Branched versus linear oligo(dimethylsiloxane): Differences in their thermodynamic interaction with solvents

Branched Versus Linear Oligo(dimethylsiloxane): Differences in

Their Thermodynamic Interaction with Solvents

FATEMEH SAMADI,1 JOHN ECKELT,1,3 BERNHARD A. WOLF,1 HANNA SCHULE,2 HOLGER FREY2

1Institute of Physical Chemistry, Universitat Mainz, Welder-Weg 13, D-55099 Mainz, Germany

2Institute of Organic Chemistry, Universitat Mainz, Duesbergweg 10-14, D-55099 Mainz, Germany

3WEE-Solve GmbH, Auf der Burg 6, D-55130 Mainz, Germany

Received 19 December 2009; revised 22 March 2010; accepted 27 March 2010

DOI: 10.1002/polb.22029

Published online in Wiley InterScience (www.interscience.wiley.com).

ABSTRACT: The thermodynamic behavior of linear and of

branched oligo(dimethylsiloxane) (O-DMS) solutions was studied

by means of vapor pressure measurements and vapor pressure

osmometry at different temperatures for the thermodynamically

favorable solvent THF. The branched material required for that

purpose was synthesized and afterwards fractionated by means

of the single solvent acetone to eliminate components of low

degrees of branching. The Flory-Huggins interaction parameters,

v, for the systems THF/O-DMS as a function of composition pass

a minimum at all temperatures (25, 40, and 60 �C) in the case of

the branched material. For the unbranched oligomer such a mini-

mum is only observed at 60 �C. At 40 �C the results are ambi-

gous whereas the dependence is definitely linear at 25 �C. This

exceptional behavior of the linear product at the latter tempera-

ture is tentatively attributed to the formation of favorable orienta-

tional order in the pure state under these conditions. At high

oligomer concentrations THF interacts more favorably with the

branched material, however, this preference is reversed upon

dilution. All measured composition dependencies of v can be

modeled quantitatively by an approach accounting for chain con-

nectivity and for the ability of the oligomers to change their con-

formation upon dilution. VC 2010 Wiley Periodicals, Inc. J Polym

Sci Part B: Polym Phys 48: 1309–1318, 2010

KEYWORDS: branched; Flory-Huggins interaction parameter;

fractionation; linear; linear and branched oligomers; molecular

architecture; polysiloxanes; solution properties; solution ther-

modynamics; thermodynamics; vapor pressure

INTRODUCTION Oligomer containing systems have earlyattracted the attention of thermodynamicists who targetedthe transition from low molecular weight mixtures to poly-mer solutions1,2 on one hand and to polymer blends3,4 onthe other. Over the years this class of compounds hasbecome of interest time and again, partly because of theirfavorable properties for instance as components of drugdelivery systems5 or for coating purposes,6 partly as interest-ing materials for theoretical studies.7,8

This work deals with the question, to which extent the ther-modynamic solution properties of linear and branched poly-mers consisting of the same monomer units depend on theirmolecular architecture. For this study, we have chosen linearand branched oligo(dimethylsiloxane) (O-DMS) in combina-tion with the solvents tetrahydrofurane (THF) and acetone(AC). The required experimental information was obtained inthe case of THF (thermodynamically favorable) in the rangeof high solute concentrations from vapor pressure measure-ment and complemented by vapor pressure osmometry withdilute solutions. The marginal solvent AC enabled the fractio-nation of the branched O-DMS; for this solvent, we havedetermined the cloud point curves of the different linear andbranched oligomers. By means of this study, we also

intended to check whether a recent approach, which hasproven to be successful for solutions of linear and branchedhomopolymers, random copolymers, and block copolymers,and for mixtures of low molecular weight liquids, alsoimproves the theoretical understanding of the solutions ofoligomers differing in their molecular architecture.

EXPERIMENTAL

MaterialsTwo types of oligo(dimethylsiloxanes) with different struc-ture were used for this study. A linear sample of O-DMS waspurchased from Sigma-Aldrich; according to vapor pressureosmometry its number average molar mass was Mn ¼ 3700g/mol; the corresponding value from GPC measurements inchloroform agrees within 6 10% and yields a polydispersityindex of 1.9. The branched O-DMS was prepared by thePt-catalyzed polyaddition of silane end-functionalized linearO-DMS macromonomers to trivinylcyclohexane as describedbelow. An excess of oligo(dimethylsiloxane) with respect tothe trivinylcyclohexane component has been used to avoidgelation of the A2/B3 system. Scheme 1 shows the structureof the materials obtained by this approach.

