0-8493-7686-6/97/$0.00+$.50 1997 by CRC Press LLC

1

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SoluAn

CONTENTS

Abstract IntroductionHildebrand Parameters aHansen Solubility ParamMethods and Problems iCalculation of the Dispe

Calculation of the Polar

Calculation of the Hydro

Supplementary CalculatiTemperature DependeSome Special EffectsEffects of Solvent MoComputer Programs

Hansen Solubility ParamConclusionReferences

ABSTRACT

Solubility parametersselection of solvents. polymers, chemical repigments, fibers, and polymers will dissolvtheir own. The basic modified to like seeksurfaces do not (usuaqualitative idea. This eter (HSP) studies. Tprocess data. The goaor, if necessary, by ex

INTRODUCTION

The solubility parameterlack of total success has swith respect to cost, solvepoint, etc. has improvedparameter concept and bility Parameters Introduction

nd Basic Polymer Solution Thermodynamicsetersn the Determination of Partial Solubility Parameters rsion Solubility Parameter, DSolubility Parameter, Pgen Bonding Solubility Parameter, Hons and Procedures nce

Temperature Changeslecular Size

eters for Water

have found their greatest use in the coatings industry to aid in theThey are used in other industries, however, to predict compatibility ofsistance, and permeation rates and even to characterize the surfaces offillers. Liquids with similar solubility parameters will be miscible, ande in solvents whose solubility parameters are not too different fromprinciple has been like dissolves like. More recently, this has beens like, since many surface characterizations have also been made andlly) dissolve. Solubility parameters help put numbers into this simplechapter describes the tools commonly used in Hansen solubility param-hese include liquids used as energy probes and computer programs tol is to arrive at the HSP for interesting materials either by calculationperiment and preferably with agreement between the two.

has been used for many years to select solvents for coatings materials. Atimulated research. The skill with which solvents can be optimally selectedncy, workplace environment, external environment, evaporation rate, flash

over the years as a result of a series of improvements in the solubility

widespread use of computer techniques. Most, if not all, commercial

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suppliers of solvents havpredict how to dissolve athe polymer by itself.

Unfortunately, this bour present state of knowments, provide some bacThe key is to determine wFor many products this madditives, pigment surfac

It is noteworthy thatsolubility, which requirebetween different polymeand adhesion. In these apliquids as energy probes, with widely different cheinteract differently with that many inorganic matesince their energies are vcan also play an importapigments, both organic aalso inorganic fibers as dcan lead to a surface wstrongly with given orgaalso those which interacto have high affinity for

Solubility parameterthe energy required to cothe total (cohesive) energliquid together are brokelater. The term cohesionphenomena.

HILDEBRAND PARASOLUTION THERMO

The term solubility par

Scatchard and others wais defined as the square

V is the molar volume oEquation 1.15). The num

than that in (cal/cm

3

)

. Trelations, as can be seen

Thermodynamics resolution process to occuby the relatione computer programs to help with solvent selection. One can now easily given polymer in a mixture of two solvents, neither of which can dissolve

ook cannot include discussion of all of the significant efforts leading toledge of the solubility parameter. An attempt is made to outline develop-kground for a basic understanding, and give examples of uses in practice.hich affinities the important components in a system have for each other.eans evaluating or estimating the relative affinities of solvents, polymers,es, filler surfaces, fiber surfaces, and substrates. the concepts presented here have developed toward not just predictings high affinity between solvent and solute, but to predicting affinitiesrs leading to compatibility, and affinities to surfaces to improve dispersionplications the solubility parameter has become a tool, using well-defined

to measure the similarity, or lack of the same, of key components. Materialsmical structure may be very close in affinities. Only those materials whichdifferent solvents can be characterized in this manner. It can be expectedrials, such as fillers, will not interact differently with these energy probesery much higher. An adsorbed layer of water on the high energy surfacent role. Regardless of these concerns, it has been possible to characterizend inorganic, as well as fillers like barium sulfate, zinc oxide, etc. and

iscussed in Chapter 5. Changing the surface energies by various treatmentshich can be characterized more readily and which often interacts morenic solvents. When the same solvents that dissolve a polymeric binder aret most strongly with a surface, one can expect the binder and the surfaceeach other.s are sometimes called cohesion energy parameters since they derive fromnvert a liquid to a gas. The energy of vaporization is a direct measure ofy holding the liquids molecules together. All types of bonds holding the

n by evaporation, and this has led to the concepts described in more detail energy parameter is more appropriately used when referring to surface

