interactions  \n\n– from dipoles due to asymmetric charge (electrons) distribution on a molecule – Polar molecules have higher dielectric constant  \n\n» Alkanes and polyethylene dielectric constant ${\\sim}2$ » Ethanol \\~ 24 and water ${\\sim}79$  \n\n• Hydrogen Bonding Short range interaction mediated between the hydrogen bonds (tends to be used as a catch-all for other interactions as well)",
        "category": " Introduction"
    },
    {
        "id": 9,
        "chunk": "# Quantitative Compatibility?  \n\nFor high miscibility or ease of replacement  the solubility parameters must be very close.  \n\nIn a three-dimensional solubility parameter co-ordinate system the square of the distance between points representing two materials is given by (like any 3-D cartesian space):  \n\n$$\n(\\Delta\\delta)^{2}=(\\delta_{\\mathrm{d1}}\\textrm{-}\\delta_{\\mathrm{d2}})^{2}+(\\delta_{\\mathrm{p1}}\\textrm{-}\\delta_{\\mathrm{p2}})^{2}+(\\delta_{\\mathrm{h1}}\\textrm{-}\\delta_{\\mathrm{h2}})^{2}\n$$  \n\nIn the original Hansen scheme this distance, $\\Delta\\delta$ , should be less than 1 for good solubility or miscibility.  \n\nExperiment seems to indicate that a more useful expression would be  \n\n$$\n1\\geq4(\\delta_{\\mathrm{d1}}-\\delta_{\\mathrm{d2}})^{2}+(\\delta_{\\mathrm{p1}}-\\delta_{\\mathrm{p2}})^{2}+(\\delta_{\\mathrm{h1}}-\\delta_{\\mathrm{h2}})^{2}\n$$  \n\nAiming for a target in solubility parameter space.  \n\nIn principle the possible   \nsolvents for the solute lie   \nwithin the sphere.   \nAnything further away from   \nthe target than $\\Delta\\delta$ is not likely to be a solvent (or replacement solvent)   \nhttp://pirika.com/NewHP/PirikaE /polymer-solvent.html   \nHas applets  \n\n![](images/e639a5d6d1b79f6d21404848d7544a327e56052e1af35745ff739e4182653c6e.jpg)",
        "category": " Results and discussion"
    },
    {
        "id": 10,
        "chunk": "# Practical application of Solubility Parameter  \n\n• (separation) radius $\\mathbf{\\Psi}=\\mathbf{\\Psi}_{1}$ does not work  \n\n$$\nR^{2}=(\\delta-\\delta_{d})^{2}+(\\delta-\\delta_{p})^{2}+(\\delta-\\delta_{h})^{2}\n$$  \n\nSphere: center $\\delta_{d},$ $\\delta_{p}$ , $\\delta_{h},$ radius $R$  \n\n• Solubility is seldom a sphere in solubility parameter space  \n\n• A better way to approach to matching materials is to plot the solubility space for each material and see how much they overlap  \n\n– More overlap the better   \n– But this requires a great deal more information   \n– Less popular",
        "category": " Results and discussion"
    },
    {
        "id": 11,
        "chunk": "# Determining Solubility Parameters  \n\n• Try many known solvents and see what works best for your unknown and deduce the values of the three components of the solubility parameter.  \n\n• Or, measure viscosity of polymer solution as a function of solubility parameter of the solvent  \n\n– Solubility parameter is given by solvent giving highest value of viscosity  \n\n» The most compatible solvent swells a polymer the most and increases viscosity the most.  \n\nCalculate values: quantum chemistry",
        "category": " Materials and methods"
    },
    {
        "id": 12,
        "chunk": "# Other considerations on choosing a perfect solvent.  \n\n• Remember – you may not want a perfect solvent – The solution viscosity may be too high if the polymer extends its conformation too far  \n\n• Not all of the reactive groups may react if the polymer, or oligomer is too tightly coiled in solution – Crosslinking density may be less than you thought it should be  \n\n• The compatibility of the ingredients may change as they react or evaporate – Phase separation leads to imperfections in the quality of the final film  \n\n<html><body><table><tr><td colspan=\"6\"></td></tr><tr><td>Quinoline</td><td>Solvent</td><td>Dispersion</td><td>Polar</td><td>Hydrogen Bonding</td><td>Molar Volume</td></tr><tr><td></td><td></td><td>19.4</td><td>7.0</td><td>7.6</td><td>118.0</td></tr><tr><td>Stearicacid</td><td></td><td>16.3</td><td>3.3</td><td>5.5</td><td>326.0</td></tr><tr><td>Styrene Succinic anhydride</td><td></td><td>18.6</td><td>1.0</td><td>4.1</td><td>115.6</td></tr><tr><td></td><td></td><td>18.6</td><td>19.2</td><td>16.6</td><td>66.8</td></tr><tr><td></td><td>1.1.2.2-Tetrabromoethane</td><td>22.6</td><td>5.1</td><td>8.2</td><td>116.8</td></tr><tr><td></td><td>1.1.2.2-Tetrachloroethane</td><td>18.8</td><td>5.1</td><td>9.4</td><td>105.2</td></tr><tr><td>Tetrachloroethylene</td><td></td><td>19.0</td><td>6.5</td><td>2.9</td><td>101.1</td></tr><tr><td>Tetraethylorthosilicate</td><td></td><td>13.9</td><td>0.4</td><td>0.6</td><td>224.0</td></tr><tr><td>*Tetrahydrofuran</td><td></td><td>16.8</td><td>5.7</td><td>8.0</td><td>81.7</td></tr><tr><td>Tetrahydronaphthalene</td><td></td><td>19.6</td><td>2.0</td><td>2.9</td><td>136.0</td></tr><tr><td>Tetramethylurea *Toluene</td><td></td><td>16.7</td><td>8.2</td><td>11.0</td><td>120.4</td></tr><tr><td></td><td></td><td>18.0</td><td>1.4</td><td>2.0</td><td>106.8</td></tr><tr><td></td><td>Tributyl phosphate</td><td>16.3</td><td>6.3</td><td>4.3</td><td>345.0</td></tr><tr><td></td><td>Trichlorobiphenyl</td><td>19.2</td><td>5.3</td><td>4.1</td><td>187.0</td></tr><tr><td>*Trichloroethylene</td><td>1.1.1-Trichloroethane</td><td>16.8</td><td>4.3</td><td>2.0</td><td>99.3</td></tr><tr><td>Trichlorofluoromethane</td><td></td><td>18.0</td><td>3.1</td><td>5.3</td><td>90.2</td></tr><tr><td></td><td></td><td>15.3</td><td>2.0</td><td>0.0</td><td>92.8</td></tr><tr><td>Tricresylphosphate</td><td>1.1.2-Trichlorotrifluoroethane</td><td>14.7</td><td>1.6</td><td>0.0</td><td>119.2</td></tr><tr><td>Tridecylalcohol</td><td></td><td>19.0</td><td>12.3</td><td>4.5</td><td>316.0</td></tr><tr><td>Triethanolamine</td><td></td><td>14.3</td><td>3.1</td><td>9.0</td><td>242.0</td></tr><tr><td>Triethylamine</td><td></td><td>17.3</td><td>22.4</td><td>23.3</td><td>133.2</td></tr><tr><td>Triethyleneglycol</td><td></td><td>17.8</td><td>0.4</td><td>1.0</td><td>138.6</td></tr><tr><td></td><td></td><td>16.0</td><td>12.5</td><td>18.6</td><td>114.0</td></tr><tr><td></td><td>Triethylene glycol monooleyl ether</td><td>13.3</td><td>3.1</td><td>8.4</td><td>418.5</td></tr><tr><td></td><td>Triethylphosphate</td><td>16.7</td><td>11.4</td><td>9.2</td><td>171.0</td></tr><tr><td></td><td>Trifluoroaceticacid</td><td>15.6</td><td>9.9</td><td>11.6</td><td>74.2</td></tr><tr><td>Water is</td><td>Trimethylbenzene</td><td>17.8</td><td>0.4</td><td>1.0</td><td>133.6</td></tr><tr><td></td><td>2.2.2.4-Trimethylpentane</td><td>14.1</td><td>0.0</td><td>0.0</td><td>166.1</td></tr><tr><td>different</td><td>2.2.4-Trimethyl-1.3-pentanediol M.I.butyral</td><td>15.1</td><td>6.1</td><td>9.8</td><td>227.4</td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>→</td><td>Trimethylphosphate</td><td>16.7</td><td>15.0</td><td>42.2</td><td>115.8</td></tr><tr><td></td><td></td><td></td><td>1.0</td><td>3.1</td><td></td></tr><tr><td>Xylene</td><td>o-xylene</td><td>17.6 17.8</td><td>1.0</td><td>3.1</td><td>123.3 121.2</td></tr></table></body></html>\n\n\\*Indicates use in author's standard set of test solvents  \n\n<html><body><table><tr><td>Solubility Parameters for Mixtures</td></tr><tr><td></td></tr><tr><td>Blending Solvents, e.g. to dissolve a particular polymer or replace another solvent:</td></tr><tr><td>Combine linearly using volume fractions, e.g.</td></tr><tr><td>8dispersion(blend) = Φ1d1+Φ2d2+Φ3d3+ ..Φndn Spolar(blend) = Φ1 p1 + Φ p2 +Φ3 p3 +..