Correspondence to: B. A. Wolf (E-mail: [email protected])

Journal of Polymer Science: Part B: Polymer Physics, Vol. 48, 1309–1318 (2010) VC 2010 Wiley Periodicals, Inc.

BRANCHED VERSUS LINEAR OLIGO(DIMETHYLSILOXANE), SAMADI ET AL. 1309

Due to the fact that the applied synthesis yields a mixture ofthe different oligomers as specified in Scheme 2, the originalproduct was fractionated for the present purpose as describedbelow. According to the GPC analysis of the original productand of the fractions, the Mn value of the high molecular prod-uct used for the present thermodynamic measurementsamounts to 4 450 g/mol. Its polydispersity is low, namely 1.3,because the product contains only four different species.

THF was purchased from Roth Chemicals (Karlsruhe, Ger-many) with a minimum purity of 0.995 and acetone fromMerck (Darmstadt, Germany) with a minimum purity of

0.998. Oligo(dimethylsiloxane) with hydrid-end groups waspurchased from Sigma-Aldrich; according to GPC analysis itsnumber average molar mass was Mn ¼ 530 g/mol and itspolydispersity index was 1.3. 1,2,4-Trivinylcyclohexane (mix-ture of isomers, 98% purity) was purchased from SigmaAldrich. Platinum-divinyltetramethyldisiloxane complex in xy-lene (Karstedt’s catalyst, 2.1–2.4% platinum concentration)was purchased from ABCR (Karlsruhe).

Polymer SynthesisOligo(dimethylsiloxane) (0.172 mol, 100 g) and trivinylcyclo-hexane (0.06 mol, 9.79 g) were dissolved in 300 mL of

SCHEME 1 Synthesis of the branched oligomers.

SCHEME 2 Molecular architecture of the branched O-DMS species.

JOURNAL OF POLYMER SCIENCE: PART B: POLYMER PHYSICS DOI 10.1002/POLB

1310 INTERSCIENCE.WILEY.COM/JOURNAL/JPOLB

toluene under nitrogen atmosphere. The solution was cooledto 0 �C and 200 lL of Karstedt catalyst were added. Conver-sion of the double bonds was controlled by the disappear-ance of the 1639 cm�1 signal in FTIR-spectroscopy. Aftercomplete conversion of the double bonds 10 mL methanolwere added to end the reaction. The solvent was removedby distillation and the raw material was diluted with 100mL diethyl ether. The product was purified by precipitationfrom acetonitrile. The obtained material (yield 85%) wasfractionated (cf. Section Materials (Fractionation)) and theend groups of resulting gel fraction were capped by means of1-hexene in the following manner: 6.0 g of this oligomer and1.6 g (25 m mol) of 1-hexen were dissolved in 7.5 mL chlor-obenzene. The solution was cooled to 0 �C and 15 lL of Kar-stedt catalyst were added. Conversion of Si-H groups wascontrolled by the disappearance of the 2130 cm�1signal inFTIR-spectroscopy. After complete conversion of Si-H groups2 mL of methanol were added to the reaction mixture. Theproduct (yield 80%) was purified by precipitation from ace-tonitrile and dried under vacuum.

GPCGel permeation chromatography was performed with an instru-ment consisting of a Waters 717 plus autosampler, a TSP Spec-tra Series P 100 pump, and a set of three PSS-SDV 5A columnswith 100, 1000, and 10000 Å porosity. THF and chloroformwere used as an eluent at 30 �C and at a flow rate of 1 mLmin�1. UV absorptions were detected by a SpectrasystemUV2000. The specific refractive index increment (dn/dc) wasmeasured at 30 �C using an Optilab DSP interferometric refrac-tometer (also RI detector) and determined with the WyattASTRA IV software (version 4.90.08). Calibration was carriedout using poly(styrene) standards provided by Polymer Stand-ards Service and performing a third order polynomial fit.

FractionationIn view of the limited available amount of the branchedO-DMS, we have modified the Continuous Spin Fractionation9

(CSF), which represents a continuous large scale technique.This method makes use of the fact that the lower molecularweight components of a polydisperse sample accumulate inthe polymer lean phase (sol) upon liquid/liquid phase sepa-ration of homogeneous solutions, whereas the high molecu-lar weight material is preferentially found in the polymerrich phase (gel). However, this principle can normally not beapplied with reasonable efforts to larger amount of materialbecause of the necessity to work with very dilute solutions.This difficulty can, however, be circumvented by pressing acomparatively concentrated homogeneous solution (thesource phase ¼ feed) into a properly chosen liquid (receiv-ing phase, inducing liquid/liquid phase separation) throughspinning nozzles. In this manner one produces thin strandsof the source phase, which quickly disintegrate into tinydroplets according to the Rayleigh instability10 once theyhave left the orifice of the spinning nozzle. This fine subdivi-sion of the coexisting phases promotes the transfer of thelower molecular weight material into the receiving phase tosuch an extent that one can work with reasonably concen-trated polymer solutions.