METERS AND BASIC POLYMER DYNAMICS

ameter was first used by Hildebrand and Scott.1,2 The earlier work ofs contributory to this development. The Hildebrand solubility parameterroot of the cohesive energy density:

(1.1)

f the pure solvent, and E is its (measurable) energy of vaporization (seeerical value of the solubility parameter in MPa is 2.0455 times largerhe solubility parameter is an important quantity for predicting solubility

from the following brief introduction.quires that the free energy of mixing must be zero or negative for ther spontaneously. The free energy change for the solution process is given

= ( ) V 1 2(1.2) G H TSM M M=

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where

G

M

is the free en

and

S

M

is the entropy c Equation 1.3 gives t

The

s are volume

Equation 1.3 is not correthat only positive heats workers that

G

Mnoncomb

discussed more in Chapt

The noncombinatorial fr

than the combinatorial eEquation 1.4 is consistenChapter 2) and can be d

heats of mixing. Thereftheoretical considerationsolubility parameters canobjections to the effect t

This discussion clearas a free energy parametplots to follow, since thesboundaries of solubilitycombinatorial entropy enexample, since the conce

It is important to nparameters for the solvesystem. It is clear that a free energy, and the posimixing to arrive at the dis possible from a thermowhich can be tolerated wenergy change equal to t

This equation clearly shois that it is the entropy ceach other for solution t

It will be seen in Chnamically better than lareffect is that solvents widissolve a polymer at larother solvents with largtaken as about 100 cc/meven though solubility pergy of mixing, HM is the heat of mixing, T is the absolute temperature,hange in the mixing process.he heat of mixing as proposed by Hildebrand and Scott:

(1.3)

fractions of solvent and polymer, and VM is the volume of the mixture.ct. This equation has often been cited as a shortcoming of this theory in

of mixing are allowed. It has been shown by Patterson, Delmas, and co-is given by the right-hand side of Equation 1.3 and not GM. This iser 2. The correct relation is3-8

(1.4)

ee energy of solution, GMnoncomb, includes all free energy effects otherntropy of solution occurring because of simply mixing the components.t with the Prigogine corresponding states theory of polymer solutions (seeifferentiated to give expressions3,4 predicting both positive and negativeore, both positive and negative heats of mixing can be expected froms and have been measured accordingly. It has been clearly shown that be used to predict both positive and negative heats of mixing. Previous

hat only positive values are allowed in this theory are not correct.ly demonstrates that one should actually consider the solubility parameterer. This is also more in agreement with the use of the solubility parametere use solubility parameters as axes and have the experimentally determined defined by the condition that the free energy of mixing is zero. Theters as a constant factor in the plots of solubility in different solvents, forntrations are usually constant for a given study.ote that the solubility parameter, or rather the difference in solubilityntsolute combination, is important in determining the solubility of thematch in solubility parameters leads to a zero change in noncombinatorialtive entropy change (the combinatorial entropy change) found on simpleisordered mixture compared to the pure components will ensure solutiondynamic point of view. The maximum difference in solubility parameters,here solution still occurs, is found by setting the noncombinatorial free

he combinatorial entropy change.

(1.5)

ws that an alternate view of the solubility situation at the limit of solubilityhange which dictates how closely the solubility parameters must match

o (just) occur.apter 2 that solvents with smaller molecular volumes will be thermody-ger ones having identical solubility parameters. A practical aspect of thisth relatively low molecular volumes, such as methanol and acetone, canger solubility parameter differences than expected from comparisons wither molecular volumes. An average solvent molecular volume is usually

H VM M= ( ) 1 2 1 2 2

G VM Mnoncomb = ( ) 1 2 1 2 2

G T SM Mcombnoncomb =ol. The converse is also true. Larger molecular species may not dissolve,arameter considerations might predict this. This can be a difficulty in

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predicting the behavior These effects are also di

A shortcoming of thregular solutions as defin

molecules, such as thoseproblem seems to have bHowever, the lack of acremain a problem. Usingheat of mixing, for exam

A more detailed deresearch reports which hbook.