中p Odn</td></tr><tr><td>Shydrogen bnding(blend) = Φ1 Sh1 + Φ2 Sh2 + Φ3 Sh3 + ... Φn Shn</td></tr><tr><td></td></tr><tr><td></td></tr><tr><td></td></tr></table></body></html>  \n\nExample Will toluene dissolve PMMA? $(\\delta_{\\mathrm{d1}}-\\delta_{\\mathrm{d2}})^{2}+(\\delta_{\\mathrm{p1}}-\\delta_{\\mathrm{p2}})^{2}+(\\delta_{\\mathrm{h1}}-\\delta_{\\mathrm{h2}})^{2}$ $(18.2\\textrm{-}18.0)^{2}+(10.3\\textrm{-}1.4)^{2}+(7.7\\textrm{-}2.0)^{2}=(10.6)^{2}>1$ Actually, a  solution is possible, depending on the molecular weight. $R$ must be larger than 1 for (probably) both materials (see elsewhere), and/or neither solubility behavior is a sphere Solubility Parameters are only a guide!",
        "category": " Results and discussion"
    },
    {
        "id": 13,
        "chunk": "# Example  \n\n• If we could mix $70\\%$ vol. Ethanol with $30\\%$ MEK, what would be the solubility parameters of the resultant (assuming miscibility)?  \n\ndispersion(blend) $=\\ 0.7\\mathrm{x}15.8\\ +\\ 0.3\\mathrm{~x}16=15.86$ polar(blend) = $0.7\\mathrm{~x~}8.8+0.3\\mathrm{~x~}9.0=8.86$ hydrogen bnding(blend) = $0.7\\textbf{x}19.4+0.3\\textbf{x}5.0=15.08$",
        "category": " Results and discussion"
    },
    {
        "id": 14,
        "chunk": "# Solubility Parameter Data for Examples  \n\n<html><body><table><tr><td>Material</td><td>8d,Dispersion</td><td>8p,Polar</td><td>Sh,Hydrogen Bonding</td><td>Radius</td></tr><tr><td>PMMA</td><td>18.2</td><td>10.3</td><td>7.7</td><td>8.6</td></tr><tr><td>Epoxy</td><td>20.4</td><td>12.0</td><td>11.5</td><td>12.7</td></tr><tr><td>Polystyrene</td><td>20.8</td><td>5.6</td><td>4.2</td><td>12.7</td></tr><tr><td>Toluene</td><td>18.0</td><td>1.4</td><td>2.0</td><td></td></tr><tr><td>MEK</td><td>16</td><td>9</td><td>5</td><td></td></tr><tr><td>Ethanol</td><td>15.8</td><td>8.8</td><td>19.4</td><td></td></tr><tr><td>Dodecane</td><td>16.0</td><td>0</td><td>0</td><td></td></tr><tr><td>Acetone</td><td>15.5</td><td>10.4</td><td>7.0</td><td></td></tr><tr><td>Texanol</td><td>15.2</td><td>6.2</td><td>9.8</td><td></td></tr></table></body></html>  \n\nUnfortunately, exact numbers depend on measurement method and the molecular weight, and details of polymer structure.  \n\nWhat works for polymers?  \n\n• Single polymers in solvents – using solubility parameters often works – Entropy changes associated with polymer solutions tend to be small – Monomers already tied up in polymer Cannot mix freely to make a big difference in entropy  \n\n• Entropy is very  important when mixing two polymers imagine difficulty of mixing two large, complicated molecules  \n\n• Compatibility between polymers or issues of molecular weight or concentration – Go to Flory - Huggins Theory  \n\nStuart Croll",
        "category": " Results and discussion"
    },
    {
        "id": 15,
        "chunk": "# Limitations Of Solubility Parameters  \n\n• Do not predict solubility of all polymers in all solvents – All models are simplifications and don’t work exactly   \n• Miscibility is governed by changes in enthalpy and does not account for entropic changes.   \n• Oversimplification of hydrogen-bonding effects   \nMolecular weight effect not included - see Flory-Huggins theory  \n\nPractical solution is to remember that it is only an approximation",
        "category": " Results and discussion"
    },
    {
        "id": 16,
        "chunk": "# Flory-Huggins Theory  \n\nFlory-Huggins theory calculates a compatibility parameter $\\boldsymbol{\\chi}$ . For miscibility $\\chi$ must be less than $\\chi_{c}$ Materials that are more similar have lower values of $\\boldsymbol{\\chi}$  \n\n$$\n\\chi_{c}=\\frac{1}{2}\\Biggl(\\frac{1}{x_{a}^{1/2}}+\\frac{1}{x_{b}^{1/2}}\\Biggr)^{2}\n$$  \n\n$x=$ degree of polymerization, $\\mathbf{\\Psi}=1$ for a solvent and large for a polymer, so $\\chi_{\\mathrm{c}}$ is ${\\sim}0.5$ $\\mathbf{\\Sigma}=$ large for both polymers in a mixture , so $\\chi_{\\mathrm{c}}$ is very small for mixing of two polymers, i.e. it is difficult for polymers to mix  \n\nFlory-Huggins is not usually invoked until we have mixtures of polymers.",