In most cases CSF uses mixed solvents (solvent þ precipi-tant) because of the possibility to tailor the thermodynamicquality of the receiving phase at constant temperature byvarying the ratio of the components. This method can, how-ever, also be applied with a single solvent if it possesses therequired thermodynamic quality at an experimentally accept-able temperature. The details of the present fractionationwill be described in Section Results and Discussion (Charac-terization and Fractionation).

Vapor PressuresThese measurements were carried out as described in theliterature11,12 by means of an apparatus consisting of theheadspace-sampler Dani HSS 3950, Milano (Italy) and a nor-mal gas chromatograph Shimadzu GC 14B Kyoto (Japan).This procedure gives access to the amount of the volatiles ina constant volume of the vapor phase, which is in thermody-namic equilibrium with the polymer solution. From thesedata it is possible to determine the ratio of p, the partialvapor pressures of a certain volatile above the solution, andpo, the vapor pressure of the pure solvent. This ratio can beeasily converted into p, the unreduced vapor pressures ofthe solvent, as a function of composition by means of pub-lished vapor pressure data for the pure solvents.

Vapor Pressure OsmometryA Gonotec Vapor Pressure Osmometer, Type Osmomat 070(Cell Unit) was used in combination with the Unit-B Osmo-mat 070/090 and the control unit SA from GONOTEC for thepresent measurements. With organic solvents the accessiblemolecular weight range extends up to 40 to 50,000 g/mol,according to the producer. Benzil was used for the calibra-tion of the instrument. Five solutions ranging in their con-centration from 0.2 to 10 wt % were measured for eachsample at 25 and 40 �C.

THEORETICAL BACKGROUND

The Flory-Huggins interaction parameter v is defined by theactivity a1 of the solvent according to the following relation

v ¼ln a1 � ln 1� uð Þ � 1� 1=Nn

� �u

u2(1)

in which u stands for the volume fraction of the solute inthe mixture and Nn represents the number of polymer seg-ments (number average) calculated from the ratio of themolar volumes of the solute and of the solvent.

The fugacity of the solvent (which is in many cases practi-cally identical with its partial vapor pressure p1) constitutesthe most important source of experimental information con-cerning v. In this case

a1 ¼ p1p1;0

(2)

where p1,0 is the vapor pressure of the pure solvent. Thepractical use of such data is, however, restricted to suffi-ciently high solute concentrations (large enough difference

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between p1 and p1.0) and to suitably low viscosities (to reachequilibria). This implies that additional information on thedilute side is highly desirable to obtain reliable informationcovering the entire range of composition.

The limiting value of the interaction parameter for infinitedilution, v0, is very helpful in this respect; it can be calcu-lated from measured second osmotic virial coefficients, A2,according to the following relation

vo ¼1

2� A2q

22V1 (3)

in which q2 is the density of the polymer and V1 is themolar volume of the solvent. Further data on dilute solutionsare accessible via osmotic pressures posm, which enable thecalculation of ln a1 according to

ln a1 ¼ � posm V1

RT(4)

and consequently provide access to v by means of eq 1.

Comprehensive analysis of experimental data on Flory-Hug-gins interaction parameters for mixtures of different com-position has demonstrated that the functions v(u) arenormally rather complicated, including the occurrence ofextrema. To rationalize this complex behavior a recentapproach13 subdivides the mixing conceptually into twoclearly separable steps. Step (i) establishes contacts betweencomponents changing neither the volume of the system northe conformation of the molecules. Step (ii) involves therelaxation into the equilibrium state by molecular rearrange-ments adjusting the volume of the system and the molecularconformation such that the Gibbs energy reaches its mini-mum. These considerations lead to the following expressionfor v, where the first term quantifies the contributions ofstep (i) and the second that of step (ii)

v ¼ a

1� muð Þ2� f kþ 2 1� kð Þuð Þ (5)