9

The slightly olde

related information, part

who divided solvents intthe approach of Blanks

nonpolar and polar. Bogreatly influenced the aufarsighted in that a correscontribution to the cohes

It can be seen frommultiplied by the tempeenergy of mixing. This does not always lead to pioneering work of Patte

ably lead to insolubility. ature can also lead to a nstill further increase in temperature, but those ofa nonsolvent with a solcondition to once moreboundary solvents on

The entropy changeswith liquidliquid misciconfiguration dictated bysolvent and cannot mix merpolymer miscibilitysolubility parameters magained from the entropy polymerpolymer miscicomonomers which interis beyond the scope of th

HANSEN SOLUBILIT

A widely used solubilitythe author. The basis of tof vaporization of a liq

dispersion forces, (molecgen bonding (electron exothers not specifically rmade. The total cohesiveof plasticizers based on data for lower molecular weight solvents only.scussed elsewhere in this book, particularly Chapters 2, 7, and 8.e earlier solubility parameter work is that the approach was limited toed by Hildebrand and Scott,2 and does not account for association between which polar and hydrogen bonding interactions would require. The lattereen largely solved with the use of multicomponent solubility parameters.

curacy with which the solubility parameters can be assigned will always the difference between two large numbers to calculate a relatively smallple, will always be problematic.

scription of the theory presented by Hildebrand and the succession ofave attempted to improve on it can be found in Bartons extensive hand-r, excellent contribution of Gardon and Teas10 is also a good source oficularly for coatings and adhesion phenomena. The approach of Burrell,11o hydrogen bonding classes, has found numerous practical applications;

and Prausnitz12 divided the solubility parameter into two components,th are worthy of mention, however, in that these have found wide use andthors earlier activities, respectively. The latter article, in particular, wasponding states procedure was introduced to calculate the dispersion energyive energy. This is discussed in more detail in Chapter 2. Equation 1.2 that the entropy change is beneficial to mixing. When

rature, this will work in the direction of promoting a more negative freeis the usual case, although there are exceptions. Increasing temperatureimproved solubility relations, however. Indeed, this was the basis of therson and co-workers,3-8 to show that increases in temperature can predict-Their work was done in essentially nonpolar systems. Increasing temper-onsolvent becoming a solvent and, subsequently, a nonsolvent again withtemperature. Polymer solubility parameters do not change much with

a liquid frequently decrease rapidly with temperature. This situation allowsubility parameter which is initially too high to pass through a soluble become a nonsolvent as the temperature increases. These are usuallysolubility parameter plots. associated with polymer solutions will be smaller than those associatedbility, for example, since the monomers are already bound into the the polymer they make up. They are no longer free in the sense of a liquidfreely to contribute to a larger entropy change. This is one reason poly- is difficult to achieve. The free energy criterion dictates that polymertch extremely well for mutual compatibility, since there is little help to becontribution when progressively larger molecules are involved. However,bility can be promoted by the introduction of suitable copolymers oract specifically within the system. Further discussion of these phenomenae present discussion; however, see Chapter 3.

Y PARAMETERS

parameter approach to predicting polymer solubility is that proposed byhese so-called Hansen solubility parameters (HSP) is that the total energyuid consists of several individual parts.13-17 These arise from (atomic)ular) permanent dipolepermanent dipole forces, and (molecular) hydro-change). Needless to say, without the work of Hildebrand and Scott 1,2 and

eferenced here such as Scatchard, this postulate could never have been energy, E, can be measured by evaporating the liquid, i.e., breaking all

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the cohesive bonds. It sha given solvent moleculesimple, and it is surprisinthe idea was first publishare found in Barton.

