PowerPoint PresentationSlide 2Slide 3Slide 4Slide 5Slide 6Slide 7Slide 8Slide 9Slide 10Slide 11Slide 12Slide 13Slide 14Slide 15Slide 16Slide 17Fundamentals of Distribution Separations (III)(08/30/13)Ci= exp -Δμ0RT= exp -Δμi - Δμi0RTextKdistribution coefficient solubilityΔμi = ΔHi – TΔSi00 0--A---B A + BqΔH = EL +EI + ED + EAB0ΔHi = ΔHi,β - ΔHi,α000Quantitative Approach for the Strength of Molecular Interactions (II)A more quantitative approach in estimating the strength of molecular interactions is to use various scales that describe molecular polarity.(a) Polarizability(b) Dipole Moments(c) Solubility parameters(b) Dipole Moments(1) The dipole moment (μ) is a measure of the electron distribution in a compounds(2) The dipole moment of a compound is determined by • The electronegativity of all atoms in the compound • The way in which these atoms are connected and the 3-D structure(3) Examples of electronegativities for some elementsElement Electronegativity (Pauling Scale)Hydrogen 2.1Carbon 2.5Sulfur 2.5Nitrogen 3.0Oxygen 3.5 Fluorine 4.0Chlorine 3.0Bromine 2.8Iodine 2.5(4) For a non-symmetrical molecule made up of neighboring atoms with different electronegativities, a partial separation of positive and negative charge is produced (i.e., a dipole). (5) The magnitude of the dipole moment in a compound is given by μ = e d Where: μ = dipole moment (Debye units) e = Magnitude of the charge (electrostatic units) d = Distance (cm)(6) Dipole moments for some common compounds are given:Compound Dipole Moment (Debye units)CO2 0CH4 0CCl4 0CH3Cl 1.87NH3 1.47HF 1.82H2O 1.87(7) advantages: Dipole moments are easy to measure Useful in predicting interactions due to dipole-dipole interactionDipole-Dipole Interactions Between Two NanorodsEdipole240r3Dipole moments of the CdSe/CdS nanorods = (1.0±0.2) × 103 D toluene 1-dodecanethiolDipole-dipole interaction (meV)977±306 832±259Dipole-dipole interaction (kT)38.2±11.8 32.5±10.1(C) Solubility parameters(1) Because of the limitation in using polarizability and dipole moments, a number of alternative scales have been developed to assess how polar a compound is, or to determine how well it will interact with another molecules.(2) The most famous such scale is that based on the Hildebrand solubility parameter (δ).(3) The value of δ for given compound is defined as follow: δ = (Δ Ev/V)1/2 Where: Δ Ev/V = energy per unit volume, required to completely vaporize a solution of pure compound (4) Δ Ev/V is also known as the cohesive energy density of the compound.In other words, it is a measure of the total interaction energy between twoMolecules or atoms of the same solute.Note: δ is a measure of the total interactions a compound has with itself.(4) Values of δ for common solvents at 25 oC Solvent δ (cal/cm3)1/2Water 23.4Ammonia 16.3Methanol 14.5Ethanol 12.7Benzene 9.2Carbon tetrachloride 8.6Cyclohexane 8.2n-Octane 7.5n-Heptane 7.4n-Hexane 7.3n-Pentane 7.1(5) By knowing the value of δ for two compounds, the solubility of one in the other may be predicted. Solubility is predicted by using the following equation for the change in total free energy due to mixing of the two compounds (ΔGm).ΔGm = ΔHm – TΔSmWhere: ΔHm = Changes in enthalpy due to mixing ΔSm = Change in entropy due to mixing(6) For the preparation of a relatively dilute solution of solute i of solvent j, the change in energy due to mixing (-T ΔSm ) is approximately given by: - T ΔSm = RTln(Xi) where: Xi =mole fraction of compound i in the final solution(7) The value of ΔHm for mixing a solution of i in j may be determined from the values of δ for the two compounds*: ΔHm = Vi (δi- δj)2Where: Vi = molar volume of pure solute i (MWi/densityi)--* J. H. Hildebrand and R. L. Scott, The solubility of noneletrolytes, 3rd ed.,Dover, New York, 1973Quantitative Approach for the Strength of Molecular Interactions (II)A more quantitative approach in estimating the strength of molecular interactions is to use vrious scales that decribe molecular polarity.(a) Polarizability(b) Dipole Moments(c) Solubility parameters (Hidebrand)(d) Kamlet-Taft parameters (solvatochromic parameter) Abraham’s paramters: (solute descriptors and system constant) “empirical model”Hamaker Theory of Van der Waals Interactions(London forces)1. Van der Waals interactions between two neighboring spherical nanoparticlesUspherical sphericalA12Rd(1 d /4R)11 d /R  d2/4R2 2l nd(1 d /4R)R(1 d /R  d2/4R2)where R is the nanoparticle radius and d is the distance of the closest approachVan der Waals interactions between two neighboring nanorodsUrod  rod3Arod  rod8CArod2z5Lrodwhere z is the center-to-center distance between two crystals, CArod is the cross-sectional area of the rods, and L is the length of the crystals.sphrodsphrodsphrodsphrodsphrodrodsphrodrodsphrodrodsphrodrodsphrodrodsphsphrodrodsphsphrodrodsphsphrodrodsphsphrodRRzRRzRRzRRzRRzRzRRzRzRRzRzRRzRzRRzRzRRRzRzRRRzRzRRRzRzRAUlnln22222222)(2)()(2)()(2)()(2)({}{}8222222222222Van der Waals interactions between a nanorod and a spherical nanoparticlewhere Lrod is the length of the nanorods, Rrod is the radius of the nanorods, Rsph is the radius of the spherical crystals, and z is the center-to-center distance.Gold-gold