The parameter a corresponds to the original Flory-Hugginsinteraction parameter and m accounts for the fact that theinteracting surfaces of the solvent molecule (defining thesize of a segment) and of the corresponding polymer seg-ment are normally not identical. The leading parameter ofthe second term is f, the conformational response, becomingzero under theta conditions. The efficacy of a given f valuedepends on the parameter k, which contains the effects ofchain connectivity (i.e., differences in the molar mass of thesolute) and of chain flexibility. For flexible polymers andoligomers, the value of k is always so close to 0.5 that it ispossible to merge the parameters f and k by substituting thek in the brackets by this value so that one obtains

v ¼ a

1� muð Þ2� fk 1þ 2uð Þ (6)

The three parameters of the above equation suffice todescribe and to rationalize all experimental findings exam-

ined so far: Typical solutions of linear homopolymers14 aswell as of linear copolymers (random15 and block16); fur-thermore it can be applied successfully to branched macro-molecules17 and to mixtures of low molecular weight compo-nents.18 In the limit of infinite dilution eq 6 simplifies to

vo ¼ a� fk (7)

containing only the leading parameters of the presentapproach.

RESULTS AND DISCUSSION

This section starts with the details of the fractionation andcharacterization of the branched oligomer via GPC. The nextpart presents the results of vapor pressure measurementswith solutions of the linear and of the branched material inTHF, plus their modeling by means of the approach formu-lated in eq 6. The subsequent section deals with the compo-sition dependence of the Flory-Huggins interaction parame-ter as obtained from these vapor pressure measurementsplus information for dilute solutions stemming from vaporpressure osmometry. The final part attempts a molecularinterpretation of the thermodynamic differences of linearand of branched O-DMS in the favorable solvent THF and inthe marginal solvent acetone (AC).

Characterization and FractionationThe number average molar mass of the linear O-DMS wasdetermined by means of vapor pressure osmometry usingTHF as the solvent; information concerning its polydispersityis obtained from GPC measurements.

For the determination of the molar mass of the branchedmaterial its separation in the different species by means ofGPC in THF yielded more reliable data than vapor pressureosmometry. The reason is that this method enables the iden-tification of the different species specified in Scheme 2. Fig-ure 1 shows the elution diagram for the synthesizedbranched O-DMS sample and its breakdown into the contri-butions of the different species. The knowledge of theirmolar masses Mi from the formulae shown in Scheme 2 andof their weight fraction wi from the analysis of the GPC dia-gram gives access to the different molecular weight averagesvia the relations

Mn ¼Xi1

wi=Mi

!�1

Mw ¼Xi1

wiMi (8)

The evaluation of the GPC information according to eq 8yields Mn ¼ 3700 g/mol and Mw ¼ 4090 g/mol. We haveremoved most of the least branched member by solubilityfractionation. This separation was (in contrast to the usualprocedure) realized by means of a single solvent, namely ac-etone (AC). Figure 2 depicts the phase separation behaviorof the original sample of the branched oligomer in AC and ofthe fractions obtained therefrom; furthermore it compares



the cloud point curves of these materials with that for thelinear O-DMS.

The most obvious information of Figure 2 concerns themuch lower solubility of the branched material in acetone,even if its molar mass is considerably lower than that of thelinear O-DMS. In the evaluation of this result, which fits intothe general thermodynamic scheme it must, however, bekept in mind that differences in interaction of the branchingunits and of the end groups of the nonlinear product, whichare presently unknown, will also contribute to the dissimilarbehavior of this material. The observation that the cloud pointcurves of the original product and the gel fraction do not differmarkedly is in agreement with the general experience with theremoval of smaller fractions of low molecular weight material.It is caused by the fact that the demixing behavior is domi-nated by the higher molecular weight components of a polydis-perse mixture. Another noteworthy feature consists in theintersection of curves for the linear product and for the solfraction of the branched oligomer. This observation, indicatingpronounced differences in the composition dependencies of theinteraction parameters, is in accordance with the exceptionalposition of the linear material concerning v(u) at low tempera-tures to be discussed later for THF instead of AC.

The cloud point curve for the original branched O-DMSshown in Figure 2 constitute the basis of the solubility frac-tionation performed at 25 �C; the technical details of thisprocedure are given in Table 1.

Figure 3 shows the GPC diagram for the gel fraction of thebranched material. The removal of most of the lowest molec-ular weight fraction resulted in a product with Mn ¼ 4450 gmol�1 and Mw ¼ 4710 g mol�1.

Vapor PressuresThe following three graphs compare the reduced vapor pres-sures of THF above the solutions of linear and of branchedO-DMS (gel fraction) at three temperatures (Figs. 4–6).