9

A l

occur when using solubisolvent molecules to inteown environment, i.e., following chapters.

Materials having sima given situation determHildebrand solubility pa

ubility parameters (26.1 v

is water soluble, while ndemonstrated in many cpolymers.

13

This could concept readily confirms

There are three majothe non-polar interactision interactions in the contain this type of attraare essentially the only csame as the dispersion co

energy of the homomorpthe three Hansen paramea corresponding states ca

The permanent dipolthe polar cohesive energ

molecules to one extent these interactions. A mothere is misuse of the termto here are well-defined,as described later. As nohigh total solubility parapropylene carbonate, tri

specifically in this approsolvents with zero dipole

The third major coh

generally an electron excbles the polar interactionamong molecules becauhydrogen bonding paramnot included in the other materials have high hydrinto separate parts, for enegative heats of mixingin Bartons handbook

9

a

been done by Karger et a

induction, proton donor, parameter has accountedof parameters to a level ould also be noted that these cohesive energies arise from interactions of with another of its own kind. The basis of the approach is, therefore, veryg that so many different applications have been possible since 1967 when

ed. A rather large number of applications are discussed in this book. Othersucid discussion by Barton18 enumerates typical situations where problemslity parameters. These occur most often where the environment causes theract with or within themselves differently than when they make up their

as pure liquids. Several cases are discussed where appropriate in the

ilar HSP have high affinity for each other. The extent of the similarity inines the extent of the interaction. The same cannot be said of the total orrameter.1,2 Ethanol and nitromethane, for example, have similar total sol-s. 25.1 MPa, respectively), but their affinities are quite different. Ethanolitromethane is not. Indeed, mixtures of nitroparaffins and alcohols were

ases to provide synergistic mixtures of two nonsolvents which dissolvednever have been predicted by Hildebrand parameters, whereas the HSP the reason for this effect.r types of interaction in common organic materials. The most general areons. These derive from atomic forces. These have also been called disper-literature. Since molecules are built up from atoms, all molecules willctive force. For the saturated aliphatic hydrocarbons, for example, theseohesive interactions, and the energy of vaporization is assumed to be thehesive energy, ED. Finding the dispersion cohesive energy as the cohesionh, or hydrocarbon counterpart, is the starting point for the calculation ofters for a given liquid. As discussed in more detail below, this is based onlculation.epermanent dipole interactions cause a second type of cohesion energy,y, EP. These are inherently molecular interactions and are found in mostor another. The dipole moment is the primary parameter used to calculatelecule can be mainly polar in character without being water soluble, so

polar in the general literature. The polar solubility parameters referred experimentally verified, and can be estimated from molecular parametersted previously, the most polar of the solvents include those with relativelymeters which are not particularly water soluble, such as nitroparaffins,

-n-butyl phosphate, and the like. Induced dipoles have not been treatedach, but are recognized as a potentially important factor, particularly for moments (see the Calculation of the Polar Solubility Parameter section).esive energy source is hydrogen bonding, EH. This can be called morehange parameter. Hydrogen bonding is a molecular interaction and resem-s in this respect. The basis of this type of cohesive energy is attraction

se of the hydrogen bonds. In this perhaps oversimplified approach, theeter has been used to more or less collect the energies from interactionstwo parameters. Alcohols, glycols, carboxylic acids, and other hydrophilicogen bonding parameters. Other researchers have divided this parameterxample, acid and base cohesion parameters, to allow both positive and

. These approaches will not be dealt with here, but can be found describednd elsewhere.19-21 The most extensive division of the cohesive energy hasl.22 who developed a system with five parameters dispersion, orientation,and proton acceptor. As a single parameter, the Hansen hydrogen bonding

remarkably well for the experience of the author and keeps the numberwhich allows ready practical usage.

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It is clear that there afor example, from inducseparate energy can be dmolecules. It was and is rtypes. The description oThis would presumably separate part of the moparameters have mainly bin the coatings industry.