        "category": " Introduction"
    },
    {
        "id": 17,
        "chunk": "# Latest Theory on how polymers solvate  \n\n• J. Dudowicz, K. F. Freed, J. F. Douglas, “Solvation of polymers as mutual association. I. General theory,” J. Chem.  Phys.,138, 164901 (2013)  \n\n• J. Dudowicz, K. F. Freed, J. F. Douglas, “Solvation of polymers as mutual association. II. Basic thermodynamic properties,” J. Chem.  Phys.,138, 164902 (2013)",
        "category": " References"
    },
    {
        "id": 18,
        "chunk": "# Evaporation Rates  \n\n• Evaporation rate is characteristic of a solvent  \n\n$\\mathbf{\\Sigma}=\\mathbf{\\Sigma}$ Weight loss/area/time   \n– Sensitive to temperature, partial vapor pressure of itself in the atmosphere, surface area vs. volume   \n– Evaporation of some solvents is sensitive to humidity (water is a solvent too) So it is usually defined relative to the rate of evaporation rate of n-butyl acetate  \n\n• Many solvents do not completely evaporate from a coating  \n\n– Enough affinity between polymer and solvent – Crosslinking traps the molecules",
        "category": " Results and discussion"
    },
    {
        "id": 19,
        "chunk": "# Evaporation?  \n\n• Molecules escape the surface of a liquid all the time (even well below their boiling point)  \n\n– Depending on how fast the molecules are moving » Depends on temperature   \n– Produces the vapor pressure   \nLiquid boils when its vapour pressure $\\mathbf{\\tau}=\\mathbf{\\tau}$ atmospheric pressure   \n• Boiling point value is a useful parameter to express the overall volatility   \n• The degree to which molecules escape depends on their attraction for each other and how much energy is needed for a molecule to get enough energy",
        "category": " Introduction"
    },
    {
        "id": 20,
        "chunk": "# The Need for Evaporation Rate Control  \n\nMany application properties are controlled by how fast solvents leave:  \n\n• Wet edge (can you paint around a window frame fast enough for the paint to blend in where you started?)   \n• Levelling depends on viscosity and surface tension   \n• Sagging depends on viscosity   \n• How wet the atomized spray is when it arrives   \n• Orange Peel effects - surface tension driven convection cells set up as solvent evaporates   \n• Will the reactants diffuse together and react well?   \n• Will the coating go hard quickly enough?   \n• Will all the solvent escape and not form a skin and blister?  \n\nStuart Croll",
        "category": " Introduction"
    },
    {
        "id": 21,
        "chunk": "# Evaporation Rate  \n\n• Relative evaporation rate $\\underline{{\\mathbf{\\omega}}}=\\underline{{\\mathrm{Time}}}_{90}.$ (N-butyl acetate) $\\mathrm{Time}_{90}$ (solvent under test)  \n\n• Measured by weighing – usually to $90\\%$ weight loss – Soaked filter paper (surface area remains constant) » Solvent and filter paper may interact – Shell “evapometer” ASTM D3539.76 (automatic weighing device)  \n\n• Can be calculated from Raoult’s Law if you know the activity coefficients of the mixture ingredients – Activity coefficients can be calculated – UNIFAC group contribution theory or computational chemistry  \n\n![](images/81990084984fcf7f9db6d56f7085acf3b12879824f5dfd404f3f6f4ed0d235e9.jpg)",
        "category": " Materials and methods"
    },
    {
        "id": 22,