Some fundamental features can already be seen from the pri-mary data displayed in Figs. 4–6. First of all: The vapor pres-sure is, with the exception of moderately concentrated solu-tions at 25 �C, always markedly larger for the linearoligomer than for the branched analog. In view of the factthat Mn value of the former is about 10% lower than that ofthe latter, this implies larger Flory-Huggins interaction pa-rameters for the linear product. To obtain a more detailedpicture on the v values and their dependence on compositionand temperature the information stemming from vapor pres-sures and from vapor pressure osmometry is converted intothis parameter by means of eqs 1–4.

Interaction ParametersThe two methods used for the measurement of the Flory-Huggins interaction parameters, headspace sampling-gaschromatography and vapor pressure osmometry, yield reli-able data in certain composition ranges only. In the formercase, a certain minimum reduction on the vapor pressures ascompared with that of the pure solvent is required. Depend-ing on the thermodynamic quality of the solvent (good sol-vents enable measurement to higher dilution) and on themolar mass of the solvent (the lower the better) the lowerlimit of composition varies. In this case, it lies between u ¼0.25 and u ¼ 0.05. The situation with the latter method ismore complicated because it is based on the establishmentof stationary states and requires calibration. Furthermore, it

FIGURE 1 GPC diagram of the branched oligo(dimethylsilox-

ane). Full line: measured GPC signal, dotted line: sum of the

individual contributions (broken lines) of the different species

specified in Scheme 2.

FIGURE 2 Cloud point curves for solutions of the unfractio-

nated O-DMSbra (open stars) and of the fractionated O-DMSbra

(full stars: gel fraction used for vapor pressure measurements;

crossed stars: corresponding sol fraction) in comparison with

that of the system AC/O-DMSlin (full circles).

TABLE 1 Fractionation of the Branched O-DMS from Solutions

in Acetone at 25 8C

wO-DMS O-DMS/g

Mn/g

mol�1

Mw/g

mol�1

Original sample 0.30 39.2 3700 4090

Gel fraction 0.60 27.4 4450 4710

w is the weight fraction of the oligomer in the different phases.

Values of the molar masses are given for R ¼ hexyl (Scheme 2).

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becomes inapplicable in the vicinity of the boiling point ofthe solvent (65.81 �C according to ref. 19). For the presentmeasurement, it turned out that it yields reliable data for25 �C and the linear oligomer only. In spite of the aforemen-tioned restrictions, we have evaluated all trustworthy pri-mary data on the basis of eq 6 in view of our experienceconcerning typical behaviors and system specific parametersfor other polymer and oligomer solutions.

At 25 �C v(u) is linear for the unbranched oligomer, wherethe data for high solute concentration are within experimen-tal uncertainty identical with that of the branched oligomer.Because of the lack of reliable data from vapor pressure os-mometry at 40 �C the actual shape of v(u) is uncertain forthe linear oligomer and this temperature. For this reason, wehave checked whether these data could also be modeledsuch that they exhibit a minimum like all the other systems(except for linear O-DMS and 25 �C). The broken curve

shown in Figure 7 (calculated by means of the parameters a¼ 1.445, m ¼ 0.249, and fk ¼ 0.65, which lie within therange typical for the other solutions) demonstrates that thisis actually the case. Despite this uncertainty for the systemTHF/linear O-DMS at 40 �C, both sets of data are shown inTable 2 for the sake of completeness. The current findingsimply that it is presently impossible to decide whether thechange in the thermodynamic behavior of the linear oligomerwith temperatures takes place gradually or in an abruptmanner. At the higher temperatures, the curves for thebranched material are shifted with respect to that for lineroligomers markedly to lower values as shown in Figure 7and 8.

At 60 �C and at high solute concentrations the oligomersinteract considerably less favorable with THF than at thelower temperatures and the shape of the curves is qualita-tively identical for the linear and for the branched productas shown in Figure 8, where v values are higher for the

FIGURE 3 Like Figure 1 but for the gel fraction of the branched

O-DMS obtained as described in section Materials (Fractionation).

FIGURE 4 Composition dependence of the reduced vapor pres-

sure of THF above solutions of either linear (open circles) or

branched O-DMS (full asterisks) at 25 �C. The curves have been

adjusted according to the eqs 1, 2, and 6.











former than for the latter oligomer. Due to the absence ofdata points for high dilution, one might think of a linearmodeling of v(u); however, this procedure would yieldtotally unrealistic, by far too small v0 values on the order of0.30 (linear) and 0.15 (branched).