Solubility and swelliof the liquids. These haequations based on moleliquids. The goal of a preparameters. The strengthimportant only to the ex

HSP do have direct they have been used to cof pigment surfaces,

10,14,1

so they could be readipolypropylene

27

(see alsbeen discussed by Barton

deserved in terms of a uin terms of similarity odecisions and plans of everyday industrial crisapproaches based on simare not surprising in vicorresponding states thethat it is the surfaces of

molecules residing in suamong molecules.

The basic equation wenergy, E, must be the s

Dividing this by the molaas the sum of the square

To sum up this sectio(density). An experimena method to arrive at a ctions based on potentialhydrogen bonding molecre other sources of cohesion energy in various types of molecules arising,ed dipoles, metallic bonds, electrostatic interactions, or whatever type ofefined. The author stopped with the three major types found in organicecognized that additional parameters could be assigned to separate energyf organometallic compounds could be an intriguing study, for example.parallel similar characterizations of surface active materials, where eachlecule requires separate characterization for completeness. The Hanseneen used in connection with solubility relations mostly, but not exclusively,

ng have been used to confirm the solubility parameter assignments of manyve then been used to derive group contribution methods and suitable

cular properties to arrive at estimates of the three parameters for additionaldiction is to determine the similarity or difference of the cohesion energy of a particular type of hydrogen bond or other bond, for example, is

tent that it influences the cohesive energy density.application in other scientific disciplines such as surface science, whereharacterize the wettability of various surfaces, the adsorption properties

6,23-26 and have even led to systematic surface treatment of inorganic fibers

ly incorporated into polymers of low solubility parameters such aso Chapter 5). Many other applications of widely different character have9 and Gardon.28 Surface characterizations have not been given the attention

nified similarity-of-energy approach. The author can certify that thinkingf energy, whether surface energy or cohesive energy, can lead to rapidaction in critical situations where data are lacking. In other words, theis situation often can be reduced in scope by appropriate systematicilarity of energy. The successes using the HSP for surface applications

ew of the similarity of predictions offered by these and the Prigogineory of polymer solutions discussed in Chapter 2. Flory also emphasized molecules which interact to produce solutions,29 so the interactions ofrfaces should clearly be included in any general approach to interactions

hich governs the assignment of Hansen parameters is that the total cohesionum of the individual energies which make it up.

(1.6)

r volume gives the square of the total (or Hildebrand) solubility parameters of the Hansen D, P, and H components.

(1.7)

(1.8)

n, it is emphasized that HSP quantitatively account for the cohesion energytal latent heat of vaporization has been considered much more reliable asohesion energy than using molecular orbital calculations or other calcula- functions. Indeed, the goal of such extensive calculations for polar andules should be to accurately arrive at the energy of vaporization.

E E E ED P H= + +

E V E V E V E VD P H= + +

2 2 2 2= + +D P H

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METHODS AND PROSOLUBILITY PARAM

The best method to calcuThe author originally ad90 liquids based on solu

nonpolar parameter acco

tional procedure is still inIt is outlined below. The bonding interactions wadata. A key to parametertwo nonsolvents could bpolymers. This meant thregion, a spheroid, fromsystems as a basis, reaso

Using the experimen

found that the Bttcher eled to a revision of the ewere also consistent withwith Equation 1.6. Furthtance, Ra, between two m

This equation was develconvenient and correctly (see Chapter 3). When thtwo parameters, essentiagreatly aids two-dimenswhere deviations can occbeing less effective solvsphere. Likewise, smalleoften appear as outliers iplacing them at a distanceRo. This dependence onand Scatchard discussed

This in turn promotes sothan predicted by compconsidered outliers.