        "chunk": "# Evaporation from Coatings  \n\n• Initial period is like the solvent (mixture) alone – Controlled by the vapor pressure of the solvent above the coating  \n\nRate slows down  \n\n– Controlled by diffusion through coating as film forms – Rate also diminishes as solvent reservoir runs out  \n\nEnergy required in baking is the heat required to raise the temperature (specific heat) of the coating to some temperature (near Boiling Point) that permits the solvent to escape suitably plus the heat of vaporization  \n\n<html><body><table><tr><td colspan=\"4\">Evaporation Rate: Examples [CRC Handbook of Chemistry and Physics; A. L. Rocklin, JCT, Vol. 48, No. 622, pp. 45 - 57 (1976)]</td></tr><tr><td colspan=\"4\">Solvent Boiling Point Specific Heat Heat of Vaporization</td></tr><tr><td>rate</td><td>℃ J/g/K</td><td>J/g (at B.P.)</td><td></td></tr><tr><td>Acetone</td><td>56 2.17</td><td>502</td><td>9.3</td></tr><tr><td>Cyclohexane</td><td>81</td><td>1.84 356</td><td>6</td></tr><tr><td>Ethanol</td><td>78</td><td>2.44 838</td><td>2.3</td></tr><tr><td>Ethyl Acetate</td><td>77</td><td>1.94 363</td><td>6</td></tr><tr><td>MEK</td><td>80</td><td>2.2 435</td><td>5.1</td></tr><tr><td>MIBK</td><td>116</td><td>2.13 345</td><td>3.3</td></tr><tr><td>Methanol</td><td>65</td><td>2.53 1100</td><td>3.2</td></tr><tr><td>N-butylacetate</td><td>126</td><td>1.96 363</td><td>1</td></tr><tr><td>Toluene</td><td>111</td><td>1.71 361</td><td>2.1</td></tr><tr><td>Water</td><td>100</td><td>4.2 2258</td><td>0.64</td></tr><tr><td colspan=\"4\">· Polar materials need more heat to raise temperature and separate molecules,particularly water. Specific heat - internal modes of vibration · Vaporization － separating molecules</td></tr></table></body></html>  \n\n<html><body><table><tr><td>Background Information: VOC Calculations</td></tr><tr><td>VOC Determination, see ASTM D 3960 In general: VOC = Total Weight of Volatiles - Total Weight of Exempt Solvent - Weight of Water</td></tr><tr><td>Total Volume of Paint - Volume of Exempt Solvent - Volume of Water</td></tr><tr><td>Solvent Systems: VOC = (1O0 - NVW) [Wt./gal.] /100</td></tr><tr><td>Conversion: VOC [gram/Liter] = 119.84 x VOC [lbs./gal.]</td></tr><tr><td>Stuart Croll 44</td></tr></table></body></html>",
        "category": " Results and discussion"
    },
    {
        "id": 23,
        "chunk": "# Organic Solvents in Coatings  \n\n• VOC solvents are easy to use – Range available to dissolve many polymers » Many polymer chemistry options available – Range of evaporation rates available – Low surface tension – Many choices of solvent – Film formation usually done from polymer solution » But other options are possible  \n\nProblems with organic solvents.  \n\n• Flammable, and therefore dangerous   \n• Fumes or liquid may be toxic or otherwise harmful   \n• Many engage in atmospheric photochemistry and the byproducts affect greenhouse effect etc. and in combination with $\\mathsf{N O}_{\\mathrm{x}}$ produce ozone at low altitudes.  \n\nThus we limit the solvent content of paints and coatings etc.  \n\nA reason for water-borne coatings",
        "category": " Introduction"
    },
    {
        "id": 24,
        "chunk": "# Water as Solvent, 1  \n\n• The solvent determines what we can get into solution – Water does not give us many options for water soluble polymers » Use latex or other emulsions, acid/base functionality, cosolvents  \n\n• Stabilization mechanism depends on dielectric properties of medium  \n\n– Water has high dielectric constant (very polar)   \n– Charge stabilization works $\\mathbf{\\Sigma}=\\mathbf{\\Sigma}$ useful (& cheap), but prone to abuse » Repulsive potential is higher in media of high dielectric constant - see DLVO theory » Don’t have to rely on steric stabilization only",
        "category": " Results and discussion"
    },
    {
        "id": 25,