The temperature dependences of the Flory-Huggins interac-tion parameters shown in Figure 7 and 8 provide access tothe signs of heats of dilution and their variation with tem-perature and composition. For the linear oligomer the dilu-

tion takes place approximately athermally at the lower tem-peratures but changes to exothermal as T increases, wherethe effects are largest for the most dilute and the most con-centrated mixtures. For the branched oligomer and concen-trations up to u values of approximately 0.45 the heats ofdilution are endothermal, whereas their sign changes withtemperature and composition.

Molecular ConsiderationsThis section deals with the question, to which extent the dif-ferences in thermodynamic behavior of linear and ofbranched oligomers, as manifested in vapor pressures, vaporpressure osmometry, and cloud point curves, can be rational-ized in terms of molecular architecture. To this end the dis-similar system specific parameters of eq 6 are analyzed forthe two types of O-DMS and the present results are com-pared with earlier findings17 concerning linear and branchedpolyisoprenes (PI) of higher molar mass and lower branch-ing density.

Figure 9 displays the system specific parameters for the twotypes of oligomers and their variation with temperature.

FIGURE 7 Flory-Huggins interaction parameters for solutions of

the oligomers in THF. The data points for the linear O-DMS are

displayed by circles; open symbols: 25 �C, crossed symbols:

results of vapor pressure osmometry at 25 �C; full symbols 40�C. The data points for the branched O-DMS are represented

by asterisks; open symbols: 25 �C, full symbols: 40 �C. The

curves are modeled by adjusting the parameters of eq 6; their

numerical values are collected in Table 2. The dotted line dem-

onstrates that the data for the linear O-DMS and 40 �C can ei-

ther be modeled in a linear manner (like at 25 �C, full line) or

to exhibit a minimum like all other systems at T > 25 �C.

TABLE 2 Parameters of eq 6 Used for the Modeling of the

Composition Dependencies of the Flory-Huggins Interaction

Parameter for the Solutions of Linear and of Branched O-DMS

in THF at the Different Indicated Temperatures

T (�C) Parameter Linear Branched

25 a 0.448 60.007 1.227 0.152

m 0.143 0.010 0.227 0.017

fk 0.000 0.086 0.512 0.111

40 a 0.448a 60.007 1.147 0.160

1.445b 0.346

m 0.143a 0.010 0.266 0.012

0.249b 0.009

fk 0.000a 0.000 0.542 0.165

0.650b 0.230

60 a 1.105 0.259 1.093 0.038

m 0.309 0.007 0.310 0.008

fk 0.503 0.181 0.543 0.038

a Setting fk in eq 6 equal to zero.b Adjusting all three parameters of eq 6.

FIGURE 8 Flory-Huggins interaction parameters for the solu-

tions of the oligomers (linear: circles, branched: stars) in THF

at 60 �C

FIGURE 9 Temperature dependence of the parameters p (i.e., a,m, and fk) of eq 6. Stars: branched oligomer, circles: linear

oligomers.

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This graph evidences the increasing similarity in the thermo-dynamic behavior of linear and branched oligomers with ris-ing T. The m values are of comparable magnitude within theentire range and increase only slightly; this observation isreasonable in view of the fact that the geometrical character-istics (surface to volume ratio of the oligomer units) shouldbe almost the identical. The parameters a and fk, on theother hand, exhibit a totally different behavior. The valuesfor the linear O-DMS increase pronouncedly with rising tem-perature. The fk values of approximately zero, resulting forthe linear product at 25 �C, are in the case of polymer solu-tions typical for theta systems. Under these special condi-tions the conformational response f becomes zero becausethe coil dimensions are practically identical in the melt andin solution.

The present finding fk � 0 for the linear oligomer can betentatively interpreted along the same lines. One may specu-late that the linear O-DMS builds up a favorable orientationalorder in the pure state at sufficiently low temperatures,which is similar to the arrangement of its monomeric unitsin solution after the conformational relaxation has takenplace. In view of reports on the ordering of n-alkanes at lowtemperatures20 this conjecture does not seem far-fetched.Furthermore, it has the advantage to explain the distinctincrease in fk observed upon raising the temperature andthe increasing similarity of v(u) of the linear polymer withthat of the branched product: Due to the destruction of theorientational order in the pure linear oligomer the conforma-tional relaxation into the equilibrium arrangements in thecourse of mixing becomes favorable (large fk values).