The molar volume issize effects. These are eexample (see Chapters 7solubility parameters witsolubility parameters by

The reason for the emore detail in Chapter 2.by the Prigogine correspused to estimate the inte

evidence that dispersion,BLEMS IN THE DETERMINATION OF PARTIAL ETERS

late the individual HSP depends to a great extent on what data are available.opted an essentially experimental procedure and established values forbility data for 32 polymers.13 This procedure involved calculation of therding to the procedure outlined by Blanks and Prausnitz.12 This calcula- use and is considered the most reliable and consistent for this parameter.

division of the remaining cohesive energy between the polar and hydrogens initially done by trial and error to fit experimental polymer solubility assignments in this initial trial and error approach was that mixtures ofe systematically found to synergistically (but predictably) dissolve givenat these had parameters placing them on opposite sides of the solubility each other. By having a large number of such predictably synergisticnably accurate divisions into the three energy types were possible.tally established, approximate, P and H parameters, Hansen and Skaarup15quation could be used to calculate the polar parameter quite well, and thisarlier values to those now accepted for these same liquids. These values the experimental solubility data for 32 polymers available at that time andermore, Skaarup developed the equation for the solubility parameter dis-

aterials based on their respective partial solubility parameter components:

(1.9)

oped from plots of experimental data where the constant 4 was foundrepresented the solubility data as a sphere encompassing the good solventse scale for the dispersion parameter is doubled compared with the otherlly spherical rather than spheroidal, regions of solubility are found. Thisional plotting and visualization. There are, of course, boundary regionsur. These are most frequently found to involve the larger molecular speciesents compared with the smaller counterparts which define the solubilityr molecular species such as acetone, methanol, nitromethane, and othersn that they dissolve a polymer even though they have solubility parameters greater than the experimentally determined radius of the solubility sphere,

molar volume is inherent in the theory developed by Hildebrand, Scott,above. Smaller molar volume favors lower GM, as discussed in Chapter 2.lubility. Such smaller molecular volume species which dissolve betterarisons based on solubility parameters alone should not necessarily be

frequently used successfully as a fourth parameter to describe molecularspecially important in correlating diffusional phenomena with HSP, for and 8). The author has preferred to retain the three, well-defined, partialh a separate, fourth, molar volume parameter, rather than to multiply thethe molar volume raised to some power to redefine them.xperimentally determined constant 4 in Equation 1.9 will be discussed in It will be noted here, however, that the constant 4 is theoretically predictedonding states theory of polymer solutions when the geometric mean is

raction in mixtures of dissimilar molecules.30 This is exceptionally strong permanent dipolepermanent dipole, and hydrogen bonding interactions

Ra D D P P H H( ) = ( ) + ( ) + ( )2 2 1 2 2 1 2 2 1 24

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all follow the geometric relating the Prigogine thsolutions.

3-8

The HSP aptypes of cohesive forces htheory. The use of the gethat of Prigogine (see Ch

The approach of optiof solubility based on exby locating the maximuused. The total free energ

that using solubility par

the combinatorial entropAnother promising a

to use multivariable analyhas not been attempted preferred approach of lois in reality the poor solvboundary (and center) rasmaller sets of data, butthose of any liquid whichis based on Equation 1.9 from such correlations.

Equation 1.9 is rearelations allow easier scarequires that Ra be less tRelative Energy Differen

An RED number of 0 is affinity; RED equal to onumbers indicate progresthan 1.0, for example, rap

It should be noted pahaving the same units as

energies. This latter quaFlory as discussed in Ch

The revised set of paprocedures developed by

who also used Fedors w

although Beerbowers laAdministration (NASA)

tions which was distribuThe majority of the dataBeerbower also develop

dipole moment and the sand has been found quite

by the author as well, giis the basis of the wholeother calculational procemean rule. Patterson and co-workers have been especially instrumental ineory to solubility parameters and to the Flory-Huggins theory of polymerproach of dividing the cohesive energy into parts derived from differentas been confirmed both by experimental studies as well as by the Prigogineometric mean is basic to this agreement between the HSP approach andapter 2).

mizing solubility data to spheres is still very much is use. Plotting regionsperimental solubility data or computer optimizing boundaries of solubilitym difference in solubility parameters allowed by Equation 1.9 are bothy of mixing, GM, is equal to zero on the boundary. It should be recognizedameters, which relate to GMnoncomb in Equation 1.4, differs from this byy of mixing.pproach to arrive at the HSP for materials based on experimental data issis of one type or another as discussed in Chapter 3. This type of approach

by the author, but it clearly has advantages in some cases. The authorscating the polymer HSP as the center of a sphere has a problem in that itents or nonsolvents located near the boundary of the sphere which fix thether than the best solvents in the middle. This may present problems for it is an advantage when extrapolating into regions of HSP higher than can be used in testing. This is discussed in Chapter 3 in more detail and

to define the limited segment of the boundary of the HSP sphere derivable

dily used on a computer (or on a hand calculator) and supplementarynning of large sets for data. It is obvious that solubility, or high affinity,han Ro. The ratio Ra/Ro has been called the RED number, reflecting thece.