        "chunk": "# Water as Solvent, 2  \n\nWater as a solvent has some disadvantages:  \n\n– High surface tension » Use surfactants   \n– Slow evaporating compared to common solvents » Evaporation greatly affected by ambient humidity   \n– High heat capacity and latent heat of evaporation   \n– Permits metallic corrosion  \n\n• Advantages  \n\n– Benign material – Plentiful, cheap supply (so far)  \n\nSummary – how to choose solvents • Viscosity – depends on compatibility • Wetting of pigments and substrates – Depends on surface tension  \n\n• Dissolution of binders etc. – Depends on compatibility • Leaving when job is done – Depends on evaporation rate",
        "category": " Introduction"
    },
    {
        "id": 26,
        "chunk": "# Background: Laws of Thermodynamics (Not for a test)  \n\n1.  The amount of work needed to change the state of a system depends only on the change effected and not the means or the intermediate stages in the process. $\\mathbf{\\sigma}=\\mathbf{\\sigma}$ You cannot win  \n\n2.  No process is possible whose sole result is the complete conversion of heat into work $\\mathbf{\\sigma}=\\mathbf{\\sigma}$ You cannot break even  \n\n3.  In a system that is in internal thermodynamic equilibrium, the entropy tends to zero as the temperature tends to zero. $\\mathbf{\\sigma}=\\mathbf{\\sigma}$ You cannot get out of the game  \n\nKieffer’s Reduction: Prof. William F. Kieffer.",
        "category": " Introduction"
    },
    {
        "id": 27,
        "chunk": "# Background: Definitions  \n\nRaoult’s Law:  \n\nVapor Pressure due to  a solution ingredient $\\mathbf{\\tau}=\\mathbf{\\tau}$ vapor pressure of pure ingredient  x its molar fraction » i.e. linear combination that works in “ideal” gases  \n\nAzeotrope is a mixed solution that boils at a constant temperature.  The vapor has same composition as the mixture.  B.P. may be higher or lower than either component by itself.  Therefore a mixture distills over, or is left.  E.g. alcohols and water.  \n\n– Non-ideal gases may provoke azeotropy if the resultant pressure is larger than the sum of the pure vapor pressures the component(s) \"don't like\" to be in the liquid phase. » this corresponds to smaller attractions between molecules in the mixture than in the pure components  \n\n– In other cases, azeotropy occurs because attractions between unlike molecules in mixtures are greater than those in the pure components.  \n\nStuart Croll  \n\n<html><body><table><tr><td>om J. H. Hildebrand and R. L. Scott, “Regular Solutions\", Prentice Englewood Cliffs,N. J. 1962</td><td></td></tr><tr><td></td><td> Scatchard-Hildebrand Equation</td></tr><tr><td></td><td>Cohesive Energy of a mole of liquid mixture ²x²++2²²</td></tr><tr><td></td><td>Mixture xv+xV -E</td></tr><tr><td></td><td>v= molar volume; x= molar fraction For pure components -E=cU etc. and if we assume that for</td></tr><tr><td></td><td>liquids at normal temperatures the vapour is ideal, we can identify -E with the heat of vapourisation</td></tr><tr><td></td><td>If we transform to volume fractions, Φ and Φ, then -EMixre =(c²+2c+C22²)(x+xV)</td></tr><tr><td></td><td>Energy of mixing:</td></tr><tr><td></td><td>△E=EMixre-Ex-Ex =(xv+x)(c-2c+C)</td></tr><tr><td></td><td>=(x+x)(c1²-c2）²</td></tr><tr><td></td><td>If c12=(C1C22)1/2 etc.</td></tr></table></body></html>",
        "category": " Introduction"
    },
    {
        "id": 28,
        "chunk": "# From same source  \n\nEntropy of mixing,  \n\n• If we have $N_{\\imath}$ and $N_{2}$ molecules of each of two sorts on a lattice, the entropy of mixing is given by:  \n\n$$\n{\\frac{\\Delta S_{M i x i n g}}{k}}=N_{1}\\ln\\left({\\frac{N_{1}+N_{2}}{N_{1}}}\\right)+N_{2}\\ln\\left({\\frac{N_{1}+N_{2}}{N_{2}}}\\right)\n$$  \n\n• Or, in entropy/mole of mixture  \n\n$$\n\\frac{\\Delta s_{M i x i n g}}{R}=-\\big(x_{1}\\ln x_{1}+x_{2}\\ln x_{2}\\big)\n$$",
        "category": " Materials and methods"
    }
]