The particularities in the temperature dependence of thesystem specific parameters a and fk shown in Figure 9 aresynonymous with the observation that the curves v(u) forthe linear and for the branched oligomers intersect (cf. Fig.7) at the two lower temperatures. For the linear product,the combination of a moderate a value with fk � 0 meansthat v rises steadily as u increases (first term of eq 6). Forthe branched oligomer, on the other hand, the parameter aas well as fk is much higher and these values imply that vdecreases with u at low solute concentration (where the sec-ond term eq 6 dominates), whereas it increases at high uvalues (where the first term eq 6 becomes decisive). In thismanner v(u) passes a minimum and the two curves intersectsuch that THF is at 25 �C a better solvent for the linearO-DMS at low u but more favorable for the branched O-DMSat high u. This particularity can no longer be observed at60 �C, because the parameters are of the same order of mag-nitude at this temperature (cf. Table 2).

From extensive experimental data for polymer solutions, it isknown that the two leading parameters of eq 6, a and fk,are not independent of each other, but are in the case ofhigh molar mass chain molecules interrelated in a linearmanner16 for a given class of polymers with comparable flex-ibility. Points for solutions of a given polymer in differentsolvents fall on a common line as well as points for a givensolution obtained at different temperatures. Figure 10 dem-

onstrates that the a and fk values for the oligomers are alsolocated on the same line and that their numerical values arecomparable to that for polymer solutions. This observationimplies that neither the number of segments of the chainmolecule nor their molecular architecture plays a major rolefor this interrelation. In the light of the ideas underlying thepresent approach this finding is conceivable. First of all theparameters characterizing the two steps of mixing cannot beindependent of each other because both involve the samecomponents. Secondly, if the formation of contacts betweenthe components is very unfavorable (large a), molecularrearrangements reducing the Gibbs energy of the system areexpected to be most efficient (large fk). The observation thatthe data for the branched O-DMS deviate noteworthy fromthe common line of Figure 10 at some temperatures as doesthe data point for the linear oligomer at 60 �C (although to alesser extent) might be due to the low molecular weight na-ture of the present oligomer samples; the parameters for sol-utions of the polymer PDMS in methyl ethyl ketone does notdeviate from this interrelation as shown in Figure 10.

THF is not the only solvent for the O-DMS samples of differ-ent architecture we have investigated. Qualitative knowledgeis also available for AC, which was used for the fractionationof the branched material. According to the cloud pointcurves shown in Figure 2 this liquid is a marginal solventfor both oligomers. This difference in the thermodynamicquality of THF and AC is already expected on the basis ofthe solubility parameter theory. According to tabulated21 sol-ubility parameters d, the differences Dd between solvent andsolute amount to 4.4 MPa1/2 for the system THF/PDMS but5.1 MPa1/2 for AC/PDMS. What appears more interesting is acomparison of the differences in the solvent quality of THFand AC for the linear or the branched oligomer. In the

FIGURE 10 Interrelation of the leading parameters of eq 6 for

the solutions of linear and branched O-DMS samples in THF as

compared with literature data for polymer solutions. TL, tolu-

ene; AC, acetone; MeAc, methyl acetate; MEK, methyl ethyl ke-

tone; IO, isooctane; P(S-ran-MMA), random copolymer of

styrene and methyl methacrylate; PMMA, poly(methyl methac-

rylate); PDMS, poly(dimethylsiloxane); PIB, polyisobutylene; PI,

polyisoprene (linear or branched).



temperature and composition regions of interest THF inter-acts more favorably with the branched material, whereas theopposite is the case for AC. Because of the complicated tem-perature and composition influences on v in the case of THFand the limited information for AC a more detailed analysisappears difficult. However, the lower solubility of thebranched O-DMS in AC could be explained in terms of thedifferent interactions of the nonsiloxane groups with eitherTHF or AC. Using solubility parameters again to estimatesuch dissimilarities yields in the former case the followingDd values: 2.6 MPa1/2 for THF/cyclohexane (CH) and 4.5 forTHF/n-hexane as compared with 3.3 for AC/CH and 5.2 forAC/n-hexane. This means that the nonmonomeric units CHand n-hexane should interact considerably less favorablywith AC than with THF in agreement with the experimentalobservations.

A further study,17 similar to the present one, concerning thethermodynamic consequences of architecture of chain mole-cules was also performed for the system cyclohexane/polyi-soprene (CH/PI). The Mn value of the branched product was13,600/g mol�1 and that of the linear product was 21,500/gmol�1, these data are approximately twice as large as in thecase of O-DMS. Another difference consists in the branchingdensity of the polymers. The number of monomeric unitsbetween the ramification amounts to approximately 30 forPI as compared to 10 for O-DMS. Because of the exceptionalbehavior of the linear O-DMS at low temperatures discussedabove, the comparison of the results confines itself to thehighest temperature. The most obvious difference lies inthe fact that the Flory-Huggins interaction parameter of thebranched component is at 60 �C for the systems THF/O-DMSat all concentrations lower than for the linear component(Fig. 8), whereas the opposite is true for CH/PI at 65 �C(Fig. 5 of ref. 17). To elucidate, which parameter of the pres-ent approach causes this converse behavior these values arecollected in Table 3.