(1.10)

found for no energy difference. RED numbers less than 1.0 indicate highr close to 1.0 is a boundary condition; and progressively higher REDsively lower affinities. Scanning a computer output for RED numbers lessidly allows location of the most interesting liquids for a given application.renthetically here that the ratio of Ra to Ro is really a ratio of quantities

the solubility parameter. The ratio (Ra/Ro)2 = (RED)2 is a ratio of cohesionntity is important for relating the HSP approach to that of Huggins andapter 2.rameters for the 90 original solvents was the basis for group contribution (most notably) van Krevelen,31 Beerbower,32 and Hansen and Beerbower,17

ork.33 These various developments have been summarized by Barton,9test values have only appeared in the National Aeronautics and Spacedocument.32 Table 1.1 is an expanded table of Beerbower group contribu-ted among those who were in contact with Beerbower in the late 1970s. in this table, as well as Table 1.2, have also appeared in Reference 34.

ed a simple equation for the polar parameter,17 which involved only thequare root of the molar volume. This is also given later (Equation 1.13)

reliable by Koenhen and Smolders.35 This equation has been found reliableving results generally consistent with Equations 1.6 to 1.8, which, again, approach. Koenhen and Smolders also give correlation coefficients for

RED Ra Ro=dures to arrive at the individual Hansen parameters.

TABLE 1.1 Group Contributions to Partial Solubility Parameters

Functional Group

Molar Volume,

a

V

(cm

3

/mol)London Parameter,

V

2D

(cal/mol)Polar Parameter,

V

2P

(cal/mol)Electron Transfer Parameter,

V

2H

(cal/mol)Total Parameter,

a

V

2

(cal/mol)

Aliphatic Aromatic

b

Alkane Cyclo Aromatic Alkane Cyclo Aromatic Aliphatic Aromatic Aliphatic Aromatic

CH

3

33.5 Same 1,125 Same Same 0 0 0 0 0 1,125 SameCH

2

< 16.1 Same 1,180 Same Same 0 0 0 0 0 1,180 SameCH< 1.0 Same 820 Same Same 0 0 0 0 0 820 Same>C< 19.2 Same 350 Same Same 0 0 0 0 0 350 SameCH

2

= olefin 28.5 Same 850 100 ? ? 25 10 ? ? 180 75 ? 1,030 SameCH>C Phe

C-5(s

C-6F

F

F

Cl

C

C

Br

B

B

I

I

2

I3O>COCHCOCO

= olefin 13.5 Same 875 100 ? ? 18 5 ? ? 180 75 ? 1,030 Same= olefin 5.5 Same 800 100 ? ? 60 10 ? ? 180 75 ? 1,030 Samenyl- 71.4 7,530 50 25 50 50c 7630 ring aturated)

16 250 0 0 0 250

ring 16 Same 250 250 0 0 0 0 0 250 25018.0 22.0 0 0 0 1,000 150 ? 700 100 0 0 1,000 800b

2 twinf 40.0 48.0 0 0 0 700 250c ? 500 250c 0 0 1,700 1,360b

3 tripletf 66.0 78.0 0 0 0 ? ? ? 0 0 1,650 1,315b24.0 28.0 1,400 100 ? 1,300 100 1,250 100 1,450 100 800 100 100 20c Same 2,760 2,200b

l2 twinf 52.0 60.0 3,650 160 ? 3,100 175c 800 150 ? 400 150c 165 10c 180 10c 4,600 3,670bl3 tripletf 81.9 73.9 4,750 300c ? ? 300 100 ? ? 350 250c ? 5,400 4,300b

30.0 34.0 1,950 300c 1,500 175 1,650 140 1,250 100 1,700 150 800 100 500 100 500 100 3,700 2,960br2 twinf 62.0 70.0 4,300 300c ? 3,500 300c 800 250c ? 400 150c 825 200c 800 250c 5,900 4,700br3 tripletf 97.2 109.2 5,800 400c ? ? 350 150c ? ? 1,500 300c ? 7,650 6,100b

31.5 35.5 2,350 250c 2,200 250c 2,000 250c 1,250 100 1,350 100 575 100 1,000 200c 1,000 200c 4,550 3,600b twine 66.6 74.6 5,500 300c ? 4,200 300c 800 250c ? 400 150c 1,650 250c 1,800 250c 8,000 6,400b triplete 111.0 123.0 ? ? ? ? ? ? ? ? 11,700 9,350b ether 3.8 Same 0 0 0 500 150 600 150 450 150 450 25 1,200 100 800 (1,650 150) ketone 10.8 Same e 2,350 400 2,800 325 (15, 000 7%)/V 1,000 300 950 300 800 250d 400 125c 4,150 SameO (23.2) (31.4) 950 300 ? 550 275 2,100 200 3,000 500 2,750 200 1,000 200 750 150 (4,050) SameO-ester 18.0 Same f ? f (56,000 12%)/V ? (338,000 10%)/V 1,250 150 475 100c 4,300 SameOH 28.5 Same 3,350 300 3,550 250 3,600 400 500 150 300 50 750 350 2,750 250 2,250 250c 6,600 Same

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OH 10.0 Same 1,770 450 1,370 500 1,870 600 700 200 1,100 300 800 150 4,650 400 4,650 500 7,120 Same(OH)2 twin

or adjacent26.0 Same 0 ? ? 1,500 100 ? ? 9,000 600 9,300 600 10,440 Same

CN 24.0 Same 1,600 850c ? 0 4,000 800c ? 3,750 300c 500 200d 400 125c 4,150 SameNONH>NNHPO

a Db Tc Bd Ine Uf T

Fro

TABLE 1.1 (continued)Group Contributions to Partial Solubility Parameters

Functional Group

Molar Volume,a

V (cm3/mol)London Parameter,

V 2D (cal/mol)Polar Parameter,V 2P (cal/mol)

Electron Transfer Parameter,V 2H (cal/mol)

Total Parameter,a

V 2 (cal/mol)

Aliphatic Aromaticb Alkane Cyclo Aromatic Alkane Cyclo Aromatic Aliphatic Aromatic Aliphatic Aromatic

202 24.0 32.0 3,000 600 ? 2,550 125 3,600 600 ? 1,750 100 400 50d 350 50c 7,000 (4,400)2 amine 19.2 Same 1,050 300 1,050 450c 150 150c 600 200 600 350c 800 200 1,350 200 2,250 200d 3,000 Same

H2 amine 4.5 Same 1,150 225 ? ? 100 50 ? ? 750 200 ? 2,000 Same2 amide (6.7) Same ? ? ? ? ? ? 2,700 550c ? (5,850) Same4 ester 28.0 Same e ? ? (81,000 10%)/V ? ? 3,000 500 ? (7,000) Same

ata from Fedors.33hese values apply to halogens attached directly to the ring and also to halogens attached to aliphatic double-bonded C atoms.ased on very limited data. Limits shown are roughly 95% confidence; in many cases, values are for information only and not to be used for computation.cludes unpublished infrared data.se formula in V2P column to calculate, with V for total compound.win and triplet values apply to halogens on the same C atom, except that V 2P also includes those on adjacent C atoms.m Hansen, C. M., Paint Testing Manual, Manual 17, Koleske, J. V., Ed., American Society for Testing and Materials, Philadelphia, 1995, 388. Copyright ASTM. Reprinted with permission.

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TABLE 1.2 Lydersen G

Group

CH3CH2>CH>CCOCHOCO2O

OHHOH primaryOH secondaryOH tertiaryOH phenolic

NH2NH>NCN

NCOHCON