The analysis of the data assembled in Table 3 reveals thatthe more favorable interaction of THF with the branchedO-DMS is primarily caused by a large reduction in the Gibbsenergy that can be achieved via conformational rearrange-ments in the second step of dilution. The preferred interac-tion of CH with the linear PI, on the other hand comes intobeing due to a less adverse contact formation in the first

step of dilution. These findings imply that the naive expecta-tion that the differences in the behavior of linear andbranched polymers should always be qualitatively identicalis not justified. Obviously the natural assumptions that the avalues do not depend on the molecular architecture and thatthe possibilities for conformational relaxation are less for thebranched material than for the linear (fkbra < fklin) is notpermissible. On second thought it is comprehensible that thevalue of a may also depend on the particular way the mono-meric units are arranged to chains because of their accessi-bility to the solvent and therefore also a may be a functionof the molecular architecture.

CONCLUSIONS

According to the present findings there does not exist a gen-erally valid distinction in the thermodynamic quality of agiven solvent for either linear or branched O-DMS. In thecase of THF (a good solvent), temperatures between 25 and60 �C and polymer concentrations exceeding approximately50 wt % the vapor pressures data clearly indicate that thissolvent is under these conditions more favorable for thebranched material than for the linear one. However, at 25 �Cand lower polymer concentration the preference becomesopposite: Now THF constitutes a better solvent for the linearthan for the branched O-DMS. These findings match theobservations for the marginal solvent acetone. The phasediagrams measured up to solute concentrations of 50 wt %demonstrate that the two phase area of the linear sample,located in the range of the lower temperatures (cf. Fig. 2), isconsiderably smaller than for the branched O-DMS. Theseuncommonly complex differences in the thermodynamicbehavior of the two types of oligomers are tentatively attrib-uted to the ability of the linear product to develop orderedstructures at low temperatures, in contrast to the branchedO-DMS, which cannot pack in a similar manner.

The most probable reason for the fundamentally differentconsequences of polymer architecture for the interactionwith a given solvent in the case of O-DMS, as compared withthat of linear or branched polyisoprenes17 (PI), lies in theunlike branching density. The naive expectations based on eq6 (identical a values and larger fk values for the linear poly-mer) are obviously only fulfilled for chain molecules of lowto moderate degrees of branching as realized with PI, wherethe individual branching sites are separated by approxi-mately 30 monomeric units. Under these conditions a givensolvent should be better for the linear PI than for thebranched PI, in agreement with the experimental observa-tion. Such considerations are, however, evidently no longerpermissible if the branching density becomes too large, aswith the present O-DMS samples, where the branching sitesare only separated by nine monomeric units. Because of thenon-negligible fraction of alien groups the branched polymercontains, the a values for the two types of oligomers needno longer be identical and also the conformational character-istics f may deviate from expectation.

In view of the importance of polymer molecules with differ-ent architecture for life science, the present findings may

TABLE 3 Comparison of the Leading Parameters of eq 6 and of

the Corresponding v0 Values (eq 7) for Solutions of Linear and

of Branched Chain Molecules in the Same Solvent

THF/O-DMS (60 �C) CH/PI (65 �C)

Linear Branched Linear Branched

a 1.105 1.093 0.724 0.786

fk 0.503 0.543 0.329 0.346

v0 0.602 0.550 0.395 0.440

CH, cyclohexane; PI, polyisoprene.

ARTICLE


also be relevant for research in this field. The observationthat eq 6 is capable of modeling the Flory-Huggins interac-tion parameters as a function of composition quantitatively,irrespective of the particular molecular architecture of thesolute, means that the central system specific parameters aand fk account adequately for the thermodynamic conse-quences of the particular arrangements of monomeric unitsin linear and in branched chain molecules.

The authors are grateful for the financial aid of the ‘‘DeutscheForschungsgemeinschaft.’’ Our thanks are also due to theMax-Planck-Institut fur Polymerforschung, in particular toProf. Th. Vilgis for stimulating discussions and to Frau Rosenauerfor performing the measurements with the vapor pressureosmometer.

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